Photon correlation spectroscopy investigations of proteins

Advances in Colloid and Interface Science 105 (2003) 201–328

Photon correlation spectroscopy investigations of proteins Vladimir M. Gun’koa,*, Alla V. Klyuevab, Yuri N. Levchukb, Roman Lebodac a

Institute of Surface Chemistry, 17 General Naumov Street, Kiev 03164, Ukraine A.V. Palladin Institute of Biochemistry, 9 Leontovich Street, Kiev 03030, Ukraine c Faculty of Chemistry, Maria Curie-Sklodowska University, Lublin 20031, Poland

b

Abstract Physical principles of photon correlation spectroscopy (PCS), mathematical treatment of the PCS data (converting autocorrelation functions to distribution functions or average characteristics), and PCS applications to study proteins and other biomacromolecules in aqueous media are described and analysed. The PCS investigations of conformational changes in protein molecules, their aggregation itself or in consequence of interaction with other molecules or organic (polymers) and inorganic (e.g. fumed silica) fine particles as well as the influence of low molecular compounds (surfactants, drugs, salts, metal ions, etc.) reveal unique capability of the PCS techniques for elucidation of important native functions of proteins and other biomacromolecules (DNA, RNA, etc.) or microorganisms (Escherichia coli, Pseudomonas putida, Dunaliella viridis, etc.). Special attention is paid to the interaction of proteins with fumed oxides and the impact of polymers and fine oxide particles on the motion of living flagellar microorganisms analysed by means of PCS. 䊚 2003 Elsevier Science B.V. All rights reserved. Keywords: Photon correlation spectroscopy; Dynamic light scattering; Static light scattering; Autocorrelation function treatment; Protein solutions; Diffusion coefficients of proteins; Protein size distribution; Protein aggregation; Protein interaction with solid particles; Motion of microorganisms

*Corresponding author. Tel.: q38-44-4449627; fax: q38-44-4243567. E-mail address: [email protected] (V.M. Gun’ko). 0001-8686/03/$ - see front matter 䊚 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0001-8686Ž03.00091-5

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Contents 1. Introduction ............................................................................................. 202 1.1. Fundamentals of PCS........................................................................... 202 1.2. Physical principles and mathematical models ............................................. 204 2. Features of PCS techniques ......................................................................... 209 2.1. Optical schemes of heterodyne and homodyne modes and some features of different PCS techniques ...................................................................................209 2.2. Relationship between PCS data and object properties .................................. 221 2.3. Analysis of the PCS data for complex systems .......................................... 223 2.4. Some PCS facilities ............................................................................. 232 3. Characteristics of protein molecules determined by means of PCS ........................ 234 3.1. Diffusion coefficients of proteins ............................................................ 234 3.2. Size distribution of molecular particles..................................................... 237 3.3. Shape of protein molecules ................................................................... 238 4. Intermolecular interactions........................................................................... 240 4.1. Protein aggregation and interaction with other compounds ............................ 240 4.2. Proteins, DNA and drugs ...................................................................... 270 4.3. Interaction of proteins with dispersed particles ........................................... 276 5. Interaction of living microorganisms with polymers and solid particles .................. 307 6. Conclusion............................................................................................... 317 Acknowledgements ........................................................................................ 317 References ................................................................................................... 317

1. Introduction 1.1. Fundamentals of PCS Light scattering occurs on polarisable solid and liquid particles (or molecules) bathed in the electromagnetic field of the light beam because of the difference in the dielectric properties of the material and the surrounding media, and the varying field induces oscillating dipoles in the particles radiating light in all directions. This phenomenon is the basis for explaining why emulsions (such as milk) and suspensions (e.g. with titania pigment) can be opaque; and it has been utilised in many areas of science to determine particle size, molecular weight, particle or macromolecule shapes, their diffusion coefficients, particle aggregation, mobility of microorganisms, etc. The intensity of scattered electromagnetic field depends on the ratio between the particle size and the incident light wavelength (l), and the shorter the l value, the smaller the particles, which can be effectively investigated due to scattering by them. Therefore, not only the visible light, but also X-ray is used in PCS to increase the resolution power. Notice that the similar physical effects (e.g. scattering of phonons) are utilised in the acoustic and electroacoustic techniques applied for investigations of the particle size distributions and related phenomena. The short-term intensity fluctuations (dynamics) of the scattered light arise from the fact that the scattering particles are in the motion, for example, diffusive Brownian motion (for particles of 5 mm diameter and smaller), own motion of living flagellar microorganisms or the particle motion under external force (e.g.

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particle sedimentation because of gravitation, electrophoretic mobility of charged particles in the external electrostatic field, etc). These motions cause short-term fluctuations in the measured intensity of the scattered light. Various terms have been used for this phenomenon: photon correlation spectroscopy (PCS), dynamic light scattering (DLS), quasi-elastic light scattering (QELS), spectroscopy of optical displacement, laser correlation spectroscopy and others. The pace of the movement is inversely proportional to the particle size (the smaller the particles are, the faster their motion or diffusion), and the pace can be detected by analysing the time dependency of the light intensity fluctuations scattered from the particles when they are illuminated with a laser beam. A similar effect is observed for mobile microorganisms, and the PCS method is used to study their vital capacity dependent on surroundings (e.g. nutrients distribution). PCS is a powerful and fruitful physical method successfully applied to solve a variety of problems in many technological and scientific branches such as colloidal chemistry, biochemistry, biophysics, molecular biology, food technology, etc. The utilisation of this method in exploration of biopolymers and microorganisms is effective, since they are appropriate objects for PCS because of their characteristic sizes over 1 nm and 10 mm. The PCS beginning could refer to 1914 when Brillouin published theoretical findings on the light scattered from an excited isotropic body or to 1955 when Forrester et al. described features of the green line of mercury splintered in the magnetic field in consequence of the Zeeman effect w1x. It should be noted that they could define the effect corresponding to 10y5 of the stochastic noise value. Then Forrester developed the optical displacement method to analyse the QELS spectra with a high resolution w2,3x. Appearance of optical quantum generators (lasers) and effective special-purpose numerators (multi-channel spectrum analysers and correlators working in the real-scale time regime) stimulated further development of the PCS method and its wide applications in scientific investigations w4x. Notice that the resolving PCS power l yDl (or n yDn) can reach up to 1015, which seems fantastic in comparison with that of the best spectral prism or diffraction apparatuses characterized by l yDl;104 ; therefore, PCS is not only high-productive method, but also a unique technique w5x. Broadening of the laser light spectrum scattered by suspended monodisperse spherical particles with polystyrene latex was firstly observed by Cummins et al. in 1964 w6x. The papers published by Glayber w7x, Lastovka and Benedek w8x, Cummins w9,10x and Berge w11x should be mentioned among others devoted to the fundamentals of the PCS method, in which the problems of optimisation of optical schemes, photo-registration and subsequent analysis of obtained data were discussed. The survey of the PCS investigations published before 1979 was made by Chu w12x. A measurement technique of the Doppler shift of frequency on electrophoretic investigations was described by Uzgiris w13–17x and Ware w18–20x. The PCS application to analyse the biological systems began in 1967 when Dubin et al. w21x published the diffusion coefficients of serum albumin, ovalbumin, lysozyme and DNA molecules. Before the First International Workshop on PCS in 1973, the diffusion coefficients were determined for 45 biopolymers and viruses by means of

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PCS w4x. On the second similar workshop in 1976, it was reported that the PCS investigations of biological matters were published in 194 papers devoted to proteins, other biopolymers, and viruses (in the period between 1973 and 1976) w22x. A major portion of the works carried out in the initial period of the PCS development dealt mainly with monodisperse systems, which are relatively simple for the PCS investigations and may be adequately modelled. It should be noted that an important problem connected to the structure of the biological solutions and suspensions related to the solvation or hydration degree of molecular particles was intensively investigated by means of PCS w23–26x. The hydrodynamic radii of molecules of different shapes were estimated w27,28x, especially in the case of the difficulties in determination of Stokes force applying scaled models w29,30x. For particles which could be observed by means of an electron microscope, the problem is simpler, as the microscope does not ‘see’ the hydrate shell, but its size could be estimated from the ratio between the hydrodynamic Rh (determined by PCS) and electronmicroscopic Re radii w29,30x. Little by little more complex problems began to be studied by means of PCS. From the end of the seventies this method has been used to investigate many phenomena such as diffusion, hydration, oligomerisation, aggregation, agglutination, complexing and polymerisation of biomolecules as well as interior dynamics of biopolymers and submolecular particles w4,5,31–34x. To elucidate some problems characteristic for the PCS investigations of many complex systems, we will briefly review the physical principles and mathematical description of the corresponding phenomena. 1.2. Physical principles and mathematical models The light scattering by microparticles or mobile parts of micro-objects is the basis of the PCS method and that is the reason such method is named as dynamic light scattering. Random motions of dissolved or suspended particles (translation diffusion), their rotations (rotation diffusion), and modulation of the form factor due to interior motions in the object are observed in colloidal solutions, emulsions and suspensions (notice that a major portion of the biological liquids belongs to such media). All kinds of these motions lead to changes in frequency of the light scattered by particles and these changes are very small in comparison with the incident light frequency. Dynamic picture of the interference appearing because of optical merge of initial and ‘shifted’ lights on a detector is characteristic for combination of vibrations with very close frequencies (known as beating). As a result, the optical amplitude ´(t), as well as the measured intensity I proportional to ´2(t), slowly changes (beats, pulsates) at a frequency equal to the difference in the interfering fields. An additional set of the frequencies Dni (is1, 2, 3,«, N; where N is a number of particles) appearing in the optical spectra of the scattered light characterizes so-called diffusive broadening nis n0yDni

(1)

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where n0 denotes the frequency of the incident light, Dni is the frequency change on scattering on i-particle. The sign ‘minus’ in Eq. (1) corresponds to energy loss by a photon on its scattering. If exterior force field is applied to particles that a cooperative motion may appear in a given direction, and the Doppler shift of frequency dni adds to the diffusive broadening w4,5,34x. Light detectors cannot measure electric fields, but they gauge light intensity I related to the electric field E (2)

IsSE*=SE

where S indicates a sum over all scatterers, E is the electric field, and * denotes the complex conjugate. The process of multiplying a number by its complex conjugate results in a scalar, not a vector. In this situation that equates to a loss of the phase information, which seems to be a formidable barrier to moving forward in the experiment. Siegert, however, proved that the phase information is still retained, and that the autocorrelation function (ACF discussed in detals below) of the intensity obeys the relation w4,5x g(2)(t)sNI2t Mg(1)2 (t)qNItM2

(3)

where NM indicate an average. It is known that the light scattering is a random process; therefore, essential information can be extracted from the PCS data analysed by using statistical methods. The simplest characteristic of a variate is its mean value. However, the mean value of the complex amplitude of the scattered electromagnetic field is equal to zero and does not contain any information. More complex and knowingly nonzero characteristic of a random process is the autocorrelation function, which is the average of products of a variate f for two different times t1 and t2 G(t1,t2)s Nf(t1)f(t2)M. The G(t1,t2) function is one of the main characteristics of random processes. In many important cases, the random variates follow Gaussian statistics, and realization probability P of Gaussian variate f can be estimated by PŽµfi∂.s

1

Ž2p.

My2

y±±G±±

expŽyGijy1fifj y2.

(4)

where Gij^ G(tiytj) is a matrix, and ±±G±± is its determinant. It should be noted that in the case of non-Gaussian statistics, the information determined by the correlators of different orders is not identical and independent. There are two random processes in PCS. The first process corresponds to fluctuating electric current at the photorecorder outcome. The second random variate is connected to the electromagnetic field, which is a complex time-space vector variate. Therefore, the correlation function of the electromagnetic field is a tensor w4,5,34x G(r1,r2,t)sNE(r1,0)ØE*(r2,t)M

(5)

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which is frequently denominated as a coherence function. There is a function of the space coherence G(r1,r2)sNE(r1)E*(r2)My wI(r1)I(r2)x0.5

(6)

where I is the intensity of the electromagnetic wave I(r)'NNE(r)N2MsSp G(r1,r2,0)

(7)

G(r1,r2) decreases with increasing distance between points r1 and r2 or with increasing angle between the directions from a radiation source to these points. Several characteristics such as coherence angle (uc), space coherence angle (Vc), coherence length (lc), coherence area (Sc) and coherence volume (Wc) are used to describe the coherence space with non-zero G(r1,r2 ) values. The pair correlation function G(t)sNE(0)E*(t)M

(8)

corresponds to overall function Eq. (5) in the same space points. Notice that in the case of S4Sc (where S is the surface area of a photodetector), an informative portion of G(t) is proportional to S=Sc but not to S 2 w34x. In PCS, single photons are detected (by a photodetector as photocurrent measured in certain time intervals) and ‘auto-correlated’. Therefore, the autocorrelation function may be determined as a convolution of the signal intensity as a function of time with delayed one. If the detected intensity is described as a function I(t), then the autocorrelation function of this signal is given by

|

`

GŽt.s

I(t)I(tqt)dt

(9)

0

where tst2y t1. The above function is also called the intensity correlation function. The time shift t is often referred as the delay time, since it represents delay between the ‘original’ and the ‘delayed’ signal. The continuous intensity correlation function cannot be measured, however, it can be evaluated in discrete time points obtained by a summation over the duration of the experiment, where the upper limit of the summation is given by the appropriate index belonging to the largest available summation term for k tyti

GkŽtk.s 8 IŽtn.IŽtnqtk.

(10)

ns0

The above general expression holds true for both linear and arbitrary delay times. To obtain the normalized intensity correlation function and makes the measured values available for further interpretation, digital correlators connected to computers

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are used. If intensity statistics of the measured signal is Gaussian (which is true for all diffusion and for most random processes) then the Siegert relation holds true. The latter states that the normalized intensity autocorrelation function can be expressed as a sum of 1 and square of the field autocorrelation function g (scaled with a coherence factor g expressing efficiency of a photon collection system) GŽt.s1qggŽt.2

(11)

This equation can be equivalently written in the discrete form with the index k. For ideal detection, the coherency factor gs1. For simplicity one can ignore the coherency factor and develop a table of gk and tk values. The ideal field correlation function of ‘hypothetical’ identical diffusing spheres is given by a single exponential decay function with a decay rate G determined by the diffusion coefficient and the wave vector of the scattered light. The main objective of the data inversion consists of finding the appropriate distribution of exponential decay functions, which best describes the measured field correlation function. This problem may be described by a Fredholm equation of the first kind with an exponential kernel. It is also known as an ill-posed problem, since relatively small amounts of noise can significantly alter the solution of the integral equation and there are a lot of solutions well fitting the experimental data. The fitting function of gk consists of a summation of single exponential functions, which are constructed as a grid of exponentials with the decay rate Gi gkfits8Aiexp(Giti)

(12)

i

The factor Ai is the area under the curve for each exponential contribution and represents the strength of that particular ith exponential function. The best fit can be found by minimizing the deviation of the fitting function from the measured data points, where a weighing factor sk is incorporated to place more emphasis on the good, rather than the noisy, data points j2s8wgkygkfitx2sks8wxgky8Aiexp(Giti)z|2sk k

k y

i

(13)

~

The weights are proportional to the intensity correlation function values, i.e. the correlation function values have a higher weight at shorter times than those at longer times. The normal procedure to find the solution of Ai’s in the grid of fitted gk expressions is to minimize the deviation j2 with respect to each Ai, and then find the solutions from the resulting system of equations. In other words, if we construct the solution out of N exponential functions there will be N differentiations of the following form ≠j2 s0 ≠Ai

(14)

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Each of the terms in the above differential contains a sum over k. The whole equation system can, therefore, conveniently be re-expressed in matrix form as shown below, where the Y-vector turns out to be a convolution of the experimental data with the kernel (the grid matrix or the exponential decays) and the matrix W consists of a convolution of the kernel with itself (15)

Yis8WikAk k

The standard procedure to solve this equation is to find the eigenfunctions and eigenvalues, and construct the solution as a linear combination of the eigenfunctions. However, when the eigenvalues are small, a small amount of noise can make the solution extremely big. To overcome the problem, a stabilizer with a regularization parameter a is added to the system of equations Zsj2qa8ŽAiyAiy1.2

(16)

i

and with the incorporation of this term, the first order regularization can be performed. The above expression is called a first order regularization, because the first derivative (in Ai) is added to the equation system. The regularization parameter a determines how much emphasis we put on this derivative or the ‘degree of smoothness’ in the solution. If a is small, it has a little influence and the solution can be quite ‘choppy’; whereas larger a will force the solution to be very ‘smooth’. The ACF of a stationary process depends only on an independent variable ts t2yt1. At ts0, G(t)sG(0)sNf 2 M is the power or the intensity of the variate and characterizes the amplitude of the f fluctuations. Fourier image of ACF (I(v)) is called as the power spectrum (PS) of the variate

|

`

GŽt.eivt dt

IŽv.s

(17)

y`

Following designations are used in PCS: G (1)(t)sNE(t)E(tqt)M corresponding to the unnormalised ACF of the scattered optical field, and G (2)(t)sNE 2(t)E 2 (tq t)M is the unnormalised ACF of the scattered light intensity. The Fourier image as the power spectrum I (2)(v) determined by Eq. (17) corresponds to the autocorrelation function G (2)(t). The G (2)(t) and I (2)(v) functions are measured on PCS experiments by using correlators and multi-channel spectrum analysers and a normalised measured ACF is gexpŽt.s

NIdŽ0.IdŽt.M 2 d

NI M

s

1 1 1 N IdŽt.IdŽtqt.dts 2 lim 8IdŽti.IdŽtiqt. 2 NIdM NIdM N™` N is0

|

(18)

where subscript d refers to the detected intensity Id, and N is a number of the

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Fig. 1. Heterodyning (a) and homodyning (b) optical schemes of the PCS: laser (1); parallel-sided plate separating a small portion (;4%) of the initial emission (2); dish with a sample (3); mirror (4); device to light angulation (5); photo-detector (6); and u is the angle of scattered light detection.

correlator channels. Information extracted from the measured ACF and PS is the same, however, treatment algorithms for them differ. The correlators (which are simpler than the multi-channel spectrum analysers, as they do not require consideration for amplitude-frequency characteristics of the channels) are used in the lion’s share of PCS measurements based on two types of the optical schemes with heterodyne or homodyne modes w4,5,34x. 2. Features of PCS techniques 2.1. Optical schemes of heterodyne and homodyne modes and some features of different PCS techniques In contrast to the ACF of the electromagnetic field oscillating with the light frequency v0, the correlation function of the fluctuations of the intensity changes slower in the case of quasi-monochrome radiation. Therefore, one can replace the field E(t) in G(2)(t)sNNE(0)N2 NE*(t)N2MyI2y1

(19)

by its amplitude ´(t) which changes over the time corresponding to reciprocal value of the width (Dv) of the radiation spectrum, and the same time scale is characteristic for G (2)(t). Thus, the information about the correlation properties of the scattered radiation can be determined on the basis of the measurements of the correlation function of photocurrent over a low-frequency range of the Dv width. Typically in the case of the Gaussian statistics for the equilibrium systems, the information contained in the correlation function of the intensity (homodyne mode) is identical to that of the pair correlation function of the field (heterodyne mode). In the case of the inequilibrium systems, (e.g. fast coagulation of colloidal particles) with the Gaussian statistics, full information about the pair correlation function may be determined from the results obtained by using both modes w34x. A heterodyne mode, i.e. simultaneous hit of incident and scattered lights on a photodetector (Fig. 1a), is rarely used in standard optical schemes of PCS w13,34– 37x. More frequently, a photocomposer directs only the scattered light onto the (2) (t)) is simpler than detector. This homodyne mode (G (2)(t)yG(2)(0)sg(2) (t)sgexp

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heterodyne one and does not need renewal of adjustment on changes in the observation angle of the scattered light (Fig. 1b), and the signal-to-noise ratio is appropriate for subsequent analysis. However, in this case, it is impossible to study a cooperative drift of the scatterers under action of exterior forces. Additionally, a disadvantage is that the obtained quantity is the square of the interesting correlation function, therefore, cross-correlation terms should also be considered. The ACF of the scattered light can be represented in a general form as follows w4,5x B ™™ E G G(1)Žt.sAexpDyDTq2±t±yiqVt C

F

(20)

where DT is the translation diffusion coefficient at temperature T, 4pn u ™ ™ qs±q±s±kfyki±s sin l 2

(21)

q is the scalar of the wave scattering vector equal to the difference between the ™ ™ final wave vector kf and the incident ki; A is constant, n is the refraction index of ™ the liquid, l is the wavelength of the incident light in vacuum, V is the vector of drift velocity of particles under applied exterior forces, and u is the observation angle of the scattered light. Eq. (21) is valid, since the amplitude of the wave vector is practically unaffected in the light scattering process. After Fourier transform of Eq. (20) one can obtain the heterodyne spectrum as a symmetric (in respect to the probe beam frequency) portion of the scattered light spectrum I(1)Žv.s

ADTq2 wB z ™™E 2 2 G2qŽDTq . | pxyDvyqV ~ C

(22)

F

A heterodyne spectrum represents a Lorentz curve centralised at the frequency ™ ™ qV with the half-width DTq 2. The last value is so-called diffusive broadening, and ™ the scalar product ™ qV is the Doppler shift. On spectral mixing of incident and scattered lights on the photodetector (optical heterodyning), there is a substantial circumstance: the photocurrent spectrum is identical with that of the scattered light with the deduction of the frequency of incident radiation v0 (vs2pn). Thus, the informative signal is in the range of low frequencies, where its analysis may be performed using typical methods of radio metering with multi-channel spectrum analysers and correlators w34,38–41x. The advantage of the heterodyne mode is that the interesting quantity is measured directly without any cross-correlation terms, but there are disadvantages, as this mode is experimentally more difficult than homodyne one and the ratio between signal and noise is significantly worse. Typical shape of the ACF (Eq. (18)) corresponding to the PS is shown in Fig. 2. The useful signal in PCS should be separated from concomitant noise (shot or

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Fig. 2. Autocorrelation function (a) and the spectrum (b) of the photo-current: shot noise (1); useful signal (2); steady component (3); GsG(0) and IsI(0).

random noise and a constant constituent corresponding to a certain baseline) w34,42,43x. On correct consideration for all the components of the measured signals, the half-width of the spectrum G and the characteristic correlation time of the translation motion of scatterers t0 are linked by the relationship Gs1y t0. Notice that useful practical criterion of optimal setting of a measuring route is the relationship between useful part of the ACF (or PS) (Fig. 2, curve portion 2) and the total number of used channels of the correlator (or spectrum analyser) corresponding to approximately 20% w34x. For monodisperse particles in random motion, normalised g (2) (ti ) is related to the modulus of the normalised field ACF g (1)(ti) g(2)Žti.s1q2

ILOIs Is2 (1) f2±g(1)Žti.±2 2 f1±g Žti.±q ŽILOqIs. ŽILOqIs.2

(23)

where Is denotes the average scattered intensity coming from the sample and ILO is the intensity not coming from the sample, but from a ‘local oscillator’ like the fibre end; f 1 and f 2 are dependent on the experimental parameters, whose values are less than unity. If the local oscillator intensity is low and the scattered field follows the Gaussian statistics, ILO
I2s f2±g(1)Žti.±2s1qf2±g(1)Žti.±2 ŽILOqIs.2

(24)

If ILO4Is that the equation simplifies to the purely heterodyne case: g(2)Žti.s1q2

ILOIs Is (1) f1±g(1)Žti.± 2 f1±g Žti.±s2 ILO ŽILOqIs.

(25)

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Thus, in heterodyne operation, the field ACF can be measured directly w44x. In the case of the heterodyne mode, mixing of studied (scattered) radiation with a given one (initial non-scattered monochromatic radiation) gives (26)

EŽt.s´0expŽiv0t.q´Žt.expŽiv0t.

where ´04´(t). Neglect of small values as (´(t)y ´0 )2 leads to the relation akin to Eq. (25) 2) G(heter Žt.s2±G(1)Žt.±y ´20

(27)

i.e. the heterodyne mode allows us to determine a real part of the field ACF. These relationships may be transformed into the Fourier images of G (i)(t), and for the homodyne mode

|

`

I(2)Žv.s

I(1)Žv9.I(1)Žvqv9. y`

dv9 2p

(28)

and the heterodyne one I(2)Žv.s

1 w (1) I Žvyv0.qI(1)Žv0yv.z~ E20 y x

|

(29)

In the case of monochromatic radiation studied, two monochrome beams (incident and scattered) hit onto the photodetector resulting in oscillations of the radiation intensity on a difference frequency. Since the photocurrent is proportional to square of the field (i.e. the photodetector is a non-linear quadric device), the beating spectrum corresponding to these beams is observed at the photodetector outcome for heterodyne mode. More complex situation is for homodyne mode with the beating spectrum of the harmonics of the studied beam, and only in the case of the Gaussian statistics, Eqs. (24) and (28) are valid w34x. The number of photons striking the detector during the course of the experiment is directly correlated with the acquisition or sample time. The more photons collected the less noise in the autocorrelation curve. Hence, longer acquisition times are synonymous with smoother correlation curves and enhanced confidence in the experimental results. Because of the correlation with photons collected, longer acquisition times are usually required at low sample concentrations, where the signal to noise (analyte to solvent) intensity ratio is inherently small. There is a down side to long acquisition times. At longer acquisition times the likelihood of a dust event is significantly increased. If a dust particle enters the scattering volume during the course of measurement, the correlation curve is shifted upward proportionally, and baseline evaluation becomes problematic. On the upside, noise in the correlation curve can also be reduced by statistical averaging, i.e. by collecting multiple runs at short acquisition times.

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It should be mentioned a new fibre-optical QELS (e.g. FOQELS Brookhaven Instruments) apparatus operating in the heterodyne mode and appropriate for concentrated (from 1 to 50% volyvol) dispersions w44x. Fouling of the optode is not an insuperable problem, although sufficient light must, of course, be able to reach the dispersion and be reflected to the detector. At concentrations below 1% volyvol, the signal-to-noise ratio is too small to record good ACFs by this heterodyne technique. When measurements are performed within a mixed homodyne–heterodyne mode using a single-fibre device, it is possible to calculate true DT determining ACF intercept (A). When these measurements are performed in the homodyne mode, the system constant K and the intercept A must be determined accurately as any slight uncertainty leads to a large error in calculated DT (i.e. particle size distribution, PSD). For measurements done in the heterodyne regime, these constraints have less influence on determined DT. Therefore, the heterodyne mode is preferable for measurements of high-concentrated dispersions when prolonged and robust operation is required. The FOQELS scheme has the advantage of being stable and very easy to align. A fibre-to-fibre coupler was introduced as an extra local oscillator source. This results in a reliable determination of DT for concentrated dispersions where the heterodyne mode appertains at every concentration. This system was compared with others and results were presented of measurements of a latex dispersion with the particle size of 176 nm and titania (particle size f230 nm) suspension w44x. The DT values measured with the FOQELS set-up clearly differed from those measured with a single optical fibre probe, which were within the mixed homodyne–heterodyne regime; when taking this degree of mixing into account, the latter results can be transferred to the value of the true DT. For prolonged and robust measurement of highly concentrated dispersion, however, direct measurements with heterodyne probes are preferred w44x. Static light scattering (SLS) is an alternative method in which the photon counts are averaged over time, providing a measure of the scattering intensity as a function of the angle. This information can then be inverted to compute the particle size distributions. A variation in the experimental set-up uses a number of optical fiber probes fixed at specific angles. While this method can also be employed to determine molecular weight distributions in solutions, it is much simpler to focus on the determination of particle sizes, where the particles range in size from roughly 0.1 to a few micrometers and are homogeneous spheres. In this case, the angular dependence of the scattered light is well described by the Mie scattering function, which depends on the refractive indices of the particles, their sizes, and the refractive index of the medium. Classical light scattering involves measurement of the total scattered intensity of light as a function of angle, concentration or both w4,5,45x. This is commonly summarised in a Zimm plot, which is described by the equation Hc 1 w r2K2 z s x1q g |q2A2C RŽu,c. Mw y 3 ~

(30)

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Here c is the concentration, R(u,c) is the excess Rayleigh ratio, K is the magnitude of the scattering vector, and H is an optical constant. Scattered light intensities are measured at several angles for each solution concentration and the pure solvent. It is then possible to determine the molecular weight, Mw, the radius of gyration, rg, and the second virial coefficient, A2, for the species under investigation. In SLS experiments, the concentration dependent scattering intensity of the sample solution can be used to determine the absolute molecular weight (M) and 2nd virial coefficient (A2) of the analyte under examination E KC B 1 sC q2A2CFPŽu. G Ru D M

(31)

In the above expression, K is an optical constant, incorporating wavelength and refractive index effects, P(u) is the shape factor, accounting for angle dependent multiple scattering from large particles, and Ru is the Rayleigh ratio of the scattered intensity to the incident intensity. For particles with diameters more than 10 times smaller than the wavelength of the incident radiation, the shape factor goes to 1. The Rayleigh ratio is calculated using the following expression Rus

E is B r2 C F 2 I0 D 1qcos u G

(32)

where is is the residual scattering intensity (sample-solvent), I0 is the incident intensity, u is the scattering angle and r is the distance from the scattering volume to the detector. The instrument dependent parameters (I0 , u and r) are difficult to measure with the precision required for acceptable molecular weight and 2nd virial coefficient calculations. Rather than attempting to measure these parameters directly, the typical approach in SLS experiments is to calibrate the instrument parameters using a standard with a well-defined Rayleigh ratio value. The expression used to describe the scattering of a dilute solution of particles is Ew KC B 1 16p2R2g 2B u Ez sC q2A2CFx1q sin C F| Gy D 2 G~ Ru D M 3l2

(33)

where C is the particle concentration, Rg is the radius of gyration and l is the vacuum wavelength of the incident radiation. The angular dependent portion of the second term arises from interference effects in consequence of multiple scattering from a single particle. For particles much smaller than the wavelength of the incident radiation, this term goes to zero, and the angular dependence of the scattered light vanishes. Under these conditions, the absolute molecular weight is determined from the concentration dependence of the Rayleigh ratio, and angular dependent data is redundant. For larger particles, it is still the concentration dependence that leads to the molecular weight, but interference effects must be accounted for. It is

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Fig. 3. Schematic illustration of polarization-sensitive laser light scattering (PSLLS) system with quartz glass cell for tested hydrosol w47x.

at this point that multi-angle instruments become necessary. As a rule of thumb, the size cut-off for angle independent Rayleigh scattering is RgF20=l w45x. Valentine et al. w46x described a new design for a microscope-based SLS instrument that provides simultaneous high-resolution images and SLS data. By correlating real space images with scattering patterns, one can interpret measurements from heterogeneous samples, which was illustrated for biological matters w46x. The scattering of light by homogeneous and layered spherical particles composed of isotropic materials can be computed readily using the conventional Lorenz–Mie theory or its modifications. However, many natural and artificial small particles have non-spherical overall shapes or lack of spherically symmetric internal structure such as biomacromolecules and microorganisms. It is now well recognized that the scattering properties of non-spherical particles can differ dramatically from those of ‘equivalent’ Mie spheres. Therefore, the ability to accurately compute or measure light scattering by non-spherical particles in order to clearly understand the effects of particle non-sphericity on scattering patterns is very important. A polarization-sensitive laser light scattering (PSLLS) method (Fig. 3) and a dual-angle laser light scattering (DALLS) method have been applied by Shimada et al. w47x for in situ measurements of submicrometer particles. The effects of light scattered by agglomerated particles (multiplets) were corrected. The DALLS system can determine smaller diameters than the PSLLS system for test particles with no light absorption. The change in scattered light intensities with particle diameter was also investigated by theoretical calculations with various refractive indexes and scattering angles. The PSLLS and DALLS systems promise to become routine measurement tools for absorbing and non-absorbing particles, respectively. The test for any particle sizing technique is its ability to determine the differential number fraction size distribution of a simple, well-defined sample w48x. The very best characterized polystyrene latex sphere standards have been measured extensively using transmission electron microscope (TEM) images of a large subpopulation of

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such samples or by means of the electrostatic classification method as refined at the National Institute of Standards and Technology (USA). The great success, in the past decade, of on-line multi-angle light scattering (MALS) detection combined with size exclusion chromatography for the measurement of polymer mass and size distributions suggested, in the early 1990s, that a similar attack for particle characterisation might prove useful as well. At that time, fractionation of particles was achievable by capillary hydrodynamic chromatography and field flow fractionation methods. The latter has proven most useful when combined with MALS to provide accurate differential number fraction size distributions for a broad range of particle classes. The MALSyfield flow fractionation combination provides unique advantages and precision relative to field flow fractionation, PCS, and capillary hydrodynamic chromatography techniques used alone. For many classes of particles, resolution of the MALSyfield flow fractionation combination far exceeds that of TEM measurements w48x. Due to technical progress in the last decade, new measurement methods for coagulation kinetics studies have evolved. Particularly, the advent of new instruments like fiber-optics-based multiangle light scattering set-ups combined with modern correlator boards leads to a significant decrease of the recording time for scattering curves and enables simultaneous time-resolved static and dynamic light scattering measurements over a wide range of scattering vectors w49x. By using a fiber-opticsbased set-up, the simultaneous measurement of the light scattering intensity at different angles w50,51x is suitable to avoid the enormous dust and bubble problem of low angle light scattering and at the same time to compensate for the problem of weak variation of the mean intensity observed for a single scattering angle. Furthermore, the use of single or few modes optical fibers in the detection unit allows the simultaneous performance of static and dynamic light scattering measurements, which provides a direct test of both methods w52,53x. Holthoff et al. w49x studied the kinetics of coagulation of monodisperse spherical colloids in aqueous suspension at the early stage of coagulation measured by means of a multiangle static and dynamic light scattering instrument using a fiber-opticsbased detection system which permits simultaneous time-resolved measurements at different angles (Figs. 4–6). The absolute coagulation rate constants were determined from the change of the scattering light intensity as well as from the increase of the hydrodynamic radius at different angles. The combined evaluation of static and dynamic light scattering results permits the determination of coagulation rate constants without the explicit use of light scattering form factors for the aggregates. For different electrolytes fast coagulation rate constants were estimated. Stability curves were measured as a function of ionic strength using different particle concentrations. Fig. 4 shows the increase of the hydrodynamic radius with time for different electrolyte concentrations w49x. With increasing electrolyte concentration the slope of the hydrodynamic radius vs. time curve increases up to an electrolyte concentration of 0.75 M. Electrolyte concentrations higher than 0.75 M lead to the same slope. This is an indisputable indication of the fast regime, where the coagulation

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Fig. 4. Hydrodynamic radius as a function of time measured on the classical pinhole goniometer for different electrolyte concentrations: 1 M (⽧); 0.75 M (h); 0.5 M (B); 0.25 M (s); 0.2 M (j); 0.075 M (n). Solid lines are spline fits w49x.

rate constant is independent of the electrolyte concentration. In Fig. 5 the scattered light intensity and the hydrodynamic radius of the fast coagulation are shown as a function of time for several angles. The scattered light intensity I(t) is normalized by the measured singlet form factor I(ts0). The scattering angle has a strong influence on the shape and the slope of the intensity vs. time curve. This qdependence of I(t)yI(ts0) is described by the optical factor I2(q)y w2I1(q)xy1 given within the Rayleigh–Gans–Debye approximation. In Fig. 6a the Rayleigh– Gans–Debye optical factor for the scattered light intensity (solid line) is plotted as a function of the scattering angles. Taking a particle diameter of 215 nm the optical factor decreases quite strongly with increasing scattering angle. Therefore, intensity measurements at small angles are more sensitive to the growth of the aggregate during the coagulation process than measurements at large angles. At the scattering angles of 43 and 1208 the condition 2aqsjp is fulfilled, where j is an integer, and the light scattering factor is zero (Fig. 6a). The scattered light intensity then remains constant during the coagulation process (Fig. 5a, us1208). For angles between 43 and 1208 the light scattering factor is negative; for these angles the scattered light intensity decreases with time (Fig. 5a, us908). The optical factor for the dynamic measurements I2(q)y w2I1 (q)x in contrast to the optical factor of the static light measurement, always has a positive sign. Therefore, as one would expect, the hydrodynamic radius increases with time at all angles (Fig. 5b) w49x.

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Fig. 5. (a) Intensity, normalized by the form factor of the singlets, I(t)yI(ts0) and (b) hydrodynamic radius Rh(t) of the fast coagulation process for three different angles simultaneously measured on the multiangle setup w49x.

In the multiangle static light scattering experiment, the linear relationship between the angular dependence of the initial slopes of the scattered light intensity and the doublet form factor was used in order to determine the coagulation rate constant. The results quantitatively agree with those obtained in DLS measurements using the multiangle fiber-optics-based set-up as well as using a classical goniometer instrument. Therefore, properly performed and evaluated SLS and DLD measurements lead to same results in the determination of absolute coagulation rate constants. According to Holthoff et al. w49x, the latter technique represents the method of choice for routine coagulation measurements. The results in the SLS as well as in the DLS measurements were obtained by assuming that the particle form factor can be described by the Rayleigh–Gans–Debye theory. However, this assumption has been verified with the combined evaluation of coagulation kinetics data from simultaneous SLS and DLS experiments, and the resulting rate constant (determined at a fixed angle without any a priori assumption for form factors) is in complete agreement with rate constants determined from the SLS and DLS experiment only. Therefore, absolute coagulation rate constants can be measured by light scattering without any reference to the optical properties of the particles. Moreover, the analysis of the simultaneous SLS and DLS measurements demonstrates that one can estimate doublet form factors of particles with arbitrary size w49x. Two limiting regimes for colloidal particle aggregation are well described in the literature: diffusion-limited cluster aggregation and reaction-limited cluster aggregation. Between these two limiting regimes, a vast transition region is expected.

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Fig. 6. Relative doublet form factor I2(q)yw2I1 (q)x measured by the static (a) and dynamic (b) light scattering. The solid line is calculated by the Rayleigh-Gans-Debye approximation. The data points were obtained from the multiangle measurements using three different electrolyte concentrations of NaClO4: 1 M (⽧); 0.25 M (s); 0.125 M (%). The measured slope of the light scattering intensity and the hydrodynamic radius were divided by the particle concentration, the estimated coagulation rate, and, in the case of the dynamic measurements, by the hydrodynamic factor (1yRh,1 yRh,2 ). Iz (q) and Rh,z is the scattered intensity and the hydrodynamic radius of a z-fold aggregate w49x.

Odriozola et al. w54x studied the transition region by means of SLS and DLS for a system of latex particles aggregated at different electrolyte concentrations. The time dependence of the average diffusion coefficient was fitted considering the Brownian kernel and the kernel proposed by Schmitt et al. w55x. The first fits the experimental data only at high electrolyte concentrations while the latter, which considers multiple clusters–cluster contacts, is found to fit the complete set of experimental data. Korolevich and Meglinsky w56x applied the PCS extension in a multiple scattering mode with so-called diffusing wave spectroscopy (DWS) to study blood samples. Multiple-scattered light from a He-Ne laser beam incident on the blood samples was detected by a photomultiplier; and temporal ACF and PS were measured by a spectrum analyser. The potentials of using DWS for the qualitative and quantitative

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determination of the structural characteristics of the blood elements were studied experimentally with the DWS for blood cells monitoring in a multiple scattering regime. The authors w56x also described the attempts at applying DWS to study the discrete blood samples of both healthy donors and patients with the cardiac ischemia. The effectiveness of cross-correlation schemes for suppressing multiple scattering in light scattering measurements was shown by Pusey w57x. Thus, measurements on turbid samples can be analysed as though the samples were transparent, i.e. exhibiting only single scattering. The methods are now being used for new research, particularly in the study of concentrated colloidal dispersions. This article w57x reviewed the current state of the field with emphasis on the two-colour and three-dimensional DLS techniques. Although these methods were originally designed to suppress multiple scattering in DLS, it has been recently recognised that they were also effective in static light scattering. The cross-correlation schemes were compared briefly with other light-scattering methods for studying turbid and opaque samples such as fibre-optic probes and DWS w57x. Another new technique based on X-ray photon correlation spectroscopy (XPCS) is also appropriate to study the diffusion in concentrated colloidal suspensions and emulsions or the dynamics of capillary fluctuations on the surface of polymer films w58,59x. XPCS holds considerable promise for the investigation of very-low-energy dynamics on molecular length scales in polymer micelle liquids. XPCS allows one to probe slow dynamics at high scattering vectors, i.e. on a microscopic length scale. It is expected to become an important tool supplementing neutron scattering, which is sensitive to faster dynamics (-10y7 s), and PCS using visible light covering the long wavelength dynamics, i.e. the range of small scattering vectors ™ q (q-4=10y2 nmy1). The study of dynamic phenomena at shorter length scales is of interest, since many polymer systems exhibit structures on a scale of approximately 10 nm (e.g. proteins, polymer coils, blockcopolymers and structured polymer surfaces). It is this range which should be accessible by using X-rays instead of visible light. Photon correlation spectroscopy probes intensity fluctuations in a dynamic interference pattern, which is typically observed in a scattering experiment using highly coherent radiation. The range of accessible scattering vectors ™ q is extended by a factor of four over that possible with the use of visible light. Riese et al. w60x have performed combined DLS and dynamic X-ray scattering experiments on dense colloidal suspensions of silica. The intermediate scattering functions obtained with these two techniques are close for optically transparent suspensions of disperse silica (particle size 112 nm). Recently, the XPCS measurements have been extended to the biological systems with DNA and Ferritin. So far the dynamics of this system was only accessible by PCS. Ferritin is a molecule, which consists of an iron filled protein shell (474 kDa, an iron storage protein with the spherical shell of 24 peptide chains joined through non-covalent interactions, the subunit of a hollow sphere of f8 nm inner diameter with walls of f20 nm thick, and the mineral core with up to 4500 iron atoms in the Fe(III) oxo-hydroxide structure). Due to electrostatic forces between the charged Ferritin molecules an intermolecular order appears leading to a peak in the static

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structure factor. Dynamic measurements on this sample give evidence of a ‘slow mode’ as seen in the intensity correlation function. The time constant of this motion is found in the time window, which is available by means of XPCS w58,59x. However, the XPCS method involves some experimental problems and it cannot be considered as a simple laboratory technique. 2.2. Relationship between PCS data and object properties After measurement of the ACF (or PS) one can compute the diffusive broadening DTq 2 and the scalar of the velocity vector of cooperative motion of particles or ™ macromolecules, V, if such a motion exists. It should be noted that in many of PCS ™ measurements, only random diffusion motion was studied at Vs0 w5,34,42– 44,58,59,61,62x. Eqs. (20) and (22) can be significantly simplified (assuming particle monodispersity and absence of their strong interaction, i.e. the suspension is strongly diluted) to determine the translation diffusion coefficient DTsGyq2

(34)

For spherical-like scatterers (which are not interacting) of close sizes being in a medium with a known dynamical viscosity (h), the hydrodynamic radius Rh is linked with DT by the Stokes–Einstein expression Rhs

kT 6pDTh

(35)

where k is Boltzmann’s constant, T is the temperature, h denotes the viscosity of the dispersing liquid at T. The aqueous suspension of monodisperse spherical particles with polystyrene latex is an ideal model, for which Eq. (35) are adequate. Similar suspensions are used for calibrating measurements or to determine the viscosity of the solution with complex composition w63,64x. Notice that Eq. (35) is appropriate only for the dispersions of the non-interacting spherical particles in lowconcentrated suspensions. Due to averaging for the suspension with different particles, the diffusion coefficient distribution is given by B™

E

8Nm2FDq,RhGD C

Ds

F

(36)

B™ E 8Nm2FDq,RhG C

F

where N is the number of particles, m is the particle mass, F(™ q,Rh) is the particle form factor dependent on the particle size R and the scattering vector ™ q. In the h

case of l4Rh, the particle shape does not affect the scattered light.

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An average size value can be estimated in respect to the intensity dPCSs8Nidi6y8Nidi5 i

(37)

i

particle number dNs8Nidiy8Ni i

(38)

i

particle area dSs8Nid3i y8Nid2i i

(39)

i

and particle volume (or weight) dVs8Nidi4y8Nid3i i

(40)

i

with inequality dNFdSFdVFdPCS (the equal sign for modisperse particles). The hydrodynamic radius of particles Rh can be deduced from decay time t RhskTtq2 y(6ph)

(41)

For strongly anisotropic particles, the decay rate of the intensity autocorrelation function depends also on the rotational diffusion coefficient DR w65,66x and Eq. (34) is replaced by GsDTq2q6DR

(42)

To characterize the PSD uniformity, a value of polydispersity (PD) w65,66x can be used as a measure of the non-uniformity, and PD can be written as follows: PDsm2 yG2

(43)

where m2s(D2*yD*2)q4

(44)

D * is the average value of the diffusion coefficient. Monodisperse particles correspond to PD-0.02, and PD between 0.02 and 0.08 represents a narrow distribution. Notice that features of aggregation (aggregation rates) of primary particles and their aggregate or agglomerate fractality depend on an initial PD value.

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On the PCS investigations of proteins, the buffer solutions are typically used and measurements are performed at different temperatures. Therefore, the DT values published by different authors were corrected to aqueous conditions at 20 8C w67x D20,wsDT

293 B hThB E C F T D h20hW G

(45)

where T is the temperature of measurements, hT is the viscosity at T, h20 is the viscosity at 20 8C, hB is the buffer viscosity at T, and hW is the viscosity of water at T. These values of the viscosity in Eq. (45) can be easily determined using latex particles of a given size. 2.3. Analysis of the PCS data for complex systems Practically any biological solution or dispersion of inorganic particles is a complex system. For instance, protein molecules are not spherical and they can form oligomers and aggregates; their diffusion is complicated by inter-molecular interactions (electrostatic and dispersion forces, etc.), different processes of aggregation in consequence of Brownian motion (perikinetic aggregation), shear flow (orthokinetic aggregation), differential sedimentation caused by gravity, cooperative effects and conformation dynamics (observed for, e.g. fibrillar proteins). Therefore, the ACFs and spectral curves are analysed using complex algorithms to obtain more or less real physical picture of the studied objects. Firstly, the PCS data (i.e. ACFs) are normalised (e.g. by dividing by G (1)(0), which is a maximal value of the ACF) and the reduced ACF of the scattered light intensity g (2)(t) is linked with the normalised ACF of optical field g (1)(t) by the relationship w4x (akin to Eq. (11)) g(2)(t)s1qswg(1)(t)x2

(46)

where s is an experimental parameter related to the coherence volume (ideally sf1). In PCS experiments, the measured and normalised ACFs of the scattered light intensity g (2)(t) are described by equations g(2)Žt.s1qwyg(1)Žt.z~2qcŽt. x

|

|

(47)

`

g(1)Žt.s

PŽG.expŽyGt.dG

(48)

0

where P(G) is a distribution function. With no consideration for noise c(t), Eq. (47) can be used to compute g (1)(t) from the paired ACF g (2)(t) directly measured in the experiments. However, consideration for noise c(t) leads to ill-posed problem, as for some t values, the radicand in g(1)(t)syg(2)(t)yc(t)y1

(49)

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can be negative; additionally, small changes in G can result in large changes in P(G), and there are many solutions of Eq. (48) fitting the experimental data containing random noise components, which do not allow one to use exact inversion formulas or iterative algorithms. Therefore, the P(G) function (i.e. diffusion coefficient or particle size distribution functions) can be computed using the regularisation w68x, singular value decomposition (SVD) w69x, and Lagrange’s multiplier methods or other similar procedures w70x, which are partially described below. For non-spherical particles, this problem is more complex. For instance, DT for ellipsoids of revolution (as a model of globular proteins) depends on the particle form factor H w71x DTs

kTH(p) 6pha

(50)

where 2 y1y2

HŽp.sŽ1yp .

ln

1qŽ1yp2.1y2 p

(51)

psbya (a and b are large and small half-axles of ellipsoid, respectively). Additionally, on aggregation of polymer molecules, the fractality of formed secondary particles (i.e. radial-averaged concentration of particle in aggregates is w(r);rDfy3, where D f is the fractal dimension) should be considered w72x as well as multiple scattering in concentrated solutions or suspensions w73,74x. However, the lion’s share of the PCS investigations deal with computation of the P(G) distributions solving Fredholm integral equation of the first kind as ill-posed problem with no consideration for the multiple scattering or the fractality of dispersed particles (assuming their spherical shape) and their aggregates and agglomerates w34,68x. Notice that too large numbers of the P(G) distributions (approximate solutions) can good fit the experimental data, but this circumstance does not mean that reasons of enhancement of the experimental accuracy are absent, since just experimental errors are one of the factors determining the kind of possible functions which can be used to obtain more accurate solution of this problem. For raw count of the size of macromolecules, one can ignore P(G) and c(t), that, however, gives too crude an estimate of the hydrodynamic size of, e.g. proteins. The first step analysis of the systems is more complex than monodisperse corresponds to modelling of the measured curve by the sum of two or three analytical functions: exponential ones for the ACF or Lorentz ones for the PS w75–78x. Then the cumulant method proposed by Koppel w25,34,79x, which shows that the logarithm of the field–field correlation function is equivalent to the cumulant-generating functions, could be applied. Information about the cumulants of the distribution of decay rates may be obtained from the ACFs measured for polydisperse samples. The method of cumulants (widely used w61,65x) allows one to write the logarithm of the field-correlation function as a polynomial of the delay time (t), and this

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function can be fitted easily using a linear least-squares technique. However, this method has several disadvantages. Most remarkably, parameters obtained by fitting are not invariant, since the number of the data points is larger than the parameter number. In addition, fitting this function requires that the long-time baseline of the intensity ACF should be assumed rather than a floating parameter. The use of the baseline as a floating parameter makes it possible to detect problems in the data and to fit the data when a little bit of noise is present. The ubiquitous use of nonlinear fitting routines makes formulation in terms of a polynomial unnecessary. Reformulating the method in terms of the moments of the distribution rather than of the cumulants results in more satisfactory and robust fits and permits independent fitting of the long-time baseline. Furthermore, it is not necessary to limit fitting to a restricted range of the data. Frisken w80x used the data from measurements of polydisperse lipid vesicles to highlight the differences between the traditional and the reformulated versions of the cumulant method. Like the original cumulant method, this reformulated moment method is most reliable for monomodal decayrate distributions of finite width w80x. The method of cumulants is based on an assumption that any measured ACF (or PS) represents certain distribution of exponential functions (Gaussian or Lorentzian). The statistical characteristics (central moments) of such a distribution are determined through the cumulants corresponding to the coefficients Kn of polynomial decomposition of ACF B

`

D

ns1

G(t)sG(0)expCy 8 Kn±t±n

1E F n! G

(52)

The first three cumulants of any distribution are equal to the first three central moments: average of distribution M1 (i.e. GsDT q 2 ), dispersion M2 (m2 in Eq. (44)) and a parameter of the distribution asymmetry M3 . Clearly, all the cumulants, except the first one, are equal to zero for monodisperse systems. For more complex systems, the first several cumulants in Eq. (52) has given a physical meaning: K1s M1 describes the average decay rate of the distribution and characterizes the mean size of particles (macromolecules); K2 sM2 corresponds to the variance or polydispersity (e.g. oligomerisation or aggregation degree of molecules); and K3sM3 determines the relationship between fast and slow relaxation processes and provides a measure of the skewness or asymmetry of the distribution. The first two cumulants must be positive, but the third cumulant can be positive or negative. Natural logarithm of the ACF of the scattered optical field can be given through the central moments lnŽg(1)Žt..syM1tq

1 1 1 M2t2y M3t3q ŽM4y3M22.t4q∆ 2! 3! 4!

(53)

Unfortunately, errors in determination of the cumulants increase with their number, and the fourth cumulant characterizing the distribution excess (peakedness) may be

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uncertainly estimated. The DLS data for polydisperse samples can be analyzed in terms of the moments about the mean of the distribution function that describes the polydispersity of the sample. The traditional fitting function, as derived from the cumulants of the distribution, has several problems associated with it. It results in parameter values that depend on the number of data points fitted, and it does not permit an independent fit of the baseline B. Frisken w80x has demonstrated how a more robust fitting function can be obtained by the avoidance of the logarithm of g (1)(t) and the direct expansion of g (1)(t) in terms of the moments about the mean. The function can be fitted to the entire data set, gives consistent results for fitting parameters when different numbers of points are fitted, is more robust to bad guesses of the initial parameters, and permits an independent fit of the baseline B. This approach used to analyse the light scattering experiments (a Model ALV DLSy SLS-5000 (ALV-Laser GmbH, Langen)) with palmitoyl-oleoyl posphatidycholine vesicles showed good fitting w80x. Notice that the method of cumulants can be successfully used to compare the PCS measurements of close samples in the same measuring cell. To compute, e.g. bacteria velocity distributions (or PSD), the spline method was also used w81x. However, numerical statistical characteristics of a distribution or the spline approximation are not enough to build up an adequate P(G) distribution, i.e. to solve the inverse spectral problem, which can be better solved by using the regularisation or similar methods (SVD, maximal entropy, Lagrange’s multipliers, etc.) w82,83x. The complete solution of this PCS problem corresponds to solution of the integral equation

|

`

KŽG,y.PŽG. dGsFŽy.

constq

(54)

0

(where F(y) is the measured ACF or PS, the kernel K(G,y)sexp(yGy) for ACF and Gy(G2qy2) for PS) in respect to P(G) dependent on characteristic diffusive broadening. The solution of Eq. (54) is unstable in respect to small deviations in F(y) (because of random noise contribution), but this is inherent in general solution for class of arbitrary functions integrated. If the class of decision functions can be narrowed because of additional conditions that one can obtain a stable solution of Eq. (54). The technique of narrowing of a given function class to provide a stable solution of the inverse problem plays an important role in the regularisation methods w68,84–86x. In most cases, only such three conditions for a solution as nonnegativity, finiteness and smoothness are sufficient. First two conditions hold true automatically for the PCS data; otherwise the solution does not have any physical meaning. The requirement of the smoothness of a solution jointly with the finiteness allows one to determine (according to the Riss criterion w87x) the function set L{a, b}, in which the required solution is necessarily. Then the problem of inversion of the Fredholm integral equation of the first kind becomes well-posed (according to Tikhonov w68x) and adds up to the standard procedure of minimisation of functional

V.M. Gun’ko et al. / Advances in Colloid and Interface Science 105 (2003) 201–328 b w y a

|

F(T)s

FŽy.y

x

227

b

|

KŽG,y.PŽG.dGx2dy

(55)

a

The smooth solutions are frequently represented as histograms with the bar width equal to s or as the set of the d functions with the interval equal to s, which is the smoothing parameter w71,88–92x. On the use of stabilising functional in the regularisation procedure according to Tikhonov w68,92x, a numerical factor at this functional is the smoothing parameter (regularisation parameter a). It should be noted that in the DYNALS (PSD analysis algorithm and software) developed by Goldin (Protein Solutions Co.) w93,94x to compute P(G), minimisation of L2 norm B

`

D

0

minC

|

E

P2ŽG. dGF

(56)

G

was successfully utilised to solve Eq. (55) to obtain stable solutions with a maximum of useful information extracted from the ACFs. Nowadays, the Protein Solutions Co. (http:yywww.protein-solution.com) is one of the leading institutions dealing with the application of the PCS method to study proteins and related objects. Many researchers: Chu w95,96x, Provencher w97–101x (who elaborated several versions of constrained regularisation CONTIN procedure to compute the molecular mass distribution, etc. which is used as one of the standard procedures incorporated into firm software distributed with the PCS apparatuses by certain companies such as Malvern Instruments (UK)), and others w48,102–107x made important contributions to development of the PCS method and handling of the experimental data related to the protein systems. It should be noted that a spherical shape of scatterers was assumed in a significant portion of the PCS investigations (performed using single scattering angle setups) of biological objects considered in this survey. Detailed analysis of the complex theoretical and experimental problems related to the light scattering by non-spherical particles given by Mishchenko et al. w107x reveals that the most valuable information for such biological objects as protein, DNA, and other non-spherical macromolecules may be obtained only accounting their shape on the basis of application of the MALS-PCS technique. The PCS experiments give discrete values of a measured function, e.g. ACF corresponding to discrete analogues of Eqs. (54) and (55) Ng

NL

ms1

is1

yks 8 cmKŽgm,yk.PŽgm.q8biLiŽyk.qok

(57)

where ks1,«,Ny, Ny is a number of experimentally measured yk values (corresponding, e.g. to the number of correlator channels), cm is the coefficients in the quadrature formula, bi is unknown parameters, Li is known functions (if NLs1, L1s1, that b1 is an additional constant); ok are the experimental errors including noise. A constrained regularisation solution of Eq. (57) corresponds to minimisation

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of equation Ny

B

Nx

E2

NregB

Nx

E2

8vkCDyky8AkjxjFG qa28CDriy8RijxjFG sminimum

ks1

js1

is1

(58)

js1

where the second term is the regularisator (V) determined by specifying the arrays r and R, a is the regularisation parameter, vk is the weights; and Nx

ykf8Akjxj

(59)

js1

Akj are known and xj are unknown. Even for arbitrary small non-zero noise levels in yk, there still exists a large set of solutions P(gm) (or P(G)) that all fit the yk to within the noise level, and the regularisation procedure, such as CONTIN, applied to Eq. (58) allows one to obtain the most appropriate solution of this ill-posed problem w97–106x. For simplicity Eq. (57) can be re-written in the operator form KPsy

(60)

and P0 is the ‘exact’ solution of Eq. (60) for exact y0 (without noise) with inequality for experimental errors s Ny0yyNFs

(61)

For the regularised solution Pa, there is an inequality Ta(Pa)sNKPay yN2qa2V2(Pa)FNKP0yy0N2qa2V2(P0)

(62)

where V2(P) is the stabilising functional (regularisator), as Pa corresponds to a minimum of the functional Ta(P). From Eqs. (61) and (62) one can write another inequality NKPayyN2qa2V2(Pa)Fs2qa2V2(P0)

(63)

that gives evaluations V2(Pa)Fs2ay2qV2(P0)

(64)

NKPayyN2Fs2qa2V2(P0)

(65)

A maximal value of the regularisation parameter a corresponds to the condition that the discrepancy NKPayyN2 should not be significantly larger than s2 and V(P0)FV0, where V0 is a constant and one may assume that

V.M. Gun’ko et al. / Advances in Colloid and Interface Science 105 (2003) 201–328

a2s(syV0)2

229

(66)

that gives inequalities

ZKPayyZFy2s

(67)

NKPayyNF(1qy2)s

(68)

From Eq. (65), the a value can tend to be zero not faster than s2. For simplicity, a may be fixed using additional information about a desired distribution function. In the CONTIN procedure w100,101x, the regularisation parameter can be determined on the basis of F-test, confidence regions for least squares, and the principle of parsimony. However, according to Goldin w94x, there are two major difficulties associated with such a method of regularisation. The first one is related to the fact that the singular numbers decay very fast while the damping factors decay slowly. If a in Eq. (58) is chosen to damp all problematic singular numbers, it will partially damp the stable ones and, therefore, only a portion of useful information will be extracted from the data. On the other hand, if a is chosen to pass all valuable information, it will also allow small singular numbers to ruin the solution. The value in the middle will partially damp the stable information and partially pass the amplified noise (by dividing it into small singular numbers) and, as a result, the optimal solution is never found. A large number of published papers have been devoted to the optimal choice of the regularisator and the regularisation parameter. Most, if not all of them, assume that the problem is linear, which in our case greatly underestimates the regularisation parameter. The reason for such underestimation is that the system of equations is to be solved under the constraint of a non-negative solution. This constraint greatly improves the stability of the problem, but causes the problem to be non-linear (by the definition of a linear problem) and the corresponding, ‘optimal’ a to become irrelevant w94x. Fernandes et al. applied a new method to evaluate the scattered light intensity distributions with particle size by means of PCS w108x. They found the least squares solution (L2 norm) and the solution that was not significantly different from the least squares solution that simultaneously minimised the sum of the modulus of the residuals (L1 norm). A simple procedure was achieved by using the Lagrange’s multipliers method. The two aspects that debilitate CONTIN were prevented in this work granting meaningful results. The developed method was applied to simulated curves, in several typical situations (mono-modal and bi-modal, narrow and broad distributions). The quality of the results was better for narrower mono-modal distributions and bi-modal distributions having well separated peaks, as expected. Latex beads (114 nm) were used to test the method in experimental conditions. According to Fernandes et al. their procedure better reproduced monodisperse distribution profiles than CONTIN and the first moments of the distributions were in agreement with the expected value in most of the analysis w108x. Iqbal w109x developed a procedure for evaluation of the PSD using PCS according to the regularisation method of first kind integral equation including Laplace

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Table 1 Summary for unimodal samples w110x Diameter (nm) 100 200 300 400 500 600 700 800 900 1000 1500 2000 2500 3000

4000

Search range (nm)

GA (nm)

MEM (nm)

20–500 20–1000 20–500 20–1000 100–1000 100–1000 300–500 100–1000 100–1000 100–1000 100–1000 100–1000 500–5000 500–5000 500–5000 500–5000 500–5000 2800–3200 2960–3040 500–5000

76 64 198 126 301 394 402 504 596 704 794 902 916 1528 1994 2522 2980 3004 3000 3988

100

CONTIN (nm)

299 400

72 86 199 196 300 400

500 600 700 800 900 991 1507 2001 2505 2980

500 600 700 800 900 991 1504 2014 2488 2990

3990

3990

200

transform by means of Bayesian strategy. This type of problem plays an important role not only in PCS, but also in fluorescent decay, sedimentation equilibrium, and in other methods of physics and applied mathematics. The method was applied to test problems and it gave a good approximation to the true solution. Hodgson w110x investigated the particle size distributions based on data from simulated SLS experiments using genetic algorithms (GAs) to extract unimodal, bimodal and trimodal distributions from data that contain differing amounts of noise. This approach was compared with the results w111,112x obtained using the maximum entropy method and constrained regularization CONTIN. The particles were assumed to be spherical and of uniform density with diameters in the range from 100 to 4000 nm (Table 1). The results shown in Table 1 reveal that the solutions obtained using different algorithms are relatively close in the total studied size range. For comparison with the results shown in Table 1, we calculated the PSD on the basis of generated ACF for monodisperse particles at ds4000 nm without (PSD maximum was found at 3988 nm) and with added 20% random noise (4040 nm) (Fig. 7) using slightly modified CONTIN procedure. These calculations show that the CONTIN solution is stable even at great random noise contribution to the ACF, however, the PSD becomes broader and its maximum slightly shifts towards larger diameter values. This may be conditioned by an increase in the regularisation parameter (unfixed and determined on the basis of F-test, confidence regions for least squares, and the principle of parsimony) because of the data deterioration. Additionally, using this modified CONTIN procedure we examined the result shown

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Fig. 7. Particle size distributions: (1) initial used for generation of the ACF; and CONTIN results (unfixed a value) with (2) no addition of noise, and (3) addition of random noise (20%).

in Table 1 at ds100 nm over the search range of 20–500 nm and obtained df100 nm, which significantly differs from that shown in Table 1 and computed by using another version of the CONTIN procedure. Additional tests of the modified CONTIN procedure also give good results for different bi and trimodal PSDs computed on the basis of the corresponding generated ACFs. For instance, Fig. 8 depicts good

Fig. 8. CONTIN result for the ACF generated on the basis of a trimodal distribution at the particle size of 100, 500 and 1500 nm.

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agreement between the CONTIN results for trimodal PSD and the PSD used to generate the ACF used. Wood and Walker w113x explored the feasibility of recovering the spectral line shape of a scattered light field by using a higher-order PCS technique. The proposed technique was outlined and a description was given of a laboratory experiment, in which an estimate was made of the line shape of light scattered by an arrangement designed to produce a well defined and asymmetric line shape. The results indicated that it was feasible to recover an asymmetric line shape, although with limited resolution. Potential applications associated with particle size using light scattering techniques were discussed. According to Murphy w114x, laser light scattering comes in two major ‘flavours’: dynamic and static. This non-invasive technique provides a means for investigating key size and shape properties of macromolecules in the solution. Thus, PCS has long been an indispensable tool to the polymer physical chemist, and is seeing increased use in exploring properties of biological macromolecules, alone and in association. As examples, recent investigations using PCS have clearly demonstrated the relationship between the self-association and activity of important regulatory enzymes, and examined conformational properties of DNA, polysaccharides and other biomacromolecules. 2.4. Some PCS facilities Certain modern and popular PCS apparatuses (which become miniature in comparison with the first PCS equipment w4,5,34x) are considered in this chapter. Nowadays all the PCS apparatuses equipped with powerful computers and effective program packages akin to CONTIN (Malvern Inst.) or special firm software, which give fast and enough accurate results for large range of the particle sizes from 1 nm (or less) to 10 mm or above for liquid (solutions, suspensions, hydrosols) and gas (aerosols) phases over wide range of concentrations. The most popular PCS apparatuses are produced by Brookhaven Instruments (e.g. 90Plus Particle Size Analyzer, FOQELS Particle Sizing in Concentrates by DLS, BI-DCP High-resolution Disc Centrifuge Particle Sizer, and BI-200SM Laser Light Scattering System) w115x and Malvern Instruments (e.g. Zetasizer HS 1000, 3000, 4700 and 3000 HS, Mastersizer 2000, PharmaVision 830, High Performance Particle Sizer, HPPS) w116x. The use of the BI-DCP and more powerful lasers allows one to explore the dispersions with particles less than 2 nm and to analyse the distributions at great concentrations w115,117x. It should be noted 18-angle DAWN-DSP instrument (Wyatt Technology Corp., Santa Barbara) equipped with a linearly polarized 5-mW He–Ne laser (operating at 632.8 nm), which was used in the MALSyFFF measurements w48x. New high-temperature option for the Brookhaven FOQELS instrument can be used for high-temperature oil applications up to 1600 8C. The Brookhaven BI200SM system can be used for studies of both SLS and DLS. In the SLS mode, time-averaged intensity measurements are made (at either fixed or variable angles) in the range from 80 to 1558 and analysed with software provided for the methods

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of Zimm, Berry, Debye, Guinier, Kratky and others. The field of DLS measurements is at least as rich as that of SLS w115x. Trials of the new Zetasizer HS option (Malvern Instruments) have demonstrated that it confers up to a 20-fold increase in sensitivity compared with existing systems. In practical terms this means that 95% of all sizing applications can now be accommodated using a single standard instrument such as the Zetasizer 3000HS. Using the latest Avalanche Photodiode Detector (APD) the Zetasizer HS systems have been engineered to produce an improved count rate equivalent to using an external 20 mW 488 nm blue laser, but without any of the technical problems. The Malvern HPPS incorporates patented technology within its Non-Invasive Back Scatter (NIBS) optics. This novel arrangement of optics maximizes the detection of scattered light while maintaining signal quality, to provide the exceptional sensitivity required for measuring molecules smaller than 1 kDa w116x. At Boehringer Ingelheim Pharma KG, particle size measurement of antibodies has been undertaken using the Zetasizer HS to demonstrate the relationship between antibody size and the production process temperature. The signal is 10–20 times greater than with the standard APD detector, providing higher resolution, enhanced reproducibility, and significantly shorter measurement times even for demanding biological applications w116x. Particle Sizing Systems is a designer and manufacturer of particle sizing instruments that are used for research and development, USP quality assurance, contamination and on-line process monitoring. Particle Sizing Systems offer a complete line of particle size analysers: The NICOMP 380 (Nicomp Instr. Corp., USA)yDLS Submicron Particle Sizer that uses DLS with a size range of 0.003–5 mm with unique modular options: AutodilutionPAT, Auto-sampler, high-power laser diodes, multi-angle option and Zeta-Potential accessory. The AccuSizer 780ySPOS Single Particle Optical Sizer (SPOS, 0.5 to 2500 mm) is an instrument that can count and size particles above 0.5 mm, one at a time. N4 Plus Submicron Particle sizer (Beckman Coulter) apparatuses are used in the PCS investigations w118x. The Coulter N4Plus apparatus provides not only mean particle size, but also size distributions computed by the industry standard CONTIN algorithm, and six measurement angles to enhance the detection of populations of particles of different sizes. A 10 mW He–Ne laser provides detection of weakly scattering particles of the size range from 3 nm to 3 mm. An 80-channel multi-t correlator (the hardwired computation circuit which characterizes the rate of fluctuations in scattered light intensity) optimises resolution across the dynamic range of the instrument. It should also be mentioned a SEMATech Dense Liquid Photon Correlation spectrometer (DL-135) equipped with 3 mW He–Ne laser developed to measure concentrated solutions and suspensions. Characterizing new therapeutic and diagnostic proteins and antibodies is a key task for the successful submission of research and production data for regulatory approvals. A fundamental component of any submission is the accurate assessment of the antibody’s size and its molecular weight or molecular weight distribution, aggregation state and stability. Proteins and antibodies can aggregate as a function

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of temperature, pH, ionic strength and concentration. Even small amounts of aggregates (dimer, trimer, etc.) can be significant as they cause conformational shifts in the molecular structure that can alter their function as an effective therapeutic or diagnostic agent. Monitoring and understanding these effects are fundamental for research, development and quality control requirements. Recent innovations in modern high speed electronic components such as high performance diode lasers, high-speed digital signal processors and modern avalanche photodiode detectors has lead to the evolution of a new combined static and dynamic laser light scattering detector (Precision Detectors, Inc., USA) w119x. This detector has a 10 ml flow cell design and is capable of characterizing both molecular weight and size for biomolecules when coupled to modern HPLCySECyFPLC instruments. This new detector and associated software provides: (i) absolute molecular weight data for each eluting component from 1 kD to 10 MD; (ii) hydrodynamic radius Rh of the biomolecules from 1 nm to 1000 nm; and (iii) high sensitivity covalent and noncovalent self-association measurements. Interpreting ‘information-rich’ intensity signals is accomplished by the 1024 channel correlator and the proprietary PrecisionDeconvolve娃 software (Precision Detectors). Through the use of a 100 mW laser with a fiber optic coupled high-speed photon counting detector. The key advances of this new DLS technology are its very high sensitivity and unique ability to operate in both a ‘flow-mode’ with a HPLCySEC system and in a batch-mode. Typical stability study applications involve characterizing aggregation andyor size variations as a function of time, temperature and pH. Chromatographic peak ‘integrity’ of the eluting protein or antibody from a SEC column can be clearly verified by determining the hydrodynamic radius and Mw of the eluting fractions across the entire peak. Any perturbation in the Rh across the peak, as it elutes, reflects a co-eluting contaminant or conformational structure variation of the molecule w119x. Thus, there are many PCS apparatuses based on different principles of measurements (DLS, SLS, PSLLS, MALS, FOQELS, XPCS) of scattered radiation of different frequencies (from red visible light to X-ray) allow one to study diluted and concentrated dispersions to determine the diffusion coefficients, particle and molecule size distributions, molecular weight distributions, particle or macromolecule shapes, particle aggregation, mobility of microorganisms and other important characteristics. 3. Characteristics of protein molecules determined by means of PCS 3.1. Diffusion coefficients of proteins Character of the PCS investigations changed with accumulating information and experience from the works illustrating possibility of this technique towards investigations devoted to specific biological problems. General problems of the PCS explorations of the protein solutions were analysed in several reviews w12,23,34,96x. Measurement of the translation diffusion coefficients of proteins in the solution is relatively simple, but it is important in the task of the PCS investigations. The data

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of these measurements allow one to estimate the size of protein particles and, in some cases (e.g. on application of techniques of MALS type), to determine the molecular shape of proteins. In addition to the studies of globular and fibrillar proteins, separated protein fragments and protein complexes and oligomers were explored. The values of the translation diffusion coefficients DT and the corresponding hydrodynamic radii Rh of proteins are shown in Table 2. This table does not pretend to the completeness, but gives clear notion about a variety of the studied protein objects over large ranges of DT (from 2.5=10y6 cm2 ys to 2.2=10y8 cm2 y s) and Rh (from 0.9 to 98 nm) values w4,34,120–135x. The hydrodynamic radius of globular proteins is close to the true geometrical size (R) of macromolecules, as RhfRqky1, where k is the Debye–Huckel parameter, and the thickness (i.e. ky1) of the electrical double layer (shear layer) is relative small because of high polarity and charging of polyelectrolyte molecules (proteins, DNA, etc.) especially far from the point of zero charge (or the isoelectric point on electrophoresis) w23,34x. However, for proteins with the shape strongly different from the spherical one, the hydrodynamic size can be considered as only a conventional or effective magnitude w34,107x dependent on the solution characteristics (pH, T and salinity). At the same time, the translation diffusion coefficient is an objective physical parameter of protein particles. Notice that changes in DT can be linked to both variations in the microstructure of individual particles and overall properties of object, e.g. the oligomerisation or aggregation degree. To elucidate the real reasons of similar phenomena, an additional experiments are necessary, namely measurements of the angle dependence of G by means of, e.g. the MALS technique w48,107x. For instance, the transition from the linear dependence of G(q 2) of the first type (Fig. 9, curve 1) to one of the second type (curve 2) would mean a significant enhancement of the polydispersity with simultaneous growth of the mean size of particles. The transition from the dependence 4 to 3 (Fig. 9, curves 4 and 3) corresponds to decomposition of molecular oligomers or aggregates with formation of the monodisperse solution. Sometimes obtaining such qualitative information may elucidate problems important for biologists. Notice that other methods such as image correlation spectroscopy, image cross-correlation spectroscopy, fluctuation correlation spectroscopy, two-photon fluorescence microscopy, electron microscopy (TEM, SEM), AFM and others are intensively used (sometimes in parallel with PCS) to study proteins in different states and different media. For instance, fluorescence line narrowing is a high-resolution spectroscopic technique that uses low temperature and laser excitation to optically select specific subpopulations from the non-uniformly broadened absorption band of the sample. When applied to the study of fluorescent groups in proteins one can obtain vibronically resolved spectra, which can be analysed to give information on spectral line shapes, vibrational energies of both the ground and excited state molecule, and the inhomogeneous distribution function of the electronic transitions. These parameters reveal information about the chromophoric prosthetic group and the protein matrix, and they are functions of geometric strains and local electric fields imposed by the protein. Examples of the use of fluorescence line narrowing were discussed w136x

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Table 2 Translation diffusion coefficients and hydrodynamic radii of protein molecules Molecule

DT (10y7 cm2 sy1)

Rh (nm)

Refs.

Glycoproteide Glycoproteide of mucous tunic of sheep Large intestine Elastin Meromyosin (dimer) Hemocyanins (HMC) Archacatina marginata Murex trunsulus Pila leopolduillensis a-HMC of edible snail b-HMC of edible snail Mollusc Meromyosin (monomer) Meromyosin (monomer)* LMM – Meromyosin (rod) LMM – Meromyosin (rod)** Light Meromyosin (LMM) Heavy Meromyosin (HMM) Human fibrinogen Bovine fibrinogen a-Crystallin Large phytochrome Prf RNA – polymerase Phenylalanine–tRNA–synthetase Small phytochrome Pr** Small phytochrome Prf** Catalase Aldolase g-Globulin 12S – Globulin LMM – myosin, fragment S2 LMM – myosin, fragment S1 Bovine serum albumin (BSA)*** BSA (monomer) G – Actin a-Chymotrypsin Haemoglobin Collagen (monomer) a-Chymotrypsinogen Histon (fortified by lysine) Lysozyme LMM–meromyosin, fragment S1 a-Lactoglobulin (Lg) Lactoglobulin (dimer) Lactoglobulin (octamer) a-Lactoglobulin (H2O buffer, 30 oC)

0.220"0.002 0.238"0.006

97.5"0.9 90.1"0.23

w120x

0.51 0.84

42.0 25.5

w122x

1.00"0.01 1.03"0.01 1.04"0.01 1.04"0.01 1.05"0.01 1.03"0.01 1.24; 1.15; 1.11 1.17; 1.19 1.24 1.41; 1.43 1.89 1.90; 1.93 1.94; 1.98 2.02; 2.40 2.2"0.02; 2.36"0.02 2.66"0.12 2.70"0.15 2.85"0.50 3.58"0.50 3.70"0.28 3.6"0.2 3.8"0.2 3.8"0.2 3.80 3.98 4.80 5.76"0.05 10.20"0.20 5.26; 6.10 6.11 6.70"0.20; 6.90"0.30 7.20"0.16 8.40"0.20 8.50 10.60"0.10 11.30 13.40 7.38 4.76 9.61

21.4"0.2 20.8"0.2 20.6"0.2 20.6"0.2 20.4"0.2 20.8"0.2 17.6; 18.3; 19.3 18.3; 18.0 17.3 15.2; 15.0 11.4 11.3; 11.1 11.2; 10.8 10.6; 8.9 9.8"0.1; 9.1"0.1 8.1 7.9 7.5 5.0 (6.0) 4.9 (5.8) 5.9"0.3 5.6"0.3 5.6"0.3 5.7 5.39 4.4 3.7 2.09 4.06; 3.52 3.5 3.2; 3.1 3.0"0.2 2.55 2.50 2.02 1.90 1.6 2.9 4.5 1.71

w4x w121x w4x w4x w4x w4x w122x w123x w122x w124x w122x w125x w126x w4x w4x w127x w4x w128x w127x w127x w4x w4x w4x w128x w122x w122x w4x w121x w123x w121x w130x w131x w121x w132x w121x w121x w133x w121x w121x w134x

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Table 2 (Continued) Molecule

DT (10y7 cm2 sy1)

Rh (nm)

Refs.

a-Lactoglobulin (pH 2) a-Lg (9 M urea in water) a-Lg (9 M ureaq10 mM DTT) a-Bile

8.05 3.5 1.0 25.20

2.04 3.08 10.78 0.85

w134x w134x w134x w135x

*

Model computation. Computation using the diffusion coefficient value. *** For the isoelectric point (pH 5.0 – 2.0); DTTs1,4-dithio-D,L-threitol. **

in respect of heme proteins, photosynthetic systems and tryptophan-containing proteins. 3.2. Size distribution of molecular particles Analysis of the polydispersity of proteins in the aqueous media is one of the overall problems of biological applications of PCS w34,137–141x, as its solution gives an answer to many questions about the protein systems. For example, a clear notion about the mean size of particles and the oligomerisation degree can be obtained even from a rough size distribution w142x. Observation of the PSD dynamics allows one to analyse the processes in the biological systems at the molecular level w143–149x. Such phenomena as conformational transition, complexation, biological polymerisation w150x, aggregation w151–155x and other changes in the state of the biological systems could be transformed to particular solutions of the overall problem. Only computations of molecular mass distributions w156x on the basis of PSDs for proteins face apart. Actually, the geometry of oligomer aggregates could differ significantly from the geometry of units forming these secondary particles

Fig. 9. Angle dependence of inverse correlation time for (1, 3) monodisperse and (2, 4) polydisperse systems.

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(due to spatial changes in the shapes of molecules on their oligomerisation or aggregation and their fractality that may lead to unexpected changes in the scattering ability of secondary particles); and similar structural features were observed in many cases. Therefore, the relationship between the diffusion coefficients of oligomers (or aggregates) and monomers is not a linear function of the number of monomers in oligomers (notice that DT;Ry1 h ). Consequently, the PSDs can only be slightly akin to the molecular mass distribution. To solve this problem, one should determine or estimate the shapes of secondary particles using such methods as circular dichroism (notice that Provercher developed a special version of CONTIN to solve the inverse problem for the latter method to estimate, e.g. the secondary structure of proteins w99–101x), multi-photon excitated fluorescence spectroscopy, XRD, SAXS, XPCS, MALS, electron microscopy, AFM, inorganic sieves and membranes. To consider polydisperse systems, such quantitative criteria of the polydispersity as Eq. (43) can be used. However, there is another dimensionless parameter of the polydispersity w4x Qs

s 2t 2 2

(69)

where s2 is the distribution dispersion, t is the mean correlation time for this distribution. Sometimes the percentage of particles different from the size of a prevailing monodisperse portion is used as a polydispersity criterion w157x. The homogeneity of a solution or a suspension is considered as a good one (narrow PSD) if the polydispersity is lower than 15%, which corresponds to Q-0.1 w34,157x. For a monodisperse system (narrow PSD), the average statistical value of the molecular mass (M) of protein particles can be determined if the sedimentation coefficient (s) and the specific partial volume (v) are known Ms

sRgT DTŽ1yvr.

(70)

where Rg is the gas constant, r is the specific density of the solvent. The v value can be determined by using a densimeter w158x 1 100 B 1 1 Ez C y F| y Pm D m1 m0 G~ y m0 w

vsVx

(71)

where V is the densimeter volume, m0 is the solution mass, m1 is the solvent mass, Pms100(cVym0), c is the protein concentration in the solution. 3.3. Shape of protein molecules Determination of the shape of protein molecules is a complex problem, however, the application of even single-scattering-angle PCS set-up can be fruitful if the

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translation friction coefficient f is used. This coefficient is linked with the translation diffusion coefficient as follows (72)

fDTskT

The asymmetry parameter of molecules corresponds to fyf0, where f 0 is the translation friction coefficient of a sphere with the equivalent mass w157x B 3Mn E1y3

f0s6phC D

4p

F

(73)

G

For globular proteins modelled by an ellipsoid of revolution w158x, f 0 is f0s

3phLŽp2y1.1y3 plnwypqŽp2y1.1y2z~ x

(74)

|

where L is the contour length of the molecular chain (for proteins, it is the length of the polypeptide chain), p is the ratio of the main axes of the ellipsoid (p)1). It should be noted that Eqs. (70) and (72) are valid independently on the shape and the size of particles. The particle (or macromolecule) form factor can be determined by means of the MALS technique w48,107x. Qualitative assessments of the shape of discovered proteins are typically performed and published in the literature very quickly, e.g. for biliprotein R-phycoerythrin IV eliminated from marine algae Phyllophora antarctica, Rh determined by using PCS is equal to 5.54 nm for a non-spherical shape of the molecule w159x. Information about the shape of biopolymers allows one to elucidate the localisation of them in the native structures. For instance, joint application of analytical centrifugation and PCS allowed Zgurskaya and Nikaido w160x to determine a large asymmetry of monomers of protein AcrA as a component of a multifunction complex AcrABTolC (Escherichia coli). The p value of this lipoprotein was equal to 8, which allowed the authors to conclude that this lipoprotein locates in periplasm but not in the lipid bilayer w160x. Understanding the mechanisms of protein folding requires knowledge of both the energy landscape and the structural dynamics of a protein. For instance, Bu et al. reported a study of the nanosecond and picosecond dynamics of native and denatured a-lactalbumin w134x. The picosecond time-scale dynamics shows that the potential barrier to side-chain proton jump motion is reduced in a molten globule and in the denatured proteins when compared to that of the native protein (Table 2, DT, Rh). The obtained results provided a dynamic view of the native-like topology established in the early stages of protein folding. More complicated picture can be observed in the case of complex solutions containing, not only proteins but also surfactants, drug, polymers, salts and other compounds affecting the structure of protein molecules and protein–protein interaction.

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4. Intermolecular interactions 4.1. Protein aggregation and interaction with other compounds Proteins in solution have a tendency to aggregate depending on physicochemical conditions. Aggregation (especially oligomerisation) is often irreversible and leads to, e.g. an undesirable loss of the protein products in the food industry. Similar phenomena can cause negative effects in the human organism or may be a sign of some serious diseases (such as Alzheimer’s and Jacob diseases). However, many proteins possess specific activity in the form of dimers, trimers or other oligomers. Therefore, investigations of protein aggregation and oligomerisation are of interest from many points of view. The processes of aggregation or oligomerisation can be effectively explored by means of the PCS method since the scattering ability is proportional to the square of the scatterer mass w4,5,34x. In the case of strong interaction of particles filling a marked portion of the scattering volume, Eq. (42) could be written with consideration for dependence of diffusion coefficients on the particle volume fraction F GFsDT,Fq2q6DR,F

(75)

where DT,FsDT(1ykTF)

(76)

DR,FsDR(1ykRF)

(77)

kT and kR are constants. Eq. (75) allows slowing down of particle motion (both translational and rotational diffusions) because of the interaction of particles. Other corrections related to multiple scattering, non-sperical shapes of particles, conformational changes in maromolecules, index matching particles, own mobility of living flagellar microorganisms, and some other effects should be considered for deeper understanding of phenomena occurring with complex bioobjects depending on external conditions. Aggregation, oligomerisation and other processes occurring with protein molecules depend on several factors such as the nature of proteins, their concentration, solvent type, availability of other organic (low and high molecular, surfactants, etc.) and inorganic (salts, metal ions, acids, bases, i.e. salinity and pH) compounds (i.e. composition of surroundings as a whole), temperature, pressure, exposition (ageing), external actions (applied electrostatic or electromagnetic fields, UV radiation, sonication, etc.). Since the corresponding investigations of different proteins and their interactions itself or with surroundings are numerous, we will mention only certain interesting results related to some human, animal and food proteins, other biomolecules (DNA, RNA, lipids, etc.), some drugs, delivery and model systems. The use of PCS to explore the behaviour of proteins under different buffer conditions during the development of the chromatographic and filtration-cleaning

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process allows one to optimise the process steps. This way, consideration is given very early to the buffer solutions to ensure that the proteins retain the desired monomer shape. Ultimately this delivers improvements in the product security and a more robust production process. PCS measurement is also used in the formulation for the development of biotechnologically produced proteins. Here the challenge is to maintain the active monomer form of the protein by adjusting the physicochemical conditions of the solution. Achieving optimal sample concentration in laser light based systems is vital to good particle size measurement. If the concentration is too low, the statistical significance of the results will be poor, whereas at too high a concentration, multiple scattering effects can lead to erroneous results (if special equipment and appropriate corrections are not applied). Proteins under physiological conditions are functional-active only at a certain composition of oligomers. For example, lactate dehydrogenase is active in the tetramer shape w161,162x but alcohol dehydrogenase from liver is functional as trimer and yeast alcohol dehydrogenase works as dimer w163x. In formate dehydrogenase (dimer), the functions of its two subunits differ, as one bonds substratum but another binds coenzyme w164x. The PCS technique can be applied to solve similar problems; and, for instance, Faraone et al. w165x showed the existence of isolated bovine serum albumin (BSA) molecules (RHs4.09 nm) and their secondary particles (CBSAs1 wt.%, pH 7.2). Polymers such as polyethylene oxide (PEO600) added to the protein solution can influence both these form concentrations. Petsev et al. w45x have studied the structure of the protein species and the protein– protein interactions in solutions containing two apoferritin molecular forms, monomers and dimers, in the presence of Naq and Cd2q ions by means of SLS and DLS techniques (Fig. 10 and Table 3), chromatographic and atomic force microscopy (AFM). Size-exclusion chromatography was used to isolate these two protein fractions. The sizes and shapes of the monomers and dimers were determined by means of the DLS and AFM methods. Although the monomer is an apparent sphere with a diameter corresponding to X-ray crystallography determinations, the dimer shape corresponds to two, bound monomer spheres. SLS was applied to characterize the interactions between solute molecules of monomers and dimers in terms of the second osmotic virial coefficients. The results for the monomers indicate that Naq ions cause strong intermolecular repulsion even at concentrations higher than 0.15 M, contrary to the predictions of the commonly applied DLVO theory w23x. Petsev et al. w45x argue that the reason for such behaviour is hydration force in consequence of the formation of a water shell around the protein molecules with the help of the sodium ions. The addition of even small amounts of Cd2q changes the repulsive interactions to attractive but does not lead to oligomer formation, at least at the protein concentrations used. Thus, the two ions provide examples of strong specificity of their interactions with the protein molecules. In solutions of the apoferritin dimer, the molecules attract even in the presence of Naq only, indicating a change in the surface of the apoferritin molecule. In view of the strong repulsion between the monomers, this indicates that the dimers and higher oligomers form only after partial denaturation of some of the apoferritin monomers. These obser-

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Fig. 10. CONTIN results for the size distribution of the apoferritin fractions after separation by fast protein liquid chromatography (FPLC) w45x.

vations suggest that aggregation and self-assembly of protein molecules or molecular subunits may be driven by forces other than those responsible for crystallization and other phase transitions in the protein solution w45x. All the proteins obtained in the crystalline form are typically studied by means of the XRD method, however, functioning of proteins occurs in liquid or semiliquid media. Clearly, the structures of proteins in the crystalline and native quasiliquid states can be strongly different. Unfortunately, the XRD data do not allow Table 3 Diffusion coefficients (D), and hydrodynamic diameter (dh ) for apoferritin fractions: monomers, dimers, and trimers in the absence of CdSO4 w45x Aggregate type

Deff=107 (cm2 ys) (second cumulant)

Deff=107 (cm2 ys) (CONTIN)

dh (nm) (second cumulant)

dh (nm) (CONTIN)

Monomers Dimers Trimers

3.19 2.21 1.48

3.57 2.37 1.43

12.70 18.40 26.75

11.40 17.10 30.00

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one to make even presupposed estimation about a number of protein molecules oligomerising in a biologically active unit. Therefore, many XRD investigations are performed simultaneously with PCS (but applied to the liquid media) w166x. The application of two powerful physical methods providing practically unambiguous interpretation of the obtained results is fruitful or even essential for preliminary estimation of the homogeneity of the solution before the crystal growth for the XRD exploration w167x. For instance, the structure of subunit of protein factor inhibiting migration of human macrophage was studied by using the XRD and PCS methods, and the last method showed that the main form of the protein in the corresponding solution is an asymmetrical trimer but not a monomer or a dimer as assumed previously w168x. Cysteine proteinase CPP32 eliminated from E. coli in the soluble form was studied by the XRD (resolution 0.23 nm) and PCS methods. It was shown that an asymmetrical unit of the enzyme contains a tetramer in accordance with the structure of the tetramer protein substratum. Mittl et al. w169x believed that obtained structural information could be useful to synthesise small inhibitors CPP32 or to create cysteine proteinase mutants. Human uroporphyrinogen decarboxylase (recombinant of an intracellular enzyme) catalysing the fifth stage in the heme biosynthesis eliminated from E. coli and purified to the homogeneous state was studied by PCS. It was shown that this protein represents dimers in the monodisperse solution; then this result was confirmed by using sedimentation analysis w170x. 4-Oxolate tautomerase studied by PCS and other methods was characterised by the translation diffusion coefficient value and the time of rotational motions (14.5 ns) showing formation of the trimerydimer structure at Mf41 kDa w171x. In the case of specific Cs phospholipase, the solution contained monomers w172x as well as for some other proteins w173x. Typically protein crystals are formed with individual molecules, however, glycine amideribonucleotide transformilase crystallises in the form of dimers at pH 6.75. According to the PCS data, this enzyme forms the solution of monomers at pH between 6.8 and 7.5. At the physiological pH values, its molecules form a mixture of monomers and dimers, and small changes in pH can modulate the enzymatic activity, which is maximal for monomers w174x. Later Mullen et al. w175x performed detailed investigations of the dependence of dimerisation of this enzyme on pH. Beretta et al. w176x studied the role of interactions involved in stability of haemoglobin, a charged protein (that can dissociate into subunits) by using the influence of pH and protein concentration on diffusive properties of bovine COhaemoglobin. The average diffusion coefficient obtained from cumulant analysis of the measured ACF of the scattered light increases vs. protein concentration. A linear fit of the data showed different slopes and intercepts depending on the pH and ionic strength. A comparison of the experimental data with a simple model for the diffusive properties of a dissociating and interacting molecule, allowed one to estimate both dissociating constant and protein charge w176x. Evolution of the relationship between the concentrations of monomer and dimer of protein phyterythrin 545 initiated by exterior conditions was explored by MacColl et al. w177x in detail by using the PCS method. Ridder et al. w178x studied the

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Table 4 Parameters of different fragments of plasmid w157x Peptide

RH (nm)

MW (kDa)

Polydispersity (%)

F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15

4.2 4.8 3.6 4.4 3.3 2.3 0.78 4.3 4.0 3.8 3.5 1.2 1.1 1.6 1.3

100 137 66 106 56 22 2.0 106 91 78 61 4.8 4.3 9.0 6.2

M M 26.3 M 25.1 15.4 39.7 39.5 37.5 M M M 50.0 M 53.8

oligomerisation degree of L-2 dehalogenase depending on the incubation time with sodium formate by means of PCS. Similar problems investigated by using PCS were discussed in other papers w179–184x. Human immunoglobulin G was investigated in detail by Jessang et al. w185x. Budzynski et al. w186x studied the kinetics of association of protein RecA (E. coli). Van Raaij et al. w157x, studying the mechanism of regulation of the activity of adenosine triphosphatase from a bovine heart, synthesizing enzymes of this protein on different fragments of plasmid and determining the level of the inhibitor activity, determined the hydrodynamic radii, the molecular weight and the polydispersity of the synthesized peptides. Some of these results are shown in Table 4. As stated above, there are several methods to estimate the polydispersity, and the authors w157x estimated that in percent, and if this parameter was less than 15% then the sample was considered as monodisperse (label M in Table 4). Den Blaauwen et al. w148x studying interaction of peripheral domains of a subunit of protein SecA as a translocase precursor eliminated from barteria B. subtilis determined the diffusion coefficient, hydrodynamic size, polydispersity and molecular weight depending on the nature of attached ligand: Mg2q, Mg2q yadenosine diphosphatase (Mg2q yADP) or Mg2q yanalog of adenylile-imidophosphate (Mg2q y AMP-PNP) shown in Table 5. Notice that the total hydrodynamic size of a complex can be smaller than the sum of the corresponding size of the components. For example, it was shown that histon F2A bonding to DNA forms a dense structure compacting DNA w186x. In the case of the complex of histon F1 with DNA, the structure is branched. This effect appears through the corresponding changes in the translation diffusion coefficients equal to 1.6=10y6 cm2 ys for individual DNA molecules, lower for DNA-F1 (1.0=10y6 cm2 ys) and greater for DNA-F2A (2.6=10y6 cm2 ys). The hydrodynamic size of tRNA synthetase phenylalanine

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Table 5 Parameters of complexes of peripheral domains of an subunit of protein SecA (translocase precursor eliminated from barteria B. subtilis) depending on the nature of attached ligand: Mg2q, Mg2qyadenosine diphosphatase (Mg2qyADP), or Mg2qyanalog of adenylile-imidophosphate (Mg2qyAMP-PNP) w148x Ligand (5 mM)

DT (10y7cm2yc)

None Mg2q Mg2qyADP Mg2qyAMP-PNP

4.55 4.33 4.30 3.98

(0) (3) (1) (1)

Radius (nm) 5.26 5.60 5.57 6.03

(0.15) (0.05) (0.04) (0.02)

Polydispersity (nm) 1.27 1.69 1.60 2.24

(0.15) (0.05) (0.04) (0.03)

MW (kDa) 164.3 189.8 189.3 229.8

(0.5) (0.8) (1.0) (1.0)

decreases if its complex with tRNAPhe, as a ligand, forms, however, for other ligands, the Rh values increase w128x. Boffi et al. w187x used DLS, radiowave dielectric spectroscopy and circular dichroism measurements to reveal the structural features of complexes (lipoplexes) formed in the interaction between DNA and cationic liposomes. Two distinct types of complexes form in these systems (as the charge ratio increases): (i) DNA-coated liposomes, where the DNA binds electrostatically to the outside of the cationic lipid vesicle, (ii) multilamellar complexes followed by rupture and reorganization of the bilayer structure or clusters of DNA-coated vesicles with alternating sheets of DNA and lipid bilayers. Analysis of the DLS data was performed using the CONTIN procedure (to calculate the f(DT) distributions) and the method of cumulants (to estimate the hydrodynamic diameter of liposomes with average value of 56 nm). The two-step neutralization process (observed by DLS) and the continuous neutralization process (observed by dielectric spectroscopy and circular dichroism methods) appear as two possible scenarios for the assembly of cationic liposome–DNA complexes because of the different conditions of the experiments. The complexes investigated by means of DLS have been formed by addition of DNA to liposome suspension (lipid initially in excess) while the inverse process (DNA initially in excess) has been used for circular dichroism and dielectric spectroscopy measurements. Since in both experimental procedures adopted, the concentration of liposomes was relatively low and aggregation induced by a purely diffusion process must be excluded, one can assume that different types of mixing give rise to lipoplexes of different structures. On the basis of DLS measurements, due to the simultaneous presence of two different aggregates of different typical sizes, it appears that lipoplex aggregation properties differ from those of more usual colloidal systems. In particular, the kinetics of the salt-induced aggregation of charge-stabilized colloidal particle suspensions gives rise to regimes that do not manifest in DNA– liposome systems. In more conventional systems, for example, polystyrene latex suspensions, (the salt-induced aggregation) after a transient regime characterized by a reaction limited aggregation proceeds according to the diffusion limited cluster aggregation regime, in the long time limit. On the contrary, in the present case, two structures of different sizes coexist in a steady state, without the formation of clusters of infinite dimension, i.e. they do not show a tendency to aggregate further.

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Table 6 DT values and Mw of DNA molecules of different origin w34x Origin

DT (10y8 cm2 sy1)

Mw (MD)

Bull calf thymus

1.9 2.23

15 3.75

E. coli Plasmid Superspiralised Linear Ring-shaped Bacteriophage ⭋29 l-Phage Phage T7 Bacteriophage fd

2.89 2.45 1.98 2.16 1.2–1.4 0.64 0.8 0.66

4.6

11.5 32.5 25 1.87

The knowledge of the complex morphology occurring in lipid–DNA lipoplex formation could provide insight for the development of efficient artificial delivery systems in genetic engineering and gene therapy w187x. The PCS method was used to estimate the characteristic parameters (such as DT and Mw) of DNA molecules of different origin (Table 6), and similar investigations were carried out for RNA molecules w34x. One can see certain differences in the shown parameters for DNA of the same origin depending on changes in its shape, which can play an important physiological role. On the PCS investigations of interaction of human serum albumin (HSA) with physiologically active compounds, the strong dependence of the particle size of HSA oligomers was found (Fig. 11) w188x. It should be mentioned that several works performed by this group and related to the PCS investigations of different protein systems w189–194x. HSA was used in many PCS studies of different biological problems, especially on interaction of proteins with other molecules (drugs, surfactants, polymers) or fine solid particles. In the pharmaceutical practice, fast reduction of the therapeutic action is frequently observed if liposomes are utilised to deliver contained medicines to the destination organs. This effect is maybe conditioned by liposome interaction with medicine components. To elucidate the mechanism of this phenomenon, the interaction of liposomes of different lipid compositions filled by mesoporthyrin with HSA was studied using model systems. It was observed that HSA evokes mesoporthyrin from vesicles relatively fast (that was controlled by using the fluorescence spectroscopy), however, in the case of non-serum protein (e.g. apomyoglobine) this effect is not observed. A similar conclusion was made on the basis of the measurements performed by means of the differential scanning calorimetry w195x. Rescic et al. w196x carried out PCS and osmotic pressure measurements of HSA (defatted (dfHSA) and with fatty acids (fHSA)) dissolved in water and in 0.01, 0.1 and 1.0 M phosphate buffer as a function of CHSA. The measured values of the osmotic coefficient were below 1, indicating large deviations from ideality even for

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Fig. 11. Oligomer size distribution of HSA at pH 8 (1), 7.4 (2), 6.4 (3) and 5.4 (4).

dilute protein solutions. The measured values increased with CHSA depending on pH. For higher concentrations of added phosphate buffer, the pH of solution had less influence on the measured osmotic pressure, which was considerably lower for dfHSA in water than that of fHSA. This effect was ascribed to the formation of dfHSA dimers. The osmotic measurements were to be complemented by the smallangle X-ray scattering (SAXS) and PCS studies of dilute HSA solutions in water. The SAXS and PCS data confirmed the dimerisation of dfHSA molecules under applied conditions. Detailed analysis of the SAXS data suggested a parallel orientation of two protein molecules in a dimer w196x. These results indicate the presence of strong attractive forces between the protein molecules and small ions (from the buffer) on dimerisation of protein molecules dfHSA. However, oligomerisation of fHSA was not observed under these conditions. Clearly, the thermodynamic properties of proteins in mixed solvents containing simple electrolytes and water are governed by complex interactions among all species in the solution. Both nonelectrostatic and electrostatic forces contribute to the non-ideality of these solutions, and a study of a model polyelectrolyte solution with dimerizing macroions indicates w197x that these two contributions are strongly correlated. The experimental data w196x were analysed using a semiempirical equation proposed by Fullerton et al. w198x. The two-parameter equation for osmotic pressure yields a reasonably good fit of the experimental data. Altogether, the osmotic behaviour of HSA solutions at higher concentration seems to be governed by various competing contributions. From the osmotic pressure measurements alone, it is difficult to identify the principal sources of non-ideality. The actual shape of protein monomers, and the type and extent of their aggregation, may depend strongly on the pH of the solution and on

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the ionic strength and composition of added electrolyte w196x. A review of recent literature indicates that there is an interest for better understanding of physicochemical properties of both the fatty acid-containing and fatty acid-free HSA solutions w199x, since similar forms of proteins can differently interact itself, but also with other bioparticles, drugs, adsorbents, etc. Many of PCS studies have demonstrated the presence of negatively charged, globular or micelle-like structures in human saliva containing proteins. Similar structures were found in parotid saliva to be initially 100–150 nm in diameter, increasing up to 450 nm 50 min after sampling w200x. The newly formed acquiredenamel pellicle appears to consist mainly of such globular structures. It has been shown that pellicle proteins may be degraded by proteolytic activity, and furthermore, the proline-rich proteins adsorbed to hydroxyapatite may be degraded by proteolytic activity isolated from salivary sediments. Young et al. w200x studied the effect of some model enzymes on the salivary micelle-like structures (SMS). The integrity of the SMS was examined by PCS prior to and following addition of trypsin, pronase E and rennin to samples of freshly collected human parotid saliva. Trypsin caused a sudden reduction in both mean particle hydrodynamic diameter and PCS intensity. Pronase E had a similar effect but slightly weaker, whereas rennin appeared to have little or no effect on SMS. Zeta-potential determinations indicated that trypsin-treated SMS had a slightly smaller net negative surface potential than untreated SMS, whereas pronase E resulted in a more negative surface potential, and rennin had no effect w200x. Young continued investigations of similar problems in another paper w201x. Salivary micelle-like globules (SMGs) closely related to the casein micelles in milk have been observed in human whole saliva (HWS) and in human parotid saliva (HPS). Isolation of the SMGs from HWS, by acidification to the isoelectric point, has been observed to result in markedly larger amounts of SMGs than for HPS. The hypotheses tested in this paper were that SMGs also exist in human submandibularysublingual saliva (HSMSL) and that the SMGs, as present in the pure salivary secretions, are precursors of the whole saliva SMGs in the oral cavity. Stimulated HPS and HSMSL saliva were collected from five subjects and examined by TEM, zeta potential, PCS and bacterial agglutination studies. Mixing HSMSL saliva and HPS in the ratio 1:3 and analysis by TEM and PCS examined possible co-aggregation of SMGs from different sources. TEM studies of HSMSL saliva showed occasional SMG-like particles and many large particulate aggregates, while PCS analysis indicated structures varying in diameter from 100 to 600 nm (mean 340 nm). The zeta potential of HSMSL at physiological pH varied among subjects from y13 to y20 mV (mean y17 mV). HSMSL saliva and SMGs isolated from HSMSL saliva could agglutinate streptococcal strains. TEM studies of the saliva mixture showed many SMGs and a few large aggregates consisting of SMG-like structures with diameters in the range of 20–80 nm. PCS analyses indicated structures in the saliva mixture from 400 to 2000 nm in diameter (mean 1.3 mm). The results showed that SMGs were also found in HSMSL and suggested that the SMGs in HWS were likely to be the result of a co-aggregation of SMGs from the pure salivary secretions w201x.

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Sabate and Estelrich w202x studied the interaction of amylase with such surfactants as n-alkylammonium bromides (C12, C14, C16) above and below their critical micellar concentrations in buffer at pH 7 and 10 by PCS, Doppler microelectrophoresis, and UV spectrophotometry methods. This interaction produces a complex that is dependent on pH. This complex appears at surfactant concentrations below the critical micellar concentrations, which means that individual surfactant molecules can bind tightly to native amylase. The complex maintains its aggregation state when the concentration of surfactants with a hydrocarbon chain of 16 carbons increases, but not for surfactants of 12 and 14 carbons. Measurements of the electrophoretic potential indicate the influence of electrostatic and hydrophobic forces. When the size of the aggregate is maximal, proteins are at their point of zero charge. In such conditions, van der Waals forces and contacts between the alkyl chain and the hydrophobic core of the protein favour the formation of a larger aggregate w202x. Schuler et al. w203x investigated the colloidal properties of a transferrin receptor (isolated from human placenta) in detergent free solution by using PCS techniques and analytical ultracentrifugation. In such a solution at 293.2 K, hTfR formed stable aggregates with an apparent hydrodynamic radius of 17 nm. The molecular mass was determined by ultracentrifugation to lie between 1722"87 kDa (sedimentation equilibrium) and 1675"46 kDa (sedimentation velocity). This implied that the aggregates were build up from nine hTfR dimers. Based on model calculations, which were in good agreement with the experimental data, the authors proposed a torus-like structure for the aggregates. Upon pH shift from pH 7.5 to 5.0 or removal of the N-linked carbohydrate chains, formation of larger aggregates was induced. These aggregates could be described in terms of porous fractal structures. The authors w203x proposed a simple model, which accounted for that behaviour assuming that the aggregation was mainly because of the reduction of negative surface charge providing repulsive forces between the hTfR units. Protein aggregation has been recognized to be a pathological indicator for several fatal diseases, such as Alzheimer’s disease, transmissible spongiform encephalopathies, Jacob disease, etc. Aggregation (or oligomerisation) usually involves conformational changes of proteins that have acquired an intermediate conformation and can occur even at low protein concentration. Recent work after Bulone et al. w204x has shown that BSA, even at a low concentration, exhibits self-association properties related to conformational changes, so providing a very convenient model system to study this class of problems. Obtained results showed that the interaction between the two species of BSA in native and intermediate form was responsible for a decrease in the thermodynamic stability of the solution. This occurred without requiring noticeable conformational changes of the native protein. These results could provide new insight on the ‘protein only’ hypothesis proposed for the formation of plaques involved in several neurodegenerative diseases w204x. Bonincontro et al. w205x studied the effect of solvent viscosity on both translational and rotational dynamics of a simple model protein: the egg white lysozyme. For this, they investigated the dynamical properties of lysozyme in mixtures of water

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Fig. 12. Relationships between the acquisition time and characteristic parameters estimated from the PCS data for the lysozyme solution w206x.

and glycerol by means of parallel measurements by PCS and dielectric relaxation spectroscopy (DRS) at radiofrequencies. In the framework of the Debye–Stokes– Einstein theory, the translational and rotational coefficients allow one to estimate the hydrodynamic radius of the protein. A decoupling between translational and rotational dynamics, observed as a different estimation of hydrodynamic radius, was reported in the literature for some systems. In order to ascertain if this effect was present also in the studied sample, PCS and DRS measurements were performed on the lysozyme–water–glycerol solutions. The content of glycerol was in the range of 0–70% wyw, with a solvent viscosity from 0.9 to approximately 10 cpoise, and the protein concentration was up to 20 mg mly1. The average sizes of lysozyme, obtained by two methods, were remarkably different at high protein concentrations. However, the values of hydrodynamic radius extrapolated to infinite dilution were coincident and independent of glycerol. These results indicated that the diffusive behaviour of lysozyme in the water–glycerol mixture was coherent with the Debye– Stokes–Einstein hydrodynamic model w205x. The influence of acquisition time on the measured radius, the signal amplitude and the fraction of ‘dust free’ measurements (Fraction Good) is shown in Fig. 12 at lysozyme concentration CLyss0.338 gyl w206x. Similar results were obtained for CLyss0.068 gyl and 0.034 gyl. As evident here, the radius and signal amplitude are invariant with acquisition time, and while not shown, the intensity was also found to be independent of the acquisition time. However, the number of observed dust events increases significantly at longer times, consistent with expectations. In

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Fig. 13. Relationships between the acquisition time and fitting errors for the lysozyme solution at different concentrations w206x.

contrast to the amplitude and intensity, the SOS fitting error shows a strong dependence on the acquisition time also depending on CLys (Fig. 13). The SOS is defined as the sum of squares difference between the predicted and measured autocorrelation functions, where the predicted curve is assumed to be a single exponential. Large SOS values indicate that the experimental curve is multi-modal andyor noisy. While not shown, the intensity of the solvent (2nd mode) peak for the lysozyme samples was dependent only on CLys and independent of the acquisition time and the type of DLS unit used. Hence, the dependence of the SOS fitting error at low acquisition time is indicative of noisy correlation functions. As the acquisition time is increased, the noise level is decreased due to statistical averaging, and the SOS fitting error goes down w206x. The PCS results are sensitive to translational diffusive motions and interparticle interactions; and the translational diffusion coefficient, at a vanishing protein concentration, yields the reciprocal of the particle hydrodynamic radius. The PCS technique was employed by Nicoli et al. w207x to study the thermal denaturation of lysozyme, by Dubin et al. w133x to investigate the denaturation of lysozyme by guanidine hydrochloride, and to elucidate the effect of 1-alcohols on the native conformation of lysozyme w208x. Standard PCS is no longer suitable to reliably estimate the rotational diffusion coefficient because of the fast rotational motion of lysozyme, characterised by a rotational correlation time smaller than 0.1 ms w205x. A valid spectroscopic technique in detecting rotational motions in a wide time domain is DRS able to reveal small variations in the conformation andyor hydration

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state of proteins by two parameters: electric dipole moment and effective hydrodynamic radius w205x. This approach was used to study lysozyme in solution under different conditions of pH, temperature and solvent composition w209–211x. The technique of intensity PCS was utilized to investigate the native conformation of lysozyme in wateryethanol and in waterytert-butanol mixtures as a function of alcohol concentration in the water-rich region of composition (cosolvent mole fraction x2-0.08) w212x. A non-trivial behaviour of the hydrodynamic radius was obtained, characterized by a minimum at x2s0.02 and a maximum at x2s0.06 in wateryethanol mixtures and by a minimum at x2s0.005 and a maximum at x2s 0.02 in waterytert-butanol mixtures. These values of x2 were close to those at which structural changes in the mixtures occur as inferred from compressibility and infrared absorption measurements. It should be appreciated that measured diffusion coefficients can be greatly affected by interparticle interactions. Hence, determination of protein size by DLS requires the diffusivity to be corrected for the influence of interactions of the scattering system. Intermolecular interactions lead to a concentration dependence of the diffusion coefficient. Representative plots of the measured mean diffusivity D0 for lysozyme in aqueous solution (x2s0) and for lysozyme in the wateryethanol mixture at the highest ethanol concentration (x2s0.075) are shown in Fig. 14a,b, respectively w213x. D increases linearly with protein concentration in both cases. It should be noted that the solvent viscosity increases monotonously from hs1.002 cp at x2s0 to hs1.96 at x2s0.075. Figs. 15 and 16 give the dependence of D0 and R0, respectively, on alcohol mole fraction. A non-trivial behaviour of R0 is obtained, characterised by a minimum at x2s0.02 and a maximum at x2s0.06. This result reflects a complicated behaviour of intermolecular interaction in the water-rich region of composition. The most important finding of the work performed by Calandrini et al. w213x, as revealed in Fig. 16, is the occurrence of minima and maxima of the hydrodynamic radius in the water-rich region. It is known that the general effect of ethanol is the destabilisation of the macromolecule native state. At very low alcohol concentration, however, one finds an opposite effect of alcohol (Fig. 16), namely, a decrease of the hydrodynamic radius, indicating a stabilisation of the compact form of the protein. Such an effect appears to be complete at the lowest alcohol concentration (x2s0.01) and even though small (DR0 yR0 approx. 5%) it is appreciably greater than the experimental error on R0. Recent results show that the stabilisation of nucleic acid and protein conformation and micellar structure in wateryalcohol mixtures is closely linked to the properties and to the anomalous behaviour of the solvent systems. The solution behaviour of alcohol molecules in the water-rich region is largely established by the phenomenon of apolar or hydrophobic hydration. Evidence from a wide range of spectroscopic and thermodynamic data on wateryalcohol mixtures at low alcohol concentration strongly suggests the formation of low entropy structures or ‘cages’ of fairly regular and longer-lived H bonds located around hydrophobic groups. It may be supposed that all these water molecules are in a state equivalent to the water molecules surrounding the hydrophobic groups of the protein. On increasing alcohol concentration a

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Fig. 14. Translational diffusion coefficient D of lysozyme vs. protein concentration: (a) water and (b) wateryethanol (x2s0.075) solution w213x.

progressive interference among these structures is expected to cause a progressive loss of the low-entropy, high connectivity character of cages. Hydrophobic interactions can be viewed as the result of this overlapping of hydration structures w213x. The analysis of both translational and rotational diffusions has been often employed to obtain information on size of globular biomolecules w34,61x. The connection between diffusion and size is usually stated in the framework of Debye–

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Fig. 15. Translational diffusion, D0 , of lysozyme in wateryethanol mixtures as a function of alcohol mole fraction x2 w213x.

Stokes–Einstein hydrodynamic model, in which the solute is considered as a Brownian particle dissolved in a continuous medium. In the model, the microscopic structure of both solute and solvent is neglected, and the only source of dissipative effects is the shear viscosity of the solvent. In previous years, a considerable amount of experimental work was provided evidence of a failure of the Stokes–Einstein law for self-diffusion in fragile glass-forming liquids approaching the glass temperature w214,215x and in supercooled liquids w216,217x, where a decoupling between viscosity and translational diffusion coefficient appears. Analogously, a decoupling between translational and rotational dynamics has been observed in some aqueous solutions of polymers and biopolymers w205x. In particular, PCS and electron-spinresonance spectroscopies have been used to measure translational and rotational diffusion coefficients of HSA w218x. In the framework of the Debye–Stokes– Einstein theory, these two coefficients yielded two significantly different values for the hydrodynamic radius of the biomolecule. However, more recently, Chirico et al. w219x have shown that the hydrodynamic radius of lysozyme in 60% wyw glycerol– acetate mixtures, obtained by polarized PCS measurements, is fully consistent with that estimated by depolarised PCS. It is well known that water–glycerol mixtures are suitable media for stabilisation of proteins in native conformation. It was proposed that this is due to ‘preferential hydration’ of the protein, i.e. exclusion of glycerol molecules from the protein surface without conformation change w220x. Thus, the protein should sense a local viscosity, due to the surrounding solvent molecules, different from that of the overall solution (this difference in the bulk

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Fig. 16. Hydrodynamic radius, R0 , of lysozyme in wateryethanol mixtures as a function of alcohol mole fraction x2. Inset: Partial molar volumes V of ethanol in wateryethanol mixtures at 30 8C w213x.

solution and interfaces also results in lowering of the freezing temperature of the interfacial water). In order to ascertain the reliability of the Debye–Stokes–Einstein theory to describe translational and rotational dynamics of proteins in the water– glycerol solution, PCS and DRS measurements were performed on lysozyme as a function of glycerol content w205x. Calandrini et al. w212,213x discussed the obtained results in connection to the effect of alcohol in modulating solvent-mediated interactions in the lysozyme solution. One important generalisation (which has emerged from the analysis of the three-dimensional structure of crystals of globular proteins by X-ray diffraction techniques) is that there is a tendency for the amino acids with polar side groups to be found at the surface of the globular structure and for those with non-polar side groups to be found in the interior w213,221x. This has been suggested that part of the free energy of stabilisation of globular proteins originates from the ‘hydrophobic interactions’. Hydrophobic interactions refer to the solvent-induced interactions between two or more apolar solute molecules. These interactions are thought to be responsible for the stability of particular conformations of biopolymers in aqueous solution, the stability of micelles and membranes, and the association equilibria of many compounds in aqueous environments w221,222x. Such interactions arise from the unique three-dimensional structure of water and should be changed considerably by variations in the solvent structure due to change in temperature or to addition of such cosolvents as monohydric alcohols. It is usually accepted that

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the hydrophobic processes are driven by positive entropy changes resulting from the release of structured water when non-polar groups interact with one another. This traditionally held view of hydrophobic processes seems incorrect. As first observed by Shinoda w223x, the more ordered hydration structure formation around the solute molecules is, indeed, accompanied by a large decrease in entropy; this is, however, more than compensated by an ever greater enthalpic effect. Thus, the net consequence of the effect of hydrophobic hydration is to enhance the solubility of nonpolar species and to disfavour their aggregation. This point of view agrees well with other recent studies of self-association of monohydric alcohols in water w224,225x and of the effect of aqueous alcohol solutions on the micellization of surfactant molecules w225,226x and on the thermal unfolding of globular proteins w227x. Consistently with Shinoda’s point of view that hydrophobic interactions at low concentration of hydrophobic groups and low temperatures are repulsive and give a destabilizing contribution to the native structure of the protein w209,228x. Therefore, the attenuation of these interactions, in consequence of addition of a small amount of monohydric alcohols, should favour clustering of hydrophobic groups and structures that are more compact. Actually, the effects of alcoholywater mixtures on the conformation of proteins are very complex: whereas the general effect of alcohols is the destabilization of the macromolecule native state, low concentrations in water seem to promote a more tightly folded conformation w209,228,229x. By using PCS, Tanaka et al. w230x investigated the kinetics of the growth of clusters in two kinds of supersaturated lysozyme solutions at pH 4.6 and 35 8C from which orthorhombic rectangular crystals and needle-like crystals appear. Although the two kinds of crystals have quite different final morphologies, the increase of the cluster size in the early stage of the crystallisation process can be commonly explained by a diffusion-limited aggregation model, which suggests that the clusters of random aggregates are formed in the early stage irrespective of the crystal’s systems or habits. The authors w230x suggested that the needle-like crystals might be what these initial clusters grow to be. The PCS technique was applied to study such proteins as a-lactoglobulin w231– 234x and a-crystallin (because of not only the importance of its direct function, but also of its other interesting properties) w235–237x. The PCS method was also used to study the turbulence suspensions w238x, co-polymer blocks w239x, small-angle measurements w240x, and other problems w241–248x. The hydrodynamic structure of the a-crystallins and their mutual interaction are the essential parameters characterizing the solution structure at low and high concentration of the protein w249x. Changes in these characteristics, as a function of temperature, can explain the activity of the a-crystallin. Absolute light scattering, PCS and equilibrium sedimentation of diluted solutions as a function of temperature yield the molar mass Mw, the hydrodynamic radius Rh,w of the equivalent hard sphere and the second virial coefficient of the molecules in a temperature range from 2 8C to 37 8C. Light scattering as a function of concentration yields the structure factor. Equilibrium sedimentation in a broad temperature range indicates a gradual decrease in molar mass and a clear transition from a slightly repulsive to a

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clearly attractive interaction between the protein particles at the in vivo ionic strength of 0.15 M and the same temperature range. These properties nicely fit the chaperonine activity of a-crystallin but can dramatically increase the light scattering at in vivo concentrations w249x. Lipoplexes (spontaneously formed complexes between oligonucleotides and cationic lipids) can be used to deliver oligonucleotides (as well as other compounds such proteins, drugs, etc.) into cells, both in vitro and in vivo w250x. Meidan et al. characterized the interactions associated with the formation of lipoplexes, specifically in terms of electrostatics, hydration and particle size. Large unilamellar vesicles (approx. 100 nm diameter) were employed as a model of cationic liposomes. Neutral vesicles were employed as control liposomes. After oligonucleotide addition to vesicles, at different mole ratios, changes in pH and electrical surface potential at the lipid–water interface were analysed by using the fluorophore heptadecyl-7hydroxycoumarin. In separate ‘mirror image’ experiments, liposomes were added at different mole ratios to fluorescein isothiocyanate-labeled oligonucleotides, thus yielding data about changes in the pH near the oligonucleotide molecules induced by the complexation with the cationic lipid. The PSD and turbidity fluctuations were analysed by the use of PCS methods. In additional fluorescent probe studies, membrane defects were estimated as well as the level of hydration at the water– lipid interface. The result indicated that mutual neutralisation of cationic lipids by oligonucleotides and vice versa was a spontaneous reaction and that this neutralisation was the main driving force for lipoplex generation. When lipid neutralisation was partial, induced membrane defects caused the lipoplexes to exhibit increased size instability w250x. It would be of interest to compare similar effects for lipoproteins. Amphiphilic polysaccharide hyaluronic acid-linked phosphatidylethanolamine (HyPE), synthesized by covalently binding dipalmitoyl-phosphatidylethanolamine (DPPE) to short chain hyaluronic acid, interacts with low-density lipoproteins (LDL) to form a ‘sugar-decoration’ of the LDL surface w251x. This interaction results in an increase in the apparent size of LDL particles, as studied by PCS, and in broadening of the 1H NMR signals of the LDL’s phospholipids. Experiments conducted with fluorescently-labelled HyPE indicate that the interaction of HyPE with LDL involves incorporation of the hydrocarbon chains of this amphiphilic polysaccharide into the outer monolayer of the LDL. This interaction also inhibits the copper-induced oxidation of the LDL polyunsaturated fatty acids, avoiding oxidation altogether when the concentration of HyPE is higher than a tenth of the concentration of the LDL’s phospholipids. This cannot be attributed to competitive binding of copper by HyPE. Schnitzer et al. proposed that the protection of LDL lipids against copper-induced oxidation was due to the formation of a sugar network around the LDL w251x. The occurrence of acid beverage floc in acidified carbonated beverages has long been attributed to the presence of saponins w252x. Morton and Murray have examined this assertion and have found evidence to suggest that traces of protein may also be a key factor, along with lipid material present in the floc. Turbidity levels of beet

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sugar protein (0.001 wt.%) and saponin (0.001 wt.%) solutions were examined over time using spectrophotometry. At neutral pH, no change in turbidity was observed in any combination (individually or mixed). Furthermore, acidified (pH 2) saponin and protein solutions, considered separately, also exhibited no change. However, a mixture of equal concentrations at pH 2 showed an initial increase in turbidity to 2 h after mixing, followed by a decrease over the ensuing 12 h. Interfacial tension measurements also indicated interactions between the protein and saponin at pH 2. The PCS (Malvern Zetasizer 4) technique was applied to quantitatively examine the PSDs and aggregation of a model, highly dilute dispersion, of bromohexadecane in 20 wt.% sucrose solution, prepared with a jet homogeniser. Beet sugar saponin (0.001 wt.%) and protein (0.001 wt.%) were added to the dispersion, and their emulsion-stabilising effects examined via oil droplet size measurement over time. At neutral pH, the size of oil droplets in the dispersion was unaffected by the addition of saponin or protein. At pH 2, the presence of saponin again caused no effect on droplet size. However, in acid conditions, protein appeared to destabilise the dispersion. The results indicate that the key to controlling the acid beverage floc problem may be the ratio of saponin to protein in the product, which may or may not stabilise dispersed lipid, depending on their interactions w252x. The associative properties of some food proteins in water dispersions were examined by Boulet et al. w253x. The association of the casein monomers into homogenous or mixed polymers (oligomers) was studied under controlled conditions and molecular weights corresponding to 2, 16 and even 50 monomers have been observed. However, some of these proteins were known to associate into much larger complexes. For example, dispersions of seed storage proteins at moderate concentrations were shown to contain large agglomerates visible under the light microscope, which showed that they were approximately spherical particles of micron size. Attempts were made to explain properties like solubility, water holding, fat binding, gelation, emulsion formation or foaming in terms of monomer or molecular protein properties but it was generally recognized that higher orders of structure, tertiary and quaternary, could play a significant role. It was important to characterize food proteins under conditions where large agglomerates were formed. Such conditions influence their rheological and functional properties. More knowledge was needed for aggregating throughout because variations of their mineral contents, especially the divalent cations, had relatively large effects on the measured properties w253x. Commercial casein, whey protein and laboratory prepared soybean protein of various pH were dispersed in distilled water at the initial concentration of 4.0% (wyv) and then diluted with NaCl solutions of known ionic strength w253x. Particle diameter was determined by PCS and the data were converted into degree of aggregation using voluminosity and weight concentration data. Results show that aggregation of proteins increases in a log relationship with the decreasing of ionic strength. Aggregation of casein and soybean protein increases with increase of pH to a maximum. Disaggregation of the protein particles as the result of the decrease in the protein concentration at fixed pH and ionic strength takes place by thermal agitation and Brownian motion. It is concluded that above a transition concentration

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of 0.04–0.07 mlyml, depending on the nature of the protein, growth of the particles takes place by means of local surface electrostatic charges attraction w253x. Moulik and Paul w254x analysed the structure, dynamics and transport behaviours of microemulsions as they are physicochemically unique and need exploration for basic understanding of their formation, state of aggregation, internal interaction and stability with reference to their probable uses. The structure factor of aqueous solutions of the globular protein b-lactoglobulin (b-lg) was determined as a function of heating time at 76 8C w255x. The intercept of G1(t) at ts0 (B) is ideally 0.5 for cross correlation of fully ergodic single scattering, but is reduced by non-idealities of the experimental set-up (for the setup used by Nicolai et al. w255x the intercept was 0.4). Multiple scattering further reduces the intercept in proportion to the relative intensity of the single scattering to the total scattering. The experimental results were corrected for the effect of multiple scattering as IrŽcorr.s

IrŽexp. A

=

B 4

(78)

where A is the transmission of the light passing through the sample, which we determined by comparing the intensity of the incident laser at 08 through the sample with that through the solvent. Ir of single scattered light is due to concentration fluctuations and is related to the osmotic compressibility (dp ydC) and the structure factor S(q) IrsKC

RgT S(q) (dpydC)

(79)

where Rg is the gas constant, and K is a contrast factor. It was shown how the effect of multiple scattering on the scattered light intensity can be effectively corrected using cross-correlation DLS even if the transmission is only 1%. The structure factor of aggregated and gelled proteins was described by the Ornstein–Zernike equation. The system was characterized by a correlation length that increased with heating time and stabilised some time after the gel was formed. The correlation length of the protein gels decreased with decreasing concentration. Measurements after progressive dilution of a sample close to the gel point showed that the protein aggregates were initially interpenetrated and disinterpenetrate upon dilution w255x. Globular proteins denature if heated, which generally leads to aggregation and eventually a gel is formed if the protein concentration is sufficient w255,256x. One of the most intensively studied globular proteins is b-lg, which is the major component of whey and has molar mass 1.86=104 gymol and radius 2 nm w257– 259x. The structure of the gels depends on external conditions such as pH, ionic strength, protein concentration and temperature w260,261x. Close to the isoelectric point (IEP 5.2) and at high ionic strength the gels are heterogeneous and contain

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dense protein domains, so-called particulate gels. Far from the isoelectric point and at low ionic strength the gels are more homogeneous, so-called finely stranded gels. Except at very low ionic strength and far from IEP heat-set protein gels are more or less turbid. In recent years the aggregation process that leads to gelation has been studied in great detail for b-lg (pH 7) using various experimental techniques w255,256,260,262,263x. At pH 7, native b-lg forms dimers in equilibrium with monomers w264–266x. This equilibrium shifts to the monomer with decreasing ionic strength and b-lg concentration and increasing temperature. It has been established that the aggregation process occurs in two steps w267x. In the first step denatured b-lg associates to form well-defined primary aggregates that contain on average approximately 100 proteins and have a hydrodynamic radius of approximately 15 nm. In the second step, these primary aggregates randomly associate to form aggregates with a self-similar structure characterized by a fractal dimension (D f ). With heating time the aggregates grow in size until they fill up the whole volume and a gel is formed. The second step of the aggregation process is inhibited by electrostatic repulsion so that at very low ionic strength and low protein concentrations only the primary aggregates are formed. The rate at which the primary aggregates are formed increases strongly with the temperature and is determined by the denaturation of the native proteins. However, it is not strongly dependent on the protein concentration. A study of the system in the presence of 0.1 M salt shows that the growth of the aggregates stagnates if most native proteins have been used to form the primary aggregates w268x. This leads to a divergence of the gel time at a concentration of approximately 7 gyl and at lower protein concentrations no gel is formed. The aggregation process can be quenched by rapidly lowering the temperature. At room temperature the aggregation is very slow and if the system is diluted it is stable as no further aggregation or break-up of the aggregates is observed for a period of months. It is thus possible to characterize the diluted aggregates using scattering techniques at different stages of the aggregation process up to the gel point. At pH 7 and 0.1 M salt the aggregates have a self-similar structure with low D f f2, which is independent of the temperature and the concentration w255x. However, it is not possible to study the more concentrated systems and the gels with standard light scattering, because they are turbid. Neutron and X-ray scattering is possible for turbid systems, but they probe the structure only on length scales below approximately 50 nm. If possible, a light scattering investigation would give information about the interaction between the aggregates and the structure of the gels. This information is complementary to direct observation by microscopy, which is either invasive or has a lower resolution w255x. In addition, it is difficult to obtain quantitative average characteristics of the structure with microscopy, while scattering techniques directly probe the average structure. It has been recently demonstrated that SLS experiments can be done on turbid suspensions if they are combined with novel cross-correlation DLS techniques w269x. In the latter, two simultaneous scattering experiments are performed on the same scattering volume and with identical scattering wave vectors (™ q), but with the detectors at different spatial positions, i.e. from different speckles. It has been shown theoretically

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Fig. 17. Cross-correlation functions measured at qs0.026 nmy1 for 20 gyL b-lg at pH 7 and 0.1 M NaCl at different heating times at 76 8C: 1 h (s); 2 h (∑); 4 h (h); and 8 h (e) w255x.

w270x and experimentally w269x that when correlating the intensities only singly scattered photons contribute to the ACF. The effect of uncorrelated multiply scattered photons is used to reduce the intercept of the ACF in proportion to their relative intensity. Therefore, the intensity of singly scattered photons can be deduced from the reduction of the intercept. It was shown that useful information could be obtained for concentrated protein aggregates and gels by means of the crosscorrelation DLS. Nicolai et al. w255x determined the static structure factor of heated b-lg at different stages of the gel formation for two concentrations at pH 7 and 0.1 M NaCl; and for one system before the gel point, the effect of dilution on the structure factor was shown. In Fig. 17 normalized intensity cross-correlation functions are shown for 2 wt.% solution of b-lg at different heating times. At ths 1 h, g2(t) is characterized by a relatively narrow relaxation time distribution, but at longer heating times we observe a fast decay followed by a slow broad decay. The terminal relaxation time becomes longer with increasing heating time and is outside the window of the correlator for th)2 h w255x. We have calculated the PSDs of b-lg on the basis of the data shown in Fig. 17

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(using the modified CONTIN procedure) and obtained a bimodal distribution with maxima at Dhf110 and 455 nm for the first curve. The PSD becomes multimodal (tri- and fourmodal) and shifts towards larger Dh with increasing heating time. The in situ heat-induced aggregation of commercial b-lg as such, or after further purification, was followed to an average hydrodynamic diameter of 15–20 nm at 59–63 8C by DLS w271x. In this temperature range, measurable increase of the hydrodynamic diameter occurred after an apparent lag period, which was strongly dependent on heating temperature, pH and initial protein concentration. The changes in time scale of the aggregation process agreed with changes in amount of unfolded b-lg, assuming a two-state model of the denaturation. The pH dependence reflected the midpoint unfolding temperature and not the sulfydryl group reactivity, suggesting that thin reactivity was not rate limiting in the aggregation. The aggregation process was modelled numerically with Fuchs–Smoluchowski kinetics w271x. The gluten proteins of wheat are of immense importance in the food industry as they confer unique biomechanical properties (a balance of elasticity and extensibility) that allow dough to be processed into bread and other food products w272x. These properties are determined largely by the glutenin group of proteins, which form high Mr polymers stabilised by interchain disulfide bonds. These polymers have been described as ‘nature’s largest polymers’ and this size (estimated as ranging to 107), combined with their low solubility even in strongly denaturing solvents, has hindered attempts at detailed characterisation. Recent work has been focused on the application of novel approaches, such as field flow fractionation, for separation and PCS for size determination w272x. Although the results of this analysis are promising the high level instrumentation is not widely available and it is unlikely that the approaches will achieve widespread use. Egorov et al. w272x, therefore, described a simple system, based on agarose gel electrophoresis in the presence of a surfactant (sodium dodecylsulfate, SDS) w273x. This separates polymers of Mr to approximately 6=106, as determined by light scattering, providing a basis for routine analyses (e.g. of polymer size distribution in relation to processing properties), as well as more detailed characterisation of polymer structure. It may also be of wider use for separating other protein polymers of similar dimensions w272x. Agarose gel electrophoresis has been used to separate the complex mixture of wheat gluten polymers into fractions ranging in Mr, determined by DLS, from approximately 5=105 to over 5=106 w272x. The separation is reliable, reproducible and well suited to the routine analysis of multiple samples. The molecular weights of eight fractions determined using DLS show that the Mr of the polymers present in these fractions decreases from 5.6=106 to 6.6=105 . The binding of SDS to the proteins and the presence of urea may also result in some expansion because of charge repulsion and partial denaturation and result in an overestimation of the Mr. Nevertheless, the DLS results confirm that the agarose gel electrophoresis procedure separates the glutenin polymers on the basis of Mr and indicates that they have Mrs ranging from approximately 5=105 to over 5=106. It therefore provides a simple method for the routine fractionation of glutenin and other high Mr protein polymers w272x.

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Dickinson and James w274x reported on changes induced by high-pressure treatment in emulsification and gelation properties of lactoglobulin in the presence of low-methoxy pectin. Oil-in-water emulsions (20 vol.% soybean oil) prepared with pressure-treated proteinqpolysaccharide solution mixtures (0.5 wt.% lactoglobulinq0.02–0.5 wt.% pectin) exhibit droplet flocculation, which is sensitive to the applied pressure, pectin content and pH. Flocculated droplet networks cause modifications to emulsion rheology, which are most evident at low pH, particularly near the protein IEP. Changes in creaming behaviour, interpreted as a diminution in the extent of depletion flocculation, are also indicative of pressure-induced lactoglobulin–pectin complexation. An electrostatic interaction is consistent with a bridging flocculation mechanism at pH-IEP, whilst maximum emulsion flocculation is exhibited at the IEP. Significant levels of flocculation at neutral pH also indicate a degree of complexation under conditions where both macromolecules carry net negative charges. This observation is supported further by gelation studies where, under neutral conditions, the presence of pectin during high-pressure treatment greatly enhances the strength of the resulting protein gels (4–8 wt.% lactoglobulin q0.1–0.5 wt.% pectin). PCS applied to the mixed biopolymer solution (pH 7.0) provided further evidence of lactoglobulin-pectin complexation following highpressure treatment, which was otherwise nearly insignificant in untreated samples. Explanations for an attractive interaction at neutral pH were offered w274x. Emulsions of n-tetradecane in water (0.1 vyv%) homogenized by ultrasounds were stabilised by 0.5 or 1.0 M ethanol and in the presence of lysozyme (4 mg 100 mly1) or 1 mM lysine monohydrochloride (14.6 mg 100 mly1) w275x. The zeta potentials and multimodal size distributions of the droplets after 5, 15, 30, 60, 120 min, and 1 and 2 days were determined by DLS technique using a Brookhaven ZetaPlus apparatus. Both parameters were determined on the same sample subsequently without any mixing. The effect of pH w4, 6.8 (natural), and 11x was also investigated. The most stable emulsions in 1 M ethanol solutions alone were at pH 6.8 and 11. The most stable emulsions with lysozyme were obtained at pH 4 and 1 M ethanol, and with lysine at pH 6.8 and 0.5 M ethanol. Except for the emulsions with lysozyme at pH 4 and 6.8, in the rest systems the zeta potentials were negative and ranged between y5 and y85 mV as a function of time and pH. The changes of zeta potential indicate that Hq ions are not much potential determining, while OHy ions increase the negative zeta potentials. However, Hq ions affect functional groups of lysozyme molecules adsorbed on the alkane droplet, what appears in essential changes of zeta potential and even reversed sign of it in some systems. The results show that stability of these emulsions may also be determined by the hydrogen bond network w275x. Water-in-oil microemulsions, or reverse micelles, were being evaluated as a reaction medium for a variety of enzymatic reactions w276x. These systems have many potential biotechnological applications. Important examples were the use of various lipase microemulsion systems for hydrolytic or synthetic reactions. Review after Stamatis et al. w276x illustrates the biotechnological applications of microemulsions as media for bioorganic reactions. The principal focus was on lipase-catalysed processes.

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Jaramillo-Flores et al. w277x studied the influence of PEG400–6000, methanol, and ethanol on aggregation steps of lipase (from wheat germ) at pH 6–9 using PCS to evaluate initial formation of clusters and trend for aggregation due to nucleation (protein crystal formation) or to random mechanisms (amorphous precipitate). In their native state, approximately 80% of the caseins in milk are associated with each other and with calcium phosphate to form colloidaly dispersed casein micelles that size depends on CCa w278x. The caseins bind to the calcium phosphate through their serine phosphate residues to produce a cross-linked network. In bovine milk, it is accepted that most of k-casein is found on the surface of the micelles whilst the distribution of the other caseins between surface and interior is less clearly cut. Casein micelles from pooled milks from goats with casein B2B2 yB2E or FFyFO1 genotypes were fractionated by centrifugation w278x. The casein composition of each fraction was analysed by cation exchange FPLC and the PSD was determined by PCS. Allele B was associated with high levels of as1-casein, allele E with medium levels and allele F with low as1-casein content. The micellar PSD curves showed that milks low in as1-casein were characterized by larger micelles than milks high in as1-casein. The proportion of k-casein increased with increasing micellar size whilst that of b-casein decreased. Smaller micelles had less as2-casein. These observations held true for both types of milk tested. However, as1-casein content decreased with micelle size in milks with the variants B or E but the opposite was observed in milks with variant F. These results suggest that as1-casein F, which is lacking a cluster of phosphoserine residues, might be located on the surface of the micelles. The changes in casein composition with micellar size were not accompanied by changes in their contents of calcium and phosphate w278x. The casein micelles of ‘high’ and ‘low’ milks were fractionated by differential centrifugation w278x. The pelleted micelles were then resuspended in milk ultrafiltrate obtained from ‘high’ and ‘low’ milks, respectively. The first fraction contained a large proportion of somatic cells and bacteria that resulted in fast proteolysis and an increase in the amount of g-caseins. This fraction accounted for less than 4% of the total micellar casein and was excluded from the statistical analysis. Estimates of micellar size were obtained by PCS, the diffusion coefficients being transformed using the Stokes–Einstein relationship for spherical particles. These sizes were largely independent of scattering angle, indicating monodisperse size distributions. Micellar size distribution curves were thus constructed by plotting the casein contents in the fractions as a function of their mean micellar diameter (Fig. 18). In ‘high’ milk approximately half of the total casein was distributed in micelles with diameter ranging from 160 to 280 nm, with a peak in the distribution curve at 225 nm. In ‘low’ milk 42% of the total casein was found in micelles with diameters ranging from 210 to 320 nm, with a peak in the size distribution curve at 294 nm. Overall, ‘low’ milks were characterised by larger micelles and narrower distribution curves than ‘high’ milks. Similar micellar size distribution patterns have also been reported by Pierre et al. w279x, who showed that milk without asl -casein had a high proportion of casein forming large micelles whilst milks high in asl-casein milks had more micelles with diameters ranging from 40 to 140 nm. The distributions of

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Fig. 18. Micellar size distributions in caprine milks of different genotypes; yyy as1-casein B2B2yB2E milk;---- as1-casein FFyFO1 milk w278x.

the colloidal calcium and phosphate paralleled that of the micellar caseins and hence the distribution of the phosphoserine residues in the micelles (Figs. 19 and 20). Thus, changes in casein composition of the fractions were not accompanied by large changes in their contents of calcium and phosphate. In fact, a strong linear correlation was found between colloidal phosphate and calcium. The ratio of CayPi was approximately 1.4 w278x and was in general agreement with that suggested for bovine casein micelles w280x. The PSDs (e.g. casein micelles in milk) in diluted food products were studied by PCS, and concentrated systems were explored by diffusing wave spectroscopy (DWS) w281x. The use of DWS is at an early stage, but it shows considerable promise as a technique, especially since it can study liquid foods in their proper concentrations. On the other hand, the problems of dilution on particle stability are not easily solved in PCS, and, perhaps more importantly, dilution seriously affects the reactions, which can occur. DWS remains more difficult to interpret; for example, the PSDs cannot be obtained, and the interpretation of even average properties depends on proper calibration and the concentration of the suspensions. Nevertheless, as an on-line analytical method it may offer more scope than PCS and may, eventually, prove to be more valuable for the study of food systems. Csaki and Csempesz w282x studied the interfacial processes controlling the structure of mixed adsorption layers of uncharged polymers at the particleysolution

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Fig. 19. Distribution of total calcium content in micelles of different sizes; yyy as1-casein B2B2yB2E milk;---- as1-casein FFyFO1 milk w278x.

interfaces. Under equilibrium conditions for simultaneous competitive adsorption from ternary polymer solutions, preferential adsorption parameters for the polymers in pairs have been determined on negatively charged colloidal dispersions and used as a measure of the affinity for surface sites of chemically different polymer molecules. The spatial properties of the interfacial polymer layers after various contact times were investigated by PCS, laser Doppler-electrophoresis and at low polymer dosages, by flocculation kinetic measurements. It was found that long-term kinetic effects have a marked effect on the structure of composite interfacial layers. At a low surface coverage, competition for partially covered particle surfaces of suitable polymers may lead to the formation of extended mixed adsorption layers. Displacement from the interfaces of the less preferred polymer results in either increase or decrease in time of both the hydrodynamic and the electrophoretic thicknesses in the mixed layers. The non-equilibrium states of the adsorbed macromolecules, existing over much longer period in the mixed layers than in the individual polymer layers, closely correlate to the preferential affinity for surface sites of the competing macromolecules w282x. The ability of reversed micelles to encapsulate proteins has received considerable attention due to its potential for biotransformation and protein extraction and purification. Biocatalysis in reversed micelles can be particularly advantageous on the conversion of water insoluble substrates. High amounts of substrate can be solubilised and the interfacial area between water and organic solvent is kept high when compared to other biphasic systems. Additionally, when hydrolases are used,

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Fig. 20. Distribution of colloidal inorganic phosphate in micelles of different sizes; yyy as1-casein B2B2yB2E milk;---- as1-casein FFyFO1 milk w278x.

the equilibrium can be shifted to the synthesis reaction by decreasing the water content. In view of these two advantages, encapsulation of lipolytic enzymes is a promising system w283x. Several studies addressing the mechanism of protein solubilisation in reversed micelles have been reported. According to Luisi et al. w284x, there are three essential questions: (i) what are the driving forces for the protein solubilisation; (ii) what is the localization of proteins in the reversed micellar phase; and (iii) what size or shape perturbation is induced in the reversed micellar droplets by the protein solubilisation? Since the pioneering work of w285x, where the protein molecule is immersed in the water pool surrounded by a water-shell (water-shell model), these issues have been addressed. Experimental data after Levashov et al. w286x point to no significant effect on the size of the reversed micelles upon solubilisation of the proteins a-chymotrypsin, lysozyme, trypsin, ovalbumin, horse liver alcohol dehydrogenase and g-globulin (fixed size model) except when the inner cavity of the micelle is smaller than the effective protein size (induced fit model). This contradicts the data obtained by Zampieri et al. w287x, where an increase in the dimensions of the micelles upon solubilisation of achymotrypsin, lysozyme and myelin basic protein was determined. Geometrical considerations and experimental data have led to envisage two situations w288,289x: a-chymotrypsin is mainly in the water pool causing an equivalent increase in the

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water pool volume (increased radius) and cytochrome c is mainly located at the surfactant interface causing a decrease in the water pool radius. Cutinase from Fusarium solani is a hydrolytic enzyme capable of degrading cutin. It is not a true lipase since it does not display interfacial activation and does not have a lid w290,291x but can be used for hydrolysis and synthesis of fats and oils w292x. After encapsulation, cutinase unfolds. It is a reversible process and occurs with rate constants approximately 0.1–8 hy1 depending on the W0 value. The fungal lipolytic enzyme cutinase, incorporated into sodium bis-(2ethylhexyl) sulfosuccinate reversed micelles has been investigated by DLS w283x. The reversed micelles formed spontaneously when water was added to a solution of sodium bis-(2ethylhexyl) sulfosuccinate in isooctane. When an enzyme was previously dissolved in the water before its addition to the organic phase, the enzyme was incorporated into the micelles. Enzyme encapsulation in reversed micelles could be advantageous namely to converse water insoluble substrates and to carry out synthesis reactions. However, protein unfolding occurred in several systems as for cutinase in sodium bis(2ethylhexyl) sulfosuccinate reversed micelles. DLS measurements of sodium bis(2ethylhexyl) sulfosuccinate reversed micelles with and without cutinase were taken at different water to surfactant ratios. The results indicated that cutinase was attached to the micellar wall and that could cause cutinase unfolding. The interactions between cutinase and the bis-(2ethylhexyl) sulfosuccinate interface were probably the driving force for cutinase unfolding at room temperature. Twenty-four hours after encapsulation, when cutinase was unfolded, a bimodal distribution was clearly observed. The radii of reversed micelles with unfolded cutinase were determined and found to be considerably larger than the radii of the empty reversed micelles. The majority of the reversed micelles were empty (90–96% of mass) and the remainder (4–10%) containing unfolded cutinase were larger by 2.6–8.9 nm w283x. Molecules that are able to stabilise foams and emulsions should be surface active and form an adsorbed layer at the interface between the different phases. As a consequence they have to possess both hydrophobic and hydrophilic regions within their structure and are, by definition, amphiphilic. Proteins forming viscoelastic films at the interfaces correspond to one of the main classes of amphiphilic molecules used in food systems. The stability of these films is governed by the protein–protein interactions in the adsorbed layer and the protein–airyprotein–lipid interactions at the interface. Such interactions involve surface charge, hydrophobicity and disulfide interchange, all of which are strongly affected by a protein’s threedimensional structure. Reviews after Vollhardt and Fainerman w293x and Bos and van Vliet w294x demonstrate the recent theoretical and experimental progress in the understanding of penetration systems at the air–water interface for dissolved amphiphile (surfactant, protein) penetrating into a Langmuir monolayer. Notice that proteins and low molecular weight surfactants are widely used for the physical stabilisation of many emulsions and foam based food products, drugs, etc. The formation and stabilization of these emulsions and foams depend strongly on the interfacial properties of the proteins and the surfactants. Although a rigorous thermodynamic analysis of penetration systems is unavailable due to their complex-

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ity, some model assumptions, e.g. the invariability of the activity coefficient of the insoluble component of the monolayer during the penetration of the soluble component result in reasonable solutions. New theoretical models describing the equilibrium behaviour of the insoluble monolayers which undergo the two-dimensional aggregation in the monolayer, and the equations of state and adsorption isotherms which assume the existence of multiple states (conformations) of a protein molecule within the monolayer and the non-ideality of the adsorbed monolayers are now available. The theories which describe the penetration of a soluble surfactant into the main phases of Langmuir monolayers were presented first for the case of the mixture of the molecules possessing equal partial molar surfaces (the mixture of homologues), with further extension of the models to include the interesting process of the protein penetration into the monolayer of two-dimensional aggregating phospholipids. This extension was based on a concept subdividing the protein molecules into independent fragments with areas equal to those of phospholipid molecule. Various mechanisms for the effect of the soluble surfactant on the aggregation of the insoluble component were considered in the theoretical models: (i) no effect on the aggregate formation process; (ii) formation of mixed aggregates; and (iii) the influence on the aggregating process through the change of aggregation constant, but without any formation of mixed aggregates. Accordingly, depending on the mechanism, different forms of the equations of state of the monolayer and of the adsorption isotherms of soluble surfactant are predicted. Based on the shape of the experimental isotherms, interesting conclusions can be drawn on the real mechanism. First experimental evidence has been provided that the penetration of different proteins and surfactants into a DPPC monolayer in a fluid-like state induces a first order main phase transition of pure DPPC. The phase transition is indicated by a break point in the P(t) penetration kinetics curves and the domain formation. Mixed aggregates of protein with phospholipid are not formed. These results agree satisfactorily with the predictions of the theoretical models. New information on phase transition and phase properties of Langmuir monolayers penetrated by soluble amphiphiles is obtained by coupling of the P(t) penetration kinetics curves. These results on the penetration of b-lactoglobulin into DPPC monolayers have shown that protein penetration occurs without any specific interactions with the DPPC molecules and the condensed phase consists only of DPPC w293,294x. The unique folded structure makes polypeptides and functional proteins w295x. The numbers of known sequences are approximately a hundred times larger than the number of known structures and the gap is increasing rapidly. The primary goal of all structure prediction methods is to obtain structure-related information on proteins, whose structures have not been determined experimentally. Besides this goal, the development of accurate prediction methods helps to reveal principles of protein folding. Simon and Fiser w295x presented a brief survey of protein structure predictions based on statistical analysis of known sequence and structure data discussing the background of these methods and attempt to elucidate principles, which govern structure formation of soluble and membrane proteins. Clearly, interactions of membrane and other proteins with drugs can strongly influence the efficiency of applied medicines.

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4.2. Proteins, DNA and drugs Interaction between proteins (transport albumins, enzymes, etc.) or DNA molecules (e.g. viruses) and drugs plays a very important role since it substantially controls the medicine efficiency. A prerequisite for the delivery of macromolecular drugs, such as peptides and proteins, to the alveolar epithelium is the design of an adequate drug carrier system w296x. The carrier should be fitted to protect the drug incorporated from the mechanical stress caused by aerolisation, and from degradation caused by enzymatic activity. When the targeting to certain cells is intended, the carrier system should be equipped with a targeting moiety bound to its surface. In order to achieve targeted drug transport to alveolar cells, the authors w296x investigated liposomal systems that were functionalised with lectins. Lectins are glycoproteins that not only specifically bind to sugar molecules on cell membranes, but may also induce endocytosis by these cells. Liposomes were prepared by the film method, followed by membrane extrusion from 50 mol.% di-palmitoylphosphatidylcholine (DPPE) and 49 mol.% cholesterol. For the coupling of avidin to the liposomes, 1 mol.% N-w4-(p-maleimido-phenyl)-butyrylx phosphatidylethanolamine (MPB-DPPE) was introduced into the liposomal membrane. Avidin was modified with the amine reactive reagent, N-succinimidyl 3-(2-pyridyldithio) propionic acid (SPDP), and coupled to the MPB-DPPE bearing liposomes by incubation. Unassociated protein was removed by gel filtration. Functionalisation was achieved by incubation with biotinated lectins, exploiting the strong biotin–avidin interaction. Liposomal size was determined by PCS. Entrapment efficiency was evaluated by employing carboxyfluorescein and FITC-dextrans of varying molecular weights as fluorescent marker substances. The stability of the liposomes obtained was tested in different surfactant preparations: an artificial protein-free surfactant preparation, Alveofac and human lung surfactant. The results showed the applicability of functionalised liposomes for the targeted drug delivery to the alveolar epithelium w296x. Synthetic polymers or multifunctional block copolymers can be used as gene delivery vectors, designed for self-assembly with expression vector DNA; and Dash et al. w297x characterized the interaction between DNA and polylysine of varying molecular weight average using ethidium bromide fluorescence to monitor formation of complexes and their disruption by poly(l)aspartic acid. All poly(l)lysines were able to form complexes with DNA, and sizes measured by PCS were greater for the larger poly(l)lysine molecular weight fractions (ranging from 37 to 207 nm average diameter). Complexes based on larger poly(l)lysines showed a sigmoidal destabilisation by poly(l)aspartic acid while complexes based on smaller pLLs showed more linear disruption. Complexes formed between DNA and a linear A– B poly(ethylene glycol)-poly(l)lysine showed an average diameter approximately 53 nm determined by PCS. The block copolymer did not improve the stability of complexes to destabilisation by poly(l)aspartic acid but did increase resistance of the complexes to nucleolytic degradation w297x. Dekie et al. w298x described the synthesis and evaluation of biodegradable derivatives of poly-L-glutamic acid as suitable vectors for gene therapy. When mixed

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with DNA the new polymers self assemble and form polyelectrolyte complexes. The formation of the complexes and determination of their stability towards disruption by serum albumin was monitored by Ethidium bromide (EtBr) fluorescence spectroscopy. All polymers were able to form complexes and their size, determined by PCS, was between 84.5"2 nm and 96.7"1.6 nm, depending on the type of polymer and the charge ratio. All complexes were stable towards serum albumin. The results from the biodegradability tests, using tritosomes, showed that the polymers were biodegradable; and the degradation rate was affected by the number of charged groups in the side chains. Haemolysis and red blood cell (RBC) agglutination were assessed and compared to poly(L-lysine) (pLL) and polyethyleneimine (pEI). RBC agglutination was monitored with optical microscopy. Results showed that the new polymers were less toxic than pLL and pEI. These preliminary transfection studies show that the polymers are suitable vectors for gene delivery w298x. The effect of beta-blockers (alprenolol, oxprenolol, atenolol, acebutolol) and the non-steroidal anti-inflammatory drug, diclofenac, on modification of low-density lipoproteins, LDL, by sodium hypochlorite (NaOCl) was investigated by Seifert et al. in vitro w299x. Beta-blockers and diclofenac inhibited the formation of thiobarbituric acid reactive substances in LDL modified by NaOCl. Beta-blockers, but not diclofenac, inhibited the hypochlorite-induced aggregation of LDL, which was determined by PCS. The intracellular accumulation of cholesterol esters in J774 macrophages was inhibited by addition of beta-blockers, but not diclofenac, to LDL prior to the addition of NaOCl. The modification inhibiting effect of beta-blockers is inversely correlated to the binding capabilities of these substances to LDL, which were assessed by laser electrophoresis. Inhibition of LDL modification in vivo by beta-blockers may reduce the risk of atheriosclerosis and, therefore, compensate for the cholesterol-raising effect of these drugs in human plasma w299x. PCS demonstrated for the first time that co-purified meningococcal TbpAqB form a complex in solution w300x. This structure bound hTf and the resultant species underwent partial dissociation after exposure to additional hTf or following prolonged incubation. Purified TbpA and TbpB had similar apparent sizes but showed distinctive profiles size suggesting that TbpA forms a largely homogeneous population while TbpB may produce more variable particle sizes under these conditions. Clomethiazole was used as a model drug to be incorporated into an emulsion vehicle w301x. The effects of drug concentration and number of homogenisation steps were evaluated using multiple linear regression method. The droplet size, measured as an average diameter by PCS, was found to be between 60 and 260 nm in the investigated range of clomethiazole concentrations, highly dependent on the concentration, but weaklier on the number of homogenisation steps. Slow-scanning high-sensitivity differential scanning calorimetry measurements showed that clomethiazole depresses the phospholipid chain melting temperature in the emulsion system, whereas 13C NMR experiments suggested that the clomethiazole molecules are to a large extent located in the surface region of the emulsion droplets. This interpretation is compatible with results from NMR self-diffusion measurements,

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which showed that most of the clomethiazole molecules are rapidly exchanged between emulsion droplets and the aqueous surrounding. One can conclude that the surface-active drug clomethiazole has a significant influence on the characteristics of phospholipid-stabilised emulsions through its ability to interact with the phospholipid interface. Thus, the results underline the importance of characterizing druglipid interactions for the development of lipid-based formulations w301x. Small angle X-ray scattering, SAXS, (as well as PCS) is a method to measure particle sizes in the order of 10 nm magnitude, which can be used to characterize reversed micellar systems, in this case reverse micelles consisting of lecithin and isopropyl myristate w302x. In this study, these micelles were loaded with different concentrations of the amphiphilic anti-glaucoma drug timolol maleate. The PCS results were consistent with those yielded by SAXS, showing a decrease of particle size with higher concentration. In addition, SAXS capable to give information about the particle shape (as well as MALS w107x) showed that micelles had an ellipsoidal shape with low drug loads transformed into nearly spherical micelles at higher drug concentrations w302x. Thermosetting microemulsions and mixed micellar solutions were investigated as drug delivery systems for anaesthetising the periodontal pocket w303x. The structure of the systems, consisting of the active ingredients lidocaine and prilocaine, as well as two block copolymers (Lutrol F127 and Lutrol F68), was investigated by NMR spectroscopy and PCS. The results obtained for dilute (1–3% wyw) solutions show discrete micelles with a diameter of 20–30 nm and a critical micellisation temperature of 25–35 8C. Gel permeation chromatography was used to study the distribution of the active ingredients, and indicates a preferential solubilisation of the active components in micelles over monomers. Analogous to the Lutrol F127 single component system these formulations display an abrupt gelation on increasing temperature. The gelation temperature was found to depend on both the drug ionisation and concentration. These systems have several advantages over emulsionbased formulations including good stability, ease of preparation, increased drug release rate and improved handling due to the transparency of the formulations w303x. Solid lipid nanoparticles (SLNTM, Lipopearls) are nanoparticles made from solid lipids by high-pressure homogenisation. Incorporation of chemically labile active ingredients into the solid lipid matrix protects against chemical degradation, which was shown for vitamin E by Dingler et al. w304x. The used solid lipid nanoparticles were physically stable in aqueous dispersions and also after incorporation into a dermal cream as proven by PCS and differential scanning calorimetry. Electron microscopy and atomic force microscopy data revealed the spherical shape of the solid lipid nanoparticles and the detailed structure of the particle surface. Ultra-fine particles formed an adhesive film leading to an occlusive effect on the skin. The occlusion promoted the penetration of vitamin E into the skin, as shown by the stripping test. In addition to chemical stabilisation of active ingredients, occlusive effects on the skin and subsequent enhanced penetration of compounds, the solid lipid nanoparticles also possess a pigment effect covering undesired colours leading to an increased aesthetic acceptance by the customer w304x.

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Cationic liposomes spontaneously interact with negatively charged plasmid DNA to form a transfection competent complex capable of promoting the expression of a therapeutic gene w305x. If gene therapy is to succeed the corrective plasmid DNA (pDNA), constructs must be delivered to the cell targets in a form that will preserve their function, penetrate the numerous barriers to cell invasion and promote the expression of the therapeutic protein. Cationic liposomes have intrinsic properties, which make them attractive as vehicles for gene delivery; they are synthetic and, as such, manufacturable to drug standard, biodegradable, non-immunogenic and able to interact with DNA to promote its transfection into both replicating and nonreplicating cells. To improve the understanding of the poorly defined mechanisms and structural rearrangements associated with the lipid–DNA interaction, Birchall et al. w305x studied dimethyl dioctadecylammonium bromide (DDAB)ydioleoyl phosphatidylethanol amine (DOPE) and 1,2-dioleoyl-3-trimethylammonium propane (DOTAP) liposomes mixed with a reporter plasmid (pADb or pCMVb) to form lipid–DNA complexes. The size and charge characteristics of the complexes as determined by PCS and microelectrophoresis were found to be dependent on the lipid:DNA ratio, with both DDAB:DOPE–DNA and DOTAP–DNA complexes aggregating at around neutral zeta potential. Negative stain transmission electron microscopy demonstrated at least three distinct complex structures being formed at the same DOTAPyDNA ratio. The authors postulated that two of these aggregates are structural moieties involved in the formation of the efficient transfection particle. Gel electrophoresis was used to determine the efficiency and extent of lipid–DNA complex formation. Results showed that only DOTAP liposomes were capable of preventing ethidium bromide intercalation with DNA and protecting the enclosed plasmid from nuclease digestion. When a range of lipid–DNA complexes were transfected into in vitro cell lines, the efficiency of reporter gene expression was found to depend on the type of liposome used in the complex, the ratio of lipidy DNA and the transfected cell line. The results challenge the requirement for DOPE to be included in the formulation of cationic lipid vectors, especially in the case of DOTAP containing liposomes w305x. Monensin is a carboxylic ionophore, which can potentiate the activity of ricinbased immunotoxins in vitro and in vivo against a variety of human tumours w306x. Monensin was encapsulated into nanoparticles by using biodegradable poly(dllactide-co-glycolide) (50:50). The nanoparticles were prepared by modified emulsification-solvent evaporation method. High shear homogenisation followed by simultaneous stirring and bath sonication was used for preparing nanoparticles. The size of nanoparticles was determined by PCS using a Brookhaven BI 90 particle sizer. The average size of nanoparticles could be decreased from 567 to 163 nm by increasing the concentration of polyvinyl alcohol from 10 to 100% of poly(dllactide-co-glycolide). The nanoparticles were spherical in shape as observed by atomic force microscopy. The concentration of monensin in the nanoparticles was analysed by HPLC and the entrapment efficiency was found to be more than 12%. The zeta potential of nanoparticles was y25.8"1.3 mV, which did not change significantly after resuspension of the freeze-dried sample. The nanoparticles were

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tested against HL-60 and HT-29 human tumour cell lines in vitro. Monensin nanoparticles potentiated the activity of immunotoxins by 40 to 50 times against these cell lines. There was, however, no difference between the nanoparticles and liposomes for their potentiating affect of immunotoxins against the two tumour cell lines w306x. The effect of ionic strength and pH of carrier solutions on the separation of liposomes by flow field-flow fractionation has been studied for the determination of accurate vesicle size distribution of liposomes w307x. Retention behaviours of liposomes (PCyPGycholesterol) were observed in typical buffer solutions (PBS and Tris–HCl) of various ionic strengths as carrier liquids in flow field-flow fractionation. The average diameters of collected fractions at each flow field-flow fractionation run were measured by PCS for the comparison with field-flow fractionation calculations at corresponding time interval of collected fractions. A reasonable separation of liposomes was observed at 0.016 M for both buffer solutions. Retention of liposomes was found that they were elongated at ionic strengths higher than an optimum condition found experimentally, but it was shortened at a lower ionic strength due to the electrostatic interaction between the channel wall and the liposomes. Finally, size distributions of liposomes were provided comparing the liposome preparations by flow field-flow fractionation w307x. Ortega-Vinuesa et al. based on their work w308x the well-established immunoassay principle of agglutination of latex particles covered by immunoproteins. In their experiments, positively charged particles act as carriers for the F(ab9)2 fragment, obtained from rabbit polyclonal IgG, active against C-reactive protein. The presence of the antigen C-reactive protein in the immunolatex system causes agglutination. The authors w308x aimed to compare different optical techniques (PCS, turbidimetry, nephelometry and angular anisotropy) capable of detecting the agglutination. The sensitivity and detection limit largely depended on the optical method. The authors w308x analysed for each optical technique the following aspects: sensitivity, reproducibility, detection limit, reaction time, amount of sample wasted and availability of the required detection device. The results presented showed that both angular anisotropy and PCS offer lower detection limits, and use little reagent, but have longer assay times than the classical optical techniques of turbidimetry and nephelometry w308x. Many reports describe the local and systemic administration of naked DNA resulting in transgene expression levels that are insignificant or too low for clinical applications w309,310x. The high net negative charge density and a hydrodynamic diameter of approximately 100–300 nm leads to opsonization of plasmids and clearance from circulation by the reticuloendothelial system. Also, uptake by their target cells is an unlikely event due to electrostatic repulsion with the cell membranes w311x. Naked plasmid DNA could successfully be transferred by direct injection into skeletal muscles of rodents and primates w312,313x. Gene expression has been shown to last for several months, but generally at relatively low levels w314x, since the p-DNA was degraded by nucleases and removed from muscle. Diffusion from the site of injection was low. Improved cellular uptake and tissue dispersion after

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i.m. injection was achieved by complexation of DNA with the synthetic polymers polyvinyl pyrrolidone and polyvinyl alcohol w315x. The administration of DNA into muscle could be therapeutically useful both for local treatment of diseases as well as depot for systemic protein delivery, e.g. for vaccination purposes w316x. Controlled release of DNA, continuous transgene expression and the protection of the genetic material from enzymatic degradation over longer periods are important prerequisites for the use of polymers as non-viral carriers for plasmids and oligonucleotides. Additionally, to allow prolonged residence times of the devices in the tissue, the materials need to be safe and biocompatible. Nanoparticles, microparticles and devices made of biodegradable and non-biodegradable polymers of synthetic or natural origin (gelatine, collagen) have been investigated as sustained-release delivery systems w317x. Controlled delivery of plasmid and continuous transfection for at least 60 days could be achieved using an atelocollagen matrix as delivery system w318x. HSA w319x has been widely used as material for nano- and microparticulate drug carrier systems w320,321x. Under physiological conditions albumin has a net negative charge and consequently HSA cannot react electrostatically with plasmids or oligonucleotides to form complexes for gene transfer. However, the charge of the native albumin can be modified by converting anionic side chain carboxylic groups with hexamethylenediamine w322,323x, thereby producing a highly cationic derivative. Cationised human serum albumin (cHSA) produced by this simple and highly reproducible technique w324x demonstrated low cytotoxicity and good biocompatibility both in vitro and in vivo, as well as enzymatic biodegradability w325–327x. Furthermore, cationised albumin contains many primary amino groups, which can be employed for conjugation with lipids and ligands such as antibodies w328x, viral proteins w329x, sugars w330x and lectins w331x. Modification of cHSA can induce tissue- and cell-specific targeting w332x or a fusogenic activity of the cHSAyDNA complexes w333x. Huckett et al. w334x used insulin-bound cationised HSA for targeted gene transfer by receptor-mediated endocytosis. By this approach they produced stable transfected HepG2 clones. However, a protocol for stable transfection was used which was not comparable with procedures necessary for in vitro and systemic or local in vivo gene transfer. Cationised human serum albumin (cHSA) could serve as a potential non-viral vector system for gene delivery w335x. Native HSA was cationised by covalent coupling of hexamethylenediamine to the carboxyl groups resulting in a shift of the isoelectric point from pH 4–5 to 7–9. The cationised HSA underwent spontaneous self-assembly with DNA as demonstrated by retardation of CMV-nlacZ plasmid in agarose gel electrophoresis. PCS showed a decrease of complex size with increasing cHSAyplasmid ratios. Under optimised conditions complexes were formed with 230–260 nm mean diameter and a homogenous, narrow size distribution. At room temperature, complexes were stable in 0.9% sodium chloride solution pH 7.4 for 1 h without aggregation. Process parameters such as HSA concentration, incubation time, temperature, pH, order of reagent addition, the presence of bivalent ions and the ionic strength of the complexation medium all influenced the complex size. Confocal laser scanning microscopy showed interactions of a Texas Red labelled

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cationised albumin with cell membranes of ECV 304 cells and an enhanced endocytic uptake compared to native albumin. The potential for introducing exogeneous DNA into cells was shown using NIH 3T3 fibroblasts. Under in vitro conditions, no toxic effect could be observed. Cationised HSA may have promised as a non-toxic vector for gene delivery, especially for DNA vaccination w335x. Davidsen et al. w336x used polyethylenoxide (PEO) covered liposomes as lipidbased drug-delivery systems. In comparison to conventional liposomes the polymercovered liposomes display a long circulation half-life in the blood stream. The influence of polyethyleneoxide-distearoylphosphatidylethanolamine (DSPE-PEO750) lipopolymer concentration on phospholipase A2 (PLA2) catalyzed hydrolysis of liposomes composed of stearoyloleoyl-phosphatidylcholine (SOPC) was explored. The characteristic PLA lag-time was determined by fluorescence and the degree of lipid hydrolysis was followed by HPLC analysis. Particle size and zeta-potential were measured as a function of DSPE-PEO750 lipopolymer concentration. A significant decrease in the lag-time, and hence an increase in enzyme activity, was observed with increasing concentrations of the anionic DSPE-PEO750 lipopolymer lipids. The observed decrease in lag-time might be related to changes in the surface potential and the PLA lipid membrane affinity w336x. 4.3. Interaction of proteins with dispersed particles Interaction of proteins with solid particles, which can lead to their adsorption, immobilisation, particle-macromolecule flocculation, etc., is of importance from both theoretical and practical points of view w23,337–347x. For instance, the adsorption of protein toxins onto adsorbent particles provides deintoxication of the organism on enterosorption or blood purification on haemosorption, however, interaction of proteins with the artificial organs in blood vessels can cause negative effects. There is a question related to preferable interaction of native or inactivated proteins (e.g. metabolism products, toxins) with adsorbent particles, as the adsorption of inactivated proteins or other biomolecules, which play a role of toxins, to remove them from the body is more appropriate than the adsorption of native biopolymers. Additionally, proteins immobilised on the adsorbent particles can change the adsorptive properties of their surfaces in respect to small molecules and ions, which can poorly adsorb onto the pristine adsorbent surfaces (e.g. cholesterol does not practically adsorb on fumed silica particles but can adsorb on the proteinysilica surfaces). The adsorption or adhesion of biological substances to artificial materials such as synthetic polymers is known as the process of bioadsorption or bioadhesion. It occurs when artificial implants are introduced in the body and includes the adsorption of biopolymers like proteins, lipids or other macromolecules and the adhesion of cells, platelets and bacteria to the biomaterial surfaces. Specific protein molecules at the surfaces of cells are believed to adsorb onto the implant surfaces leading to bioadhesion. It is an almost universally accepted opinion that the adsorption of proteins to the surface of a biomaterial is the first of many steps, which ultimately lead to the failure of an implanted device. In the last several decades, there has

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been considerable interest in the interactions of proteins with the materials used in medical implant devices. Protein adsorption to artificial surfaces is a complex process that is controlled by a number of driving forces. The conformational stability and the surface energetics of the protein molecules and synthetic materials determine the rates and the strengths of this adsorption process. On the surfaces of hydrophobic materials, the hydrophobic interaction dominates protein adsorption. In order to enhance the biocompatibility of these materials, one strategy is to focus on minimizing the protein’s affinity for the surfaces w348x. The adsorption isotherm of bovine submaxillary gland mucin (BSM) onto a hydrophobic polystyrene surface was determined by using the solution depletion method, in which mucin concentrations were analysed by amino acid analysis w348x. Adsorption and desorption kinetics of BSM onto hydrophobic polystyrene surfaces were also studied by the solution depletion method, in which mucin solution concentrations were determined by measuring UV absorbance at a wavelength of 280 nm and by a colorimetric assay with final calibration by amino acid analysis. From the adsorption isotherm, the authors found that the saturated surface concentration (amax) was 2.3 mgym2, and the adsorption constant (K) was calculated as 0.099 (mlymg). By using a Langmuir adsorption model and non-linear fitting, kinetics parameters, kon and koff, were found to be 8.13=10y3 cm3 mgy1 sy1 and 5.67=10y4 sy1, respectively. The coating was found to be very stable with very limited desorption (less than 2%) from a long-term observation (28 h). The mucin coating layer thickness was investigated by several analytical techniques: flow field–flow–fractionation, PCS, scanning electron microscopy and atomic force microscopy. The thickness was measured as 4–5 nm, from which a monolayer coating was concluded. Finally, the average molecular weight of purified BSM was determined as 1.6 MDa by using SLS w348x. Polyelectrolyte–gelatine complexation was studied by Bowman et al. by using the PCS method w349x. More complex process with formulation of highly soluble poly(ethylene glycol)-peptide DNA condensates was explored by Kwok et al. w350x. Bovine casein was adsorbed onto negatively charged polystyrene latex particles of various sizes and the changes in the hydrodynamic diameters of the particles were monitored by PCS w351x. The latex particle diameters were increased on addition of small amounts of casein, and plateaued once a maximum adsorption was attained. The size increase was approximately 25 nm regardless of the initial size of the latex particle, indicating that the surface arrangement of casein was similar on all latex sizes. Treatment of the casein micelles in skim milk and the casein-coated latex particles with chymosin initially decreased the particle diameter by approximately 10 nm after which the particle diameter rapidly increased as the aggregation reaction proceeded. The action of chymosin on both the casein micelles and the casein-coated latex particles was retarded with increasing NaCl concentration. The similarity between the casein-coated latex particles and the casein micelles in milk, especially their behaviour towards chymosin, indicates that these latex particles may be a simple model system for studying some casein micelle properties under controlled conditions w351x.

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The manufacturing conditions for nanoparticles in the range of 100–500 nm are difficult to control w352x. Novel biodegradable, brush-like branched polyesters with a negatively charged hydrophilic backbone, poly(2-sulfobutyl-vinyl alcohol)-gpoly(lactide-co-glycolide), facilitate their preparation by a modified solvent displacement procedure. Furthermore, the structure and the surface properties of the colloidal systems were investigated. Nanoparticles were characterized by PCS, z-potential measurement, particle charge detection, NMR spectroscopy and TEM. Varying the manufacturing conditions, nanoparticles with mean diameters of approximately 100 to 500 nm and, depending on polymer composition, negatively charged surfaces were obtained w352x. The nanoparticles visualised by TEM showed smooth surfaces. Furthermore, surface characterisation and NMR studies suggested a coreycorona structure of the particles. This study demonstrates that a simple solvent displacement technique can be used for the reproducible preparation of discrete nanoparticles with defined negatively charged surfaces and narrow size distributions. These nanoparticles may have potential for peroral or parenteral protein delivery systems w352x. Adsorption of proteins on the surfaces of fine oxide particles depends on media parameters (polarity, permittivity, pH, salinity and temperature), topology and chemical nature of the oxide surfaces, particle size distribution and protein composition w23x. Fumed silica (Aerosil A-300, 99.5% purity, and the specific surface area (SBETf300 m2 gy1), fumed alumina (150 m2 gy1), fumed titania (50 m2 gy1) and binary fumed silicaytitania (ST) at CTiO2s9 (ST9 ), 20 (ST20) and 36 (ST36) wt.% (SBETf215, 70 and 90 m2 gy1, respectively) and silicayalumina (SA) at CAl2O3s 1.28 (SA1), 3 (SA3), 23 (SA23) and 30.6 (SA31) wt.% and SBETf220, 180, 170 and 170 m2 gy1, respectively, and fumed Al2O3 ySiO2 yTiO2 (AST) (f22 wt.% Al2O3, f28 wt.% SiO2, f50 wt.% TiO2 , SBETf32 m2 gy1) (Pilot Plant of Institute of Surface Chemistry, Kalush, Ukraine) were used for preparation of aqueous suspensions to study interaction between these oxides and proteins w353x. Such proteins as bovine (BSA) (Reachem) and human (HAS) (Reanal) serum albumins, gelatine (molecular weighting f3.4=105), and ovalbumin (pharmaceutical purity, molecular weighting f4.3=104), and polyvinyl pyrrolidone (PVP) (pharmaceutical purity, molecular weight of 12 600"2700) were used as received. For alumina (IEPAl2O3f9.8) and titania (IEPTiO2f6) in XySiO2, possessing acidic properties (IEPXySiO2-IEPSiO2), the charge distribution is non-uniform and strongly differs from one for silica with changes in pH. Zeta potential of ST and SA depends slightly on the nature and the concentration of the second oxide and is close to that for fumed silica w354x. Typical dependence of BSA adsorption on ultrafine oxide particles is shown in Fig. 21. Aqueous suspension of oxide (10 ml) and 10 ml of albumin solution were mixed and the pH value was adjusted by addition of 0.1 M HCl or NaOH solutions to a desired value. Thereupon the suspension was stirred for 1 h, then centrifuged at 5000 rev.ymin for 15 min and the concentration of albumin in separated solution was measured spectrophotometrically. Steady-state adsorption of albumin was calculated from the difference between its initial and final concentrations in the

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Fig. 21. Adsorption of BSA in (a) mg per m2 of surface or (b) per g of different fumed oxides as a function of pH.

solution. Measurements of the pH values of solutions and suspensions were performed using an Ionometer EV-74 apparatus before and after adsorption. The pH changes due to adsorption were "0.2. The ultimate pH values for the equilibrium states (relatively to adsorption and pH values) of the oxide suspensionyprotein solution were used in all represented dependencies of adsorption on pH. Comparison of BSA adsorption on different oxides shows the highest adsorption (in mgym2) on ternary oxide aluminaytitaniaysilica (Fig. 21) having the smallest SBET. For ST, a maximal adsorption (in mgyg) increases with decreasing S. For different SA, such an effect is insignificant as the difference in the S value is smaller than that for different ST and adsorption onto silica or SA is close to that for ST9 having the specific surface area close to SSA1. However, the efficiency of adsorption of BSA (in %) from solution is the greatest for silica possessing the largest SBET value from the studied oxides (Fig. 21). The differences in the adsorptive ability (in both %

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Table 7 Plateau adsorption of ovalbumin and gelatine on individual and mixed fumed oxides without pretreatment of aqueous suspensions w357x Oxide

SiO2 Al2O3 TiO2 SA3 SA23 ST9 ST20

Apparent density

Ovalbumin

(g ly1)

(mg g

38 147 86 28 32 33 75

270 87 36 180 330 180 72

y1

)

Gelatine (mg m

y2

)

0.90 0.58 0.72 1.0 1.94 0.84 1.0

(mg gy1)

(mg my2)

360 84 93 300 380 290 130

1.20 0.56 1.86 1.67 2.24 1.35 1.81

and mg my2) of ST and SA at a low concentration (Cx) of the second phase are small. Adsorption of BSA at low concentrations of oxides (Cox) increases up to 5 gyg with decreasing Cox and slightly depends on the nature of oxides. However, reduction in Cox is accompanied by a strong decrease in the efficiency of protein adsorption. A maximal adsorption is observed for SA23 (Table 7) with the maximal number of ^ Si–O(H)–Al^ bridges (i.e. B-sites, which can strongly interact with amino groups of proteins). Pure titania gives a great value of adsorption of gelatine that is in agreement with the large adsorption of BSA by this oxide (Fig. 21) and the ratio in adsorption of gelatine and ovalbumin by ST9 and ST20 (Table 7) is close to that Table 8 Characteristics of fumed silicas and plateau adsorption of BSA and gelatine w353,358x No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 a

Sa

COH

BSA

(m2yg)

(mmol my2)

(mg gy1)

(mg my2)

(mg gy1)

(mg my2)

102 148 197 192 270 293 300 275 308 308 368 384 390 410 411

4.8 3.8 3.6 3.5 3.2 2.9 2.9 3.0 3.0 3.0 2.6 2.8 2.6 2.4 2.4

200

1.96

210 230 310 280

1.06 1.19 1.14 0.95

320 350 380 450 410 430 380

1.03 1.14 1.03 1.17 1.05 1.05 0.92

170 243 295 200 275 320 346 315 307 380 250 420 470 450 200

1.67 1.62 1.49 1.04 1.01 1.09 1.15 1.14 1.0 1.23 0.68 1.09 1.21 1.10 0.48

Gelatine

The specific surface area S was evaluated using argon adsorption data.

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Fig. 22. Model of interaction between two fumed silica particles and a molecule of globular protein with the participation of water molecules located between them.

upon adsorption of BSA. An increase in SBET enhances the adsorption (in mgyg) of both proteins (Table 8), however, adsorption in mgym2 goes down with SBET due to reduction of accessible silanols (COH decreases). Relatively large protein molecules can bind several oxide particles of a comparable size (Fig. 22) that can lead to a significant enhancement of adsorption at their low concentration. Consequently, adsorptive ability of fumed oxides depends on the oxide treatment, but the relationship between protein adsorption by oxides of the different origin depends on the concentration of the second oxide phase. Powders prepared by drying of the suspensions of silica with drugs or polymers can be of interest as possible medicines. The structural characteristics of the solid residual of the suspension of fumed silica differ significantly from those of the pristine silica powder (Table 9, Fig. 23); for instance, the specific surface area SBET decreases, but the pore volume (Vp) increases and a marked peak of the pore size distribution f(Rp) appears at Rp)10 nm. Structural characteristics of the initial and treated oxides and dried residue with oxideypolymer were determined on the basis of nitrogen adsorption–desorption isotherms measured at 77.4 K by means of a Micromeritics ASAP 2405 N analyser. The specific surface area SBET was computed using BET method. The pore volume (Vp) was estimated from adsorption

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Table 9 Structural parameters of pristine powders and dried residue of the suspensions of fumed silica, silicayPVP, silicayovalbumin and silicaygelatine w353x Powder

CX (wt.%) (XsPVP, Albumin)

SBET m2yg

Vp cm3yg

a

– – 5 10 – – 17.2 23.0 27.6 21.1 31.3

342 182 170 157 322 275 175 157 138 143 123

0.566 0.612 0.923 0.383 0.613 1.147 0.903 0.868 0.724 0.745 0.701

A-300 A-300 b A-300yPVP b A-300yPVP a A-300* b A-300* b A-300*yAlbumin b A-300*yAlbumin b A-300*yAlbumin b A-300*yGelatine b A-300*yGelatine b

Note: aPristine powder, and bdried powders from solid residue of the suspensions.

at relative pressure pyp0 f0.98–0.99 converting the volume of adsorbed nitrogen to the volume of liquid one. The pore size distributions f(Rp) for pristine silica and suspended-centrifuged-dried polymerysilica were calculated using the overall isotherm equation based on the combination of the modified Kelvin equation and the statistical adsorbed film thickness applied to two models of pores as gaps between spherical particles or slit-like pores at Rp-0.7 nm and cylindrical pores at Rp)0.7 nm (these two models of pores give relatively close f(Rp) distributions). The nitrogen desorption data (as the overall isotherms) were utilized to compute f(Rp) using regularization-SVD procedure (modified CONTIN program) under nonnegativity condition for f(Rp) with a fixed regularization parameter as0.01 w353x. Addition of 5 wt.% of PVP (in respect to CSiO2) enhances Vp but reduces SBET and f(Rp) peak shifts toward larger Rp . Addition of 10 wt.% of PVP leads to strong reduction in Vp and a small diminution in SBET that is in agreement with the displacement of the main f(Rp) peak towards smaller Rp . In the case of the albumin or gelatine adsorbed on silica (Table 8), changes in the structural characteristics are smaller than those for PVPysilica (Fig. 23). The PSDs for PVPysilica suspensions determined by PCS w354x can be multi- or monomodal depending on the component concentrations and pH. However, small aggregates give the main contribution for all the samples due to decomposition of agglomerates and large aggregates of primary silica particles under action of polymer molecules. This result is in agreement with the f(Rp) distributions for PVPysilica powders (Fig. 23) showing decomposition of silica structures responsible for formation of large mesopores at Rp)15 nm. The peaks of the PSDs in respect to the light scattering (PSD(I)) shift toward larger dPCS in comparison with PSD(N) and PSD(V). In the case of ovalbuminy silica (suspended–dried–suspended), the PSDs depend on the albumin concentration (Calb) (Fig. 24) and the distributions become more complex with Calb. At a maximal

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Fig. 23. Pore size distributions for pristine fumed silica A-300 and powders prepared by drying aqueous suspensions of (a) silica, ovalbuminysilica, and gelatineysilica and (b) silica and PVPysilica.

Calb value, a large peak of PSD(V) appears at dPCS)1 mm (Fig. 24c) corresponding to agglomerates with the main contribution of protein molecules as PSD(I) has a low intensity in this region (clearly, the scattering capability of protein molecules is lower than that of silica particle aggregates and agglomerates). Additionally, small particles at dPCS)30 nm can correspond to both albumin molecules and silica particles as PSD(I) has low intensity at dPCS between 30 and 100 nm. For all the proteinysilica samples, the PSD(V) peaks lie to the left from PSD(I) that corresponds to the availability of large agglomerates of protein molecules with smaller contribution of silica particles. Therefore, one can assume that interaction of ovalbumin with silica surface is weaker than intra-molecular interactions in protein molecules (i.e. globular structure of proteins does not decompose) in contrast to PVP molecules, which interact with the silica surfaces stronger than one molecule with another. This feature of protein– silica interactions results in a weak influence of protein molecules on the pore

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Fig. 24. Particle size distributions in respect to the light scattered intensity (solid lines), particle volume (dashed lines), and particle number (dot-dashed lines) (calculated using Eqs. (34)–(40) with Malvern Instruments software) for the aqueous suspensions of silicayovalbumin at CSiO2s0.25 wt.% and CalbyCSiO2s(a) 0.172, (b) 0.23 and (c) 0.276.

formation on drying of the proteinysilica suspensions (Fig. 23), but opposite results is observed for PVPysilica. Strong adsorption of PVP corresponds to 100–150 mg per gram of silica. PVP in the amounts above 10 wt.% (gs0.1) provides disturbing of a major portion of accessible ^ SiOH groups, as the IR band of free silanols group at 3750 cmy1 practically disappears at CPVPs17.5 wt.%. In the case of BSAysilica samples, this band is else observed at significantly larger BSA concentrations, e.g. CBSAs30 wt.%, than CPVP. Consequently, one can assume that PVP molecules adsorb in the unfolded form in contrast to proteins. Additionally, strong interaction between

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unfolded PVP and primary particles leads to decomposition of secondary particles. Therefore, interaction between silica particles covered by PVP molecules at QG1 inhibiting the formation of secondary silica particles on drying results in the structures characterized by markedly lower mesoporosity in comparison with that for dried pure silica or proteinysilica powders (Fig. 23). Interaction of fumed silica A-300 (SBET s297 m2 gy1 ) with bovine serum albumin (prepared by different methods), ovalbumin, human haemoglobin and gelatine was studied depending on pH, salinity, and concentrations of components in aqueous medium by means of adsorption and PCS methods w355x. Comparison of equilibrium (incubation time tif1 h) adsorption of proteins on A-300, minute (tif1 min) flocculation rate, and the particle size distributions measured by the PCS method shows different rearrangement of particle aggregates and agglomerates depending on pH, salinity and concentration of proteins, especially at pH close to IEP of silica or proteins. Electrokinetic mobility of proteinysilica swarms is greater than that of individual components at pH far from IEP of proteins. Changes in the Gibbs free energy (DG) on protein adsorption depend on pH (yDG is minimal at pH 2 close to IEP of silica and maximal at pH between IEP of protein and silica), concentration (yDG is maximal at Cp between 1 and 6 mgyml), type of proteins, and their preparation technique. Fumed silica A-300 (Pilot Plant of Institute of Surface Chemistry, Kalush, Ukraine; 99.9% purity, specific surface area SBETs297 m2 gy1) was heated at 673 K for several hours to remove residual HCl and other adsorbed compounds. Features of aqueous suspensions of fumed silica depending on its type and concentration, pH, salinity, temperature and pretreatment of the suspensions, and the presence of organic compounds (ethanol, polyvinyl pyrrolidone, etc.) were described in detail elsewhere w353–360x. Ovalbumin (Biom, Omutninsk, Russia, molecular weight Mf4.4=104 Da, pH(IEP)f4.6), gelatine (Moskhimfarmpreparaty, Moscow, Russia, Mf3.5=105 Da), BSA1 (TTM, Moscow, Russia, prepared by salting-out method, Mf6.7=104 Da, pH(IEP)f4.8, total concentration of lipids and fatty acids Clfaf1 wt.%), BSA2 (Allergen, Stavropol, Russia, prepared by ethanol fractionating), BSA (Sigma, Clfa0.01 wt.%) (BSA(S)), BSA (Olaine, Latvia, Clfaf2 wt.%) (BSA(O)), and human haemoglobin (VMU, Vinnica, Ukraine, HHb, Mf6.5=104 Da, pH(IEP)f6.8) were used as received. Adsorption of proteins was studied using the aqueous suspension of fumed silica A-300 (CSiO2s3.6 wt.%) added to the protein solution agitated for 0.5 h (Ts293 K). Adsorption (G) was measured after exposure for 1 h (plateau adsorption), and the suspension was centrifuged at 6000 rev.ymin for 15 min. The Biuret (or Benedict) reactant (4 ml) was added to the supernatant (1 ml). After agitating, the solution was exposed for 0.5 h, then its optical density was measured at ls540 nm to calculate the adsorbed amount of proteins comparing with the initial solution w355,361,362x. Notice that dependence of adsorption of albumins onto fumed oxides on pH was studied in details w356–358x. To evaluate the rate of protein adsorptiony flocculation, changes in the optical density (DD1) of the aqueous suspension of A-

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300 after addition of the protein solution and shaking for 1 min (i.e. tis1 min) were measured spectrophotometrically. The measurements were performed with or without the presence of NaCl (0.9 wt.% as the physiological solution). Notice that HSA adsorption onto silica surfaces at Cps1 mgyml during 1–2 min was close to the plateau adsorption, however, at lower Cps0.02 mgyml, adsorption at short incubation time was f50% of the plateau one w363x. Consequently, the minute adsorption of proteins can be used as a measure of the efficiency of fast flocculation of protein molecules with silica particles w355x. Photon correlation spectroscopy investigations were performed using a Zetasizer 3000 (Malvern Instruments) apparatus (ls632.8 nm, Qs908) at 298 K. Deionised distilled water was used for preparation of fumed silica suspension (CSiO2s0.09– 3.0 wt.%) sonicated for 10 min using an ultrasonic disperser (Sonicator Misonix Inc.) (22 kHz, 500 W). The protein (BSA(S), BSA(O), BSA2, or ovalbumin) solution was added to this aqueous suspension then shaken for 1 min (this preparation is analogous to that applied on DD1 measurement but at lower CSiO2 values). The pH values measured by a precision digital pH meter were adjusted by addition of a required amount of 0.1 M HCl or NaOH solutions, and the salinity was zero. To compute the particle size distribution (PSD) and Def (average hydrodynamic effective diameter, i.e. the particle diameter plus the double shear layer (EDL) thickness), the Malvern Instruments software (version 1.3) was utilized, assuming that particles had the rough spherical shape. The electrophoretic mobility (Ue) measurements were performed in parallel to the PSD study of the aqueous suspensions. Comparison of equilibrium adsorption (Fig. 25) and minute protein adsorptiony flocculation (using DD1 as a function of the total protein concentration Cp shown in Fig. 26) on fumed silica demonstrates strong but different effects of pH and salinity. Adsorption of proteins was studied using the aqueous suspension of fumed silica A-300 (CSiO2s3.6 wt.%) added to the protein solution agitated for 0.5 h (Ts 293 K). Adsorption (G) was measured after exposure for 1 h (plateau adsorption), and the suspension was centrifuged at 6000 rev.ymin for 15 min. The Biuret (or Benedict) reactant (18) (4 ml) was added to the supernatant (1 ml). After agitating, the solution was exposed for 0.5 h, then its optical density was measured at ls 540 nm to calculate the adsorbed amount of proteins comparing with the initial solution. To evaluate the rate of protein adsorptionyflocculation, changes in the optical density (DD1) of the aqueous suspension of A-300 after addition of the protein solution and shaking for 1 min (i.e. tis1 min) were measured spectrophotometrically. The measurements were performed with or without the presence of NaCl (0.9 wt.% as the physiological solution). Notice that HSA adsorption onto silica surfaces at Cps1 mgyml during 1–2 min was close to the plateau adsorption, however, at lower Cps0.02 mgyml, adsorption at short incubation time was f50% of the plateau one. Consequently, the minute adsorption of proteins can be used as a measure of the efficiency of fast flocculation of protein molecules with silica particles. The equilibrium adsorption of proteins is up to Gf1 mgym2 (or f300 mgyg) at pH 3.5 (i.e. between pH(IEP) of silica and proteins) for BSA with 0.9

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Fig. 25. Adsorption isotherms of different proteins: (a) BSA1, (b) BSA2, (c) BSA(S), (d) ovalbumin, and (e) gelatine on fumed silica A-300 (3.6 wt.%) at different pH values, which with asterisk show the systems with addition of 0.9 wt.% NaCl.

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Fig. 26. Changes in the optical density (DD1) in 1 min after addition of different proteins: (a) BSA1, (b) BSA2, (c) BSA(S), (d) ovalbumin, (e) gelatine and (f) haemoglobin to fumed silica A-300 suspension (3.6 wt.%) at different pH values, which with asterisk show the systems with addition of 0.9 wt.% NaCl.

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wt.% NaCl and gelatine without NaCl or at pH(IEP) of protein for ovalbumin without NaCl. The lowest equilibrium adsorption Gf0.1–0.2 mgym2 is typically observed at pH 2, which is close to pH(IEPSiO2)f2.2, and without NaCl (Fig. 25). It should be noted that the maximal Gmax values for BSA preparations with marked amounts of lipids and fatty acids can be up to 600 mgyg (concentrated A-300 suspensions at CSiO2s3–5 wt.%) and significantly lower (280–300 mgyg) for pure BSA (such as BSA(S)) that can be caused by the impact of hydrophobic admixtures on the structure of adsorbed complexes, as polar and charged proteins should shield hydrophobic compounds from the interfacial water. In the case of diluted suspensions (CSiO2s0.1–0.2 wt.%), Gmax can increase up to 1500–4500 mgyg due to very intensive flocculation of proteins with silica aggregates and agglomerates (typically observed in diluted or weakly treated suspensions w354x) because of formation of protein bridges between them, which is also affected by lipids and fatty acids present in the BSA preparations w356–358x. In the case of BSA (Fig. 25a,b and c), addition of 0.15 M NaCl leads to enhancement of adsorptionyflocculation, however, in the case of ovalbumin, the opposite effect is observed (Fig. 25d and Fig. 26d). One can see an increase in minute flocculation at different pH values with Cp except pH 2 (for all the samples without NaCl) and 3.5 (BSA2 and BSA(S)) with a DD1(Cp) maximum (Fig. 26). At low concentrations and pH 2 or 3.5, DD1(Cp) (connected with the adsorptiony flocculation rate) is higher than that at greater pH values. Thus, fast (tis1 min) flocculation gives a complex picture depending on pH with a DD1(Cp) maximum marked at pH 2. The position of this maximum depends on the type of proteins (Fig. 26), as it is at Cp-1 mgyml for BSA and HHb but for gelatine it is at Cp) 1 mgyml. For ovalbumin, maximal DD1 values are observed at Cp)0.5 mgyml and pH 2, 3.5 and 4.6. A similar maximum at pH 2 is also observed on the adsorption isotherms but at higher protein concentration (Fig. 25). According to the literature w364x, the S-like shape of the BSA adsorption isotherms (Fig. 25a) can be explained by ordering of protein due to interaction between nonadsorbed and adsorbed segments resulting in enhancement of adsorption and changes in the protein conformation approaching to native one. Other authors w365,366x explained this type of the isotherm by self-association of protein molecules leading to increase in the effective molecular weight of protein. Additionally, the steps on the isotherms can be due to reorientation of adsorbed ellipsoid-like molecules from the horizontal position to vertical one w367x. Addition of BSA1 (pH(IEP)s4.8, prepared by the salting-out method) to the silica suspension gives a minimal stability (maximal DD1 ) at low pH values (2 and 3.5) (Fig. 26a). However, the stability increases with Cp)1 mgyml at pH 2 as DD1 decreases sharply. Minute flocculation of BSA1 molecules with silica particles increases with Cp at pH 6.5 greater than that at pH 4.8 (without NaCl). However, the isotherms at these pH values are close (Fig. 25a). This is in agreement with the previous data w342,356–358,363,368–376x showing that BSA could adsorb on hydrophilic surfaces at high pH values when the surfaces and molecules were charged negatively, since electrostatic repulsive interaction could be weaker than

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attractive polar interaction and hydrophobic effects related to ordering of the interfacial water. Additional attractive effect can be caused by lipids and fatty acids present in BSA1 and ordering interfacial water stronger (as more hydrophobic) than more polar (and charged) protein molecules (ions). Larger DD1 values at pH 3.5 and 6.5 than at pH(IEP)s4.8 (in contrast to the equilibrium adsorption (Fig. 25a)) can correspond to adsorption of protein molecules in the unfolded state w191,368– 373x. Addition of NaCl leads to decrease in the difference in DD1(Cp) with changes in pH values, however, these DD1(Cp) curves lie over those for the system without NaCl (Fig. 26a) and drop with pH in contrast to ovalbumin (Fig. 26d) or gelatine (Fig. 26e) due to different contributions of electrostatic, polar and hydrophobic interactions of these proteins (and present admixtures) with the silica surfaces and the interfacial water. Minute flocculation of BSA2 (prepared by ethanol fractionating and containing lower amounts of lipids and fatty acids than BSA1) with fumed silica particles (Fig. 26b), as well as equilibrium adsorption (Fig. 25b), differs from that for BSA1, especially at pH 3.5. The suspension is less stable at low pH 2 and low Cp. Increase in Cp leads to enhancement of the suspension stability, as DD1 decreases with Cp. At pH 4.8 and 6.5, the DD1 values (as well as equilibrium adsorption) were very small and could not be measured. However, addition of NaCl leads to significant adsorptionyflocculation of BSA2 (Fig. 25b and Fig. 26b), which is minimal at pH 6.5. Notice that adsorption of BSA2 can differ from that of BSA1 due to the difference in the methods of their preparation w377x, and BSA1 includes larger amounts of lipids and fatty acids than BSA2 w378x that can affect their interaction with fumed silica in the aqueous medium. For BSA(S) (containing very low amounts of lipids and fatty acids), a DD1 maximum is observed at pH 2 too (Fig. 26c) due to aggregation of protein molecules with large silica agglomerates (formed at pH close to pH(IEPSiO2 ) (Fig. 27)) at low Cp. Increase in Cp leads to decomposition of these large silica agglomerates due to interaction with protein molecules and DD1 decreases at pH 2 and 3.5 similar to BSA2. Enhancement of pH at low Cp values is responsible for increase in the stability of the suspension (as DD1 decreases) (Fig. 26c) similar to other proteins. Notice that DD1 could not be measured at pH 4.8 and 6.5 without addition of NaCl. As a whole, adsorption BSA(S) is akin to that of BSA2, as both preparations are characterized by low amounts of lipids and fatty acids. For ovalbumin (pH(IEP)s4.6) at low Cp, the suspension stability is minimal at pH 2 when the surface charge density on silica particles is zero and large agglomerates are observed (Fig. 27), however, a DD1 (Cp ) maximum similar to that for BSA is absent (Fig. 26d). In addition, to flocculation effect of protein, aggregation of fumed silica particles at pH close to pH(IEPSiO2)s2.2 can give a marked contribution, as the effective diameter Def increases more than by order in comparison with that at pH)5 (Fig. 27). The DD1 values become nearly constant with increasing Cp of ovalbumin, especially at pH 2 and 3.5 (Fig. 26d), as adsorptionyflocculation of positively charged protein molecules is restricted due to their electrostatic lateral interactions. At pH 3.5 and low Cp (between 0.7 and 2.6

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Fig. 27. Effective diameter of particles as a function of pH in the aqueous suspensions of fumed silica (A-300 and A-330) and proteinyA-300.

mgyml), DD1 is maximal (Fig. 26d) due to different charges of ovalbumin molecules and silica surface, but DD1 changes slower at pH 4.6 (IEP of ovalbumin) with Cp, as its long-range electrostatic interaction with the silica surface reduces. Negative charges of the silica surfaces and ovalbumin molecules at pH 6.5 provide more stable suspensions (without NaCl), as DD1(Cp) minimal, especially at low Cp. However, increase in Cp to 4 mgyml leads to enhancement of the aggregation rate (Fig. 26d) as well as the equilibrium adsorption (Fig. 25d). Addition of NaCl (0.9 wt.%) provides a lower effect than that for BSA (Fig. 25) and does not give enhancement of ovalbumin adsorption at pH 2, 3.5 and 4.6. A similar picture is observed for DD1(Cp) (Fig. 26). From comparison of adsorption of BSA and ovalbumin, one can assume that BSA molecules are softer than ovalbumin ones. The DD1 values for gelatine increase with Cp (except pH 2) (Fig. 26e). Since gelatine is a product of collagen hydrolysis and does not possess a native conformation that its adsorptive and aggregative capabilities depend on pH weaker than that of BSA. Adsorption of gelatine occurs mainly due to formation of the hydrogen bonds with silica particles, and the number of these bonds can decrease with pH)2 w337x. The DD1 values and equilibrium adsorption decrease with pH from 3.5 to 6.5. The suspension is less stable at pH 2 and Cp-1 mgyml (as well as for other proteins) (Fig. 26e), however, equilibrium adsorption is minimal at this pH value as well as for BSA (Fig. 25). Addition of NaCl gives a weaker effect for

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minute flocculation of gelatine with A-300 than that for BSAyA-300, but it is akin to that of ovalbuminyA-300 (Fig. 26). The impact of human haemoglobin (pH(IEP)f6.8, plateau adsorption onto fine silica with SBETf200 m2 yg is approximately 2 h w344x) on the stability of the aqueous suspension of fumed silica is the most typical among the studied proteins, as the DD1 values decreases with pH (except pH 2 with a maximum of DD1(Cp)) (Fig. 26f) that corresponds to enhancement of the stability of the HHbyA-300 suspension with increasing pH values and shows the importance of electrostatic contribution to repulsive interaction between protein molecules and silica surface both negatively charged. Thus, despite the difference in the aggregative effects of the studied proteins, an important contribution to their interaction with the silica surfaces is connected with the electrostatic interaction increasing with pH values that results in the enhancement of the aggregative stability of the suspensions. At pH 2 close to pH(IEPSiO2)s2.2, a low amount of protein leads to marked flocculation of particles (Fig. 27) such as large silica agglomerates, which are not decomposed (rearranged) at low protein concentration and protein molecules form bridges between them. At higher pH values (or at longer incubation time on the equilibrium adsorption, as similar maximum is observed at greater protein concentration (Fig. 25)), greater amounts of proteins are needed for neutralization of the negative surface charges and for fast flocculation (Fig. 26), as decomposition (corresponding to diminution of DD1) of large silica agglomerates can occur due to interaction with protein molecules with increasing electrostatic interaction between silica surfaces and protein molecules. For soft proteins such as BSA and HHb, the aggregation rate can depend not only on adsorption values but also on the conformation state of protein molecules dependent on pH, which can also change due to adsorption and lateral interaction. To elucidate some of these effects, the PCS measurements of the proteinyA-300 systems were performed. The Def(pH) graphs have a maximum close to pH(IEP) of proteins (Fig. 27). However, at pH far from pH(IEP) of proteins the PSDs of proteinyA-300 are akin to those for the pure silica suspension but Def is smaller than that for pure silica due to decomposition of silica agglomerates and aggregates under action of protein molecules. This effect is independent of the protein type, as interaction of protein molecules with silica particles can be stronger than that between silica particles per se especially in loose agglomerates w354–358x. Therefore, the G and DD1 maxima are observed for all the studied systems at pH 2 (Fig. 25 and 26). The PSDs of A-300 in the aqueous suspension at CSiO2 from 0.1 to 3 wt.% (without NaCl) and far from IEP of silica are typically bimodal and correspond to small aggregates of 20–60 nm (including from several to dozens of primary particles with the size of 5–12 nm) and larger ones with the size up to 500 nm (up to dozens of thousands of primary particles) (Fig. 28). Agglomerates (which are typical for untreated or weakly treated suspensions w354x) with the size dPCS)1 mm are not observed in the strongly sonicated suspensions at pH)5. Addition of 0.15 M NaCl to 3% suspension (Fig. 28f) results in disappearance of the first PSD

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Fig. 28. Particle size distributions in the aqueous suspensions of fumed silica A-300 at different pH values and concentrations: (a) 0.1, (b) 0.2, (c) 0.5, (d) 1 and (e, f) 3 wt.% with respect to the light scattering intensity, particle volume and number (calculated using Eqs. (34)–(40) with Malvern Instruments software); (f) with 0.9 wt.% NaCl.

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Fig. 29. PSDs of BSA(S) oligomers at pH (a) 3.92, (b) 6.34, and (c, d) 8.5 and concentration Cps(a, b, c) 0.07 wt.% and (d) 0.7 wt.% (calculated using Eqs. (34)–(40) with Malvern Instruments software).

peak at dPCS between 10 and 30 nm observed without NaCl (Fig. 28e). As a whole, the bimodal PSD (Fig. 28f) slightly shifts toward larger dPCS in comparison with other PSDs shown in Fig. 28. The PSDs of BSA(S) (Fig. 29) depict large aggregates of protein molecules with the main peak over the 60–200 nm range, since special conditions (T, pH, Cp, salinity) to decompose these protein molecule aggregates were not applied. Notice that for BSA2, Def)1 mm at different pH values (3.39, 5.19, 6.96 and 8.08) and Cps0.045 wt.%; and for ovalbumin, Def)3 mm at pH 6.69 and Cps0.1 and 1 wt.%. Three types of BSA (Figs. 30–32) and ovalbumin (Fig. 33) interacting with secondary silica particles typically give the PSDs shifted toward larger dPCS values near or above 100 nm (except BSA(S)yA-300 at pH 8.53 (Fig. 30d)). However, only a minor number of the secondary particles is larger than 1 mm (Figs. 30–33, curves 3), especially at pH far from pH(IEP) of proteins. Notice that larger aggregates and agglomerates give greater contributions to the PSDs with respect to the light scattering (curves 1) and particle volume (curves 2) than that of the PSDs

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Fig. 30. Particle size distributions in the aqueous suspensions of fumed silica A-300yBSA(S) at the concentrations of 0.45 wt.% A-300 and 0.07 wt.% BSA and different pH values: (a) 3.24, (b) 3.84, (c) 6.37 and (d) 8.53 with respect to the light scattering intensity, particle volume and number (calculated using Eqs. (34)–(40) with Malvern Instruments software).

connected to the particle number (curves 3). Similar relationships are characteristic for the aqueous suspensions of fumed oxides w354x due to features of the PCS method (relatively long wavelength of the used lasers) and the type of the PSDs of fumed silicas including different types of secondary particles. At pH values close to the IEP of proteins, their aggregation with fumed silica particles more effective and the Def value becomes larger than 1 mm (Fig. 27) and the PSDs depict only large secondary particles (therefore, these PSDs are not shown in figures). Notice that pH(IEP) of the studied proteins slightly differs that can give a small displacement of the Def(pH) curves. The displacement towards higher or lower pH values gives diminution of Def (Fig. 27) and aggregates even smaller than 100 nm appear in the PSDs (Figs. 30–33), and the higher or lower the pH value than pH(IEP) of proteins, the smaller the aggregates and the Def value. For ovalbuminy A-300 at Cps1 mgyml (Fig. 33), changes in the PSDs with pH are in agreement with analogous changes in DD1 (Fig. 26d). For example, a minimal Def is observed at pH 6.71 (Fig. 33f), the next one is at pH 2.48 (Fig. 33a), and large Def is

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Fig. 31. Particle size distributions in the aqueous suspensions of fumed silica A-300 and BSA2 at the concentrations of 0.18 wt.% A-300 and 0.045 wt.% BSA and different pH values: (a) 2.52, (b) 3.46, (c) 5.48, (d) 6.96 and (e) 8.31 with respect to the light scattering intensity, particle volume and number (calculated using Eqs. (34)–(40) with Malvern Instruments software).

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Fig. 32. Particle size distributions in the aqueous suspensions of fumed silica A-300 and BSA(O) at the concentration of 0. 09 wt.% A-300 and 0.011 wt.% BSA and pH 6.65 with respect to the light scattering intensity, particle volume and number (calculated using Eqs. (34)–(40) with Malvern Instruments software).

observed at pH 4.04 (Fig. 33c), 4.21 (Fig. 33d) and 5.17 (Fig. 33e) and this order is akin to that for DD1 at similar Cp values (Fig. 26d). For BSA(S) and BSA2, changes in the PSDs (Figs. 30 and 31) and DD1 (Fig. 26c and b) at low pH are not so compatible as that for ovalbumin maybe due to lower CSiO2 values. However, at high pH values, e.g. at pH 6.96 (Fig. 31d), the PSDs for BSA2yA-300 and A300 (Fig. 28b) are very similar that is in agreement with very low DD1 values (not measured) for BSA2yA-300 at pH 6.5. The PSD for BSA(S)yA-300 at high pH (Fig. 30d) is similar to that for A-300 at pH 6.37 (Fig. 28c), and DD1 values for BSA(S)yA-300 were very low at pH 6.5 (Fig. 26c). Notice that the PSDs for more concentrated suspensions with proteinyA-300 (CSiO2 s3.6 wt.%) were not measured by the PCS method due to strong scattering effects. Since in many cases, the lion’s share of particles (especially according to the PSDs calculated with respect to the particle number) corresponded to dPCS
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Fig. 33. Particle size distributions in the aqueous suspensions of fumed silica A-300 and ovalbumin (OA) at the concentrations of 0.9 wt.% A-300 and 0.1 wt.% OA and different pH values: (a) 2.48, (b) 3.13, (c) 4.04, (d) 4.21, (e) 5.17 and (f) 6.71 with respect to the light scattering intensity, particle volume and number (calculated using Eqs. (34)–(40) with Malvern Instruments software).

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Fig. 34. Electrophoretic mobility as a function of pH of particles of pure A-300, BSA(S), BSA2, and proteinyA-300.

is greater than that of A-300 or the corresponding proteins far from pH(IEP) of proteins, as their mobility is close to zero at this pH. Consequently, the Ue values of proteinysilica swarms depend mainly on the protein coverage of silica particles. Strong interaction between protein molecules and silica particles does not give significant changes in the PSDs far from pH(IEP) of proteins (Figs. 30–34) but Def of proteinyA-300 is smaller than that of silica (Fig. 27), and their surface charge density s0 can be higher (e.g. due to orientation of –COOy groups of adsorbed protein molecules outside) than that for pure silica, which is relatively low at pH-7 (Fig. 35). To evaluate the surface charge density, potentiometric titration was performed using a Teflon thermostated vessel in nitrogen atmosphere free from CO2 at 25 8C. The solution pH was measured by using a PHM240 Research pH-meter (G202C and K401 electrodes) coupled with REC-61 recorder. The surface charge density was calculated using the potentiometric titration data for a blank electrolyte solution and fumed silica suspension (0.1 wt.%) at a constant salinity of 10y3 M NaCl from difference of acid or base volume utilized to obtain the same pH value as that for the background electrolyte of the same ionic strength DVcF according to following equation s0s , where DVsVsyVe is the difference mSBET between the base (acid) volume added to electrolyte solution Ve and suspension Vs to achieve the same pH; F is the Faraday constant, c is the concentration of base (acid), m is the weight of oxide.

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Fig. 35. Surface charge density for A-300 in the aqueous suspension (CSiO2 s0.2 wt.%) at 0.001 M NaCl as a function of pH (measured by titration method).

Additionally, according to the infrared spectroscopy data w353x, interaction between protein molecules and fumed silica particles leads to disturbance of a significant portion of ^ SiOH groups at a low amount of protein and to their entire disturbance at CBSA yCSiO2f0.4. This is possible if a major portion of oligomers and polymers of BSA molecules decomposes on interaction with fumed silica, whose aggregates and agglomerates are decomposed too. Thus, the enhancement of Ue of proteinysilica comparing with that of individual protein molecules or silica particles can be explained by changes in the structure of adsorbed protein molecules leading to augmentation of the charge density at the shear plane in the EDL, as well as by partial decomposition of silica aggregates and protein oligomers due to their interaction. Adsorption of gelatine at pH 3.5 corresponds to maximal changes in the Gibbs free energy of adsorption (DG) (Fig. 36e) calculated as follows DGsyRgTln

x 1yx

(80)

where xsCads yCp, Cads is the adsorbed protein concentration, and Rg is the gas constant. Similar DG values (relatively large) are characteristic for BSAysilica at the same pH but with addition of NaCl (Fig. 36a,b,c), as this pH value corresponds to different sign of the charges of silica particles and protein molecules giving their attractive electrostatic interaction. For ovalbuminysilica, the maximal yDG values are smaller (Fig. 36d) maybe due to lower contribution of this interaction. Notice that maximal values of the DG module close to 8–10 kJymol are typical for adsorption of proteins onto oxide surfaces w363,368–373x. The presence of lipids and fatty acids in the BSA preparations can give a slight diminution of yDG

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301

Fig. 36. Changes in the Gibbs free energy (DG) due to adsorption of different proteins: (a) BSA1, (b) BSA2, (c) BSA(S), (d) ovalbumin, and (e) gelatine on fumed silica A-300 (3.6 wt.%) at different pH values, which with asterisk show the systems with addition of 0.9 wt.% NaCl.

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(comparing BSA1 (Clfaf2 wt.%) (Fig. 36a) and BSA(S) (Clfa-0.01 wt.%) (Fig. 36c) at pH 3.5 with NaCl) due to the differences in the structures of adsorption complexes caused by the necessity to reduce the ordering action of hydrophobic admixtures on the interfacial water. To compute the distributions of changes in the Gibbs free energy (f(DG)) on protein adsorption, the Langmuir equation w379x was used as the kernel of the adsorption isotherm equation in the form of Fredholm integral equation of the first kind CeqexpŽyDGyRgT.

| 1qC

us

eq

expŽyDGyRgT.

fŽDG.dŽDG.

(81)

where usGyGm is the relative adsorption, and Gm is the monolayer coverage. This equation was solved using a modified regularization procedure CONTIN w100,101x. It should be noted that the f(DG) peak positions are independent on Gm values in contrast to the intensity of these peaks. The graphs of f(DG) (Fig. 37) as well as DG(Cp ) (Fig. 36) show that the yDG values are typically greater on addition of 0.15 M NaCl. This effect can be due to several reasons such as changes in (i) the EDL of protein molecules (ions) and charged silica particles and electrostatic interaction between them; (ii) the structure of protein molecules; (iii) aggregation of these molecules per se or with silica particles; and (iv) PSDs of silica aggregates and agglomerates. The f(DG) distribution for BSA(S)ysilica (with NaCl) shifts toward large yDG values comparing with that for BSA1 (Fig. 37b) (due to the mentioned effect of hydrophobic admixtures), as the BSA(S) adsorption isotherm is steeper (Fig. 25a and c). However, f(DG) for ovalbuminysilica (with NaCl) lies at higher yDG that that for adsorbed BSA(S) due to elevating adsorption with decreasing Ceq-1 mgyml (Fig. 25d). Similar results are seen at pH 2 for a high-energy peak at yDG)15 kJymol (Fig. 37a), however, for ovalbumin, a low-energy peak at yDG-5 kJymol is also observed. Opposite order of the f(DG) curves for these proteins is seen at their IEP (Fig. 37c). Notice that some difference in the positions of the high-energy f(DG) peaks (Fig. 37) and the DG minima (Fig. 36) can be caused not only by approximate calculations of these values using simplified equations but also by experimental errors for the G(Ceq) graphs. Consequently, changes in the free energy on protein adsorption onto fumed silica depend strongly on pH, salinity, presence of hydrophobic admixtures and protein concentration. Thus, according to measurements of flocculation of protein molecules with fumed silica particles at short incubation time of 1 min, low amounts of proteins (taking part in two main processes: flocculation with silica particles and decomposition of secondary silica particles with weak inter-aggregate binding in agglomerates and inter-particle binding in aggregates) do not provide significant decomposition of large silica agglomerates at pH 2 (close to IEP of fumed silica A-300) and protein molecules can form several bonds with particles from neighbouring aggregates that results in appearance of the DD1(Cp) maximum corresponding to maximal floccu-

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Fig. 37. The distributions of changes in the Gibbs free energy (f(DG)) due to adsorption of proteins on fumed silica A-300 (3.6 wt.%) at pH (a) 2, (b) 3.5, (c) pH(IEP) of proteins (4.8 or 4.6), and d 6.5; asterisk (and solid symbols) shows the systems with addition of 0.9 wt.% NaCl.

lation. A similar maximum is observed upon equilibrium adsorption at pH 2 but at greater protein concentration due to changes in different secondary particles rearrangement during longer incubation time of 1 h. Increase in pH from 3.5 to 6.5 gives decrease in the equilibrium and minute adsorptionyflocculation of proteins on A-300. Increase in the protein concentration and addition of 0.15 M NaCl differently affect adsorptionyflocculation at the incubation time of 1 min and 1 h. The PCS measurements show that intensive rearrangement of secondary particles of fumed silica occurs at pH close to IEP of silica under action of protein molecules at high concentrations, which is in agreement with the adsorption data. Maximal flocculation of proteins with silica is observed at pH close to IEP of proteins, as effective diameter of secondary particles increases by order. Electrokinetic mobility of proteiny silica swarms is greater than that of individual protein molecules or silica particles at pH far from IEP of proteins. Changes in the Gibbs free energy on protein

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adsorption depend on: (i) pH: yDG is minimal at pH 2 close to IEP of silica and maximal at pH between IEP of protein and silica; (ii) protein concentration: yDG is maximal at Cp between 1 and 6 mgyml; (iii) type of proteins: yDG is smaller for ovalbumin than BSA or gelatine; and (iv) protein preparation technique: yDG is greater for the BSA preparations with lower concentrations of lipids and fatty acids. The adsorption behaviour of the mussel adhesive protein Mefp-1 on a hydrophilic surface was studied by surface plasmon resonance and PCS methods at pH values of 4.5 and 6.5 under aerobic conditions and at the salinity of 0.1 M NaCl w380x. In this environment, Mefp-1 molecules aggregate by cross-linking, likely via Dopa– Dopa quinone charge transfer interactions. The initial rate of aggregation increases with increasing pH, as could be derived from PCS measurements. The degree of aggregation determines the adsorption plateau value of Mefp-1. Step-like adsorption curves have been found at pH 6.5, as well as at pH 4.5, which can be interpreted as the adsorption of an ad-layer of Mefp-1 aggregates onto the initially adsorbed Mefp-1 layer on the surface. The rate of formation of this second layer increases with increasing pH and Mefp-1 concentration. The affinity of the ad-layer for the first adsorbed layer appears to be much smaller than the affinity of the first layer for the surface (polyvinyl alcohol). Probably, also the ad-layer formation proceeds by the establishment of specific cross-links with the first layer of adsorbed Mefp-1 w381x. Silica nanoparticles synthesised with covalently linked cationic surface modifications demonstrated their ability to electrostatically bind, condense and protect plasmid DNA. These particles could be utilised as DNA carriers for gene delivery w381x. All nanoparticles were sized between 10 and 100 nm and displayed surface charge potentials from q7 to q31 mV at pH 7.4. They were produced by modification of silica particles with either N-(2-aminoethyl)-3-aminopropyltrimethoxysilane or N-(6-aminohexyl)-3-aminopropyltrimethoxy silane. All particles formed complexes with pCMVbeta plasmid DNA as evidenced by ratio dependent retardation of DNA in the agarosegel and co-sedimentation of soluble DNA with nanoparticles. High salt and alkaline pH did inhibit complex formation. Absorption onto the particles also decreased the hydrodynamic dimensions of plasmid DNA as shown by PCS. Complexes formed in water at a wyw ratio of Si26H:DNA (pCMVbeta) of 300 were smallest with a mean hydrodynamic diameter of 83 nm. For effective condensation a wyw ratio of Si26H:DNA of 30 was sufficient. Absorbed DNA was protected from enzymatic degradation by DNase I w381x. Characterisation of immunoglobulin G bound to latex particles was performed by Ortega-Vinuesa et al. w382x using surface plasmon resonance, electrophoretic mobility, and PCS methods studying passive adsorption and covalent coupling of a polyclonal IgG and a monoclonal preparation of IgG against HSA to a carboxyl latex particle. The functional activity of the coupled protein was then assessed by quantitative immunoassays for the antigen. The antibody-labeled particles were studied with respect to electrokinetic behaviour in pH and ionic strength titration, stability, antibody functionality and immunoaggregation reactions. Important differ-

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ences were observed between the two sets of particle preparations throughout the series of experiments. The differences could be attributed to the coupling of the IgG molecules to the particles by the two different adsorption protocols. When proteins were chemically bound to the polymer surface, it was necessary to activate the carboxyl groups with a carbodiimide moiety that in our case was positively charged. The differences in characteristics between the adsorbed and the coupled antibody particles are thought to be due to the fact that in the covalent coupling protocol some carbodiimide molecules remained linked to the particles, which altered the average electrical state of the outer layer in comparison with those samples where antibodies were physically adsorbed. However, the isoelectric point of the monoclonal antibody was lower (5.4) than the IEP of the polyclonal antisera (6.9), which could explain why the IgG-latex complexes created with monoclonal molecules were colloidally more stable at neutral pH than those created with the polyclonal antisera w382x. Olivier et al. w383x proposed orosomucoid-coated polyisobutylcyanoacrylate nanoparticles as a biomimetic drug carrier. Stability of the modifier layer was evaluated in the presence of serum. According to the PCS and turbidimetry data, nanoparticle degradation was mainly responsible for orosomucoid desorption. With diluted human serum, oromucoid desorption was reduced, which allowed the study of the effect of the orosomucoid layer on serum protein adsorption, which decreases dramatically. According to investigations w353–355,380–382,384–388x, highly dispersed oxides (such as fumed silica, alumina, titania and mixed oxides) can very effectively interact with proteins. The theoretical sedimentation time of a 1 mm particle is approximately 210 days; for a 10 mm particle it is 50 h and for a 100 mm particle 30 min. Therefore, for fumed silica interacting with proteins the sedimentation is not important effect as in the case of larger particles (e.g. with latex or precipitated silica) at d)100 mm. Porous or highly dispersed silicas with modified surfaces can provide selective adsorption of various chemical substances including toxic metabolites and xenobiotics, which may persist in human organism (‘sorption medicine’) w388x. However, differently modified silicas may have diverse effects on cell membranes. It is well known that silica of numerous polymorphic forms reacts with membranes of mammal, red blood cells (RBCs), etc. causing haemolysis. Therefore, perspective samples of silicas to be modified should be tested for their membranotoxicity prior to the clinical applications. The impact of thermally treated and chemically modified fumed silica on RBCs was examined by optical measurements by using flow cytometry w388x based on the PCS method, which is a powerful technique to study different biocells, e.g. red blood cells w107,388–390x. Additionally, this technique is an important tool in the biomedical sciences for identifying and separating various populations of white blood cells w107x. Makino et al. w390x prepared four types of hydrophilic gel microcapsules (MC) containing water by an interfacial polymerisation method. The microcapsule membranes were hydrophilic and soft and had two-sublayer structures from electrophoretic mobility measurements and from the analysis of the data with Ohshima’s

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electrokinetic theory for soft particles. The outer sublayers of two MCs were negatively charged and those of others were slightly positively charged and the latter surfaces were softer. By PEGylation, the surface charge density in the membranes decreased and the surface became softer. The membrane of red blood cells (RBC) is also soft and is composed of two-sublayers, the outer sublayer of which is negatively charged and the inner one is positively charged. The interaction of four types of microcapsules with RBC was studied. It was found that microcapsules with soft surfaces did not interact with RBC, even though the microcapsule surfaces were positively charged and the surface of RBC was negatively charged. However, microcapsules with negatively charged but harder surfaces interacted with RBC to introduce haemolysis. The membrane surface of MC 2, which was obtained by PEGylation of MC 1, becomes softer than that of MC 1 so that the interaction with RBC was weakly suppressed. From these, it was concluded that the dominant factor to control the interaction between synthetic polymer surfaces and biological cell surfaces is not the surface charges carried by the polymer surfaces but the softness of the polymer surfaces w390x. The light scattered (forward, FSC, usually at 18-u-38 and sideward scattered, SSC, at us908) by cells interacting with silica was observed during the first 5 min of the reaction with a FACSCalibur flow cytometer (Becton–Dickinson Immunocytometry Systems) equipped with a 15 mW argon-ion laser (488 nm) w388x. The FSC and SSC signals were collected in linear mode. Analysis of the data was performed with CELLQuest software (Becton Dickinson). Cell debris and aggregates were eliminated from the analysis. In the first set of experiments, washed human RBCs were used to interact with fumed silica A-300 and silicas prepared from the initial A-300 by dehydroxylation under various thermal conditions. Their light scatter (forward and side light scatter) in 0.01% silica colloidal dispersion was measured uninterruptedly within the first 5 min of the reaction by means of the flow cytometry. The haemolytic effect of fumed silica particles was evaluated by photometric measurement of haemoglobin in the supernatant for 1.5 h. The light scatter of affected RBCs in conjunction with the degree of haemolysis revealed that silica particles with different surface properties had a different influence on the RBCs. After thermal treatment of silica, samples, in general, showed the tendency to increase, and then, to decrease their membranotoxic effect with the maximum for the sample heated at 600 8C. Thus, the spatial organisation or particle secondary particles and surface hydroxyls are likely to be a critical point in the adsorptive behaviour of silicas. In the second set of experiments, the authors w388x examined the haemolytic properties of silicas modified by –CH3, –RCOOH and –RNH2 groups. The initial A-300 provides the most haemolytic effect in comparison with modified samples. The haemolytic activity of ‘aminoaerosil’ was equal to 1y3 of the initial A-300 activity. However, silicas modified by –CH3 and –COOH groups actually did not cause RBC lysis due to changes in the electrical double layer and electrostatic interaction between silica surfaces and cells. The authors w388x concluded that RBCs respond to silica in a sample-specific and non-random manner. Because of ready availability and high sensitivity to external factors, RBCs offer a

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convenient and informative model for probing the surface properties of silica. The method of ‘flow erythrogram’ allows one to analyse cell responses on the initial phase of silica–cell interaction w388x. Delgado-Calvo-Flores et al. w391x studied dependence of the effective diffusion coefficient on ionic strength of isolated monodisperse polystyrene particles (f200 nm in diameter) with different superficial groups, sulfonated and carboxylic, by means of PCS. The sulfonated latexes behave as could be expected according to the DLVO theory of colloidal stability. However, the carboxylic latexes exhibit a stabilisation at ionic strengths higher than their critical coagulation concentration (CCC). Although the hairy layer model can explain the results below the CCC, it cannot explain re-stabilisation. Due to both the charge and the hydrophilic character of carboxylic latexes, the authors suggest the possible existence of a hydration force at high salt concentration. This would give rise to repulsive interaction energy between particles that could be responsible for stabilisation of these systems at high ionic strengths w391x. Similar effects can influence interaction of protein molecules with organic or inorganic particles. Additionally, the physicochemical properties of proteins can change under action of external pressure and electric fields w392x. Notice that the most food dispersions (emulsions and foams) are stabilised by low-molecular-weight emulsifiers, proteins and their mixtures w393x. The functional properties of proteins in foods are related to their structural and other physicochemical characteristics. A fundamental understanding of the physical, chemical and functional properties of proteins and the changes in these properties undergo during processing is essential if the performance of proteins in foods is to be improved and if under-utilised proteins, such as plant proteins and whey proteins, are to be increasingly used in traditional and processed food products w394x. The precise role of protein structure and how its structural transformation in a food contributes to functional properties are not well understood and are the topic of much research w395,396x. The physical principles governing the formation and stability of food colloids (foams and emulsions) are complex, especially if protein macromolecules are involved as emulsifiers w397,398x. The dynamic behaviour of protein films is recognized as being of importance to the formation and stability of food colloids in which proteins are added as the emulsifier w399,400x. The study of such dynamic behaviour can be described by interfacial rheology and PCS. 5. Interaction of living microorganisms with polymers and solid particles Mobility of bacteria was studied by many authors by means of PCS (w34,401– 404x and Refs. in these papers). This ability of PCS is of importance in respect of elucidation of the influence of media on living microorganisms. Clearly, determination of the size distribution of mobile microorganisms by the standard PCS techniques gives the Rh values smaller (in contrast to contribution of the electrical double layer (shear layer) increasing effective Rh ) than true R because of contribution of own mobility of microorganisms to their summary motion. The difference between their Rh (estimated with PCS) and Re (measured with electron microscopy methods) values may be used to evaluate the microorganism mobility. The velocity

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distribution P(V) can be estimated using the DT,i value for inactivated microorganisms and equation w402,405x w (2)

g Žt.s1qe

xbqŽ1yb.|

`

y2DT,iq2t

y

0

z2 B ™ E sinD™ qVtG PŽV.dV ™ ™ qVt C

F

|

(82)

~

where b is a portion of inactivated microorganisms. In the case of the Maxwell isotropic distribution of the velocity w

B

V E2z F| D 2V0 G ~

PŽV.s4pV2Ž2pV02.y1.5expxyC y

(83)

where V0 is the average velocity, that the ACF can be written as follows w

B qVt E2z

y

D

G(1)Žt.sexpxyC

y2

F| G ~

(84)

If the linear velocity distribution corresponds to the gamma-distribution that the ACF is the Lorentzian one. For isotropic motions, there is a relationship

|

I(1)Žv.;

`

PŽV. v yq

dV V

(85)

or dI(1)Žv. dv

1 BvE ; PC F v DqG

(86)

The latter equation reveals that the information about the velocity distribution may be obtained by differentiation of the heterodyne spectrum. The isotropic velocity distribution and isotropic form factor (required condition qR<1) results also in qt scaling of G (1)(t). This method was applied to investigate the mobility of, for example, Pseudomonas putida w405x, Dunaliella viridis w406x and E. coli w407x, etc. This approach was also used to study the impact of enterosorbent (fumed silica) particles and such medicinal polymer as polyvinyl pyrrolidone (PVP) on the mobility of living flagellar microorganisms Proteus mirabilis 187 (PM187). Solution of Eq. (82) was obtained with the CONTIN procedure modified by one of the authors to compute not only the PSDs but also the velocity distributions w353x. It should be noted that the DT,i value in Eq. (82) can be esily determined, since the f(DT) distribution for living (mobile flagellar) and partially inactivated microorganisms includes separated two peaks (Fig. 38) corresponding to the motion of

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Fig. 38. Distribution function of the diffusion coefficient of individual P. mirabilis 187 (PM 187) 106ycm3 in the physiological buffer. Two peaks correspond to (1) inactivated (i.e. participating only in Brownian motion) and (2) living mobile (ownqBrownian motion) microorganisms.

inactivated (participating only in Brownian motion) and living mobile (characterised by both own and Brownian motions) microorganisms (P. mirabilis 187). One can assume that the interaction of microorganisms with fine silica particles is determined to a great extent by interaction of protein molecules incorporated into their membranes with oxide particle surfaces, since the latter strongly interacts with protein molecules w355,384,385,388x. An increase in concentration of fumed silica A-300 (SBETf300 m2 yg) in the aqueous suspension (buffered) leads to decrease in the mobility of a portion of PM187 (concentration CPMf106 yml). However, the characteristic movements of living PM187 are also observed (Figs. 39 and 40). Features of PVPyfumed silica swarms forming in the aqueous suspension reflect in interactions with PM187 (CPMf106 yml) depending on CPVP. It should be noted that PVP has polar N–C_ O bonds similar to those in proteins which can form strong hydrogen bonds with both SiOH groups on silica particles and hydroxyls, RNHq and other similar groups of protein and other molecules in membranes of microorganisms. PVPyfumed silica affects the PSDs stronger than individual fumed silica does, as PSD markedly shifts towards larger size for PM187yPVPysilica (Fig. 39a) w353x and diffusion coefficient decreases (Fig. 40a). In the later system, the proper mobility of flagellar PM187 decreases significantly (Fig. 39b and Fig. 40) because of the interaction with PVPysilica in contrast to interaction of PM187 with pure silica in the diluted suspensions (CSiO2s0.033–0.1 wt.%). This interaction depends on CPVP and CSiO2 (Figs. 39 and 40). To elucidate these effects we may also analyse some results of the investigations of interaction of PVP with fumed

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Fig. 39. (a) PSDs for pure silica (MCA-suspension), living microorganisms P. mirabilis 187 (PM 187), mixture of silica and PVPySiO2 with PM 187; and (b) velocities of PM 187 and their mixture with silica or PVPysilica computed at unfixed regularization parameter.

silica performed by PCS, 1H NMR, IR, rheology, adsorption and thermally stimulated depolarisation (TSD) methods w353,354,357–360x. The average diameter of PVPysilica swarms can decrease in comparison with that of secondary particles of pure silica due to decomposition of silica agglomerates by PVP adsorbed in the unfolded state (Figs. 28 and 41) w353,354,359x. Additionally, the adsorption potential computed in respect to the disturbed interfacial water using the 1H NMR spectra with entire freezing-out of the bulk water and layer-by-layer freezing-out of the interfacial water at 210 K-T-273 K shows that the concentration of weakly bound water (Table 10, Cwuw ) are lower in the pure silica suspension or the pure PVP solution than that for PVPysilica, however, for the latter, the amounts of strongly bound water (Csuw) decreases w353,360x. Besides, the thermally stimulated depolarisation study of the PVPysilica suspensions shows changes in the state of water and polymer molecules at the interfaces with increasing CPVP and

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Fig. 40. (a) Distribution function of the diffusion coefficient for individual P. mirabilis 187 (PM 187) 106ycm3, and with addition of fumed silica A-300 (0.1 wt.%), PVP, and PVPyA-300; (b) velocity distribution function for individual PM 187, and with addition of A-300 (0.1 wt.%) and 0.014 wt.% PVPy0.1 wt.%A-300 with unfixed regularisation parameter a.

CSiO2 (Fig. 42) w353,360x. Silica particles in the concentrated aqueous suspension (CSiO2s7 wt.% (Fig. 42, curve 4) or 14 wt.% (curve 6)) disrupt the hydrogen bond network in water in a significant portion, as the bulk free water (a peak the distribution of the activation energy of TSD (f(Ea)) at 44 kJymol in curve 1) is practically absent at such a concentration of silica. In the case of PVPysilica suspension at the same CSiO2 (curves 5 and 7) or lower CSiO2 (curve 3), the amounts of the bulk (practically undisturbed) water are larger than that for pure silica suspensions. However, the displacement of this peak towards lower energy with CSiO2 is observed (i.e. average number of hydrogen bonds per a molecule tends to diminish). Consequently, shielding of the silica surface by polymer molecules results in appearance of nearly free bulk water disappearing in the PVPysilica suspensions at large CSiO2s14 wt.% (curve 7) or in pure silica suspension (curves 4 and 6) or pure PVP solution at CPVPs0.56 wt.% (Fig. 42, curve 8). Additionally, increase in

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Fig. 41. Particle size distributions for PVPysilica at CSiO2 s1 wt.% and CPVP s0.04 wt.%, and different pH values: (a) 5.44, (b) 5.8, (c) 7.0, (d) 8.4 and (e) 10.0.

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Table 10 Parameters of interfacial water layer for pure silica and silicayPVP suspensions (CSiO2f6 wt.%) w353x System

yDGs (kJymol)

yDGw (kJymol)

Csuw (mgyg)

A-300 a A-300q0.3 wt.% PVP A-200 1 wt.% PVP A-200q1 wt.% PVP

3.2 2.5 3.0 1.6 3.0

1.3 1.0 1.4

700 500 730 300 520

2

y1

0.9

Cwuw (mgyg)

gS (mJym2)

700 900 680

253 186 279

1400

220

a

Note: SN2f300 and 190 m g for A-300 and A-200, respectively; in the physiological buffer solution; DGs and DGw are the changes in the Gibbs free energy of water strongly and weakly disturbed w by silicayPVP, respectively; Csuw and Cuw are the concentrations of the unfrozen waters strongly and weakly bound to the surfaces; gS is the change in free surface energy.

the concentration of silica in PVPysilica dispersion results in appearance of water molecules with a low number of hydrogen bonds per a molecule corresponding to the f(Ea) peak at low Eas10-15 kJymol, which shifts towards lower Ea with increasing CSiO2qCPVP. These results are in agreement with changes in the Gibbs free energy of the interfacial water in the aqueous suspensions with PVPysilica (Table 10) w353,360x.

Fig. 42. Distributions of the activation energy of thermally stimulated depolarisation (TSD) for pure water (curve 1), water (7 wt.%) adsorbed on silica in the gas phase (2); silica suspension at CSiO2s (4) 7 and (6) 14 wt.% (4); PVPysilica at (3) CSiO2 s3 wt.% and CPVP s0.12 wt.%; (5) CSiO2s7 wt.% and CPVPs0.28 wt.%; (7) CSiO2s14 wt.% and CPVP s0.56 wt.%; and pure PVP solution at CPVPs0.56 wt.% (8).

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Fig. 43. (a) Turbidity of PVPysilica suspension vs. CPVP at constant CSiO2s6 wt.% (curve 1) and Dmin (average diameter for the first peak in the particle size distribution) as a function of CPVP (curve 2); and (b) effective viscosity of PVPysilica suspension vs. (a) CPVP at constant CSiO2 s6 wt.% for fresh (curve 1) and aged for 3 months (curve 2) dispersions; and sediment volume as a function of CPVP for suspension aged during 10 days (curve 3); and (b) CSiO2 at CPVPyCSiO2s0.1. (Rheological investigations of the ball-milled or sonicated suspensions of PVPysilica were performed using a Rheotest 2.1 (VEB MLW Prufgerate-Werk Medingen Sitz Ftreital, Germany) rotary viscometer with a cylinder–cylinder system at the clearance between the cylinders of 0.4 mm. The effective viscosity (h) was determined at the shear rate bss1312 cy1 at 293 K).

Immobilisation of even low amounts of PVP results in changes in the particle size distribution (Fig. 41), and the size of large agglomerates is lowered, however, the diameter of the smallest particles (Dmin) grows then decreases with CPVP (Fig. 43a), since interaction between PVP molecules (at great surface coverage) is weaker than that between them and silica surfaces (at low coverage) w353,354,359x. Consequently, PVP molecules disrupt agglomerates and a portion of aggregates. Complete decomposition of aggregates by PVP molecules is possible (according to the IR spectra w353x), but re-arrangement of aggregates with PVP and silica particles

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Table 11 Influence of PVP pre-adsorbed on fumed silica A-300 on ovalbumin and gelatine adsorption from the aqueous solution w353x CA300 (wt.%)

CPVP (wt.%)

Covalb (mgyg)

Cgelatine (mgyg)

3 3 3 4 4 4

0 0.15 0.3 0 0.2 0.4

170 80 30 180 102 40

380 210 116 224 190 100

makes difficult to analyse this effect. Dmin growing with CPVP (Fig. 43) is maximal at CPVPs0.24 wt.%, which is lower than CPVP required for statistical monolayer coverage (CPVP yCSiO2s0.18–0.2) or CPVP for PVP strongly bound (CPVP yCSiO20.09) to the silica surface. The suspension turbidity (t) (Fig. 43a, curve 1), as well as Dmin, rises due to PVP aggregation with small oxide aggregates with simultaneous decomposition of large agglomerates with increasing CPVP to 0.4 wt.%. However, t changes slightly with subsequent enhancement of CPVP to 1.2 wt.%. The sediment volume formed during 10 days depends on CPVP (Fig. 43b, curve 3). The PVPy silica suspension is stable at CPVPs0.12–0.24 wt.% and does not practically exfoliate for 10 days. At the last CPVP value, a maximal viscosity is observed (Fig. 43b, curve 2) due to suspension structurisation on suspension aging. Formed structures are disrupted on rheological investigations and decomposition of interparticle bonds with increasing shear rate (bs) gives deviation of the curves from those for Newton liquid flow. If the rate of rearrangement of decomposed bonds is less than that of their decomposition that the viscosity tapers off (on rheological measurements) until equalisation of the rates of direct and reverse processes. The viscosity dependence on CPVP at bss1312 cy1 changes due to aging of the suspension. For suspension aged for 3 months, h has a higher maximum at CPVPf0.2 wt.% and lower values at CPVP)0.4 wt.% (Fig. 43b, curve 2) than that for freshly prepared suspension (Fig. 43b, curve 1), as dispersion structurisation is a long process, which can result in alterations in the structure of both dense adsorbed layer and inter-particles bonds with CPVP w354,359x. Thus, aggregation in the PVPy SiO2 system increase with CPVP and a maximal viscosity is observed at CPVP y CSiO2f0.24. Notice that these effects caused by PVP (in respect to the cell surfaces) are utilised in certain drug compositions. Pre-adsorbed PVP reduces the adsorption of albumin or gelatine (Table 11) because of shielding of surface silanols responsible for intermolecular interaction with proteins. However, at the same time, immobilised PVP increases interaction of PVPysilica swarms with PM187 with increasing CPVP (that leads to reduction of the mobility of PM187 (Fig. 39 and 40)) similar to enhancement of the viscosity and turbidity of PVPysilica suspension with CPVP (Fig. 43). The mentioned investigations of the aqueous suspensions of PVPysilica by means of NMR, TSD,

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Fig. 44. Distribution function of the diffusion coefficient of living P. mirabilis 187 (PM 187) (concentration 106ycm3) in the physiological buffer (1), and after their treatment with addition of (2) penicillin and (3) penicillinyethanol.

PCS and adsorption methods (Figs. 41–43, Table 10 and Fig. 11) reveal significant changes not only in the particle size distribution, but also in the inner structure of agglomerates and aggregates the interfacial layers with increasing CPVP that may affect the interaction between PVPysilica and microorganisms PM187 observed by the PCS method (Figs. 39 and 40). Thus, even at a low concentration, PVPysilica reduces the vital functions (own mobility) of P. mirabilis 187 significantly stronger than pure silica does due to high adhesion properties of PVP. PCS is also a sensitive tool for discriminating between cell types or between healthy and malignant cells or for probing changes in cells resulting from stimuli, i.e. physiological and morphological information on living cells can be retrieved using PCS. The size and type of bacteria, identification of bacteria, nuclear and cellular morphology, the effect of antibiotics (penicillin, etc.), ethanol (Fig. 44), absorbents (e.g. silica, silicayPVP) on bacteria, changes in heat-treated bacteria etc. were studied by means of PCS w34,107x. It should be noted that useful information about biomacromolecules, cells, and microorganisms can be obtained by means of electrophoresis based on PCS w34x. The use of single scattering set-ups in PCS for biomedical and biophysical applications is widespread and has proven to be an invaluable tool in both practical (e.g. clinical, biomedical, etc.) and pure research environments. From a theoretical viewpoint, light scattering from biological cells can be seen as the problem of scattering from irregularly shaped near index matching particles. This concept opens the potential of a number of scattering theories and many of them have been used with varying success. The state of polarization of the scattered light carries a significant amount of relevant biophysical and biomedical information, as was

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shown in many experiments (partially analysed here). At the same time despite many remarkable results, the theoretical analysis and experimental exploitation of the complete scattering matrix for biological particles still is rather unexplored and may expect to see many exiting new results in the coming few years w107x. 6. Conclusion Successful applications of the PCS methods (such as DLS, SLS, MALS and other modes) to the solutions of proteins or other biomacromolecules individual or interacting with solid particles of different origins or organics show that these techniques are very flexible and appropriate for a variety of the biological, food and pharmaceutical problems. New facilities allow one to study concentrated suspensions and solutions (up to 50% vyv with Brookhaven FOQELS) at a high resolution (approx. 0.5–1 nm) using, e.g. new effective Brookhaven apparatuses or Malvern HPPS and perspective XPCS technique. Developed mathematical procedures and computational program packages provide fast and accurate calculations of the distribution functions in respect to the particle size and shape, molecular weight and shape, diffusion of particles and own mobility of living microorganisms, etc. The multi-angle PCS analysis is fruitful for investigations of structural features of macromolecules and intramolecular motions, as well as shapes of submicron particles, however, the problems related to multi-scattered light effects should be considered more accurate for concentrated suspensions and solutions. The applications of the PCS methods allow one to analyse the mechanism of interaction of proteins with other bioobjects and to model their behaviour in the body and cell. The use of the PCS techniques is very fruitful for solution of the problems in food industry, e.g. estimation of quality of foods, and medicine (pharmokinetics, drug delivery, drug interaction with bioobjects, absorption of protein toxins by tiny adsorbent particles, etc). The application of PCS is very effective in combination with other powerful methods such as XRD, SAXS, electron microscopy, AFM, NMR, fluorescent spectroscopy and others giving more complete information about complex bioobjects (macromolecules, cells, microorganisms). Thus, PCS is very powerful and perspective technique developed to solve biological, food, medicinal, environment protection and related problems and its inherent potentialities are not settled. Acknowledgments This research was supported by NATO (Grants EST.CLG.976890 (V.M.G. and R.L.) and EST.CLG.979845 (V.M.G.)). The authors thank Dr E.F. Voronin, Prof. I.I. Geraschenko and I.V. Mikhailova for preparation of some samples and protein adsorption measurements, and Dr V.I. Zarko and Prof. W. Januzs for certain PCS measurements. References w1x A. Berne, T. Forrester, R.A. Gudmundsen, O. Johnson, Phys. Rev. 99 (1955) 1691. w2x A.T. Forrester, J. Opt. Soc. Amer. 51 (1961) 253.

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