- Email: [email protected]
Dynamic light scattering evidence of a `fragile' character of protein aqueous solutions
27 August 1999
Chemical Physics Letters 310 Ž1999. 130–136 www.elsevier.nlrlocatercplett
Dynamic light scattering evidence of a ‘ fragile’ character of protein aqueous solutions M. Placidi a , S. Cannistraro
b,)
a
b
INFM, Dipartimento di Fisica dell’UniÕersita, ´ I-06100 Perugia, Italy Dipartimento di Scienze Ambientali, UniÕersita´ della Tuscia, I-01100 Viterbo, Italy Received 10 November 1998; in final form 11 March 1999
Abstract Dynamic light scattering has been used to measure the mutual diffusion coefficient Dm of bovine serum albumin as a function of temperature at different protein concentrations. A deviation from the Arrhenius behaviour is observed, at each protein concentration investigated, corresponding to a characteristic temperature TA , whose value is found to be dependent on the protein concentration itself. In the whole temperature range, the dependence of Dm on T is well represented by a Vogel–Fulcher–Tamman law. The results are discussed in the framework of the so-called strongr fragile classification scheme for glass-forming liquids, connected to the peculiar properties of the water–protein system. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Departure from the Arrhenius relaxation kinetics in glass-forming liquids, approaching the glass transition temperature Tg , is perhaps the most important canonical feature of these systems w1–4x together with the change in the heat capacity Cp at Tg w1x. In this context, Angell w1,5x has proposed a classification scheme placing glass-forming liquids along a scale between strong and fragile liquid extremes according to their deviation from the Arrhenius relaxation kinetics. Strong glass-forming liquids, which are observed to be those with self-reinforcing tetrahedral network structures, have a built-in resistance to structural changes and show little structural reorganization despite a wide variation of temperature; ) Corresponding author. Fax: q39-075-44666; e-mail: [email protected]
consequently small changes in heat capacity are observed as the glass transition is traversed w4x. They show an Arrhenius-like variation of the structural relaxation time or transport properties, such as solution shear viscosity h or diffusion coefficient D, in a broad range of temperature between the glass temperature Tg and the high-temperature limit of the type w2x
h , Dy1 ; e D ErŽ RT . ,
Ž 1.
where D E is the activation energy. Conversely, fragile glass-forming liquids, which are characterized by simple non-directional Coulomb attractions or by van der Waals interactions, exhibit a liquid structure that fluctuates over a wide variety of different particle coordinate states also with little variation in temperature, and consequently have large increases in heat capacity at Tg w4x. As the temperature is lowered toward Tg , the above-mentioned
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 7 6 5 - 4
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
quantities, h or Dy1 , vary in a strongly nonArrhenius fashion when a characteristic temperature referred to as TA is crossed w2,3x, often according to the Vogel–Fulcher–Tamman ŽVFT. equation
h , Dy1 ; e BrŽTyT 0 . ,
Ž 2.
where the temperature T0 is related to Tg w1,4x. In principle, the formalism developed above is equally applicable to all glass-forming liquids, whether strong or fragile, and the ‘strength’ of a liquid may be quantified by adopting the modified VFT equation
h , Dy1 ; eŽ D T 0 .rŽTyT 0 . ,
Ž 3.
where the parameter D in the exponential reflects the extent to which the system deviates or obeys the Arrhenius behaviour w1,4,5x; this latter condition being obtained in the limit D ™ `. Hence, an high D value indicates a strong glass-forming liquid while lower values of D classify a liquid as fragile. Recently w4–7x this phenomenology has been connected to the collective potential energy function of these systems, which describes the interaction between the particles that constitute the medium; the ‘strength’ of a system has been directly related to the density and depth of the minima in the hypersurface which describes this function and revealing different peculiarities depending on the bonding character of the systems w4x. The diffusive motion of particles in the medium is strictly related to the landscape of the collective potential energy function set up by the host particles and the diffusion process may be viewed as evolving on the energy landscape from one minima to another. Such a description, principally adopted to describe the features of simple molecular liquids, can also find an application in the study of binary mixtures and colloidal suspensions. As a matter of fact, colloidal and polymer systems, when studied as a function of solute concentration at isothermal conditions, show some analogies with simple molecular glass-forming liquids w8,9x. In particular, for colloidal solutions of biological macromolecules, the physical properties of the solution play a major role in determining some of the physiologically relevant phenomena, such as diffusion controlled macromolecular reactions w10x or the onset of critical be-
131
haviours, and phase transitions, in concentrated protein solutions w11,12x. In a previous study w13x, the transport properties of water have been found to be modulated by the amount of protein in solution, and, recently, in order to explain the anomalous behaviour in the protein diffusion coefficient as a function of protein concentration under isothermal conditions, we have considered the role played by the protein–water interface in the complex solvent colloid interactions w14,15x. In this respect, it would be interesting to investigate the role of the protein in the modulation of the solution energy landscape as studied in the framework of Angell’s classification scheme, by varying the temperature of the system. Therefore, we have studied, by using dynamic light scattering ŽDLS., the temperature dependence of the mutual diffusion coefficient Dm of a globular protein, bovine serum albumin ŽBSA., in aqueous solution by varying the protein concentration from 2 to 10 grdl. At all protein concentrations investigated, a deviation of Dm from simple Arrhenius behaviour is observed corresponding to a characteristic temperature TA and the dependence of Dm on the temperature is found to be well represented by Eq. Ž2.. Both the temperatures TA and T0 in Eq. Ž2. are found to increase with the protein concentration, while a decrease of the parameter D with increasing protein concentration is also found. The observed deviation of Dm from the Arrhenius behaviour is indicative of a glass character of the protein–water solution; moreover, the ‘strength’ of the system comes out to fall in the fragile side of the Angell’s classification scheme, and this fragile character is found to be enhanced by increasing the amount of the protein in solution.
2. Experiment Bovine serum albumin ŽSigma Aldrich Co.., a globular protein with a molecular weight of M s 6.5 ˚ was dissolved = 10 4 grmol and a radius R , 35 A, at the desired concentration in acetate buffer at a pH corresponding to the isoelectric point ŽpH s 4.7. and at high ionic strength Ž0.1 M NaCl.. Gel-filtration chromatography was used to obtain a monomeric
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
132
BSA fraction, whose concentration was determined spectrophotometrically by using an absorptivity value of 6.67 dlrg cm at 280 nm. In order to investigate the transport properties of BSA in aqueous solution, we used the DLS technique which measures the time autocorrelation function ŽACF. ² nŽ q,0.,nŽ q,t .: of the photocounts due to the light scattered by the sample, where nŽ q,t . is the number of photons counted by the detector placed at the scattering angle u at the time t in the sampling time D t, and q is the amplitude of the exchanged wave vector given by q s Ž4 p nrl. sinŽ ur2.; l and n being the incident light wavelength and the solution refractive index, respectively. The quantity ² nŽ q,0.,nŽ q,t .: is related to the spontaneous fluctuations in the protein concentration by ² n Ž q,0 . ,n Ž q,t . : ² n Ž q . :2
s 1 q A gŽ 1 . Ž t .
2
,
being determined by the freezing point of the sample. A series of 10 ACFs have been taken, approximately in steps of 3 K, waiting long enough to let the sample reach thermal equilibrium.
3. Results and discussion Fig. 1 shows, in an Arrhenius plot, the measured BSA mutual diffusion coefficient Dm as a function
Ž 4.
where A is a constant depending on the number of coherence areas subtended by the detector and g Ž1. Ž t . is the first-order normalized correlation function of the scattered electric field. The function g Ž1. Ž t . decays from a value of 1 to a value of 0 when t ™ ` and, in monodisperse samples, this decay is exponential in time according to 2
g Ž1. Ž t . s ey2 D m q t ,
Ž 5.
where Dm is the mutual diffusion coefficient of the protein in solution. In order to check any deviation from the simple monoexponential decay of Eq. Ž5. all the measured ACF have been characterized in terms of the cumulants K n , limiting our analysis to the second cumulant K 2 w16x. A normalized second cumulant K 2rK 12 - 0.06, characteristic of a narrow distribution of decay times, has been obtained at all temperatures and concentrations investigated. The experimental apparatus consists of a digital correlator ŽBI-9000 Brookhaven Instr.. with an Arq ˚ with a power laser source operating at l s 4880 A of 80 mW. All the measurements were performed on samples previously treated with a 0.22 mm Millipore filter to avoid the presence of dust, at a fixed scattering angle of u s 908. The ACF have been obtained at temperatures ranging from 303 to 260 K, the latter temperature
Fig. 1. Arrhenius plot of the BSA mutual diffusion coefficient Dm at two different protein concentrations: 2 grdl Župper figure. and 10 grdl Žlower figure.. The solid line is a fit of the data according to an Arrhenius law ŽEq. Ž1., up to T )TA .; the dotted line is a fit with a VFT equation. Inset: A measured autocorrelation function given as an example in order to show the monoexponential character found in all the measurements performed.
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
of temperature T for the two selected protein concentrations of 2 and 10 grdl. In the inset of Fig. 1, as an example, a measured ACF obtained from the sample at the protein concentration of 10 grdl and at a temperature of T s 265.8 K, is given in a log scale. As can be seen, the ACF given is characterized by a monoexponential decay rate: the same behaviour was found at all concentrations studied and in the entire temperature range investigated. For all the samples studied, it was found that the Arrhenius law fails to describe the temperature dependence of Dm in the whole temperature range investigated, Eq. Ž1. appearing to be valid only for Dm values measured at temperatures above a crossover temperature TA . This is shown for the two selected samples ŽFig. 1. where the solid line is a fit, limited to the range of temperatures in which Eq. Ž1. holds reasonably well. Deviation from the Arrhenius behaviour appears to be more evident in the sample at higher protein concentration; such a feature is associated with a variation of TA , which can be approximately estimated to vary between 270 and 280 K, from the lowest up to the highest concentration, respectively. On the other hand, the temperature dependence of Dm is found to be described in the whole temperature range by a VFT law ŽEq. Ž2... Actually, the dotted line in Fig. 1 corresponds to a best fit of the Dm data according to this law. All the parameters obtained from the best fits performed with Eqs. Ž1. and Ž2. appear to be dependent on the protein concentration and are given in Table 1 together with the crossover temperature TA . Such a temperature turns out to be shifted toward higher values as long as the protein concentration increases; in other words, the onset of the observed VFT-like behaviour for Dm – indeed reminiscent of a glass-like behaviour – occurs at higher and higher temperatures as the protein concentration in the solution is increased. Moreover, under the assumption that T0 is directly related to the glass transition temperature Tg w1,4x, its trend seems to indicate that the glass-like behaviour can be steered by varying the protein concentration. It is interesting to note that, in glass-forming systems, a variation of some characteristic parameters Žsuch as TA or T0 . has been reported to occur by changing some external condition, like pressure, which leads
133
Table 1 Values of the parameter D E, as obtained from a best fit of the Dm data with an Arrhenius behaviour ŽEq. Ž1., up to T )TA ., and of the parameters Dm 0 , T0 and D as obtained from a best fit with a VFT law Dm s Dm 0 PeŽ D T 0 .rŽTyT 0 . being Dm 0 the diffusion coefficient at the high temperature limit w4x i.e. as T ™`. TA being the crossover temperature between the Arrhenius and the VFT behaviour of Dm C DE Dm 0 T0 Žgrdl. Žkcalrmol. Žcm2 rs.=10 7 Ž K .
D
TA ŽK.
2 4 6 8 10
5.4 "0.2 4.0 "0.1 2.2 "0.1 1.9 "0.1 1.24"0.05
271 277 278 281 284
5.20"0.10 5.13"0.06 4.89"0.08 4.73"0.04 4.50"0.10
630"19 372"11 135"5 102"3 63"2
135"2 150"2 173"2 179"1 194"2
to a consequent variation in the molecular packing of the glass-forming liquid w4x. In our case, the variation is induced by the biopolymer concentration and is probably connected with the protein–solvent interactions which lead to a modification of the solvent properties. Concerning D E, an opposite trend is observed. In fact, the D E values given in Table 1 appear to decrease with the protein concentration and result to be comprised between 4.5 and 5.2 kcalrmol, at the highest and lowest protein concentration, respectively. These values fall in the widely accepted range Ž2–6 kcalrmol. characteristic of the H-bond energy w17x. These results should not be surprising if we consider that the protein diffusional motion is driven by a thermally activated process which involves the forming and breaking of hydrogen bonds w10x. Moreover, the observed concentration dependence of D E can reflect a modification in the arrangement of the H-bond network in the protein–water solution, as induced by the protein macromolecules. In fact, there is experimental evidence w18,19x that, in a protein solution, the H-bond network is separated into two distinct domains: a bulk component which is characterized by a binding structure not far from that of the bare solvent and a protein-related fraction, exhibiting an arrangement of H-bonds falling between water and amorphous ice w18,20x, which is consistent with a more accentuated solvent molecular disorder. Hence, on increasing the protein concentration, the H-bond network associated to the bulk water component is smoothly reduced and, consequently, a loss of
134
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
organization in the H-bond patches of the water molecules is registered. This could lead to a lower amount of energy required for a protein macromolecule to diffuse and, accordingly, the parameter D E, which is directly related to this process, is found to decrease with the protein concentration. On the other hand, we have fitted the diffusion coefficient data according to Eq. Ž3.. In Fig. 2, the mutual diffusion coefficients Dm measured at all the concentrations, are given in a log scale as a function of the dimensionless reduced temperature T0rŽT y T0 ., taking as T0 the value obtained from the data best fit previously performed with Eq. Ž2.. Clearly, the data show a linear dependence of Dm on the variable T0rŽT y T0 . at each protein concentration investigated. The dotted lines are the best fit of the data according to Eq. Ž3. and the slopes of the fitting lines give the values of the D parameter in this equation. In the inset of Fig. 2, the value of D is shown as a function of the BSA concentration. It turns out to decrease as a function of protein concentration according to a relation of the type D s D0 eyk C ,
Ž 6.
with D0 s 7.7 " 1.1 and k s 0.185 " 0.016 dlrg, where D0 is the D parameter at zero protein concentration, i.e., of the pure solvent.
As mentioned in Section 1, within the characteristic phenomenology of glass-forming systems, the parameter D quantifies the ‘strength’ of a system. Indeed, strong glass-forming liquids such as SiO 2 or GeO 2 , exhibit D values around D ; 100, conversely, the most fragile glass-forming liquid systems yet identified, such as polyvinyl chloride, show a D value around 2. In this respect, for our water– protein system we obtain values of D which, at each protein concentration, are placed in the fragile side of the Angell’s classification scheme. Furthermore, D is found to decrease with the protein concentration according to Eq. Ž6.. From this result, it appears that each solution can be viewed as a different glass-forming liquid, depending on the value assumed from the parameter D at a particular protein concentration. This latter aspect is also inferred by the variation of the high temperature limit value of Dm , namely Dm0 ŽTable 1., the trend of Dm0 being found to decrease with increasing protein concentration. Such a result is due to the increase of the solution viscosity with the protein concentration which leads to a decrease of the particle mobility even at the high temperature limit w4,14x. It should be noted that the ‘strength’ of a system, and consequently D, has been directly related w6x to the density of the minima in the hypersurface of the
Fig. 2. BSA mutual diffusion coefficient Dm as a function of the reduced temperature T0rŽT y T0 . at all the protein concentrations investigated. The dotted line for each concentration is a fit of the experimental data with a VFT law Dm s Dm 0 P eŽ D T 0 .rŽTyT 0 .. Inset: Parameter D, as extracted from the best fits with Eq. Ž3. shown in the main figure, reported as a function of the protein concentration; the dotted line is the best fit of the data according to Eq. Ž6..
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
collective potential energy function of the system and to the height of the energy barriers between them. For the sake of clarity, it should be considered that the protein itself is characterized by a landscape in the energy of the conformational substates w21x which can be described by an inherent collective potential energy function. However, we would like to stress that in the present case we are considering the landscape of the collective potential energy function of the binary protein–solvent system. In particular, the quantity D has been shown to be proportional to the ratio w5x
135
of the protein biomolecules in the aqueous solution. This result, which implies that the whole system is able to explore a wide variety of different particles coordinate states as the protein concentration increases, supports the hypothesis of a loss of organization in the H-bond water network, as deduced from the D E dependence on the protein concentration. It should be noted that no enhancement in the intensity of the scattered light or anomalous decay in the autocorrelation function is observed; therefore any onset of critical behaviour can be ruled out.
Dm D;
DCp
,
Ž 7.
where D m can be identified with the barrier height separating the minima and Cp is the configurational heat capacity which can be related to the density of minima in the potential energy surface. This topographical aspect is strictly connected to the number of configurations that the liquid can assume when the temperature is changed. For instance, a fragile liquid would be that with a high density of minima in the hypersurface and relatively low barriers between them; in this manner, considering that at each minimum a stable arrangement of the system corresponds, a wide number of stable particles coordinate states can be easily experienced by the system. On the contrary, surfaces with few minima and high barriers between them will generate strong liquids, due to the few stable arrangements which can be explored by the system w5x. Intermediate stages between strong and fragile can be viewed as being obtained with a suitable arrangement of minima and barrier heights between the minima. Therefore, the reported trend of D versus C contains information about the evolution of the collective potential energy function of the system with the protein concentration; this behaviour could be reminiscent of the complex nature of the protein–water interface. In fact, the reported behaviour of D can be viewed as an indication that the system goes towards a collective potential energy function characterized by an increase in the minima number andror minima separated by lower energy barriers, and, more significantly, this feature result is governed by the amount
4. Conclusions The mutual diffusion coefficient Dm of BSA in aqueous solution has been measured with a DLS technique as a function of the temperature and at different protein concentrations. The results given show a deviation of Dm from the Arrhenius-like behaviour below a characteristic temperature TA . This temperature is shifted toward higher values as the protein concentration increases. On the other hand, the temperature dependence of Dm is found to be described, in the whole temperature range, by a VFT law, reminiscent of a glass-like behaviour, whose characteristic parameters, i.e., T0 and D, are found to be dependent on the protein concentrations. This result suggest that each solution, at different protein concentration, may be viewed as a distinct glass-forming liquid whose ‘strength’ is steered from the amount of the protein in the solution. The ‘strength’ of the system might be connected to the landscape of the potential energy function of these systems consistently with an increase in the minima number andror minima separated by lower energy barriers in the potential energy hypersurface.
References w1x C.A. Angell, Science 267 Ž1995. 1924. w2x E.W. Fischer, Physica A 201 Ž1993. 183. w3x M. Ediger, C.A. Angell, R. Nagel, J. Phys. Chem. 100 Ž1996. 13200. w4x C.A. Angell, P.H. Poole, J. Shao, Il Nuovo Cimento 16 Ž1994. 993.
136 w5x w6x w7x w8x w9x w10x w11x w12x w13x w14x
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136 C.A. Angell, J. Non-Cryst. Solids 131 Ž1991. 13. F.H. Stillinger, Science 267 Ž1995. 1935. C.A. Angell, Nature 393 Ž1998. 521. E. Bartsch, V. Frenz, H. Sillescu, J. Non-Cryst. Solids 172 Ž1994. 88. J. Stellbrink, J. Allgaier, D. Richter, Phys. Rev. E 56 Ž1997. 3772. R.B. Gregory, Protein-Solvent Interactions, Dekker, New York, 1995. C. Ishimoto, T. Tanaka, Phys. Rev. Lett. 39 Ž1977. 474. B.M. Fine, J. Pande, A. Lomakin, O.O. Ogun, J.B. Benedek, Phys. Rev. Lett. 74 Ž1995. 198. R. Lamanna, M. Delmelle, S. Cannistraro, Phys. Rev. E 49 Ž1994. 5878. M. Placidi, S. Cannistraro, Europhys. Lett. 43 Ž1998. 476.
w15x G. Chirico, M. Placidi, S. Cannistraro, J. Phys. Chem. B 103 Ž1999. 1746. w16x D.E. Koppel, J. Chem. Phys. 57 Ž1972. 4814. w17x F.H. Stillinger, Science 209 Ž1980. 451. w18x I.D. Kuntz, W. Kauzmann, Adv. Protein Chem. 28 Ž1974. 239. w19x W. Doster, A. Bachleitner, R. Dunau, M. Hiebl, E. Luscher, ¨ Biophys. J. 50 Ž1986. 213. w20x R. Lamanna, M. Delmelle, S. Cannistraro, Chem. Phys. Lett. 172 Ž1990. 312. w21x E.T. Iben, D. Braunstein, W. Doster, H. Frauenfelder, M.K. Hong, J.B. Johnson, S. Luck, P. Ormos, A. Schulte, P.J. Steinbach, A.H. Xie, R.D. Young, Phys. Rev. Lett. 62 Ž1989. 1916.
Chemical Physics Letters 310 Ž1999. 130–136 www.elsevier.nlrlocatercplett
Dynamic light scattering evidence of a ‘ fragile’ character of protein aqueous solutions M. Placidi a , S. Cannistraro
b,)
a
b
INFM, Dipartimento di Fisica dell’UniÕersita, ´ I-06100 Perugia, Italy Dipartimento di Scienze Ambientali, UniÕersita´ della Tuscia, I-01100 Viterbo, Italy Received 10 November 1998; in final form 11 March 1999
Abstract Dynamic light scattering has been used to measure the mutual diffusion coefficient Dm of bovine serum albumin as a function of temperature at different protein concentrations. A deviation from the Arrhenius behaviour is observed, at each protein concentration investigated, corresponding to a characteristic temperature TA , whose value is found to be dependent on the protein concentration itself. In the whole temperature range, the dependence of Dm on T is well represented by a Vogel–Fulcher–Tamman law. The results are discussed in the framework of the so-called strongr fragile classification scheme for glass-forming liquids, connected to the peculiar properties of the water–protein system. q 1999 Elsevier Science B.V. All rights reserved.
1. Introduction Departure from the Arrhenius relaxation kinetics in glass-forming liquids, approaching the glass transition temperature Tg , is perhaps the most important canonical feature of these systems w1–4x together with the change in the heat capacity Cp at Tg w1x. In this context, Angell w1,5x has proposed a classification scheme placing glass-forming liquids along a scale between strong and fragile liquid extremes according to their deviation from the Arrhenius relaxation kinetics. Strong glass-forming liquids, which are observed to be those with self-reinforcing tetrahedral network structures, have a built-in resistance to structural changes and show little structural reorganization despite a wide variation of temperature; ) Corresponding author. Fax: q39-075-44666; e-mail: [email protected]
consequently small changes in heat capacity are observed as the glass transition is traversed w4x. They show an Arrhenius-like variation of the structural relaxation time or transport properties, such as solution shear viscosity h or diffusion coefficient D, in a broad range of temperature between the glass temperature Tg and the high-temperature limit of the type w2x
h , Dy1 ; e D ErŽ RT . ,
Ž 1.
where D E is the activation energy. Conversely, fragile glass-forming liquids, which are characterized by simple non-directional Coulomb attractions or by van der Waals interactions, exhibit a liquid structure that fluctuates over a wide variety of different particle coordinate states also with little variation in temperature, and consequently have large increases in heat capacity at Tg w4x. As the temperature is lowered toward Tg , the above-mentioned
0009-2614r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 9 9 . 0 0 7 6 5 - 4
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
quantities, h or Dy1 , vary in a strongly nonArrhenius fashion when a characteristic temperature referred to as TA is crossed w2,3x, often according to the Vogel–Fulcher–Tamman ŽVFT. equation
h , Dy1 ; e BrŽTyT 0 . ,
Ž 2.
where the temperature T0 is related to Tg w1,4x. In principle, the formalism developed above is equally applicable to all glass-forming liquids, whether strong or fragile, and the ‘strength’ of a liquid may be quantified by adopting the modified VFT equation
h , Dy1 ; eŽ D T 0 .rŽTyT 0 . ,
Ž 3.
where the parameter D in the exponential reflects the extent to which the system deviates or obeys the Arrhenius behaviour w1,4,5x; this latter condition being obtained in the limit D ™ `. Hence, an high D value indicates a strong glass-forming liquid while lower values of D classify a liquid as fragile. Recently w4–7x this phenomenology has been connected to the collective potential energy function of these systems, which describes the interaction between the particles that constitute the medium; the ‘strength’ of a system has been directly related to the density and depth of the minima in the hypersurface which describes this function and revealing different peculiarities depending on the bonding character of the systems w4x. The diffusive motion of particles in the medium is strictly related to the landscape of the collective potential energy function set up by the host particles and the diffusion process may be viewed as evolving on the energy landscape from one minima to another. Such a description, principally adopted to describe the features of simple molecular liquids, can also find an application in the study of binary mixtures and colloidal suspensions. As a matter of fact, colloidal and polymer systems, when studied as a function of solute concentration at isothermal conditions, show some analogies with simple molecular glass-forming liquids w8,9x. In particular, for colloidal solutions of biological macromolecules, the physical properties of the solution play a major role in determining some of the physiologically relevant phenomena, such as diffusion controlled macromolecular reactions w10x or the onset of critical be-
131
haviours, and phase transitions, in concentrated protein solutions w11,12x. In a previous study w13x, the transport properties of water have been found to be modulated by the amount of protein in solution, and, recently, in order to explain the anomalous behaviour in the protein diffusion coefficient as a function of protein concentration under isothermal conditions, we have considered the role played by the protein–water interface in the complex solvent colloid interactions w14,15x. In this respect, it would be interesting to investigate the role of the protein in the modulation of the solution energy landscape as studied in the framework of Angell’s classification scheme, by varying the temperature of the system. Therefore, we have studied, by using dynamic light scattering ŽDLS., the temperature dependence of the mutual diffusion coefficient Dm of a globular protein, bovine serum albumin ŽBSA., in aqueous solution by varying the protein concentration from 2 to 10 grdl. At all protein concentrations investigated, a deviation of Dm from simple Arrhenius behaviour is observed corresponding to a characteristic temperature TA and the dependence of Dm on the temperature is found to be well represented by Eq. Ž2.. Both the temperatures TA and T0 in Eq. Ž2. are found to increase with the protein concentration, while a decrease of the parameter D with increasing protein concentration is also found. The observed deviation of Dm from the Arrhenius behaviour is indicative of a glass character of the protein–water solution; moreover, the ‘strength’ of the system comes out to fall in the fragile side of the Angell’s classification scheme, and this fragile character is found to be enhanced by increasing the amount of the protein in solution.
2. Experiment Bovine serum albumin ŽSigma Aldrich Co.., a globular protein with a molecular weight of M s 6.5 ˚ was dissolved = 10 4 grmol and a radius R , 35 A, at the desired concentration in acetate buffer at a pH corresponding to the isoelectric point ŽpH s 4.7. and at high ionic strength Ž0.1 M NaCl.. Gel-filtration chromatography was used to obtain a monomeric
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
132
BSA fraction, whose concentration was determined spectrophotometrically by using an absorptivity value of 6.67 dlrg cm at 280 nm. In order to investigate the transport properties of BSA in aqueous solution, we used the DLS technique which measures the time autocorrelation function ŽACF. ² nŽ q,0.,nŽ q,t .: of the photocounts due to the light scattered by the sample, where nŽ q,t . is the number of photons counted by the detector placed at the scattering angle u at the time t in the sampling time D t, and q is the amplitude of the exchanged wave vector given by q s Ž4 p nrl. sinŽ ur2.; l and n being the incident light wavelength and the solution refractive index, respectively. The quantity ² nŽ q,0.,nŽ q,t .: is related to the spontaneous fluctuations in the protein concentration by ² n Ž q,0 . ,n Ž q,t . : ² n Ž q . :2
s 1 q A gŽ 1 . Ž t .
2
,
being determined by the freezing point of the sample. A series of 10 ACFs have been taken, approximately in steps of 3 K, waiting long enough to let the sample reach thermal equilibrium.
3. Results and discussion Fig. 1 shows, in an Arrhenius plot, the measured BSA mutual diffusion coefficient Dm as a function
Ž 4.
where A is a constant depending on the number of coherence areas subtended by the detector and g Ž1. Ž t . is the first-order normalized correlation function of the scattered electric field. The function g Ž1. Ž t . decays from a value of 1 to a value of 0 when t ™ ` and, in monodisperse samples, this decay is exponential in time according to 2
g Ž1. Ž t . s ey2 D m q t ,
Ž 5.
where Dm is the mutual diffusion coefficient of the protein in solution. In order to check any deviation from the simple monoexponential decay of Eq. Ž5. all the measured ACF have been characterized in terms of the cumulants K n , limiting our analysis to the second cumulant K 2 w16x. A normalized second cumulant K 2rK 12 - 0.06, characteristic of a narrow distribution of decay times, has been obtained at all temperatures and concentrations investigated. The experimental apparatus consists of a digital correlator ŽBI-9000 Brookhaven Instr.. with an Arq ˚ with a power laser source operating at l s 4880 A of 80 mW. All the measurements were performed on samples previously treated with a 0.22 mm Millipore filter to avoid the presence of dust, at a fixed scattering angle of u s 908. The ACF have been obtained at temperatures ranging from 303 to 260 K, the latter temperature
Fig. 1. Arrhenius plot of the BSA mutual diffusion coefficient Dm at two different protein concentrations: 2 grdl Župper figure. and 10 grdl Žlower figure.. The solid line is a fit of the data according to an Arrhenius law ŽEq. Ž1., up to T )TA .; the dotted line is a fit with a VFT equation. Inset: A measured autocorrelation function given as an example in order to show the monoexponential character found in all the measurements performed.
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
of temperature T for the two selected protein concentrations of 2 and 10 grdl. In the inset of Fig. 1, as an example, a measured ACF obtained from the sample at the protein concentration of 10 grdl and at a temperature of T s 265.8 K, is given in a log scale. As can be seen, the ACF given is characterized by a monoexponential decay rate: the same behaviour was found at all concentrations studied and in the entire temperature range investigated. For all the samples studied, it was found that the Arrhenius law fails to describe the temperature dependence of Dm in the whole temperature range investigated, Eq. Ž1. appearing to be valid only for Dm values measured at temperatures above a crossover temperature TA . This is shown for the two selected samples ŽFig. 1. where the solid line is a fit, limited to the range of temperatures in which Eq. Ž1. holds reasonably well. Deviation from the Arrhenius behaviour appears to be more evident in the sample at higher protein concentration; such a feature is associated with a variation of TA , which can be approximately estimated to vary between 270 and 280 K, from the lowest up to the highest concentration, respectively. On the other hand, the temperature dependence of Dm is found to be described in the whole temperature range by a VFT law ŽEq. Ž2... Actually, the dotted line in Fig. 1 corresponds to a best fit of the Dm data according to this law. All the parameters obtained from the best fits performed with Eqs. Ž1. and Ž2. appear to be dependent on the protein concentration and are given in Table 1 together with the crossover temperature TA . Such a temperature turns out to be shifted toward higher values as long as the protein concentration increases; in other words, the onset of the observed VFT-like behaviour for Dm – indeed reminiscent of a glass-like behaviour – occurs at higher and higher temperatures as the protein concentration in the solution is increased. Moreover, under the assumption that T0 is directly related to the glass transition temperature Tg w1,4x, its trend seems to indicate that the glass-like behaviour can be steered by varying the protein concentration. It is interesting to note that, in glass-forming systems, a variation of some characteristic parameters Žsuch as TA or T0 . has been reported to occur by changing some external condition, like pressure, which leads
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Table 1 Values of the parameter D E, as obtained from a best fit of the Dm data with an Arrhenius behaviour ŽEq. Ž1., up to T )TA ., and of the parameters Dm 0 , T0 and D as obtained from a best fit with a VFT law Dm s Dm 0 PeŽ D T 0 .rŽTyT 0 . being Dm 0 the diffusion coefficient at the high temperature limit w4x i.e. as T ™`. TA being the crossover temperature between the Arrhenius and the VFT behaviour of Dm C DE Dm 0 T0 Žgrdl. Žkcalrmol. Žcm2 rs.=10 7 Ž K .
D
TA ŽK.
2 4 6 8 10
5.4 "0.2 4.0 "0.1 2.2 "0.1 1.9 "0.1 1.24"0.05
271 277 278 281 284
5.20"0.10 5.13"0.06 4.89"0.08 4.73"0.04 4.50"0.10
630"19 372"11 135"5 102"3 63"2
135"2 150"2 173"2 179"1 194"2
to a consequent variation in the molecular packing of the glass-forming liquid w4x. In our case, the variation is induced by the biopolymer concentration and is probably connected with the protein–solvent interactions which lead to a modification of the solvent properties. Concerning D E, an opposite trend is observed. In fact, the D E values given in Table 1 appear to decrease with the protein concentration and result to be comprised between 4.5 and 5.2 kcalrmol, at the highest and lowest protein concentration, respectively. These values fall in the widely accepted range Ž2–6 kcalrmol. characteristic of the H-bond energy w17x. These results should not be surprising if we consider that the protein diffusional motion is driven by a thermally activated process which involves the forming and breaking of hydrogen bonds w10x. Moreover, the observed concentration dependence of D E can reflect a modification in the arrangement of the H-bond network in the protein–water solution, as induced by the protein macromolecules. In fact, there is experimental evidence w18,19x that, in a protein solution, the H-bond network is separated into two distinct domains: a bulk component which is characterized by a binding structure not far from that of the bare solvent and a protein-related fraction, exhibiting an arrangement of H-bonds falling between water and amorphous ice w18,20x, which is consistent with a more accentuated solvent molecular disorder. Hence, on increasing the protein concentration, the H-bond network associated to the bulk water component is smoothly reduced and, consequently, a loss of
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M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
organization in the H-bond patches of the water molecules is registered. This could lead to a lower amount of energy required for a protein macromolecule to diffuse and, accordingly, the parameter D E, which is directly related to this process, is found to decrease with the protein concentration. On the other hand, we have fitted the diffusion coefficient data according to Eq. Ž3.. In Fig. 2, the mutual diffusion coefficients Dm measured at all the concentrations, are given in a log scale as a function of the dimensionless reduced temperature T0rŽT y T0 ., taking as T0 the value obtained from the data best fit previously performed with Eq. Ž2.. Clearly, the data show a linear dependence of Dm on the variable T0rŽT y T0 . at each protein concentration investigated. The dotted lines are the best fit of the data according to Eq. Ž3. and the slopes of the fitting lines give the values of the D parameter in this equation. In the inset of Fig. 2, the value of D is shown as a function of the BSA concentration. It turns out to decrease as a function of protein concentration according to a relation of the type D s D0 eyk C ,
Ž 6.
with D0 s 7.7 " 1.1 and k s 0.185 " 0.016 dlrg, where D0 is the D parameter at zero protein concentration, i.e., of the pure solvent.
As mentioned in Section 1, within the characteristic phenomenology of glass-forming systems, the parameter D quantifies the ‘strength’ of a system. Indeed, strong glass-forming liquids such as SiO 2 or GeO 2 , exhibit D values around D ; 100, conversely, the most fragile glass-forming liquid systems yet identified, such as polyvinyl chloride, show a D value around 2. In this respect, for our water– protein system we obtain values of D which, at each protein concentration, are placed in the fragile side of the Angell’s classification scheme. Furthermore, D is found to decrease with the protein concentration according to Eq. Ž6.. From this result, it appears that each solution can be viewed as a different glass-forming liquid, depending on the value assumed from the parameter D at a particular protein concentration. This latter aspect is also inferred by the variation of the high temperature limit value of Dm , namely Dm0 ŽTable 1., the trend of Dm0 being found to decrease with increasing protein concentration. Such a result is due to the increase of the solution viscosity with the protein concentration which leads to a decrease of the particle mobility even at the high temperature limit w4,14x. It should be noted that the ‘strength’ of a system, and consequently D, has been directly related w6x to the density of the minima in the hypersurface of the
Fig. 2. BSA mutual diffusion coefficient Dm as a function of the reduced temperature T0rŽT y T0 . at all the protein concentrations investigated. The dotted line for each concentration is a fit of the experimental data with a VFT law Dm s Dm 0 P eŽ D T 0 .rŽTyT 0 .. Inset: Parameter D, as extracted from the best fits with Eq. Ž3. shown in the main figure, reported as a function of the protein concentration; the dotted line is the best fit of the data according to Eq. Ž6..
M. Placidi, S. Cannistraror Chemical Physics Letters 310 (1999) 130–136
collective potential energy function of the system and to the height of the energy barriers between them. For the sake of clarity, it should be considered that the protein itself is characterized by a landscape in the energy of the conformational substates w21x which can be described by an inherent collective potential energy function. However, we would like to stress that in the present case we are considering the landscape of the collective potential energy function of the binary protein–solvent system. In particular, the quantity D has been shown to be proportional to the ratio w5x
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of the protein biomolecules in the aqueous solution. This result, which implies that the whole system is able to explore a wide variety of different particles coordinate states as the protein concentration increases, supports the hypothesis of a loss of organization in the H-bond water network, as deduced from the D E dependence on the protein concentration. It should be noted that no enhancement in the intensity of the scattered light or anomalous decay in the autocorrelation function is observed; therefore any onset of critical behaviour can be ruled out.
Dm D;
DCp
,
Ž 7.
where D m can be identified with the barrier height separating the minima and Cp is the configurational heat capacity which can be related to the density of minima in the potential energy surface. This topographical aspect is strictly connected to the number of configurations that the liquid can assume when the temperature is changed. For instance, a fragile liquid would be that with a high density of minima in the hypersurface and relatively low barriers between them; in this manner, considering that at each minimum a stable arrangement of the system corresponds, a wide number of stable particles coordinate states can be easily experienced by the system. On the contrary, surfaces with few minima and high barriers between them will generate strong liquids, due to the few stable arrangements which can be explored by the system w5x. Intermediate stages between strong and fragile can be viewed as being obtained with a suitable arrangement of minima and barrier heights between the minima. Therefore, the reported trend of D versus C contains information about the evolution of the collective potential energy function of the system with the protein concentration; this behaviour could be reminiscent of the complex nature of the protein–water interface. In fact, the reported behaviour of D can be viewed as an indication that the system goes towards a collective potential energy function characterized by an increase in the minima number andror minima separated by lower energy barriers, and, more significantly, this feature result is governed by the amount
4. Conclusions The mutual diffusion coefficient Dm of BSA in aqueous solution has been measured with a DLS technique as a function of the temperature and at different protein concentrations. The results given show a deviation of Dm from the Arrhenius-like behaviour below a characteristic temperature TA . This temperature is shifted toward higher values as the protein concentration increases. On the other hand, the temperature dependence of Dm is found to be described, in the whole temperature range, by a VFT law, reminiscent of a glass-like behaviour, whose characteristic parameters, i.e., T0 and D, are found to be dependent on the protein concentrations. This result suggest that each solution, at different protein concentration, may be viewed as a distinct glass-forming liquid whose ‘strength’ is steered from the amount of the protein in the solution. The ‘strength’ of the system might be connected to the landscape of the potential energy function of these systems consistently with an increase in the minima number andror minima separated by lower energy barriers in the potential energy hypersurface.
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