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Structure and dynamics in Apoferritin solutions with paracrystalline order
Chemical Physics 292 (2003) 425–434 www.elsevier.com/locate/chemphys
Structure and dynamics in Apoferritin solutions with paracrystalline order Wolfgang H€ außler * Institut Laue–Langevin, TOF-HR, BP 156, 38042 Grenoble Cedex 9, France Received 4 December 2002; in final form 11 April 2003
Abstract The globular protein Apoferritin consists of 24 parts assembled to a spherical shell (outer diameter 12 nm) which is negatively charged at pH 5. In aqueous solution Apoferritin displays a complex dynamic picture. In photon correlation spectroscopy (PCS) slow dynamics have recently been found at low-ionic strength, which cannot be attributed to polydispersity effects because of the high monodispersity of these biopolymer systems. In the same systems a pronounced peak in the static structure factor SðqÞ indicates ordering due to intermolecular interactions. In order to answer the question if the slow dynamics found are due to heterogeneity of the solution, we have investigated the structure and dynamics of ordered Apoferritin solutions in the vicinity of the SðqÞ peak at q . Studies at the respective q-values and on the respective time scale are only possible at the high-resolution neutron spin echo (NSE) spectrometer IN15 at the Institute Laue–Langevin (Grenoble). In previous elastic small angle scattering experiments, indications of the formation of crystallites had been found in low salt solutions. However, in the present work we show that the normalized intermediate scattering function resembles qualitatively the shape of SðqÞ in the vicinity of q and that the dynamics is completely relaxed at the highest q-values under study. Coinciding with extrapolated low-q results of previous PCS experiments on high-salt solutions, at q > q being accessible only by means of NSE, the diffusion coefficients of both low and high salt systems approach the free-particle value of Apoferritin monomers. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Apoferritin systems [1] represent unique model systems for studying the solution structure and dynamics of colloidal-like biopolymers, because the form factor of Apoferritin (MW ¼ 450–475 kDa) is well-known (spherical shell, outer diameter 12 nm) [2–4]. Moreover, the high monodispersity of monomers of this protein allows for unambiguous interpretation of the experimental data. During the last decade, both the structure in aqueous solution and the crystallization process of Apoferritin have been studied intensely. The Apoferritin shell consisting of 24 proteins has a net negative charge at pH 5 [4,5] causing electrostatic
*
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interparticle interactions [4,6]. In small angle neutron scattering (SANS) and X-ray scattering (SAXS) studies, ordering in moderately concentrated solutions over several intermolecular distances was reported. This is reflected in a pronounced peak at the value of the momentum transfer q in the scattered intensity IðqÞ [6] and, consequently, in the static structure factor SðqÞ [4]. The position of the SðqÞ peak varies with the number concentration indicating evenly distributed particles. In addition to the spatial ordering in solution, temperature dependent crystalline clustering of Apoferritin molecules was supposed to take place near the freezing transition [6]. While the appearance of a correlation peak in SðqÞ is well-known from systems of charged colloids in solution, the occurrence of heterogeneity – as the formation of crystallites – is a rare finding at moderate concentration [6], and was elsewhere rather reported from supersaturated protein solutions, for example in Lysozyme solutions [7]. Further evidence of aggregation and equilibrium between monomer and aggregates, which is supposed to be the starting point of crystallization, has also been found in other protein systems [7–10]. Recently, different methods have been developed to control the crystallization process of Apoferritin, commonly initiated by the addition of cadmium ions [11,12]. The influence of primary solution inhomogeneity on the shape of the resulting crystals has been studied [13] motivated by the fact that commercially available solutions are generally microheterogeneous. A peculiarity of the SANS results is, that intermolecular ordering over distances of several molecular sizes appears at the same time with the formation of crystallites [6], both at relatively low Apoferritin concentration. Intermolecular ordering at this concentration values can be explained by long-range electrostatic repulsion between Apoferritin molecules, while phase separation appearing at the same time in such moderately concentrated systems has only been reported in this study. Very little is known about the dynamics of Apoferritin solutions. Previous studies were performed at intermediate ionic strength [5] confirming the existence of Apoferritin aggregates in commercially available solutions. Photon correlation spectroscopy (PCS) demonstrated complex dynamical behavior in low-salt solutions [4]. On the one hand, the diffusive dynamics is influenced by electrostatic interactions, on the other hand slow dynamics appear in the long time diffusion. Standard theories developed for polyelectrolyte systems are applicable for the description of the fast dynamics [15,16]. The origin of the slow dynamics is still under discussion. On the one hand, the appearance of a slow mode is a common phenomenon in various polyelectrolyte solutions. On the other hand, the spherical shape of the Apoferritin polyelectrolyte represents a peculiarity, because all other systems with a slow-mode consist of linearly shaped and more or less flexible molecules. The present study was motivated by the peculiarities found in previous studies on low-salt solutions of moderate Apoferritin concentration. Until now, in Apoferritin solutions of moderate protein concentration, phase transitions have not been reported, apart from the supposed coexistence of liquid phase and small crystallites [6] as mentioned above. However, it is well known that Apoferritin crystallizes at high protein concentration [11–14]. As a consequence of the two findings reported – heterogeneity and slow dynamics – in moderately concentrated solutions of interacting Apoferritin molecules, the question can be posed if these phenomena are correlated, and if the slow dynamics are due to large Apoferritin aggregates. Therefore, a study investigating the structure and dynamics of identical Apoferritin systems is desirable. In this paper, we present results of combined small angle neutron scattering (SANS) and neutron spin echo (NSE) [17] studies on Apoferritin solutions. Structure and dynamics of systems of different protein and salt content are investigated in the q-range around and above q , in contrast to earlier studies restricted to low q-values [4,5]. Only by means of NSE, the structures formed by the relatively small Apoferritin molecules in solution are accessible, and the impact of the structure on the dynamics can be studied. Moreover, NSE gives insight into free-particle dynamics as it is able to reach q-values larger than q , in contrast to PCS. Thereby, special data analysis takes into account the wavelength spread used (as usual) in NSE. We find that the shape of SðqÞ is reflected in the dynamics, as expected and that the peculiarities of the Apoferritin systems interacting by the combination of a soft protein shell carrying positive and negative charge, have no
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particular impact on the dynamical picture found by NSE. Notably, the NSE relaxation curves show no signature of heterogeneity. The relaxation times are comparable to previous PCS results, and the data show no elastic offset. The paper is distributed in three parts following this introduction: Section 2 describes the experimental techniques and the way of sample preparation. Section 3 reports and discusses the NSE results and in Section 4 final conclusions are made.
2. Experimental 2.1. Samples Horse spleen Apoferritin (Sigma, stock concentration 51 mg/ml, sodium salt content 100 mM) was dialyzed in D2 O resulting in solutions of varying protein and salt concentration. In order to standardize the concentration small amounts (3 ml) of the stock solution were concentrated by a factor of 5–6 in 10 kDafilters (Millipore ‘‘Ultrafree’’) using a centrifuge at 8000 rpm. Dialysis was repeated with an additional 3 ml D2 O and subsequent concentration of the diluted solution. To obtain a 99.9% deuterated solvent, this procedure was repeated 4–5 times. In the last dialysis step, different amounts of pure, or salty D2 O (NaCl, Riedel de Haen) were added. The concentration was determined by measuring the volume before dialysis and weighting the protein solution before and after dialysis. Both protein and salt concentration were adjusted to values comparable to the systems studied in H2 O [4]. The pH of the D2 O systems were in the same range as previously reported: 5:1 < pH < 5:3. For the neutron scattering measurements, 1–2 ml of the sample solution were poured into flat quartz cuvettes (Hellma, Germany, 30 35 mm2 ). The sample thickness was 1–2 mm for all sample solutions. The transmission through empty cuvettes was about 95%, and the transmission of the cuvettes filled with sample was 69–82%. The polarization of the scattered intensity normalized by the polarization measured with graphite was 0.97–1. We conclude, that the amount of spin flip scattering is negligible. Therefore, the scattered intensity is coherent [18], and in the NSE experiments, collective dynamics is measured. 2.2. Neutron spin echo measurements The neutron spin echo experiments were performed at the Institute Laue–Langevin (ILL, Grenoble) at with wavelength spread 15% (FWHM) the high-resolution spectrometer IN15. Wavelengths of 14.7–15.2 A were used. The maximum field integral was 2:7 105 Oe cm and the maximum spin echo time sSE ¼ 190 ns. 1 < q < 0.1 A 1 . The maximum divergence of the beam was The scattering vector covered the range 0.02 A 0.17 mrad. A multidetector with 32 32 pixels was used distributed into 3–6 s. The sample temperature was 293 K. The data were corrected for background scattering from the sample cell and solvent. The normalized intermediate scattering function was extracted from the spin echo measurements by dividing NSE raw data through the elastic polarization. The q-values were determined taking into account the beam cross section, wavelength spread and area of the detector sections. 2.3. Neutron small angle measurements In order to obtain static and dynamic data of identical q-smearing, SANS data were also extracted from the data measured at IN15. By choosing overlapping detector positions, effects of varying detector efficiency were corrected. Background scattering was determined by measuring the scattering from a cuvette filled with pure D2 O, corrected for transmission and subtracted, as in the analysis of the dynamic data.
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3. Results and discussion 3.1. Neutron small angle measurements Fig. 1 shows the results of the SANS measurements. The main feature of samples with low solvent salt content is the appearance of a maximum in the scattered intensity. The position and shape of the maximum agrees with previously published SANS and SAXS curves [4,6]. The Apoferritin concentration c of the curves displaying a peak was 156 and 201 mg/ml, respectively. The respective solvent salt content was 0.01– 0.02 mM. The peak position depends on the Apoferritin concentration as it shifts to higher q-values with increasing concentration, in agreement with previous results [4]. The scattered intensity IðqÞ depends on both the interparticle interactions and the Apoferritin form factor. For a mono-disperse ensemble of isotropically interacting particles, IðqÞ factorizes as [19] IðqÞ / F 2 ðqÞ SðqÞ;
ð1Þ 2
with the particle form factor F (q) and the static structure factor SðqÞ. In order to verify correct sample preparation, samples of high solvent salt content were also prepared and measured. At high ionic strength the interparticle interactions are screened and, therefore, short-ranged. With decreasing protein content the interparticle distances became large and the interparticle interactions were minimized. Although very low Apoferritin concentrations are desired in order to measure the form factor, in practice the dilution is limited by the scattered intensity decreasing with dilution. In order to acquire high quality data at higher q-values, we used high-salt samples at two different Apoferritin concentrations (52 mg/ml, volume fraction / ¼ 5%) and (156 mg/ml, / ¼ 15%). The salt content was 40 mM NaCl and 130 mM NaCl, respectively. The high concentration data differ only at low q-values from the low concentration data. At high q-values the data sets are indistinguishable. This indicates negligible electrostatic interparticle interactions at high salt, however, hard sphere interactions are still visible (see below).
Fig. 1. SANS intensities IðqÞ from high-salt and low-salt Apoferritin solutions are shown together with a model function for spherical particles using the parameters from the best fit to high-salt data (dashed line, see text). IðqÞ of the low-salt data is fitted to the product of structure factor and form factor (lines, see text).
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3.2. High-salt systems and the Apoferritin form factor The Apoferritin form factor is well known from SAXS measurements [3,4]. Due to the shape of the Apoferritin particle consisting of 24 proteins building a hollow bead, its form factor is that of a spherical shell [19] ð2Þ F ðq; r1 ; r2 Þ ¼ 3ðsinðqr1 Þ qr1 cosðqr1 ÞÞ ðsinðqr2 Þ qr2 cosðqr2 ÞÞ=q3 r13 r23 ; with the outer radius of the sphere r1 the inner radius of the sphere r2 . In Fig. 1, a model function is shown according to Eq. (2) after having been modified in order to allow for small, Gaussian-distributed deviations Dr1;2 of the outer and inner radius from their mean values and taking into account the neutron wavelength 2 . Removing small q-values is spread (15%). This function is fitted to the high salt data for q > 0.4 A necessary, because the finite dilution influences the data at smaller q as can be seen from Fig. 1. The parameters of the best fit, r1 ¼ (6.0 0.2) nm, r2 ¼ (3.8 0.2) nm, are in good agreement with literature values [3,4]. A detailed analysis shows, that the outer and inner radius variation was correlated (deviations are directed in the same direction), and that the inner radius fluctuates over a wider range: Dr1 /r1 ¼ 2.7%, Dr2 /r2 ¼ 5.4% (FWHM). However, these small numbers demonstrate the good homogeneity of the sample. Moreover, the measured polydispersity is mainly due to elastic deformations of the protein shell, so that the mean size is even more regular [4]. 2 differ from the From Fig. 1 it is clearly seen that the data obtained in high salt solutions at q < 0.4 A form factor increasingly with the Apoferritin concentration. This indicates non-negligible hard sphere interactions and SðqÞ gets smaller than unity in this q-range. In describing SðqÞ, an analytical expression based on the Percus–Yevick closure relation [20] is used / 2 2 1 SðqÞ ¼ 1 þ 24 3 A ðsinðuÞ u cosðuÞÞ þ B 1 u cosðuÞ þ 2 sinðuÞ u u2 u A 24 6 12 24 þ/ þ 4 1 2 sinðuÞ 1 2 þ 4 u cosðuÞ ; ð3Þ 2 u3 u u u 2
4
2
4
with u ¼ q r, A ¼ ð1 þ 2 /Þ ð1 /Þ and B ¼ 3=2 / ð/ þ 2Þ ð1 /Þ , where r is the radius of model hard spheres and / is the volume fraction. In order to obtain IðqÞ fit functions, the respective expressions for SðqÞ are multiplied by F2 (q) and, finally, integrated over the wavelength band. Fig. 1 shows the fit functions obtained. Intensity data and theory are in good agreement. Moreover, from Fig. 2, where the respective SðqÞ fit curves are shown, it can 2 the deviation from unity is small, at least for the dilute system, and the form be seen that at q > 0.4 A factor fit to the data (see above) is justified in this q-range. 3.3. Paracrystalline order As reported above, the low-salt systems under study show correlation peaks, which can be explained by long-range electrostatic interactions between the Apoferritin molecules. Due to the neutron wavelength spread, the structure factor data of solutions with paracrystalline order can not be derived by simple division of the measured intensity by the form factor. R 2 The wavelength spread resembles a summation (integration) of data at different q-values: IðqÞ ¼ F ðqÞSðqÞ dq. Thus, division of IðqÞ through R the measured form factor data F 2 ðqÞ dq results in slight deviation from SðqÞ. Therefore, instead of calculating structure factor data, the intensity data IðqÞ of ordered solutions are described theoretically by convoluting a theoretical structure factor function and the form factor. For SðqÞ of the low salt solutions the Hosemann–Bacchi paracrystalline theory [21,22] is used analogously to the description applied in [4]
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Fig. 2. Structure factors SðqÞ of high-salt and low-salt Apoferritin solutions are shown together with model functions. The data are compared with the respective paracrystalline and Percus–Yevick theory curves (solid and dashed lines). The data peaks are broader than the theory peaks because of the wavelength spread of the neutrons (see text). The theory peak heights approach the data peak heights after having been convoluted with a function taking into account the wavelength spread (thin lines, see text).
% 1 þ exp 12 q2 Da21 i qa cosðHÞ SðqÞ ¼ du dHRe 1 exp 12 q2 Da21 i qa cosðHÞ $ % 1 þ exp 12 q2 Da21 i qa cosðuÞ sinðHÞ Re 1 exp 12 q2 Da21 i qa cosðuÞ sinðHÞ $ ! % 1 þ exp 12 q2 Da21 i qa sinðuÞ sinðHÞ sinðHÞ 1 expðq2 Da22 Þ þ 1; Re 1 exp 12 q2 Da21 i qa sinðuÞ sinðHÞ Z Z
$
ð4Þ
where a is the mean distance between the Apoferritin particles in solution, Da1 is the standard deviation from the mean distance a, and Da2 is the displacement due to thermal vibrations. In order to obtain IðqÞ fit functions the respective paracrystalline expressions are folded by a Gaussian taking into account the means size of ordered regions [4], then multiplied by the form factor and integrated over the wavelength band. Fig. 1 shows the fit functions obtained. Intensity data and theory are in good , Da1 ¼ 26 A , Da2 ¼ 14 A ; and 201 mg/ml, agreement. The fit values are: 156 mg/ml, 0.01 mM: a ¼ 187 A , Da1 ¼ 22 A , Da2 ¼ 10 A . 0.02 mM: a ¼ 171 A The error mentioned above in the division of the intensity data by the form factor are only small, if the dominant structures in the respective curves are much broader than the relative bandwidth similar to high salt solutions. In order to determine the error made in the division, ‘‘structure factor’’ data have been calculated in this way and are shown in Fig. 2 (156 and 201 mg/ml). The data are compared with both the structure factor functions SðqÞ used in the IðqÞ fits (Fig. 1) and with the same functions after having been integrated over q corresponding to a certain q-smearing. As can be seen from Fig. 2, both structure factor functions do not agree with the divided data. This shows, that the division process does not lead to usable data. The real structure factors (Fig. 2, lines) display peaks being much more pronounced than the divided data, while the smeared functions are too flat. Moreover, comparison between IðqÞ and SðqÞ shows, that the SðqÞ maximums are shifted slightly to higher q-values due to the negative slope of the form factor in the
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q-range under consideration. Only at high q-values does the wavelength spread have negligible influence on the division process. It has to be mentioned, that this is the reason the data shown in Fig. 2 are normalized in such a way that they fit to the theory at high q. 3.4. Dynamics in disordered and ordered solutions Fig. 3 displays the NSE relaxation rates extracted by means of a single exponential fit to the NSE data from low and high salt Apoferritin solutions. For high-salt systems, a linear dependence of the relaxation rate on q2 is expected, because for diffusion of non-interacting spherical particles, the normalized intermediate scattering function is given by Sðq; tÞ ¼ expðq2 D0 tÞ;
ð5Þ
with the Stokes–Einstein free-particle diffusion constant D0 ¼
kT ; 6pgrH
ð6Þ
where k is the Boltzmann factor, g is the viscosity of the solvent and rH the hydrodynamic radius of the spheres. This theoretical description is based on the assumption that the time scale of the experiment exceeds the short time fluctuations of the dissolved particles due to collisions with solvent molecules [23]. This assumption is justified when the experiment is sensitive to times above the Brownian relaxation time sB m=6pgr, where m is the mass and r the radius of the particle. For a particle of r ¼ 6 nm dissolved in aqueous solvent at room temperature, the Brownian relaxation time amounts to a few nanoseconds. The spin echo times used were 5–190 ns. The experimental data show a linear dependence with q2 in good agreement with theory (Fig. 3). The linear fit to the high salt data gives the diffusion constant of Apoferritin in D2 O: D0 ¼ 2.5 107 cm/s. The hydrodynamic radius rH of Apoferritin arises to 6.9 nm being slightly larger than r1 ¼ 6 nm found in
Fig. 3. Relaxation rates for the systems from Fig. 1. The high-salt data show free-particle diffusion as the relaxation rate C q2 . In low-salt solutions at low q, the dynamics is much faster and the relaxation rate C does not follow the free diffusion dependency C q2 . In addition, the C-curves cross the free-particle diffusion curve (line). Following the shape to higher q-values, the relaxation turns towards the free-particle diffusion line.
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the form factor fit. This deviation, consistent with literature values, is due to the hydration shell around the molecule in aqueous solution [24–26]. For interacting particles in low salt solution, Sðq; tÞ can be expanded at short times as l l ð7Þ lnðSðq; tÞÞ Deff q2 t þ 2 t2 þ 3 t3 ; 2 6 with the effective diffusion coefficient Deff (q) and the higher cumulants l2;3 . Similarly to the calculation above, a rough estimation of the interaction time sI needed by a non-interacting sphere of radius r ¼ 6 nm in order to diffuse a distance roughly equal to its radius in water, gives: sI r2 =D0 > 1 ls. This time exceeds the maximum spin echo times available at todayÕs NSE spectrometers, Eq. (7) is therefore applicable. Fig. 3 shows, that at low q, the dynamics in interacting solutions is faster than in non-interacting solutions, and the relaxation rate C does not pursue the free diffusion dependency C q2 . In addition, the relaxation rate crosses the free-particle diffusion line which is added to the plot. Following the shape to higher q-values, the relaxation turns towards the free diffusion line. This behavior is expected. The spatial resolution of the highq data is sensitive to small scale dynamics. Therefore, the intermediate scattering function (Eq. (5)) reflects self correlations at high q-values above q [27]. Because the relaxation rate approaches the curve describing the dynamics in non-interacting solutions, no sign of formation of aggregates in low salt systems is visible. Aggregation would lead to particles of larger hydrodynamic radius rH . However, the free diffusion relaxation is identical in all Apoferritin systems and the free diffusion hydrodynamic radius agrees with PCS results as it scales accordingly to C q2 . Finally, it has to be pointed out, that the intermediate scattering function decreases to almost zero at high spin echo times and high q-values. This was confirmed in all systems under study and can be seen clearly from the NSE data for the sample of 156 mg/ml Apoferritin concentration and 0.01 mM salt content measured with best statistics (Fig. 4). A primary result of the present study is that the dynamics of the Apoferritin system are completely relaxed. If there would be crystalline regions which are static on the time scale of the NSE experiment, the intermediate scattering function would approach a plateau value and the base line would not be rear zero. However, the NSE data show unambiguously that the diffusive motion of all particles contained by the sample solution is fast enough to be resolved in the given time window.
Fig. 4. Dynamic structure factors Sðq; tÞ measured on the sample of 156 mg/ml Apoferritin concentration and 0.01 mM salt content. Sðq; tÞ is fitted by a single exponential function for all curves taken at different q-values. Sðq; tÞ reaches almost zero for high q-values.
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All NSE data were fitted by means of a single exponential function. As this Gaussian approximation is valid only in the short time limit (Eq. (7)), we also fitted the data with a function taking into account the higher cumulants. However, the fitted values for the first cumulant did not differ from the values extracted from the single exponential fit, and the higher orders were close to zero.
4. Conclusions The present neutron scattering study was designed to determine if the slow mode found in paracrystalline ordered solutions of Apoferritin is due to heterogeneity by formation of crystallites in solution. We performed SANS and NSE experiments on Apoferritin solutions of varying protein and salt concentration. The shell-like form factor obtained from the high salt data is evidence that mainly Apoferritin monomers exist with only small polydispersity in the purified stock solution. The high salt solutions under study show Percus–Yevick-like structure, whereas low-salt Apoferritin solutions are described by the paracrystalline theory, being ordered due to electrostatic interactions. These systems are characterized analogously to the systems studied in [6], where formation of crystallites has been reported, and to the systems reported in [4], where slow dynamics has been found by means of PCS. The static solution structure of the systems under study resembles both earlier SAXS [4] and SANS results [6]. The previously reported features: (1) monodispersity, (2) paracrystalline order in interacting solutions, (3) crystallites found near the freezing transition and (4) appearance of slow dynamics [4,6] have raised the questions if crystallites forming in interacting solutions are responsible for the slow dynamics found by means of PCS. The present study shows that at q-values above q , the dynamics in solutions with electrostatic interactions present, approaches the diffusion found in non-interacting solutions. The free particle diffusion constant was found to agree with literature and previous PCS data. The dynamic structure factor obtained by means of NSE gives no evidence of elastic scattering, as the dynamics is completely relaxed at high q-values. The complex dynamical picture of Apoferritin in solution (the behavior at the PCS q-values [4,5]) can not be explained by heterogeneity of the solution. More likely is the presence of fluctuations on a large spatial scale, probably temporal ‘‘aggregates’’ in addition to the diffusive dynamics. In PCS, the scattered intensity is dominated by large scale density fluctuations. The formation of both large temporal aggregates and of fix aggregates or crystallites could equally lead to a drastic decrease of the relaxation rate in PCS, so they are indistinguishable. However, the dynamic structure factor measured in the present work by NSE shows no non-zero baseline, confirming the presence of Apoferritin monomers moving quasi-free at least over nm distances. These results exclude the explanation of the slow dynamics by static aggregates or crystallites.
Acknowledgements We would like to thank B. Farago for help with the NSE instrument IN15, and Christopher Bauser for correcting the manuscript.
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Structure and dynamics in Apoferritin solutions with paracrystalline order Wolfgang H€ außler * Institut Laue–Langevin, TOF-HR, BP 156, 38042 Grenoble Cedex 9, France Received 4 December 2002; in final form 11 April 2003
Abstract The globular protein Apoferritin consists of 24 parts assembled to a spherical shell (outer diameter 12 nm) which is negatively charged at pH 5. In aqueous solution Apoferritin displays a complex dynamic picture. In photon correlation spectroscopy (PCS) slow dynamics have recently been found at low-ionic strength, which cannot be attributed to polydispersity effects because of the high monodispersity of these biopolymer systems. In the same systems a pronounced peak in the static structure factor SðqÞ indicates ordering due to intermolecular interactions. In order to answer the question if the slow dynamics found are due to heterogeneity of the solution, we have investigated the structure and dynamics of ordered Apoferritin solutions in the vicinity of the SðqÞ peak at q . Studies at the respective q-values and on the respective time scale are only possible at the high-resolution neutron spin echo (NSE) spectrometer IN15 at the Institute Laue–Langevin (Grenoble). In previous elastic small angle scattering experiments, indications of the formation of crystallites had been found in low salt solutions. However, in the present work we show that the normalized intermediate scattering function resembles qualitatively the shape of SðqÞ in the vicinity of q and that the dynamics is completely relaxed at the highest q-values under study. Coinciding with extrapolated low-q results of previous PCS experiments on high-salt solutions, at q > q being accessible only by means of NSE, the diffusion coefficients of both low and high salt systems approach the free-particle value of Apoferritin monomers. Ó 2003 Elsevier Science B.V. All rights reserved.
1. Introduction Apoferritin systems [1] represent unique model systems for studying the solution structure and dynamics of colloidal-like biopolymers, because the form factor of Apoferritin (MW ¼ 450–475 kDa) is well-known (spherical shell, outer diameter 12 nm) [2–4]. Moreover, the high monodispersity of monomers of this protein allows for unambiguous interpretation of the experimental data. During the last decade, both the structure in aqueous solution and the crystallization process of Apoferritin have been studied intensely. The Apoferritin shell consisting of 24 proteins has a net negative charge at pH 5 [4,5] causing electrostatic
*
Tel.: +33-47620-7041; fax: +33-47620-7688. E-mail address: [email protected] (W. H€außler).
0301-0104/03/$ - see front matter Ó 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0301-0104(03)00183-6
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interparticle interactions [4,6]. In small angle neutron scattering (SANS) and X-ray scattering (SAXS) studies, ordering in moderately concentrated solutions over several intermolecular distances was reported. This is reflected in a pronounced peak at the value of the momentum transfer q in the scattered intensity IðqÞ [6] and, consequently, in the static structure factor SðqÞ [4]. The position of the SðqÞ peak varies with the number concentration indicating evenly distributed particles. In addition to the spatial ordering in solution, temperature dependent crystalline clustering of Apoferritin molecules was supposed to take place near the freezing transition [6]. While the appearance of a correlation peak in SðqÞ is well-known from systems of charged colloids in solution, the occurrence of heterogeneity – as the formation of crystallites – is a rare finding at moderate concentration [6], and was elsewhere rather reported from supersaturated protein solutions, for example in Lysozyme solutions [7]. Further evidence of aggregation and equilibrium between monomer and aggregates, which is supposed to be the starting point of crystallization, has also been found in other protein systems [7–10]. Recently, different methods have been developed to control the crystallization process of Apoferritin, commonly initiated by the addition of cadmium ions [11,12]. The influence of primary solution inhomogeneity on the shape of the resulting crystals has been studied [13] motivated by the fact that commercially available solutions are generally microheterogeneous. A peculiarity of the SANS results is, that intermolecular ordering over distances of several molecular sizes appears at the same time with the formation of crystallites [6], both at relatively low Apoferritin concentration. Intermolecular ordering at this concentration values can be explained by long-range electrostatic repulsion between Apoferritin molecules, while phase separation appearing at the same time in such moderately concentrated systems has only been reported in this study. Very little is known about the dynamics of Apoferritin solutions. Previous studies were performed at intermediate ionic strength [5] confirming the existence of Apoferritin aggregates in commercially available solutions. Photon correlation spectroscopy (PCS) demonstrated complex dynamical behavior in low-salt solutions [4]. On the one hand, the diffusive dynamics is influenced by electrostatic interactions, on the other hand slow dynamics appear in the long time diffusion. Standard theories developed for polyelectrolyte systems are applicable for the description of the fast dynamics [15,16]. The origin of the slow dynamics is still under discussion. On the one hand, the appearance of a slow mode is a common phenomenon in various polyelectrolyte solutions. On the other hand, the spherical shape of the Apoferritin polyelectrolyte represents a peculiarity, because all other systems with a slow-mode consist of linearly shaped and more or less flexible molecules. The present study was motivated by the peculiarities found in previous studies on low-salt solutions of moderate Apoferritin concentration. Until now, in Apoferritin solutions of moderate protein concentration, phase transitions have not been reported, apart from the supposed coexistence of liquid phase and small crystallites [6] as mentioned above. However, it is well known that Apoferritin crystallizes at high protein concentration [11–14]. As a consequence of the two findings reported – heterogeneity and slow dynamics – in moderately concentrated solutions of interacting Apoferritin molecules, the question can be posed if these phenomena are correlated, and if the slow dynamics are due to large Apoferritin aggregates. Therefore, a study investigating the structure and dynamics of identical Apoferritin systems is desirable. In this paper, we present results of combined small angle neutron scattering (SANS) and neutron spin echo (NSE) [17] studies on Apoferritin solutions. Structure and dynamics of systems of different protein and salt content are investigated in the q-range around and above q , in contrast to earlier studies restricted to low q-values [4,5]. Only by means of NSE, the structures formed by the relatively small Apoferritin molecules in solution are accessible, and the impact of the structure on the dynamics can be studied. Moreover, NSE gives insight into free-particle dynamics as it is able to reach q-values larger than q , in contrast to PCS. Thereby, special data analysis takes into account the wavelength spread used (as usual) in NSE. We find that the shape of SðqÞ is reflected in the dynamics, as expected and that the peculiarities of the Apoferritin systems interacting by the combination of a soft protein shell carrying positive and negative charge, have no
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particular impact on the dynamical picture found by NSE. Notably, the NSE relaxation curves show no signature of heterogeneity. The relaxation times are comparable to previous PCS results, and the data show no elastic offset. The paper is distributed in three parts following this introduction: Section 2 describes the experimental techniques and the way of sample preparation. Section 3 reports and discusses the NSE results and in Section 4 final conclusions are made.
2. Experimental 2.1. Samples Horse spleen Apoferritin (Sigma, stock concentration 51 mg/ml, sodium salt content 100 mM) was dialyzed in D2 O resulting in solutions of varying protein and salt concentration. In order to standardize the concentration small amounts (3 ml) of the stock solution were concentrated by a factor of 5–6 in 10 kDafilters (Millipore ‘‘Ultrafree’’) using a centrifuge at 8000 rpm. Dialysis was repeated with an additional 3 ml D2 O and subsequent concentration of the diluted solution. To obtain a 99.9% deuterated solvent, this procedure was repeated 4–5 times. In the last dialysis step, different amounts of pure, or salty D2 O (NaCl, Riedel de Haen) were added. The concentration was determined by measuring the volume before dialysis and weighting the protein solution before and after dialysis. Both protein and salt concentration were adjusted to values comparable to the systems studied in H2 O [4]. The pH of the D2 O systems were in the same range as previously reported: 5:1 < pH < 5:3. For the neutron scattering measurements, 1–2 ml of the sample solution were poured into flat quartz cuvettes (Hellma, Germany, 30 35 mm2 ). The sample thickness was 1–2 mm for all sample solutions. The transmission through empty cuvettes was about 95%, and the transmission of the cuvettes filled with sample was 69–82%. The polarization of the scattered intensity normalized by the polarization measured with graphite was 0.97–1. We conclude, that the amount of spin flip scattering is negligible. Therefore, the scattered intensity is coherent [18], and in the NSE experiments, collective dynamics is measured. 2.2. Neutron spin echo measurements The neutron spin echo experiments were performed at the Institute Laue–Langevin (ILL, Grenoble) at with wavelength spread 15% (FWHM) the high-resolution spectrometer IN15. Wavelengths of 14.7–15.2 A were used. The maximum field integral was 2:7 105 Oe cm and the maximum spin echo time sSE ¼ 190 ns. 1 < q < 0.1 A 1 . The maximum divergence of the beam was The scattering vector covered the range 0.02 A 0.17 mrad. A multidetector with 32 32 pixels was used distributed into 3–6 s. The sample temperature was 293 K. The data were corrected for background scattering from the sample cell and solvent. The normalized intermediate scattering function was extracted from the spin echo measurements by dividing NSE raw data through the elastic polarization. The q-values were determined taking into account the beam cross section, wavelength spread and area of the detector sections. 2.3. Neutron small angle measurements In order to obtain static and dynamic data of identical q-smearing, SANS data were also extracted from the data measured at IN15. By choosing overlapping detector positions, effects of varying detector efficiency were corrected. Background scattering was determined by measuring the scattering from a cuvette filled with pure D2 O, corrected for transmission and subtracted, as in the analysis of the dynamic data.
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3. Results and discussion 3.1. Neutron small angle measurements Fig. 1 shows the results of the SANS measurements. The main feature of samples with low solvent salt content is the appearance of a maximum in the scattered intensity. The position and shape of the maximum agrees with previously published SANS and SAXS curves [4,6]. The Apoferritin concentration c of the curves displaying a peak was 156 and 201 mg/ml, respectively. The respective solvent salt content was 0.01– 0.02 mM. The peak position depends on the Apoferritin concentration as it shifts to higher q-values with increasing concentration, in agreement with previous results [4]. The scattered intensity IðqÞ depends on both the interparticle interactions and the Apoferritin form factor. For a mono-disperse ensemble of isotropically interacting particles, IðqÞ factorizes as [19] IðqÞ / F 2 ðqÞ SðqÞ;
ð1Þ 2
with the particle form factor F (q) and the static structure factor SðqÞ. In order to verify correct sample preparation, samples of high solvent salt content were also prepared and measured. At high ionic strength the interparticle interactions are screened and, therefore, short-ranged. With decreasing protein content the interparticle distances became large and the interparticle interactions were minimized. Although very low Apoferritin concentrations are desired in order to measure the form factor, in practice the dilution is limited by the scattered intensity decreasing with dilution. In order to acquire high quality data at higher q-values, we used high-salt samples at two different Apoferritin concentrations (52 mg/ml, volume fraction / ¼ 5%) and (156 mg/ml, / ¼ 15%). The salt content was 40 mM NaCl and 130 mM NaCl, respectively. The high concentration data differ only at low q-values from the low concentration data. At high q-values the data sets are indistinguishable. This indicates negligible electrostatic interparticle interactions at high salt, however, hard sphere interactions are still visible (see below).
Fig. 1. SANS intensities IðqÞ from high-salt and low-salt Apoferritin solutions are shown together with a model function for spherical particles using the parameters from the best fit to high-salt data (dashed line, see text). IðqÞ of the low-salt data is fitted to the product of structure factor and form factor (lines, see text).
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3.2. High-salt systems and the Apoferritin form factor The Apoferritin form factor is well known from SAXS measurements [3,4]. Due to the shape of the Apoferritin particle consisting of 24 proteins building a hollow bead, its form factor is that of a spherical shell [19] ð2Þ F ðq; r1 ; r2 Þ ¼ 3ðsinðqr1 Þ qr1 cosðqr1 ÞÞ ðsinðqr2 Þ qr2 cosðqr2 ÞÞ=q3 r13 r23 ; with the outer radius of the sphere r1 the inner radius of the sphere r2 . In Fig. 1, a model function is shown according to Eq. (2) after having been modified in order to allow for small, Gaussian-distributed deviations Dr1;2 of the outer and inner radius from their mean values and taking into account the neutron wavelength 2 . Removing small q-values is spread (15%). This function is fitted to the high salt data for q > 0.4 A necessary, because the finite dilution influences the data at smaller q as can be seen from Fig. 1. The parameters of the best fit, r1 ¼ (6.0 0.2) nm, r2 ¼ (3.8 0.2) nm, are in good agreement with literature values [3,4]. A detailed analysis shows, that the outer and inner radius variation was correlated (deviations are directed in the same direction), and that the inner radius fluctuates over a wider range: Dr1 /r1 ¼ 2.7%, Dr2 /r2 ¼ 5.4% (FWHM). However, these small numbers demonstrate the good homogeneity of the sample. Moreover, the measured polydispersity is mainly due to elastic deformations of the protein shell, so that the mean size is even more regular [4]. 2 differ from the From Fig. 1 it is clearly seen that the data obtained in high salt solutions at q < 0.4 A form factor increasingly with the Apoferritin concentration. This indicates non-negligible hard sphere interactions and SðqÞ gets smaller than unity in this q-range. In describing SðqÞ, an analytical expression based on the Percus–Yevick closure relation [20] is used / 2 2 1 SðqÞ ¼ 1 þ 24 3 A ðsinðuÞ u cosðuÞÞ þ B 1 u cosðuÞ þ 2 sinðuÞ u u2 u A 24 6 12 24 þ/ þ 4 1 2 sinðuÞ 1 2 þ 4 u cosðuÞ ; ð3Þ 2 u3 u u u 2
4
2
4
with u ¼ q r, A ¼ ð1 þ 2 /Þ ð1 /Þ and B ¼ 3=2 / ð/ þ 2Þ ð1 /Þ , where r is the radius of model hard spheres and / is the volume fraction. In order to obtain IðqÞ fit functions, the respective expressions for SðqÞ are multiplied by F2 (q) and, finally, integrated over the wavelength band. Fig. 1 shows the fit functions obtained. Intensity data and theory are in good agreement. Moreover, from Fig. 2, where the respective SðqÞ fit curves are shown, it can 2 the deviation from unity is small, at least for the dilute system, and the form be seen that at q > 0.4 A factor fit to the data (see above) is justified in this q-range. 3.3. Paracrystalline order As reported above, the low-salt systems under study show correlation peaks, which can be explained by long-range electrostatic interactions between the Apoferritin molecules. Due to the neutron wavelength spread, the structure factor data of solutions with paracrystalline order can not be derived by simple division of the measured intensity by the form factor. R 2 The wavelength spread resembles a summation (integration) of data at different q-values: IðqÞ ¼ F ðqÞSðqÞ dq. Thus, division of IðqÞ through R the measured form factor data F 2 ðqÞ dq results in slight deviation from SðqÞ. Therefore, instead of calculating structure factor data, the intensity data IðqÞ of ordered solutions are described theoretically by convoluting a theoretical structure factor function and the form factor. For SðqÞ of the low salt solutions the Hosemann–Bacchi paracrystalline theory [21,22] is used analogously to the description applied in [4]
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Fig. 2. Structure factors SðqÞ of high-salt and low-salt Apoferritin solutions are shown together with model functions. The data are compared with the respective paracrystalline and Percus–Yevick theory curves (solid and dashed lines). The data peaks are broader than the theory peaks because of the wavelength spread of the neutrons (see text). The theory peak heights approach the data peak heights after having been convoluted with a function taking into account the wavelength spread (thin lines, see text).
% 1 þ exp 12 q2 Da21 i qa cosðHÞ SðqÞ ¼ du dHRe 1 exp 12 q2 Da21 i qa cosðHÞ $ % 1 þ exp 12 q2 Da21 i qa cosðuÞ sinðHÞ Re 1 exp 12 q2 Da21 i qa cosðuÞ sinðHÞ $ ! % 1 þ exp 12 q2 Da21 i qa sinðuÞ sinðHÞ sinðHÞ 1 expðq2 Da22 Þ þ 1; Re 1 exp 12 q2 Da21 i qa sinðuÞ sinðHÞ Z Z
$
ð4Þ
where a is the mean distance between the Apoferritin particles in solution, Da1 is the standard deviation from the mean distance a, and Da2 is the displacement due to thermal vibrations. In order to obtain IðqÞ fit functions the respective paracrystalline expressions are folded by a Gaussian taking into account the means size of ordered regions [4], then multiplied by the form factor and integrated over the wavelength band. Fig. 1 shows the fit functions obtained. Intensity data and theory are in good , Da1 ¼ 26 A , Da2 ¼ 14 A ; and 201 mg/ml, agreement. The fit values are: 156 mg/ml, 0.01 mM: a ¼ 187 A , Da1 ¼ 22 A , Da2 ¼ 10 A . 0.02 mM: a ¼ 171 A The error mentioned above in the division of the intensity data by the form factor are only small, if the dominant structures in the respective curves are much broader than the relative bandwidth similar to high salt solutions. In order to determine the error made in the division, ‘‘structure factor’’ data have been calculated in this way and are shown in Fig. 2 (156 and 201 mg/ml). The data are compared with both the structure factor functions SðqÞ used in the IðqÞ fits (Fig. 1) and with the same functions after having been integrated over q corresponding to a certain q-smearing. As can be seen from Fig. 2, both structure factor functions do not agree with the divided data. This shows, that the division process does not lead to usable data. The real structure factors (Fig. 2, lines) display peaks being much more pronounced than the divided data, while the smeared functions are too flat. Moreover, comparison between IðqÞ and SðqÞ shows, that the SðqÞ maximums are shifted slightly to higher q-values due to the negative slope of the form factor in the
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q-range under consideration. Only at high q-values does the wavelength spread have negligible influence on the division process. It has to be mentioned, that this is the reason the data shown in Fig. 2 are normalized in such a way that they fit to the theory at high q. 3.4. Dynamics in disordered and ordered solutions Fig. 3 displays the NSE relaxation rates extracted by means of a single exponential fit to the NSE data from low and high salt Apoferritin solutions. For high-salt systems, a linear dependence of the relaxation rate on q2 is expected, because for diffusion of non-interacting spherical particles, the normalized intermediate scattering function is given by Sðq; tÞ ¼ expðq2 D0 tÞ;
ð5Þ
with the Stokes–Einstein free-particle diffusion constant D0 ¼
kT ; 6pgrH
ð6Þ
where k is the Boltzmann factor, g is the viscosity of the solvent and rH the hydrodynamic radius of the spheres. This theoretical description is based on the assumption that the time scale of the experiment exceeds the short time fluctuations of the dissolved particles due to collisions with solvent molecules [23]. This assumption is justified when the experiment is sensitive to times above the Brownian relaxation time sB m=6pgr, where m is the mass and r the radius of the particle. For a particle of r ¼ 6 nm dissolved in aqueous solvent at room temperature, the Brownian relaxation time amounts to a few nanoseconds. The spin echo times used were 5–190 ns. The experimental data show a linear dependence with q2 in good agreement with theory (Fig. 3). The linear fit to the high salt data gives the diffusion constant of Apoferritin in D2 O: D0 ¼ 2.5 107 cm/s. The hydrodynamic radius rH of Apoferritin arises to 6.9 nm being slightly larger than r1 ¼ 6 nm found in
Fig. 3. Relaxation rates for the systems from Fig. 1. The high-salt data show free-particle diffusion as the relaxation rate C q2 . In low-salt solutions at low q, the dynamics is much faster and the relaxation rate C does not follow the free diffusion dependency C q2 . In addition, the C-curves cross the free-particle diffusion curve (line). Following the shape to higher q-values, the relaxation turns towards the free-particle diffusion line.
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the form factor fit. This deviation, consistent with literature values, is due to the hydration shell around the molecule in aqueous solution [24–26]. For interacting particles in low salt solution, Sðq; tÞ can be expanded at short times as l l ð7Þ lnðSðq; tÞÞ Deff q2 t þ 2 t2 þ 3 t3 ; 2 6 with the effective diffusion coefficient Deff (q) and the higher cumulants l2;3 . Similarly to the calculation above, a rough estimation of the interaction time sI needed by a non-interacting sphere of radius r ¼ 6 nm in order to diffuse a distance roughly equal to its radius in water, gives: sI r2 =D0 > 1 ls. This time exceeds the maximum spin echo times available at todayÕs NSE spectrometers, Eq. (7) is therefore applicable. Fig. 3 shows, that at low q, the dynamics in interacting solutions is faster than in non-interacting solutions, and the relaxation rate C does not pursue the free diffusion dependency C q2 . In addition, the relaxation rate crosses the free-particle diffusion line which is added to the plot. Following the shape to higher q-values, the relaxation turns towards the free diffusion line. This behavior is expected. The spatial resolution of the highq data is sensitive to small scale dynamics. Therefore, the intermediate scattering function (Eq. (5)) reflects self correlations at high q-values above q [27]. Because the relaxation rate approaches the curve describing the dynamics in non-interacting solutions, no sign of formation of aggregates in low salt systems is visible. Aggregation would lead to particles of larger hydrodynamic radius rH . However, the free diffusion relaxation is identical in all Apoferritin systems and the free diffusion hydrodynamic radius agrees with PCS results as it scales accordingly to C q2 . Finally, it has to be pointed out, that the intermediate scattering function decreases to almost zero at high spin echo times and high q-values. This was confirmed in all systems under study and can be seen clearly from the NSE data for the sample of 156 mg/ml Apoferritin concentration and 0.01 mM salt content measured with best statistics (Fig. 4). A primary result of the present study is that the dynamics of the Apoferritin system are completely relaxed. If there would be crystalline regions which are static on the time scale of the NSE experiment, the intermediate scattering function would approach a plateau value and the base line would not be rear zero. However, the NSE data show unambiguously that the diffusive motion of all particles contained by the sample solution is fast enough to be resolved in the given time window.
Fig. 4. Dynamic structure factors Sðq; tÞ measured on the sample of 156 mg/ml Apoferritin concentration and 0.01 mM salt content. Sðq; tÞ is fitted by a single exponential function for all curves taken at different q-values. Sðq; tÞ reaches almost zero for high q-values.
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All NSE data were fitted by means of a single exponential function. As this Gaussian approximation is valid only in the short time limit (Eq. (7)), we also fitted the data with a function taking into account the higher cumulants. However, the fitted values for the first cumulant did not differ from the values extracted from the single exponential fit, and the higher orders were close to zero.
4. Conclusions The present neutron scattering study was designed to determine if the slow mode found in paracrystalline ordered solutions of Apoferritin is due to heterogeneity by formation of crystallites in solution. We performed SANS and NSE experiments on Apoferritin solutions of varying protein and salt concentration. The shell-like form factor obtained from the high salt data is evidence that mainly Apoferritin monomers exist with only small polydispersity in the purified stock solution. The high salt solutions under study show Percus–Yevick-like structure, whereas low-salt Apoferritin solutions are described by the paracrystalline theory, being ordered due to electrostatic interactions. These systems are characterized analogously to the systems studied in [6], where formation of crystallites has been reported, and to the systems reported in [4], where slow dynamics has been found by means of PCS. The static solution structure of the systems under study resembles both earlier SAXS [4] and SANS results [6]. The previously reported features: (1) monodispersity, (2) paracrystalline order in interacting solutions, (3) crystallites found near the freezing transition and (4) appearance of slow dynamics [4,6] have raised the questions if crystallites forming in interacting solutions are responsible for the slow dynamics found by means of PCS. The present study shows that at q-values above q , the dynamics in solutions with electrostatic interactions present, approaches the diffusion found in non-interacting solutions. The free particle diffusion constant was found to agree with literature and previous PCS data. The dynamic structure factor obtained by means of NSE gives no evidence of elastic scattering, as the dynamics is completely relaxed at high q-values. The complex dynamical picture of Apoferritin in solution (the behavior at the PCS q-values [4,5]) can not be explained by heterogeneity of the solution. More likely is the presence of fluctuations on a large spatial scale, probably temporal ‘‘aggregates’’ in addition to the diffusive dynamics. In PCS, the scattered intensity is dominated by large scale density fluctuations. The formation of both large temporal aggregates and of fix aggregates or crystallites could equally lead to a drastic decrease of the relaxation rate in PCS, so they are indistinguishable. However, the dynamic structure factor measured in the present work by NSE shows no non-zero baseline, confirming the presence of Apoferritin monomers moving quasi-free at least over nm distances. These results exclude the explanation of the slow dynamics by static aggregates or crystallites.
Acknowledgements We would like to thank B. Farago for help with the NSE instrument IN15, and Christopher Bauser for correcting the manuscript.
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