Formation of the Dynamic Clusters in Concentrated Lysozyme Protein

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Formation of the Dynamic Clusters in Concentrated Lysozyme Protein Solutions )

Lionel Porcar,† Peter Falus,† Wei-Ren Chen,‡ Antonio Faraone,§, Emiliano Fratini,^ Kunlun Hong,# Piero Baglioni,^ and Yun Liu*,§,3 ILL, B. P. 156, F-38042 Grenoble CEDEX 9, France, ‡NSS Division, Spallation Neutron Source, ORNL, Oak Ridge, Tennessee 37831, §NCNR, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, Department of Materials Science and Engineering, University of Maryland, College Park, Maryland 20742, ^ Department of Chemistry and CSGI, University of Florence, Florence, I-50019, Italy, #CNMS, ORNL, Oak Ridge, Tennessee 37831, and 3Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716

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ABSTRACT Neutron spin echo (NSE) and small angle neutron scattering (SANS) were used to investigate the correlation between structure and short-time dynamics of lysozyme solutions in the presence of protein clusters as previously reported. It was found that, upon increasing protein concentration, the selfdiffusion coefficient at the short time limit becomes much smaller than that of the corresponding hard-sphere and charged colloidal suspensions at the same volume fraction. Contrary to literature conclusions, we find that, at relatively low concentrations, the system consists mostly of monomers or dimers, while, at high concentrations, large dynamic clusters dominate. Our results will benefit the understanding of colloidal systems with both a short-range attraction and an electrostatic repulsion that are ubiquitous in many biologically relevant systems. SECTION Dynamics, Clusters, Excited States

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It is our understanding that the additional correlation peak observed in the SANS/SAXS patterns can result from clustering effect originating from different dynamical mechanisms: one scenario is the previously proposed permanent cluster model, which envisions the cluster as tightly bound protein aggregates.1,11 In this picture, the thermodynamic properties are governed by the cluster entities rather than the protein monomers. Another possibility is the idea of transient clusters describing the physical origin of the clusters with a lifetime so short that the constituent proteins move almost independently. Within the same structure, it is also possible that the proteins move together in a short time period similar to those in a permanent cluster, but escaping from the cluster after a certain time. In this dynamic cluster model, a finite lifetime is associated with any given cluster whose aggregation number and overall shape fluctuate dramatically. Despite large differences of the dynamic properties among the three pictures, all should present a common feature, i.e., a cluster peak in SANS/ SAXS patterns. The transient cluster model is similar to the physical picture of the conclusion of Shukla et al. Up to now, only elastic scattering techniques, which provide structural information, have been used to investigate this peculiar phase behavior. The dynamical properties of these systems, which contain critical information to resolve the current controversy, remain unexplored.

he investigation of intercolloidal interaction in solutions provides critical information for understanding the phase behaviors of colloidal suspensions and has long been an active research subject of soft matter studies.1-5 Recently, observations of colloidal clusters have been reported in various systems and triggered a lively debate regarding their physical origin and properties.1,4,6-9 Small angle neutron scattering (SANS) experiments show that, in addition to the commonly observed protein-protein correlation peak, the formation of clusters is revealed by an additional intercluster correlation peak located at a much smaller scattering vector Q.1,6,10 These characteristics are attributed to the competition between the intercolloidal short-range attraction and long-range repulsion.1,4,7,10 Intriguingly, in concentrated lysozyme solutions, SANS experiments revealed no change of the cluster peak position upon increasing concentration from 3 mg/mL-1 to 273 mg/mL-1, indicating an invariance of the cluster number density and a linear dependence of the protein association number on concentration.1 These clusters have been considered as long-lived permanent clusters.1,11 However, these results have recently been questioned by the outcome of a joint SANS/small angle X-ray scattering (SAXS) study performed at the very same experimental conditions: Shukla et al. definitely excluded the existence of an equilibrium cluster phase and claimed that the system contains largely repulsive individual lysozyme proteins.12 Thus, the existence and the physical nature of these clusters remain unclear.

r 2009 American Chemical Society

Received Date: October 12, 2009 Accepted Date: November 3, 2009 Published on Web Date: November 10, 2009

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DOI: 10.1021/jz900127c |J. Phys. Chem. Lett. 2010, 1, 126–129

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Figure 1. SANS results of lysozyme solutions at different concentrations and temperatures. The curves with open black circles and green stars are taken at 25 and 8 C, respectively. Error bars are smaller than the symbol size.

To thoroughly understand the clustering phenomenon, we have conducted a synergistic study of lysozyme protein solutions using SANS and neutron spin echo (NSE) at the NIST Center for Neutron Research (NCNR) (NG3, NG7, and NG5) and the Institute Laue-Langevin (ILL) (D22 and IN15), to simultaneously access the relevant length and time scales. In this letter, we found that lysozyme solutions actually behave quite differently at different concentrations. One model is not adequate enough to describe the system behavior at the wide range of concentrations. At low protein concentration, the system dynamics are mostly dominated by the motion of monomers or dimers, despite the clear presence of a cluster peak in the corresponding SANS patterns, which agrees with the conclusion of Shukla et al. However, when the concentration increases, larger dynamic clusters are formed whose average hydrodynamic radius increases rapidly with the concentration. Lysozyme D2O solutions were prepared with different mass fractions ranging from 5 wt % to 22.5 wt % in 20 mM HEPES buffer. The details of sample preparation are given elsewhere.10,13 SANS patterns are shown in Figure 1. Quantitative analysis of the scattered intensity using a model fitting based on statistical mechanic theories10 yield a value of about 4 kBT for the short-range attractive potential at ambient temperature in good agreement with earlier reports.10,14 Furthermore, at high concentrations, the cluster peak at Qc ≈ 0.08 Å-1 shifts to lower Q values as the temperature decreases, while the protein-protein correlation peak position, Qm, remains at ∼0.22 Å-1.9,12 Therefore, our samples are similar to those studied previously.1,10,12 To understand the dynamics of these clusters, the normalized coherent intermediate scattering function (ISF), S(Q,t)/ S(Q), was measured using NSE at different lysozyme concentrations.15 In the short time limit, namely for time scale shorter than the structural relaxation time but longer than the momentum and viscous relaxation time, the ISF can be expressed as exp[-Q2Dc(Q)t], where Dc(Q) is the collective diffusion coefficient and can be formulated as Dc(Q) = D0H(Q)/S(Q),16 where D0 is the diffusion coefficient at infinite dilution, S(Q) is the interparticle structure factor, and H(Q) is the hydrodynamic function.


Figure 2. (a) S(Q,t)/S(Q) is shown for a mass fraction of 5% lysozyme solution. (b) S(Q,t)/S(Q) is shown for a mass fraction of 22.5% lysozyme solution. (c) Dc(Q) is shown at different concentrations. All measurements were taken at 25 C. Vertical lines are error bars representing one standard deviation.

The measured ISFs at mass fractions of 5% and 22.5% are given in Figure 2a,b. Clearly, the ISF can be well-described by a single exponential function for t < 25 ns, but it begins to deviate from a single exponential function at longer times. The Dc(Q) extracted by fitting the ISF at t < 25 ns is shown in Figure 2c. Within the studied range, Dc(Q) progressively slows down with increasing concentration. Interestingly, Dc(Q) remains essentially constant versus Q for Q > Qc for all the concentrations. These results are different from previous observations obtained for hard sphere (HS),17 charged colloidal (CS) systems,18 and apoferritin protein solutions,19 which all present no equilibrium clusters. In these systems, Dc(Q) reaches a minimum value around the Q value of the first peak position of the structure factor. Hence, 1/Dc(Q) shows a Q dependence similar to S(Q). It is noticed that the Q dependence of Dc(Q) found in our system is qualitatively similar to that of myoglobin solutions.20 In Figure 2c, the increase of Dc at Q < Qc is due to the collective diffusion, while there is hardly any enhanced diffusion at high Q, where intermonomer movement could be detected. The short-time self-diffusion coefficient Ds can be approximated by the asymptotic value of Dc at high Q, an approach commonly used in dynamic light scattering (DLS).21 Ds normalized to D0 is given in Figure 3a as a function of lysozyme volume fraction, φ, calculated using the protein density reported in ref 22. In general, for a one-component system without cluster formation, Ds/D0 = η0/η¥C(φ), where η0 is the solvent viscosity, η¥ is the viscosity of the solution in

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the high frequency limit, and C(φ) is the correction term.23 For an HS system, C(φ) = 1 þ 0.67φ and η¥/η0 = 1 þ 2.5φ þ 5.0023φ2 þ 9.09φ3, while for a CS system, Ds/D0 ≈ 1 - 2.5φ4/3 for φ < 0.3.18,23 As a result of increasing φ, Ds decreases due to hydrodynamic interactions.21,23,24 However, Ds for lysozyme solutions shows a much faster decay than that of the typical HS system (black circles) or a CS system (blue triangles). This dynamical slowing down can be quantified via a simple linear fitting of Ds/D0 = 1 - λφ. For lysozyme solutions, λ is found to be ∼3.9, which is significantly larger than the λ value for HS (λ ≈ 1.8) and CS (λ < 1.8) systems.25,26 This unusual slower diffusion can be due to the formation of dynamic clusters. At the short-time limit, there is essentially no difference between dynamic clusters and permanent clusters once a cluster is formed. This is because the probed correlation time is smaller than that of the lifetime of a dynamic cluster. Thus, we could estimate the hydrodynamic radius of clusters by the generalized Einstein-Stokes relation with the appropriate values of η¥/η0 and C(φ). Since η¥/η0 and C(φ) are not sensitive to the interparticle potential,18,27 theories of an HS system will be used. In addition, when the proteins form clusters, the repulsion starts to dominate the intercluster interaction.7 And the inclusion of an additional repulsive interaction changes η¥/η0 and C(φ) by only about 10% compared to that of an HS system.23 Therefore, the estimation based on theories of HS systems is expected to be reasonably accurate at high concentrations too. We will estimate the average cluster size approximately using the following relation: Rh/R0 = (D0/Ds)(η0 /η¥)C(φ),28 where Rh and R0 are the hydrodynamic radius of a cluster and a protein monomer respectively. The results are presented in Figure 3b), which shows a general monotonic increase of Rh as a function of φ. At a mass fraction of 5%, Rh/R0 is only about 1.2, indicating that the majority of proteins still remain in a monomer or dimer state. When the concentration increases, Rh increases to about 2.5R0 at φ ≈ 0.2, indicating the progressive formation of larger dynamic clusters in the solution. At such a large concentration, clusters may touch each other so that Qm/Qc can be a good estimate of Rh/R0. The measured Rh/R0 indeed approaches the maximum allowed value defined by Qm/Qc = 2.75. This further supports that our approximation is reasonable. Although Shukla et al. have suggested that there are no permanent clusters, we show here that proteins can still form clusters in a short time at high concentrations. However, eventually protein monomers will escape from clusters as a result of Brownian motions. Hence, what is observed in lysozyme solutions are dynamic clusters with a finite lifetime. It is reasonable to assume that the average lifetime of a dynamic cluster is larger than 25 ns, as S(Q,t)/S(Q) can be well fitted with a single exponential function for t < 25 ns.29 Since decreasing temperature shifts the cluster peak to smaller Q values, it is therefore interesting to understand how Rh changes with temperature. Figure 4a shows the Q dependence of Dc at 25 and 5 C for the protein concentration of 22.5 wt %. The estimated Rh is found to increase from 2.5R0 to 3.6R0, indicating that the cluster size increases with decreasing temperature. This is quantitatively consistent with the shift of Qc from ∼0.08 Å-1 to ∼0.06 Å-1 when the


Figure 3. (a) Diffusion coefficients normalized by D0 (10.6 Å2/ns in D2O at 25 C) as a function of volume fraction φ. (b) Normalized hydrodynamic radius (see text for details). The vertical lines give error bars with one standard deviation. Lines are guides for the eyes.

Figure 4. (a) Diffusion coefficients of lysozyme protein solution at a mass fraction of 22.5% measured at two different temperatures. (b) The ratio of Dc/D0 at different temperatures (see text for details). The vertical lines are error bars representing one standard deviation.

temperature decreases from 25 to 8 C as shown in Figure 1d. The average maximum cluster size is estimated to be ∼3.7R0 at 8 C, very close to the measured value. In addition, as expected, Dc remains constant for Q > Qc because lowering the temperature increases the lifetime of the dynamic clusters. Figure 4b shows the ratio of Dc/D0 between these two temperatures. It is interesting to observe that there seems to be a minimum around 0.06 Å-1, indicating that, at 5 C, there might be additional slowing down of dynamics at the length scale corresponding to the cluster peak position. In summary, the short-time dynamics of concentrated lysozyme solutions are investigated in this joint NSE/SANS study. The near-constant value of Dc at Q > Qc in our time window implies that there is hardly any intermonomer (intracluster) protein dynamics within a cluster in our dynamic window. We found that Ds/D0 decays much faster as a function of concentration compared to other model systems. Moreover, based on the average cluster size, it is concluded that very few dynamic clusters exist at relatively

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low concentrations. However, more and more dynamic clusters are formed upon increasing concentration, and the properties of the protein solution are essentially determined by the properties of the dynamic clusters in the short-time limit. Because of the ergodic nature of dynamic clusters, the macroscopic properties of the long time limit are still determined by monomeric proteins. Therefore, the OrnsteinZernike integral equation approach can be still valid to analyze SANS/SAXS data. It is instructive to point out that the concept of dynamic clusters is different from that of a micelle. Although there is still molecular exchange in a micelle, the size and shape fluctuation are much less pronounced than for a dynamic cluster. Therefore the thermodynamic properties of a micellar system are still determined by the intermicellar interaction. In this regard, micelle is intrinsically similar to the previously defined permanent clusters.

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SUPPORTING INFORMATION AVAILABLE Derivation of

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the equation for the estimation of the apparent hydrodynamic radius of clusters. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION Corresponding Author:

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*To whom correspondence should be addressed. E-mail address: [email protected].

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ACKNOWLEDGMENT This manuscript was prepared under cooperative agreement 70NANB7H6178 from NIST, U.S. Department of Commerce. E.F. and P.B. acknowledge financial support from MIUR and CSGI.

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Formation of the Dynamic Clusters in Concentrated Lysozyme Protein

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