Monte Carlo study of phase separation in aqueous protein solutions

Abstract

The binary liquid phase separation of aqueous solutions of γ-crystallins is utilized to gain insight into the microscopic interactions between these proteins. The interactions are modeled by a square-well potential with reduced range λ and depth ε. A comparison is made between the experimentally determined phase diagram and the results of a modified Monte Carlo procedure which combines simulations with analytic techniques. The simplicity and economy of the procedure make it practical to investigate the effect on the phase diagram of an essentially continuous variation of λ in the domain 1.05≤λ≤2.40. The coexistence curves are calculated and are in good agreement with the information available from previous standard Monte Carlo simulations conducted at a few specific values of λ. Analysis of the experimental data for the critical volume fractions of the γ-crystallins permits the determination of the actual range of interaction appropriate for these proteins. A comparison of the experimental and calculated widths of the coexistence curves suggests a significant contribution from anisotropy in the real interaction potential of the γ-crystallins. The dependence of the critical volume fraction φc and the reduced critical energy ε̂c upon the reduced range λ is also analyzed in the context of two ‘‘limiting’’ cases; mean field theory (λ→∞) and the Baxter adhesive sphere model (λ→1). Mean field theory fails to describe both the value of φc and the width of the coexistence curve of the γ-crystallins. This is consistent with the observation that mean field is no longer applicable when λ≤1.65. In the opposite case, λ→1, the critical parameters are obtained for ranges much shorter than those investigated in the literature. This allows a reliable determination of the critical volume fraction in the adhesive sphere limit, φc(λ=1)=0.266±0.009.

Colloidal Characterization and Thermodynamic Stability of Binary Eye Lens Protein Mixtures

“…The SW potential, in particular, has already been successfully used to model the phase behavior of γ-crystallins. 23 The choice of SW potential is certainly not unique, and other shapes of the potential could also be considered. However, when the range of a spherically symmetric model attraction is smaller than the diameter of the particles, the phase diagram, liquid structure, and dynamics of the system are scarcely dependent on the exact shape of the potential, the second virial coefficient being the relevant parameter for both statics and dynamics.…”

“…The discovery of a metastable liquid-liquid phase separation provided the evidence for a short-range attraction between γ-crystallins, and the use of the corresponding colloid model has led to a quantitative description of the phase behavior. [19][20][21][22][23][24] Crystallin aggregation and liquid-liquid phase separation can both produce density inhomogeneities that are principal sources of increased light scatter in cataract and therefore continue to be major themes of lens protein research. Liquid-liquid phase separation not only gives rise to the so-called cold cataract 25 but also dramatically enhances light scattering at body temperature, well above the critical point.…”

Self-diffusion of reversibly aggregating spheres

“…It leads to different equilibrium states depending on the volume fraction (φ) of the particles and the strength of the interaction energy (u). Weak attraction results in the formation of transient aggregates at low φ and a transient percolating network at high φ, while strong attraction may drive phase separation into a high and a low density liquid [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]. The strength of the interaction and thus the equilibrium properties are determined by the ratio of the bond formation (α) and the bond breaking (β) probability [32,33,34,35,36,37,38,39,40,41,42,43,44,45], while the kinetics of such systems depend on the absolute values of α and β.…”

Strong weak and metastable liquids structural and dynamical aspects of the liquid state

“…Recently it was realized that the explanation for the metastability in these protein systems probably lies again in the fact that the interaction range is small compared to the protein size [19,[27][28][29][30][31].…”