The phase diagram of globular colloids is studied using a combined analytic and computational representation of the relevant chemical potentials. It is shown how the relative positions of the phase boundaries are related to the range of interaction and the number of contacts made per particle in the solid phase. The theory presented successfully describes the features of the phase diagrams observed in a wide variety of colloidal systems. [S0031-9007(96)
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 This is consistent with the observation that mean field is no longer applicable when λ≤1.65.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.
Protein crystallization, aggregation, liquidliquid phase separation, and self-assembly are important in protein structure determination in the industrial processing of proteins and in the inhibition of protein condensation diseases. To fully describe such phase transformations in globular protein solutions, it is necessary to account for the strong spatial variation of the interactions on the protein surface. One difficulty is that each globular protein has its own unique surface, which is crucial for its biological function. However, the similarities amongst the macroscopic properties of different protein solutions suggest that there may exist a generic model that is capable of describing the nonuniform interactions between globular proteins. In this paper we present such a model, which includes the short-range interactions that vary from place to place on the surface of the protein. We show that this aeolotopic model [from the Greek aiolos (''variable'') and topos (''place'')] describes the phase diagram of globular proteins and provides insight into protein aggregation and crystallization.Simple isotropic models that treat the protein molecules as spherical particles with short-range attractive interactions explain certain features of the protein phase diagram (1-5). In particular, liquid-liquid coexistence turns out to be metastable with respect to solidification when the range of interaction is less than one quarter of the particle diameter (6-10). This metastability has been observed for a variety of protein solutions (11-15) and in colloidal solutions (16-18), but not in simple fluids where the range of interaction is long (19). The isotropic model, however, fails to describe the phase diagram of protein solutions quantitatively and cannot address phenomena such as protein aggregation and self-assembly.We use a simple model in which the energy of each particle depends only on its position relative to other particles and on its own orientation but is independent of the orientation of other particles. In this model, the pair potential of particles i and j has the form w(Here, r ij is the vector distance between particles i and j while ⍀ represents the three Euler angles that define the orientation of the particle. For such an additive model, it is possible to define the orientation-averaged free energy, f i ({r ij }), of an individual particle asAs usual, N is the number of particles, and  ϭ 1͞k B T, where k B is Boltzmann's constant and T is the absolute temperature. The free energy f i ({r ij }) of a particle depends on the positions of all of the particles with which it interacts. . To study the conditions under which the aeolotopic potential u(⍀ i , r ij ) is ''averageable,'' i.e., accurately approximated by the effective potential U(r ij ), we use the following modified squarewell model. A protein molecule is represented by a spherical particle with a ''map'' of attractive regions covering a fractional area a of the surface. In this work, maps consisted of s non-overlapping spots of equal area...
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