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)

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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 This is consistent with the observation that mean field is no longer applicable when λ≤1.65.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...

Several human genetic cataracts have been linked recently to point mutations in the ␥D crystallin gene. Here we provide a molecular basis for lens opacity in two genetic cataracts and suggest that the opacity occurs because of the spontaneous crystallization of the mutant proteins. Such crystallization of endogenous proteins leading to pathology is an unusual event. Measurements of the solubility curves of crystals of the Arg-58 to His and Arg-36 to Ser mutants of ␥D crystallin show that the mutations dramatically lower the solubility of the protein. Furthermore, the crystal nucleation rate of the mutants is enhanced considerably relative to that of the wild-type protein. It should be noted that, although there is a marked difference in phase behavior, there is no significant difference in protein conformation among the three proteins.H uman ␥D crystallin is a member of a highly homologous family of mammalian lens proteins called the ␥ crystallins (1). Together with the ␣ and ␤ crystallins, these proteins are essential for maintaining lens transparency. However, the ␥ crystallins differ from the ␣ and ␤ crystallins in one important respect: the interactions between the ␥ crystallins are attractive (2). This feature reduces the osmotic pressure in the lens, but it also makes the ␥ crystallins more susceptible to aggregation and phase separation, phenomena that diminish the homogeneity of the lens and lead to cataract (3). Yet, despite these attractive interactions, the ␥ crystallins remain soluble for many years at high concentrations and with little turnover, maintaining the proper refractive index gradient of the lens (4).It is well known that random mutations in proteins dramatically affect their solubility (5). In this article, we show that the Arg-58 to His (R58H) mutant [linked to the aculeiform cataract (Fig. 1a; ref. 6)] and the Arg-36 to Ser (R36S) mutant [linked to another form of genetic (congenital) cataract ( Fig. 1b; ref. 7)] are much less soluble than the wild-type human ␥D crystallin protein (HGD). We also show that these mutants are more prone to crystallize than the wild-type. Indeed, Kmoch et al. (7) recently extracted crystals of the R36S mutant from the eye of a young patient. To determine the mechanism of cataract formation caused by these mutations, we compared the conformation, stability, and phase behavior of the recombinant HGD, R58H, and R36S proteins in solution. Materials and MethodsCloning, Expression, and Isolation of Proteins. Recombinant human ␥D crystallin was prepared by the amplification of the coding sequence from a human fetal lens cDNA library as detailed (8). Overexpression of ␥D crystallin, and isolation and purification of the protein, were all done according to procedures as described (8). Mutant proteins were prepared as follows.(i) The R58H mutant. To introduce a histidine mutation in place of Arg-58, the following oligonucleotide primers were made: 5Ј-CCAGTACTTCCTGCACCGCGGCGACTATGC-3Ј as the forward primer and 5Ј-GCATAGTCGCCGCGGTGCAG-GAAGTACTGG-3Ј as the reverse prime...

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We have expressed recombinant wild-type human ␥D crystallin (HGD) and its Arg-14 to Cys mutant (R14C) in Escherichia coli and show that R14C forms disulfide-linked oligomers, which markedly raise the phase separation temperature of the protein solution. Eventually, R14C precipitates. In contrast, HGD slowly forms only disulfide-linked dimers and no oligomers. These data strongly suggest that the observed cataract is triggered by the thiolmediated aggregation of R14C. The aggregation profiles of HGD and R14C are consistent with our homology modeling studies that reveal that R14C contains two exposed cysteine residues, whereas HGD has only one. Our CD, fluorescence, and differential scanning calorimetric studies show that HGD and R14C have nearly identical secondary and tertiary structures and stabilities. Thus, contrary to current views, unfolding or destabilization of the protein is not necessary for cataractogenesis.I n the hereditary, juvenile-onset cataract described by Stefan et al. (1), the lens, which is clear at birth, develops punctate opacities progressively, such that by two years of age the cataract is readily detectable, and matures by early childhood or adolescence. The punctate opacities seen in this cataract are in the nucleus and inner cortex, regions of the lens that are enriched in the ␥-crystallins. In the human lens, only two members of the ␥-crystallin family, ␥C and ␥D, are expressed in appreciable amounts, and only ␥D crystallin continues to be expressed until late childhood (2, 3). In affected individuals, a single point mutation has been identified in the ␥D crystallin gene that corresponds to the substitution of Arg-14 by a Cys. The identification of this mutation and the parallel between the time course of the pathology and the physiological expression of human ␥D crystallin strongly implicate the Arg-14 3 Cys mutant of ␥D in the development of this cataract. However, the molecular mechanism invoked to explain the observed opacity has been speculative (1).In the past, it has not been possible to conduct detailed studies on human ␥D crystallin because of the difficulty of obtaining sufficient quantities of pure protein from young, normal human lenses (4). Therefore, to characterize the normal protein thoroughly and investigate the mechanism by which the Arg-14 3 Cys mutation in ␥D could lead to cataract, we cloned and expressed human ␥D crystallin and its Arg-14 3 Cys mutant in Escherichia coli. Both the wild-type recombinant ␥D crystallin (HGD) and its Arg-14 3 Cys mutant (R14C) folded efficiently in E. coli and accumulated as soluble proteins. We isolated and purified the HGD and R14C proteins and determined their solution properties. Our results suggest that the disulfidecrosslinked oligomerization of R14C is responsible for the observed cataract. Furthermore, such oligomerization occurs without significant change in protein structure, conformation, and stability. Materials and MethodsCloning, Expression, and Isolation of Proteins. The human ␥D crystallin coding sequence was amplif...

We have studied the effect of polyethylene glycol (PEG) on the liquid-liquid phase separation (LLPS) of aqueous solutions of bovine ␥D-crystallin (␥D), a protein in the eye lens. We observe that the phase separation temperature increases with both PEG concentration and PEG molecular weight. PEG partitioning, which is the difference between the PEG concentration in the two coexisting phases, has been measured experimentally and observed to increase with PEG molecular weight. The measurements of both LLPS temperature and PEG partitioning in the ternary ␥D-PEGwater systems are used to successfully predict the location of the liquid-liquid phase boundary of the binary ␥D-water system. We show that our LLPS measurements can be also used to estimate the protein solubility as a function of the concentration of crystallizing agents. Moreover, the slope of the tie-lines and the dependence of LLPS temperature on polymer concentration provide a powerful and sensitive check of the validity of excluded volume models. Finally, we show that the increase of the LLPS temperature with PEG concentration is due to attractive protein-protein interactions.PEG ͉ ternary mixtures ͉ solubility ͉ partitioning P olyethylene glycol (PEG) is a hydrophilic nonionic polymer used in many biochemical and industrial applications. Due to its nontoxic character, this chemical can be found in cosmetics, food, and pharmaceutical products. The mild action of PEG on the biological activity of cell components explains the success of this polymer in biotechnological applications. PEG is commonly used for liquid-liquid partitioning and precipitation of biomacromolecules (1, 2). In protein crystallography, PEG is considered the most successful precipitating agent for the production of protein crystals, the crucial step for the determination of the molecular structure of a protein. All these applications make PEG by far the most widely used polymer in aqueous solutions of biological molecules (1, 3).Due to the extensive practical use of PEG as a precipitating agent for proteins, it is of fundamental importance to understand protein-protein and protein-PEG interactions in protein-PEGwater ternary systems. These interactions are often described in terms of a depletion force, which arises because the polymer is depleted in the region between adjacent proteins (4, 5). Depletion force models have been successful in describing the effect of nonadsorbing polymers on colloidal suspensions (6-10).Protein-PEG-water solutions have been investigated by several techniques (4,5,(11)(12)(13)(14). Small-angle x-ray-(4) and lightscattering (5) measurements generally confirmed that total protein-protein interactions can be described in terms of depletion effects. The microscopic interpretation used in the above studies is derived from colloid-polymer models. To model the effect of PEG, a depletion component is added to the original protein-protein pair interaction potential. This microscopic modeling, however, does not provide information about the actual protein-PEG intera...