Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein–protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim’s thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid–liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer–salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

The statistical mechanical approach to a fluid of dimerizing hard spheres proposed recently by Wertheim is extended to a two-component mixture of oppositely charged hard spheres. The pair potential is represented as a sum of the short-range hard-sphere potential, an intermediate-range square-well potential between the oppositely charged spheres, and a long-range Coulomb potential. The square-well potential, which is responsible for association, results from a single auxiliary site. If the site is located in such a way that only dimers are formed, the model presented here can be viewed as a model of chemical association in a fluid consisting of molecular ions. The model with the site located in the centre of hard sphere can be used to describe the formation of contact ion pairs in ionic systems. An analytical solution of the Ornstein-Zernike-like integral equation is obtained within a mixed Percus-Yevick and mean spherical approximation closure. The fraction of unbonded ions and the radial distribution functions are presented, and are studied as a function of the system density, the inverse reduced temperature, and the depth of the square well.

Results for the structural and thermodynamic properties of the primitive model of water obtained from the currently available theories and their modifications, namely from the generalized RISM, corrected RAM (cRAM), Dahl-Andersen (DA), and Wertheim (W) theories, and from a lattice model are compared with simulation data. It is shown that the first-order DA and W theories are reasonably accurate for both the internal energy and pressure and percentage occurrence of hydrogen bonded oligomers. Results for the structural properties are uniformly worse.

The multidensity formalism proposed recently by Wertheim is reformulated in order to describe the effects of association in fluids with spherically symmetric interactions. The basic idea is to separate the total potential into nonassociative and associative parts and make different approximations for each part of the potential. The idea is realized by assuming that the maximum number of particles which can be associated simultaneously with a particular particle is limited and equal to n _s. This property of steric saturation is introduced explicitly into the theory via the resummation of diagrams in the activity expansion of the logarithm of the grand partition function. The diagrams appearing in the activity expansion of the one-point density are classified in terms of the number of associative bonds incident upon the labelled white circle. The topological reduction of the diagrams carried out on the basis of this classification leads to an expansion in terms of n _s + 1 densities. A generalized version of the Ornstein-Zernike (OZ) equation is derived and closures are discussed. It is pointed out that the OZ equation yields, in the complete association limit, a new integral equation that is “proper” in the sense of Chandler and coworkers. The equation is appropriate to an important class of interaction site models, including a one parameter family of models that range from simple interaction site diatoms to highly cross-linked polymers. Off the complete association limit, our OZ equation provides a “proper” equation for partially associated systems of particles, including the central-force models introduced by Stillinger and his colleagues.

The structure and thermodynamic properties of a model of associating particles that dimerize into fused-sphere dumbbells are investigated by MC simulation and by integral-equation theory. The model particles, introduced by Cummings and Stell, associate as a result of shielded attractive shells. The integral equation theories are of two types. The first is an extension of Wertheim’s associative Percus–Yevick (APY) equation to the case of the shielded sticky shell model, which is the limiting case of the shielded attractive shell model that can be handled analytically. The second is the extended mean spherical approximation (EMSA) of Zhou and Stell applied to the shielded sticky shell model. In the case of partially associated systems, the EMSA requires as input the equilibrium association constant, which is obtained here using an exact relation between monomer density and a cavity correlation function, together with an equation of state due to Boublik. The structure obtained from the EMSA is in good agreement with the predictions of the MC simulation over a substantial density range that includes liquid-state densities, while the thermodynamic input from Boublik’s equation is in excellent agreement with the simulation results for all densities. Predictions of the APY approximation are also in good agreement with the simulation results as long as the density of the system is relatively low or, at high density, when the hard-core volume of a dimer is not substantially less than that of the two free monomers from which it is formed. There is an intermediate density range in which neither integral-equation theory gives correlation functions of high quantitative accuracy.

We develop an analytical theory for a simple model of liquid water. We apply Wertheim’s thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation function of the model water at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.