For biotechnological drugs, it is desirable to formulate antibody solutions with low viscosities. We go beyond previous colloid theories in treating protein–protein self–association of molecules that are antibody–shaped and flexible and have spatially specific binding sites. We consider interactions either through fragment antigen (Fab–Fab) or fragment crystalizable (Fab–Fc) binding. Wertheim's theory is adapted to compute the cluster–size distributions, viscosities, second virial coefficients, and Huggins coefficients, as functions of antibody concentration. We find that the aggregation properties of concentrated solutions can be anticipated from simpler–to–measure dilute solutions. A principal finding is that aggregation is controllable, in principle, through modifying the antibody itself, and not just the solution it is dissolved in. In particular: (i) monospecific antibodies having two identical Fab arms can form linear chains with intermediate viscosities. (ii) Bispecific antibodies having different Fab arms can, in some cases, only dimerize, having low viscosities. (iii) Arm–to–Fc binding allows for three binding partners, leading to networks and high viscosities.

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 cloudpoint 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.phase separation | protein aggregation | Hofmeister series P rotein molecules can aggregate with each other. This process is important in many ways (1). First, a key step in developing biotech drugs-which are mostly mABs-is to formulate proteins so that they do not aggregate. This is because good shelflife requires long-term solution stability, and because patient compliance requires liquids having low viscosities. The importance of such formulations comes from the fact that the world market for protein biologicals is about the same size as for smartphones. Second, protein aggregation in the cell plays a key role in protein condensation diseases, such as Alzheimer's, Parkinson's, Huntington's, and others. Third, much of structural biology derives from the 100,000 protein structures in the Protein Data Bank, a resource that would not have been possible without protein crystals, a particular state of protein aggregation. Also, it is not yet possible to rationally design the conditions for proteins to crystallize.However, protein aggregation is poorly understood. Atomistic-level molecular simulations are not practical for studying multiprotein interactions as a function of concentration, and in liquid solutions that are themselves fairly complicated-that account for salts of different types and concentrations as well as other ligands, excipients, stabilizers, or metabolites. So, a traditional approach is to adapt colloid theories, such as the DerjaguinLandau-Verwey-Overbeek (DLVO) (2) theory. In those treatments, proteins are represented as spheres that interact through spherically symmetric van der Waals and electrostatic interactions in salt water, using a continuum representation of solvent and a Debye-Hückel screening for salts. DLVO often gives correct trends for the pH and salt concentration dependencies. However, DLVO does not readily account for protein sequence-structure properties, salt bridges (which are commonly the "glue" holding protein crystals together), explicit waters in general, or Hofmeister effects, where different salts have widely different powers of protein precipitation...

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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.

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