Incorporation of Hard and Soft Protein–Protein Interactions into Models for Crowding Effects in Binary and Ternary Protein Mixtures. Comparison of Approximate Analytical Solutions with Numerical Simulation

In order to better understand how nonspecific interactions between solutes can modulate specific biochemical reactions taking place in complex media, we introduce a simplified model aimed at elucidating general principles. In this model, solutions containing two or three species of interacting globular proteins are modeled as a fluid of spherical particles interacting through square well potentials that qualitatively capture both steric hard core repulsion and longer-ranged attraction or repulsion. The excess chemical potential, or free energy of solvation, of each particle species is calculated as a function of species concentrations, particle radii, and square well interaction range and depth. The results of analytical models incorporating two-body and three-body interactions are compared with the estimates of free energy obtained via Widom insertion into simulated equilibrium square-well fluids. The analytical models agree well with results of numeric simulations carried out for a variety of model parameters and fluid compositions up to a total particle volume fraction of ca. 0.2.