Assessing accumulated solvent near a macromolecular solute by preferential interaction coefficients

Biological macromolecules are often studied in mixed solvents. To understand cosolvent-macromolecule interactions, the preferential interaction coefficient, Gamma(3), may help determine surface solvent compositions' Gamma(3) measures the amounts of water, B-1, and cosolvent, B-3, within the local domain, the (possibly far-reaching) region surrounding the macromolecule where the solvent is nonbulk-like. The local domain's boundary is, however, vague and it is unclear which molecules are counted in B-1. It is useful to explore a simple model system to make B-1 more concrete and to understand which aspects of the surface solvent distribution, p(x), are sampled by Gamma(3). We performed computer simulations on a two-dimensional (2D) system consisting of a hard-wall solute (the macromolecule) in a mixed solvent (hard disks of different radii). We simultaneously calculated Gamma(3) and p(x). We found that 1) in practice, the local domain's boundary is demarked by the outer limit of the first cosolvent (not water) layer; B-1 mainly counts the solvent near the macromolecule; 2) assuming B-1 to count only the waters within the first water layer is a poor approximation; 3) when determining B-1 and B-3 water and cosolvent molecules must be counted from the same region of space. We speculate that these 2D results may serve as a first-order approximation for the dominant contributions to Gamma(3) even in three dimensions, so long as the cosolvent is not strongly excluded from the macromolecular surface and there is no significant long-ranged solvent structure.