(450b) Coarse-Graining Binary Reactive Mixtures to Effective One-Component Systems: from Hard Spheres to Globular Proteins

We investigate the chemical equilibria and fluid phase behavior of assymetric binary reacting mixtures of particles interacting via spherically symmetric short-ranged potentials. We first integrate over the degrees of freedom of the smaller particles with a McMillan-Mayer framework to obtain an effective Hamiltonian for the one-component system of larger particles. Neglecting the three- and higher-body contributions, we obtain an expression for the effective Hamiltonian in terms of partition functions for zero, one, and two particles of larger spheres in a bath of smaller spheres at a given fugacity. We then use highly efficient transition-matrix Monte Carlo simulations for the effective one-component system in the grand canonical ensemble to obtain the equilibrium mole fractions and fluid phase boundaries for the binary mixture. Within the above framework, we study binary mixtures of varying complexity from hard-spheres to a solution of model globular proteins with denatured and native states. We also assess the validity of the effective one-component coarse-graining scheme by comparing to the behavior of the full two-component systems.