Theory of molecular crowding in Brownian hard-sphere liquids with application to the polymer coil-globule transition

Abstract

We derive an analytical pair potential of mean force for Brownian molecules in the liquid-state. Our approach accounts for many-particle correlations of crowding particles of the liquid, and for diffusive transport across the spatially modulated local density of crowders in the dense environment. Specializing on the limit of equal-size particles, we show that this diffusive transport leads to additional density- and structure-dependent terms in the interaction potential, and to a much stronger attraction (by a factor ~4 at average volume fraction of crowders 0.25) than in the standard depletion interaction where the diffusive effects are neglected. As an illustration of the theory, we use it to study the size of a polymer chain in a solution of inert crowders. Even in the case of athermal background solvent, when a classical chain should be fully swollen, we find a sharp coil-globule transition of the ideal chain collapsing at a critical value of the crowder volume fraction ~0.145.