Abstract
It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection-diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions. The interplay between advection and diffusion leads to behaviour that differs significantly from Brownian diffusion. We show that biologically plausible distributions of macromolecules can lead to highly non-Gaussian probability densities for the small particle position, including asymmetrical and multimodal densities. We confirm all our results using hard-sphere Brownian dynamics simulations.