  Assembly of protein complexes like virus shells, the centriole, the nuclear
pore complex or the actin cytoskeleton is strongly determined by their spatial
structure. Moreover it is becoming increasingly clear that the reversible
nature of protein assembly is also an essential element for their biological
function. Here we introduce a computational approach for the Brownian dynamics
of patchy particles with anisotropic assemblies and fully reversible reactions.
Different particles stochastically associate and dissociate with microscopic
reaction rates depending on their relative spatial positions. The translational
and rotational diffusive properties of all protein complexes are evaluated
on-the-fly. Because we focus on reversible assembly, we introduce a scheme
which ensures detailed balance for patchy particles. We then show how the
macroscopic rates follow from the microscopic ones. As an instructive example,
we study the assembly of a pentameric ring structure, for which we find
excellent agreement between simulation results and a macroscopic kinetic
description without any adjustable parameters. This demonstrates that our
approach correctly accounts for both the diffusive and reactive processes
involved in protein assembly.
