  Brownian dynamics simulations are an increasingly popular tool for
understanding spatially-distributed biochemical reaction systems. Recent
improvements in our understanding of the cellular environment show that volume
exclusion effects are fundamental to reaction networks inside cells. These
systems are frequently studied by incorporating inert hard spheres (crowders)
into three-dimensional Brownian dynamics simulations, however these methods are
extremely slow owing to the sheer number of possible collisions between
particles. Here we propose a rigorous "crowder-free" method to dramatically
increase simulation speed for crowded biochemical reaction systems by
eliminating the need to explicitly simulate the crowders. We consider both the
case where the reactive particles are point particles, and where they
themselves occupy a volume. We use simulations of simple chemical reaction
networks to confirm that our simplification is just as accurate as the original
algorithm, and that it corresponds to a large speed increase.
