  We present a multiscale approach to model diffusion in a crowded environment
and its effect on the reaction rates. Diffusion in biological systems is often
modeled by a discrete space jump process in order to capture the inherent noise
of biological systems, which becomes important in the low copy number regime.
To model diffusion in the crowded cell environment efficiently, we compute the
jump rates in this mesoscopic model from local first exit times, which account
for the microscopic positions of the crowding molecules, while the diffusing
molecules jump on a coarser Cartesian grid. We then extract a macroscopic
description from the resulting jump rates, where the excluded volume effect is
modeled by a diffusion equation with space dependent diffusion coefficient. The
crowding molecules can be of arbitrary shape and size and numerical experiments
demonstrate that those factors together with the size of the diffusing molecule
play a crucial role on the magnitude of the decrease in diffusive motion. When
correcting the reaction rates for the altered diffusion we can show that
molecular crowding either enhances or inhibits chemical reactions depending on
local fluctuations of the obstacle density.
