Simulating Reaction-Diffusion with State-Dependent Diffusion Coefficients

The present models and simulation algorithms of intracellular kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even for small prokaryotic cells. In this work we first present a mathematical description of the diffusion induced by concentration gradient. In our model the diffusion coefficients and mechanical quantities as frictional forces are dependent on the local values of solutes concentration. We then present an algorithm implementing our model and simulating a reaction-diffusion system. The algorithm is an efficient modification of the well known Gillespie algorithm, adapted for systems that are both reactive and diffusive.