Modeling Diffusion Between Regions with Different Diffusion Coefficients

Biological systems often include spatial regions with different diffusion coefficients. Explicitly simulating their physical causes is computationally intensive, so it is typically preferable to simply vary the coefficients. This raises the question of how to address the boundaries between the regions. Making them fully permeable in both directions seems intuitively reasonable, but causes molecular motion to be simulated as active diffusion, meaning that it arises from energy that is continuously added to the system; in this case, molecules accumulate on the slow-diffusing side. However, molecular motion in most biochemical systems is better described as thermal diffusion, meaning that it occurs even at equilibrium. This can be simulated by reducing the transmission probability into the slow-diffusing side, which yields the correct result that spatially varying diffusion coefficients that arise from macromolecular crowding, changes in viscosity, or other energy-neutral influences do not affect equilibrium molecular concentrations. This work presents transmission coefficients and transmission probability equations for simulating thermal diffusion, including for cases with free energy differences and/or volume exclusion by crowders. They have been implemented in the Smoldyn particle-based simulation software.