Reduced models of facilitated diffusion: Quasi-steady state approximation for carrier-mediated transport

Quasi-Steady State Approximation approach is used to derive reduced models of facilitated diffusion for the cases where adjusted concentration of mediators located on the boundary separating two compartments is much smaller compared with the concentration of particles in these compartments transported across the boundary via carrier-mediated transport mechanism. The cases of a generic mediator kinetics scheme as well as of more realistic mediator reactions are studied for symmetric boundary permeable in both directions. It is shown that for the generic case, under condition of sinks and sources absence, the newly derived reduced facilitated diffusion formula can be transformed to a model of an ordinary diffusion between compartments following Fick's Law. However, for the more realistic kinetics case, such transformation is not possible due to the presence of non-linearity in the corresponding reduced model. For semi-permeable boundary, i.e., when the particles can be transported across the boundary only in one direction, from one compartment to another, but not in the opposite direction, the derived formulas can be further reduced to produce, as a special case, the classical Michaelis - Menten - Henri kinetics approximation. The derived approximate formulas are intended for use in multiple medical, neuroscience, biological, and other applications.