A diffusion model and optimal cell loading for immobilized cell biocatalysts.

A diffusion model based on the random pore model is derived for immobilized cell biocatalysts and verified with 19 sets of experimental diffusion data. The predicted effective diffusivity relative to that for the support matrix reflects a quadratic dependence on the cell loading and contains a single parameter that depends on the intracellular diffusivity and the chemical partitioning coefficient. The model is used to predict optimal cell loadings that maximize the total reaction rate in an immobilized cell biocatalyst. A rule of thumb based on the diffusion model is obtained to the effect that the cell loading should be at least (1/3) for single reactions regardless of the kinetics and diffusional resistances. A means of calculating improved lower bounds is provided for cases where the cellular diffusional resistance is known but the kinetics are not. The optimal cell loadings for reversible first-order and for Michaelis-Menten kinetics are presented and demonstrated to be within the range of conditions of practical interest. Copyright 2000 John Wiley & Sons, Inc. Biotechnol Bioeng 69: 639-647, 2000.