Mechanistic modeling, parametric study, and optimization of immobilization of enzymatic cascades in porous particles

Advances in enzymatic cascade reactions have directed a lot of attention towards enzyme co-immobilization in porous particles in the past few years. Enzymes can be immobilized in porous particles using different spatial immobilization distributions (SIDs). The conditions under which different SIDs are advantageous are not fully understood. Further, methods for simulation and optimization of such systems are yet to be developed. The present work provides a theoretical framework for modeling enzymatic cascade reactions catalyzed by enzymes immobilized in porous particles. The developed framework was used to study and characterize four different SIDs for a two-step enzymatic cascade reaction: individual immobilization, homogeneous co-immobilization and two heterogeneous co-immobilization strategies. Through the analytical solution of the model equations and Monte Carlo sampling of parameters, general conclusions are derived for the conditions under which the different SIDs are advantageous. Homogeneous co-immobilization was found to significantly outperform individual immobilization when diffusion of the intermediate was slow compared to the reaction rates. In cases where diffusion was fast compared to the reaction rates little is gained with co-immobilization. When either the reaction rate or the diffusion of the substrate of an enzyme catalyzed reaction is slow, co-immobilizing heterogeneously, while positioning the corresponding enzyme at the entry of the pore, was found to be an advantageous strategy.