Investigating the robustness of the classical enzyme kinetic equations in small intracellular compartments

TL;DR

This paper develops mesoscopic enzyme kinetic equations that incorporate molecular noise and physical transport mechanisms, revealing significant deviations from classical kinetics in small intracellular compartments, especially under vesicle-mediated transport.

Contribution

It introduces novel mesoscopic rate equations accounting for molecular noise and transport mechanisms, extending classical enzyme kinetics to small intracellular environments.

Findings

Deviations from classical kinetics can reach hundreds of percent in compartments smaller than 200nm.

Transport mode and molecular noise significantly affect enzyme reaction velocities.

Implications for modeling intracellular networks and drug dosage calculations are substantial.

Abstract

Classical descriptions of enzyme kinetics ignore the physical nature of the intracellular environment. Main implicit assumptions behind such approaches are that reactions occur in compartment volumes which are large enough so that molecular discreteness can be ignored and that molecular transport occurs via diffusion. Starting from a master equation description of enzyme reaction kinetics and assuming metabolic steady-state conditions, we derive novel mesoscopic rate equations which take into account (i) the intrinsic molecular noise due to the low copy number of molecules in intracellular compartments (ii) the physical nature of the substrate transport process, i.e. diffusion or vesicle-mediated transport. These equations replace the conventional macroscopic and deterministic equations in the context of intracellular kinetics. The latter are recovered in the limit of infinite compartment volumes. We find that deviations from the predictions of classical kinetics are pronounced (hundreds of percent in the estimate for the reaction velocity) for enzyme reactions occurring in compartments which are smaller than approximately 200nm, for the case of substrate transport to the compartment being mediated principally by vesicle or granule transport and in the presence of competitive enzyme inhibitors. This has implications for the common approach of modelling large intracellular reaction networks using ordinary differential equations and also for the calculation of the effective dosage of competitive inhibitor drugs.