Enhanced and non-monotonic effective kinetics of solute pulses under Michaelis–Menten reactions

Abstract : Michaelis–Menten kinetics describe a broad range of physical, chemical, and biological processes. Since they are non-linear, spatial averaging of reaction kinetics is non-trivial, and it is not known how concentration gradients affect the global effective kinetics. Here, we use numerical simulations and theoretical developments to investigate the effective kinetics of diffusing solute pulses locally subject to Michaelis–Menten reaction kinetics. We find that coupled diffusion and reaction lead to non-monotonic effective kinetics that differ significantly from the local kinetics. The resulting effective reaction rates can be significantly enhanced compared to those of homogeneous batch reactors. We uncover the different regimes of effective kinetics as a function of the Damköhler number and Michaelis–Menten parameters and derive a theory that explains and quantifies these upscaled kinetics using a weakly-coupled description of reaction and diffusion. We illustrate the consequences of these findings on the accelerated consumption of nutrient pulses by bacteria. These results are relevant to a large spectrum of reactive systems characterized by heterogeneous concentration landscapes.