Cross-diffusion induced patterns for a single-step enzymatic reaction

TL;DR

This paper investigates how single-step enzymatic reactions can generate spatial enzyme patterns through feedback mechanisms, highlighting the role of specific transport models and enzyme-substrate interactions.

Contribution

It demonstrates that enzyme transport feedback can produce spatial patterns with a single-step reaction, depending on the transport model and interactions.

Findings

Patterns form only in certain transport models.

Nonspecific repulsive interactions lead to enzyme accumulation in low substrate areas.

Reactions amplify substrate fluctuations, reinforcing enzyme patterns.

Abstract

Several different enzymes display an apparent diffusion coefficient that increases with the concentration of their substrate. Moreover, their motion becomes directed in substrate gradients. Currently, there are several competing models for these transport dynamics. Here, we analyze whether the enzymatic reactions can generate a significant feedback from enzyme transport onto the substrate profile. We find that this feedback can generate spatial patterns in the enzyme distribution, with just a single-step catalytic reaction. However, patterns are formed only for a subclass of transport models. For such models, nonspecific repulsive interactions between the enzyme and the substrate cause the enzyme to accumulate in regions of low substrate concentration. Reactions then amplify local substrate fluctuations, causing enzymes to further accumulate where substrate is low. Experimental analysis of this pattern formation process could discriminate between different transport models.