Phoresis and Enhanced Diffusion Compete in Enzyme Chemotaxis

TL;DR

This paper develops a microscopic theory explaining enzyme chemotaxis, revealing two competing mechanisms—phoresis and binding-induced diffusion changes—that determine movement direction based on substrate concentration.

Contribution

The study introduces a comprehensive theory for enzyme chemotaxis, incorporating both non-specific interactions and specific binding effects, and identifies the conditions under which each mechanism dominates.

Findings

Phoresis dominates at high substrate concentrations.

Binding-induced diffusion changes dominate at low substrate concentrations.

The theory explains experimental observations of enzyme chemotaxis directions.

Abstract

Chemotaxis of enzymes in response to gradients in the concentration of their substrate has been widely reported in recent experiments, but a basic understanding of the process is still lacking. Here, we develop a microscopic theory for chemotaxis, valid for enzymes and other small molecules. Our theory includes both non-specific interactions between enzyme and substrate, as well as complex formation through specific binding between the enzyme and the substrate. We find that two distinct mechanisms contribute to enzyme chemotaxis: a diffusiophoretic mechanism due to the non-specific interactions, and a new type of mechanism due to binding-induced changes in the diffusion coefficient of the enzyme. The latter chemotactic mechanism points towards lower substrate concentration if the substrate enhances enzyme diffusion, and towards higher substrate concentration if the substrate inhibits enzyme diffusion. For a typical enzyme, attractive phoresis and binding-induced enhanced diffusion will compete against each other. We find that phoresis dominates above a critical substrate concentration, whereas binding-induced enhanced diffusion dominates for low substrate concentration. Our results resolve an apparent contradiction regarding the direction of urease chemotaxis observed in experiments, and in general clarify the relation between enhanced diffusion and chemotaxis of enzymes. Finally, we show that the competition between the two distinct chemotactic mechanisms may be used to engineer nanomachines that move towards or away from regions with a specific substrate concentration.