Diffusion and steady state distributions of flexible chemotactic enzymes

TL;DR

This paper investigates passive mechanisms behind enzyme enhanced diffusion and chemotaxis, deriving analytical expressions for diffusion coefficients and analyzing enzyme distribution patterns in substrate gradients.

Contribution

It extends previous models by providing exact formulas for enzyme diffusion and analyzing steady state distributions considering phoresis and binding effects.

Findings

Exact long-time diffusion coefficient derived using Taylor dispersion.

Chemotactic enzyme distributions can either accumulate or deplete in substrate regions.

Analytical expressions simplify understanding of enzyme transport mechanisms.

Abstract

Many experiments in recent years have reported that, when exposed to their corresponding substrate, catalytic enzymes undergo enhanced diffusion as well as chemotaxis (biased motion in the direction of a substrate gradient). Among other possible mechanisms, in a number of recent works we have explored several passive mechanisms for enhanced diffusion and chemotaxis, in the sense that they require only binding and unbinding of the enzyme to the substrate rather than the catalytic reaction itself. These mechanisms rely on conformational changes of the enzyme due to binding, as well as on phoresis due to non-contact interactions between enzyme and substrate. Here, after reviewing and generalizing our previous findings, we extend them in two different ways. In the case of enhanced diffusion, we show that an exact result for the long-time diffusion coefficient of the enzyme can be obtained using generalized Taylor dispersion theory, which results in much simpler and transparent analytical expressions for the diffusion enhancement. In the case of chemotaxis, we show that the competition between phoresis and binding-induced changes in diffusion results in non-trivial steady state distributions for the enzyme, which can either accumulate in or be depleted from regions with a specific substrate concentration.