Diffusion and steady state distributions of flexible chemotactic enzymes

Ramin Golestanian,Jaime Agudo-Canalejo

doi:10.1140/epjst/e2020-900224-3

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.

Highlights

Enzymes have attracted much attention in recent years as biocompatible nanomachines that may perform work and undergo directed motion, with many biomedical and nanoengineering applications [1,2,3,4]
The observation of enhanced diffusion for aldolase, a slow and endothermic enzyme, which was observed in the presence of its substrate and in the presence of an inhibitor [11], demanded a change of paradigm from active to passive mechanisms
We have shown that conformational changes of the enzyme induced by specific binding to the substrate may be sufficient to account for enhanced diffusion [12,21]

Summary

Introduction

Enzymes have attracted much attention in recent years as biocompatible nanomachines that may perform work and undergo directed motion, with many biomedical and nanoengineering applications [1,2,3,4]. The observation of enhanced diffusion for aldolase, a slow and endothermic enzyme, which was observed in the presence of its substrate and in the presence of an inhibitor (which binds to the enzyme but does not induce a catalytic step) [11], demanded a change of paradigm from active to passive mechanisms. In this context, we have shown that conformational changes of the enzyme induced by specific binding to the substrate (or inhibitor) may be sufficient to account for enhanced diffusion [12,21].

Theory and closure approximation

Separation into position and internal degrees of freedom

Long-time diffusion-drift

Binding-unbinding kinetics of the enzyme

General expression for the diffusion coefficient

Explicit expansion for the diffusion coefficient

Changes in diffusion due to substrate binding

Steady-state enzyme distribution in the presence of a gradient

Conclusion