Eur. Phys. J. Special Topics 229, 2791–2806 (2020)
https://doi.org/10.1140/epjst/e2020-900224-3

Regular Article

Diffusion and steady state distributions of flexible chemotactic enzymes

¹ Max Planck Institute for Dynamics and Self-Organization (MPIDS), D-37077 Göttingen, Germany
² Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, UK
³ Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, USA

^a e-mail: jaime.agudo@ds.mpg.de
^b e-mail: ramin.golestanian@ds.mpg.de

Received: 10 October 2019
Accepted: 27 July 2020
Published online: 16 November 2020

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.