Nonreciprocality of a micromachine driven by a catalytic chemical reaction

TL;DR

This paper introduces a model for a micromachine driven by catalytic reactions, analyzing its nonreciprocal behavior based on mechano-chemical coupling and reaction dynamics, revealing how energy barriers influence its functionality.

Contribution

It presents a novel model linking chemical reaction dynamics to micromachine nonreciprocality, with explicit calculations of time scales and energy barrier effects.

Findings

Nonreciprocality is proportional to the square of the mean first transition path time.

Nonreciprocality is inversely proportional to the square of the catalytic energy barrier.

Explicit time scale calculations support the model's predictions.

Abstract

We propose a model that describes cyclic state transitions of a micromachine driven by a catalytic chemical reaction. We consider a mechano-chemical coupling of variables representing the degree of a chemical reaction and the internal state of a micromachine. The total free energy consists of a tilted periodic potential and a mechano-chemical coupling energy. We assume that the reaction variable obeys a deterministic stepwise dynamics characterized by two typical time scales, i.e., the mean first passage time and the mean first transition path time. To estimate the functionality of a micromachine, we focus on the quantity called "nonreciprocality" and further discuss its dependence on the properties of catalytic reaction. For example, we show that the nonreciprocality is proportional to the square of the mean first transition path time. The explicit calculation of the two time scales within the decoupling approximation model reveals that the nonreciprocality is inversely proportional to the square of the energy barrier of catalytic reaction.