Passive propulsion of molecular machines by the asymmetric distribution of reaction products with various site reaction rates and non-local interactions
Institute for Advanced Study, Shenzhen University, Nanshan, 518060, Shenzhen, Guangdong, China
Accepted: 7 October 2021
Published online: 16 October 2021
In this paper, we consider the simplest type of molecular motor models, where the movement of a single spherical swimmer/motor is not only driven by hydrolyzing nearby solutes through a fixed site for the digestion of enzyme but also the non-local interactions between product particles. We assume that the non-local effects are weak, homogeneous and time-independent so that analytical solutions can be obtained. In this case, the motion of the swimmers is not only determined by the rate of production of enzyme, but also affected by the global concentration of product particles. It is interesting to notice that the trajectory of swimmers is determined by the two simple poles of the velocity for swimmers via inverse Fourier transformation. Particularly in the non-local cases, different values for the motor’s radius R and the proportionality coefficient c induce nonlinear effects on the swimmer’s dynamics. We find that those parameters can alter the poles of the swimmer’s velocity significantly so that the trajectory of swimmers could be manually controlled. The present research discovers the possible control of motors using the non-local effects, the release rate of product particles and the inertia of swimmers, where external fields are completely absent. The present theoretical results hold great promises in designing smart passive molecular machines.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021