Regular Article - Soft Matter
Force-velocity relation and load-sharing in the linear polymerization ratchet revisited: the effects of barrier diffusion
Department of Physics, Indian Institute of Technology Madras, 600036, Chennai, India
Accepted: 29 March 2022
Published online: 13 April 2022
We study the velocity-force (V-F) relation for a Brownian ratchet consisting of a linear rigid polymer growing against a diffusing barrier, acted upon by a opposing constant force (F). Using a careful mathematical analysis, we derive the V-F relations in the extreme limits of fast and slow barrier diffusion. In the first case, V depends exponentially on the load F, in agreement with the well-known formula proposed by Peskin, Odell and Oster (1993), while the relationship becomes linear in the second case. For a bundle of two filaments growing against a common barrier, equal sharing of load in the corresponding V-F relation is predicted by a mean-field argument in both limits. However, the scaling behaviour of velocity with the number of filaments is different for the two cases. In the limit of large D, the validity of the mean-field approach is tested, and partially supported by a detailed and rigorous analysis. Our principal predictions are also verified in numerical simulations.
© The Author(s), under exclusive licence to EDP Sciences, SIF and Springer-Verlag GmbH Germany, part of Springer Nature 2022