Transport of Molecular Motor Dimers in Burnt-Bridge Models

TL;DR

This paper provides an exact theoretical analysis of the dynamics and force generation of molecular motor dimers moving along burnt-bridge models, revealing limits on their velocity and force compared to monomers, with implications for biological motors.

Contribution

It introduces a detailed stochastic model for dimer molecular motors on burnt-bridge lattices and compares their properties with monomers, highlighting velocity and force constraints.

Findings

Dimer velocity ratio to monomer is at most 2.

Dispersions of dimer and monomer are similar.

Maximum force ratio of dimer to monomer is 2, except in special cases.

Abstract

Dynamics of molecular motor dimers, consisting of rigidly bound particles that move along two parallel lattices and interact with underlying molecular tracks, is investigated theoretically by analyzing discrete-state stochastic continuous-time burnt-bridge models. In these models the motion of molecular motors is viewed as a random walk along the lattices with periodically distributed weak links (bridges). When the particle crosses the weak link it can be destroyed with a probability $p$, driving the molecular motor motion in one direction. Dynamic properties and effective generated forces of dimer molecular motors are calculated exactly as a function of a concentration of bridges $c$ and burning probability $p$ and compared with properties of the monomer motors. It is found that the ratio of the velocities of the dimer and the monomer can never exceed 2, while the dispersions of the dimer and the monomer are not very different. The relative effective generated force of the dimer (as compared to the monomer) also cannot be larger than 2 for most sets of parameters. However, a very large force can be produced by the dimer in the special case of $c=1/2$ for non-zero shift between the lattices. Our calculations do not show the significant increase in the force generated by collagenase motor proteins in real biological systems as predicted by previous computational studies. The observed behavior of dimer molecular motors is discussed by considering in detail the particle dynamics near burnt bridges.