Force-velocity relation for growing biopolymers

The process of force generation by the growth of biopolymers is simulated via a Langevin-dynamics approach. The monomer-monomer interaction forces are taken to have simple forms that favor the growth of straight fibers from solution, and they are taken to grow against a flat obstacle. The force-velocity relation is obtained from the simulations for two versions of the monomer-monomer force field. We evaluate corrections to the simplest analytic theory based on thermal motion of the obstacle, which yields an exponential velocity decay with applied force. For most orientations of the growing fiber tip, the corrections are small. However, for orientations in which the surface of the growing fiber is parallel to the obstacle, large corrections are obtained in the direction of reduced fiber velocity. These results are explained on the basis of the diffusion properties of monomers near the fiber tip. It is also found that the mobility of the obstacle has little effect on the growth rate over a broad range of possible values.