Growth of a semi-flexible polymer close to a fluctuating obstacle: application to cytoskeletal actin fibres and testing of ratchet models

We consider the growth of a semiflexible clamped polymer, or fibre, incident at an angle on a fluctuating two-dimensional obstacle moving against an applied load. This system models a cytoskeletal actin fibre close to a fluctuating membrane or to a diffusing obstacle, such as an artificial bead or a bacterium moving in the cytosol of the host, and under actin polymerization. We review the existing semi-analytic theories and their predictions, and compare them with the results of three-dimensional Monte Carlo dynamic simulations. This allows us to separate the effect of tip and obstacle diffusion on the overall motion. We characterize the statistics of pushing catastrophes, which occur when the fibre tip loses contact with the obstacle and the fibre grows away from or parallel to the obstacle. We discuss the effect of changing the polymerization and depolymerization rates at the fibre tip, which controls the stalling force needed to stop fibre growth, on the obstacle motion. We also consider how our results are modified if the fibres are bundled via attractive interactions, as is believed to be the case in filopodia, and if the wall becomes 'soft', which should better represent a fluctuating and diffusing membrane patch. We find that in both these cases the obstacle moves at a larger speed than predicted by the ratchet model, and we pinpoint the physical mechanisms leading to this velocity enhancement.