Imre Derenyi

We consider the collective motion of finite-sized, overdamped Brownian particles (e.g., motor proteins) in a periodic potential. Simulations of our model have revealed a number of novel cooperative transport phenomena, including (i) the reversal of direction of the net current as the particle density is increased and (ii) a very strong and complex dependence of the average velocity on both the size and the average distance of the particles.

Recently individual two-headed kinesin molecules have been studied in in vitro motility assays revealing a number of their peculiar transport properties. In this paper we propose a simple and robust model for the kinesin stepping process with elastically coupled Brownian heads showing all of these properties. The analytic and numerical treatment of our model results in a very good fit to the experimental data and practically has no free parameters. Changing the values of the parameters in the restricted range allowed by the related experimental estimates has almost no effect on the shape of the curves and results mainly in a variation of the zero load velocity which can be directly fitted to the measured data. In addition, the model is consistent with the measured pathway of the kinesin ATPase.

We consider the collective motion of finite size Brownian particles induced by a one-dimensional, spatially asymmetric, periodic potential which is turned "on" and "off" dichotomously. The particles interact through simple hard-core repulsion. We show analytically that this simple system exhibits an interesting collective behavior: (i) the direction of motion can change many times as the density of particles is increased; (ii) close to the maximal density, the average velocity depends on the size of the particles in a very complex way, both in sign and magnitude.