Motor proteins have highly correlated brownian engines

Publisher Summary This chapter describes motor proteins that have highly correlated brownian engines. The attempt to understand the detailed mechanism of motor protein motion in the cytoskeleton has led to the study of several stochastic ratchet models. The simplest model involves one over damped particle representing, for instance, the motor protein kinesin, moving in a periodic but not symmetrical force field that is driven by different types of correlated noises. The periodic forces are exerted by the 8 nm long partially asymmetrical tubulin dimers on kinesin, while the noise terms represent the fluctuating environment. This model leads to a macroscopic particle current in a specific direction determined by the potential asymmetry and by the properties of the noises. A simple single-particle stochastic ratchet model for motor proteins shows reasonably good qualitative and even quantitative agreement with biological experiments when the correlation time of the noise is high. In this regime, the particle motion is controlled by Kramers rate that depends strongly (exponentially) on the correlations of the fluctuating environment.