Directional Newtonian motion and reversals of molecular motors

Several biological molecular motors, for instance kinesin and non-claret disjunctional (ncd), belonging to the same superfamily of motor proteins move towards opposite ends of microtubules. It is clear that motor protein motion is powered through ATP hydrolysis, but neither the specifics of the chemical to mechanical energy transduction nor the molecular basis for motion directionality are precisely known. While the protein catalytic domain seems to be responsible for the processibility of the motor on the microtubule, the "neck" region adjacent to the motor heads was found recently to control the directionality of movement. We show here that a simple Newtonian model of two motor head particles connected through a neck coiled-coil spring whose rest length changes with each ATP hydrolysis event captures the essential motor dynamics features. In particular, the observed directionality reversal in chimaeras with different coiled-coil regions results in the model from a change in the stiffness of the spring coefficient. We find that motor speed is determined by the average ATP absorption rate while the effect of ambient temperature is relatively small, leading to essentially non-Brownian, deterministic motor motion.