The energetics, chemistry, and mechanics of a processive motor protein

When kinesin moves along microtubule, it can occasionally malfunction and make a backward step. Recent single molecule experiments on moving kinesin have revealed that the forward to backward step ratio depends exponentially on the load force. We introduce a model of a Brownian step that accounts for recorded data with great accuracy. We find that the forward to backward step ratio does not depend on any structural features of the kinesin. The stepping statistics appear fully determined by the 8 nanometer stepsize, the energy that drives the step, and k(B)T, which is the natural "quantum" of thermal energy. With this model we next analyze the energetics of the Brownian stepper. We derive force-velocity relations for the vicinity of the "static head" case, which is when the applied force is close to the stopping force. We also derive force-velocity relations for the close-to-equilibrium case, i.e. a small load and a small ATP-ADP chemical potential.