Discrete step sizes of molecular motors lead to bimodal non-Gaussian velocity distributions under force

Abstract

Fluctuations in the physical properties of biological machines are inextricably linked to their functions. Distributions of run-lengths and velocities of processive molecular motors, like kinesin-1, are accessible through single molecule techniques, yet there is lack a rigorous theoretical model for these probabilities up to now. We derive exact analytic results for a kinetic model to predict the resistive force (F) dependent velocity (P(v)) and run-length (P(n)) distribution functions of generic finitely processive molecular motors that take forward and backward steps on a track. Our theory quantitatively explains the zero force kinesin-1 data for both P(n) and P(v) using the detachment rate as the only parameter, thus allowing us to obtain the variations of these quantities under load. At non-zero F, P(v) is non-Gaussian, and is bimodal with peaks at positive and negative values of v. The prediction that P(v) is bimodal is a consequence of the discrete step-size of kinesin-1, and remains even when the step-size distribution is taken into account. Although the predictions are based on analyses of kinesin-1 data, our results are general and should hold for any processive motor, which walks on a track by taking discrete steps.