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Fluctuations in the physical properties of biological machines areinextricably linked to their functions. Distributions of run-lengths andvelocities of processive molecular motors, like kinesin-1, are accessiblethrough single molecule techniques, yet there is lack a rigorous theoreticalmodel for these probabilities up to now. We derive exact analytic results for akinetic model to predict the resistive force ($F$) dependent velocity ($P(v)$)and run-length ($P(n)$) distribution functions of generic finitely processivemolecular motors that take forward and backward steps on a track. Our theoryquantitatively 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 toobtain 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 discretestep-size of kinesin-1, and remains even when the step-size distribution istaken into account. Although the predictions are based on analyses of kinesin-1data, our results are general and should hold for any processive motor, whichwalks on a track by taking discrete steps.

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