Free-energy-based method for step size detection of processive molecular motors

We report a free-energy-based algorithm to estimate the step size of processive molecular motors from noisy, experimental time position traces. In our approach, the problem of estimating step sizes reduces to the evaluation of the free energy of directed lattice polymers in a random potential. The present approach is Bayesian in spirit as we do not aim to determine the most likely underlying time trace but rather to determine the step size and stepping frequency that are most likely to yield the observed data. We test this method on synthetic data for the simple case of noisy traces with fixed underlying step size and Poissonian stepping statistics. We find that the present scheme can work at signal-to-noise levels that are about 40% worse than those where the best existing step detection methods fail. More importantly, the present approach yields a much more accurate estimate of the step size. Although we focus on the case of non-reversing walks with a single step size, we show that we can detect if this assumption is violated. In principle, the method can be extended to more complex stepping scenarios but we find that for noisy data, multi-parameter fits are not reliable.