Learning the nonlinear interactions from particle trajectories

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a novel statistical analysis technique for learning the characteristics of the nonlinear potential from the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of kurtosis of the displacement distribution of the particle traveling on a membrane in a cage-type potential. Results of numerical simulations are supported by analytical predictions. We show that the approach allows robust identification of the potential for the much lower temporal resolution compare with the mean square displacement analysis.