  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.
