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Non-Gaussianity in single-particle tracking: Use of kurtosis to learn the characteristics of a cage-type potential

Pavel M. Lushnikov1, Petr Šulc2, and Konstantin S. Turitsyn3

  • 1Department of Mathematics and Statistics, University of New Mexico, Albuquerque, New Mexico 87131, USA
  • 2Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3NP, UK
  • 3Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA

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Phys. Rev. E 85, 051905 – Published 14 May, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.051905

Abstract

Nonlinear interaction of membrane proteins with cytoskeleton and membrane leads to non-Gaussian structure of their displacement probability distribution. We propose a statistical analysis technique for learning the characteristics of the nonlinear potential from the time dependence of the cumulants of the displacement distribution. The efficiency of the approach is demonstrated on the analysis of the 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 some characteristics of the potential for the much lower temporal resolution compared with the mean-square displacement analysis and we demonstrate robustness to experimental errors in determining the particle positions.

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Phys. Rev. E 85, 051905– Published 14 May, 2012
  • Received 17 February 2011
Article part of CHORUS

©2012 American Physical Society

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