Distribution of directional change as a signature of complex dynamics

Stanislav Burov, S. M. Ali Tabei, Toan Huynh, Michael P. Murrell, Louis H. Philipson, Stuart A. Rice, Margaret L. Gardel, Norbert F. Scherer, Aaron R. Dinner

Research output: Contribution to journalArticlepeer-review

88 Scopus citations


Analyses of random walks traditionally use the mean square displacement (MSD) as an order parameter characterizing dynamics. We show that the distribution of relative angles of motion between successive time intervals of random walks in two or more dimensions provides information about stochastic processes beyond the MSD. We illustrate the behavior of this measure for common models and apply it to experimental particle tracking data. For a colloidal system, the distribution of relative angles reports sensitively on caging as the density varies. For transport mediated by molecular motors on filament networks in vitro and in vivo, we discover self-similar properties that cannot be described by existing models and discuss possible scenarios that can lead to the elucidated statistical features.

Original languageEnglish
Pages (from-to)19689-19694
Number of pages6
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number49
StatePublished - 3 Dec 2013
Externally publishedYes


  • Angular correlation
  • Cytoskeleton
  • Random walks


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