Distribution of directional change as a signature of complex dynamics

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 pr...

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Bibliographic Details
Published in:Proceedings of the National Academy of Sciences - PNAS 2013-12, Vol.110 (49), p.19689-19694
Main Authors: Burov, Stanislav, Tabei, S. M. Ali, Huynh, Toan, Murrell, Michael P., Philipson, Louis H., Rice, Stuart A., Gardel, Margaret L., Scherer, Norbert F., Dinner, Aaron R.
Format: Article
Language:English
Subjects:
Actin Cytoskeleton - chemistry
Biological Sciences
Brownian motion
Colloids
Colloids - chemistry
Data Interpretation, Statistical
Ergodic theory
Insulin
Models, Theoretical
Motion
Movement
Musical intervals
Particle tracks
Particle trajectories
Physical Sciences
Random walk
Signatures
Statistical analysis
Stochastic models
Stochastic Processes
Trajectories
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Summary: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.
ISSN:0027-8424
1091-6490
DOI:10.1073/pnas.1319473110