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Nat Phys. 2015 Oct;11(10):839-843.

Polar Pattern Formation in Driven Filament Systems Require Non-Binary Particle Collisions.

Author information

1
Lehrstuhl für Biophysik (E27), Technische Universität München, 85748 Garching, Germany.
2
Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany; Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, 80333 Munich, Germany.
3
Arnold Sommerfeld Center for Theoretical Physics and Center for NanoScience, Department of Physics, Ludwig-Maximilians-Universität München, 80333 Munich, Germany.

Abstract

Living matter has the extraordinary ability to behave in a concerted manner, which is exemplified throughout nature ranging from the self-organisation of the cytoskeleton to flocks of animals [1-4]. The microscopic dynamics of constituents have been linked to the system's meso- or macroscopic behaviour in silico via the Boltzmann equation for propelled particles [5-10]. Thereby, simplified binary collision rules between the constituents had to be assumed due to the lack of experimental data. We report here experimentally determined binary collision statistics by studying the recently introduced molecular system, the high density actomyosin motility assay [11-13]. We demonstrate that the alignment effect of the binary collision statistics is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, which indicates that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. The presented findings demonstrate that the unique properties of biological active matter systems require a description that goes well beyond a gas-like picture developed in the framework of kinetic theories.

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