Polar pattern formation in driven filament systems requires non-binary particle collisions

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From the self-organization of the cytoskeleton to the synchronous motion of bird flocks, living matter has the extraordinary ability to behave in a concerted manner1,2,3,4. The Boltzmann equation for self-propelled particles is frequently used in silico to link a system’s meso- or macroscopic behaviour to the microscopic dynamics of its constituents5,6,7,8,9,10. But so far such studies have relied on an assumption of simplified binary collisions owing to a lack of experimental data suggesting otherwise. We report here experimentally determined binary-collision statistics by studying a recently introduced molecular system, the high-density actomyosin motility assay11,12,13. We demonstrate that the alignment induced by binary collisions is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, indicating 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. Our findings demonstrate that the unique properties of biological active-matter systems require a description that goes well beyond that developed in the framework of kinetic theories.

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Figure 1: Experimental binary collisions.
Figure 2: Experimentally obtained binary-collision statistics for the actomyosin motility assay.
Figure 3: Comprehensive binary-collision statistics pj(ηj|θ12) and their symmetry properties.
Figure 4: Evidence of multi-filament collisions.


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This research was supported by the European Research Council in the framework of the Advanced Grant 289714-SelfOrg, Deutsche Forschungsgemeinschaft via project No. B2 within the SFB No. 863, and the German Excellence Initiative via the programme ‘NanoSystems Initiative Munich’ (NIM).

Author information

R.S., C.A.W., E.F. and A.R.B. designed the project. R.S. and A.R.B. performed and designed all experiments. C.A.W. and E.F. theoretically analysed the experimental data. All authors participated in interpreting the experimental and theoretical results and in writing the manuscript.

Correspondence to Erwin Frey or Andreas R. Bausch.

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Suzuki, R., Weber, C., Frey, E. et al. Polar pattern formation in driven filament systems requires non-binary particle collisions. Nature Phys 11, 839–843 (2015) doi:10.1038/nphys3423

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