Statistical and Biological Physics

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

Ryo Suzuki, Christoph A. Weber, Erwin Frey, Andreas Bausch

It has been exactly 20 years since the first physical studies which attempted to connect macroscopic collective behaviours in biological active matter systems to phase transitions and nonequilibrium physics. During the years, it has become clear that the precise knowledge of the interaction among the constituents is the key for understanding the emergence of order. In recent years, Boltzmann equations for propelled particles have been developed in order to connect the microscopic dynamics of the individual constituents to the meso- or macroscopic behaviour of the system. However due to the lack of quantitative experimental data, all models relied on very crude assumption of the interaction – most times simple digital interaction were assumed: collisions below 90 degrees align, above they are unaffected by the collision.

To fill this gap of information, we use the actomyosin motility assay, a paradigmatic biological active system, to extract for the first time an experimental binary collision rule for an active matter system. This data sets the basis for all further developments in the field.

Further on, we employ the Boltzmann equation for propelled particles with the experimentally obtained binary collision rule and find that such Boltzmann description is not sufficient to explain the polar ordering seen in the experiments – contrary to all common beliefs.

In addition, we show that the ordering transition has a sensitive dependence on the filament length, demonstrating that multi-filament collisions are the cause for the experimentally observed transition to polar order, and not simply two-body interactions. This generates a paradigm shift in the field, and calls upon the development of new concepts, based on multi-particle interactions. Analogies in different fields, where the realisation of the importance of multi-particle interactions was decisive for further progress are just for example physics of glass, cage effects and dense granular systems.