# Random bursts determine dynamics of active filaments

Christoph A. Weber, Ryo Suzuki, Volker Schaller, Igor S. Aranson, Andreas R. Bausch, Erwin Frey

Active matter is a fascinating new field in soft matter physics aiming to understand how macroscopic properties of interacting active particles emerge from properties of the constituent particles as well as their interactions. To this end, kinetic theory has been successfully applied to connect the physics at the microscopic scale with the corresponding macroscopic description; it was able to predict the emergent patterns and collective dynamics for interacting propelled particle systems. One central finding is that the degree of alignment of colliding active particles competes with the strength of randomness of the individual’s persistent random walks. This randomness arises from the inherent active fluctuations of each particle, i.e. the non-thermal and local input and dissipation of energy.

It is typically assumed that an active persistent random walk shares many properties to thermal fluctuations, such as spectrum, negligible correlations in time and space and that the amplitude can be captured by a redefinition of the system’s temperature, often referred to as 'effective temperature'. However, the concept is not generic and cannot capture deviations from Gaussian statistics as well as the emergence of overpopulated tails. There is a lack of studies addressing the origin of deviations from the thermal statistics as well as its quantification.

We report a combined theoretical and experimental study of the actin filament gliding-assay, which has become a paradigmatic system for studying the physics of active matter. In particular, we investigate contour fluctuations of single actin filaments. We find that the curvature statistics is anomalous and exhibits an exponential tail. This is fundamentally distinct from the expected Gaussian statistics for actin filaments subject to thermal fluctuations. We provide a kinetic theory argument as well as a numerical simulation model that explain all features of the shape fluctuations quantitatively. Moreover, we introduce a mechanism on how non-thermal distributions may emerge. It involves the interplay between local and random injection of energy, acting analog to a thermal heat bath, and energy dissipation due to sudden jump-like changes in the system's dynamic variables. Such a mechanism leads to a non-thermal distribution of filament curvatures with a universal shape.

We believe that our findings of a general principle how active fluctuations emerge are of great interest to a broad audience of physicists. It would be interesting to scrutinize this principle for other active systems such as swimming biological organisms or flocking animals.