Probing pattern formation and dynamics of nanoscale “swarms”


A model system based on actin filaments is yielding insights into "flocking" or "swarming" behavior on the biomolecular level.
A model system based on actin filaments is yielding insights into “flocking” or “swarming” behavior on the biomolecular level. (Image: Bausch & Suzuki / TUM

“Flocking” or “swarming” behavior is omnipresent in the living world, observed in birds, fish, and even bacteria. Strikingly similar collective action can also be seen in biomolecules within and between cells. Such self-organization processes are the basis of life – without them no living cell would exist – yet they are not well understood. New insights into how this action is coordinated at the biomolecular level are emerging from studies of a model system based on actin filaments. Experimental evidence proves the inadequacy of widely accepted explanations, according to collaborators at the Technical University of Munich (TUM), Ludwig-Maximilians-Universität München (LMU), and the Max Planck Institute for the Physics of Complex Systems (MPI-PKS).

Living matter, which consists largely of diverse polymeric structures assembled from various types of subunits, often exhibits striking behaviors, such as a capacity for self-organization and active motion. Physicists are interested in teasing out the elementary mechanisms that underlie the “self-organized” formation of such ordered structures and collective motions. Prof. Andreas Bausch and Dr. Ryo Suzuki of TUM, Prof. Erwin Frey of LMU, and Dr. Christoph Weber of MPI-PKS report progress toward this goal. Nanoscale filaments, made up of subunits of the protein actin, form the basis of the experimental model system they are investigating. Two papers, in the journals Nature Physics and the Proceedings of the National Academy of Sciences (PNAS), present their latest results.

Experiments disprove popular theory

In their experiments the researchers first immobilize motor proteins by fixing them to a glass slide. When actin filaments are added, together with a source of biochemical energy, they interact with the motors and exhibit active gliding motions. Moreover, individual filaments were found to locally adopt strongly curved configurations. The team analyzed their statistics to understand what happens when filaments collide and under what conditions interacting filaments align themselves in collective, streaming motions.

In living organisms, actin microfilaments are involved in the active migration of nucleated cells and in intracellular transport processes. According to the most popular theory, the fact that thin actin filaments bend as they are propelled by motor proteins is attributable to random thermal fluctuations, i.e., Brownian motion. But this assumption is false, says Christoph Weber, first author of the PNAS paper. Brownian motion has only a very weak impact on the form of the filaments. The researchers found that the molecular motors are not only responsible for propelling the fibers, but also for causing them to form strong bends.

“The filaments exhibit a range of local curvatures, the statistical distribution of which is incompatible with thermally driven motion,” explains Ryo Suzuki, first author of the paper in Nature Physics.

Two by two won’t do

In addition, the assumption that the interactions in the system are always binary in nature is not sufficient to explain the fact that, at high densities, filaments can align with each other and begin to display directed, collective motions. In fact, simultaneous encounters involving multiple agents appear to be required to account for the emergence of such collective motion. In this case, the filaments, each of which is composed of multiple subunits, apparently remain in stable alignment with each other and interact not only pairwise, but also with many other partners.

The scientists observed that, depending on the density and the mean length of the filaments, a phase transition occurs in which a state of non-directed movements is abruptly transformed into one characterized by collective motions (“swarm formation”). This transition resembles the condensation of a gas into the liquid state, except that in this case, it is not the pattern of microscopic molecular motions that changes but the orientation of the molecules in the system.

From a theoretical point of view, this strengthens the argument that the currently favored model for the motions of actively driven particles, which is based on the kinetic theory of gases, cannot adequately account for the behavior of such systems. Instead, it appears as if the filaments themselves act in a coordinated fashion, like molecules in a fluid state. “To understand how collective motion arises in these systems, we need to develop new theoretical concepts which go beyond the assumptions of the kinetic theory of gases,” says LMU Prof. Erwin Frey.

Exactly what happens at the microscopic level when filaments come into alignment, i.e., how their subunits interact with neighbors or exchange places, is not yet clear. “A better understanding of the physics of active systems,” says TUM Prof. Andreas Bausch, “opens the way to determining the basic mechanisms leading to structures and patterns enabling life, and could permit scientists to construct entirely novel nanosystems based on collective behaviors.”

This research was supported by the European Research Council in the framework of the Advanced Grant 289712-SelfOrg, the German Research Foundation (DFG) within the Collaborative Research Center (SFB) No. 863, and by the German Excellence Initiative through the Excellence Cluster Nanosystems Initiative Munich (NIM).


Ryo Suzuki, Christoph A. Weber, Erwin Frey and Andreas R. Bausch: Polar pattern formation in driven filament systems requires non-binary particle collisions. Nature Physics 2015, 10.1038/nphys3423.

Christoph A. Weber, Ryo Suzuki, Volker Schaller, Igor S. Aranson, Andreas R. Bausch, and Erwin Frey: Random bursts determine dynamics of active filaments. Proceedings of the National Academy of Sciences (PNAS) 2015, 10.1073/pnas.1421322112.