Formation of swarms in nanosystems

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, who now works at the Max-Planck-Institute for the Physics of Complex Systems in Dresden. Brownian motion has only a very weak impact on the form of the filaments. Instead, as the Munich researchers show, the molecular motors are not only responsible for propelling the fibers, they also cause them to form strong bends. “The filaments exhibit a range of local curvatures, the statistical distribution of which is incompatible with thermally driven motion,” Ryo Suzuki explains.

The role of non-binary interactions

In addition, the researchers have shown that 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 in a non-binary manner. In their experiments, 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’). Furthermore, 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 implies 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 Erwin Frey, whose work is supported by the Nanosystems Initiative Munich (NIM), a Cluster of Excellence. 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. At all events, a better understanding of the physics of actively propelled systems would permit scientists to construct entirely novel nanosystems that display collective behaviors.
(Nature Physics 2015)
(Proceedings of the National Academy of Sciences (PNAS) 2015)