Individual swimming bacteria are known to bias their random trajectories in search of food and to optimize survival. The motion of bacteria within a swarm, wherein they migrate as a collective group over a solid surface, is fundamentally different as typical bacterial swarms show large-scale swirling and streaming motions involving millions to billions of cells. Here by tracking trajectories of fluorescently labelled individuals within such dense swarms, we find that the bacteria are performing super-diffusion, consistent with Lévy walks. Lévy walks are characterized by trajectories that have straight stretches for extended lengths whose variance is infinite. The evidence of super-diffusion consistent with Lévy walks in bacteria suggests that this strategy may have evolved considerably earlier than previously thought.
Over the past decade, technological advances in experimental and animal tracking techniques have motivated a renewed theoretical interest in animal collective motion and, in particular, locust swarming. This review offers a comprehensive biological background followed by comparative analysis of recent models of locust collective motion, in particular locust marching, their settings, and underlying assumptions. We describe a wide range of recent modeling and simulation approaches, from discrete agent-based models of self-propelled particles to continuous models of integro-differential equations, aimed at describing and analyzing the fascinating phenomenon of locust collective motion. These modeling efforts have a dual role: The first views locusts as a quintessential example of animal collective motion. As such, they aim at abstraction and coarse-graining, often utilizing the tools of statistical physics. The second, which originates from a more biological perspective, views locust swarming as a scientific problem of its own exceptional merit. The main goal should, thus, be the analysis and prediction of natural swarm dynamics. We discuss the properties of swarm dynamics using the tools of statistical physics, as well as the implications for laboratory experiments and natural swarms. Finally, we stress the importance of a combined-interdisciplinary, biological-theoretical effort in successfully confronting the challenges that locusts pose at both the theoretical and practical levels.
The principal interactions leading to the emergence of order in swarms of marching locust nymphs was studied both experimentally, using small groups of marching locusts in the lab, and using computer simulations. We utilized a custom tracking algorithm to reveal fundamental animal-animal interactions leading to collective motion. Uncovering this behavior introduced a new agent-based modeling approach in which pause-and-go motion is pivotal. The behavioral and modeling findings are largely based on motion-related visual sensory inputs obtained by the individual locust. Results suggest a generic principle, in which intermittent animal motion can be considered as a sequence of individual decisions as animals repeatedly reassess their situation and decide whether or not to swarm. This interpretation implies, among other things, some generic characteristics regarding the build-up and emergence of collective order in swarms: in particular, that order and disorder are generic meta-stable states of the system, suggesting that the emergence of order is kinetic and does not necessarily require external environmental changes. This work calls for further experimental as well as theoretical investigation of the neural mechanisms underlying locust coordinative behavior.
Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.
Bacterial swarming is a rapid mass-migration, in which thousands of cells spread collectively to colonize a surface. Physically, swarming is a natural example of active particles that use energy to generate motion. Accordingly, understanding the constraints physics imposes on the dynamics is essential to understand the mechanisms underlying the swarming phenomenon. We present new experiments of swarming Bacillus subtilis mutants with different aspect ratios and densities. Analyzing the dynamics reveals a rich phase diagram of qualitatively distinct swarming regimes, describing how the shape and density of cells govern the global dynamical characteristics of the entire swarm. Moreover, we show that under standard conditions bacteria inhabit a region of phase space that is associated with rapid mixing and robust dynamics, with homogeneous density and no preferred direction of motion. This contrasts characteristic clustering behavior of selfpropelled rods that is recovered only for very elongated mutant species. Thus, bacteria have adapted their physics to optimize the principle functions assumed for swarming. 2 Micro-organisms such as bacteria, sperm-, epithelial-and cancer-cells, as well as immune T-cells and even inanimate active particles, generate collective flows and demonstrate a wealth of newly discovered emergent dynamical patterns [Szabó Be'er 2019]. This report addresses the dynamics of swarming bacteria a biological state to which some bacterial species transition, in which rod-shaped cells, powered by flagellar rotation, migrate rapidly on surfaces en-mass [Harshey 2003; Darnton 2010; Kearns 2010; Tuson 2013]. Swarming allows efficient expansion and colonization of new territories, even under harsh and adverse conditions such as starvation or antibiotic stress [Lai 2009; Benisty 2015]. Revealing the biological and physical mechanisms underlying bacterial swarming is therefore a key to our understanding of how bacteria spread and invade new niches. The transition to swarming involves several critical intra-cellular processes such as an increase in flagellar number and changes in cell shape, suggesting these changes promote favorable swarming conditions [Harshey 2003; Kearns 2010; Tuson 2013; Mukherjee 2015; Be'er 2019]. Quantifying the "quality" of swarming can be done using the tools of statistical physics by analyzing the dynamical properties of large, out-ofequilibrium, self-propelled collectives [Ramaswamy 2010; Vicsek 2012; Bär 2019].Accordingly, one of the primary goals of such quantification is to obtain a phase diagram that would describe the possible dynamical states of swarms as a function of controlled parameters such as density and cell aspect ratio. As bacteria move and grow, they trace an effective path through the phase diagram, transitioning between different swarming regimes. Thus, a phase diagram provides a map that explains how the microscopic mechanical properties of cells, which are regulated by complex bio-
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