Self-Propelled Rods: Insights and Perspectives for Active Matter

Bär, Markus; Großmann, Robert; Heidenreich, Sebastian; Peruani, Fernando

doi:10.1146/annurev-conmatphys-031119-050611

Cited by 258 publications

(203 citation statements)

References 168 publications

(342 reference statements)

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“…Swarming bacteria and self-propelled rods A popular model to account for the basic physics of interacting self-propelled agents such as swarming bacteria is the self-propelled rods (SPR) with steric interactions [Peruani 2006;Wensink 2012;Abkenar 2013;Weitz 2015;Shi 2018, Großmann 2019, Bär 2019. The experiments presented here do have features predicted in simulations of self-propelled rods, such as the transition from an exponentially decay cluster size distribution (CSD) in the swarming phase to a clustering phase with a bimodal CSD as shown in Fig.…”

Section: Supplementary Textmentioning

confidence: 79%

“…In comparison to simulation results for interacting self-propelled rods [Peruani 2006;Ginelli 2010;Wensink 2012;Abkenar 2013;Shi 2018, Jeckel 2019, Bär 2019 and experiments with artificial inanimate systems [Narayan 2007, Kudrolli 2008, Bricard 2013, the swarming phase diagram has several unique characteristics that are not observed in other active systems. These properties may alter, constrain, or even control cells' ability to move collectively in an efficient manner, mix within the colony and spread.…”

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confidence: 91%

“…A phase with small clusters (SC) composed of a few bacteria is observed if the density is above 0.1 Strikingly, above densities of around 0.25, cells transition into another phase and form large clusters (LC) that can become of the order of the observation window employed here. This transition is reminiscent of behavior of self-propelled rods with short-range alignment interactions (typically due to volume exclusion) in simulations and experiments, see [Bär 2019] and references therein. The observed cluster-size distributions are in line with a kinetic theory describing occurrence of large moving clusters as a specific type of microphase separation characteristic for rod-shaped moving particles like bacteria [Peruani 2006, Peruani 2013.…”

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confidence: 92%

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A phase diagram for bacterial swarming

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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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Section: Supplementary Textmentioning

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A phase diagram for bacterial swarming

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“…Orientational symmetry breaking and the emergence of collective motion due to velocity alignment is another cornerstone of active matter 22 – 27 . Effective alignment interactions may occur, for example, due to inelastic collisions of colloidal particles 28 observed in ensemble of vertically shaken discs 18 , due to hydrodynamic interactions 20 , 21 , or by combined interactions such as hydrodynamic-electric ones in Quicke rollers 29 and hydrodynamic-magnetic ones in magnetic rollers 30 , 31 .…”

Section: Introductionmentioning

confidence: 99%

A particle-field approach bridges phase separation and collective motion in active matter

2020

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Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media.

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“…In this work, we developed a novel membrane-based microfluidic device that we named the extensive microperfusion system (EMPS), which can realize a uniformly controlled environment for wide-area observations of microbes. We believe that the EMPS has potential applications in a wide range of problems with dense cellular populations, including living active matter systems ( Bär et al (2019) ; Be’er and Ariel (2019) ) and biofilm growth ( Hall-Stoodley et al (2004) ; Boudarel et al (2018) ; Fuqua et al (2019) ). Here we focused on statistical characterizations of single cell morphology during the reductive division of E. coli .…”

Section: Resultsmentioning

confidence: 99%

Scale invariance during bacterial reductive division observed by an extensive microperfusion system

Shimaya

Okura

Wakamoto

et al. 2020

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In stable environments, cell size fluctuations are thought to be governed by simple 9 physical principles, as suggested by recent finding of scaling properties. Here we show, using E. coli, 10 that the scaling concept also rules cell size fluctuations under time-dependent conditions, even 11 though the distribution changes with time. We develop a microfluidic device for observing dense 12 and large bacterial populations, under uniform and switchable conditions. Triggering bacterial 13 reductive division by switching to non-nutritious medium, we find that the cell size distribution 14 changes in a specific manner that keeps its normalized form unchanged; in other words, scale 15 invariance holds. This finding is underpinned by simulations of a model based on cell growth and 16 intracellular replication. We also formulate the problem theoretically and propose a sufficient 17 condition for the scale invariance. Our results emphasize the importance of intrinsic cellular 18 replication processes in this problem, suggesting different distribution trends for bacteria and 19 eukaryotes. 20 21 Biswas et al. (2014a)), have been obtained under steady environments, for which our understanding 37 of single-cell growth statistics has also been significantly deepened recently (Ho et al. (2018); Jun 38 et al. (2018); Cadart et al. (2019)). By contrast, it is unclear whether such a simple concept as 39 1 of 25 Manuscript submitted to eLife scale invariance is valid under time-dependent conditions, where different regulations of cell cycle 40 kinetics may come into play in response to environmental variations. In particular, when bacterial 41 cells enter the stationary phase from the exponential growth phase, they undergo reductive division, 42 during which both the typical cell size and the amount of DNA per cell decrease (Nyström (2004); 43 Kaprelyants and Kell (1993); Arias et al. (2012); Gray et al. (2019)). Although this behavior itself is 44 commonly observed in test tube cultivation, little is known about single-cell statistical properties 45 during the transient. The bacterial reductive division is therefore an important model case for 46 studying cell size statistics under time-dependent environments and testing the robustness of the 47 scale invariance against environmental changes. 48 It has been, however, a challenge to observe large populations of bacteria under uniform yet 49 time-dependent growth conditions. For steady conditions, the Mother Machine (Wang et al. (2010)), 50 which allows for tracking of bacteria trapped in short narrow channels, was proved to be a powerful 51 tool for measuring cell size statistics. In such experiments, the channel width needs to be adapted 52 to cell widths in a given condition, and this renders the application to time-dependent conditions 53 difficult. If we enlarge the channels, depletion of nutrients in deeper regions of the channels 54 induces spatial heterogeneity, as discussed in ref.(Cho et al. (2007); Mather et al. (2010)) and later 55 in this article. Hence, it is als...

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Self-Propelled Rods: Insights and Perspectives for Active Matter

Cited by 258 publications

References 168 publications

A phase diagram for bacterial swarming

A phase diagram for bacterial swarming

A particle-field approach bridges phase separation and collective motion in active matter

Scale invariance during bacterial reductive division observed by an extensive microperfusion system

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