A phase diagram for bacterial swarming

Abstract

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-

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

“…Thereby, we shed light on the importance of anisotropic repulsion as a source of orientational alignment, particularly on how the interrelation of particle shape, rigidity, and self-propulsion determines emergent collective behavior—key elements to be considered in the design of biomimetic materials. Unifying seemingly different phenomena at the heart of active matter within one theoretical framework is expected to pave the way toward a comprehensive understanding of soft and deformable active matter such as bacterial colonies 4 , 63 or driven filaments 41 – 43 .…”

Biofilm and swarming emergent behaviours controlled through the aid of biophysical understanding and tools

“…Swirling patterns in swarms, lasting for several seconds, are inherent to systems composed of rod-shaped active particles [ 18 , 49 ]. Therefore, cell shape, more specifically the aspect ratio (ratio between the width and the length of the cells), is one of the key parameters that fundamentally define swarming dynamics [ 50 ]. In B. subtilis swarms, low aspect ratios (from 1 to 9) enable the normal swarming behaviour, characterised by a unimodal distribution of surface densities and a Gaussian distribution of the velocities (kurtosis close to 3).…”

“…The velocity distribution gives very large kurtosis (indicating heavy-tailed distributions) unlike in the small aspect ratio phase. The aspect ratio also affects the magnitude of the velocity, peaking at 50 μm/s (aspect ratio of 5) [ 50 ], which decreases by nearly 5-fold when the aspect ratio is changed to 3.8 or 8.…”

“…This bottom threshold is slightly reduced by increasing aspect ratios, suggesting that high aspect ratio promotes swarming at low surface densities. Increasing surface densities up to a threshold of ∼0.8 enhances swarming motility but, for higher values, cells stop moving efficiently and form a jam phase [ 18 , 50 ]. This threshold again depends on the aspect ratio since larger aspect ratios permit swarming at surface coverage slightly greater than 0.8.…”

Mechanistic underpinning of nonuniform collective motions in swarming bacteria

“…A number of prior studies have focused on mainly understanding the swarming dynamics with respect to the properties like cell-density or packing fraction and cell-aspect ratio, constant and density-dependent self-propulsion forces, a mixture of motile and non-motile cells [13,17,[30][31][32][33]. For a statistical physics view on bacterial swarming dynamics we refer [34].…”