Continuum modeling of myxobacteria clustering

Harvey, Cameron W.; Alber, Mark; Tsimring, Lev S.; Aranson, Igor S.

doi:10.1088/1367-2630/15/3/035029

Cited by 25 publications

(22 citation statements)

References 37 publications

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“…Thus, we assume that at each point x, y we may have two concentrations of bacteria c þ and c − , swimming in opposite directions, n and −n (compare with Ref. [38]). …”

Section: Modelmentioning

confidence: 99%

Topological Defects in a Living Nematic Ensnare Swimming Bacteria

et al. 2017

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Active matter exemplified by suspensions of motile bacteria or synthetic self-propelled particles exhibits a remarkable propensity to self-organization and collective motion. The local input of energy and simple particle interactions often lead to complex emergent behavior manifested by the formation of macroscopic vortices and coherent structures with long-range order. A realization of an active system has been conceived by combining swimming bacteria and a lyotropic liquid crystal. Here, by coupling the well-established and validated model of nematic liquid crystals with the bacterial dynamics, we develop a computational model describing intricate properties of such a living nematic. In faithful agreement with the experiment, the model reproduces the onset of periodic undulation of the director and consequent proliferation of topological defects with the increase in bacterial concentration. It yields a testable prediction on the accumulation of bacteria in the cores of þ1=2 topological defects and depletion of bacteria in the cores of −1=2 defects. Our dedicated experiment on motile bacteria suspended in a freestanding liquid crystalline film fully confirms this prediction. Our findings suggest novel approaches for trapping and transport of bacteria and synthetic swimmers in anisotropic liquids and extend a scope of tools to control and manipulate microscopic objects in active matter.

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“…Thus, we assume that at each point x, y we may have two concentrations of bacteria c þ and c − , swimming in opposite directions, n and −n (compare with Ref. [38]). …”

Section: Modelmentioning

confidence: 99%

Topological Defects in a Living Nematic Ensnare Swimming Bacteria

et al. 2017

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“…Thus global polar order arises whereas the interaction is purely nematic. [30] Note that such global order, made of nonlinear structures, is not in contradiction with the theoretical arguments at linear level [26,31,32] precluding the emergence of homogeneous polar order in systems with nematic interactions.…”

mentioning

confidence: 98%

Collective Motion of Self-Propelled Particles with Memory

et al. 2015

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We show that memory, in the form of underdamped angular dynamics, is a crucial ingredient for the collective properties of self-propelled particles. Using Vicsek-style models with an OrnsteinUhlenbeck process acting on angular velocity, we uncover a rich variety of collective phases not observed in usual overdamped systems, including vortex lattices and active foams. In a model with strictly nematic interactions the smectic arrangement of Vicsek waves giving rise to global polar order is observed. We also provide a calculation of the effective interaction between vortices in the case where a telegraphic noise process is at play, explaining thus the emergence and structure of the vortex lattices observed here and in motility assay experiments.PACS numbers: 05.65.+b, 45.70.Vn, 87.18.Gh Self-propelled particles are nowadays commonly used to study collective motion and more generally "dry" active matter, where the surrounding fluid is neglected. Real world relevant situations include shaken granular particles [1][2][3][4][5], active colloids [6][7][8], bio-filaments displaced by motor proteins [9][10][11]. The trajectories of moving living organisms (from bacteria to large animals such as fish, birds and even human crowds) are also routinely modeled by such particles, see e.g. [12][13][14][15][16][17].Many of these 'active particles' travel at near-constant speed with their dynamics modeled as a persistent random walk with some stochastic component acting directly on their orientation [18]. This noise, which represents external and/or internal perturbations, produces jagged irregular trajectories. Most of the recent results on active matter have been obtained in this context of overdamped dynamics.In many situations, however, the overdamped approximation is not justified. In particular, trajectories can be essentially smooth, as for chemically propelled rods [19,20], birds, some large fish that swim steadily [16], or even biofilaments in motility assays with a high density of molecular motors [10]. Whether underdamped dynamics can make a difference at the level of collective asymptotic properties is largely unknown. Interesting related progress was recently reported for starling flocks [21]. Underdamped "spin" variables are instrumental there for efficient, fast transfer of information through the flock, allowing swift turns in response to threats during which speed is modulated in a well coordinated manner. In the other examples cited above, speed remains nearlyconstant and the persistently turning tracks of fish or microtubules reveal some finite, possibly large, memory of the curvature. In this context an Ornstein-Uhlenbeck (OU) process acting on the angular velocity was shown to be a quantitatively-valid representation [10,16]. The collective motion of self-propelled particles with such underdamped angular dynamics remains largely unknown.In this Letter, we explore minimal models of aligning self-propelled particles with memory similar to that used in [10] to study the emergence of large-scale vortices in mot...

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“…This factor increases with the density and diverges to infinity as ǫ → 1 at u = 1, which causes the bacterial population to migrate faster at higher density. This singularity has appeared in similar models using different approaches [22,23,[29][30][31][32]40]. Fortunately, the velocity in Eq.…”

Section: Dimensionless Equationsmentioning

confidence: 99%

Mechanically-driven spreading of bacterial populations

Ngamsaad

Suantai

2016

Communications in Nonlinear Science and Numerical Simulation

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The effect of mechanical interactions between cells in the spreading of bacterial populations was investigated in one-dimensional space. A continuummechanics approach, comprising cell migration, proliferation, and exclusion processes, was employed to elucidate the dynamics. The consequent nonlinear reaction-diffusion-like equation describes the constitution dynamics of a bacterial population. In this model, bacterial cells were treated as rod-like particles that interact with each other through hard-core repulsion, which introduces the exclusion effect that causes bacterial populations to migrate quickly and at high density. The propagation of bacterial density as a traveling wave front over extended times was also analysed. The analytical and numerical solutions revealed that the front speed was enhanced by the exclusion process, which depended upon the cell-packing fraction. Finally, we qualitatively compared our theoretical results with experimental evidence.

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Continuum modeling of myxobacteria clustering

Cited by 25 publications

References 37 publications

Topological Defects in a Living Nematic Ensnare Swimming Bacteria

Topological Defects in a Living Nematic Ensnare Swimming Bacteria

Collective Motion of Self-Propelled Particles with Memory

Mechanically-driven spreading of bacterial populations

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