A generalized discrete model linking rippling pattern formation and individual cell reversal statistics in colonies of myxobacteria

Börner, Uwe; Deutsch, Andreas; Bär, Markus

doi:10.1088/1478-3975/3/2/006

Cited by 17 publications

(10 citation statements)

References 27 publications

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“…Examples include bacteria that swim by executing nonreciprocal motions, 1, 2 and molecular motors that undergo conformational changes that lead to directed motion on filaments to carry out active transport tasks in the cell. [6][7][8] In some respects the phenomena seen in these micron-scale self-propelled objects are similar to those observed in other active materials such as forced granular matter, 9,10 active liquid crystals, 11,12 or even the flocking behavior of macroscopic active objects like birds or fish. 3 In addition to the individual motions of these selfpropelled motors and swimmers, ensembles of such active objects exhibit distinctive collective motions.…”

Section: Introductionsupporting

confidence: 64%

Self-propelled nanodimer bound state pairs

Thakur

Kapral

2010

The Journal of Chemical Physics

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A pair of chemically powered self-propelled nanodimers can exist in a variety of bound and unbound states after undergoing a collision. In addition to independently moving unbound dimers, bound Brownian dimer pairs, whose center-of-mass exhibits diffusive motion, self-propelled moving dimer pairs with directed motion, and bound rotating dimer pairs, were observed. The bound pairs arise from a solvent depletion interaction, which depends on the nonequilibrium concentration field in the vicinity of dimers. The phase diagram reported in the paper shows regions in monomer interaction energy-diameter plane where these bound and unbound states are found. Particle-based simulations and analytical calculations are used to provide insight into the nature of interaction between dimers that gives rise to the observed bound states.

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Section: Introductionsupporting

confidence: 64%

Self-propelled nanodimer bound state pairs

Thakur

Kapral

2010

The Journal of Chemical Physics

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“…A further aspect where the described model for reversing bacteria may become important is the modeling of collective behaviors like rippling, clustering and other forms of collective motion of bacteria. Earlier studies on myxobacterial rippling [30,50] compared simulation results with experimental data [30,51] based on the reversal time statistics of labeled bacteria in colonies assuming identical cell behaviors. The presented model, in contrast, allows for the modeling of the variability (stochasticity) of individual cells that is expressed in the runtime distributions displayed in figure 9.…”

Section: Discussionmentioning

confidence: 99%

Diffusion properties of active particles with directional reversal

2016

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The diffusion properties of self-propelled particles which move at constant speed and, in addition, reverse their direction of motion repeatedly are investigated. The internal dynamics of particles triggering these reversal processes is modeled by a stochastic clock. The velocity correlation function as well as the mean squared displacement is investigated and, furthermore, a general expression for the diffusion coefficient for self-propelled particles with directional reversal is derived. Our analysis reveals the existence of an optimal, finite rotational noise amplitude which maximizes the diffusion coefficient. We comment on the relevance of these results with regard to biological systems and suggest further experiments in this context. IntroductionActive matter systems-ensembles of self-driven particles-are a central subject of non-equilibrium statistical physics [1-4]:examples include micron-sized active colloids and rods driven by chemical reactions [5,6] or by the Quincke effect [7,8] as well as macroscopic collective motion patterns in bird flocks or sheep herds [9][10][11]. In particular, the study of bacterial systems as well as their theoretical analysis within simple self-propelled particle models has lead to interesting insights into the physics of active matter-consider, for example, the clustering of myxobacteria [12,13] or the dynamic vortex formation in dense suspensions of swimming bacteria [14][15][16][17].In order to understand the cooperative behavior of active particles as well as the associated pattern formation processes, reliable knowledge of the dynamics of individual entities is crucial. In this work, we therefore focus on the dynamics of individual active particles. We particularly consider particles that are able to reverse their direction of motion repeatedly. More precisely, particles follow an alternating motion pattern where rather persistent motion is interrupted by sudden reversals of the direction of motion.This type of motion has been reported in a variety of bacterial systems [18][19][20][21][22][23][24][25][26]. For instance, the soil bacterium Myxococcus xanthus constitutes a paradigmatic example of a bacterium exhibiting periodic reversals in the direction of motion:internal oscillations of the protein dynamics cause switches in cell polarity and, correspondingly, in the direction of motion [18,19,27,28]. Under certain conditions, the reversals of several, densely packed bacteria appear synchronously leading to remarkable accordion wave patterns [29,30]. Apart from myxobacteria, a variety of marine microorganisms exhibit run-and-reverse motion [20], such as Pseudoalteromonas haloplanktis and Shewanella putrefaciens [21]. Similar motion patterns were reported for Pseudomonas citronellolis [31], Paenibacillus dendritiformis [22] and Pseudomonas putida [23][24][25][26].More complex, three-step (run-reverse-flick) motion patterns, composed of rather straight runs, directional reversals and 90°turns, were found in the marine bacterium Vibrio alginolyticus [32,33]. In this con...

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“…Actually, this biological mechanism seems to be crucial for the formation of ripples, as observed in discrete models (Börner et al 2002(Börner et al , 2006, parabolic models (Igoshin et al 2001, as well as nonlocal hyperbolic models (Eftimie et al 2007a). (We will revisit this pattern in Sect.…”

Section: Density-dependent Turning Ratesmentioning

confidence: 98%

Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review

Eftimie

2011

J. Math. Biol.

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We briefly review hyperbolic and kinetic models for self-organized biological aggregations and traffic-like movement. We begin with the simplest models described by an advection-reaction equation in one spatial dimension. We then increase the complexity of models in steps. To this end, we begin investigating local hyperbolic systems of conservation laws with constant velocity. Next, we proceed to investigate local hyperbolic systems with density-dependent speed, systems that consider population dynamics (i.e., birth and death processes), and nonlocal hyperbolic systems. We conclude by discussing kinetic models in two spatial dimensions and their limiting hyperbolic models. This structural approach allows us to discuss the complexity of the biological problems investigated, and the necessity for deriving complex mathematical models that would explain the observed spatial and spatiotemporal group patterns.

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A generalized discrete model linking rippling pattern formation and individual cell reversal statistics in colonies of myxobacteria

Cited by 17 publications

References 27 publications

Self-propelled nanodimer bound state pairs

Self-propelled nanodimer bound state pairs

Diffusion properties of active particles with directional reversal

Hyperbolic and kinetic models for self-organized biological aggregations and movement: a brief review

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