Cooperative Formation of Chiral Patterns during Growth of Bacterial Colonies

Ben‐Jacob, Eshel; Cohen, Ilan; Shochet, Ofer; Tenenbaum, Adam; Czirók, András; Vicsek, Tamás

doi:10.1103/physrevlett.75.2899

Cited by 127 publications

(99 citation statements)

References 16 publications

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“…6, where it is plotted together with the analytic result (17). From this we can see that the average branch width from the simulations agree with the analytic result obtained from the linear stability analysis of the model.…”

Section: Comparison To Simulationssupporting

confidence: 76%

“…These models are able to reproduce the observed patterns, ranging from Eden-like [13] and dense branched morphologies [14] to DLA-like patterns [15]. Another approach by Ben-Jacob et al [16,17] is to model the bacteria as clusters of discrete walkers which obey dynamical rules. This model also agrees well with experimental data and is more biologically realistic compared to the reactiondiffusion approach.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of a hybrid cellular automaton model of cell colony growth

Gerlee

Anderson

2007

Phys. Rev. E

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Cell colonies of bacteria, tumour cells and fungi, under nutrient limited growth conditions, exhibit complex branched growth patterns. In order to investigate this phenomenon we present a simple hybrid cellular automaton model of cell colony growth. In the model the growth of the colony is limited by a nutrient that is consumed by the cells and which inhibits cell division if it falls below a certain threshold. Using this model we have investigated how the nutrient consumption rate of the cells affects the growth dynamics of the colony. We found that for low consumption rates the colony takes on a Eden-like morphology, while for higher consumption rates the morphology of the colony is branched with a fractal geometry. These findings are in agreement with previous results, but the simplicity of the model presented here allows for a linear stability analysis of the system. By observing that the local growth of the colony is proportional to the flux of the nutrient we derive an approximate dispersion relation for the growth of the colony interface. This dispersion relation shows that the stability of the growth depends on how far the nutrient penetrates into the colony. For low nutrient consumption rates the penetration distance is large, which stabilises the growth, while for high consumption rates the penetration distance is small, which leads to unstable branched growth. When the penetration distance vanishes the dispersion relation is reduced to the one describing Laplacian growth without ultra-violet regularisation. The dispersion relation was verified by measuring how the average branch width depends on the consumption rate of the cells and shows good agreement between theory and simulations.

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Section: Comparison To Simulationssupporting

confidence: 76%

Section: Introductionmentioning

confidence: 99%

Stability analysis of a hybrid cellular automaton model of cell colony growth

Gerlee

Anderson

2007

Phys. Rev. E

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“…Coordinated multicellular activities such as aggregation, development of specialized structures, and colony pattern formation are visible, population-scale manifestations of individual cellular behaviors or properties (30,158,248). Examples of such organized phenomena include fruiting-body development in myxobacteria, mound and slug formation in Dictyostelium discoideum, chiral colony morphology in Bacillus subtilis, and coordinated movement (e.g., traveling waves, whirls, and jets) within populations of myxobacteria or B. subtilis (158,248).…”

Section: Relating Microscopic Mesoscopic and Macroscopic Observationsmentioning

confidence: 99%

Single-Cell Microbiology: Tools, Technologies, and Applications

Brehm-Stecher

Johnson

2004

Microbiol Mol Biol Rev

447

316

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The field of microbiology has traditionally been concerned with and focused on studies at the population level. Information on how cells respond to their environment, interact with each other, or undergo complex processes such as cellular differentiation or gene expression has been obtained mostly by inference from population-level data. Individual microorganisms, even those in supposedly “clonal” populations, may differ widely from each other in terms of their genetic composition, physiology, biochemistry, or behavior. This genetic and phenotypic heterogeneity has important practical consequences for a number of human interests, including antibiotic or biocide resistance, the productivity and stability of industrial fermentations, the efficacy of food preservatives, and the potential of pathogens to cause disease. New appreciation of the importance of cellular heterogeneity, coupled with recent advances in technology, has driven the development of new tools and techniques for the study of individual microbial cells. Because observations made at the single-cell level are not subject to the “averaging” effects characteristic of bulk-phase, population-level methods, they offer the unique capacity to observe discrete microbiological phenomena unavailable using traditional approaches. As a result, scientists have been able to characterize microorganisms, their activities, and their interactions at unprecedented levels of detail

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“…fish schools, bird flocks, bacterial colonies) exhibits a large variety of emergent phenomena [1,2,3,4,5,6,7,8]. Synchronized motion, symmetrical group formations (e.g., V shaped) or swirling patterns emerge in spite of the apparently simple behavioral rules of the individual flock members [9,10].…”

Section: Inroductionmentioning

confidence: 99%

Turning with the Others: Novel Transitions in an SPP Model with Coupling of Accelerations

Szabó

Nagy

Vicsek

2008

2008 Second IEEE International Conference on Self-Adaptive and Self-Organizing Systems

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We consider a three dimensional, generalized version of the original SPP model for collective motion. By extending the factors influencing the ordering, we investigate the case when the movement of the self-propelled particles (SPP-s) depends on both the velocity and the acceleration of the neighboring particles, instead of being determined solely by the former one. By changing the value of a weight parameter s determining the relative influence of the velocity and the acceleration terms, the system undergoes a kinetic phase transition as a function of a behavioral pattern. Below a critical value of s the system exhibits disordered motion, while above it the dynamics resembles that of the SPP model. We argue that in nature evolutionary processes can drive the strategy variable s towards the critical point, where information exchange between the units of a system is maximal. InroductionCollective motion of organisms (e.g. fish schools, bird flocks, bacterial colonies) exhibits a large variety of emergent phenomena [1,2,3,4,5,6,7,8]. Synchronized motion, symmetrical group formations (e.g., V shaped) or swirling patterns emerge in spite of the apparently simple behavioral rules of the individual flock members [9,10]. The self propelled particles (SPP) model was proposed by Vicsek et al.[11] to describe the onset of ordered motion within a group of self-propelled particles in the presence of perturbations. Taking into the effects of fluctuations inevitably present in biological systems was an essential generalization of the prior deterministic flocking models such as that of Reynolds [12]. The original model considers point-like particles moving at constant velocity on a two dimensional surface with periodic boundary conditions. The only rule is that, at each time step, every particle approximates, with some uncertainty, the average direction of motion of the particles within its neighborhood of radius R. This model exhibits spontaneous self-organization; by decreasing the noise parameter, the system undergoes a kinetic phase transition from a disordered state to an ordered one where all the particles move approximately in the same direction. Due its simplicity and analogy with biological systems comprised of many, locally interacting particles, the SPP model soon became a reference model for the flocking behavior of organisms [13,14,15,16,17,18,19,20,21,22,23].The individual based behavioral rules, determining collective motion, are of particular interest. Important elements of behavioral rules are the nature of the perceived information and the affected behavioral traits. [24,25,26]. A frequent assumption in models is that the information, perceived by the particles, is restricted to the velocity of their neighbors. The interaction range is usually defined by metric distances, but Ballerini et al. [24] recently showed that topological distance is the one determining the flocking of starlings. The assumption of reflecting on the momentary velocity only may not be enough for adequately describing a number o...

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Cooperative Formation of Chiral Patterns during Growth of Bacterial Colonies

Cited by 127 publications

References 16 publications

Stability analysis of a hybrid cellular automaton model of cell colony growth

Stability analysis of a hybrid cellular automaton model of cell colony growth

Single-Cell Microbiology: Tools, Technologies, and Applications

Turning with the Others: Novel Transitions in an SPP Model with Coupling of Accelerations

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