Lattice gas cellular automation model for rippling and aggregation in myxobacteria

Department of Mathematics, Interdisciplinary Center for the Study of Biocomplexity, University of Notre Dame, Notre Dame, IN 46556-5670, USA
Physica D Nonlinear Phenomena (Impact Factor: 1.64). 05/2004; 191(3-4):343-358. DOI: 10.1016/j.physd.2003.11.012


A lattice gas cellular automation (LGCA) model is used to simulate rippling and aggregation in myxobacteria. An efficient way of representing cells of different cell size, shape and orientation is presented that may be easily extended to model later stages of fruiting body formation. This LGCA model is designed to investigate whether a refractory period, a minimum response time, a maximum oscillation period and non-linear dependence of reversals of cells on C-factor are necessary assumptions for rippling. It is shown that a refractory period of 2–3 min, a minimum response time of up to 1 min and no maximum oscillation period best reproduce rippling in the experiments of Myxococcus xanthus. Non-linear dependence of reversals on C-factor is critical at high cell density. Quantitative simulations demonstrate that the increase in wavelength of ripples when a culture is diluted with non-signaling cells can be explained entirely by the decreased density of C-signaling cells. This result further supports the hypothesis that levels of C-signaling quantitatively depend on and modulate cell density. Analysis of the interpenetrating high density waves shows the presence of a phase shift analogous to the phase shift of interpenetrating solitons. Finally, a model for swarming, aggregation and early fruiting body formation is presented.

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Available from: Mark Alber, Oct 05, 2015
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    • "The total count is T = c x− + c x+ + c y− + c y+ , which leads to defining the directional weights, c 1 = c y+ /T , c 2 = c y− /T , c 3 = c x+ /T and c 4 = c x− /T . Drawing a random number, r 2 , from the interval [0] [1] and comparing it to the concatenation of the weights, 0 ≤ c 1 ≤ c 1 + c 2 ≤ c 1 + c 2 + c 3 ≤ c 1 + c 2 + c 3 + c 4 = 1, determines the direction the agent moves (e.g. if 0 < r 2 < c 1 , the agent moves in the positive y-direction). "
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    • "The conversion between MCS and experimental time depends on the average value of DH/T m . In biologically-meaningful situations, MCS and experimental time are proportional (Alber et al., 2002, 2004; Novak et al., 1999; Cickovski et al., 2007). "
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    • "To resolve the conflicts of these models for rippling our LGCA model was designed to test different assumptions [1]. In our models for rippling and aggregation , we define the size and shape of the cell as a 3 × rectangle, where is cell length. "
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