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**Analysis and computer simulation of accretion patterns in bacterial cultures.**
*(English)*
Zbl 0808.92010

Summary: Patterned growth of bacteria created by interactions between the cells and moving gradients of nutrients and chemical buffers is observed frequently in laboratory experiments on agar pour plates. This has been investigated by several microbiologists and mathematicians usually focusing on some hysteretic mechanisms, such as dependence of cell uptake kinetics on pH. We show here that a simpler mechanism, one based on cell torpor, can explain patterned growth.

In particular, we suppose that the cell population comprises two subpopulations – one actively growing and the other inactive. Cells can switch between the two populations depending on the quality of their environment (nutrient availability, pH, etc.) We formulate here a model of this system, derive and analyze numerical schemes for solving it, and present several computer simulations of the system that illustrate various patterns formed. These compare favorably with observed experiments.

In particular, we suppose that the cell population comprises two subpopulations – one actively growing and the other inactive. Cells can switch between the two populations depending on the quality of their environment (nutrient availability, pH, etc.) We formulate here a model of this system, derive and analyze numerical schemes for solving it, and present several computer simulations of the system that illustrate various patterns formed. These compare favorably with observed experiments.

### MSC:

92C15 | Developmental biology, pattern formation |

35Q92 | PDEs in connection with biology, chemistry and other natural sciences |

65C20 | Probabilistic models, generic numerical methods in probability and statistics |

92D40 | Ecology |

### Keywords:

pattern formation; patterned growth of bacteria; moving gradients of nutrients; cell uptake kinetics; pH
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\textit{C. Chiu} et al., J. Math. Biol. 32, No. 8, 841--855 (1994; Zbl 0808.92010)

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### References:

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