Graduate School of Information Science, University of Hyogo, Kobe, 650-0047, Japan.
Bull Math Biol. 2022 Sep 1;84(10):113. doi: 10.1007/s11538-022-01071-x.
Aggregation of chemotactic bacteria under a unimodal distribution of chemical cues was investigated by Monte Carlo (MC) simulation based on a kinetic transport equation, which considers an internal adaptation dynamics as well as a finite tumbling duration. It was found that there exist two different regimes of the adaptation time, between which the effect of the adaptation time on the aggregation behavior is reversed; that is, when the adaptation time is as small as the running duration, the aggregation becomes increasingly steeper as the adaptation time increases, while, when the adaptation time is as large as the diffusion time of the population density, the aggregation becomes more diffusive as the adaptation time increases. Moreover, the aggregation profile becomes bimodal (volcano) at the large adaptation-time regime when the tumbling duration is sufficiently large while it is always unimodal at the small adaptation-time regime. A remarkable result of this study is the identification of the parameter regime and scaling for the volcano effect. That is, by comparing the results of MC simulations to the continuum-limit models obtained at each of the small and large adaptation-time scalings, it is clarified that the volcano effect arises due to the coupling of diffusion, adaptation, and finite tumbling duration, which occurs at the large adaptation-time scaling.
通过基于动力学输运方程的蒙特卡罗 (MC) 模拟研究了在化学线索单峰分布下趋化细菌的聚集，该方程考虑了内部适应动力学以及有限的翻滚持续时间。结果发现，适应时间存在两种不同的状态，适应时间对聚集行为的影响在这两种状态之间发生反转；也就是说，当适应时间与运行时间一样短时，随着适应时间的增加，聚集变得越来越陡峭，而当适应时间与种群密度的扩散时间一样长时，随着适应时间的增加，聚集变得更加扩散。此外，当翻滚持续时间足够大时，在大适应时间状态下聚集分布呈现双峰（火山）状，而在小适应时间状态下始终呈现单峰状。这项研究的一个显著结果是确定了火山效应的参数范围和标度。也就是说，通过将 MC 模拟的结果与在小和大适应时间标度下获得的连续体极限模型进行比较，可以清楚地看出，由于扩散、适应和有限翻滚持续时间的耦合，在大适应时间标度下出现了火山效应。
