论文标题

表型异质性对趋化性自我组织的影响

The impact of phenotypic heterogeneity on chemotactic self-organisation

论文作者

Macfarlane, Fiona R, Lorenzi, Tommaso, Painter, Kevin J

论文摘要

通过化学敏感运动汇总的能力形成了自我组织的范式,其中涵盖了细胞和动物系统。一种基本机制假设具有表型均质的人群,该人群分泌自身的吸引剂,而众所周知的系统在五十年前引入了凯勒(Keller)和塞格尔(Segel),证明在建模研究中绝对流行。然而,种群表型均匀性的典型假设通常与自然系统的异质性不一致,在这种情况下,种群可能构成不同的表型,这些表型根据其趋化能力而变化,吸引人的分泌,{\ it等}。为了了解这种多样性如何影响自身聚集,我们提出了对经典凯勒和透落模型的简单扩展,其中种群被分为两种不同的表型:那些执行化学趋化性和生产吸引力的表型。使用线性稳定性分析和数值模拟的组合,我们证明了这些表型状态之间的切换会改变人群自我聚集的能力。此外,我们表明,基于本地环境(种群密度或化学吸收剂水平)的切换会导致不同的模式,并提供了一种途径,人口可以有效地遏制聚集体的大小和密度。我们在现实世界中趋化聚集的例子以及模型的理论方面(例如全球存在和解决方案的爆炸)中讨论结果。

The capacity to aggregate through chemosensitive movement forms a paradigm of self-organisation, with examples spanning cellular and animal systems. A basic mechanism assumes a phenotypically homogeneous population that secretes its own attractant, with the well known system introduced more than five decades ago by Keller and Segel proving resolutely popular in modelling studies. The typical assumption of population phenotypic homogeneity, however, often lies at odds with the heterogeneity of natural systems, where populations may comprise distinct phenotypes that vary according to their chemotactic ability, attractant secretion, {\it etc}. To initiate an understanding into how this diversity can impact on autoaggregation, we propose a simple extension to the classical Keller and Segel model, in which the population is divided into two distinct phenotypes: those performing chemotaxis and those producing attractant. Using a combination of linear stability analysis and numerical simulations, we demonstrate that switching between these phenotypic states alters the capacity of a population to self-aggregate. Further, we show that switching based on the local environment (population density or chemoattractant level) leads to diverse patterning and provides a route through which a population can effectively curb the size and density of an aggregate. We discuss the results in the context of real world examples of chemotactic aggregation, as well as theoretical aspects of the model such as global existence and blow-up of solutions.

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