A Nonlocal Model for Contact Attraction and Repulsion in Heterogeneous Cell Populations

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• 作者：K. J. Painter ; J. M. Bloomfield ; J. A. Sherratt…
• 关键词：Nonlocal partial differential equations ; Pattern formation ; Contact mediated attraction ; repulsion ; Neural crest cell dispersion ; Zebrafish pigmentation
• 刊名：Bulletin of Mathematical Biology
• 出版年：2015
• 出版时间：June 2015
• 年：2015
• 卷：77
• 期：6
• 页码：1132-1165
• 全文大小：4,324 KB
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• 作者单位：K. J. Painter (1)
  J. M. Bloomfield (1)
  J. A. Sherratt (1)
  A. Gerisch (2)
  
  1. Department of Mathematics, Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, UK
  2. Fachbereich Mathematik, Technische Universit?t Darmstadt, Dolivostr. 15, 64293, Darmstadt, Germany
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  
• 出版者：Springer New York
• ISSN：1522-9602

文摘

Instructing others to move is fundamental for many populations, whether animal or cellular. In many instances, these commands are transmitted by contact, such that an instruction is relayed directly (e.g. by touch) from signaller to receiver: for cells, this can occur via receptor–ligand mediated interactions at their membranes, potentially at a distance if a cell extends long filopodia. Given that commands ranging from attractive to repelling can be transmitted over variable distances and between cells of the same (homotypic) or different (heterotypic) type, these mechanisms can clearly have a significant impact on the organisation of a tissue. In this paper, we extend a system of nonlocal partial differential equations (integrodifferential equations) to provide a general modelling framework to explore these processes, performing linear stability and numerical analyses to reveal its capacity to trigger the self-organisation of tissues. We demonstrate the potential of the framework via two illustrative applications: the contact-mediated dispersal of neural crest populations and the self-organisation of pigmentation patterns in zebrafish.