A nonlocal model for contact attraction and repulsion in heterogeneous cell populations

K. J. Painter*, J. M. Bloomfield, J. A. Sherratt, A. Gerisch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)
68 Downloads (Pure)


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.

Original languageEnglish
Pages (from-to)1132-1165
Number of pages34
JournalBulletin of Mathematical Biology
Issue number6
Publication statusPublished - Jun 2015


  • Contact mediated attraction-repulsion
  • Neural crest cell dispersion
  • Nonlocal partial differential equations
  • Pattern formation
  • Zebrafish pigmentation

ASJC Scopus subject areas

  • General Agricultural and Biological Sciences
  • General Biochemistry,Genetics and Molecular Biology
  • General Environmental Science
  • Immunology
  • General Mathematics
  • Computational Theory and Mathematics
  • General Neuroscience
  • Pharmacology


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