Selecting a common direction: I. How orientational order can arise from simple contact responses between interacting cells

Alex Mogilner, Leah Edelstein-Keshet

Research output: Contribution to journalArticle

39 Scopus citations

Abstract

We present results and analysis of models for contact-induced turning responses and alignment in populations of interacting individuals. Such models describe distributions of orientation, and how these evolve under different assumptions about the turning behaviour of individuals. One of these models was first used to describe interactions between mammalian cells called fibroblasts in Edelstein-Keshet and Ermentrout (1990) J. Math. Biol. 29: 33–58 (henceforth abbreviated EKE 1990). Here the original model is generalized to encompass motion in both 2 and 3 dimensions. Two modifications of this model are introduced: in one, the turning is described by a gradual direction shift (rather than abrupt transition). In another variant, the interactions between individuals changes as the density of the population increases to include the effects of crowding. Using linear stability analysis and synergetics analysis of interacting modes we describe the nature and stability properties of the steady state solutions. We investigate how nonhomogeneous pattern evolves close to the bifurcation point. We find that individuals tend to cluster together in one direction of alignment.

Original languageEnglish (US)
Pages (from-to)619-660
Number of pages42
JournalJournal of Mathematical Biology
Volume33
Issue number6
DOIs
StatePublished - 1995
Externally publishedYes

Keywords

  • Angular distributions
  • Cell alignment
  • Self-organization

ASJC Scopus subject areas

  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Modeling and Simulation

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