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A Mathematical Model for Eph/Ephrin-Directed Segregation of Intermingled Cells

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Listed:
  • Rotem Aharon
  • Peter W Janes
  • Anthony W Burgess
  • Kais Hamza
  • Fima Klebaner
  • Martin Lackmann

Abstract

Eph receptors, the largest family of receptor tyrosine kinases, control cell-cell adhesion/de-adhesion, cell morphology and cell positioning through interaction with cell surface ephrin ligands. Bi-directional signalling from the Eph and ephrin complexes on interacting cells have a significant role in controlling normal tissue development and oncogenic tissue patterning. Eph-mediated tissue patterning is based on the fine-tuned balance of adhesion and de-adhesion reactions between distinct Eph- and ephrin-expressing cell populations, and adhesion within like populations (expressing either Eph or ephrin). Here we develop a stochastic, Lagrangian model that is based on Eph/ephrin biology: incorporating independent Brownian motion to describe cell movement and a deterministic term (the drift term) to represent repulsive and adhesive interactions between neighbouring cells. Comparison between the experimental and computer simulated Eph/ephrin cell patterning events shows that the model recapitulates the dynamics of cell-cell segregation and cell cluster formation. Moreover, by modulating the term for Eph/ephrin-mediated repulsion, the model can be tuned to match the actual behaviour of cells with different levels of Eph expression or activity. Together the results of our experiments and modelling suggest that the complexity of Eph/ephrin signalling mechanisms that control cell-cell interactions can be described well by a mathematical model with a single term balancing adhesion and de-adhesion between interacting cells. This model allows reliable prediction of Eph/ephrin-dependent control of cell patterning behaviour.

Suggested Citation

  • Rotem Aharon & Peter W Janes & Anthony W Burgess & Kais Hamza & Fima Klebaner & Martin Lackmann, 2014. "A Mathematical Model for Eph/Ephrin-Directed Segregation of Intermingled Cells," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-19, December.
    • Handle: RePEc:plo:pone00:0111803
    DOI: 10.1371/journal.pone.0111803
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    References listed on IDEAS

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    1. Michaël Reber & Patrick Burrola & Greg Lemke, 2004. "A relative signalling model for the formation of a topographic neural map," Nature, Nature, vol. 431(7010), pages 847-853, October.
    2. Simpson, Matthew J. & Landman, Kerry A. & Hughes, Barry D. & Fernando, Anthony E., 2010. "A model for mesoscale patterns in motile populations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(7), pages 1412-1424.
    3. Georg Mellitzer & Qiling Xu & David G. Wilkinson, 1999. "Eph receptors and ephrins restrict cell intermingling and communication," Nature, Nature, vol. 400(6739), pages 77-81, July.
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