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Spatiotemporal Patterning in Models of Juxtacrine Intercellular Signalling with Feedback

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Mathematical Models for Biological Pattern Formation

Part of the book series: The IMA Volumes in Mathematics and its Applications ((4522,volume 121))

Abstract

Juxtacrine signalling is the class of intercellular communication mediated by ligands and receptors that are both anchored in the cell membrane. Two particularly well documented examples of such signalling pathways are the Delta-Notch and tgf α-egf-r interactions. In this review, we discuss mathematical models for juxtacrine signalling, focussing on these two specific examples. We discuss the various model formulations that have been used, and consider gradient, travelling front, and spatial pattern type solutions. We show that juxtacrine mechanisms can explain a wide range of observed behaviours in each of these categories, in a manner that is genuinely different from that in traditional diffusion-based models for intercellular signalling.

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Authors and Affiliations

  1. Mathematical Modelling and Genetic Epidemiology Group, Division of Molecular and Genetic Medicine, University of Sheffield, Royal Hallamshire Hospital, Sheffield, S10 2JF, UK

    Nicholas A. M. Monk

  2. Centre for Theoretical Modelling in Medicine, Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    Jonathan A. Sherratt

  3. Nonlinear and Complex Systems Group, Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire, LE11 3TU, UK

    Markus R. Owen

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Editors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK

    Philip K. Maini

  2. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Hans G. Othmer

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Monk, N.A.M., Sherratt, J.A., Owen, M.R. (2001). Spatiotemporal Patterning in Models of Juxtacrine Intercellular Signalling with Feedback. In: Maini, P.K., Othmer, H.G. (eds) Mathematical Models for Biological Pattern Formation. The IMA Volumes in Mathematics and its Applications, vol 121. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0133-2_8

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