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Dynamics of Notch Activity in a Model of Interacting Signaling Pathways

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Abstract

Networks of interacting signaling pathways are formulated with systems of reaction-diffusion (RD) equations. We show that weak interactions between signaling pathways have negligible effects on formation of spatial patterns of signaling molecules. In particular, a weak interaction between Retinoic Acid (RA) and Notch signaling pathways does not change dynamics of Notch activity in the spatial domain. Conversely, large interactions of signaling pathways can influence effects of each signaling pathway. When the RD system is largely perturbed by RA-Notch interactions, new spatial patterns of Notch activity are obtained. Moreover, analysis of the perturbed Homogeneous System (HS) indicates that the system admits bifurcating periodic orbits near a Hopf bifurcation point. Starting from a neighborhood of the Hopf bifurcation, oscillatory standing waves of Notch activity are numerically observed. This is of particular interest since recent laboratory experiments confirm oscillatory dynamics of Notch activity.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, Ontario, K1S-5B6, Canada

    Majid Bani-Yaghoub & David E. Amundsen

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  1. Majid Bani-Yaghoub
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Correspondence to Majid Bani-Yaghoub.

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Bani-Yaghoub, M., Amundsen, D.E. Dynamics of Notch Activity in a Model of Interacting Signaling Pathways. Bull. Math. Biol. 72, 780–804 (2010). https://doi.org/10.1007/s11538-009-9469-8

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