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Reaction-diffusion modelling of somite formation : computed dynamics and bifurcation analysis

University of British Columbia

Living organisms exhibit pattern in many forms. The processes underlying this organization, in general, are not well understood. This thesis proposes a candidate model for the dynamic eruption of somites (the precursors for the structures associated with the spinal column) in vertebrate embryos. We apply the Brusselator reaction-diffusion chemical model in a dynamic setting to not only produce the desired pattern, but also to mimic the propagation of the region of somite production (the "cohesive zone") along the embryo. The model can be rendered into a system of partial differential equations, and studied analytically and numerically. A bifurcation analysis is performed on a certain trajectory in the system's parameter space. Further numerical analysis on a more biologically robust version of the problem yields evidence for more than one stable, steady-state solution for certain parameter sets. Movement of the region of somite formation is simulated by adding a feedback mechanism between the peak value of the X morphogen, and a gradient in the source chemical B. Finally, investigation of the effect of adding a diffusion barrier yields some results that may be tested experimentally, creating evidence either for or against the possibility that a Brusselator-like chemical system is responsible for somite production in vertebrate embryos.

Thesis/Dissertation

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2009-02-17

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http://hdl.handle.net/2429/4664

Mathematics

University of British Columbia

UBCV

DSpace