Reaction-diffusion patterns in plant tip morphogenesis: bifurcations on spherical caps.
We study a chemical reaction-diffusion model (the Brusselator) for pattern formation on developing plant tips. A family of spherical cap domains is used to represent tip flattening during development. Applied to conifer embryos, we model the chemical prepatterning underlying cotyledon ("seed leaf") formation, and demonstrate the dependence of patterns on tip flatness, radius, and precursor concentrations. Parameters for the Brusselator in spherical cap domains can be chosen to give supercritical pitchfork bifurcations of patterned solutions of the nonlinear reaction-diffusion system that correspond to the cotyledon patterns that appear on the flattening tips of conifer embryos.
Department of Mathematics, University of British Columbia, Vancouver, British Columbia, Canada, V6T 1Z2, nagata@math.ubc.ca.
Wayne
W
Nagata
Hamid R Z
HR
Zangeneh
David M
DM
Holloway
D019521:Body Patterning; D019295:Computational Biology; D055641:Mathematical Concepts; D008954:Models, Biological; D063245:Plant Development; D010944:Plants / Q000196:embryology