IIMAS - FENOMEC
UNAM
Resumen:
Pattern formation aspects in a 2-D reaction-diffusion (RD)
sub-cellular model characterizing the effect of a spatial
gradient of a plant hormone distribution on a family of
G-proteins associated with root-hair (RH) initiation in the
plant cell Arabidopsis thaliana are analyzed. The activation
of these G-proteins, known as the Rho of Plants (ROPs), by the
plant hormone, auxin, is known to promote certain
protuberances on root hair cells, which are crucial for both
anchorage and the uptake of nutrients from the soil. The
mathematical model for the activation of ROPs by the auxin
gradient is an extension of the model proposed by Payne and
Grierson [PLoS ONE, 12(4), (2009)], and consists of a
two-component generalized Schnakenberg RD system with
spatially heterogeneous coefficients on a 2-D domain. The
nonlinear kinetics in this RD system model the nonlinear
interations between the active and inactive forms of ROPs. By
using a singular perturbation analysis to study 2-D localized
spatial patterns of active ROPs, it is shown that the spatial
variations in certain nonlinear terms in the reaction
kinetics, due to the auxin gradient, lead to a slow spatial
alignment of the localized regions of active ROPs along the
longitudinal midline of the plant cell. Numerical bifurcation
analysis, together with time-dependent numerical simulations
of the RD system are used to illustrate 2-D localized patterns
in the model, as well as the spatial alignment of localized
structures.
Informes: coloquiomym@gmail.com, o al 5622-3564.