Seminario Especial de Matemáticas Aplicadas


por el

Dr. Victor Breña

Centro de Ciencias Matemáticas, Morelia - UNAM

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.

 Jueves 23 de febrero, 2017.
17:00 hrs.
Salón 203, Edificio Anexo, IIMAS

Informes:, o al 5622-3564.