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Spot dynamics in a reaction-diffusion model of plant root hair initiation

Avitabile, Daniele; Brena-Medina, Victor F.; Ward, Michael J.


Daniele Avitabile

Victor F. Brena-Medina

Michael J. Ward


We study pattern formation 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. 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. Our mathematical model for the activation of ROPs by the auxin gradient is an extension of the model of Payne and Grierson [PLoS ONE, 12(4), (2009)], and consists of a twocomponent Schnakenberg-type RD system with spatially heterogeneous coefficients on a 2-D domain. The nonlinear kinetics in this RD system model the nonlinear interactions 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 the nonlinear 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 both 2-D localized patterns in the model, and the spatial alignment of localized structures.


Avitabile, D., Brena-Medina, V. F., & Ward, M. J. (2018). Spot dynamics in a reaction-diffusion model of plant root hair initiation. SIAM Journal on Applied Mathematics, 78(1),

Journal Article Type Article
Acceptance Date Oct 4, 2017
Publication Date Jan 31, 2018
Deposit Date Oct 6, 2017
Publicly Available Date Jan 31, 2018
Journal SIAM Journal on Applied Mathematics
Print ISSN 0036-1399
Electronic ISSN 1095-712X
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 78
Issue 1
Public URL
Publisher URL


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