Dynamical features of a biochemical interaction in a plant root hair cell: A long story short

Abstract

In this chapter, we briefly discuss key dynamical features of a generalised Schnakenberg model. This model sheds light on the morphogenesis of plant root hair initiation process. Our discussion is focused on the plant called Arabidopsis thaliana, which is a prime plant-model for plant researchers as is experimentally well known. Here, relationships between physical attributes and biochemical interactions that occur at a sub-cellular level are revealed. The model consists of a two-component non-homogeneous reaction-diffusion system, which takes into account an on-and-off switching process of small G-protein family members called Rho-of-Plants (ROPs). This interaction however is catalysed by the plant hormone auxin, which is known to play a crucial role in many morphogenetic processes in plants. Upon applying semi-strong theory and performing numerical bifurcation analysis, all together with time-step simulations, we present results from a thorough analysis of the dynamics of spatially localised structures in 1D and 2D spatial domains. These compelling dynamical features are found to give place to a wide variety of patterns. Key features of the full analysis are discussed.