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.
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Acknowledgements
I specially thank D. Avitabile, A. Champneys, C. Grierson and M. Ward who have travelled along my side on this dynamical journey. Also, my thanks to the organisers of the Biological Physics Mexico City 2017 Conference for the well-organised meeting. This research has partially been supported by UNAM–PAPIIT grant IA104316–RA104316 (Mexico).
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Breña-Medina, V.F. (2018). Dynamical Features of a Biochemical Interaction in a Plant Root Hair Cell. In: Olivares-Quiroz, L., Resendis-Antonio, O. (eds) Quantitative Models for Microscopic to Macroscopic Biological Macromolecules and Tissues. Springer, Cham. https://doi.org/10.1007/978-3-319-73975-5_10
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DOI: https://doi.org/10.1007/978-3-319-73975-5_10
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