Modeling auxin fluxes and Arabidopsis root ramification at different scales

Plant primary growth occurs in two opposite directions, stems and roots both generating branched patterns during their development. However, where stem development appears extremely regular, based on phyllotactic patterns, root architecture appears somewhat random, controlled essentially by external clues such as nutrients concentration (Malamy et al. 2005). The regularity of stem development has been ground to a large panel of pure mathematical and physical modeling (Adler et al. 1997). By contrast, the apparent chaos of root development has essentially directed the modeling effort toward ecophysiological and environmentally constrained models (Doussan et al. 2003). Yet, as the biological knowledge of development and the available microscopy tools evolves, mathematicians and computer scientists are now able to glimpse at the cellular level of development. They can create new models taking into account previously ignored mechanisms and giving rise to new perception on ancient problems, as described by Barbier de Reuille et al. (2006), Jönsson et al. (2006), and Smith et al. (2006) on the topic of phyllotaxis. Until recently, root systems development was considered too chaotic to be modelled on the same basis as shoot development. However, recent biological results suggest that lateral root initiation (LRI), main determinant of root architecture, may itself be more regular than first supposed (Dubrovsky et al. 2000; Dubrovsky et al. 2006; De Smet et al. 2007; Lucas et al. 2007). Global root architecture now appears as the superposition of regular LRI and irregular emergence, the latter phenomenon being more strongly subjected to environmental conditions. As LRI and root development both depend on complex auxin fluxes and genetic interactions, we used a modeling approach to integrate the large biological knowledge available on root development and the complexity of flux dynamics. The models we choose to develop address the control of LRI by auxin fluxes. Our aim was to test various hypotheses concerning LRI regularity and the positioning of root primordia.