Mathematical modelling of auxin dynamics in the model plant Arabidopsis thaliana

The plant hormone auxin plays a crucial role in many aspects of plant development including growth, organ initiation, and tropic responses. In the root tip of Arabidopsis thaliana, auxin is transported via influx (AUX1/LAX) and efflux (PIN/ABCB) carriers, as well as diffusing through plasmodesmata. Existing mathematical models of auxin transport in the root-tip capture the auxin maxima seen experimentally around the quiescent centre region of the root tip, however, these models often rely on a simplified fixed auxin concentration boundary condition at the root-shoot boundary. By working towards the formulation of a hybrid seedling model that captures cell-scale auxin transport in the root-tip and long-distance auxin transport via the phloem, work in this thesis aims to understand how environmental conditions at the shoot can influence auxin patterning in the root tip of Arabidopsis thaliana. The initial development of a root-tip auxin transport model with a constant flux boundary condition at the root-shoot-boundary, highlighted the important role of auxin biosynthesis in root tissues on root-tip auxin patterning. The incorporation of the constant flux boundary condition, in order to consider proportions of shootderived and root-derived auxin, emphasised the need to include a more biologically relevant auxin delivery mechanism to the root tip. We expanded upon phloem transport models in the literature to include the transport of a second small solute alongside sugar (in this thesis considered auxin). Model simulations revealed how environmental conditions that influence sugar dynamics can effect the amount of auxin delivered to the root tip in the case of passively loaded hormones. Finally, these models were coupled together with an additional shoot compartment to create a novel hybrid model of auxin dynamics in a “virtual” seedling. The hybrid model captures how environmental cues can effect auxin and sugar concentration in cotyledons and how this affects phloem transport velocity, auxin delivery to the root tip, and auxin patterning within the root tip. Results highlight the importance of considering the influence of environmental cues on both sugar and auxin parameters when investigating root-tip auxin patterning