Speaker
Description
Auxin is a hormone that plays key regulatory roles in plant development. Its diverse functions are enabled by its directional (polar) transport through cells and the feedback between this transport and the intracellular localisation of auxin transporters (PINs). These mechanisms are traditionally modelled using discrete compartmental ODEs, where each compartment represents a single cell.
Here we develop coarse-grained continuum models of polar auxin transport that are better suited to larger biological domains and enable analytical progress. By seeking an asymptotic expansion, we derive a single partial differential equation (PDE) that governs long-time auxin dynamics. We use this reduction to characterise the parameter regimes and feedback structures under which the continuum model reproduces qualitative behaviours observed in cell-based discrete models. Specifically, we investigate the emergence of patterned auxin peaks generated by up-the-gradient PIN polarisation and explore canal-like patterns arising from with-the-flux feedback mechanisms. In doing so we highlight the conditional validity of a simple quasi-steady state assumption.
Finally, we use the continuum framework to identify which mechanisms persist under coarse-graining and which are inherently dependent on the cellular scale, providing a robust comparison between cell-level and tissue-level transport dynamics.
