Speaker
Description
The self-organization of microtubule (MT) polymers along the inner surface (cortex) of the plant cell membrane is an essential element in facilitating directional cell growth. The key questions are: what gives rise to the ordering and orientation of MT patterns? Mathematical and computational modelling has proven successful in providing insights: the process is distilled into a system of interacting curves on a 2D surface. There has been interest in the role of cell geometry in this process. Our recent work revisited a common assumption, that MT shapes are described by geodesics. More realistically, MTs are relatively rigid filaments and should seek to minimizing bending, resulting in elastic curves. Our model of elastic curves on cylindrical cells has shown that the curvature influence on MTs should orient MTs in directions opposite to what is biologically favourable. I present our work in generalizing this model to other geometries: we solve for elastic curves on various surfaces to show bifurcations and diverse curves resulting from non-local curvature sensing. This opens the field to realistic models on complex geometries. Our model indicates that there must be additional processes involved to overcome geometric influences. The identity of these processes is the subject of active debates, with many hypotheses being proposed. Lastly, I present the current state of the field and the ongoing effort to overcome the associated modelling challenges.
