Mathematical Biology seminar Tim Tian University of Utah "Modeling Plant Cortical Microtubules: Elastic Curves on Smooth Surfaces" Monday, September 14, 2026 12-1pm in ST E1105 The self-organization of microtubules (MTs) along the inner surface (cortex) of the plant cell membrane is an essential element in the development of plant cells. MTs are dynamic polymers found within many cell types, serving roles in vital cellular processes. Within plants, the organization of MTs into ordered patterns is necessary for directional cell growth. The key questions are: what gives rise to the ordering and orientation of MT patterns? Mathematical and computational modeling has proven successful in providing insights: the process is distilled into a system of interacting curves on a 2D surface. There has been recent 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. Our model of MTs as elastic curves on cylindrical cells has shown that the curvature influence on MTs should orient in directions opposite to what is biologically favourable. Building on this, 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. This work 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 modeling challenges.