UBC Math Department Colloquium: Tim Tian

Pattern formation is a fundamental element of many processes in developmental biology. One example is the self-organization of microtubules (MTs) along the inner surface (cortex) of the plant cell membrane. MTs are dynamic polymers found within many cell types, serving roles in vital cellular processes. Within plants, the organization of MTs into ordered arrays is necessary for directional cell growth. The key questions are: what gives rise to the ordering and orientation of MT arrays? Mathematical and computational modelling has proven successful in providing insights: the process is distilled into a system of colliding curves on a 2D surface, with each curve stochastically switching between growth and shrinkage. We revisit a common assumption in these models: that MT shapes are described by geodesics. More realistically, MTs are relatively rigid filaments and should seek to minimizing bending, generally differing in shape from geodesics. We model MTs as elastic curves to show that curvature influences MTs to orient in directions opposite to what is biologically favourable, and that there must be additional processes involved to overcome such influence. The identity of such processes is the subject of active debates. Lastly, I will present the ongoing international effort to understand this system and overcome the associated modelling challenges. Familiarity with the concept of plants is helpful, but not necessary.