Reaction-diffusion model is one of the attractive models used to study pattern formation in different biological systems, from individual cell components to developing tissues. In this talk, I will introduce several reaction-diffusion models arising from the studies of cell polarization and tissue pattern formation.
In the first part, I will present a two-equation reaction-diffusion model for studying cell polarization, which is central to carry out processes such as differentiation, migration and development. I will perform linear stability analysis, in particular Turing stability analysis to the model to derive conditions of parameters for which cell polarity emerges without any spatial cue. I will apply live cell imaging and mathematical modeling to understand how diploid daughter cells in budding yeasts establish polarity preferentially at the pole distal to the previous division site.
In the second part, I will introduce several morphogen-mediated patterning models to study how tissue pattern formation is robust to the environmental noises and perturbations. Morphogens are important signaling molecules governing the pattern formation of multicellular organisms during embryo development. In this talk, I will discuss how two mechanisms, the expansion-repression mechanism and presence of non-signaling receptors, play a role for overcoming the effect of the fluctuations in morphogen and receptor production rates.