Bibhash Mukhopadhyay and Liyun Zeng
Establishment and maintenance of cell polarity is a fundamental question in cell biology with the prime molecular protagonists, the Par proteins, being conserved across the evolutionary spectrum. The overall goal of the project is to create a mathematically rigorous yet biologically realistic model of Par protein function in generating asymmetric within cells Towards this, two-fold attempt is made at: (a) analysis of temporal dynamics of Par-3, Par-6 and aPKC during the maintenance phase of polarity development; (b) an elementary analysis of spatial dynamics of Par proteins that segregate in a domain specific manner during establishment phase of polarity development. Spatial and temporal bistability is observed in the system and an simulation approximation for cortical flow during establishment is created. It is hoped that with a complete analysis, emergent behavior, unknown so far, can be studied, thus providing experimentally testable hypotheses for model validation.
Network diagram of the Par proteins of interest, their interactions, and relevant rate constants. |
Nullspace (left) and phase portrait (right) of a reduced system of the network. Intersections of the planes in the nullspace indicate the steady states (values of the variables that remain the same over time), and the phase portrait demonstrates the existence of two stable steady states, since all trajectories (the lines in the phase space that correspond to a specific initial condition) converge on one of two possible steady states. |
