Speaker
Description
A classic model of a cell fate transition, following on Waddington, treats distinct cell phenotypes as attractors emerging from the nonlinear dynamics of biochemical signaling pathways. Transitions between phenotypes are achieved by external modulation of the system, which produces bifurcations among the stable states and otherwise drives the system from one attractor to another. This talk presents efforts to apply optimal control theory to derive new, universal results on the response of such systems to upstream morphogen signals. We pose an optimal control problem in which a system near a pitchfork bifurcation is driven to a target state with minimal effort. Optimality conditions are derived using the Pontryagin Maximum Principle and then studied asymptotically. Across different scaling regimes, we assess the applicability of the standard center-manifold reductions to this class of systems, and, under certain soft constraints on control effort, we construct analytical optimal feedback laws that match the lowest-order behavior. These results are validated numerically for both single-cell and spatially extended models.
