Hierarchical Control of Biological Self-Organization

Classic mechanisms of spatial pattern formation in developmental biology are characterized by high degrees of multistability and sensitivity to initial conditions. These traits are commonly seen as undermining the capacity of these processes to exhibit robust morphogenesis. However, a growing body of experimental evidence suggests developing organisms can accomplish robust pattern selection in reaction-diffusion processes with relatively simple spatiotemporal forcings. To better understand this phenomenon, we perform a series of systematic investigations into the optimal controllability of a minimal pattern-forming system. Using machine-learning-inspired techniques, we generate simple optimal control protocols to drive an underactuated system to a desired steady state. We numerically demonstrate the effectiveness of control in two universal scenarios of pattern formation: within a weakly nonlinear regime associated with a supercritical Turing instability and for localized states associated with homoclinic snaking.