Robust and efficient numerical methods for the optimal control of spatially distributed biological systems

In silico experimentation has opened new ways to analyze biological systems behavior under different conditions. The incorporation of an outer optimization loop may help to find the right operation conditions to achieve specific goals (maximization of a given product concentration, minimization of process energy/time, etc.). Mathematically, this is stated as a dynamic optimization problem being particularly challenging when the system is described by nonlinear sets of partial differential equations as well as when constraints are considered. These issues impose a number of difficulties, such as the presence of suboptimal solutions, which call for robust and efficient numerical techniques. In this work, the control vector parametrization approach is combined with reduced order methods and suitable hybrid global optimization methods to overcome such difficulties. The capabilities of this strategy are illustrated considering the solution of two challenging problems: bacterial chemotaxis and the FitzHugh-Nagumo model. The presented methodology can be used for the efficient dynamic optimization of generic distributed biological systems.