Integration of bifurcation analysis and optimal control of a molecular network

Molecular biological networks are highly nonlinear systems that exhibit limit point singularities. Bifurcation analysis and multiobjective nonlinear model predictive control (MNLMPC) of a molecular network problem represented by the Pettigrew model were performed. The Matlab program MATCONT (Matlab continuation) was used for the bifurcation analysis and the optimization language PYOMO (python optimization modeling objects) was used for performing the multiobjective nonlinear model predictive control. MATCONT identified the limit points, branch points, and Hopf bifurcation points using appropriate test functions. The multiobjective nonlinear model predictive control was performed by first performing single objective optimal control calculations and then minimizing the distance from the Utopia point, which was the coordinate of minimized values of each objective function. The presence of limit points (albeit in an infeasible region) enabled the MNLMPC calculations to result in the Utopia solution. MNLMPC of the partial models also resulted in Utopia solutions.