Mixed-integer minimax dynamic optimization for structure identification of glycerol metabolic network

Abstract

Cell metabolism is a dynamic regulation process, in which its network structure and/or regulatory mechanisms can change constantly over time due to internal and external perturbations. This paper models glycerol metabolism in continuous fermentation as a nonlinear mixed-integer dynamic system by defining the time-varying metabolic network structure as an integer-valued function. To identify the dynamic network structure and kinetic parameters, we establish a mixed-integer minimax dynamic optimization problem with concentration robustness as its objective functional. By direct multiple shooting strategy and a decomposition approach consisting of convexification, relaxation and rounding strategy, the optimization problem is transformed into a large-scale approximate multistage parameter optimization problem. It is then solved using a competitive particle swarm optimization algorithm. We also show that the relaxation problem yields the best lower bound for the optimization problem, and its solution can be arbitrarily approximated by the solution obtained from rounding strategy. Numerical results indicate that the proposed mixed-integer dynamic system can better describe cellular self-regulation and response to intermediate metabolite inhibitions in continuous fermentation of glycerol. These numerical results show that the proposed numerical methods are effective in solving the large-scale mixed-integer dynamic optimization problems.