Dynamic optimization in B. subtilis's central carbon metabolism under nutrient shift conditions using adaptive control vector parameterization

Abstract:
Since biological organisms are an outcome of mutation and selection processes, one can expect that their functions have been optimized during evolution. Hence, the idea of this study is that biological adjustments can be rationalized by using optimization approaches. We apply dynamic optimization to predict enzyme profiles in a simplified model of central carbon metabolism in B. subtilis. The enzyme profiles were observed in nutrient shift experiments, in which cell cultures were grown on either glucose or on malate and subsequently subjected to the addition of the other substrate. Metabolite concentrations and protein abundances were measured. The model is based on the assumption that the enzyme regulation is controlled such that they maximize the chosen objective function. Thus, the simulated enzyme profiles have no mechanistic foundation, but may rationalize certain regulation mechanisms that govern the expression of proteins.

The optimization is solved by adaptive control vector parameterization, which is implemented in the software tool DyOS. The goal of this study was to test if DyOS is well suited for optimization problems in systems biology. The problems treated in this work are nonlinear multistage dynamic optimization problems.

The results predict different utilisation strategies for different nutrients. The calculated enzyme profiles are in partial agreement with the experimental data and can predict some of the experimental findings. The study shows that dynamic optimization is a useful tool to rationalize enzyme profiles. Even if dynamic optimization cannot reveal underlying mechanisms, it can help rationalize biological observations. Furthermore, DyOS has proved to be a suitable and efficent tool to solve multistage dynamic optimization problems in systems biology.

Keywords:
Optimal control; DyOS; B. subtilis