Using optimal control to understand complex metabolic pathways

Abstract

Background: We revisit the idea of explaining and predicting dynamics in biochemical pathways from first-principles. A promising approach is to exploit optimality principles that can be justified from an evolutionary perspective. In the context of the cell, several previous studies have explained the dynamics of simple metabolic pathways exploiting optimality principles in combination with dynamic models, i.e. using an optimal control framework. For example, dynamics of gene expression in small metabolic models can be explained assuming that cells have developed optimal adaptation strategies. Most of these works have considered rather simplified representations, such as small linear pathways, or reduced networks with a single branching point.Results: Here we consider the extension of this approach to more realistic scenarios, i.e. biochemical pathways of arbitrary size and structure. We first show that exploiting optimality principles for these networks poses great challenges due to the complexity of the associated optimal control problems. Second, in order to surmount such challenges, we present a computational framework based on multicriteria optimal control which has been designed with scalability and efficiency in mind, extending several recent methods. This framework includes mechanisms to avoid common pitfalls, such as local optima, unstable solutions or excessive computation time. We illustrate its performance with several case studies considering the central carbon metabolism of S. cerevisiae and B. subtilis. In particular, we consider metabolic dynamics during nutrient shift experiments. Conclusions:We show how multi-objective optimal control can be used to predict temporal profiles of enzyme activation and metabolite concentrations in complex metabolic pathways. Further, we show how the multicriteria approach allows us to consider general cost/benefit trade-offs that have been likely favored by evolution. In this study we have considered metabolic pathways, but this computational framework can also be applied to analyze the dynamics of other complex pathways, such as signal transduction networks.