### Multi-Criteria Optimization of Regulation in Metabolic Networks

Abstract

Determining the regulation of metabolic networks at genome scale is a hard task. It has been hypothesized that biochemical pathways and metabolic networks might have undergone an evolutionary process of optimization with respect to several criteria over time. In this contribution, a multi-criteria approach has been used to optimize parameters for the allosteric regulation of enzymes in a model of a metabolic substrate-cycle. This has been carried out by calculating the Pareto set of optimal solutions according to two objectives: the proper direction of flux in a metabolic cycle and the energetic cost of applying the set of parameters. Different Pareto fronts have been calculated for eight different "environments'' (specific time courses of end product concentrations). For each resulting front the so-called knee point is identified, which can be considered a preferred trade-off solution. Interestingly, the optimal control parameters corresponding to each of these points also lead to optimal behaviour in all the other environments. By calculating the average of the different parameter sets for the knee solutions more frequently found, a final and optimal consensus set of parameters can be obtained, which is an indication on the existence of a universal regulation mechanism for this system. The implications from such a universal regulatory switch are discussed in the framework of large metabolic networks.