Evolutionary optimization of metabolic pathways. Theoretical reconstruction of the stoichiometry of ATP and NADH producing systems

Oliver Ebenhöh, Reinhart Heinrich

The structural design of ATP and NADH producing systems, such as glycolysis and the citric acid cycle (TCA), is analysed using optimization principles. It is assumed that these pathways combined with oxidative phosphorylation have reached, during their evolution, a high efficiency with respect to ATP production rates. On the basis of kinetic and thermodynamic principles, conclusions are derived concerning the optimal stoichiometry of such pathways. Extending previous investigations, both the concentrations of adenine nucleotides as well as nicotinamide adenine dinucleotides are considered variable quantities. This implies the consideration of the interaction of an ATP and NADH producing system, an ATP consuming system, a system coupling NADH consumption with ATP production and a system consuming NADH decoupled from ATP production. It is examined in what respect real metabolic pathways can be considered optimal by studying a large number of alternative pathways. The kinetics of the individual reactions are described by linear or bilinear functions of reactant concentrations. In this manner, the steady-state ATP production rate can be calculated for any possible ATP and NADH producing pathway. It is shown that most of the possible pathways result in a very low ATP production rate and that the very efficient pathways share common structural properties. Optimization with respect to the ATP production rate is performed by an evolutionary algorithm. The following results of our analysis are in close correspondence to the real design of glycolysis and the TCA cycle. (1) In all efficient pathways the ATP consuming reactions are located near the beginning. (2) In all efficient pathways NADH producing reactions as well as ATP producing reactions are located near the end. (3) The number of NADH molecules produced by the consumption of one energy-rich molecule (glucose) amounts to four in all efficient pathways. A distance measure and a measure for the internal ordering of reactions are introduced to study differences and similarities in the stoichiometries of metabolic pathways.