Understanding optimality principles shaping the evolution of regulatory networks controlling metabolism is crucial for deriving a holistic picture of how metabolism is integrated into key cellular processes such as growth, adaptation and pathogenicity. While in the past the focus of research in pathway regulation was mainly based on stationary states, more recently dynamic optimization has proved to be an ideal tool to decipher regulatory strategies for metabolic pathways in response to environmental cues. In this short review, we summarize recent advances in the elucidation of optimal regulatory strategies and identification of optimal control points in metabolic pathways. We discuss biological implications of the discovered optimality principles on genome organization and provide examples how the derived knowledge can be used to identify new treatment strategies against pathogens. Furthermore, we briefly discuss the variety of approaches for solving dynamic optimization problems and emphasize whole-cell resource allocation models as an important emerging area of research that will allow us to study the regulation of metabolism on the whole-cell level.

For producing ATP, tumour cells rely on glycolysis leading to lactate to about the same extent as on respiration. Thus, the ATP synthesis flux from glycolysis is considerably higher than in the corresponding healthy cells. This is known as the Warburg effect (named after German biochemist Otto H. Warburg) and also applies to striated muscle cells, activated lymphocytes, microglia, endothelial cells and several other cell types. For similar phenomena in several yeasts and many bacteria, the terms Crabtree effect and overflow metabolism respectively, are used. The Warburg effect is paradoxical at first sight because the molar ATP yield of glycolysis is much lower than that of respiration. Although a straightforward explanation is that glycolysis allows a higher ATP production rate, the question arises why cells do not re-allocate protein to the high-yield pathway of respiration. Mathematical modelling can help explain this phenomenon. Here, we review several models at various scales proposed in the literature for explaining the Warburg effect. These models support the hypothesis that glycolysis allows for a higher proliferation rate due to increased ATP production and precursor supply rates.

Elementary-modes analysis has become a well-established theoretical tool in metabolic pathway analysis. It allows one to decompose complex metabolic networks into the smallest functional entities, which can be interpreted as biochemical pathways. This analysis has, in medium-size metabolic networks, led to the successful theoretical prediction of hitherto unknown pathways. For illustration, we discuss the example of the phosphoenolpyruvate-glyoxylate cycle in Escherichia coli . Elementary-modes analysis meets with the problem of combinatorial explosion in the number of pathways with increasing system size, which has hampered scaling it up to genome-wide models. We present a novel approach to overcoming this obstacle. That approach is based on elementary flux patterns, which are defined as sets of reactions representing the basic routes through a particular subsystem that are compatible with admissible fluxes in a (possibly) much larger metabolic network. The subsystem can be made up by reactions in which we are interested in, for example, reactions producing a certain metabolite. This allows one to predict novel metabolic pathways in genome-scale networks.