Formalizing the law of diminishing returns in metabolic networks using an electrical analogy

Abstract

The way biological systems respond to changes in parameter values caused by mutations is a key issue in evolution and quantitative genetics, as it affects fundamental aspects such as adaptation, selective neutrality, robustness, optimality, evolutionary equilibria, etc. We address this question using the enzyme–flux relationship in a metabolic network as a model of the genotype–phenotype relationship. The lack of a suitable mathematical tool from biochemical theory to investigate this relationship led us to use an analogy between electrical circuits and metabolic networks with uni–uni reactions. We show that a behaviour of diminishing returns, which is commonly observed at various phenotypic levels, is inevitable, irrespective of the complexity of the system. We also present a possible generalization to metabolic networks with both uni–uni and bi–bi reactions.

Keywords

• diminishing returns
• metabolic flux
• electrical circuit
• robustness