Enzyme allocation problems in kinetic metabolic networks: Optimal solutions are elementary flux modes

TL;DR

This paper proves that optimal solutions in enzyme allocation problems within kinetic metabolic networks are elementary flux modes, advancing understanding of metabolic efficiency and resource allocation.

Contribution

It provides a rigorous proof that optimal solutions are elementary flux modes in kinetic metabolic networks, a novel theoretical insight.

Findings

Optimal solutions are elementary flux modes.

The result applies to general kinetics.

Implications for metabolic switch identification.

Abstract

The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.