The number of active metabolic pathways is bounded by the number of cellular constraints at maximal metabolic rates

PLoS Comput Biol. 2019 Mar 11;15(3):e1006858. doi: 10.1371/journal.pcbi.1006858. eCollection 2019 Mar.


Growth rate is a near-universal selective pressure across microbial species. High growth rates require hundreds of metabolic enzymes, each with different nonlinear kinetics, to be precisely tuned within the bounds set by physicochemical constraints. Yet, the metabolic behaviour of many species is characterized by simple relations between growth rate, enzyme expression levels and metabolic rates. We asked if this simplicity could be the outcome of optimisation by evolution. Indeed, when the growth rate is maximized-in a static environment under mass-conservation and enzyme expression constraints-we prove mathematically that the resulting optimal metabolic flux distribution is described by a limited number of subnetworks, known as Elementary Flux Modes (EFMs). We show that, because EFMs are the minimal subnetworks leading to growth, a small active number automatically leads to the simple relations that are measured. We find that the maximal number of flux-carrying EFMs is determined only by the number of imposed constraints on enzyme expression, not by the size, kinetics or topology of the network. This minimal-EFM extremum principle is illustrated in a graphical framework, which explains qualitative changes in microbial behaviours, such as overflow metabolism and co-consumption, and provides a method for identification of the enzyme expression constraints that limit growth under the prevalent conditions. The extremum principle applies to all microorganisms that are selected for maximal growth rates under protein concentration constraints, for example the solvent capacities of cytosol, membrane or periplasmic space.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Algorithms
  • Catalysis
  • Enzymes / metabolism
  • Kinetics
  • Metabolic Flux Analysis*
  • Metabolic Networks and Pathways*
  • Proteins / metabolism


  • Enzymes
  • Proteins

Grant support

DHdG and BT were supported by NWO VICI grant 865.14.005 (, and by Era-Industrial Biotechnology project nr. 053.80.772 ( CvB was supported by NWO STAR grant 022.005.031 ( The funders played no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.