Significance Organisms use the central carbon metabolism for both breakdown of substrate into biomass precursors and extraction of energy, making the pathways overlapping. We present a modeling concept that can decompose the overlapping pathways and hence account for protein cost for each of them. This enables comparisons between pathways within an organism or between organisms. Using this concept, we model energy metabolism for Escherichia coli and Saccharomyces cerevisiae, and accurately predict metabolic switches. Besides, we find that the total mass of the proteins involved in energy metabolism is conserved across conditions, which is simulated to correlate with ATP production rate in cells growing at unlimited conditions.

Abstract Cells require energy for growth and maintenance and have evolved to have multiple pathways to produce energy in response to varying conditions. A basic question in this context is how cells organize energy metabolism, which is, however, challenging to elucidate due to its complexity, i.e., the energy-producing pathways overlap with each other and even intertwine with biomass formation pathways. Here, we propose a modeling concept that decomposes energy metabolism into biomass formation and ATP-producing pathways. The latter can be further decomposed into a high-yield and a low-yield pathway. This enables independent estimation of protein efficiency for each pathway. With this concept, we modeled energy metabolism for Escherichia coli and Saccharomyces cerevisiae and found that the high-yield pathway shows lower protein efficiency than the low-yield pathway. Taken together with a fixed protein constraint, we predict overflow metabolism in E. coli and the Crabtree effect in S. cerevisiae, meaning that energy metabolism is sufficient to explain the metabolic switches. The static protein constraint is supported by the findings that protein mass of energy metabolism is conserved across conditions based on absolute proteomics data. This also suggests that enzymes may have decreased saturation or activity at low glucose uptake rates. Finally, our analyses point out three ways to improve growth, i.e., increasing protein allocation to energy metabolism, decreasing ATP demand, or increasing activity for key enzymes.

ATP is the energy currency in living cells and the key to drive energy-consuming processes such as growth, motility, and stress-related functions. The energy utilized for growth, e.g., macromolecular synthesis and growth-associated maintenance, can be defined as growth-associated energy costs (GAEC), while the energetic cost of other processes is referred to as non–growth-associated maintenance (NGAM). Accordingly, at steady state the total energy generated in cells should be allocated between GAEC and NGAM. Cells seem to have an upper bound of ATP production capacity as higher level of stress usually results in slower growth (1, 2), indicating a competition between GAEC and NGAM for the limited energy that can be provided by metabolism. Therefore, an interesting question is how to increase the maximal ATP production capacity. This is expected to improve fitness of cells, and thereby important in industrial processes and biotechnological applications.

ATP is mostly produced by a few pathways in the central carbon metabolism (CCM), which, in heterotrophs, e.g., Escherichia coli and Saccharomyces cerevisiae, includes glycolysis, by-product formation pathways, the tricarboxylic acid (TCA) cycle, and oxidative phosphorylation. These pathways together are defined as energy metabolism in this study, which is typically divided into 2 different strategies. One is glycolysis followed by the TCA cycle and oxidative phosphorylation, namely respiration, and the other is glycolysis followed by by-product formation pathways, namely fermentation. Moreover, the CCM acts as not only energy producer to extract ATP from substrate but also biomass producer to break down the substrate into biomass precursors, meaning that ATP-producing and biomass formation pathways are heavily overlapping and intertwined within the CCM. Another 2 questions accordingly arise, why cells select a particular ATP-producing mode for a given condition and how cells allocate resource between energy generation and biomass formation?

It has been proposed that there is a tradeoff between yield and rate of ATP production by the different metabolic modes (3). For example, cells prefer to use respiration when a high ATP yield is favorable, while they activate fermentation when a high rate is favorable. This hypothesis is, however, not sufficient to explain the concurrent use of both respiration and fermentation observed in glucose-limited chemostats (4⇓⇓⇓⇓⇓–10). This may be explained by another tradeoff, which is between ATP yield and protein required for carrying the fluxes (11). The hypothesis that a higher yield pathway requires more protein than a lower yield pathway for the same glucose uptake rate has been predicted by computational analysis based on thermodynamics (12) or enzyme kinetics data (13), and experimentally confirmed by proteomics measurement (14). Furthermore, genome-scale metabolic models (GEMs) with the integration of protein constraints have shown improved predictions of metabolic switches (15⇓⇓–18).

Here, inspired by these efforts, we propose a modeling concept to investigate energy metabolism for E. coli and S. cerevisiae, the best-studied prokaryal and eukaryal microorganisms, respectively. We firstly decomposed energy metabolism into biomass formation and ATP-producing pathways, allowing for independent estimation of ATP yield and protein efficiency for each pathway. With the models we accurately predicted metabolic switches observed in experiments by fixing the protein constraint, which is in good agreement with the finding that protein allocation to energy metabolism is conserved. On the other hand, model simulations showed that increasing protein mass of energy metabolism or fraction of flux through low-yield ATP-producing pathway can improve ATP production rate. The former seems to be common in reality as we found in cells growing at unlimited conditions a strong correlation between protein mass of energy metabolism and the ATP production rate. Besides, we found that improved growth rate of evolved strains is caused by increased protein allocation and/or decreased ATP demand. Finally, we predicted that increasing the activity of some key enzymes in energy metabolism is an effective strategy for improving the specific growth rate.

Materials and Methods All of the materials and methods are detailed in SI Appendix: modeling energy metabolism for E. coli and S. cerevisiae; protein cost analysis; model simulations; adjustment of protein efficiency; proteomics data analysis; calculating apparent saturation. All of the simulations were performed in MATLAB with the COBRA toolbox (51). Codes and models are available at https://github.com/SysBioChalmers/Energy_metabolism_model.

Acknowledgments We acknowledge funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement 686070. We also acknowledge funding from the Novo Nordisk Foundation (Grant NNF10CC1016517) and the Knut and Alice Wallenberg Foundation.

Footnotes Author contributions: Y.C. and J.N. designed research; Y.C. performed research; Y.C. contributed new reagents/analytic tools; Y.C. and J.N. analyzed data; and Y.C. and J.N. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1906569116/-/DCSupplemental.