Overflow metabolism originates from growth optimization and cell heterogeneity

Reviewer #1 (Public Review):

Summary:
Cell metabolism exhibits a well-known behavior in fast-growing cells, which employ seemingly wasteful fermentation to generate energy even in the presence of sufficient environmental oxygen. This phenomenon is known as Overflow Metabolism or the Warburg effect in cancer. It is present in a wide range of organisms, from bacteria and fungi to mammalian cells.

In this work, starting with a metabolic network for Escherichia coli based on sets of carbon sources, and using a corresponding coarse-grained model, the author applies some well-based approximations from the literature and algebraic manipulations. These are used to successfully explain the origins of Overflow Metabolism, both qualitatively and quantitatively, by comparing the results with E. coli experimental data.

By modeling the proteome energy efficiencies for respiration and fermentation, the study shows that these parameters are dependent on the carbon source quality constants K_i (p.115 and 116). It is demonstrated that as the environment becomes richer, the optimal solution for proteome energy efficiency shifts from respiration to fermentation. This shift occurs at a critical parameter value K_A(C).

This counterintuitive result qualitatively explains Overflow Metabolism.

Quantitative agreement is achieved through the analysis of the heterogeneity of the metabolic status within a cell population. By introducing heterogeneity, the critical growth rate is assumed to follow a Gaussian distribution over the cell population, resulting in accordance with experimental data for E. coli. Overflow metabolism is explained by considering optimal protein allocation and cell heterogeneity.

The obtained model is extensively tested through perturbations: 1) Introduction of overexpression of useless proteins; 2) Studying energy dissipation; 3) Analysis of the impact of translation inhibition with different sub-lethal doses of chloramphenicol on Escherichia coli; 4) Alteration of nutrient categories of carbon sources using pyruvate. All model perturbation results are corroborated by E. coli experimental results.

Strengths:
In this work, the author employs modeling methods typical of Physics to address a problem in Biology, standing at the interface between these two scientific fields. This interdisciplinary approach proves to be highly fruitful and should be further explored in the literature. The use of Escherichia coli as an example ensures that all hypotheses and approximations in this study are well-founded in the literature. Examples include the approximation for the Michaelis-Menten equation (line 82), Eq. S1, proteome partition in Appendix 1.1 (lines 68-69), and a stable nutrient environment in Appendix 1.1 (lines 83-84). The section "Testing the model through perturbation" heavily relies on bacterial data. The construction of the model and its agreement with experimental data are convincingly presented.

Weaknesses:
In Section Appendix 6.4, the author explores the generalization of results from bacteria to cancer cells, adapting the metabolic network and coarse-grained model accordingly. It is argued that as a consequence, all subsequent steps become immediately valid. However, I remain unconvinced, considering the numerous approximations used to derive the equations, which the literature demonstrates to be valid primarily for bacteria. A more detailed discussion about this generalization is recommended. Additionally, it is crucial to note that the experimental validation of model perturbations heavily relies on E. coli data.

Reviewer #2 (Public Review):

Summary
This paper has three parts. The first part applied a coarse-grained model with proteome partition to calculate cell growth under respiration and fermentation modes. The second part considered single-cell variability and performed population average to acquire an ensemble metabolic profile for acetate fermentation. The third part used model and simulation to compare experimental data in literature and obtained substantial consistency.

Strengths and major contributions
(i) The coarse-grained model considered specific metabolite groups and their inter-relations and acquired an analytical solution for this scenario. The "resolution" of this model is in between the Flux Balanced Analysis/whole-cell simulation and proteome partition analysis.

(ii) The author considered single-cell level metabolic heterogeneity and calculated the ensemble average with explicit calculation. The results are consistent with known fermentation and growth phenomena qualitatively and can be quantitatively compared to experimental results.

Weaknesses
(i) If I am reading this paper correctly, the author's model predicts binary (or "digital") outcomes of single-cell metabolism, that is, after growth rate optimization, each cell will adopt either "respiration mode" or "fermentation mode" (as illustrated in Figure Appendix - Figure 1 C, D). Due to variability enzyme activity k_i^{cat} and critical growth rate λ_C, each cell under the same nutrient condition could have either respiration or fermentation, but the choice is binary.

The binary choice at the single-cell level is inconsistent with our current understanding of metabolism. If a cell only uses fermentation mode (as shown in Appendix - Figure 1C), it could generate enough energy but not be able to have enough metabolic fluxes to feed into the TCA cycle. That is, under pure fermentation mode, the cell cannot expand the pool of TCA cycle metabolites and hence cannot grow.

This caveat also appears in the model in Appendix (S25) that assumes J_E = r_E*J_{BM} where r_E is a constant. From my understanding, r_E can be different between respiration and fermentation modes (at least for real cells) and hence it is inappropriate to conclude that cells using fermentation, which generates enough energy, can also generate a balanced biomass.

(ii) The minor weakness of this model is that it assumes a priori that each cell chooses its metabolic strategy based on energy efficiency. This is an interesting assumption but there is no known biochemical pathway that directly executes this mechanism. In evolution, growth rate is more frequently considered for metabolic optimization. In Flux Balanced Analysis, one could have multiple objective functions including biomass synthesis, energy generation, entropy production, etc. Therefore, the author would need to justify this assumption and propose a reasonable biochemical mechanism for cells to sense and regulate their energy efficiency.

My feeling is that the mathematical structure of this model could be correct, but the single-cell interpretation for the ensemble averaging has issues. Each cell could potentially adopt partial respiration and partial fermentation at the same time and have temporal variability in its metabolic mode as well. With the modification of the optimization scheme, the author could have a revised model that avoids the caveat mentioned above.

Discussion and impact for the field
Proteome partition models and Flux Balanced Analysis are both commonly used mathematical models that emphasize different parts of cellular physiology. This paper has ingredients for both, and I expect after revision it will bridge our understanding of the whole cell.

Reviewer #3 (Public Review):

Summary:
In the manuscript "Overflow metabolism originates from growth optimization and cell heterogeneity" the author Xin Wang investigates the hypothesis that the transition into overflow metabolism at large growth rates actually results from an inhomogeneous cell population, in which every individual cell either performs respiration or fermentation.

Weaknesses:
The paper has several major flaws. First, and most importantly, it repeatedly and wrongly claims that the origins of overflow metabolism are not known. The paper is written as if it is the first to study overflow metabolism and provide a sound explanation for the experimental observations. This is obviously not true and the author actually cites many papers in which explanations of overflow metabolism are suggested (see e.g. Basan et al. 2015, which even has the title "Overflow metabolism in E. coli results from efficient proteome allocation"). The paper should be rewritten in a more modest and scientific style, not attempting to make claims of novelty that are not supported. In fact, all hypotheses in this paper are old. Also the possiblility that cell heterogeneity explains the observed 'smooth' transition into overflow metabolism has been extensively investigated previously (see de Groot et al. 2023, PNAS, "Effective bet-hedging through growth rate dependent stability") and the random drawing of kcat-values is an established technique (Beg et al., 2007, PNAS, "Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity"). Thus, in terms of novelty, this paper is very limited. It reinvents the wheel and it is written as if decades of literature debating overflow metabolism did not exist.

Moreover, the manuscript is not clearly written and is hard to understand. Variables are not properly introduced (the M-pools need to be discussed, fluxes (J_E), "energy coefficients" (eta_E), etc. need to be more explicitly explained. What is "flux balance at each intermediate node"? How is the "proteome efficiency" of a pathway defined? The paper continues to speak of energy production. This should be avoided. Energy is conserved (1st law of thermodynamics) and can never be produced. A scientific paper should strive for scientific correctness, including precise choice of words.

The statement that the "energy production rate ... is proportional to the growth rate" is, apart from being incorrect - it should be 'ATP consumption rate' or similar (see above), a non-trivial claim. Why should this be the case? Such statements must be supported by references. The observation that the catabolic power indeed appears to increase linearly with growth rate was made, based on chemostat data for E.coli and yeast, in a recent preprint (Ebenhöh et al, 2023, bioRxiv, "Microbial pathway thermodynamics: structural models unveil anabolic and catabolic processes").

All this criticism does not preclude the possibility that cell heterogeneity plays a role in overflow metabolism. However, according to Occam's razor, first the simpler explanations should be explored and refuted before coming up with a more complex solution. Here, it means that the authors first should argue why simpler explanations (e.g. the 'Membrane Real Estate Hypothesis', Szenk et al., 2017, Cell Systems; maximal Gibbs free energy dissipation, Niebel et al., 2019, Nature Metabolism; Saadat et al., 2020, Entropy) are not considered, resp. in what way they are in disagreement with observations, and then provide some evidence of the proposed cell heterogeneity (are there single-cell transcriptomic data supporting the claim?).