Centrum Wiskunde & Informatica, Life Sciences, Science Park 123, 1098 XG Amsterdam, The Netherlands

Netherlands Institute for Systems Biology, Science Park 123, 1098 XG Amsterdam, The Netherlands

Netherlands Consortium for Systems Biology, Amsterdam, The Netherlands

Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Abstract

Background

Low-yield metabolism is a puzzling phenomenon in many unicellular and multicellular organisms. In abundance of glucose, many cells use a highly wasteful fermentation pathway despite the availability of a high-yield pathway, producing many ATP molecules per glucose,

Results

Using flux balance analysis with molecular crowding (FBAwMC), a recent extension to flux balance analysis (FBA) that assumes that the total flux through the metabolic network is limited, we investigate the differences between

Conclusions

Maintaining redox balance is key to explaining why some microbes decrease the flux through the high-yield pathway, while other microbes use "overflow-like" low-yield metabolism.

Background

One of the key steps in energy metabolism is to transfer the energy carried by sugars, including glucose, to the biological "energy currency" adenosine triphosphate (ATP). The number of ATP molecules generated by metabolizing one molecule of glucose—the ATP yield—is one of the most basic measures of an organism's energy efficiency. One would perhaps expect that evolution has selected organisms for the ability to extract energy from their food at optimal efficiency by maximizing ATP yield. Yet surprisingly, many organisms switch between a high-yield pathway, _{2 }in aerobic, glucose-limited conditions. But in abundance of glucose, glucose is converted into ethanol

Microbial species show remarkable differences in their metabolic switching strategies. At low glucose concentrations and low growth rates, _{2 }and water. At higher glucose concentrations and fast growth rates, it redirects part of the glucose influx into a low-yield fermentation pathway, keeping oxidative phosphorylation fully active

A plausible explanation for metabolic switching is "overflow metabolism". It assumes that organisms only switch to low-yield metabolism if the high-yield pathway is operating at maximum rate and cannot process any more molecules

Recent studies have suggested that the limited amount of metabolic enzymes fitting inside the cell may be key to low-yield metabolism

If cells need to trade off fast metabolism and high-yield metabolism, then why do we still observe overflow metabolism, as in

Simplified reaction scheme for the 3 organisms studied

**Simplified reaction scheme for the 3 organisms studied**. A.

To predict the metabolic switches these three organisms can perform, we make use of a variant of Flux Balance Analysis (FBA), a method that calculates fluxes through metabolic networks given constraints on the network and given an objective function to maximize. By maximizing growth rate, FBA often correctly predicts cellular metabolism, including uptake, excretion and growth rates of cells

For this reason, we use an extension of FBA, Flux Balance Analysis with Molecular Crowding (FBAwMC) _{cat}

with _{i }
_{prot }
_{i }
_{i }
_{i }

Because crowding coefficients for most metabolic enzymes are unknown, previous studies proposed a range of strategies to estimate them. Beg

Although the study of an estimated, specific set of crowding coefficients or an average can provide some insight, in reality metabolic networks may operate under an entirely different set of crowding coefficients. Therefore, in the absence of accurate, experimental estimates of crowding coefficients, FBAwMC cannot decide on one real situation. Studying growth yield predictions for large samples of biochemically-plausible sets of crowding coefficients can give more robust insights into the metabolic network than studies with single crowding coefficient estimates, because it reveals what growth yields are most plausible and what are the alternative behaviors of the network.

Our analysis suggests that mechanisms to maintain NAD^{+}/NADH ratio are key to the metabolic differences between the two types of metabolic switches. Organisms in which both the high-yield and low-yield pathways reduce NADH may downregulate high-yield metabolism at high growth rates. If organisms have an additional energy-yielding pathway that does not consume NADH (

Results

Predicted yield distributions reflect metabolic switching strategy

Using genome-scale stoichiometric networks of _{i }
_{i}

FBAwMC growth simulations, compared with experimental data (discs)

**FBAwMC growth simulations, compared with experimental data (discs)**. The best fitting simulation is indicated with a solid line, the mean and standard deviations with dashed lines. Experimental data are indicated with black dots. We scaled the growth rate of the simulations and the experimental observations to the maximal growth rate. Mean and standard deviations are calculated from all simulations that switch to low-yield metabolism at high growth rates (yield < 0.3 gr dry weight/gr glucose). A.

Figure

Distribution of growth yields predicted by the model with 1000 randomly selected sets of crowding coefficients

**Distribution of growth yields predicted by the model with 1000 randomly selected sets of crowding coefficients**. A.

The distribution of growth yields only gives information of the metabolic behavior at maximal growth rates. Next we tested if individual simulations show overflow-like metabolism or not. Figure

Flux decrease through the high-yield pathway, relative to the maximum flux through the high-yield pathway

**Flux decrease through the high-yield pathway, relative to the maximum flux through the high-yield pathway**. This is a measure of the decrease in flux through the high-yield pathway during the metabolic switch. As in Figure 2, we only report simulations that resulted in low-yield metabolism, with yield < 0.3 gr dry weight/gr glucose. Dashed lines indicate experimental values. A.

Acetate excretion makes E. coli use overflow-like switching

What could explain that

A key difference that sets

Although acetate production is a "cheap" way—in terms of the number of enzymes required—to produce additional ATP from pyruvate, it poses an additional challenge to ^{+}. Thus such waste product formation is a "fast" way to restore a sufficiently high NAD^{+}/NADH-ratio. Acetate production does not restore the NAD^{+}/NADH-ratio, so acetate production might deplete the available NAD^{+ }in the cell. So, ^{+}/NADH ratio.

This analysis suggests that, if ^{+}/NADH ratio

Acetate fermentation

**Acetate fermentation vs. lactate and ethanol fermentation in E. coli**. Histograms of the decrease in oxygen uptake rate, relative to the maximum oxygen uptake rate. A. Simulations that result in acetate fermentation (without lactate or ethanol fermentation); B. Simulations that result in ethanol or lactate fermentation.

To further confirm the hypothesis that at high growth rates overflow metabolism is optimal in ^{+}/NADH ratio by producing the alternative waste products lactate or ethanol. This model observation agrees with experiments by De Mey

Metabolic switching in model with blocked acetate excretion

**Metabolic switching in model with blocked acetate excretion**. Distribution of growth yields predicted by the modified metabolic model with blocked acetate excretion of

**Figure S1**. Histogram of decrease in oxygen uptake for

Click here for file

To confirm that an additional ATP-producing pathway can indeed lead to an additional optimal growth mode, we developed a simplified metabolic network model

Simplified network model of acetate production in

**Simplified network model of acetate production in E. coli**. A. Simplified metabolic network. Reaction 1: glycolysis, reaction 2: acetate excretion, reaction 3: lactate/ethanol excretion, reaction 4: TCA-cycle, reaction 5: Oxidative phosphorylation; B. Growth yield distribution of the full simplified network; C. Growth yield distribution in simplified model with blocked acetate excretion.

Discussion

We have computationally compared metabolic switching at high growth rates in ^{+}/NADH-ratio. ^{+}. In addition to lactate and ethanol fermentation and oxidative phosphorylation, ^{+}/NADH-ratio must be restored elsewhere. Our model suggests that in this case it is optimal to keep oxidative phosphorylation running, instead of calling in low-yield pathways to reduce NADH,

To test the idea that acetate production is the cause of overflow metabolism in

Our model results suggest that restoring the redox balance is key in metabolic switching, agrees with experimental observation. Vemuri

To check whether our model is consistent with these experiments, we mimicked them in the FBAwMC models for

Effect of NOX or AOX overexpression on low-yield metabolism

**NOX**

**AOX**

96%

98%

100%

97%

16%

We report the percentage of simulations that result in a decrease in acetate fermentation (for

The computational results presented in this paper are contingent on two underlying, biological assumptions of FBAwMC that may limit the applicability of our approach to strains growing in well-mixed, nutrient-rich lab conditions: a) evolution optimizes cells' growth rates instead of yields, and b) a solvent constraint (

The optimality assumption is not necessarily correct in all environments. Apart from the fact that evolution does not always lead to optimality

The second key assumption of FBAwMC, namely that cells have evolved regulation mechanisms to activate production of enzymatic machinery for the pathway giving optimal growth rate

Conclusions

Why, at high rates, do some microbes use low-yield metabolism in addition to the high-yield pathway—overflow metabolism—whereas other microbes downregulate their high-yield pathways? Here we show that maintaining redox balance is key to understanding overflow metabolism in

Methods

Flux balance analysis with molecular crowding

We have used FBAwMC

FBAwMC assumes that the metabolic network is in steady state

where _{ij }
_{ij }
_{ij }

where _{lb, n }
_{ub, n }

Here _{n }
_{n }
_{prot }
_{prot }
_{prot }
_{prot }
_{prot }

**Table S1**. Table describing the summary of fitting _{prot }
_{prot }
_{prot}
_{prot }
_{max, fit }
_{max, obs}
_{max, obs}
^{2}+((_{max, fit }
_{max, obs}
_{max, obs}
^{2}. Here, _{max, fit}
_{max, obs }
_{max, fit}
_{max, obs }
_{ineff }

Click here for file

Crowding coefficients

To obtain the crowding coefficients _{i }
_{i }
_{i }
_{max}

**Figure S2**. Excel file with turnover numbers and enzyme masses used to calculate the crowding coefficients.

Click here for file

As there is insufficient data for

**Figure S3**. Histograms of turnover numbers (1/s) (A) and crowding coefficients (gram DW hr/mmol) (B) of

Click here for file

**Figure S4**. Histograms of turnover numbers (1/s) (A,C) and crowding coefficients (gram DW hr/mmol) (B,D) of

Click here for file

In silico growth experiments

We initiated each simulation with randomly select crowding coefficients from the obtained distributions. We assigned a crowding coefficient of 0 to non-enzymatic reactions. The COBRA Toolbox

The

**Table S2**. Excel file describing, for every reaction, the lower and upper bounds used in the simulations.

Click here for file

Matlab code to reproduce the simulations are included in Additional file

**Mini-website with Matlab code and instructions for reproducing the simulations**.

Click here for file

Abbreviations

AOX: Alternative oxidase; ATP: Adenosine triphosphate; BiGG: Biochemical Genetic and Genomic knowledgebase of large scale metabolic reconstructions; CO_{2}: Carbon dioxide; COBRA: COnstraints Based Reconstruction and Analysis; FBA: Flux-balance analysis; FBAwMC: Flux-balance analysis with molecular crowding; GTP: Guanosine-5'-triphosphate; NAD^{+}: Nicotinamide Adenine Dinucleotide; NADH: Reduced form of NAD^{+}; NOX: NADH oxidase.

Competing interests

The authors declare that they have no competing interests.

Authors' contributions

MvH designed the model and performed the simulations. RM and MvH conceived of the study and drafted the manuscript. All authors read and approved the final manuscript.

Acknowledgements

We thank three anonymous referees for their constructive comments that have helped us to improve the manuscript. This work was cofinanced by the Netherlands Consortium for Systems Biology (NCSB), which is part of the Netherlands Genomics Initiative/Netherlands Organisation for Scientific Research.