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Conceived and designed the experiments: ER TS TB. Performed the experiments: TB. Analyzed the data: ER TS TB. Contributed reagents/materials/analysis tools: ER TS. Wrote the paper: ER TS TB. Analyzed the results: ER TS TB RS EG.

The authors have declared that no competing interests exist.

The Warburg effect - a classical hallmark of cancer metabolism - is a counter-intuitive phenomenon in which rapidly proliferating cancer cells resort to inefficient ATP production via glycolysis leading to lactate secretion, instead of relying primarily on more efficient energy production through mitochondrial oxidative phosphorylation, as most normal cells do. The causes for the Warburg effect have remained a subject of considerable controversy since its discovery over 80 years ago, with several competing hypotheses. Here, utilizing a genome-scale human metabolic network model accounting for stoichiometric and enzyme solvent capacity considerations, we show that the Warburg effect is a direct consequence of the metabolic adaptation of cancer cells to increase biomass production rate. The analysis is shown to accurately capture a three phase metabolic behavior that is observed experimentally during oncogenic progression, as well as a prominent characteristic of cancer cells involving their preference for glutamine uptake over other amino acids.

Cancer cells, as opposed to normal cells, produce a substantial amount of energy inefficiently via aerobic glycolysis, even in the presence of sufficient oxygen to support mitochondrial respiration. Despite the fact that this phenomenon, called the Warburg effect, has already been discovered back in 1924, its causes remain poorly understood. Here we utilize a genome-scale human metabolic network model and show that by accounting for cellular capacity for metabolic enzymes, the Warburg effect is a direct consequence of cancer cells' adaptation to fast proliferation. We demonstrate that our model accurately captures several metabolic phenotypes observed experimentally during cancer development, as well as the preference of cancer cells to glutamine uptake over other amino acids.

The Warburg effect, a phenomenon discovered by Otto Warburg in 1924, reflects a shift to an inefficient metabolism in cancer cells, in which an increase in the inefficient production of adenosine 5′-triphosphate (ATP) via glycolysis leads to the secretion of non-oxidized carbons in the form of lactate, even in the presence of oxygen (termed

Over the years, several hypotheses were raised regarding the potential cause of the Warburg effect: (i) Defective mitochondrion hypothesis – suggesting that cancer cells have defective mitochondria and hence rely on glycolysis

Previous computational investigations of the Warburg effect studied the role of either energy or biomass production in causing the Warburg effect, focusing solely on central carbon metabolism. For example, the study of Vander Heiden

In this paper, we study the causes of the Warburg effect by accounting for both energy production and anabolism of essential biomass constituents, in a genome-scale stoichiometric network model

We utilized a genome-scale human metabolic network that includes 3,742 reactions

To predict plausible metabolic fluxes in cancer, we first employed a standard FBA method to identify a feasible flux distribution that satisfies stoichiometric mass-balance, while maximizing biomass production yield (see

A strictly stoichiometric analysis, such as the one presented above, implicitly assumes that metabolic flux rates can be tuned to achieve high biomass production yields, without considering constraints imposed by enzyme concentrations and catalytic rates, which are prime determinants of metabolic flux. Specifically, while cells might be free to regulate enzyme concentrations according to metabolic demands

We applied the approach described above (FBA with solvent capacity constraint) to predict human cellular flux distributions that maximize the biomass production rate. To simulate varying growth rates we performed the optimization across a wide range of different glucose uptake rates. Indeed, under these combined sets of constraints we find that biomass yield does decline at high growth rates – in accordance with the Warburg effect _{2} uptake). The increase in aerobic glycolysis flux (

(A) Predicted maximalgrowth yield of human cells (per unit of glucose uptake; y-axis) for a range of growth rates (x-axis), based strictly on reactions' stoichiometry (dotted) and by considering also enzyme mass and enzyme solvent capacity (solid). Vertical dashed lines indicate the borders between: phase I (high yield, no lactate secretion), phase II (medium yield, increased oxidative phosphorylation) and phase III (low yield, lactate secretion). (B) Predicted lactate secretion flux (red lines) and oxygen consumption flux (blue lines) for a range of growth rates. Growth rates were manipulated by varying the glucose uptake rate limit from 0 until the uptake value needed to reach the maximal growth rate. Fluxes were normalized by the glucose uptake rate. (C) Experimentally determined lactate secretion rates (red; squares) and oxygen uptake rates (blue; circles) during tumor development of H-RasV12/E1A transformed fibroblasts. NRFU: Normalized relative fluorescence units; see

(A) as predicted across phases I-III in the model and (B) based on experimental measurements taken from BJ fibroblast cell lines representing the path towards tumorigenic conversion (CL1-CL4;

To further validate the plausibility of the model, we examined the correlation between its enzyme concentration predictions (based on predicted flux distributions; see

The shift towards _{A}_{A}_{B}_{B}

The axes (A, B) describe the growth rate obtained from flux distributions A and B, respectively. The blue lines represent two different constraints on the glucose uptake rate, and the red line represents the maximal concentration constraint. Green dashed lines are the contours of the growth rate maximization objective function – the further the line is from the origin, the higher the growth rate. When the glucose uptake U is limiting (dark grey feasible region), the maximal growth rate is obtained via A only (Solution 1; left green diamond). When both the uptake and the enzyme concentration constraints are limiting (light grey feasible region), maximal growth rate (G) is obtained via a combination of A and B (Solution 2; right green diamond), resulting in a shift to a less efficient metabolism and lactate secretion. This can be explained by the fact that the slope of the growth-rate (middle green) line (-1) is larger than the slope of the enzyme concentration limit (red) line (

Concretely, analyzing the results of our model, flux distribution

The role of glutamine in cancer has been a topic of major interest as cancer cells are known to have a significant high glutamine uptake rate

The increase in proliferation rate achievable by the increased uptake of each of the 20 amino-acids in addition to glucose (relative to the baseline growth rate achieved when only glucose is available), as predicted by the stoichiometric model (A) and by the model accounting for the solvent capacity constraint (B). Glutamine uptake (highlighted in yellow) enables to achieve the highest increase in growth rate according to the solvent capacity model, in agreement with experimental data showing preference for high glutamine uptake rates in cancer.

We carefully examined the flux distribution obtained with glutamine in the growth medium (achieving a growth rate of 0.062 1/h) vs. the one obtained with glutamate (growth rate = 0.056 1/h). Interestingly, when glutamate is present in the medium, a large quantity of it is transformed into glutamine in an ATP consuming reaction catalyzed by the enzyme glutamine synthetase (EC 6.3.1.2). This satisfies the glutamine biomass requirement as well as the production of nucleotide precursors, among others. When removing the ATP requirement from this reaction, the growth rate achieved with glutamate in the medium increases to 0.059 1/h, which explains 50% of the growth rate difference. Notably, while this provides some intuitive explanation for the predicted preference for glutamine, we cannot identify a simple explanation for the entire effect due to the high complexity of the network model employed.

Metabolic adaptation to elevated growth requirements during cancer development has been recently suggested as the possible cause of the Warburg effect, a long-standing enigma of cancer metabolism. In this work we rigorously study this hypothesis using a genome-scale human metabolic model and demonstrate that stoichiometric considerations solely are insufficient to explain the shift to inefficient metabolism, in difference from recent claims

The importance of enzyme solvent capacity in metabolic modeling has already been recognized in the earlier work of Beg

In a recent study by Molenaar

While the data on reactions' stoichiometry is considered accurate and comprehensive, enzyme kinetic constant data are noisy and are currently available for only about 15% of the reactions in the model. In the analysis presented here, we addressed this problem by assigning enzymes with missing turnover rates with the median rate computed over the set of known turnover rates. Notably, the model's main findings are robust to random sampling of turnover rates from a distribution of known rates, as shown in

In our work we accounted for a solvent capacity constraint assuming a limited protein mass per cell, without considering the effect of enzymes' sub-cellular compartmentalization. To investigate how the latter would affect our predictions, we repeated the analysis while considering separate solvent capacity constraints for cytoplasm and mitochondria (

The presented modeling approach is likely to contribute to more accurate metabolic modeling of highly proliferating human cells in general (as was already shown regarding genome-scale models of microorganisms

The Duarte

Equation 2 imposes the steady state constraints on the system, assuming that the metabolite concentrations remain constant in time. Thermodynamic constraints determining the reaction directionalities are accounted for via the flux limits

A constraint on the total enzyme concentration was added to the biomass production FBA model:

The enzyme mass (per mg dry weight (DW) of cells) required to maintain the flux in the i-th reaction (_{i}_{i}_{i}_{cat}_{cat}_{cat}_{cat}_{cat}

Flux distributions were computed under maximal growth rates in the three growth phases (phase I – 0.0243 1/h; phase II – 0.0515 1/h; phase III – 0.0557 1/h). For each phase, the median flux distribution across 1000 different uniform samples was calculated using ACHR sampling

Gene expression readouts for 1,269 metabolic genes across 60 cell lines from the NCI-60 collection

Each of the 20 amino acids was added, in turn, to the growth media, resulting in 20 different maximal biomass production rates calculated based on (i) the stoichiometric model, and on (ii) a model additionally accounting for the solvent capacity constraint. The maximal amino-acid uptake rate was set to the same uptake rate as glucose; the results are shown to be robust to the choice of this value (

Human biomass composition.

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Enzyme molecular weight data for the reactions in the model.

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Enzyme turnover number data for the reactions in the model.

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Validating the robustness of the results to various model parameters and exploring additional changes in the model.

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Special thanks to Christoph Kaleta and Stefan Schuster for their many detailed comments and suggestions that have served to significantly improve our manuscript.