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, e.g
., aerobic respiration that yields more than thirty moles of ATP per mole glucose, and a highly inefficient, low-yield fermentation pathway that yields only two or three moles ATP per mole of glucose. This effect is known as the Crabtree-effect in the baker's yeast Saccharomyces cerevisiae. S. cerevisiae
turns glucose into CO2
in aerobic, glucose-limited conditions. But in abundance of glucose, glucose is converted into ethanol [1
], even if oxygen levels do not limit aerobic metabolism. Many bacteria also use a high-yield metabolic pathway in glucose-limited conditions and a low-yield pathway in excess of glucose. Examples are Escherichia coli
], Bacillus subtilis
] and lactic acid bacteria, e.g
., Lactobacillus plantarum
and Lactococcus lactis
]. The effect is also found in multicellular eukaryotes, including human cancer cells, where it is called the Warburg effect [6
]. Muscle cells switch to low-yield metabolism during heavy exercise [7
], fermenting glucose into lactic acid. Why cells would produce less ATP per glucose molecule than they can is a long-standing question in biology [8
Microbial species show remarkable differences in their metabolic switching strategies. At low glucose concentrations and low growth rates, E. coli
uses high-yield metabolism, aerobically converting glucose into CO2
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 [2
]. S. cerevisiae
uses high-yield, aerobic respiration at slow growth rates; at fast growth rates it ferments most glucose into ethanol, and downregulates aerobic respiration, keeping aerobic respiration active at a much lower rate. Although L. lactis
does not have an aerobic respiration pathway, it still performs a metabolic switch. At fast growth rates it makes a full switch to lactic acid fermentation [4
], which yields about 50% less ATP than the higher-yield mixed acid fermentation pathway, that produces formate, acetate and ethanol.
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 [13
]. The remainder would then spill into the low-yield pathway. This explanation requires the low-yield pathway to operate at a faster rate than the high-yield pathway, which is likely the case [8
]. Thus overflow metabolism plausibly explains concurrent use of high-yield and low-yield pathways, as in E. coli
. However, a problem with overflow metabolism is that it does not explain why organisms like S. cerevisiae
or L. lactis
would partly switch off their high-yield pathways at high growth rates.
Recent studies have suggested that the limited amount of metabolic enzymes fitting inside the cell may be key to low-yield metabolism [12
]. Simply because cells can host only a finite number of metabolic enzymes, they may need to trade off investment into the bulky enzymatic machinery required for low-throughput, high-yield metabolism, or alternatively to invest into many more "lean" glycolytic enzymes producing a high-throughput, low yield metabolism. Thus, according to this view, high glucose uptake rate should correlate with low yield metabolism, and vice versa. Indeed, this is observed in comparative studies of metabolism in yeast species of the Saccharomyces
] and in comparative studies of glucose metabolism of various bacterial species [20
If cells need to trade off fast metabolism and high-yield metabolism, then why do we still observe overflow metabolism, as in E. coli? We address this question by comparing the optimal metabolic switching strategies of L. lactis, S. cerevisiae, and E. coli as predicted by a genome-scale computational model. These three organisms use different pathways to metabolize glucose. In Figure a simplified reaction scheme of the most important glucose degrading pathways in these three organisms is presented. E. coli can use oxidative phosphorylation, lactate fermentation, ethanol fermentation and acetate fermentation. L. lactis can use mixed-acid fermentation, producing formate, acetate and ethanol, or lactate fermentation. S. cerevisiae can use oxidative phosphorylation, ethanol fermentation and acetate fermentation.
Simplified reaction scheme for the 3 organisms studied. A. L. lactis; B. S. cerevisiae; C. E. coli.
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 [2
]. However, because the glucose uptake rate is fixed in these simulations, growth yield
(defined as the growth rate divided by the glucose uptake rate) is effectively maximized [16
]. Therefore, FBA cannot satisfactorily predict low-yield metabolism.
For this reason, we use an extension of FBA, Flux Balance Analysis with Molecular Crowding (FBAwMC) [17
]. In contrast to FBA, FBAwMC calculates the optimal flux distribution through a metabolic network under the physiologically-plausible constraint that only a finite number of metabolic enzymes fit into a cell. Because each of the enzymes has a maximum turnover number (kcat
), molecular crowding naturally results in a constraint on the total metabolic flux through the network:
being the flux through reaction i
the volume fraction of macromolecules devoted to metabolic enzymes and ci
the "crowding coefficient" of reaction i
. The crowding coefficient of reaction i
is defined as the volume that needs to be occupied with enzymes to reach unit flux through reaction i
and is given by
is the cell mass, V
the cell volume, vi
the molar volume of the enzyme catalyzing reaction i
, and bi
a variable describing the proportionality between enzyme concentration and flux through reaction i
]. Intuitively, the crowding coefficient can be seen as the protein cost of a reaction: enzymes with low crowding coefficients have small molecular volume or catalyse fast reactions. FBAwMC correctly predicts low-yield metabolism: e.g
., growth curves of E. coli
], and the Warburg effect in cancer cells [18
]. Therefore, FBAwMC is well suited for our aim: to unravel the metabolic differences between microbes that decrease the flux through the high-yield pathway at high growth rates and those that keep the high-yield pathway always fully active.
Because crowding coefficients for most metabolic enzymes are unknown, previous studies proposed a range of strategies to estimate them. Beg et al.
] fitted an average crowding coefficient
in order to obtain a good match between predicted and measured growth rates. Shlomi et al.
] obtained 15% of crowding coefficients from experimental data and assigned the median of the known crowding coefficient values to the remaining unknown crowding coefficients. Vazquez et al.
] sampled crowding coefficients randomly from a range of physiologically-plausible values obtained from on-line, biochemical databases, and presented averages and variations of the metabolic fluxes predicted for a large random sample of crowding coefficients.
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 (e.g., acetate production in E. coli), it is optimal to keep both the low-yield and high-yield pathways active at high growth rates.