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Why Do Fast-Growing Bacteria Enter Overflow Metabolism? Testing the Membrane Real Estate Hypothesis

Open ArchivePublished:July 26, 2017DOI:https://doi.org/10.1016/j.cels.2017.06.005
      Bacteria and other cells show a puzzling behavior. At high growth rates, E. coli switch from respiration (which is ATP-efficient) to using fermentation for additional ATP (which is inefficient). This overflow metabolism results in a several-fold decrease in ATP produced per glucose molecule provided as food. By integrating diverse types of experimental data into a simple biophysical model, we give evidence that this onset is the result of the membrane real estate hypothesis: Fast growth drives cells to be bigger, reducing their surface-to-volume ratios. This decreases the membrane area available for respiratory proteins despite growing demand, causing increased crowding. Only when respiratory proteins reach their crowding limit does the cell activate fermentation, since fermentation allows faster ATP production per unit membrane area. Surface limitation thus creates a Pareto trade-off between membrane efficiency and ATP yield that links metabolic choice to the size and shape of a bacterial cell. By exploring the predictions that emerge from this trade-off, we show how consideration of molecular structures, energetics, rates, and equilibria can provide important insight into cellular behavior.

      Keywords

      Main Text

      A major priority of a cell is obtaining and managing its energy. Many cells show a puzzling behavior. On the one hand, in dilute glucose environments with ample oxygen, many organisms obtain their energy almost exclusively from aerobic respiration. In this process, glucose is fully oxidized by glycolysis and the tricarboxylic acid (TCA) cycle, with the captured energy used by the electron transport chain to make ATP. On the other hand, in concentrated glucose environments, Escherichia coli and other organisms switch and obtain some of their energy anaerobically (without using oxygen) by acetate fermentation, even when oxygen is plentiful (
      • Farmer I.S.
      • Jones C.W.
      Energetics of Escherichia-coli during aerobic growth in continuous culture.
      ,
      • Kayser A.
      • Weber J.
      • Hecht V.
      • Rinas U.
      Metabolic flux analysis of Escherichia coli in glucose-limited continuous culture. I. Growth-rate-dependent metabolic efficiency at steady state.
      ,
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Vazquez A.
      • Beg Q.K.
      • Demenezes M.A.
      • Ernst J.
      • Bar-Joseph Z.
      • Barabasi A.-L.
      • Boros L.G.
      • Oltvai Z.N.
      Impact of the solvent capacity constraint on E. coli metabolism.
      ,
      • Molenaar D.
      • van Berlo R.
      • de Ridder D.
      • Teusink B.
      Shifts in growth strategies reflect tradeoffs in cellular economics.
      ,
      • Zhuang K.
      • Vemuri G.N.
      • Mahadevan R.
      Economics of membrane occupancy and respiro-fermentation.
      ,
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ,
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      ,
      • Peebo K.
      • Valgepea K.
      • Maser A.
      • Nahku R.
      • Adamberg K.
      • Vilu R.
      Proteome reallocation in Escherichia coli with increasing specific growth rate.
      ,
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ). This so-called overflow metabolism is puzzling because acetate fermentation produces far fewer ATP per glucose molecule than respiration does (
      • Neidhardt F.C.
      • Curtiss R.
      Escherichia coli and Salmonella: Cellular and Molecular Biology.
      ). Why should fast-growing cells switch to a more inefficient mechanism of energy utilization? Does the cell become driven by some fitness objective that does not require efficient production of energy?
      Various explanations have been proposed for the onset of overflow metabolism. These include the hypothesis that it results from the repression of the TCA cycle (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Nahku R.
      • Valgepea K.
      • Lahtvee P.J.
      • Erm S.
      • Abner K.
      • Adamberg K.
      • Vilu R.
      Specific growth rate dependent transcriptome profiling of Escherichia coli K12 MG1655 in accelerostat cultures.
      ) or acetate recycling enzymes (
      • Nahku R.
      • Valgepea K.
      • Lahtvee P.J.
      • Erm S.
      • Abner K.
      • Adamberg K.
      • Vilu R.
      Specific growth rate dependent transcriptome profiling of Escherichia coli K12 MG1655 in accelerostat cultures.
      ), possibly due to catabolite repression (
      • Nahku R.
      • Valgepea K.
      • Lahtvee P.J.
      • Erm S.
      • Abner K.
      • Adamberg K.
      • Vilu R.
      Specific growth rate dependent transcriptome profiling of Escherichia coli K12 MG1655 in accelerostat cultures.
      ). Others propose that fermentation is preferred at high growth rates due to its lower biosynthesis cost relative to the electron transport chain (
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ). Finally, some propose that respiration is limited due to the finite space within the inner membrane, where the electron transport chain is located (
      • Andersen K.B.
      • Meyenburg K.V.
      Are growth-rates of Escherichia coli in batch cultures limited by respiration.
      ,
      • Zhuang K.
      • Vemuri G.N.
      • Mahadevan R.
      Economics of membrane occupancy and respiro-fermentation.
      ).
      Different modeling approaches have been used to test these hypotheses. One approach entails flux-balance models, which treat the detailed stoichiometry of metabolic reactions (
      • Vazquez A.
      • Beg Q.K.
      • Demenezes M.A.
      • Ernst J.
      • Bar-Joseph Z.
      • Barabasi A.-L.
      • Boros L.G.
      • Oltvai Z.N.
      Impact of the solvent capacity constraint on E. coli metabolism.
      ,
      • Vazquez A.
      • Liu J.
      • Zhou Y.
      • Oltvai Z.N.
      Catabolic efficiency of aerobic glycolysis: the Warburg effect revisited.
      ,
      • O’Brien E.J.
      • Lerman J.A.
      • Chang R.L.
      • Hyduke D.R.
      • Palsson B.O.
      Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction.
      ,
      • van Rijsewijk B.
      • Nanchen A.
      • Nallet S.
      • Kleijn R.J.
      • Sauer U.
      Large-scale C-13-flux analysis reveals distinct transcriptional control of respiratory and fermentative metabolism in Escherichia coli.
      ,
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ,
      • Zhuang K.
      • Vemuri G.N.
      • Mahadevan R.
      Economics of membrane occupancy and respiro-fermentation.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ). Given a set of input constraints such as maximal glucose uptake and oxygen consumption, these models predict the fluxes that optimize an objective-like growth rate. Another approach is more coarse-grained in having many fewer components, for example dividing all the proteins in the proteome into a few classes, for the purpose of exploring principles, such as the optimal allocation of the proteome (
      • Molenaar D.
      • van Berlo R.
      • de Ridder D.
      • Teusink B.
      Shifts in growth strategies reflect tradeoffs in cellular economics.
      ,
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ). Yet another approach, which does not treat the spatial aspects per se, focuses on speed versus efficiency of metabolic pathways (
      • Flamholz A.
      • Noor E.
      • Bar-Even A.
      • Liebermeister W.
      • Milo R.
      Glycolytic strategy as a tradeoff between energy yield and protein cost.
      ,
      • Noor E.
      • Bar-Even A.
      • Flamholz A.
      • Reznik E.
      • Liebermeister W.
      • Milo R.
      Pathway thermodynamics highlights kinetic obstacles in central metabolism.
      ). However, in common among these models is their neglect of structural properties of the individual proteins, such as their physical sizes, shapes, and packing, and the forces that partition them between the bulk and the membrane.
      Here, we approach the problem of overflow metabolism in E. coli using such considerations. We consider the hypothesis that membrane space can become too limited for a cell to “breathe enough,” called the “membrane economics hypothesis” by Mahadevan (
      • Zhuang K.
      • Vemuri G.N.
      • Mahadevan R.
      Economics of membrane occupancy and respiro-fermentation.
      ). Although it is just terminology, we prefer a slightly different term—the membrane real estate hypothesis—to make clear that the constraint is on lateral space in the membrane, not on costs in energy or biomass. To test this hypothesis, we use experimental data on cell length and width to demonstrate that the packing of the electron transport chain and other inner membrane proteins reaches its limit concurrently with the onset of overflow metabolism. Furthermore, we derive respiration capacity from molecular kinetic data and show that the capacity of the electron transport chain to generate ATP is saturated as it reaches a concentration at which the membrane runs out of space. Finally, we show that the membrane real estate model predicts the steep rise in the [NADH]/[NAD+] ratio observed prior to the onset of fermentation. The model thus suggests that overflow metabolism is triggered by membrane crowding to avoid NADH imbalance (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ). By bringing together multiple types of data—on protein structures, energy balance, and rates and equilibria—we make a plausibility case for the triggering of overflow metabolism.
      Our modeling of E. coli metabolism begins from two basic assumptions. First, we assume the cell's capacity to produce energy is proportional to the cell membrane surface area S, since this physically limits the cell's glucose uptake and respiratory capacity under the conditions studied here. Second, we assume the cell's rate of energy demand is proportional to the cell's volume V at a given growth rate, because expenditures are mostly on the synthesis required to replicate a cell. Under steady-state growth conditions, the cell's rate of energy expenditure cannot be greater than the cell's rate of energy production. These are fundamental physical constraints that act on any cell growing at a fixed rate.
      Underlying these assumptions is an important empirical fact: E. coli's surface area S and volume V both depend on growth rate. Figure 1A shows experimental measurements of E. coli's length and width at different growth rates and nutrient conditions (
      • Volkmer B.
      • Heinemann M.
      Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling.
      ). Faster-growing cells are both longer and wider than slower-growing cells (
      • Woldringh C.L.
      • de Jong M.A.
      • van den Berg W.
      • Koppes L.
      Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.
      ,
      • Osborn M.J.
      • Rothfield L.
      Cell shape determination in Escherichia coli.
      ,
      • Volkmer B.
      • Heinemann M.
      Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling.
      ). To compute the surface area and volume of the cell (variables governing energy production capacity and expenditure rate), we use the approximation that the cell is cylindrical with hemispherical ends. The resulting surface-to-volume (S/V) ratio of the cell computed using these measured lengths and widths is plotted in Figure 1A. These results show a significant 30%–40% reduction in E. coli's S/V as growth rate increases over the range shown. In the sections below, we use these values of S and V to reason about the microscopic factors that affect the cell's energy balance and illustrate how our assumptions generate biologically meaningful constraints on cellular metabolism.
      Figure thumbnail gr1
      Figure 1Mechanism of Glucose Uptake
      (A) The surface-to-volume (S/V) ratio decreases with growth rate due to changes in cell length and cell width, in conflict with the cell's increasing demand for membrane space (
      • Volkmer B.
      • Heinemann M.
      Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling.
      ).
      (B) Glucose uptake is a two-step process in which diffusion through outer membrane porins is followed by active uptake through inner membrane transporters modeled by the Michaelis-Menten function MT([Gp]). While outer membrane influx is proportional to external glucose concentration [Go], inner membrane uptake is dependent on periplasmic glucose concentration [Gp]. We relate these through the factor ϕ. The total uptake per cell volume scales with S/V of the cell.

      Assumption 1. The Cell's Capacity to Produce Energy Is Proportional to the Cell Membrane Surface Area: The Problem of Glucose Uptake

      Figure 1B shows how glucose and other nutrients are taken up by E. coli in two steps: (1) passive diffusion through porin channels in the outer membrane, followed by (2) active uptake by transporters in the inner membrane. Transport through outer membrane porins plays a critical part in uptake kinetics (
      • Koch A.L.
      • Wang C.H.
      How close to the theoretical diffusion limit do bacterial uptake systems function?.
      ). Diffusion of nutrients through their water-filled pore can be modeled using the Renkin-modified diffusion equation (
      • Renkin E.M.
      Filtration, diffusion, and molecular sieving through porous cellulose membranes.
      ,
      • Nikaido H.
      • Rosenberg E.Y.
      Effect on solute size on diffusion rates through the transmembrane pores of the outer membrane of Escherichia coli.
      ). This equation relates the rate of influx to measurable physical quantities such as pore diameter, depth, and abundance, as well as the effective diameter of the nutrient. Using this model, the uptake rates of nutrients varying in size from lactose to glucose to glycerol were shown to be consistent with a diffusive bottleneck through pores with a diameter of 1.2 nm (
      • Nikaido H.
      • Rosenberg E.Y.
      Effect on solute size on diffusion rates through the transmembrane pores of the outer membrane of Escherichia coli.
      ), consistent with the size of porin channels (
      • Nikaido H.
      • Rosenberg E.Y.
      Porin channels in Escherichia coli: studies with liposomes reconstituted from purified proteins.
      ). We compute the permeability of the E. coli outer membrane to glucose as roughly 3 μm/s (Table S1A). While permeability could be increased by expanding the pore diameter, this has been observed to increase sensitivity to toxins, suggesting that porins also play a protective role for the cell (
      • Kojima S.
      • Nikaido H.
      Permeation rates of penicillins indicate that Escherichia coli porins function principally as nonspecific channels.
      ).
      The second step of glucose uptake is through inner membrane transporters. We estimate that glucose transporters occupy only 1% of the membrane area when overflow metabolism begins, and thus make a much smaller contribution to inner membrane crowding than the electron transport chain (Figure 2A and Box 1). This number is obtained using the area of a glucose transporter dimer (48 ± 10 nm2) (
      • Jeckelmann J.M.
      • Harder D.
      • Mari S.A.
      • Meury M.
      • Ucurum Z.
      • Muller D.J.
      • Erni B.
      • Fotiadis D.
      Structure and function of the glucose PTS transporter from Escherichia coli.
      ), its maximum uptake rate (kT = 180 ± 40 glucose/s), the surface-to-volume ratio of a cell (Figure 1A), and the cell's total glucose uptake rate (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • O’Brien E.J.
      • Lerman J.A.
      • Chang R.L.
      • Hyduke D.R.
      • Palsson B.O.
      Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction.
      ) (Table S1A). Thus, while glucose transporters can saturate at high glucose concentrations, the abundance of these transporters can be increased to keep up with the non-saturating influx through porins (
      • Koch A.L.
      • Wang C.H.
      How close to the theoretical diffusion limit do bacterial uptake systems function?.
      ). As shown in Figure 1B, the net uptake rate RG through both steps can therefore be expressed by the influx through porins, multiplied by the fraction ϕ of glucose molecules diffusing in through porins that are taken up by inner membrane transporters rather than escaping back out into the environment.
      Figure thumbnail gr2
      Figure 2Increasing Demand for ATP Drives Electron Transport Chain Surface Occupancy
      (A) Black bars: estimated occupancy of the inner membrane by standard electron transport chain complexes, from experimental data (
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      ) (B). Red line: the minimal amount of electron transport chain needed to maintain a purely respiratory metabolism. The crossing point at 0.32 ± 0.10 hr−1 indicates that respiration alone is not sufficient to supply the cell's ATP needs above this growth rate, leading to overflow metabolism (
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ).
      (B) The total inner membrane protein density (cyan points) follows the trend predicted from a Carnahan-Starling model of protein crowding (cyan curve) for a protein packing limit of one-third (fitting parameter, see text). This differs from the density needed to maintain fixed stoichiometry between membrane and cytosolic proteins, approximated here by V/S (black curve). Inner membrane proteins appear to reach their packing limit concurrently with the onset of fermentation at λ = 0.3 hr−1. Inset: steric pressure from protein crowding increases linearly with growth rate.
      (C) Prior to the inner membrane reaching its protein packing limit, both glucose transporters (red) and electron transport chain (blue) have space to increase. But once the packing limit is reached, higher growth rates require increases only in glucose transporters to fuel acetate fermentation due to its greater surface efficiency for generating ATP (see ).
      Error bars represent SDs of experimental abundances.
      Membrane Requirements of ATP Production
      Respiration and acetate fermentation are the two major routes to ATP generation in E. coli grown aerobically on glucose (
      • Neidhardt F.C.
      • Curtiss R.
      Escherichia coli and Salmonella: Cellular and Molecular Biology.
      ). While E. coli can perform several different kinds of fermentation, acetate is the predominant end product of overflow metabolism in glucose media (
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ,
      • O’Brien E.J.
      • Lerman J.A.
      • Chang R.L.
      • Hyduke D.R.
      • Palsson B.O.
      Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction.
      ). ATP generation by both routes can be divided into electron transport chain-dependent and electron transport chain-independent parts. This is shown in the Figure B1, where α represents the number of ATP produced independently of the electron transport chain, while n represents the number of NADH equivalents produced that are used by the electron transport chain to generate ATP (Table S1C).
      Figure thumbnail grB1
      Figure B1Acetate Fermentation Is More Surface-Efficient than Respiration
      (Left) NADH and ATP production depends on how glucose is partitioned between biomass production, acetate fermentation, and respiration. NADH is consumed by the electron transport chain to produce ATP. Top right: membrane real estate occupied per electron transport chain complex and per respiratory unit, normalizing to ATP synthase. Middle right: surface efficiency of electron transport chain (ETC)-independent energy generation (transporter + cytosolic processes) and ETC-dependent processes (only ETC). Bottom right: the net surface efficiency of each metabolic mode depends on its component efficiencies. Our calculations assume a phosphate/oxygen (P/O) ratio of 1.0 (
      • Hempfling W.P.
      • Mainzer S.E.
      Effects of varying the carbon source limiting growth on yield and maintenance characteristics of Escherichia coli in continuous culture.
      ,
      • Farmer I.S.
      • Jones C.W.
      Energetics of Escherichia-coli during aerobic growth in continuous culture.
      ,
      • Noguchi Y.
      • Nakai Y.
      • Shimba N.
      • Toyosaki H.
      • Kawahara Y.
      • Sugimoto S.
      • Suzuki E.
      The energetic conversion competence of Escherichia coli during aerobic respiration studied by 31P NMR using a circulating fermentation system.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ) for conversion of NADH to ATP via the electron transport chain (A and S1B).
      For each part, we can define surface efficiency as the number of ATP/s produced from a given amount of membrane area. The electron transport chain-independent part requires only glucose transporters (48 ± 10 nm2/dimer), which can supply a maximum of 180 ± 40 glucose/s that each yield 4 ATP in both respiration and acetate fermentation. This gives a surface efficiency of 15 ± 5 ATP/s/nm2. The surface efficiency of the electron transport chain-dependent part can be estimated from experimental electron transport chain protein structures, abundances, and kinetics (
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      ,
      • Etzold C.
      • DeckersHebestreit G.
      • Altendorf K.
      Turnover number of Escherichia coli f0f1 ATP synthase for ATP synthesis in membrane vesicles.
      ). Normalizing abundances to the terminal ATP synthase, an estimated 84 nm2 of electron transport chain is required to generate 270 ± 40 ATP/s, the maximum speed of ATP synthase (
      • Etzold C.
      • DeckersHebestreit G.
      • Altendorf K.
      Turnover number of Escherichia coli f0f1 ATP synthase for ATP synthesis in membrane vesicles.
      ), resulting in a surface efficiency of only 3 ± 1 ATP/s/nm2 (Tables S1B and S1D). The electron transport chain stoichiometry shown in the table below represents averages across growth rates (
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      ) (Table S1B).
      A key conclusion from these calculations is that the larger number of NADH equivalents produced from acetyl-CoA by the TCA cycle (7.2, Table S1C [
      • Alberts B.
      • Johnson A.
      • Lewis J.
      • Raff M.
      • Roberts K.
      • Walter P.
      Molecular Biology of the Cell.
      ]) compared with acetate fermentation (0) is both the source of respiration's greater ATP yield and its lower surface efficiency, as it creates a high demand for surface-inefficient electron transport chain. It therefore follows that once the inner membrane reaches its protein packing limit, the cell can continue to increase its ATP production rate and growth rate by gradually increasing the fraction of glucose directed to acetate fermentation rather than the TCA cycle, as observed experimentally (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ,
      • O’Brien E.J.
      • Lerman J.A.
      • Chang R.L.
      • Hyduke D.R.
      • Palsson B.O.
      Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction.
      ).
      Why do cells not express even more inner membrane transporters for a given nutrient concentration? Once inner membrane transporters have become so abundant that the uptake capacities of the two membranes are comparable, there is diminishing value in producing more. This two-step mechanism may also resolve a puzzling observation (
      • Koch A.L.
      • Wang C.H.
      How close to the theoretical diffusion limit do bacterial uptake systems function?.
      ): glucose uptake and growth rate do not always follow the saturating kinetics expected by
      • Monod J.
      The growth of bacterial cultures.
      . Instead, they can show extremely linear behavior when glucose uptake is rate-limited by the non-saturating process of diffusion through porins, as modeled previously (
      • Koch A.L.
      • Wang C.H.
      How close to the theoretical diffusion limit do bacterial uptake systems function?.
      ,
      • Nikaido H.
      • Rosenberg E.Y.
      Effect on solute size on diffusion rates through the transmembrane pores of the outer membrane of Escherichia coli.
      ).

      Assumption 2. The Cell's Rate of Energy Demand Is Proportional to the Cell Volume: The Problem of ATP Production

      Above, we reasoned about the effect of S and V on the rate of glucose uptake, that is, the raw material for the cell's energy supply. They are also intimately related to the cell's rate of ATP demand. But how large is this demand and how much membrane space is needed to supply it? We define RATP-demand as the number of ATP molecules per unit time, per unit cell volume, that must be produced in order for a cell to sustain a growth rate λ. The amount of ATP, αB, needed to produce E. coli biomass aerobically on glucose is roughly 18 billion ATP molecules per femtoliter of cell volume (
      • Stouthamer A.H.
      • Bettenhaussen C.W.
      A continuous culture study of an ATPase-negative mutant of Escherichia coli.
      ,
      • Hempfling W.P.
      • Mainzer S.E.
      Effects of varying the carbon source limiting growth on yield and maintenance characteristics of Escherichia coli in continuous culture.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ) (Table S1A). In this work, our term ATP is shorthand that includes all nucleotide triphosphates. To support a growth rate λ, the cell demands ATP at a rate
      RATP-demand=αBλ.
      (Equation 1)


      Now, at steady state, this rate of ATP demand must be met by the rate of ATP supply. For the cell to achieve this via respiration, there is a minimum fraction of the bacterial inner membrane that must be electron transport chain. We can estimate this fraction from the known electron transport chain structural and kinetic properties (Tables S1A and S1B), according to
      ETCdemand=RATP-demandfETCAETCkATPVS.
      (Equation 2)


      fETC is the fraction of RATP-demand generated by the electron transport chain (the remainder by glycolysis and the TCA cycle; Box 1 and Table S1C). This ATP demand can be converted to an electron transport chain surface area by multiplying the first term by the surface efficiency of the electron transport chain, given by AETC/kATP. AETC is the membrane area occupied by a single “respiratory unit,” defined as the amount of electron transport chain needed to power a single ATP synthase at its maximum speed kATP = 270 ± 40 ATP/s (
      • Etzold C.
      • DeckersHebestreit G.
      • Altendorf K.
      Turnover number of Escherichia coli f0f1 ATP synthase for ATP synthesis in membrane vesicles.
      ). The area of a respiratory unit, roughly 84 nm2, is calculated from the cross-sectional areas of the five electron transport chain complexes' protein structures and their abundances relative to ATP synthase (Box 1; Tables S1B and S1D). The final term accounts for the reasonable assumption that ATP demand for replication scales with the volume V of the cell. To express ETCdemand as a fraction of total membrane area, we divide by S, resulting in Equation 2.
      Thus far, we have estimated the membrane demands of the electron transport chain, assuming that ATP is produced by a purely respiratory metabolism. Would less membrane area be needed if acetate fermentation was used instead? In other words, is acetate fermentation more surface efficient? A detailed calculation of the surface efficiency of both acetate fermentation and respiration can be found in Box 1. We find the membrane efficiency of acetate fermentation to be 15 ± 5 ATP/s/nm2, significantly higher than respiration's 4 ± 1 ATP/s/nm2. Acetate fermentation can therefore produce the same amount of ATP as respiration using roughly a quarter of the membrane space, at the expense of a much lower ATP yield per glucose (
      • Neidhardt F.C.
      • Curtiss R.
      Escherichia coli and Salmonella: Cellular and Molecular Biology.
      ) (Box 1).
      This observation illustrates the fundamental tension captured in the membrane real estate hypothesis. When sufficient membrane space is available to run on a fully respiratory metabolism, the cell will do so to maximize the flow of glucose to biomass (rather than for ATP) and thus maximize growth rate and yield. However, if membrane space becomes limiting, the cell can only fuel higher growth rates by producing additional ATP through more surface-efficient means, thus beginning overflow metabolism.

      Consequences of the Membrane Real Estate Hypothesis

      Limits of Respiration

      Figure 2 shows a key test of the membrane real estate hypothesis. In E. coli, the onset of fermentation typically occurs at growth rates of 0.3–0.5 hr−1 (
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ,
      • Ishii N.
      • Nakahigashi K.
      • Baba T.
      • Robert M.
      • Soga T.
      • Kanai A.
      • Hirasawa T.
      • Naba M.
      • Hirai K.
      • Hoque A.
      Multiple high-throughput analyses monitor the response of E-coli to perturbations.
      ,
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ). But why? Our calculation of the minimal amount of electron transport chain needed to fuel growth, summarized in Equation 2 and shown by the red line in Figure 2A, demonstrates how rapidly the electron transport chain's membrane requirements increase with growth rate, eventually becoming untenable. For comparison, the black bars in Figure 2A show the experimentally measured membrane occupancies of electron transport chain proteins at different growth rates. We determined these occupancies by combining the protein concentrations measured experimentally (
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      ) with their cross-sectional areas determined from protein structures (Box 1 and Table S1B). The black bars show that faster-growing cells have increased electron transport chain densities in the inner membrane, up to a growth rate of 0.3 hr−1, beyond which densities roughly plateau. The mild decline in electron transport chain densities above 0.3 hr−1 is thought to be from competition with glucose transporters (
      • Zhuang K.
      • Vemuri G.N.
      • Mahadevan R.
      Economics of membrane occupancy and respiro-fermentation.
      ) and other growth-related functions (Box 1). Importantly, the saturation in electron transport chain densities is predicted to cause the cell's maximum respiratory capacity (black bars) to cross the line of ATP demand (red curve) at a growth rate of roughly 0.32 ± 0.10 hr−1. This suggests that the cell needs to switch from using pure respiration to a mixture of respiration and acetate fermentation at this growth rate. This is a key prediction of this work and serves as an upper limit for the onset of acetate fermentation, λferm, as it assumes the electron transport chain is kinetically saturated. Consistent with the membrane real estate hypothesis, this predicted λferm is very close to the onset point of 0.27 hr−1 observed by the same group that measured the protein abundances used here (
      • Valgepea K.
      • Adamberg K.
      • Vilu R.
      Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
      ,
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      ).
      Figure 2A also shows the prediction that fermentation begins when electron transport chain complexes occupy 8%–9% of the total inner membrane area. If the membrane real estate hypothesis is valid, then why is the saturating electron transport chain occupancy not 100%? First, the integrity of the membrane requires some minimal number of lipid molecules to solvate each protein complex. Second, the cell could not function without additional, non-electron transport chain membrane proteins. To estimate the absolute membrane occupancy of these non-respiratory proteins, we (1) use data from
      • Valgepea K.
      • Adamberg K.
      • Seiman A.
      • Vilu R.
      Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
      to determine relative abundances of non-electron transport chain proteins at each growth rate and (2) use the independent experimental observation that metabolic functions, predominantly electron transport chain, make up roughly one-third of all inner membrane proteins (
      • Papanastasiou M.
      • Orfanoudaki G.
      • Koukaki M.
      • Kountourakis N.
      • Sardis M.F.
      • Aivaliotis M.
      • Karamanou S.
      • Economou A.
      The Escherichia coli peripheral inner membrane proteome.
      ) (Table S1B). Adding this estimate of non-electron transport chain occupancies to the electron transport chain densities in Figure 2A, we determine the membrane crowding for the whole inner membrane proteome, shown in Figure 2B. Like the electron transport chain, total inner membrane crowding appears to reach its limit at a growth rate of roughly 0.3 hr−1, concurrently with the onset of acetate fermentation. This is consistent with the hypothesis that further increases in electron transport chain are limited by membrane crowding.

      Driving Forces of Membrane Crowding

      What is the mechanism by which proteins become crowded within the inner membrane? What drives electron transport chain concentrations to increase with growth rate at slow growth, then reach a plateau at fast growth? Here is the simplest physical mechanism, we believe, that captures the saturating behavior observed experimentally. At slow growth rates, the cell has sufficiently high S/V relative to its metabolic needs that the densities of electron transport chain and other inner membrane proteins can increase with growth rate. However, the densities cannot increase indefinitely, as the increasing steric repulsions between close-packed proteins would limit further protein insertion into the membrane. This simple idea, in which lateral steric repulsion (measured in terms of pressure P) depends on the packing density in the inner membrane, can be expressed by the two-dimensional Carnahan-Starling model (
      • Scalise O.H.
      • Zarragoicoechea G.J.
      • Gonzalez L.E.
      • Silbert M.
      Phase equilibria of the two-dimensional Lennard-Jones fluid: reference systems and perturbation theories.
      ). By representing membrane proteins as sterically repulsive disks in the two dimensions of the membrane, the Carnahan-Starling model predicts that the pressure P grows as
      Pη[1+cη2(1η)2],where c=7343π,
      (Equation 3)


      η is the filling fraction occupied by disks, and c is a packing constant (
      • Scalise O.H.
      • Zarragoicoechea G.J.
      • Gonzalez L.E.
      • Silbert M.
      Phase equilibria of the two-dimensional Lennard-Jones fluid: reference systems and perturbation theories.
      ). Given that the transmembrane regions of proteins are generally smaller and occupy less lateral space than their solvent-exposed domains adjacent to the membrane (e.g., electron transport chain proteins, transporters, and ribosomes docked to translocation machinery), our calculated membrane occupancies can only be related to η up to a multiplicative “bulbosity” factor that accounts for the steric clash of these much larger bulbous outer regions. Here, we want η(P) rather than P(η), so we invert the function above. A similar relation has been used previously to assess membrane curvature due to protein packing in unilamellar vesicles (
      • Stachowiak J.C.
      • Schmid E.M.
      • Ryan C.J.
      • Ann H.S.
      • Sasaki D.Y.
      • Sherman M.B.
      • Geissler P.L.
      • Fletcher D.A.
      • Hayden C.C.
      Membrane bending by protein-protein crowding.
      ,
      • Scheve C.S.
      • Gonzales P.A.
      • Momin N.
      • Stachowiak J.C.
      Steric pressure between membrane-bound proteins opposes lipid phase separation.
      ).
      The Carnahan-Starling model gives an analytical expression for the expected saturation function describing membrane crowding. Like air in a balloon, Equation 3 quantifies the intuition that when few proteins are in the membrane, corresponding to low η, crowding-pressure is very low. As η approaches 1, representing the case where the inner membrane is crammed with proteins, the pressure grows rapidly. Like the balloon, this pressure represents the physical force that would be required to make enough space to insert another protein. In fitting the Carnahan-Starling model to the data, we assume that pressure depends linearly on growth rate.
      Figure 2B displays the two main findings. First, the data are consistent with the Carnahan-Starling model in Equation 3 (cyan curve) for a linear P(λ) relation (inset). Note that P does not go to zero at λ = 0 hr−1, as proteins are constantly being degraded and newly inserted, and thus there is a pressure-producing driving force even in the absence of overall growth (the intercept corresponds to a 20-hr protein half-life, albeit with large uncertainty). Second, the fit predicts that membrane proteins behave sterically like objects that are 3-fold larger than their transmembrane region estimated in this work (the bulbosity factor), thus limiting their maximum membrane occupancy to one-third. This value is plausible, given that the molecular structures of electron transport chain complexes are, on average, estimated to be 2-fold larger outside the membrane than within it (Table S1B). This bulbous nature of membrane proteins could also resolve why the mitochondrial inner membrane, among the most densely packed ever recorded, is estimated to be “only” around 40% protein within the membrane (
      • Schwerzmann K.
      • Cruz-Orive L.M.
      • Eggman R.
      • Sanger A.
      • Weibel E.R.
      Molecular architecture of the inner membrane of mitochondria from rat liver: a combined biochemical and stereological study.
      ). In summary, despite increasing driving forces, steric crowding appears to limit overall inner membrane protein densities, and thus the electron transport chain content, of an E. coli cell. We hope that these intriguing observations will spur future investigations into the nature of these driving forces and their effect on protein insertion.

      Predictions of the Membrane Real Estate Hypothesis

      The [NADH]/[NAD+] Ratio

      What is the signal that initiates overflow metabolism? We believe it to be the [NADH]/[NAD+] redox ratio. This ratio is a critical regulator of cell metabolism (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ) in both single cells (
      • Shen L.C.
      • Atkinson D.E.
      Regulation of pyruvate dehydrogenase from Escherichia coli. Interactions of adenylate energy charge and other regulatory parameters.
      ) and multicellular organisms (
      • Imai S.-I.
      The NAD World 2.0: the importance of the inter-tissue communication mediated by NAMPT/NAD+/SIRT1 in mammalian aging and longevity control.
      ), with changes in the [NADH]/[NAD+] ratio known to be important in both cancer (
      • Vander Heiden M.G.
      • Cantley L.C.
      • Thompson C.B.
      Understanding the Warburg effect: the metabolic requirements of cell proliferation.
      ,
      • Chiarugi A.
      • Dolle C.
      • Felici R.
      • Ziegler M.
      The NAD metabolome—a key determinant of cancer cell biology.
      ,
      • Fan J.
      • Hitosugi T.
      • Chung T.W.
      • Xie J.
      • Ge Q.
      • Gu T.L.
      • Polakiewicz R.D.
      • Chen G.Z.
      • Boggon T.J.
      • Lonial S.
      • et al.
      Tyrosine phosphorylation of lactate dehydrogenase A is important for NADH/NAD(+) redox homeostasis in cancer cells.
      ,
      • Pelicano H.
      • Xu R.H.
      • Du M.
      • Feng L.
      • Sasaki R.
      • Carew J.S.
      • Hu Y.
      • Ramdas L.
      • Hu L.
      • Keating M.J.
      • et al.
      Mitochondrial respiration defects in cancer cells cause activation of Akt survival pathway through a redox-mediated mechanism.
      ) and aging (
      • Imai S.-I.
      The NAD World 2.0: the importance of the inter-tissue communication mediated by NAMPT/NAD+/SIRT1 in mammalian aging and longevity control.
      ). A major role of NADH (the reduced form of NAD+) is to supply electrons to the electron transport chain, driving the production of ATP. The levels of NADH necessary to fuel the electron transport chain are produced in slow-growing cells by glycolysis and the TCA cycle (see the bottom-left cartoon in Figure 3).
      Figure thumbnail gr3
      Figure 3Fermentation Prevents NADH Imbalance
      The concentration of NADH depends on the balance between NADH production via glycolysis, the TCA cycle, acetate fermentation, and biomass production, which scales with cell volume, and the consumption of NADH by the electron transport chain, which scales with cell surface area. At low growth rates (bottom left), sufficient electron transport chain exists to keep the [NADH]/[NAD+] ratio low. At high growth rates, electron transport chain surface limitation would make it impossible to metabolize all of the NADH created, leading to NADH imbalance and potential toxicity due to lack of [NAD+] (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Imai S.-I.
      The NAD World 2.0: the importance of the inter-tissue communication mediated by NAMPT/NAD+/SIRT1 in mammalian aging and longevity control.
      ) (top right; red curve in plot, model). By producing fewer NADH per ATP, fermentation allows the cell to produce sufficient ATP while avoiding NADH imbalance (lower right; experimental points, curve is guide to the eye).
      Consider two possible fast-growth scenarios. First, suppose there were no membrane limitations. With increasing growth rate, higher production of NADH could be matched by increasing electron transport chain concentration. This would allow NADH levels to remain low. However, in cells with surface limitations, while NADH production is proportional to the volume of the cell, the electron transport chain increases only in proportion to the surface area. So at steady state, NADH concentration would rise sharply. The red dashed curve in Figure 3 shows this expectation. However, high concentrations of NADH are toxic to the cell, because it competes for NAD+ binding sites, reducing the activities of many enzymes and causing glycolysis to stop (
      • Houtkooper R.H.
      • Canto C.
      • Wanders R.J.
      • Auwerx J.
      The secret life of NAD+: an old metabolite controlling new metabolic signaling pathways.
      ,
      • Shen L.C.
      • Atkinson D.E.
      Regulation of pyruvate dehydrogenase from Escherichia coli. Interactions of adenylate energy charge and other regulatory parameters.
      ). Hence, under surface limitation, purely oxidative respiration would become toxic at high growth rates (top-right cartoon in Figure 3).
      To quantitatively test the role of surface limitation in controlling NADH levels, we determine the rise of NADH expected for pure respiration, using a simple binding calculation (the red line in Figure 3). We start with the S/V versus growth rate data shown in Figure 1. We assume that electron transport chain densities follow the Carnahan-Starling relation in Figure 2B with a packing limit of approximately 10% of total membrane area, as shown in Figure 2A. Now, if NADH is consumed entirely by the electron transport chain following Michaelis-Menten kinetics (
      • Hayashi M.
      • Miyoshi T.
      • Takashina S.
      • Unemoto T.
      Purification of NADH-ferricyanide dehydrogenase and NADH-quinone reductase from Escherichia coli membranes and their roles in the respiratory chain.
      ), the NADH concentration can be predicted by setting the rate of NADH production equal to its rate of consumption. This gives
      RG[(1ψB)nR+ψBnB]=kNADH[ETC]1+KNADH/[NADH],
      (Equation 4)


      where ψB is the fraction of glucose used for biomass (the remainder used for ATP), nR and nB are the numbers of NADH produced per glucose from respiratory and biomass pathways, respectively, and [ETC] is the concentration of respiratory units per cell volume (Box 1). The maximum rate of NADH consumption per respiratory unit, kNADH, is taken to be the maximum rate of ATP synthesis per ATP synthase (270 ATP/s [
      • Etzold C.
      • DeckersHebestreit G.
      • Altendorf K.
      Turnover number of Escherichia coli f0f1 ATP synthase for ATP synthesis in membrane vesicles.
      ]) divided by the phosphate/oxygen ratio (1.0). KNADH is the Michaelis-Menten binding constant of NADH to NADH dehydrogenase I (NDH-I), described below. Rearranging Equation 4 gives
      [NADH]=KNADH(kNADH[ETC]RG[(1ψB)(nR)+ψBnB]1)1.
      (Equation 5)


      The behavior of the [NADH]/[NAD+] ratio predicted from membrane crowding (Equation 5) is shown by the red curve in Figure 3. This curve is computed using a Michaelis-Menten fit value of KNADH = 74 μM, remarkably close to the experimental estimate of 96.5 μM (
      • Hayashi M.
      • Miyoshi T.
      • Takashina S.
      • Unemoto T.
      Purification of NADH-ferricyanide dehydrogenase and NADH-quinone reductase from Escherichia coli membranes and their roles in the respiratory chain.
      ), given the uncertainly in the underlying parameters. Note that comparison of the [NADH] curve with data on the [NADH]/[NAD+] ratio requires knowledge of [NAD+]. Luckily, [NAD+] has been shown experimentally to be roughly constant across the growth rates studied here (4 mM is used here [
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Andersen K.B.
      • Meyenburg K.V.
      Charges of nicotinamide adenine-nucleotides and adenylate energy-charge as regulatory parameters of metabolism in Escherichia coli.
      ]). This minimalist calculation in Equation 5 indicates that the rise in NADH levels is likely a direct consequence of surface limitation, which forces the onset of fermentation to avoid NADH imbalance that would deplete essential [NAD+] (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Imai S.-I.
      The NAD World 2.0: the importance of the inter-tissue communication mediated by NAMPT/NAD+/SIRT1 in mammalian aging and longevity control.
      ).
      Now, suppose instead that the cell begins to use acetate fermentation when respiration becomes membrane limited, diverting glucose away from the TCA cycle where much of the NADH is made. As a result, acetate fermentation produces fewer NADH per ATP than respiration does, 1-to-1 compared to 2.5-to-1 (Box 1 and Table S1C). The onset of fermentation thus allows the cell to avoid NADH imbalance while generating the ATP necessary to fuel high growth rates (bottom-right cartoon and blue curve in Figure 3). Acetate fermentation has the further advantage of producing more ATP per glucose than other forms of fermentation (
      • Neidhardt F.C.
      • Curtiss R.
      Escherichia coli and Salmonella: Cellular and Molecular Biology.
      ).
      The role of the [NADH]/[NAD+] ratio in controlling the onset of overflow metabolism is supported by its known roles in regulating the activity of several glycolytic and TCA cycle enzymes (
      • Shen L.C.
      • Atkinson D.E.
      Regulation of pyruvate dehydrogenase from Escherichia coli. Interactions of adenylate energy charge and other regulatory parameters.
      ). Further support comes from the observation that the same triggering ratio is reached in both wild-type E. coli and a NOX+ mutant strain expressing a cytosolic NADH-consuming enzyme (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ). This trigger appears to be controlled by the ArcAB system, which is thought to sense and respond to either the [NADH]/[NAD+] ratio or the oxidation state of quinones within the respiratory chain (
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ). Both are expected to respond similarly to the saturating respiratory kinetics modeled here.

      Flexibility of Overflow Metabolism

      The present model makes additional predictions, which could be tested experimentally. If the surface-to-volume ratio is indeed a key factor in the fermentation switch, different organisms or strains having different surface-to-volume ratios should have different fermentation onset points, λferm. We compute the relationship between the onset point and S/V by setting the electron transport chain demand (Equation 2) equal to its maximum membrane occupancy (ETCmax). Solving for λferm gives
      λferm=[1αBfETCkATPAETCETCmax]SV.
      (Equation 6)


      Equation 6 predicts that variation in λferm can arise from two sources: either through cell-level changes in S/V or through changes in the prefactor in brackets. While published data on cell sizes suggest that S/V can vary by a factor of 2 between strains (
      • Woldringh C.L.
      • de Jong M.A.
      • van den Berg W.
      • Koppes L.
      Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.
      ,
      • Volkmer B.
      • Heinemann M.
      Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling.
      ) or within a long-term evolution experiment (
      • Lenski R.E.
      • Travisano M.
      Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial populations.
      ), the variability of the prefactor requires closer attention. First, fundamental costs of biosynthesis (
      • Neidhardt F.C.
      • Curtiss R.
      Escherichia coli and Salmonella: Cellular and Molecular Biology.
      ) would suggest little variation in αB on a given food source. Similarly, the maximum speed of ATP synthase (kATP) is likely to be tightly constrained by evolutionary selection. The greatest sources of variation are thus expected to be the inner membrane's maximum electron transport chain fraction (ETCmax), the electron transport chain surface area per ATP synthase (AETC), and the fraction of ATP produced by the electron transport chain (fETC).
      While determination of the degree of variability in the maximum electron transport chain fraction, ETCmax, will require future experiments, we can estimate the extent of variation allowed in fETC and AETC from existing data. First, the fraction of ATP derived from the electron transport chain (fETC) depends on the number of ATP produced per NADH equivalent. This number, called the phosphate/oxygen (P/O) ratio, is a measure of electron transport chain energy efficiency. If P/O = 1 (1 ATP per NADH), as measured experimentally (
      • Hempfling W.P.
      • Mainzer S.E.
      Effects of varying the carbon source limiting growth on yield and maintenance characteristics of Escherichia coli in continuous culture.
      ), fETC is simply the number of NADH equivalents produced per glucose (11.2; Box 1) divided by the total amount of ATP produced (4 + 11.2), giving fETC = 0.74. For P/O = 2, these numbers would be 22.4 and 26.4, giving fETC = 0.85 (Table S1C). Thus the higher the P/O ratio, the greater the fraction of ATP produced by the electron transport chain. Given that ATP synthase is already working at close to maximum speed at the onset of fermentation (Figure 2A), the required number of electron transport chain units under a fully respiratory metabolism should therefore increase with fETC.
      Second, for AETC, E. coli is known to have isoforms of both NADH dehydrogenase (NDH-I and NDH-II) and the terminal oxidases (Cyo, Cyd-I, and Cyd-II) that have greater speeds per unit membrane area, at the expense of pumping fewer protons and thus producing fewer ATP per NADH (
      • Zhuang K.
      • Vemuri G.N.
      • Mahadevan R.
      Economics of membrane occupancy and respiro-fermentation.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ). In light of our estimate that NADH dehydrogenases and terminal oxidases in total account for roughly half of the electron transport chain's membrane occupancy (Box 1), the fast isoforms are unlikely to increase the surface efficiency of the electron transport chain by more than a factor of two, even if the isoforms were infinitely small or fast (Table S1B). Note that the use of these less efficient isoforms is a major cause for lower P/O ratios; hence fETC and AETC are expected to covary.
      The trade-off in expressing these different electron transport chain isoforms can be seen by defining two types of efficiency: the effectiveness of producing high amounts of ATP from glucose (ATP efficiency) and the effectiveness at utilizing membrane area (surface efficiency). This trade-off is shown as a Pareto surface in Figure 4A (Tables S1B and S1C). Moving toward the upper left the cell gets more ATP per glucose at the expense of lower surface surface efficiency, while moving toward the bottom right gives more efficient usage of membrane space but a lower ATP yield per glucose.
      Figure thumbnail gr4
      Figure 4Efficiency Trade-Offs Are Predicted to Affect the Growth Rate at which Overflow Metabolism Begins
      (A) Isoforms of NADH dehydrogenase (NDH-I and NDH-II) and terminal oxidases (Cyo, Cyd-I, and Cyd-II) give the cell flexibility to adapt the respiratory chain's surface efficiency (ATP/s per membrane area) and ATP efficiency (ATP per acetyl-CoA) along a speed-efficiency Pareto surface. The position along this surface can be defined by the phosphate/oxygen (P/O) ratio, a measure of respiratory efficiency.
      (B) The flexibility in electron transport chain efficiency, when combined with the observed variation in S/V, results in a range of possible growth rates at which the demand for ATP exceeds the electron transport chain's capacity (shaded region). The minimum and maximum P/O ratios of 0.5 and 2 define the right and left boundaries of the allowed region, while the central line shows the demand for the P/O value of 1 observed experimentally (
      • Hempfling W.P.
      • Mainzer S.E.
      Effects of varying the carbon source limiting growth on yield and maintenance characteristics of Escherichia coli in continuous culture.
      ,
      • Farmer I.S.
      • Jones C.W.
      Energetics of Escherichia-coli during aerobic growth in continuous culture.
      ,
      • Noguchi Y.
      • Nakai Y.
      • Shimba N.
      • Toyosaki H.
      • Kawahara Y.
      • Sugimoto S.
      • Suzuki E.
      The energetic conversion competence of Escherichia coli during aerobic respiration studied by 31P NMR using a circulating fermentation system.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ) and used in this work. Likewise, the S/V values in (among the largest measured) and double this value (among the smallest [
      • Woldringh C.L.
      • de Jong M.A.
      • van den Berg W.
      • Koppes L.
      Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.
      ]) constrain the electron transport chain capacities to the lower and upper boundaries of the shaded region. This region predicts the range of growth rates λferm at which overflow metabolism is expected to begin. This flexibility may underlie the large variation in λferm observed experimentally (yellow triangles) (
      • Meyer H.-P.
      • Leist C.
      • Fiechter A.
      Acetate formation in continuous culture of Escherichia coli K12 d1 on defined and complex media.
      ,
      • Holms H.
      Flux analysis and control of the central metabolic pathways in Escherichia coli.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ,
      • Nanchen A.
      • Schicker A.
      • Sauer U.
      Nonlinear dependency of intracellular fluxes on growth rate in miniaturized continuous cultures of Escherichia coli.
      ,
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Nahku R.
      • Valgepea K.
      • Lahtvee P.J.
      • Erm S.
      • Abner K.
      • Adamberg K.
      • Vilu R.
      Specific growth rate dependent transcriptome profiling of Escherichia coli K12 MG1655 in accelerostat cultures.
      ,
      • Peebo K.
      • Valgepea K.
      • Maser A.
      • Nahku R.
      • Adamberg K.
      • Vilu R.
      Proteome reallocation in Escherichia coli with increasing specific growth rate.
      ,
      • Ishii N.
      • Nakahigashi K.
      • Baba T.
      • Robert M.
      • Soga T.
      • Kanai A.
      • Hirasawa T.
      • Naba M.
      • Hirai K.
      • Hoque A.
      Multiple high-throughput analyses monitor the response of E-coli to perturbations.
      ,
      • Renilla S.
      • Bernal V.
      • Fuhrer T.
      • Castano-Cerezo S.
      • Pastor J.M.
      • Iborra J.L.
      • Sauer U.
      • Canovas M.
      Acetate scavenging activity in Escherichia coli: interplay of acetyl-CoA synthetase and the PEP-glyoxylate cycle in chemostat cultures.
      ,
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ) and makes a prediction for the phenotype of three strains that do not ferment (blue diamonds) (
      • Monk J.M.
      • Koza A.
      • Campodonico M.A.
      • Machado D.
      • Seoane J.M.
      • Palsson B.O.
      • Herrgård M.J.
      • Feist A.M.
      Multi-omics quantification of species variation of Escherichia coli links molecular features with strain phenotypes.
      ).
      By changing its position along this Pareto surface, a cell can alter its fermentation onset point, as shown by Equation 6. This may have enabled the large variation in published values of λferm to evolve (
      • Meyer H.-P.
      • Leist C.
      • Fiechter A.
      Acetate formation in continuous culture of Escherichia coli K12 d1 on defined and complex media.
      ,
      • Holms H.
      Flux analysis and control of the central metabolic pathways in Escherichia coli.
      ,
      • Feist A.M.
      • Henry C.S.
      • Reed J.L.
      • Krummenacker M.
      • Joyce A.R.
      • Karp P.D.
      • Broadbelt L.J.
      • Hatzimanikatis V.
      • Palsson B.Ø.
      A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
      ,
      • Nanchen A.
      • Schicker A.
      • Sauer U.
      Nonlinear dependency of intracellular fluxes on growth rate in miniaturized continuous cultures of Escherichia coli.
      ,
      • Vemuri G.N.
      • Altman E.
      • Sangurdekar D.P.
      • Khodursky A.B.
      • Eiteman M.A.
      Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
      ,
      • Nahku R.
      • Valgepea K.
      • Lahtvee P.J.
      • Erm S.
      • Abner K.
      • Adamberg K.
      • Vilu R.
      Specific growth rate dependent transcriptome profiling of Escherichia coli K12 MG1655 in accelerostat cultures.
      ,
      • Peebo K.
      • Valgepea K.
      • Maser A.
      • Nahku R.
      • Adamberg K.
      • Vilu R.
      Proteome reallocation in Escherichia coli with increasing specific growth rate.
      ,
      • Ishii N.
      • Nakahigashi K.
      • Baba T.
      • Robert M.
      • Soga T.
      • Kanai A.
      • Hirasawa T.
      • Naba M.
      • Hirai K.
      • Hoque A.
      Multiple high-throughput analyses monitor the response of E-coli to perturbations.
      ,
      • Renilla S.
      • Bernal V.
      • Fuhrer T.
      • Castano-Cerezo S.
      • Pastor J.M.
      • Iborra J.L.
      • Sauer U.
      • Canovas M.
      Acetate scavenging activity in Escherichia coli: interplay of acetyl-CoA synthetase and the PEP-glyoxylate cycle in chemostat cultures.
      ,
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ,
      • Monk J.M.
      • Koza A.
      • Campodonico M.A.
      • Machado D.
      • Seoane J.M.
      • Palsson B.O.
      • Herrgård M.J.
      • Feist A.M.
      Multi-omics quantification of species variation of Escherichia coli links molecular features with strain phenotypes.
      ). By inserting the range of possible values of fETC and AETC into ETCdemand, together with the experimental range of S/V, Equation 6 allows us to predict the range of possible values of λferm that different strains could explore. Not only does the predicted range, shown by the shaded region in Figure 4B, capture the inter-strain variability in λferm (triangles), it also makes a statement about three exceptions. A recent study of different E. coli strains found that three do not ferment, even at the fastest growth rates on glucose minimal medium (
      • Monk J.M.
      • Koza A.
      • Campodonico M.A.
      • Machado D.
      • Seoane J.M.
      • Palsson B.O.
      • Herrgård M.J.
      • Feist A.M.
      Multi-omics quantification of species variation of Escherichia coli links molecular features with strain phenotypes.
      ) (diamonds in Figure 4B). From molecular data, our model suggests that these strains are at the edge of the possible onset region. By residing at the right corner of the shaded region, our model makes the further predictions that these strains, together with those possessing very high λferm, must rely heavily on the fast, inefficient isoforms of the electron transport chain, have low P/O ratios, and be small in size, permitting large S/V.
      The shaded region can also be shifted by other means. Overexpression of non-respiratory inner membrane proteins is predicted to move this shaded region by effectively decreasing the available S/V. This causes fermentation to be triggered at lower growth rates, as observed experimentally (
      • Wagner S.
      • Baars L.
      • Ytterberg A.J.
      • Klussmeier A.
      • Wagner C.S.
      • Nord O.
      • Nygren P.A.
      • van Wijk K.J.
      • de Gier J.-W.
      Consequences of membrane protein overexpression in Escherichia coli.
      ). A key prediction that distinguishes the membrane real estate hypothesis from other models (
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ) is that it predicts that λferm is more sensitive to the overexpression of “dummy” proteins that reside in the inner membrane rather than the cytosol, as the former directly competes with the electron transport chain for membrane space. Unfortunately, aggregation and membrane leakage have made verification of this prediction experimentally challenging (
      • Wagner S.
      • Baars L.
      • Ytterberg A.J.
      • Klussmeier A.
      • Wagner C.S.
      • Nord O.
      • Nygren P.A.
      • van Wijk K.J.
      • de Gier J.-W.
      Consequences of membrane protein overexpression in Escherichia coli.
      ). Nonetheless, we hope that the model's targeted predictions motivate future experimental testing.
      Finally, why did E. coli not evolve a larger S/V ratio? We do not know, but several lines of evidence suggest that larger S/V surely has fitness penalties too. First, it has been estimated that E. coli spends up to half of its energy maintaining ion gradients across a leaky inner membrane (
      • Stouthamer A.H.
      • Bettenhaussen C.W.
      A continuous culture study of an ATPase-negative mutant of Escherichia coli.
      ), with this leakiness plausibly increasing as S/V. Second, surface structures account for roughly one-third of E. coli's dry mass, consisting of inner and outer membrane proteins, lipids, and carbohydrates, much greater than the 1%–2% of dry mass in electron transport chain (
      • Neidhardt F.C.
      • Curtiss R.
      Escherichia coli and Salmonella: Cellular and Molecular Biology.
      ,
      • Basan M.
      • Hui S.
      • Okano H.
      • Zhang Z.
      • Shen Y.
      • Williamson J.R.
      • Hwa T.
      Overflow metabolism in Escherichia coli results from efficient proteome allocation.
      ). Thus, if the inner membrane does indeed reach its protein packing limit, as our analysis suggests, it follows that any increases in S/V for the purpose of increased respiration comes at a cost many times greater than just the synthesis of the electron transport chain. Such considerations imply that E. coli's S/V constrains its respiration, rather than the reverse.

      Conclusions

      We have explored here how physical properties of proteins constrain bacterial “decisions” about how best to generate energy. E. coli and other cells use inefficient metabolism when growing fast. Even when oxygen is present, cells switch from respiration (which is ATP-efficient) to using fermentation for additional ATP (which is ATP-inefficient). What is the fundamental cause of this puzzling switching? We make numerical estimates indicating that this behavior is consistent with limitations in membrane surface area. For sufficiently fast growth, the ATP demands of the cell exceed the available membrane space to house respiratory complexes. This limitation requires that additional ATP be produced through acetate fermentation, as this produces several-fold more ATP per unit membrane area. This membrane real estate hypothesis is consistent with multiple lines of evidence, including the observation that both membrane protein packing and electron transport chain kinetics reach their respective limits concurrently with the onset of fermentation. Furthermore, the membrane real estate hypothesis suggests that the sharp rise in the [NADH]/[NAD+] ratio at the onset of overflow metabolism is the direct result of surface limitation and acts as a signal that triggers overflow metabolism to avoid NADH imbalance. The onset of fermentation thus serves as an example of how a cell's behavior and evolution are limited by the physical sizes and shapes of its proteins.

      Acknowledgments

      We appreciate the support of the Laufer Center for Physical and Quantitative Biology . We thank Ron Milo, Jorg Schwender, Gabor Balazsi, Dan Bogenhagen, Arijit Maitra, and Purushottam Dixit for very helpful comments.

      Supplemental Information

      References

        • Alberts B.
        • Johnson A.
        • Lewis J.
        • Raff M.
        • Roberts K.
        • Walter P.
        Molecular Biology of the Cell.
        Fourth Edition. Garland Science, 2002
        • Andersen K.B.
        • Meyenburg K.V.
        Charges of nicotinamide adenine-nucleotides and adenylate energy-charge as regulatory parameters of metabolism in Escherichia coli.
        J. Biol. Chem. 1977; 252: 4151-4156
        • Andersen K.B.
        • Meyenburg K.V.
        Are growth-rates of Escherichia coli in batch cultures limited by respiration.
        J. Bacteriol. 1980; 144: 114-123
        • Basan M.
        • Hui S.
        • Okano H.
        • Zhang Z.
        • Shen Y.
        • Williamson J.R.
        • Hwa T.
        Overflow metabolism in Escherichia coli results from efficient proteome allocation.
        Nature. 2015; 528: 99-104
        • Chiarugi A.
        • Dolle C.
        • Felici R.
        • Ziegler M.
        The NAD metabolome—a key determinant of cancer cell biology.
        Nat. Rev. Cancer. 2012; 12: 741-752
        • Etzold C.
        • DeckersHebestreit G.
        • Altendorf K.
        Turnover number of Escherichia coli f0f1 ATP synthase for ATP synthesis in membrane vesicles.
        Eur. J. Biochem. 1997; 243: 336-343
        • Fan J.
        • Hitosugi T.
        • Chung T.W.
        • Xie J.
        • Ge Q.
        • Gu T.L.
        • Polakiewicz R.D.
        • Chen G.Z.
        • Boggon T.J.
        • Lonial S.
        • et al.
        Tyrosine phosphorylation of lactate dehydrogenase A is important for NADH/NAD(+) redox homeostasis in cancer cells.
        Mol. Cell. Biol. 2011; 31: 4938-4950
        • Farmer I.S.
        • Jones C.W.
        Energetics of Escherichia-coli during aerobic growth in continuous culture.
        Eur. J. Biochem. 1976; 67: 115-122
        • Feist A.M.
        • Henry C.S.
        • Reed J.L.
        • Krummenacker M.
        • Joyce A.R.
        • Karp P.D.
        • Broadbelt L.J.
        • Hatzimanikatis V.
        • Palsson B.Ø.
        A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information.
        Mol. Syst. Biol. 2007; 3: 121
        • Flamholz A.
        • Noor E.
        • Bar-Even A.
        • Liebermeister W.
        • Milo R.
        Glycolytic strategy as a tradeoff between energy yield and protein cost.
        Proc. Natl. Acad. Sci. USA. 2013; 110: 10039-10044
        • Hayashi M.
        • Miyoshi T.
        • Takashina S.
        • Unemoto T.
        Purification of NADH-ferricyanide dehydrogenase and NADH-quinone reductase from Escherichia coli membranes and their roles in the respiratory chain.
        Biochim. Biophys. Acta. 1989; 977: 62-69
        • Hempfling W.P.
        • Mainzer S.E.
        Effects of varying the carbon source limiting growth on yield and maintenance characteristics of Escherichia coli in continuous culture.
        J. Bacteriol. 1975; 123: 1076-1087
        • Holms H.
        Flux analysis and control of the central metabolic pathways in Escherichia coli.
        FEMS Microbiol. Rev. 1996; 19: 85-116
        • Houtkooper R.H.
        • Canto C.
        • Wanders R.J.
        • Auwerx J.
        The secret life of NAD+: an old metabolite controlling new metabolic signaling pathways.
        Endocr. Rev. 2010; 31: 194-223
        • Imai S.-I.
        The NAD World 2.0: the importance of the inter-tissue communication mediated by NAMPT/NAD+/SIRT1 in mammalian aging and longevity control.
        NPJ Syst. Biol. Appl. 2016; 2: 16018
        • Ishii N.
        • Nakahigashi K.
        • Baba T.
        • Robert M.
        • Soga T.
        • Kanai A.
        • Hirasawa T.
        • Naba M.
        • Hirai K.
        • Hoque A.
        Multiple high-throughput analyses monitor the response of E-coli to perturbations.
        Science. 2007; 316: 593-597
        • Jeckelmann J.M.
        • Harder D.
        • Mari S.A.
        • Meury M.
        • Ucurum Z.
        • Muller D.J.
        • Erni B.
        • Fotiadis D.
        Structure and function of the glucose PTS transporter from Escherichia coli.
        J. Struct. Biol. 2011; 176: 395-403
        • Kayser A.
        • Weber J.
        • Hecht V.
        • Rinas U.
        Metabolic flux analysis of Escherichia coli in glucose-limited continuous culture. I. Growth-rate-dependent metabolic efficiency at steady state.
        Microbiology. 2005; 151: 693-706
        • Koch A.L.
        • Wang C.H.
        How close to the theoretical diffusion limit do bacterial uptake systems function?.
        Arch. Microbiol. 1982; 131: 36-42
        • Kojima S.
        • Nikaido H.
        Permeation rates of penicillins indicate that Escherichia coli porins function principally as nonspecific channels.
        Proc. Natl. Acad. Sci. USA. 2013; 110: E2629-E2634
        • Lenski R.E.
        • Travisano M.
        Dynamics of adaptation and diversification: a 10,000-generation experiment with bacterial populations.
        Proc. Natl. Acad. Sci. USA. 1994; 91: 6808-6814
        • Meyer H.-P.
        • Leist C.
        • Fiechter A.
        Acetate formation in continuous culture of Escherichia coli K12 d1 on defined and complex media.
        J. Biotechnol. 1984; 1: 355-358
        • Molenaar D.
        • van Berlo R.
        • de Ridder D.
        • Teusink B.
        Shifts in growth strategies reflect tradeoffs in cellular economics.
        Mol. Syst. Biol. 2009; 5: 323
        • Monk J.M.
        • Koza A.
        • Campodonico M.A.
        • Machado D.
        • Seoane J.M.
        • Palsson B.O.
        • Herrgård M.J.
        • Feist A.M.
        Multi-omics quantification of species variation of Escherichia coli links molecular features with strain phenotypes.
        Cell Syst. 2016; 3: 238-251
        • Monod J.
        The growth of bacterial cultures.
        Annu. Rev. Microbiol. 1949; 3: 371-394
        • Nahku R.
        • Valgepea K.
        • Lahtvee P.J.
        • Erm S.
        • Abner K.
        • Adamberg K.
        • Vilu R.
        Specific growth rate dependent transcriptome profiling of Escherichia coli K12 MG1655 in accelerostat cultures.
        J. Biotechnol. 2010; 145: 60-65
        • Nanchen A.
        • Schicker A.
        • Sauer U.
        Nonlinear dependency of intracellular fluxes on growth rate in miniaturized continuous cultures of Escherichia coli.
        Appl. Environ. Microbiol. 2006; 72: 1164-1172
        • Neidhardt F.C.
        • Curtiss R.
        Escherichia coli and Salmonella: Cellular and Molecular Biology.
        Second Edition. ASM Press, 1996
        • Nikaido H.
        • Rosenberg E.Y.
        Effect on solute size on diffusion rates through the transmembrane pores of the outer membrane of Escherichia coli.
        J. Gen. Physiol. 1981; 77: 121-135
        • Nikaido H.
        • Rosenberg E.Y.
        Porin channels in Escherichia coli: studies with liposomes reconstituted from purified proteins.
        J. Bacteriol. 1983; 153: 241-252
        • Noguchi Y.
        • Nakai Y.
        • Shimba N.
        • Toyosaki H.
        • Kawahara Y.
        • Sugimoto S.
        • Suzuki E.
        The energetic conversion competence of Escherichia coli during aerobic respiration studied by 31P NMR using a circulating fermentation system.
        J. Biochem. 2004; 136: 509-515
        • Noor E.
        • Bar-Even A.
        • Flamholz A.
        • Reznik E.
        • Liebermeister W.
        • Milo R.
        Pathway thermodynamics highlights kinetic obstacles in central metabolism.
        PLoS Comput. Biol. 2014; 10: e1003483
        • O’Brien E.J.
        • Lerman J.A.
        • Chang R.L.
        • Hyduke D.R.
        • Palsson B.O.
        Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction.
        Mol. Syst. Biol. 2013; 9: 693
        • Osborn M.J.
        • Rothfield L.
        Cell shape determination in Escherichia coli.
        Curr. Opin. Microbiol. 2007; 10: 606-610
        • Papanastasiou M.
        • Orfanoudaki G.
        • Koukaki M.
        • Kountourakis N.
        • Sardis M.F.
        • Aivaliotis M.
        • Karamanou S.
        • Economou A.
        The Escherichia coli peripheral inner membrane proteome.
        Mol. Cell. Proteomics. 2013; 12: 599-610
        • Peebo K.
        • Valgepea K.
        • Maser A.
        • Nahku R.
        • Adamberg K.
        • Vilu R.
        Proteome reallocation in Escherichia coli with increasing specific growth rate.
        Mol. Biosyst. 2015; 11: 1184-1193
        • Pelicano H.
        • Xu R.H.
        • Du M.
        • Feng L.
        • Sasaki R.
        • Carew J.S.
        • Hu Y.
        • Ramdas L.
        • Hu L.
        • Keating M.J.
        • et al.
        Mitochondrial respiration defects in cancer cells cause activation of Akt survival pathway through a redox-mediated mechanism.
        J. Cell Biol. 2006; 175: 913-923
        • Renilla S.
        • Bernal V.
        • Fuhrer T.
        • Castano-Cerezo S.
        • Pastor J.M.
        • Iborra J.L.
        • Sauer U.
        • Canovas M.
        Acetate scavenging activity in Escherichia coli: interplay of acetyl-CoA synthetase and the PEP-glyoxylate cycle in chemostat cultures.
        Appl. Microbiol. Biotechnol. 2012; 93: 2109-2124
        • Renkin E.M.
        Filtration, diffusion, and molecular sieving through porous cellulose membranes.
        J. Gen. Physiol. 1954; 38: 225-243
        • Scalise O.H.
        • Zarragoicoechea G.J.
        • Gonzalez L.E.
        • Silbert M.
        Phase equilibria of the two-dimensional Lennard-Jones fluid: reference systems and perturbation theories.
        Mol. Phys. 1998; 93: 751-755
        • Scheve C.S.
        • Gonzales P.A.
        • Momin N.
        • Stachowiak J.C.
        Steric pressure between membrane-bound proteins opposes lipid phase separation.
        J. Am. Chem. Soc. 2013; 135: 1185-1188
        • Schwerzmann K.
        • Cruz-Orive L.M.
        • Eggman R.
        • Sanger A.
        • Weibel E.R.
        Molecular architecture of the inner membrane of mitochondria from rat liver: a combined biochemical and stereological study.
        J. Cell Biol. 1986; 102: 97-103
        • Shen L.C.
        • Atkinson D.E.
        Regulation of pyruvate dehydrogenase from Escherichia coli. Interactions of adenylate energy charge and other regulatory parameters.
        J. Biol. Chem. 1970; 245: 5974-5978
        • Stachowiak J.C.
        • Schmid E.M.
        • Ryan C.J.
        • Ann H.S.
        • Sasaki D.Y.
        • Sherman M.B.
        • Geissler P.L.
        • Fletcher D.A.
        • Hayden C.C.
        Membrane bending by protein-protein crowding.
        Nat. Cell Biol. 2012; 14: 944-949
        • Stouthamer A.H.
        • Bettenhaussen C.W.
        A continuous culture study of an ATPase-negative mutant of Escherichia coli.
        Arch. Microbiol. 1977; 113: 185-189
        • Valgepea K.
        • Adamberg K.
        • Vilu R.
        Decrease of energy spilling in Escherichia coli continuous cultures with rising specific growth rate and carbon wasting.
        BMC Syst. Biol. 2011; 5: 106
        • Valgepea K.
        • Adamberg K.
        • Seiman A.
        • Vilu R.
        Escherichia coli achieves faster growth by increasing catalytic and translation rates of proteins.
        Mol. Biosyst. 2013; 9: 2344-2358
        • Vander Heiden M.G.
        • Cantley L.C.
        • Thompson C.B.
        Understanding the Warburg effect: the metabolic requirements of cell proliferation.
        Science. 2009; 324: 1029-1033
        • van Rijsewijk B.
        • Nanchen A.
        • Nallet S.
        • Kleijn R.J.
        • Sauer U.
        Large-scale C-13-flux analysis reveals distinct transcriptional control of respiratory and fermentative metabolism in Escherichia coli.
        Mol. Syst. Biol. 2011; 7: 477
        • Vazquez A.
        • Beg Q.K.
        • Demenezes M.A.
        • Ernst J.
        • Bar-Joseph Z.
        • Barabasi A.-L.
        • Boros L.G.
        • Oltvai Z.N.
        Impact of the solvent capacity constraint on E. coli metabolism.
        BMC Syst. Biol. 2008; 2: 7
        • Vazquez A.
        • Liu J.
        • Zhou Y.
        • Oltvai Z.N.
        Catabolic efficiency of aerobic glycolysis: the Warburg effect revisited.
        BMC Syst. Biol. 2010; 4: 58
        • Vemuri G.N.
        • Altman E.
        • Sangurdekar D.P.
        • Khodursky A.B.
        • Eiteman M.A.
        Overflow metabolism in Escherichia coli during steady-state growth: transcriptional regulation and effect of the redox ratio.
        Appl. Environ. Microbiol. 2006; 72: 3653-3661
        • Volkmer B.
        • Heinemann M.
        Condition-dependent cell volume and concentration of Escherichia coli to facilitate data conversion for systems biology modeling.
        PLoS One. 2011; 6: e23126
        • Wagner S.
        • Baars L.
        • Ytterberg A.J.
        • Klussmeier A.
        • Wagner C.S.
        • Nord O.
        • Nygren P.A.
        • van Wijk K.J.
        • de Gier J.-W.
        Consequences of membrane protein overexpression in Escherichia coli.
        Mol. Cell. Proteomics. 2007; 6: 1527-1550
        • Woldringh C.L.
        • de Jong M.A.
        • van den Berg W.
        • Koppes L.
        Morphological analysis of the division cycle of two Escherichia coli substrains during slow growth.
        J. Bacteriol. 1977; 131: 270-279
        • Zhuang K.
        • Vemuri G.N.
        • Mahadevan R.
        Economics of membrane occupancy and respiro-fermentation.
        Mol. Syst. Biol. 2011; 7: 500