A theoretical study on the amount of ATP required for synthesis of microbial cell material

Adaptation games between microorganisms sharing a common substrate niche

Microorganisms adapt their enzymic outfit to the ambient substrate supply. If several species compete for a limiting substrate, then reciprocal influence on the state of adaptation results, which has been envisaged in the paper as strategic game. The most important types of strategies, which are assessed by the governing selection rule, are called aggressive, neutral and cooperative. A cooperative strategy brings the highest advantage, but triggers the temptation to increase the gain by defection. The neutral strategy, i.e. acting as if the competitor were alone in the medium, is promising only when the selection rule favours product maximization, whereas as aggressive strategy, e.g. maximizing the difference between own and foreign profit, is most effective on growth rate maximization as selection criterion. Gruelling competition reduces the metabolic output and weakens the community as a whole against other systems.

The bioenergetics of methanogenesis

The reduction of CO2 or any other methanogenic substrate to methane serves the same function as the reduction of oxygen, nitrate or sulfate to more reduced products. These exergonic reactions are coupled to the production of usable energy generated through a charge separation and a protonmotive-force-driven ATPase. For the understanding of how methanogens derive energy from C-1 unit reduction one must study the biochemistry of the chemical reactions involved and how these are coupled to the production of a charge separation and subsequent electron transport phosphorylation. Data on methanogenesis by a variety of organisms indicates ubiquitous use of CH3-S-CoM as the final electron acceptor in the production of methane through the methyl CoM reductase and of 5-deazaflavin as a primary source of reducing equivalents. Three known enzymes serve as catalysts in the production of reduced 5-deazaflavin: hydrogenase, formate dehydrogenase and CO dehydrogenase. All three are potential candidates for proton pumps. In the organisms that must oxidize some of their substrate to obtain electrons for the reduction of another portion of the substrate to methane (e.g., those using formate, methanol or acetate), the latter two enzymes may operate in the oxidizing direction. CO2 is the most frequent substrate for methanogenesis but is the only substrate that obligately requires the presence of H2 and hydrogenase. Growth on methanol requires a B12-containing methanol-CoM methyl transferase and does not necessarily need any other methanogenic enzymes besides the methyl-CoM reductase system when hydrogenase is present. When bacteria grow on methanol alone it is not yet clear if they get their reducing equivalents from a reversal of methanogenic enzymes, thus oxidizing methyl groups to CO2. An alternative (since these and acetate-catabolizing methanogens possess cytochrome b) is electron transport and possible proton pumping via a cytochrome-containing electron transport chain. Several of the actual components of the methanogenic pathway from CO2 have been characterized. Methanofuran is apparently the first carbon-carrying cofactor in the pathway, forming carboxy-methanofuran. Formyl-FAF or formyl-methanopterin (YFC, a very rapidly labelled compound during 14C pulse labeling) has been implicated as an obligate intermediate in methanogenesis, since methanopterin or FAF is an essential component of the carbon dioxide reducing factor in dialyzed extract methanogenesis. FAF also carries the carbon at the methylene and methyl oxidation levels.(ABSTRACT TRUNCATED AT 400 WORDS)

Compositions and characteristics of strains of Streptococcus bovis

Streptococcus bovis strains JB1, 26, 581AXY2, 21096C, and 45S1 grew on glucose, maltose, starch, sucrose, cellobiose, and lactose. None of these strains grew on xylose or ribose, but arabinose was a suitable energy source for strains 2109C and K27FF4. All strains grew at 45 degrees C, but incubation at 50 degrees C prevented growth. Growth was permitted in 2% sodium chloride, but 6.5% sodium chloride was inhibitory. Doubling times ranged from 24 to 27 min, and final pH on glucose was approximately 4.6. None of the strains had a requirement for amino acids, and growth was rapid in media containing glucose salts and B vitamins. There was no ammonia production from arginine. All strains showed aminoendopeptidase activity, but there was considerable strain variation. Strain 7H4, reported as Streptococcus bovis, was noticeably different from the other six strains. It had a doubling time that was more than four times as long, and it grew poorly on starch or in the absence of an amino acid source. Six-and-a-half percent sodium chloride was not inhibitory, and it produced ammonia from arginine. Cell morphology was coccoid rather than ovoid. Based on these criteria, classification of strain 7H4 as Streptococcus bovis seemed doubtful. Other experiments with strain 7H4 indicated that Streptococcus bovis was devoid of diaminopimelic acid. In these experiments strain 7H4 contained significant diaminopimelic acid. The six Streptococcus bovis strains all contained diaminopimelic acid as well, but concentration varied.

Fermentation of Peptides by Bacteroides ruminicola B 1 4

The maximum growth rate of Bacteroides ruminicola B 1 4 was significantly improved when either Trypticase or acetate and C 4 -C 5 fatty acids were added to defined medium containing macrominerals, microminerals, vitamins, hemin, cysteine hydrochloride, and glucose. The organism was unable to grow with peptides as the sole energy source, but growth yields from glucose were significantly improved when Trypticase was added to batch cultures containing basal medium, acetate, and C 4 -C 5 volatile fatty acids. During periods of rapid growth, very little peptide was deaminated to ammonia, but after growth ceased there was a linear increase in ammonia. Fifteen grams of Trypticase per liter resulted in maximum ammonia production. In glucose-limited chemostats, ammonia production from peptides was inversely proportional to the dilution rate, and 87% of the variation in ammonia production could be explained by retention time in the culture vessel. Chemostats receiving Trypticase had higher theoretical maximum growth yields and lower maintenance energy expenditures than similar cultures not receiving peptide. Cells from the Trypticase cultures contained more carbohydrate, and this difference was most evident at rapid dilution rates. When corrections were made for cell composition and the amount of peptides that were fermented, it appeared that peptide carbon skeletons could be used for maintenance energy. B. ruminicola B 1 4 was unable to grow on peptides alone because it was unable to utilize peptides at a fast enough rate to meet its maintenance requirement.

The influence of the cost of growth on ectotherm metabolism

A new model of ectothermic growth and metabolism is proposed. This model differs from most earlier models in representing explicitly the contribution of the "cost of growth" to ectotherm metabolism. It is shown that the cost of growth may constitute between 17 and 29% of the metabolism of an "average" ectotherm population. Furthermore, the metabolism of an "average" growing ectotherm may be between 40 and 79% greater than that of a non-growing ectotherm. As many environmental factors induce changes in metabolic rates of this magnitude, it is suggested that many factors which cause changes in metabolic rates do so indirectly by altering growth rates. In particular, it is suggested that body size, food availability and temperature often indirectly influence metabolic rates through their effects on growth rates, rather than by directly determining metabolic rates as has usually been assumed.

Thermodynamic efficiency of microbial growth is low but optimal for maximal growth rate

Thermodynamic efficiency of microbial growth on substrates that are more oxidized than biomass approaches 24%. This is the theoretical value for a linear energy converter optimized for maximal output flow at optimal efficiency. For growth on substrates more reduced than biomass, thermodynamic efficiencies correspond to those predicted for optimization to maximal growth rate (or yield) only.

Thermodynamics of growth. Non-equilibrium thermodynamics of bacterial growth. The phenomenological and the mosaic approach

Microbial growth is analyzed in terms of mosaic and phenomenological non-equilibrium thermodynamics. It turns out that already existing parameters devised to measure bacterial growth, such as YATP, mu, and Q substrate, have as thermodynamic equivalents flow ratio, output flow and input flow. With this characterisation it becomes possible to apply much of the already existing knowledge of phenomenological non-equilibrium thermodynamics to bacterial growth. One of the conclusions is that the frequent observation that YATP is only 50% of its theoretical maximum does not mean that the microbe corresponds to a thermodynamic system that has been optimized for maximal output power, as has been suggested. Rather, at least in some cases, it corresponds to a system that has been optimized towards maximum growth rate. When the degree of reduction of the (single) carbon source is significantly smaller than that of the biomass produced, the efficiency of biomass synthesis has been kept as high (i.e., about 24%) as is consistent with maximization of the growth rate at optimal efficiency. Mosaic thermodynamics allows an analysis of processes which in microbial metabolism may be responsible for any particular growth behaviour. Equations are derived that predict the effect of uncoupling through leaks, futile cycling, or 'slip' on microbial growth. It turns out that uncoupling is expected to affect both the growth rate-independent and the growth rate-dependent 'maintenance coefficient'. The effect on the latter is different when catabolic substrate limits growth than when anabolic substrate limits growth. In the latter case, the growth rate-dependent maintenance coefficient is negative. It is concluded that mosaic non-equilibrium thermodynamics will be a powerful theoretical tool especially in future experimental analyses of the metabolic basis for microbial growth characteristics and growth regulation.

Biochemistry of the chemolithotrophic oxidation of inorganic sulphur

A historical review is presented of the elucidation of the mechanisms of oxidation of inorganic sulphur compounds and of electron transport in the thiobacilli. A unitary mechanism, consistent with current knowledge, is proposed. The significance of polythionates is discussed. The relations between oxidation mechanisms, substrate-level and electron transport-dependent phosphorylation, energy-dependent NAD+ reduction and efficiency of growth are assessed in order to evaluate the efficiency of energy conservation in different species. The unresolved problems are identified for the benefit of those planning further assaults on the last redoubts of the thiobacilli.

Microbial ecology and activities in the rumen: part 1

This review describes the progress which has been made during the last 10 to 15 years in the field of rumen microbiology. It is basically an account of new discoveries in the bacteriology, protozoology, biochemistry, and ecology of the rumen microbial population. As such it covers a wide range of subjects including the isolation and properties of methanogenic bacteria, the role of rumen phycomycete fungi, anaerobic energy conservation, and general metabolic aspects of rumen microorganisms. It also attempts, however, to describe and develop new concepts in rumen microbiology. These consist principally of interactions of the microbemicrobe, microbe-food and microbe-host types, and represent the main areas of recent advance in our understanding of the rumen ecosystem. The development of experimental techniques such as chemostat culture and scanning electron microscopy are shown to have been instrumental in progress in these areas. The paper is concluded with an assessment of our present knowledge of the rumen fermentation, based on the degree of success of experiments with gnotobiotic ruminants inoculated with defined flora and in mathematical modeling of the fermentation. The efficacy of chemical manipulation of the fermentation in ruminant is also discussed in this light.

Microcalorimetric studies of the growth of sulfate-reducing bacteria: comparison of the growth parameters of some Desulfovibrio species

We performed a comparative study of the growth energetics of some species of Desulfovibrio by measuring microcalorimetric and molar growth yield values. Lactate and pyruvate were used as energy sources for sulfate reduction. On lactate-sulfate media Desulfovibrio desulfuricans Norway, Desulfovibrio gigas, and Desulfovibrio africanus exhibited molar growth yields of 4.1 +/- 0.6, 3.7 +/- 1.7, and 1.8 +/- 0.1 g/mol, respectively, whereas on pyruvate-sulfate media the molar growth yields were higher (8.5 +/- 0.8, 7.7 +/- 1.6, and 3.5 +/- 0.5 g/mol, respectively). Thus, we found that D. africanus was the least efficient species in converting energy into cell material. The uncoupling of energy in this strain was obvious since its catabolic activities were high compared with those of the two other strains. The enthalpy changes associated with lactate and pyruvate metabolism were -49 +/- 0.7 and -70.2 +/- 6.0 jK/mol, respectively, for D. desulfuricans, -76.6 +/- 1.8 and -91.2 +/- 1.1 kJ/mol, respectively, for D. gigas, and -78.8 +/- 7.2 and -88.0 +/- 6.2 kJ/mol, respectively, for D. africanus. D. gigas and D. africanus produced only acetate, CO2 and hydrogen sulfide as metabolic end products. In addition to these normal end products, D. desulfuricans Norway produced a small amount of butanol. This butanol production was interpreted as reflecting a regulatory system of electron flow during the catabolism of both substrates. Such metabolism was comparable to that reported for D. vulgaris, which lost part of the reducing power of its energy sources through hydrogen evolution.

Effect of inorganic sulfide on the growth and metabolism of Methanosarcina barkeri strain DM

Minimal growth of Methanosarcina barkeri strain DM occurred when sulfide was omitted fromthe growth medium, and addition of either sodium sulfate or coenzyme M to sulfide-depleted media failed to restore growth. Optimal growth occurred in the presence of 1.25 mM added sulfide, giving a molar growth yield (YCH4) of 4.4 mg (dry weight) of cells per mmol of CH4 produced. Increasing sulfide to 12.5 mM led to decrease in YCH4 (1.9 mg [dry weight]/mmol of CH4), in the specific growth rate and in be intracellular levels of adenosine triphosphate. However, the specific rate of methane production increased. The data suggested that at elevated sulfide levels (12.5 mM) the decrease in YCH4 might be a result of an increase in the relative energy needed for maintnenace and of uncoupling of growth from energy production.

Investigation of the significance of a carbon and redox balance to the measurement of gaseous metabolism of Saccharomyces cerevisiae

A complete carbon and redox balance for Saccharomyces cerevisiae grown in batch culture with ethanol as the limiting carbon and energy source is reported. A novel method, which allowed the determination of carbon dioxide contained in the culture medium and biomass, is described and revealed amounts considerably in excess of what was expected from equilibrium data. Furthermore, elemental composition of the biomass was used to calculate the amount of oxygen required for biosynthetic reactions. When these corrections are applied to experimentally measured gas metabolism data, apparently anomalous results are shown to be consistent with the overall metabolism of bakers' yeast. These findings have wide implications to the quantitative study of the metabolism and energetics of facultative aerobes.

A continuous culture study of an ATPase-negative mutant of Escherichia coli

For anaerobic glucose-limited chemostat cultures of Escherichia coli a value of 8.5 was found for YmaxATP. For anaerobic glucose- or ammoniumlimited chemostat cultures of the ATPase-negative mutant M2-6 of E. coli YmaxATP values of 17.6 and 20.0 were found, respectively. From these data it can be concluded that in the wild type during anaerobic growth 51-58% of the total ATP production is used for energetization of the membrane. Using the YATP values obtained in the anaerobic experiments a P/O ratio of 1.46 could be calculated for aerobic experiments with the wild type. It is concluded that from the energy obtained by respiration in wild type E. coli about 60% is used for membrane energetization and only about 40% for the actual formation of ATP. No dramatic difference in the maintenance requirement for ATP or glucose has been observed between glucose- and ammonium-limited chemostat cultures of the mutant. The large difference in maintenance requirement observed for such cultures of the wild type is therefore supposed to be made possible by ATP hydrolysis by the ATPase.

ATP formation associated with fumarate and nitrate reduction in growing cultures of Veillonella alcalescens

Molar growth yields, fermentation balances and enzyme activities were measured in Veillonella alcalescens grown anaerobically with different substrates in the absence or presence of fumarate or nitrate. The molar growth yields on malate (14.3 g dry wt bacteria/mole substrate) and citrate (19.3) were higher than that on lactate (8.6). The molar growth yield on lactate was increased to 15.5 or 19.8 by the addition of fumarate or nitrate, respectively, to the growth medium, and the molar growth yield on citrate was increased to 25.3 by addition of nitrate. Active growth on pyruvate was only observed in the presence of nitrate, and the molar growth yield was 25.5. From fermentation balances and fermentation systems similar YATP values (g dry wt bacteria/mole ATP) were calculated for all substrates or mixtures of substrates assuming that one mole of ATP is generated at the electron transport from pyruvate, NADH and NADPH to nitrate or fumarate whereas ATP is not produced in the electron transport from lactate to fumarate or nitrate, and, therefore, this assumption was considered to reflect the actual situation. The mean YATP value at a doubling time of 1 h was 16.5 g dry wt bacteria/mole ATP for growth without an added hydrogen acceptor, 14.4 for growth with fumarate, and 14.2 for growth with nitrate.

Nutrition and factors limiting the growth of a methanogenic bacterium (Methanobacterium thermoautotrophicum)

The purification of Methanobacterium thermoautotrophicum from a culture contaminated with a heterotrophic organism is described. A defined inorganic medium under H2/CO2 (80:20 v/v) has been developed to support growth of M. thermoautotrophicum up to a concentration of at least 1.7 g dry weight/l. In a conventional medium iron and nitrogen sources were found to be growth-limiting factors. Throughout most of the culture period the rate of transfer of hydrogen or carbon dioxide from gas to liquid was the factor which controlled the growth rate. The growth yields of bacteria were in the range of 0.6-1.6 g dry weight/mole CH4.

Energy conservation during aerobic growth in Paracoccus denitrificans

Paracoccus denitrificans was aerobically grown in chemostat culture with succinate or gluconate as carbon source. Due to the presence of two phosphorylation sites in the respiratory chain and the absence of branching, theoretical P/O ratios of 1.71 and 1.82 were calculated for cells growing respectively with succinate and gluconate as carbon source. Using these data, 95% confidence intervals for the P/O ratio were determined, via a mathematical model, at 0.91-1.15 and 1.00-1.37 for sulphate-limited cultures, with respectively succinate and gluconate as carbon source. These results and measurements of P/O ratios in membrane particles and of proton translocation in whole cells have led to the conclusion that site I phosphorylation is affected under sulphate-limited conditions. Under conditions of carbon source-limitation the endogenous leads to H+/O ratio is about 7-8. Average values of 3.40 and 4.78 were respectively found for sulphate-limited succinate- and gluconate grown cells. For starved cells, oxidizing succinate as exogenous substrate, the leads to H+/O ratios were determined at about 3-4, independent of the growth limiting factor. It is concluded that the number of protons ejected per pair of electrons per energy-conserving site (leads to H+/site ratio) is about 3-4, instead of 2 as postulated by the chemiosmotic hypothesis.

Energy conservation during nitrate respiration in Paracoccus denitrificans

P/2e ratios were calculated from anaerobic chemostat cultures of Paracoccus denitrificans with nitrogenous oxides as electron acceptor. P/2e ratios were calculated, using the YmaxATP values determined for aerobic cultures. When succinate was the carbon and energy source the average P/2e values of the sulphate- and succinate-limited cultures with nitrate as electron acceptor were 0.5 and 0.7, respectively, and of the nitrite-limited culture 0.9. With gluconate as carbon and energy source and average P/2e values of the gluconate-limited with nitrate as electron acceptor and nitrate limited cultures were 0.9 and 1.1, respectively. leads to H+/O ratios measured in cells obtained from sulphate-, succinate, nitrite-, gluconate- and nitrate-limited cultures yielded respective average values of 3.4, 4.5, 3.5, 4.8 and 6.2 for endogenous substrates. From our data we conclude that sulphate- and nitrite- limitation causes the loss of site I phosphorylation. Nitrite has no influence on the maximum growth yield on ATP. We propose that metabolism in heterotrophically grown cells of Paracoccus dentrificans is regulated on the level of phosphorylation in the site I region of the electron transport chain.

Energetic aspects of anaerobic growth of Aerobacter aerogenes in complex medium

Molar growth yields for anaerobic growth of Aerobacter aerogenes in complex medium were much higher than for growth in minimal medium. In batch cultures the molar growth yield for glucose varied from 44 to 50 and YATP from 17.1 to 18.8. For glucose-limited chemostat cultures a value of 17.5 g/mole was found for Y max ATP and a value of 2.3 mmoles ATP/g dry weight h for the maintenance coeficient. Growth-dependent pH changes were used to control the addition of fresh medium, containing excess of glucose to a continuous culture. The specific growth rate and the population density were dependent on the pH difference between the inflowing medium and the culture. At a mu value of 1.44 h-1 the molar growth yield for glucose was about 70 and Y ATP about 28.5. An equation is presented, which gives the relation between theoretical and experimental Y max ATP values.

Energy metabolism of Saccharomyces cerevisiae discrepancy between ATP balance and known metabolic functions

The contribution of metabolic pathways to the catabolism of glucose, galactose and ethanol by Saccharomyces cerevisiae in aerobiosis has been studied. The results suggest that: 1. Of the total ATP formed in catabolism yeast obtain as much as 60% from ethylic fermentation during logarithmic growth on glucose. However, about 80% of ATP is formed in oxidation of galactose. Oxidation seems to be the only important catabolic pathway of ethanol. 2. The ratios between growth yield and ATP formed in catabolism were approx. 9, 7 and 3 g dry yeast/mol ATP in glucose, galactose and ethanol cultures, respectively. 3. The balance between ATP produced in catabolism of substrates and the requirements of ATP for the biosynthesis of cellular material indicates that as much as 60% of ATP is spent in functions other than net biosynthesis. 4. The rate of ATP expenditure in non net-biosynthetic functions during growth was approx. 20 mmol/g dry yeast per h. 5. In conditions in which no growth occurred but cell viability was maintained, that is, in the absence of exogenous carbon and nitrogen source, the ATP production rate was approx. 1 mmol ATP/g dry yeast per h. 6. These results indicate that the ATP required for maintaining the yeast alive, what would be considered maintenance energy "sensu stricto", is only a minor proportion of the ATP spent in non net-biosynthetic functions during growth. The identification of the processes related to growth which spend more energy than that required for net biosynthesis could lead to important insights in cell biology.

Metabolism and growth yields in Bacteroides ruminicola strain b14

Metabolism of D-glucose by Bacteroides ruminicola subsp. brevis, strain B14, has been examined. Growth yield studies gave molar growth yields, corrected for storage polysaccharide, of approximately 66 g (dry weight)/mol of glucose fermented. The storage polysaccharide amounted to about 14% of the total dry weight, or 55% of the total cellular carbohydrate, at full growth. After correcting glucose utilization for incorporation into cellular carbohydrate, measurement of product formation showed that 1.1 succinate, 0.8 acetate, and 0.35 formate are produced and 0.5 CO2 net is taken up during the fermentation of 1 glucose under the conditions used. The implication of these results with respect to adenosine 5'-triphosphate (ATP) molar growth yield calculations is discussed. If substrate-level phosphorylation reactions alone are responsible for ATP generation, then the ATP molar growth yield must be about 23 g (dry weight)/mol of ATP. Alternatively, if anaerobic electron transfer-linked phosphorylation also occurs, the ATP molar growth yield will be lower.

The energetics of Escherichia coli during aerobic growth in continuous culture

1. The energetics of Escherichia coli W growing aerobically in continuous culture have been investigated. Conditions were chosen such that growth was limited by the availability of carbon or oxygen (energy-limited cultures), or of ammonium of sulphate ions (excess energy cultures). 2. Under glycerol-limited conditions YmaxO2 (true molar growth yield with respect to oxygen) and YmaxATP (true molar growth yield with respect to ATP equivalents) were 50.9 g cells-mol O-02(-1) and 12.7 g cells-mol ATP equivalents-1 respectively; these values were not substantially altered during growth limited by oxygen, ammonium or sulphate. In contrast, M (the energy requirement for maintenance purposes) increased from approximately 2 mmol ATP equivalents-h-1-g cells-1 during energy-limited growth to 16.8 and 30.8 mmole ATP equivalents-h-1-g cells-1 when growth was limited by ammonium and sulphate ions respectively. 3. Replacement of glycerol by other limiting carbon sources caused YmaxATP to alter within the range 13.9 (glucose) to 7.1 (acetate) g cells-mol ATP equivalents-1 in the order glucose greater than galactose greather than arabinose greater than fructose greater than glycerol greater than fumarate greater than lactate greater than pyruvate greater than acetate. In each case the experimental value of YmaxATP was less than or equal to 55% of the theoretical value calculated from the known energy requirements for the biosynthesis of cell materials. 4. It is concluded from these results that neither M nor Ymax ATP are constant values for E. coli. M varies with the energy supply, being highest under excess energy growth conditions where it may reflect energy wastage by the cell. On the other hand, YmaxATP varies with the nature of the growth substrate and thus reflects the different energy requirements for the synthesis of cell material from different carbon sources.

Oxidative phosphorylation in Micrococcus denitrificans: calculation of the P/O ratio in growing cells

P/O ratios were measured in membrane particles obtained from cells of Micrococcus denitrificans, while growing on different carbon sources. The membrane particles obtained from cells growing actively on glucose, succinate, ethanol and propanol as the carbon and energy sources catalyzed oxidative phosphorylation and yielded respective P/O ratios of 1.4, 1.2, 0.8, and 0.5 with NADH, and 0.8, 0.6, 0.6, and 0.5 with succinate as the electron donors. Not such a difference in P/O ratio is observed in intact resting cells grown with different carbon sources. It is concluded that the influence of the carbon source is probably directed towards the efficiency of oxidative phosphorylation in membrane particles and not in the growing cells. For the aerobic carbon source-limited chemostat cultures the following maximum growth yields were determined: 40.2 and 34.2 for succinate and oxygen, 41.7 and 36.5 for malate and oxygen, 81.4 and 39.4 for mannitol and oxygen, and 77.8 and 43.4 for gluconate and oxygen respectively. With a mathematical model (de Kwaadsteniet et al., in press) the P/O ratio was valued at 1.4-1.7. YATP at mu=0.2 was valued at 8.7-10.9; YmaxATP at 9.6-13.2 and me at 0.6-4.5 for the most precise experiment (gluconate-limited). The calculation of these growth parameters has been discussed.