Does the understanding of the dynamics of biochemical networks in vivo, in terms of the properties of their components determined in vitro, require the latter to be determined all under the same conditions? An in vivo-like assay medium for enzyme activity determination was designed based on the concentrations of the major ionic constituents of the Escherichia coli cytosol: K+, Na+, Mg2+, phosphate, glutamate, sulfate and Cl−. The maximum capacities (Vmax) of the extracted enzymes of two pathways were determined using both this in vivo-like assay medium and the assay medium specific for each enzyme. The enzyme activities differed between the two assay conditions. Most of the differences could be attributed to unsuspected, pleiotropic effects of K+ and phosphate. K+ activated some enzymes (aldolase, enolase and glutamate dehydrogenase) and inhibited others (phosphoglucose isomerase, phosphofructokinase, triosephosphate isomerase, glyceraldehyde 3-phosphate dehydrogenase, phosphoglycerate kinase, phosphoglycerate mutase), whereas phosphate inhibited all glycolytic enzymes and glutamine synthetase but only activated glutamine 2-oxoglutarate amidotransferase. Neither a high glutamate concentration, nor macromolecular crowding affected the glycolytic or nitrogen assimilation enzymes, other than through the product inhibition of glutamate dehydrogenase by glutamate. This strategy of assessing all pathway enzymes kinetically under the same conditions may be necessary to avoid inadvertent differences between in vivo and in vitro biochemistry. It may also serve to reveal otherwise unnoticed pleiotropic regulation, such as that demonstrated in the present study by K+ and phosphate.
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Escherichia coli can almost synthesize itself from the two basic nutrients, glucose and ammonium, obtaining its Gibbs energy solely from the catabolism of glucose; the glycolytic and nitrogen assimilation pathways are central in the metabolism of this organism. Glycolysis in E. coli consists of the phosphotransferase system (PTS) sugar transport system, which phosphorylates glucose, and nine cytosolic enzymes that catalyze the conversion of glucose 6-phosphate to pyruvate, storing Gibbs energy in A(T)P, and reducing power in NAD(H) during the process . Nitrogen assimilation engages two alternative routes: one using the glutamate dehydrogenase (GDH) enzyme, catalyzing the synthesis of glutamate from ammonium and α-ketoglutarate, and the other using the couple glutamine synthetase (GS) and glutamine 2-oxoglutarate amidotransferase (GOGAT). GS catalyzes the formation of glutamine from ammonium and glutamate at the expense of ATP, and GOGAT catalyzes the reductive synthesis of two molecules of glutamate from glutamine and α-ketoglutarate. The properties of the individual enzymes of these two central pathways have been studied extensively [2, 3]. Yet how the integration of the kinetic activities of the individual enzymes leads to the functioning of both pathways as a whole is not yet understood in a rigorous way. Initials attempts at achieving such understanding have proven useful. In other organisms, the integration of the knowledge about individual enzymes has led to the discovery of new functions and vital regulatory mechanisms [4, 5], as well as new targets for antibiotics . For E. coli, the integration of the ammonia assimilation biochemistry with signal transduction information led to the discovery of several parallel robustness mechanisms [7-11].
Most kinetic reconstructions of pathways make good use of databases such as BRENDA [12, 13]. These contain rate equations for and kinetic parameters of many enzymes of well-studied ‘model’ organisms such as E. coli, which have been determined with purified enzymes or in cell extracts. The biochemical assays have been optimized to obtain the best possible signal-to-noise ratio and this optimization has led to the assay conditions for the different enzymes in the same pathways being different. Of course, in an actual pathway, all enzymes operate under precisely the same conditions to the extent that the pathway proceeds in a single intracellular compartment. By studying all the enzymes under the same condition, the pathway properties (i.e. the properties of the enzymes that only come about when they function in the pathway) can be better understood and, ultimately, this strategy may lead to an understanding of the entire cellular metabolism . If, in addition, the conditions are similar to the conditions in vivo, the pathway properties found may actually elucidate more of the functioning of the actual organism. For the cytosolic enzymes inside E. coli, typically, this is high ionic strength, a pH of approximately 7.5, and relatively high concentrations of K+, phosphate and glutamate.
In particular, this approach may be important for the acquisition of more reliable kinetic data (Vmax and apparent affinity constants for substrates, products and effectors) that are necessary for the improvement of existent (as well as for the development of new) mathematical models of metabolism. It may also be important for the analysis of the epistemological difficulties in biochemical research in general and of the problematic in vitro–in vivo relationship in particular [15-17]. It is important to exclude the possibility that differences between the in vivo and in vitro media are behind this before more intriguing explanations such as metabolite channelling are invoked [18, 19].
Unfortunately, it is technically very difficult to completely mimic all of the properties of the E. coli cytosol in vitro as a result of the high number of different small molecules present in the cytosol (i.e. the ‘metabolome’ is estimated to comprise approximately 1000 molecular species) , as well as its crowdedness and colloidal properties. Nevertheless, what can be relatively easily accomplished instead is the development of an assay medium with similar concentrations of the major ionic components and with a pH similar to the intracellular pH. We designed such an in vivo-like assay medium for the determination of enzyme capacities using the concentration values reported in the literature. We then evaluated the activity of nine glycolytic reactions [phosphoglucose isomerase (PGI), phosphofructokinase (PFK), aldolase (ALD), triosephosphate isomerase (TPI), glyceraldehyde 3-phosphate dehydrogenase (GAPDH), phosphoglycerate kinase (PGK), phosphoglycerate mutase (PGM), enolase (ENO) and pyruvate kinase (PYK)] and the three central nitrogen assimilation enzymes (GS, GOGAT, GDH) in this medium. For eight out of 12 enzymes the activity differed significantly between the in vivo-like assay medium and their specific medium. Our findings suggest that the cytosolic components K+ and phosphate have an important pleiotropic modulating effect on the core carbon and nitrogen metabolism of E. coli to the extent that the approach implemented in the present study becomes essential for understanding the pathway.
The in vivo-like assay medium
To develop a suitable assay medium for the enzymatic activity that mimics the cytosol of E. coli, yet was functional and simple to prepare, only the major components of the cytosol were taken into account (i.e. K+, Na+, Mg2+, phosphate, glutamate, sulfate, Cl−), plus the minor component Ca2+. In Table 1, the concentrations of these compounds in the in vivo-like medium are compared with the concentrations reported in the literature.
Table 1. In vivo-like assay medium composition. The reported intracellular concentrations of the components are given, along with the relevant references. The final column shows the concentrations of the components in the in vivo-like medium (pH 7.5) proposed in the present study
Although the cytoplasmic pH will vary to some extent with the pH of the growth medium, it is reasonable to choose a pH of 7.5 for the in vivo-like assay medium. For more or less neutral media (i.e. with a pH in the range 6.0–8.0), the intracellular pH is homeostatically controlled at values of approximately 7.5 [21-24]. The buffering capacity of this in vivo-like medium, mainly determined by phosphate and, to a lesser extent by glutamate, was measured by titration with either a base (NaOH) or an acid (HCl). This capacity was compared with that of two regular buffers commonly used to measure the activity of some of the enzymes of the glycolytic and nitrogen assimilation pathways: triethanolamine (100 mm; pH 7.5) and Hepes (40 mm; pH 7.5). The in vivo-like medium had a buffering capacity of 31 mm protons·pH unit−1, which is similar to the capacity of 100 mm triethanolamine (45 mm protons·pH unit−1) and stronger than that of the hepes buffer (27 mm protons·pH unit−1). Under normal conditions, the buffering capacity of the cytoplasm of E. coli cytoplasm can be ascribed to inorganic phosphate, glutamate and protein amino acid chains , and probably also to phosphorylated metabolites. At a cytoplasmic pH of 7.5, it can be estimated to amount to 30–40 mm protons·pH unit−1 . In view of these considerations, including 25 mm phosphate and 10 mm glutamate in the in vivo-like assay medium is a good compromise: (a) its buffering capacity is within the calculated range of the in vivo buffering capacities; (b) the phosphate concentration is within the range of concentrations that can be expected in vivo; and (c) the use of a nonphysiological buffer is avoided.
Capacity of the glycolytic and nitrogen assimilation enzymes under in vivo-like conditions
All the enzymes measured in the present study, the reactions catalyzed, the gene names, as well as the methodology used for their measurement in each one of the specific media, are referred to in Table S1 and Doc. S2. Initially, the enzymatic activities in their specific media were determined at three different dilutions of the extract to check the linearity of the assays. In all but three cases, the maximal specific activity (Vmax) was the same for each of the three dilutions and, in the remaining cases (TPI, PGK and PGM), the two higher dilutions were linear (comprising the 0,0 point), whereas the lower dilution rendered a lower activity; hence, the intermediate extract dilution was chosen and used to carry out the rest of the experiments. To correct for the variation in the Vmax values between extracts, extracts were used as ‘blocking factors’ during statistical analysis.
The logarithmically transformed (ln) 100% Vmax values for the glycolytic and nitrogen assimilation enzymes measured with the specific assay media are shown in Table 2. The mean Vmax of the glycolytic and nitrogen assimilation enzymes in the in vivo-like assay medium expressed as a percentage of the Vmax in their specific medium are shown in Fig. 1. The thick solid horizontal line depicts the 100% values for the enzymes and the vertical bars represent the 95% confidence interval for the percentage difference per enzyme. If the bar does not cross the horizontal 100% reference line, the Vmax as measured in the in vivo-like assay medium (in vivo Vmax) is statistically different from the respective value in the specific medium (specific Vmax). Thus, the in vivo Vmax values of PFK, TPI, GAPDH, PGK, PGM, PYK and GS are significantly lower, and that of GDH is significantly higher, than their specific Vmax values. The in vivo Vmax values of PFK, TPI, GAPDH, PGK, PYK and GS are 30–75% below, and that of GDH is some 300% above, the 100% reference line. The in vivo Vmax values of the four remaining enzymes (PGI, ALD, ENO and GOGAT) are all below the 100% reference line, although their 95% confidence intervals cross the line. The observation that, in most cases, the activity in the in vivo-like assay medium was lower than in the reference media was not unexpected because the individual protocols developed for the measurement of each enzyme had been optimized for obtaining maximal activity. Similar observations have been reported for the glycolytic enzymes of Saccharomyces cerevisiae  and Lactococcus lactis , although no pattern in the differences among the three microorganisms could be discerned.
Table 2. Logarithmically transformed (ln) 100% Vmax values for the glycolytic and nitrogen assimilation enzymes. The mean values of the natural logarithm of the maximal activities (nmol substrate·min−1·mg protein−1) measured with the specific assay media are shown per enzyme, along with n (number of independent extracts; three technical replicates per extract), the SEM and the 95% confidence interval. The 100% values are used in Figs 1–3 and Table S1. ENO was measured with the PEP method. In this case, there were two technical replicates per extract
Mean ln (Vmax)
K+, phosphate, phosphorylated metabolites and macromolecular crowding, and the maximum activities of the glycolytic and nitrogen assimilation enzymes
To dissect the effects of the main in vivo-like medium components (i.e. K+ and phosphate) from each other, as well as from the effect of the other components, all the assays were carried out in the respective enzyme-specific media, although now with the addition of either KCl (200 mm) or H3PO4 (25 mm). In the latter case, extra NaOH (30 mm) had to be added to maintain the pH at 7.5. As explained below, the presence of 30 mm Na+ is not expected to have any effect on Vmax, except perhaps for ALD, GDH and GOGAT. The results are shown in Fig. 2. For most of the reactions, the Vmax measured in the in vivo-like medium (Fig. 1) could be reproduced to a reasonable degree by adding up the individual effects that K+ and phosphate had on the activities in the specific media; the sum of K+ and phosphate effects did not differ by more than ± 20% from the in vivo inhibition. However, for some enzymes, this was not the case: for PGI, PFK and PGM, the in vivo effect was less strong than the sum of the K+ and phosphate effects, whereas, for GS, it was stronger: PGI (19% inhibition by K+ and 24% by phosphate compared to a 8% lower activity in the in vivo-like medium; all compared to the PGI-specific medium); PFK (15% inhibition by K+ and 37% by phosphate compared to a 29% lower activity in the in vivo-like medium); PGM (24% inhibition by K+ and 29% by phosphate compared to a 20% lower activity in the in vivo-like medium); and GS (6% inhibition by K+ and 21% by phosphate compared to a 55% lower activity in the in vivo-like medium). Three possible explanations might be given for these observations: (a) K+ and/or phosphate have a different effect in the in vivo-like medium compared to these enzyme-specific media; (b) the effects of K+ and phosphate are not additive; or (c) other components of the in vivo-like medium also exert some effect(s) on the activities. This was not investigated in further detail in the present study.
Above, the enzymes ALD, GDH and GOGAT were set apart because, in these cases, the observed effects of phosphate are possibly caused by the Na+ that is required to maintain a pH of 7.5. In an experiment described below (Fig. 3B,C), 100 mm Na+ is shown to have strong effects on ALD, GDH and GOGAT. Therefore, with these enzymes, the possibility cannot be excluded that the observed effects (shown in Fig. 2B) are to be corrected for the effects of Na+, although its concentration (30 mm) is lower. If true, phosphate would then inhibit ALD, stimulate GOGAT and have no effect on GDH.
Remarkably, phosphate inhibited all the glycolytic enzymes, although there is only indirect evidence for ALD. The inhibition varied from moderate to strong (i.e. from 20% to 59%). We surmised that this effect might not be limited to inorganic phosphate; phosphorylated glycolytic intermediates might have a similar inhibitory effect. Indeed, phosphoenolpyruvate (PEP) has been shown in vitro to inhibit PGI and, to a lesser extent, PFK-1 and ALD-1 , although this intermediate is not present at millimolar concentrations in vivo . To test this hypothesis, the effects of three of the most abundant phosphorylated metabolites present in E. coli growing exponentially on glucose [i.e. fructose 1,6-bisphosphate (10 mm), ATP (5 mm) and glucose 6-phosphate (3 mm)] [28-30] were measured for some of the glycolytic enzymes. (fructose 1,6,-biphosphate was tested for all glycolytic enzymes, except PFK and ALD, ATP for PGI and TPI, and G6P for TPI, GAPDH, PGK, PGM, ENO and PYK) (Table S2). However, in contrast to phosphate, only in two cases was there a statistically significant effect: the enzymes PGI and ENO were inhibited by 32% and 23%, respectively, by 10 mm fructose 1,6-bisphosphate.
Another important aspect of the bacterial cytosol is its high concentration of macromolecules (proteins and nucleic acids), which, via the phenomenon of macromolecular crowding , increase the effective concentration of macromolecules without affecting those of small molecules to any great extent. Macromolecular crowding substantially influences the flux through the PTS in E. coli . The concentration of macromolecules is much lower in the usual cytosolic extract dissolved in a protein free medium than in the cytosol itself. Hence, macromolecular crowding and its effects will be absent during Vmax measurements under the usual essay conditions. To test whether it could have any effect on the capacities of the glycolytic and nitrogen assimilation enzymes, we mimicked macromolecular crowding by adding poly(ethylene glycol) 6000 (5% w/v) to the enzyme-specific media. However, none of the maximal capacities was affected by the presence of poly(ethylene glycol) (Fig. 3A).
PYK is inactivated by the phosphate of the in vivo-like medium
Strong accumulation of intracellular PEP during glucose starvation has been observed for both L. lactis  and E. coli . At the same time, the intracellular free phosphate pool rises and the fructose 1,6-bisphosphate concentration decreases substantially in both organisms [33, 35]. Although the contribution of the inhibition of PYK by phosphate to the accumulation of PEP has been recognized for L. lactis , in the case of E. coli, it was argued that the only contribution was a decrease in PEP consumption by the PTS when no glucose (or another PTS sugar) was available to be phosphorylated. Our results obtained with extracts made from cells exponentially growing on excess glucose, however, also show that the PYK of E. coli is significantly inhibited by phosphate when tested in the presence of its activator fructose 1,6-bisphosphate (Fig. 2B). Upon glucose starvation, high phosphate levels concomitantly with low fructose 1,6-bisphosphate concentrations are to be expected and, hence, we tested the effect of phosphate on PYK inhibition both in the presence and in the absence of its activator fructose 1,6-bisphosphate (Fig. 4). The results revealed that the PYK activity was completely abolished by 25 mm phosphate in the absence (and inhibited for 70% in the presence) of fructose 1,6-bisphosphate. In addition, PYK activity was not observed in the in vivo-like medium (which contains 25 mm phosphate) in the absence of fructose 1,6-bisphosphate (data not shown). These results suggest that, at least under some conditions (glucose and other PTS sugar starvation), the inhibition of PYK by phosphate can contribute to the accumulation of PEP in E. coli.
GDH is activated by the cations of the in vivo-like medium
The observed 230% activation of forward GDH by 200 mm K+ (Fig. 2A) may be relevant to the physiology of E. coli because it has been shown that K+ transport is probably linked to nitrogen assimilation  and glutamate (the product of forward GDH), together with its counterion K+, can accumulate to high levels inside cells [29, 37]. Therefore, we studied this effect in more detail. The activity of GDH in its specific medium was titrated with KCl (Fig. 5) and a dose–response relationship up to the highest concentration assayed (500 mm) was found. To verify that K+ was responsible for the activation (and not Cl−), 200 mm K+ was added as KCl, KI or K2SO4. Indeed, similar levels of activation for all these three compositions were observed (Fig. S1).
Another point of interest is whether the activation of GDH by K+ is specific for K+, or is an effect of an increase in ionic strength or osmolarity. To examine this: (a) another monovalent cation (Na+ at 200 mm); (b) two divalent cations (Ca2+or Mg2+ both at 100 mm); and (c) other non-ionic osmolytes [5% poly(ethylene glycol) and 400 mm sucrose] were added to the GDH enzymatic assay. Figure S1 shows that the activity was perhaps slightly higher in the presence of the non-ionic osmolyte sucrose, and was similarly stimulated by Na+ compared to K+, but was much more strongly activated by the divalent cations Mg2+ and Ca2+ (by 800%). When combining data from Figs 5 and S1, there appeared to be no obvious relationship between stimulation and osmolarity, anion ionic strength or total ionic strength, although Vmax increased approximately linearly with cation ionic strength (not shown).
Effect of glutamate in the in vivo-like medium on the maximum activities of the glycolytic and the nitrogen assimilation enzymes
Glutamate is a key metabolite involved in nitrogen assimilation, being the nitrogen donor for at least one of the amino groups of 11 amino acids and for the polyamines . Glutamate is also fundamental in the regulation of turgor pressure by functioning as the major counterion of K+ , as well as in the maintenance of intracellular pH  and survival at acidic extracellular pH via the AR2 decarboxylase/antiporter-dependent acid resistance system . Furthermore, under some growth conditions, rather high intracellular glutamate concentrations can be observed in the range 70–100 mm in exponentially growing cells up to 150 mm upon a sudden ammonium upshift [29, 40]. Therefore, we tested whether such high glutamate concentrations may also have an effect on the activity of the glycolytic and nitrogen-assimilation enzymes. The effect of the addition of 100 mm Na-glutamate to the media specific for each enzyme was assayed; the addition of 100 mm NaCl served as a control. The results are shown in Fig. 3(B). Na-glutamate had no or a moderately inhibitory effect (up to 33%) on the glycolytic enzymes, with the sole exception of ALD, where it has a strong stimulatory affect (+130%). In all cases, most of the observed inhibition/activation can be attributed to Na+ rather than to glutamate because similar effects were exhibited by NaCl (Fig. 3C). In the case of the nitrogen assimilation enzymes, the effects were different for each of the three enzymes. Neither Na-glutamate, nor NaCl had an effect on GS. Na-glutamate inhibited (30%) GOGAT, where the NaCl inhibitory effect was stronger (56%). The apparent absence of product inhibition by glutamate contrasts with the observation of inhibition of purified GOGAT by glutamate [41, 42] but is consistent with the proposed active in vivo role of GOGAT at high internal glutamate concentrations . GDH was activated by NaCl (+132%), as expected (Fig. 3C), although Na-glutamate had no effect. The latter can be explained if the stimulation by Na+ is counteracted by product inhibition by glutamate.
ENO Vmax is severely underestimated by the NADH coupling assay
Originally, ENO was assayed by coupling PEP production with NADH consumption using PYK and LDH as coupling enzymes . However, we noted that the ENO Vmax obtained by this method was much lower than the Vmax values of the other glycolytic enzymes. Therefore, we decided to measure the Vmax of ENO by an alternative method: ENO was assayed by simply recording the PEP production from 2-phosphoglyceric acid, monitoring the increase in A240 . A more than 20-fold higher activity was obtained with the PEP monitoring method than with the NADH monitoring method. Similar results were obtained when the same two methods were applied to extracts of S. cerevisiae (data not shown), whereas no such difference was observed for the enolase of L. lactis . The above results indicate that the coupling enzyme-NADH method  may lead to a severe underestimation of the ENO Vmax and suggests that the assay contains some component that inhibits ENO. We are currently investigating this in more detail.
Devising a single and practical in vivo medium for all enzyme assays
Until recently, the behaviour, mechanism and kinetics of the enzymes of E. coli and other microorganisms have been studied under conditions that had been optimized towards maximum activity of each particular enzyme. We have enumerated the specific assay conditions for the individual enzymes of glycolysis and ammonia assimilation. Although these enumerations show that they differ significantly between the individual enzymes, they do not yet demonstrate whether these differences are sufficiently large to have implications for the kinetic properties measured. To examine this issue, we compared kinetic properties determined in the enzyme-specific media with the same properties determined in a single medium.
It would make most sense if that single medium were identical to the medium the enzymes are experiencing in vivo. But what is the precise medium composition inside E. coli? Metabolomics has suggested that the core of the metabolome consists of some 1000 metabolites [45-47] but has quantified only 100–200 of these [29, 48]. This confirms existing knowledge of metabolism and the genome wide metabolic map . These many metabolites are in addition to the thousands of possibly expressed mRNA and protein molecules [4489 genes] [50, 51] and the chromosome. Clearly, an exact mimic of the cytosol of E. coli for use in routine enzyme assays is not practicable. We had to achieve a compromise between realism and practicality.
One important aspect of the present study is the description of the in vivo-like assay medium that we propose for the determination of kinetic parameters (Km, Ki, Ka, Vmax) of the cytosolic enzymes of E. coli. We hope that either the medium is adopted by others who are increasingly aware of the importance of determining macromolecular behaviour under in vivo-like conditions, or that the findings of the present study become the basis for a discussion leading to such a consensus standard in vivo-like medium. If the community engages in the use of such a standard medium, the more realistic parameters determined in multiple and diverse laboratories can be compared at last, and also be used for an improvement of existing understanding and the generation of new hypotheses concerning the functioning of E. coli as a whole: not only metabolism takes place in the common medium, but also signal transduction and gene expression. A similar initiative was recently undertaken for S. cerevisiae  and L. lactis . Of course, standardization has been preceded in other fields, such as transcriptomics , data reporting , metabolomics [53-55] and modelling , although here the issue is more complex in the sense that in vivo-like conditions are sought in addition to commonality.
The in vivo-like medium that we propose does carry compromises that are worthy of discussion. First, we did not even attempt to put the large number of components that exist in vivo into the proposed medium. This would make it very difficult, if not, impossible to prepare the in vivo-like media. In addition to the level of resolution of the metabolomics, the medium composition varies between experimental conditions . It was considered that the in vivo-like medium should only represent the physical chemical generics of the in vivo state, and not its specifics. The physical chemical generics of the in vivo state are probably limited to temperature, pH, ionic strength, osmolarity, the concentration of important divalent cations, electroneutrality and macromolecular crowding/colloid osmotic pressure. The proposed in vivo-like medium does not contain any macromolecules. One reason for this is that the use of a reproducible composition of macromolecules is impracticable. Three additional reasons are that we did not observe significant effects of macromolecular crowding on the many enzymes examined in the present study (Fig. 3A), that we only expect such effects where reactions are catalyzed by more than one enzyme acting together in complexes , and that, at the intracellular macromolecule concentrations where any such effects are expected, media become so viscous as to be unmanageable in medium-throughput experimental assays.
Potassium was chosen as the major cation supporting the intracellular ionic strength and osmolarity. We did not use electrically neutral compounds in our in vivo-like medium because sugars tend to be phosphorylated in E. coli rather than accumulate in their neutral form. Chloride was chosen as the major anion at a concentration of 150 mm, which was much higher than the reported in vivo concentrations. In E. coli, many of the anions are macromolecules such as proteins and nucleic acids, which we did not want to put into the medium for the reasons discussed above. Chloride, phosphate and glutamate stand in for these macromolecular negative charges. Because, at higher concentrations, phosphate and glutamate had specific effects on enzyme activities, we considered that they would not be proper stand-ins for the macromolecules. Chloride appeared to be inert. Indeed, to our knowledge, the specific effects of chloride in enzyme kinetics have not been reported.
We added sulfate to stand-in for divalent anions. Mg2+ can have a rather strong effect on the kinetic properties of many enzymes. Because it binds avidly to molecules such as ATP and some other divalent anions, its free concentration can become ill-defined when concentrations of such anions are varied in assays, which is sometimes necessary for the assay itself (e.g. because of coupling enzymes). We therefore decided to make its total concentration sufficiently high to guarantee that the free Mg2+ concentration exceeded 0.5 mm (for PGM and GS, the free Mg2+ concentration may have been somewhat lower, yet higher than 0.2 mm). For similar reasons of definedness, we had the total calcium concentration exceed the concentration reported in the literature for calcium. We used phosphate to stand in for the many organic phosphates that are present in the cytoplasm and glutamate for the many amino acids. We made the pH equal to 7.5, which is the value that is homeostatically controlled during growth at pH 6–8 [24, 57].
The choice of pH is perhaps the one that best highlights an additional problem faced when defining an in vivo-like assay medium: in vivo, that medium will vary with growth or experimental conditions. For example, the internal pH can be lower than 7.5 under conditions where acetate is present . Also, the glutamate  and phosphate  levels may vary in vivo. In this sense, our in vivo medium should be considered as a compromise and specific variations should be examined as they become important in any given context.
Why in vivo may not equal in vitro: kinetic effects of components of the intracellular medium
We had expected the differences in the kcat values between the enzyme-specific media and the in vivo-like medium to be a result of the effects of components of the enzyme specific media. After all, the latter had been optimized for the activity of the individual enzymes. Unexpectedly, two medium components that are inescapably part of any in vivo-like medium for E. coli were together responsible for most of the observed discrepancies in kcat: potassium and phosphate. K+ (200 mm) activated some enzymes (ALD, ENO and GDH), inhibited others (PGI, PFK, TPI, GAPDH, PGK and PGM) and had no or little effect on the remaining enzymes (PYK, GOGAT and GS). By contrast, phosphate (25 mm) activated GOGAT but inhibited all the remaining enzymes, except GDH. Indeed, for most of the enzymes tested, the differences observed between the activities in the in vivo-like medium and the reference specific media appear to reflect the effects of K+ and phosphate.
K+ as a potential regulator of central nitrogen metabolism
For GDH, the in vivo-like medium kcat for the forward reaction was 330% higher than that in the GDH-specific assay medium, mainly as a result of activation by the K+ present in the in vivo-like medium. This observation confirms the finding of Measures , who observed activation of E. coli GDH by K+. Also for other bacterial species, the NADPH-dependent GDH capacity was found to be stimulated by K+ [59, 60]. We showed for E. coli that the activation of GDH is related to the ionic strength of cations. Because K+ is the major cation of E. coli, ionic regulation by cation ionic strength will often come down to regulation by K+. The activation of GDH by K+ is relevant for E. coli cells growing in normal isotonic media because the intracellular potassium concentration in such cells is approximately 200 mm . It is perhaps even more relevant when E. coli grows in hypertonic media, where K+ is accumulated to very high intracellular concentrations (0.5–0.9 m) [36, 62, 63]. Also, glutamate accumulates to high levels under such conditions, although not as high as K+ [63-66]. K+ and glutamate are considered to represent the primary ionic osmolytes taken up or produced, respectively, immediately after an osmotic up shock.
To our knowledge, the effects of K+ that we observed for most of the glycolytic (iso)enzymes of E. coli present in our extracts are new. However, the effects on PYK and ALD require some further discussion.
There are two isoforms of ALD. Because the synthesis of ALD-1 and ALD-2 is favoured under gluconeogenic and glycolytic conditions, respectively , our extracts are likely to contain predominantly ALD-2. We therefore suggest that ALD-2 is stimulated by K+ (200 mm). By contrast, purified ALD-2 was reported not to be stimulated by K+ (200 mm) .
In general, there are two PYK isoenzymes, of which only PYK-1 is dependent on K+ . Because our extracts are likely to contain PYK-1, our observation that K+ did not stimulate activity appears to be in conflict with activation by K+. However, the contradictory result can be explained by the fact that the PYK-specific assay medium used as contrast already contains K+. The addition of extra K+ apparently does not result in any extra stimulation.
Finally, our observation that eight out of 12 enzymes from the bacterium E. coli were inhibited or unaffected by K+ strongly contrasts with the activation by K+ found for numerous plant and animal enzymes .
Phosphate as a potential regulator of central carbon metabolism
To our knowledge, the inhibition by phosphate of all of the glycolytic (iso)enzymes present in extracts of our E. coli cells has not been reported previously. In this respect, it is noteworthy that, in the case of PFK, phosphate was shown to act as an inhibitor of purified isoenzyme PFK-2 . However, extracts prepared from cells grown with glucose contain the major PFK-1, which is known to be inhibited by PEP and ATP. Thus, we suggest that PFK-1 is also substantially inhibited (40%) by phosphate (25 mm). In the case of PYK, PYK-2 has been shown to be inhibited by phosphate, whereas this effect was completely antagonized by activators such as ribose 5-phosphate [72, 73]. In the present study, we show that PYK-1, most likely present in our extracts, is substantially inhibited by phosphate in the absence or presence of its activator fructose 1,6-bisphosphate (Fig. 4).
The inhibition by phosphate of all of the glycolytic enzymes is intriguing because it suggests that the concentration of (free) phosphate may modulate the activity of the glycolytic pathway as a whole. However, (a) four of the glycolytic reactions (PGI, TPI, GAPDH and PGK) were measured in the reverse direction and (b) phosphate itself is a substrate of the GAPDH forward reaction. In the latter case, the observed 35% inhibition of the reverse reaction by phosphate may be a result of product inhibition. Free phosphate is likely to constitute a part of the cytosolic buffering capacity . At the same time, phosphate availability is connected to the glycolytic rate because, under conditions of active glycolysis, free phosphate tends to be depleted as a result of the accumulation of the various phosphorylated glycolytic intermediates by up to as much as 25 mm . In addition, under some conditions, free phosphate is released from dihydroxyacetone phosphate, leading to the electrophile methylglyoxal, which then needs to be detoxified . All of these observations emphasize the importance of maintaining a proper balance between carbon metabolism, intracellular pH and free phosphate concentrations.
For L. lactis, it has been shown that intracellular phosphate is a major factor in the control of glycolysis . We have shown that PYK in E. coli is also strongly inhibited by phosphate, both in the absence and presence of the activator fructose 1,6-biphosphate, and the relationship between phosphate and glycolysis might be similar to that in L. lactis. In sum, a role of free phosphate as a regulator of the glycolytic pathway, completely neglected in E. coli, deserves to be explored further.
Does the understanding of the dynamics of intracellular networks in vivo, in terms of the properties of their components, require the latter to be determined all under the same in vivo-like conditions?
One of the stipulations of the integration of molecular and mathematical biology into systems biology is that it will make biology more predictive . The molecular properties of the components of living organisms can now be measured experimentally under well-defined conditions, in vitro, and the integration of all such molecular information can be achieved by mathematical modelling . A prerequisite for this silicon cell approach is that the kinetic parameters that go into the mathematical models are realistic in vivo. Because many parameters are being taken from kinetic databases and these databases have been populated by using all the relatively scarce information available in the literature, there is a substantial risk that kinetic parameter values are used that do not really belong together: although trivial, it remains true that enzymes functioning in the same pathway assume the kinetic properties that they exhibit under the same pathway conditions. Furthermore, kinetic parameters have mostly been determined under conditions that differ between enzymes, for reasons that were good for the molecular biochemistry but not good for systems biology. In the present study, we have elaborated a strategy that should deal with this problem. It first designs a medium that may correspond reasonably well to that in vivo, and it then determines the enzyme kinetic properties of all the pathway enzymes under the same condition in that medium. We have shown that deploying this strategy is relevant for the activities of the individual enzymes. A major implication is that differences between the predictions of systems biology models based on kinetic constants taken from databases and determined in enzyme-specific media, as well as experimental results obtained in vivo, may be partly attributable to this problem. In our own work, we have observed such differences with respect to in vivo and in vitro [77, 78], and we shall now need to determine the enzyme kinetic properties under identical and improved in vivo circumstances [25, 79]. We shall also need to do this to enhance our model of ammonia assimilation in E. coli . Accordingly, we should be able to greatly enhance the power of systems biology to make discoveries of important regulatory principles [4, 8, 80, 81], concomitant drug targets  and, potentially, channelling [19, 82].
E. coli strain YMC10 endA1 thi-1 hsdR17 supE44 ΔlacU169 hutC  was used for all the experiments. Evans minimal medium  supplemented with glucose (15 mm) and NH4Cl (15 mm) was used to pre-culture the bacteria (obtained from single colonies on LB plates streaked from glycerol stocks). Cells were grown at 37 °C with shaking (250 r.p.m.) for approximately 15 h. Thereafter, 55 mL of Evans minimal medium supplemented with glucose (5 mm) and NH4Cl (4 mm) was inoculated with 1 mL of the pre-culture and grown aerobically at 37 °C with shaking (250 r.p.m.) up to the mid exponential phase (D540 of 0.6). The cells were then harvested and used to prepare cell-free extracts.
Preparation of cell-free extracts
For the preparation of cell-free extracts, samples were harvested by centrifugation for 10 min at 4000 g at 4 °C, washed once with Hepes buffer (40 mm, pH 7.5), concentrated approximately 10-fold in the same buffer and then sonicated in ice for five cycles of 20 s with intervals of 30 s (samples were kept on ice in between cycles). Finally, the samples were centrifuged for 12 min at 20 000 g at 4 °C to remove the unbroken cells and cell debris; in all the extracts prepared, lysis of 95–99% of the bacteria was achieved (as calculated from the decrease in D540 in all cases and confirmed by viable counts in some cases). Also, other methods for disrupting the cells were attempted (French press and bead beating), although these two methods gave less reliable results than sonication in terms of the reproducibility of the extracting (amount of total protein) and preservation of enzyme integrity.
Protein determination used the Bicinchoninic Acid kit (BCA™ Protein assay kit; Pierce, Rockford, IL, USA) with BSA (2 mg·mL−1 stock solution; Pierce) as a standard.
All the reagents and coupling enzymes were purchased from Sigma-Aldrich Co. (St Louis, MO, USA) or Hoffmann-la Roche Ltd (Basel, Switzerland). All the reactions were assayed with extracts made from at least three (see below) independent batch cultures and per extract each Vmax was determined in triplicate at 30 °C via an NAD(P)H-linked method in a Novostar spectrophotometer (BMG Labtech, Ortenberg, Germany) at 340 nm. Using 96-well microtitre plates (Greiner Bio-One, Kremsmuenster, Austria), in all cases, a final volume of 300 μL per reaction per well was assayed, including 30 μL of the cell-free extracts. The Vmax was determined from the initial linear decrease or increase of the A340 and was corrected for absorbance changes in the absence of the committing substrate. ENO activity in the forward direction was assayed by monitoring the appearance of PEP by measuring its A240 with a UV-spectrophotometer (Ultrospec III; Pharmacia LKB, Uppsala, Sweden); per extract, Vmax was determined in duplicate in a final volume of 1 mL, using 100 μL of cell-free extract. All enzyme activities were expressed as substrate converted (nmol substrate·min−1·mg protein−1). The Vmax of each reaction was measured in assay media: (a) enzyme-specific medium (optimized for maximal activity); (b) the in vivo-like medium (Table 1); (c) enzyme-specific medium plus one of the following compounds: KCl (200 mm), or H3PO4 (25 mm) (adjusted to pH 6.5 with 30 mm NaOH) or Na-glutamate (100 mm), or NaCl (100 mm), or 5% (w/v) poly(ethylene glycol) 6000. In addition, some enzymes were assayed in their specific medium plus one of the following phosphorylated metabolites: 10 mm d-fructose 1,6-bisphosphate (trisodium salt), 5 mm ATP (disodium salt) or 3 mm d-glucose 6-phosphate (disodium salt). In all cases, the substrates and coupling enzymes were added in the same (or similar) amounts as described in the protocols for the specific media (Table S1). For the in vivo-like medium, a two-fold concentrated stock solution of the in vivo-like medium was freshly prepared for each experiment using KCl (250 mm), K3PO4 (50 mm), monosodium glutamate (20 mm), MgSO4 (10 mm) and CaCl2 (2 μm). To avoid precipitation, water was added first, then all components except MgSO4, the pH was adjusted to 7.5 with HCl and, finally, the MgSO4 was added.
All the enzymatic activities were measured in the forward direction unless it is stated that they were measured in the reverse direction. The specific medium that was used for each enzyme is described in Doc. S1.
For the determination of the effect of phosphate on the PYK activity (Fig. 4), the specific PYK assay described above was used, adding different amounts of H3PO4 (0–50 mm; adjusted to pH 6.5 with NaOH), both in the presence and absence of d-fructose 1,6-bisphosphate trisodium salt (1.0 mm).
For the determination of the effect of K+, other cations and the osmotic solutes sucrose and poly(ethylene glycol) on GDH activity (Fig. S1), the specific GDH assay described above was used, adding different amounts of KCl or KI (200 mm), K2SO4 (100 mm), NaCl (200 mm), CaCl2 (100 mm), MgSO4 (100 mm), sucrose (400 mm) or poly(ethylene glycol) 6000 (5% w/v). The 100% Vmax value measured in the specific medium was 18 and 35 nmol NADPH·min−1·mg protein−1 for Figs 5 and S1, respectively.
Design and statistical analysis
The Vmax values obtained for each enzyme and extract in the specific assay medium were considered as the ‘control’ with which to compare the Vmax values observed for the same enzyme and the same extract in the specific assay medium plus an extra compound [poly(ethylene glycol), KCl, Pi, Na-glutamate, NaCl, fructose 1,6-bisphosphate, ATP or glucose 6-phosphate] or measured in the in vivo-like assay medium (together referred to as ‘treatment’ below). For most experiments, three extracts were used; occasionally, four or five extracts were used. In total, 61 unique extracts were used in 142 experiments, most of which were used more than once as controls (62 × once, 41 × twice, 35 × three times and 4 × four times). Measurements were replicated three (for ENO two) times for each extract, treatment and enzyme combination. In total, for this part of the study, some 1200 Vmax measurements were carried out.
For each enzyme investigated, this procedure resulted in data structured as randomized incomplete blocks with replications, with ‘extract’ as the blocking factor. The replicates were averaged over each extract and treatment combination. These averaged data were analyzed using a two-way factorial mixed analysis of variance without replication (general linear model procedure in SPSS, version 17.0.2; SPSS Inc., Chicago, IL, USA). The effects of each treatment were estimated as simple contrasts with the control (specific medium) using the pooled variance for the calculation of the SEs. The SEs used to calculate the 95% confidence intervals for the differences can be considered to be based on estimated variances of both treatment-extract interaction and residual. Because the effect of a treatment can be expected to be fairly enzyme-concentration independent when taken relative to the Vmax values in the controls, data were ln-transformed before analysis and the estimated contrasts could be conveniently expressed as the percentage change relative to the controls (Figs 1–3 and Table S2).
To obtain the additional data for PYK, again two extracts were used, and subjected to all (i.e. 10) combinations of treatments with two factors (with and without FBP; five different concentrations of inorganic phosphate): data were analyzed with a straightforward factorial analysis of variance (Fig. 4). For the additional data for GHD, only two extracts were used, and they were subjected to all treatments including the control: there were no missing values. The data were analyzed according to a randomized complete block design (Figs 5 and S1).
This research was supported by FP6-NEST-STREP project 043235 (EC-MOAN) and, to a smaller extent, by BBSRC, EPSRC (BBD0190791, BBC0082191, BBF0035281, BBF0035521, BBF0035521, BBF0035361, BBG5302251, SySMO P49), EU-FP7 (BioSim, NucSys), UniCellSys and ZON-MW (91206069) (http://www.systembiology.net/support).