B. Teusink, Systems Bioinformatics IBIVU/Netherlands Consortium for Systems Biology, Faculty of Earth and Life Sciences, Vrije Universiteit Amsterdam, De Boelelaan 1085, 1081 HV Amsterdam, The Netherlands Fax: +31(0)205989435 Tel: + 31(0)205989435 E-mail: firstname.lastname@example.org
Lactic acid-producing bacteria survive in distinct environments, but show common metabolic characteristics. Here we studied the dynamic interactions of the central metabolism in Lactococcus lactis, extensively used as a starter culture in the dairy industry, and Streptococcus pyogenes, a human pathogen. Glucose-pulse experiments and enzymatic measurements were performed to parameterize kinetic models of glycolysis. Significant improvements were made to existing kinetic models for L. lactis, which subsequently accelerated the development of the first kinetic model of S. pyogenes glycolysis. The models revealed an important role for extracellular phosphate in the regulation of central metabolism and the efficient use of glucose. Thus, phosphate, which is rarely taken into account as an independent species in models of central metabolism, should be considered more thoroughly in the analysis of metabolic systems in the future. Insufficient phosphate supply can lead to a strong inhibition of glycolysis at high glucose concentrations in both species, but this was more severe in S. pyogenes. S. pyogenes is more efficient at converting glucose to ATP, showing a higher tendency towards heterofermentative energy metabolism than L. lactis. Our comparative systems biology approach revealed that the glycolysis of L. lactis and S. pyogenes have similar characteristics, but are adapted to their individual natural habitats with respect to phosphate regulation.
a low-molecular-weight, heat-stable protein, part of PTS
HPr(ser-P)-activated sugar-phosphate phosphatase II
unbound inorganic phosphate
GA3P and dihydroxyacetone
Lactic acid-producing bacteria are Gram-positive bacteria that survive in distinct biotopes, including foods and plants, and even the human body . Some lactic acid-producing bacteria play an essential role in the fermented food and beverage industry, while others possess pathogenic features. Therefore, the impact of this type of bacteria on our daily life is significant. There is great biodiversity amongst lactic acid-producing bacteria with respect to their genetics and consequent biochemistry alternatively metabolism would also be better, which is reflected in differences in flavour production, acidification rates, pathogenicity and health benefits. Such diversity has been studied using various comparative and pan-genomics focus on the full complement of genes of an organism [2–6]. In this paper we illustrate the use of a comparative systems biology approach. Comparative systems biology tries to understand similarities and differences in behaviour as a result of how the components interact dynamically. Moreover, similarly to the way that comparative genomics provides a knowledge base, comparative systems biology holds the promise of accelerating model development.
Here, our comparative systems biology approach focused on the primary metabolism of two specific lactic acid-producing bacteria: the beneficial Lactococcus lactis, frequently used in dairy products, and the human pathogen Streptococcus pyogenes. L. lactis is a nonpathogenic, noninvasive, noncolonizing and facultative anaerobic bacterium that can be found on plants and within the digestive tract of cows, but is mostly studied for its use in dairy fermentations . S. pyogenes colonizes the skin or throat and causes many important human diseases, ranging from mild superficial infections of the skin and mucous membranes of the nasopharynx to severe systemic and invasive diseases . Thus, the natural environments of L. lactis and S. pyogenes differ considerably in nutrients, temperature, oxygen availability and pH, but the similarities in their central metabolism are striking: they essentially ferment glucose to lactic acid and rely on substrate-level phosphorylation for ATP synthesis. In general, S. pyogenes and L. lactis are reported to be homofermentative and convert sugars primarily to generate energy . Moreover, under certain conditions, such as glucose limitation, the metabolism of these bacteria shifts from homolactic to mixed-acid fermentation, resulting in the production of formate, acetate and ethanol [10,11].
In contrast to L. lactis, the dynamics of the S. pyogenes metabolism has barely been studied. Some S. pyogenes-specific allosteric regulations of glycolysis have been identified, but no dynamic model of S. pyogenes glycolysis exists to evaluate the impact of these. The focus has been particularly on the molecular mechanisms behind virulence rather than on metabolism. We used a comparative systems biology approach to accelerate the construction of a kinetic model for the poorly studied S. pyogenes, starting with a well-described model of L. lactis glycolysis and subsequent improvement by a limited set of model-driven measurements on enzyme kinetics and metabolic analyses upon glucose perturbations.
Several kinetic models have been developed for L. lactis glycolysis by us and others, to study metabolic flux distributions [12,13], metabolic regulation [14,15] and pH control . Upon inspection, these models have limitations in their ability to fit phosphate-containing species, in particular the fructose-1,6-bisphosphate [Fru(1,6)P2] levels [13,16]. In the current communication we present (a) an improved kinetic model of L. lactis glycolysis, which accurately simulates our measured metabolite profiles quantitatively and is also consistent with published 13C- and 31P-NMR data , (b) the first kinetic model of S. pyogenes glycolysis, constructed using the L. lactis model as a blueprint to accelerate model development (the model reproduces our measured metabolite profiles for this species) and (c) a comparison of the dynamics of glycolysis in both lactic acid-producing bacteria, with a special focus on the allosteric regulation by extracellular phosphate. The comparison revealed differences in S. pyogenes and L. lactis that are robust against parameter uncertainties and make sense in the light of differences in the phosphate levels of their natural environment.
Therefore, comparative systems biology comprises an experimental and modelling approach to efficiently study systems properties that are responsible for differences in the behaviour of distinct, yet closely related, organisms.
Kinetic modelling of L. lactis uncovers imbalance in phosphate pools of NMR data
At the start of our study, we tested existing models for their ability to describe published data sets. We found that previous models consistently predict maximum Fru(1,6)P2 levels of ∼ 20 mm [13,16], while measured Fru(1,6)P2 levels reached values of 50 mm . Upon inspection, we found a mismatch between the total measured phosphate pool under starved and glycolysing conditions. Phosphate is primarily incorporated in the phosphoenolpyruvate pool (3-PGA, 2-PGA and phosphoenolpyruvate) (about 20 mm) and as unbound inorganic phosphate (Pi) (45 mm) during starvation, and shifts towards Fru(1,6)P2 (50 mm) and ATP (8 mm) during glycolysis. The sum of the total measured phosphate concentration is therefore ∼ 60 mm during starvation but ∼ 110 mm during glycolysis (Fig. 1A). Hereby, we assume that Fru(1,6)P2 and ATP are almost depleted in starving cells because these are the levels to which the cells return after using up all glucose. Unidentified phosphorylated compounds [18–20] or phosphate in the cell wall are not likely to explain this difference of ∼ 50 mm between these two physiological states, as the disappearance of phosphate upon starvation shows such fast kinetics.
To quantify intracellular metabolites, Neves and coworkers performed 13C-NMR experiments in 50 mm KPi buffer . However, they repeated their measurements of Pi and nucleoside triphosphates (NTPs) with 31P-NMR in a phosphate-free Mes/KOH buffer, to allow measurements of Pi and NTPs. A subsequent literature survey showed that the concentration of phosphate in the medium appears to have a pronounced effect on the intracellular Fru(1,6)P2 concentration during glucose consumption. Thus, it appears that the Fru(1,6)P2 pools increase with the extracellular phosphate concentration [10,21–23] (see Fig. 1B). This implies that the pool of free and bound phosphate [in phosphoenolpyruvate, Fru(1,6)P2 and so forth] is critically dependent on the external phosphate concentration.
We carried out experiments similar to those performed by Neves et al.  by use of NAD+/NADP+-coupled enzymatic assays. This revealed a dependency of the build-up of Fru(1,6)P2 on the extracellular phosphate concentration (see Fig. 2 and Fig. S1). Therefore, we concluded that the observed differences in the total phosphate pool between glycolysing and starving cells is probably a result of differences in external phosphate concentrations. In summary, we have shown that the internal phosphate pool depends on the extracellular phosphate concentrations, which implies that the phosphate exchange over the membrane should be included in the respective kinetic models.
Quantitative simulation of the dynamic profiles of glycolytic intermediates in L. lactis
Setting up the kinetic model for L. lactis on the basis of existing models necessitated a (re)assessment of all relevant processes and their respective regulation, as described later in this paragraph. In L. lactis, the main part of the external sugar is taken up via the high-affinity phosphoenolpyruvate-dependent phosphotransferase system (PTS; EC 22.214.171.124) and is converted directly into glucose 6-phosphate (Glc6P) , which is modelled as a single-step reaction for L. lactis. A low-affinity glucose permease is present, but its contribution to the overall uptake of glucose is limited . Therefore, we omitted this permease in our model. The conversion of glucose to its product pyruvate proceeds via the Embden–Meyerhof–Parnas pathway. Thereby, the pyruvate kinase (EC 126.96.36.199) is allosterically activated by Fru(1,6)P2 and inhibited by Pi . Under conditions of glucose excess, the majority of pyruvate synthesized is converted into lactate, a process catalysed by l-lactate dehydrogenase (LDH; EC 188.8.131.52). LDH in L. lactis is allosterically activated and inhibited by Fru(1,6)P2 and Pi, respectively . The pyruvate formate-lyase (EC 184.108.40.206) is inhibited by glyceraldehyde 3-phosphate (GA3P) [28,29]. Acetyl CoA is metabolized to acetate via acetylphosphate or, alternatively, via acetaldehyde to ethanol . The compounds acetate, ethanol and formate are synthesized and subsequently transported out of the cell. An ATPase reaction is included as a sink for the ATP generated in glycolysis, replacing all ATP-consuming reactions.
To account for the influence of external phosphate concentrations on the metabolic intermediates during glycolysis, we included phosphate exchange over the cytoplasmic membrane. Therefore, we extended the model with an ATP-driven phosphate uniporter in L. lactis, which is inhibited by intracellular phosphate . Phosphate leakage was assumed to be negligible .
To simplify the model and reduce the number of parameters, some metabolites were lumped based on near-equilibrium timescale separation: (a) Glc6P and fructose 6-phosphate were placed in the Glc6P pool, (b) dihydroxyacetone phosphate and GA3P were placed in the GA3P and dihydroxyacetone (triose-P) pool, (c) 2-phosphoglycerate (2-PGA), 3-phosphoglycerate (3-PGA) and phosphoenolpyruvate were placed in the phosphoenolpyruvate pool and (d) all mixed-acid products (formate, ethanol and acetate) were placed in a single mixed-acids pool. The last choice is justified by the fact that under the conditions for which we developed the model, mixed-acid formation was negligible, as accounted for by the fact that the lactate concentration measured in the medium at the end of the experiments corresponded to approximately double the concentration of glucose entered (Fig. 2). The ATP/ADP, NAD+/NADH and Pi pools are set as free-state variables, in contrast to other kinetic models [14,31,32]. Fig. 3A shows the structure of the L. lactis model.
The parameters in the model were optimized with parameter estimation to fit in vivo time-series data (see Tables S1–6 for the parameters and the Materials and methods for more information on the fitting procedure). These time-series data comprised our own measurements (Fig. 2) as well as the NMR data published by Neves et al.  (Fig. 4). For the two different data sets, the initial concentrations of metabolites (both measured and fitted) were allowed to differ, as was the activity of the ATPase. In addition, the initial concentrations that were not measured in our own or in the respective NMR data were fitted for our own data sets or the respective data sets of Neves et al. Thus, the initial concentrations of phosphoenolpyruvate, extracellular lactate, ATP (without phosphate in the medium), ADP, intracellular phosphate and NAD were fitted for our experiments (at 10 and 50 mm extracellular phosphate). For the data of Neves et al., the initial concentrations of ATP, ADP and phosphate for the 13C-NMR data set and of Fru(1,6)P2, lactate, NAD, phosphoenolpyruvate and ADP for the 31P-NMR data set were fitted. All other parameters stayed the same, irrespective of the assumption that the Vmax values (that include the enzyme expression levels) for the two different experimental data sets will certainly not be exactly the same. However, the model with these constraints is able to fit the data almost perfectly as long as phosphate uptake is included in the model. Without this reaction, the data cannot be fitted.
As the experimental data do not allow an unambiguous fit of the data and the parameters are not identifiable (between the different fits, all parameters varied over a wide range within the set boundaries), we performed 300 fits and subjected the best 50 (based on the objective value and visual inspection) to the analysis below in order to ensure that we were observing robust effects that do not depend on the exact choice of the parameters.
In summary, it is clear that Pi exchange plays an important role in sustaining a large intracellular total Pi pool, affecting the levels of phosphorylated metabolic intermediates. This L. lactis model (Fig. 3A and Tables S1–S6) subsequently formed a scaffold for the first kinetic model of S. pyogenes glycolysis (Fig. 3B and Tables 7–12).
Setting up the S. pyogenes model using L. lactis as a blueprint
The primary metabolism of S. pyogenes largely resembles that of L. lactis with respect to allosteric regulation and general enzyme characteristics. A few additional enzymes are present, as indicated later. Our measurements of the kinetics of pyruvate kinase of S. pyogenes and LDH showed differences in allosteric regulation by phosphate and Glc6P, respectively (see Table S10). Finally, our experimental data uncovered that S. pyogenes has a larger heterofermentative capacity than L. lactis . Thus, as shown in Fig. 5, the experimentally observed accumulated lactate levels do not represent twice the amount of glucose entered. This motivated a more detailed description of the mixed-acid branch for the S. pyogenes model.
We transformed the L. lactis model into a S. pyogenes model by including or changing the following. (a) Decomposition of PTS to a low-molecular-weight, heat-stable protein (HPr) and serine-phosphorylated HPr (HPr-ser-P), including regulation by Fru(1,6)P2, Pi and ATP [33,34]. This was motivated by (b) removal of fructose-1,6-bisphosphatase (EC 220.127.116.11) as the gene for this enzyme is not present in the genome. Instead, an expulsion mechanism of Glc6P was introduced, which is catalyzed by the HPr-ser-P-activated sugar-phosphate phosphatase II (PaseII; EC 18.104.22.168) . (c) Inclusion of a glucose permease that removes some of the glucose produced from dephosphorylated Glc6P by PaseII and a glucokinase (EC 22.214.171.124), which is allosterically inhibited by Glc6P and ADP . (d) Incorporation of the nonphosphorylating NADP+-dependent glyceraldehyde-3-phosphate dehydrogenase (GAPN; EC 126.96.36.199). This GAPN catalyses the irreversible conversion of GA3P to 3-PGA by reducing NADP+ to NADPH. As the oxidative part of the pentose phosphate pathway is missing in S. pyogenes, it functions as an alternative mechanism for the production of NADPH . Additionally, an NADP+-regenerating reaction is introduced. (e) Changing pyruvate kinase activation by Fru(1,6)P2 into Glc6P  and adding NADH inhibition of glyceraldehyde-3-phosphate dehydrogenase (GAPDH; EC 188.8.131.52) . (f) Allosteric regulation of LDH by NAD+ (inhibition) and Fru(1,6)P2 and Pi (both activation), which we determined experimentally (Table S10). (g) Pyruvate-controlled export of lactate  and (h) division of the mixed-acid branch in acetate and ethanol production and inclusion of an allosteric inhibition of Fru(1,6)P2 and ATP, respectively [41,42].
Finally, with the analysis of the experimental data in mind, we investigated the mechanism of Pi uptake in S. pyogenes. Based on the experimental findings we incorporated facilitated diffusion of Pi, which is inhibited by ATP and activated by extracellular phosphate  and, additionally, ATP-dependent uptake of Pi . Figure 3B gives a schematic overview of the molecular interactions of the S. pyogenes glycolysis model.
Like the L. lactis model, the S. pyogenes model needed additional parameter fitting to simulate the profiles of our in vivo experimental data. Again, the model is able to fit the experimental data (Fig. 5), as long as the phosphate-uptake system is in place. However, and again, the parameters are underdetermined and the resulting parameter set is not unique. Therefore, and similarly to the L. lactis model, we repeated fitting 300 times and analysed the best 50 fits subsequently. The parameters of the S. pyogenes model are listed in Tables S7–S12.
Comparative systems biology of L. lactis and S. pyogenes glycolysis
The uptake of Pi in L. lactis and S. pyogenes proceeds via active transport [30,44] and in S. pyogenes also via facilitated diffusion . As described earlier, our glucose-pulse experiments in resting cells with different concentrations of extracellular Pi (0, 10 and 50 mm) showed that the levels of Fru(1,6)P2 in both species are affected by the extracellular Pi concentration. This is reflected and reproduced by our kinetic models. Although a slightly different set of initial conditions is used for each perturbation in extracellular Pi in order to fit the slightly different experimental conditions, we verified the impact of the external Pi concentration within each model by simulating the Fru(1,6)P2 level and the glucose-uptake rate with varying external concentrations of Pi and left the remaining initial concentrations unchanged. Therefore, we conclude that the observed effects are caused by responses to external conditions and not by different initial concentrations. The experiments were reproduced several times with an exemplary data set displayed in Figs 2 and 5.
The rate of glucose uptake was also slightly altered by extracellular Pi in L. lactis and to a greater extent in S. pyogenes (Figs 2A and 5A) with glucose-uptake rates that were higher in S. pyogenes than in L. lactis. Once again, our models reproduce this behaviour very well (see Figs 2B and 5B). Interestingly, the glucose-uptake rate in S. pyogenes did not simply correlate with the extracellular phosphate concentration. Rather, in the simulations of the model with the indicated parameters, low extracellular phosphate concentrations (e.g. around 1 mm) decreased the glucose uptake slightly compared with no phosphate in the environment, whereas higher phosphate concentrations increased the glucose uptake rate (see Fig. 6). This observation is not easy to explain. Because free phosphate has such a pronounced effect on glycolysis and glucose uptake, we studied the behaviour of intracellular phosphate in our model. Intracellular phosphate is extremely difficult to determine experimentally in the presence of extracellular phosphate. Insights from computational models are therefore advantageous. Curiously, we observed that the intracellular phosphate level in L. lactis simply increases with increasing extracellular levels of phosphate, but this does not hold for S. pyogenes (Fig. 6). As mentioned before, both bacteria possess an ATP-dependent phosphate-uptake system. S. pyogenes also has an energy-independent phosphate transporter that is modelled as facilitated diffusion and is inhibited by ATP and activated by extracellular phosphate . Hereby, the net uptake is determined by the difference in the extracellular and intracellular phosphate levels, which implies that an efflux of phosphate occurs if the intracellular phosphate concentration is higher than the extracellular level and some external phosphate is present. Therefore, owing to the combination of active and passive phosphate transport, a low concentration of extracellular phosphate can lead to a small decrease of intracellular phosphate in S. pyogenes, if the concentration gradient is pointing to the outside of the cell. Figure 6 displays a parameter scan of intracellular phosphate against extracellular phosphate as well as the effect of extracellular phosphate on the flux through the passive phosphate transport system for S. pyogenes. For a low extracellular phosphate level (e.g. around 1 mm), the flux through the phosphate transporter is directed towards the outside, removing phosphate from the cytosol, whereas higher phosphate concentrations result in phosphate uptake. Thus, it is obvious that certain low concentrations of extracellular phosphate lead to a decreased concentration of intracellular phosphate compared with no extracellular phosphate. In turn, intracellular phosphate activates the PTS and is an important substrate for GAPDH and acetate kinase (EC 184.108.40.206). Therefore, a decreased concentration of intracellular phosphate leads to a decreased glucose-uptake rate.
Because of the nonidentifiability of the parameters, we studied the 50 best fits of S. pyogenes with respect to this behaviour. The behaviour reported above was the same in many (∼ 60%) of the fits, but not in all. As an example, Fig. 7 shows the dependency of the PTS flux on the initial extracellular phosphate concentration for both organisms and for different parameter sets, which all resulted in a reasonable fit of the experimental data. Obviously, there are differences in the quantitative behaviour. However, the qualitative behaviour is the same. As this behaviour is not completely robust in all of the fits, it is obviously crucial to verify experimentally the observations resulting from this analysis. The effect on glucose uptake was also observed experimentally and the respective data (which were not used for fitting of the model) are also shown in Fig. 6. The validation showed that the computationally predicted behaviour indeed coincided qualitatively with the experimental results. The experimentally observed effect was even more pronounced than the computationally predicted effect.
We performed additional in silico experiments with our kinetic models of S. pyogenes and L. lactis, in which extracellular glucose and phosphate levels were varied. Our experimental fermentation studies showed that glucose uptake in S. pyogenes ceases when extracellular glucose levels rise above 20 mm under the experimental conditions employed. We observed that S. pyogenes consumes 5–10 mm of the pulse and subsequently stops sugar uptake. In contrast to S. pyogenes, extracellular glucose levels of ≥ 20 mm do not hinder glucose uptake in L. lactis. We therefore varied the amount of extracellular glucose in our simulation for all fitted parameter sets in the models of L. lactis and S. pyogenes. In all models, if no or low external phosphate was present for S. pyogenes, the glucose uptake was completely stopped or severely inhibited at high glucose levels (the exact numerical value varied between the different fits). Often the actual value was much higher (and nonphysiological) compared with the experimental set-up (ranging between 113 mm and 89 m), but qualitatively this was robust behaviour irrespective of the exact parameter set. This effect could also be seen in several of the models for L. lactis, but at even higher external glucose concentrations (between 40 mm and 95 m). Once again, this inhibition could be overcome by adding phosphate, underlining again the crucial importance of this substance for glucose uptake and glycolysis in general.
The goal of this study was to apply a comparative systems biology approach to investigate glycolysis in two closely related lactic acid-producing bacteria that live in nutrient-rich, but rather distinct, environments. First of all, we formulated a kinetic model of L. lactis glycolysis, which was able to capture, with improved accuracy, dynamic profiles of intracellular metabolites after glucose-pulse experiments. Previous models of L. lactis glycolysis did not quantitatively fit the NMR data of Neves et al. [17,23,31]. Incorporation of the effects of extracellular Pi on the intracellular phosphorylated glycolytic intermediates was found to be key. It should be noted that Neves et al. , in the Materials and methods section of their study, mentioned that they observed no difference in the Fru(1,6)P2, phosphoenolpyruvate and 3-PGA levels when using a phosphate-free buffer compared with the published time-series with 50 mm external phosphate. We are not able to explain this finding here since the earlier described obvious phosphate uptake during glucose consumption in their experiments should result in differences in phosphorylated compounds when no phosphate is available. Our own experimental data showed a clear dependency with respect to external phosphate. Perhaps the distribution of differences in phosphorylated compounds in their strain (which was different from that used in the present study) was somewhat different and difficult to observe.
All previously published models omitted Pi transport [12,13,15,16] or considered Pi as a constant input [14,31,32]. Consequently, the simulated Fru(1,6)P2 and intracellular Pi levels were considerably lower in these studies, which affected the regulation of many glycolytic processes, amongst which are PTS , pyruvate kinase  and LDH . Our L. lactis model is the first to (a) quantitatively describe the dynamics of extracellular metabolites (glucose and lactate), the main glycolytic intermediates (Fru(1,6)P2, Glc6P and phosphoenolpyruvate) and cofactors (ADP/ATP, NAD+/NADH and Pi), (b) fit the dynamics for different strains (i.e. MG1363 for the Neves experiments  and NZ9000, a MG1363 derivative, for our glucose-pulse experiments) with one single thermodynamically consistent parameter set (although with variable ATPase activities) and (c) take into account the effects of varying amounts of extracellular phosphate. In particular, the high Fru(1,6)P2 concentration during glycolysis appeared to be crucial for the regulation of several glycolytic enzymes and the glucose-uptake rate, and was a direct result of the extracellular phosphate concentration.
It should be noted that in glycolytic models of most other organisms, Pi is rarely a free metabolite (e.g. yeast ). This is actually surprising in view of the many effects of phosphate on enzyme kinetics and as a result of the fact that phosphate is a factor which determines the free-energy of ATP hydrolysis (being its product). Classical experiments by Harden and Young, in yeast extracts, have already demonstrated the importance of phosphate for glycolytic flux [47,48]. Our study suggests and reinforces the fact that major improvements can be made by studying phosphate dynamics more carefully in all organisms.
The structure and modelling framework of L. lactis served as a scaffold for the first kinetic model of S. pyogenes glycolysis to reduce the amount of man-hours needed for such an effort. Furthermore, it strongly facilitates interspecies comparisons. We adapted the model structure of L. lactis, acquired kinetic details of LDH and performed glucose-pulse experiments to optimize the model of S. pyogenes. Interestingly, our LDH kinetics measurements indicated allosteric activation of LDH by Pi in S. pyogenes, which is significantly different from L. lactis. Despite little knowledge about S. pyogenes, we developed a model that was able to describe our experimental data quantitatively, except for the triose-P level, which in our simulations was lower than the experimentally determined level. This might have been caused by placing metabolites in pools in our computational model.
On the one hand, our comparative systems approach helped to develop a model for a less commonly studied organism (S. pyogenes) based on the knowledge of a closely related well-described lactic acid bacteria (L. lactis) but, on the other hand, this might also lead to a certain bias when comparing the species. The model was constructed by incorporating known differences between both species (i.e. distinct phosphate uptake, regulation and parametrization). Therefore, differences between the two models must have been caused by the introduced variance. We were able to explain the differences observed in our experiments just by taking these identified biochemical differences into account, which is certainly interesting, but obviously there might be more, so far unidentified, differences that add to this picture.
The role of phosphate is crucial in both organisms, even though uptake and regulation show some differences. Experimental approaches showed that an increase in the extracellular phosphate concentration induced an elevation in Fru(1,6)P2 in both species and an increased glucose-uptake rate in S. pyogenes. In the latter, the relationship of extracellular phosphate concentration and glucose uptake is not monotonic. Rather, we find that a low extracellular phosphate concentration can actually hamper glucose uptake, whereas high concentrations stimulate it. This is not the case in L. lactis and we could ascribe this difference in behaviour mainly to the differences in phosphate-uptake mechanisms because passive transport (even well-regulated passive transport) will allow phosphate efflux if the concentration gradient points in this direction. In S. pyogenes, phosphate uptake also seems to prevent a stalling of glucose metabolism at high glucose concentrations. This is also seen in our model simulations without any additional parameter fitting: when no phosphate is provided extracellularly, S. pyogenes fails to consume all glucose but this process is stalled before the glucose is fully consumed. Owing to the nonidentifiability of the kinetic parameters in our models with the current set of experimental data, it is important to note here that the observed computational results are robust and resulted from an analysis of 50 different parameter fits.
Having revealed the fundamental role of free phosphate for the metabolism of these species, it is interesting to see how the two bacteria cope with the phosphate available in their respective natural environment. S. pyogenes, which is present in the human body (e.g. on skin and mucous membrane and in blood (0.8–1.8 mm Pi in the latter)) at relatively constant and low concentrations of phosphate, has passive and active phosphate-uptake mechanisms. Both have to supply sufficient phosphate to the cells to enable them to metabolize glucose efficiently in order to grow and multiply. However, according to the above, the relatively low phosphate concentrations are not optimal conditions for glucose uptake by this organism. This raises the question of why S. pyogenes still uses the passive transport mechanism. The answer might lie in the fairly constant supply of phosphate and glucose in the compartments of the human body. Thus, while not allowing optimal glucose-uptake rates, the passive transport system permits a cheap and guaranteed uptake of minimal phosphate (the phosphate concentration in its natural environment will certainly never drop much) that is sufficient to sustain glycolysis. Interestingly, only recently has the putative gene sequence of a sodium phosphate symporter been reported for S. pyogenes (see accession number B5XHT4 in UniProt ).
L. lactis, on the other hand, initially encounters relatively high phosphate levels (∼ 20 mm) in fresh milk. However, here, the situation is similar to batch experiments in that there is no further supply of phosphate in the milk once it has left the body and L. lactis starts to reside in it. Thus, an active mechanism, as found for phosphate uptake in these bacteria, makes sense, even though one may wonder why the bacteria do not have a passive transporter that would allow them to make use of the initially high phosphate concentration without wasting ATP. As seen for S. pyogenes, a passive transporter can slow down glucose uptake if the extracellular phosphate concentration starts to deplete. This might be dangerous for a species that encounters highly variable environmental conditions. For L. lactis, no putative sodium phosphate symporter has so far been identified. Sugar uptake is activated by intracellular phosphate in both organisms but is stimulated more strongly by extracellular phosphate in S. pyogenes than in L. lactis. This was also observed in the experimental data.
Another interesting difference is that S. pyogenes possesses an NADP+-dependent GAPDH (GAPN) that is not present in the genome of L. lactis. Although initially introduced to produce NADPH for biosynthesis (recall that S. pyogenes lacks an oxidative part of the pentose phosphate pathway), this reaction enables S. pyogenes to produce phosphoenolpyruvate required for sugar uptake in the absence of phosphate. This may compensate slightly for the unfavourable low external phosphate concentrations. Indeed, removing the NADP+-dependent GAPDH reaction from our model led to a much stronger reduction of glucose uptake at low external phosphate concentrations.
Another interesting observation is the fact that S. pyogenes seems to be more efficient in converting glucose to ATP, while exhibiting a higher glucose-uptake rate, than L. lactis. The model shows this to be a direct consequence of the antagonistic effects of allosteric regulators (Fru(1,6)P2, Pi, NAD+ and NADH). Pyruvate kinase and especially LDH are differently regulated in L. lactis (Fig. 3A) and S. pyogenes (Fig. 3B). In L. lactis, LDH is allosterically regulated by Fru(1,6)P2 and antagonistically regulated by Pi, indicating that during glycolysis where Pi is low and Fru(1,6)P2 is high, the flux is directed towards the less efficient lactate production. S. pyogenes LDH lacks this antagonistic regulation by Fru(1,6)P2 and Pi. Here, both Fru(1,6)P2 and Pi activate LDH, whereas the product NAD+ inhibits LDH. This indicates that LDH activity is submaximal during glycolysis and more flux can be diverted to the more efficient mixed-acid fermentation.
The above observations on the phosphate regulation of LDH are corroborated at the kinetic level by the differences between plant and dairy strains of L. lactis. Van Niel et al.  measured that LDH activity is differentially regulated in plant and dairy strains of L. lactis: dairy strains use Fru(1,6)P2 and Pi, whereas the LDHs of plant isolates are regulated by the NADH/NAD+ ratio. As a plant environment is virtually devoid of phosphate , these observations support a close link between the organism’s natural environment and its metabolic regulation.
To summarize, our comparative systems biology approach resulted in (a) an improved kinetic model for L. lactis, (b) an acceleration of the development of the first kinetic model of the pathogenic S. pyogenes for which very limited metabolic information was available and (c) insight into the crucial role of Pi transport and Pi regulation of glycolysis, which we could relate to the Pi availability in the environmental niches of these organisms. We expect that comparative approaches at the systems level will significantly enhance our understanding of the function of biological networks.
Materials and methods
Mathematical models of L. lactis and S. pyogenes
Mathematical models were formulated using ordinary differential equations, as specified in Data S1–S4 in Supporting information. Simulations were performed with the LSODA algorithm, as implemented in COPASI .
For both models, we performed an extensive literature search in the SABIO-RK and BRENDA databases [52,53] for enzyme-specific activities. From the measured dry weight of our experiments, the fact that 42% of cellular dry weight consists of protein  and an assumed intracellular to reactor volume ratio of 30 mL·L−1, we were able to calculate Vmax values from the specific activities taken from Even et al. and Rimpiläinen et al. [55,56] (see also Tables S1 and S7). For the Michaelis constants, we took the values from previously published kinetic models [12,16], and regulator binding constants [26–28] and Hill coefficients  from previous publications. These values were used as initial estimates for parameter estimation (discussed later). For S. pyogenes, only kinetic constants of PaseII and the phosphate transporter were found in the literature [35,43]. For pyruvate kinase and LDH, the results from our own experiments were used. Most of the Michaelis constants were derived from enzymes of related organisms found in the literature [13,34,36,40,43,57–64], for example, from Streptococcus mutans or Streptococcus thermophilus. If no information was available, we adopted the missing parameters from the L. lactis model. Enzyme-specific activities were converted into Vmax values as described for L. lactis. Vmax values were derived from previous publications [13,35–37,39,43,57–59,62–65].
For both species, we implemented kinetic rate equations as convenience kinetics [66,67]. The equilibrium constants for the glycolytic reactions are known and were taken from the literature . The rate equations, parameter values and additional information about the initial conditions are provided in the Supporting information.
As in vitro measurements can deviate considerably from in vivo conditions , and not all kinetic parameters were determined in L. lactis or S. pyogenes, we used parameter fitting methods to tune the parameters to match the time-series data for various concentrations of extracellular Pi. For both organisms, parameters found in the literature were used as initial guess and were allowed to vary between -90% and +900% of their initial values. Unknown parameters were modified over an even larger range (i.e. binding constants were varied from 0.01 to 100 mm and Vmax values from 0.1 to 103 mm·s−1). To correct the volume of multicompartment reactions, the transport reactions have to be multiplied by a correction factor. In our models this factor was incorporated in the velocity constants of the transport reactions. Therefore, the range for these Vmax values was wider (0.001–1000 mm·s−1). Subsequently, the Neves data  for L. lactis and our fermentation experiments for both organisms were used as input for a parameter estimation using the particle swarm algorithm (swarm size = 100), as implemented in COPASI .
L. lactis cells were grown anaerobically at 37 °C in CDM-LAB medium [11,68] which contains (per liter): 1 g of K2HPO4, 5 g of KH2PO4, 0.6 g of ammonium citrate, 1 g of acetate, 0.25 g of tyrosine, 0.24 g of alanine, 0.125 g of arginine, 0.42 g of aspartic acid, 0.13 g of cysteine, 0.5 g of glutamic acid, 0.15 g of histidine, 0.21 g of isoleucine, 0.475 g of leucine, 0.44 g of lysine, 0.275 g of phenylalanine, 0.675 g of proline, 0.34 g of serine, 0.225 g of threonine, 0.05 g of tryptophan, 0.325 g of valine, 0.175 g of glycine, 0.125 g of methionine, 0.1 g of asparagine, 0.2 g of glutamine, 10 g of glucose, 0.5 g of l-ascorbic acid, 35 mg of adenine sulfate, 27 mg of guanine, 22 mg of uracil, 50 mg of cystine, 50 mg of xanthine, 2.5 mg of d-biotin, 1 mg of vitamin B12, 1 mg of riboflavin, 5 mg of pyridoxamine-HCl, 10 μg of p-aminobenzoic acid, 1 mg of pantothenate, 5 mg of inosine, 1 mg of nicotinic acid, 5 mg of orotic acid, 2 mg of pyridoxine, 1 mg of thiamine, 2.5 mg of lipoic acid, 5 mg of thymidine, 200 mg of MgCl2, 50 mg of CaCl2, 16 mg of MnCl2, 3 mg of FeCl3, 5 mg of FeCl2, 5 mg of ZnSO4, 2.5 mg of CoSO4, 2.5 mg of CuSO4 and 2.5 mg of (NH4)6Mo7O24. S. pyogenes cells were grown in THY medium. This medium consists of 36.4 g·L−1 of Todd-Hewit Broth (Oxoid, Basingstoke, UK) and 5 g·L−1 of yeast extract (Oxoid).
Cells grown to mid-exponential phase were harvested by centrifugation at 4068 g for 10 min at room temperature, washed twice with 50 mm Mes buffer (pH 6.5) and finally suspended in the indicated buffer solution. Anaerobic conditions were established by flushing with nitrogen for 10 min. Glucose was added, and 400-μL samples were taken at regular time intervals and mixed immediately with 200 μL of a cold perchloric acid (3.5 m) solution. The extracts were kept on ice for maximally 60 min. The pH was neutralized with 160 μL of 2 M KOH. The pH-adjusted samples were centrifuged and the supernatants were stored at −80 °C for subsequent analysis. All metabolites were quantified by enzymatic methods coupled to the spectrophotometric determination of NAD(P)H.
Kinetic analysis of LDH of S. pyogenes
For heterologous expression of the LDH of S. pyogenes, chromosomal DNA of an M49 serotype strain was isolated according to the Qiagen Blood and Tissue Kit (Qiagen, Hilden, Germany) and used as a template for PCR amplification with the Phusion™ High Fidelity PCR Kit (Finnzymes, Vantaa, Finland) and the forward/reverse primer pair 5′-AGATGTTTAGGATCCACTGCAACTAAACAA-3′/5′-TCTCTTTTGGTCGACGTTTTTAGCAGC-3′. The resulting PCR fragment was ligated into the pASK-IBA2 vector (IBA GmbH, Göttingen, Germany) system via BamHI and SalI restriction sites. The recombinant vector was heat-shock transformed into CaCl2-competent Escherichia coli DH5α cells. Correct insertion of the PCR product was confirmed by plasmid sequencing. For heterologous expression of the corresponding enzyme, recombinant E. coli strains were grown in 200 mL of Luria–Bertani (LB) medium at 37 °C under vigorous shaking. At an absorbance (A600 nm) of about 0.4, expression was induced by the addition of anhydrotetracycline (0.2 μg·mL−1) and growth of the bacteria was allowed for another 2–4 h. Then, the cells were harvested by centrifugation and the bacterial pellets were stored overnight at −20 °C, subsequently thawed, suspended in 1 mL of Buffer W (100 mm Tris/HCl, pH 8.0, 1 mm EDTA and 150 mm NaCl) and disrupted using a Ribolyzer. Cell debris was removed by centrifugation for 10 min at 13 000 g and 4 °C. Clear supernatants were diluted 1 : 10 with Buffer W and applied to StrepTactin sepharose (IBA GmbH) columns. After washing the sepharose three times with 10 mL of Buffer W, recombinant Strep-tagged protein was eluted with 6 × 0.5 mL of Buffer E (Buffer W including 2.5 mm desthiobiotin). Elution fractions were checked for recombinant protein by SDS/PAGE and western blots using Strep-Tag-specific antibodies.
For LDH activity measurements, protein concentrations in the purified recombinant protein fractions were determined using the Bradford method (Bio-Rad Protein Assay Kit; Bio-Rad, Munich, Germany). The standard assay for determination of LDH activity was carried out by adding 50 μL of protein solution, 25 μL of Fru(1,6)P2 (20 mm) and 25 μL of NADH (6.75 mm) to 800 μL of sodium-phosphate buffer (50 mm, pH 6.8). The mixture was heated to 37 °C and the reaction was started by adding 100 μL of prewarmed (37 °C) sodium pyruvate (100 mm) to the reaction mixture. The LDH activity was assayed by measuring the decrease of NADH in the mixture at 340 nm in a spectrophotometer for 5 min. The conversion of 1 μmol of NADH (εNADH = 6220 L·mol−1·cm−1) to NAD+ per minute was defined as one unit of LDH activity. The activity was expressed as U per mg of protein. For determination of Km values and allosteric regulation, the standard assay was modified by using varying concentrations of Pi, sodium pyruvate, Fru(1,6)P2, NADH, ATP and NAD+. For determination of the Km values for the reverse reaction, NADH and sodium pyruvate were replaced with varying concentrations of NAD+ and l-lactate.
Kinetic analysis of pyruvate kinase of S. pyogenes
Kinetic measurements of S. pyogenes pyruvate kinase were performed in protein crude extracts. For this purpose, cells from 50 mL of an exponentially growing S. pyogenes culture in CDM-LAB medium [11,68] were harvested by centrifugation. Bacteria were washed twice in 1 × NaCl/Pi (PBS), suspended in 1 × NaCl/Pi to an absorbance (A600 nm) of 10 and lysed with 100 U of Phagelysin C (PlyC) per ml for 15 min at 37 °C [69,70]. Subsequently, cell debris was removed by centrifugation (10 min, 15 000 g) and the supernatant was filter-sterilized by passing through a 0.22-μm pore-size filter. For the standard pyruvate-kinase assay, 20 μL of protein crude extract was mixed with 880 μL of prewarmed (37 °C) reaction buffer (120 mm cacodylic acid, 120 mm KCl, 12 mm ADP, 1.2 mm Fru(1,6)P2, 30 mm MgCl2, 0.18 mm NADH, 5 U·mL−1 LDH). The reaction was started by the addition of 100 μL of prewarmed (37 °C) phosphoenolpyruvate (20 mm). The pyruvate kinase activity was assayed by measuring the decrease of NADH in the mixture at 340 nm in a spectrophotometer for 5 min. The conversion of 1 μmol of NADH (εNADH = 6220 L·mol−1·cm−1) to NAD+ per minute was defined as one unit of pyruvate kinase activity. The activity was expressed as U per mg of protein. For determination of Km values the concentrations of the respective substrates were modified in the standard assay.
This work was financially supported by SysMO-LAB (Systems Biology of Microorganisms – Lactic acid bacteria). Bas Teusink and Domenico Bellomo are also supported through the Kluyver Center for Genomics of Industrial Fermentation, funded by the Netherlands Genomics Initiative. The authors would like to thank A. Z. Andersen for providing the Berkeley Madonna files of the Andersen model, H. Santos & A. R. Neves for answering our questions regarding their NMR data and J. Snoep for fruitful discussions. Finally, we would like to thank Susanne Roth and Nadine Veith for extensive literature search on S. pyogenes.