When we screened the available molecular knowledge of central metabolism to understand E. coli
's adaptations from growth on glucose to acetate and vice versa, we noted that:
- Four TFs have been identified that regulate the expression of central metabolic enzymes and whose activities are modulated by binding of central metabolites:• Cra-fructose-1,6-bisphosphate (Cra-FBP) (Ramseier et al, 1993)• Crp-cyclic AMP (Crp-cAMP) (Botsford and Harman, 1992)• IclR-glyoxylate (IclR-GLX) and IclR-pyruvate (IclR-PYR) (Lorca et al, 2007)• PdhR-pyruvate (PdhR-PYR) (Quail and Guest, 1995).
- Each of the four involved metabolites assumes distinct levels during glycolytic and gluconeogenic growth across available published experimental data sets (Lowry et al, 1971; Botsford and Harman, 1992; Bettenbrock et al, 2007; Bennett et al, 2009).
- The expression levels of central metabolic enzymes regulated by these TFs are markedly distinct for growth on glycolytic and gluconeogenic carbon sources (Oh et al, 2002).
- The levels of these enzymes correlate with the activities of the regulating TFs due to distinct levels of their activating/inhibiting effectors (during glycolytic and gluconeogenic growth). For instance, on glucose, the PYR dehydrogenase (Pdh) level is high (compared with acetate), which is consistent with that enzyme's transcriptional repressor PdhR being inhibited by a comparatively high PYR concentration.
The fact that this set of differentially expressed pathways covers central metabolism (excluding the pentose phosphate pathway), and the promising results of earlier work on the role of TF–metabolite interactions in cellular recognition and adjustments (Martinez-Antonio et al, 2006
; Reece et al, 2006
; Seshasayee et al, 2006
) let us to hypothesize that the current knowledge of E. coli
's metabolism can already explain the molecular adaptations between glycolytic and gluconeogenic carbon sources. Specifically, we hypothesized that these adaptations are accomplished by a system-wide regulation architecture that emerges when the known enzymatic and transcriptional regulations become coupled through the five listed TF–metabolite interactions. To (1) assess whether such coupled molecular interactions can indeed work together to adapt metabolic operation, and if yes, (2) to understand this system-level adaptation in molecular-level detail, we constructed a comprehensive differential equation model that is centered on the coupling of enzymatic and transcriptional regulation, which is accomplished by the five above listed TF–metabolite interactions.
The model topology, shown in , comprises the Embden–Meyerhoff pathway (EMP) (also known as the glycolysis or gluconeogenesis pathway, depending on flux direction), the tricarboxylic acid (TCA) cycle, the GLX shunt, the anaplerotic reactions, the diversion of carbon flux to the GLX shunt through phosphorylation of isocitrate dehydrogenase, the uptake of glucose through phosphorylation of PTS proteins, the uptake and excretion of acetate, the allosteric regulation of enzymes in the mentioned pathways and their transcriptional regulation by the above listed TFs, and the regulation of these TFs' activities through the above listed TF–metabolite interactions. Overall, the model comprises two compartments, the cell and its environment. The cellular compartment contains 12 metabolites, 22 enzymes and 2 PTS proteins, 4 TFs, 17 transcriptional regulations, 28 enzymatic regulations, 26 metabolic reactions, 2 kinase and 2 phosphatase reactions, 5 TF–metabolite interactions, the expression of 16 genes, and the degradation of the produced proteins as well as their dilution due to cell growth. The environmental compartment contains two carbon sources. The cell and the environment are coupled through glucose uptake as well as acetate uptake and excretion reactions.
Figure 1 Topology of the model. The model comprises two compartments, the cell and its environment. Bold metabolite names are biomass precursors and as such substrates for first-order reactions to void. Reactions and metabolites in quotation marks represent lumped (more ...)
This model topology is centered on the above listed TF–metabolite interactions, as illustrated in , and includes the known molecular interactions in E. coli
's central metabolism, retrieved from the EcoCyc database (Keseler et al, 2009
). The followed strategy for the systematic assembly of these interactions (see Supplementary information
) (1) ensures the inclusion of all known interactions between modeled compounds, (2) minimizes the number of omitted interactions across the system boundary, which occur, for instance, when a modeled reaction is regulated by a metabolite outside the system boundary, and (3) omits energy, cofactor, oxygen, and proton balances. These measures establish a system boundary that cuts out the studied adaptation mechanism from the rest of the cell. This approach rests on the modularity of cellular regulation (Wolf and Arkin, 2003
), which increases the autonomy of cellular subsystems. Because of this modularity, it is very likely that the in silico
dynamics of the modeled regulatory subsystem, which adapts metabolism between glycolytic and gluconeogenic growth, are in vivo
only modulated but not fundamentally changed by the activity of omitted regulations across the system boundary, which, for instance, balance the energy, cofactor, oxygen, and proton requirements.
Figure 2 The model topology is centered around the known TF–metabolite interactions and establishes a feedback loop from the metabolic layer through the transcriptional regulatory layer and the gene expression layer back to the metabolic layer. The metabolic (more ...) Kinetic equations
The focus of this study is to investigate whether the coupling of enzymatic and transcriptional regulation can accomplish dynamic adaptations between different steady-state growth conditions. Because of the importance of metabolite levels for controlling transcriptional regulation (see above), we needed to follow a modeling approach that accounts for metabolite dynamics shaped by enzyme kinetics and enzymatic regulation. These dynamics can only be adequately captured by a kinetic model, as, for example, existing constraint-based models with Boolean regulatory architecture such as developed and used by Covert et al (2004
) and Shlomi et al (2007
) ignore enzymatic regulation. Specifically, these models assume a rigid, positive correlation between metabolic flux and metabolite levels (neglecting the fact that this correlation can also be negative, see Kremling et al (2008
), and nuanced, see below). The problem of many uncertain parameter values of kinetic models is mitigated by the fact that the structure of mechanistic systems biology models already tightly constrains the possible system behaviors, leaving most parameter values unimportant (Brown et al, 2004
; Gutenkunst et al, 2007
Following a kinetic modeling approach, we translated the topology into differential equations by assigning the most appropriate rate law to each interaction (see Supplementary Tables S1 and S2
). To formulate the rate equation for the biomass-generating reaction, we back-calculated the requirements for metabolites outside the system boundary to their respective precursors inside the system boundary. We included the growth-rate dependency of the gene expression rates due to growth rate-dependent levels of DNA polymerases and ribosomes (Bremer and Dennis, 2008
The resulting 47 ordinary differential equations contain 193 parameters and are of the form
the vector of dynamic state variables (the concentrations of intracellular compounds and extracellular carbon sources), f
the vector of kinetic rate equations, p
the vector of parameters, and S
the stoichiometric matrix. Refer to the Supplementary information
for the full-model equations as well as for a MATLAB and SBML version of the model.
Parameter values for the rate equations were estimated through application of the ‘divide-and-conquer approach' (Kotte and Heinemann, 2009
) on published experimental steady state-omics data sets for balanced growth on either glucose or acetate (see Supplementary information
Supplementary Table S5
lists the values of a single parameter vector that excellently reproduces the steady state data (see Supplementary Tables S3 and S4
) for balanced growth on either glucose or acetate with the coefficient of determination R2
≈0.999, and with the sensitivities shown in Supplementary Figure S2
. These parameter values are used for all simulations presented in this paper.
Reproduction of known physiological behavior
To test whether the model is indeed capable of adapting to changing carbon sources, we subjected it to a sequence of three consecutive environments. The first environment contains glucose as the sole carbon source and is ‘inoculated' with glucose-adapted in silico cells, meaning that the initial conditions of the in silico cells were set to the steady state values of glucose growth. shows that the in silico cells grow on glucose, produce acetate from glucose, and after glucose depletion commence their adaptation to acetate, which they re-consume until it is depleted. The in silico cells are then ‘transferred' to a second environment that contains acetate as the sole carbon source, which the cells consume to successfully complete their adaptation to the acetate-adapted steady state. Finally, the in silico cells are ‘transferred' to a third environment that contains both glucose and acetate as carbon sources. Although at this point the cells are adapted to the present acetate, they quickly adapt to glucose instead, produce acetate from glucose, and then re-adapt to acetate following glucose depletion.
The model reproduces E. coli's known physiological behaviors of preferential glucose uptake and of acetate production from glucose.
These simulations show that the model reproduces E. coli
's known physiological behavior of glucose repression, which is the preferential uptake of glucose over acetate, and of an overflow metabolism, which is the production of acetate from glucose. Further, Supplementary Figures S4–S8
show that (1) throughout the transitions, all intracellular metabolite and enzyme levels remain within physiologically reasonable bounds and (2) all compound levels and reaction rates approach their measured steady state values for balanced growth. Whereas the measured steady states and the physiological behavior are correctly reproduced, the simulated trajectories of the intracellular compound levels during the transitions from one of the two steady states to the other (see Supplementary information
) are uncertain. The uncertainty of the simulated trajectories arises from (1) uncertainty in the parameter values, (2) uncertainty in the model structure due to ambiguity in the selection of rate laws, and (3) possible effects of not modeled cellular regulations, that is, those ensuring the omitted energy, cofactor etc. balances, onto the simulated trajectories.
The simulated trajectories of the intracellular compounds is thus one among many possible responses that reproduce the data. However, the possible behaviors of systems biology models are already tightly constrained by the model structure and generally rest on few crucial parameters (Brown et al, 2004
; Gutenkunst et al, 2007
)—alterations of most rate laws and variations of parameters only modulate but do not fundamentally change the overall system behavior. Exploiting this property, we investigate one possible response that has the remarkable property of adapting central metabolism to changing carbon sources. We aim at (1) understanding in detail how the interplay of molecular interactions accomplishes the adaptation, to (2) identify the general conceptual functions realized by these molecular interactions.
Recognition of extracellular carbon sources
As the in silico cells successfully adapt to fluctuating levels of glucose and acetate, they must have a mechanism to recognize these carbon sources. But how does an in silico cell recognize acetate without a transmembrane sensor for extracellular acetate or a TF binding to intracellular acetate? Similarly, it is unclear whether the glucose sensing function of the PTS is the exclusive mechanism to recognize glucose, or whether this sensing function is integrated into a larger sensing architecture.
As a sensing mechanism translates environmental information into TF activity, either through phosphorylation or effector binding, the sensing mechanism of the in silico
cell is identified once it is understood how an extracellular carbon source affects intracellular TF activities. Whereas phosphorylation of the TFs Cra, Crp, IclR and PdhR has as yet not been reported, these TFs' activities are known to respond to concentration changes of their effectors (Botsford and Harman, 1992
; Ramseier et al, 1993
; Quail and Guest, 1995
; Lorca et al, 2007
). Therefore, we here exclude the possibility of phosphorylation; the only remaining possibility to modulate these TFs' activities are concentration changes of their effectors. Our model simulations revealed that the TFs' effectors indeed respond to changes in the availability of extracellular carbon sources with a concentration change that modulates the TFs' activities (see Supplementary Figure S8
). But what links the levels of the intracellular effectors to the presence of extracellular carbon sources? The only entity capable of providing this missing link is metabolic flux, which must therefore form an integral part of the sensing mechanism. With this constraint, we deduced the following tripartite sensing mechanism.
First, the cell ensures a basal expression of the relevant carbon source transporter and uptake pathway. Hence, when that carbon source enters the cell's environment, it is taken up at least at a basal rate. In the in silico cell, such basal uptake is realized by a constitutive expression of the glucose-transporting PTS, and by a basal expression of the acetate-transporting ‘super-enzyme' Acs, which in the model lumps the acetate transport reaction and the subsequent conversion to acetyl-CoA (note that on glucose, acetate is both produced through the ‘Acoa2act' reaction and re-consumed through the Acs reaction at a lower rate). As the uptake of a carbon source propagates as intracellular flux through downstream metabolic pathways, the ensured uptake of a carbon source whenever present causes intracellular fluxes to respond to the presence of this carbon source.
Second, the enzyme kinetics and enzymatic regulation in pathways affected by the uptake flux is such that a certain metabolic intermediate in these pathways responds to the uptake flux in a characteristic way. The function of the enzyme kinetics and enzyme regulations is to establish a measurable signal for metabolic flux, which, being a rate, is an entity that the cell cannot measure directly. The in silico
cell uses two distinct motifs to establish such flux-signaling metabolites
- The motif pathway usage, illustrated in the left panel of Figure 4, places the flux-signaling metabolite in a pathway that is only used in one growth condition but not in the other; hence, synthesis of the metabolite, that is a high metabolite concentration, signals pathway usage. The in silico cell uses this motif to establish distinct levels of cAMP and GLX (see Figure 5). In both cases, the differential pathway induction is realized through fast changes in protein phosphorylation states. The phosphorylation of the PTS protein EIIA, which induces the formation of cAMP, is directly coupled to glucose uptake; the coupling of acetate uptake to flux through the GLX shunt is achieved by the regulation of the phosphorylation of isocitrate dehydrogenase, which diverts flux from the TCA cycle to the GLX shunt.
- The motif flux direction, illustrated in the right panel of Figure 4, places the flux-signaling metabolite in a reversible pathway that is operated in different directions depending on carbon source availability. As different flux directions mean that different enzymes ‘consume' the metabolite, these enzymes' kinetics can have different ‘flux resistances' such that the metabolite assumes high levels for one flux direction and low levels for the other; hence, the metabolite level signals flux direction. The in silico cell uses this motif to create distinct levels of the flux-signaling metabolites FBP and PYR (see Figure 5).
Third, the flux-signaling metabolites bind to target TFs and modulate their activities. These TF–metabolite interactions can be interpreted as a measurement of metabolite levels by TFs. The joint systems of TF–metabolite interactions and either of the above-described motifs, which ensure that the flux-signaling metabolite levels carry information about metabolic fluxes, conceptually form (indirect) sensors for metabolic fluxes. A molecular sensor for intracellular metabolic flux is thus defined as a system of regulations and enzyme kinetics, comprising (1) either of the two motifs pathway usage or flux direction and (2) the binding of the thus established flux-signaling metabolites to TF(s). Note that this definition makes a clear distinction between the direct physical measurement, that is of the flux-signaling metabolite levels by TFs, and the flux sensor's conceptually measured entity, that is the metabolic fluxes, which are not directly measurable and hence translated into a measurable signal. Note that metabolic flux sensors are conceptually analogous to man-made sensors—for instance, the not directly measurable velocity of an aircraft (a rate, like metabolic flux) is commonly inferred from physical measurements of the (velocity signaling) air pressure in so-called pitot tubes, which are constructed such that the air pressure inside the tubes carries velocity information.
The in silico cell is equipped with four flux sensors. Three of these sensors ultimately measure at different positions of the flux direction (and possibly its magnitude) through the EMP. Cra-FBP measures the flux through the upper EMP where FBP is located. On glucose, PdhR-PYR measures the lower glycolytic flux that is fed into the TCA cycle through PYR, whereas on acetate, PdhR-PYR measures the flux through the malic enzymes that is fed into the lower EMP. When glucose is taken up, the PTS-coupled Crp-cAMP sensor reports the glucose uptake and thus the glycolytic flux into the upper EMP; on acetate, the PTS-coupled cAMP level equilibrates with the PEP/PYR ratio that results from gluconeogenic flux into the lower EMP. The fourth of these flux sensors, IclR-GLX, senses the flux through the GLX shunt and is further modulated by the PYR signal (through IclR-PYR).
shows that the levels of the in silico
cell's four flux-signaling metabolites as well as the activities of the four target TFs are distinct not only for balanced growth on either glucose or acetate, but also for lower uptake rates of these substrates. Thus, the property of distinct TF activities is robust to changes in the substrate uptake rates, which may arise, for example, from fluctuating concentrations of the carbon sources. Because of this robustness, the TFs reliably sense the presence of extracellular glucose and acetate through binding ‘endogeneous' (Martinez-Antonio et al, 2006
; Seshasayee et al, 2006
) metabolite signals. Note that in some cases (e.g. Cra-FBP on glucose, see the fourth column in ), the gradual differences in TF activity resulting from variations in substrate uptake rates vary sensitively and monotonously with the magnitude of the sensed flux, which conceptually enables the sensing of intracellular flux magnitudes.
Figure 4 Two general motifs to establish flux-signaling metabolites. The first motif, pathway usage, places the flux-signaling metabolite in a pathway that is used in one growth condition but not in the other. The second motif, flux direction, places the flux-signaling (more ...)
Figure 5 The four flux sensors of the in silico cell. The four flux-signaling metabolites are established through enzyme kinetics and regulations that realize the motifs ‘pathway usage' and ‘flux direction.' The simulated dependencies of the flux-signaling (more ...)
As the in silico cell establishes and uses sensors for several intracellular metabolic fluxes, the overall sensing architecture infers the present carbon sources from a pattern of metabolic fluxes and is as such of a distributed nature. We therefore termed this architecture distributed sensing of intracellular metabolic fluxes. The core of this sensing architecture is formed not by transmembrane sensors but by the four flux sensors shown in , which establish flux-signaling metabolites according to the two presented general motifs. These flux sensors use intracellular metabolic flux as a means to correlate the presence of extracellular carbon sources with the levels of intracellular metabolites. The recognition of glucose through the PTS transmembrane complex is embedded as one flux sensor in this distributed sensing architecture; the other three flux sensors function without the help of transmembrane complexes.
Coupling of recognition and adjustment
Having identified the sensing mechanism, it still needs to be understood how the recognition of carbon sources is followed by an adjustment of metabolic operation to the recognized changes.
The in silico cell achieves the coupling between recognition and adjustment through its TFs, whose activities respond to the available carbon sources and at the same time regulate the expression of target genes. This combined recognition and adjustment, centered on the four TFs, closes four global feedback loops that overarch the metabolic and genetic layers as illustrated in . The first half of these four loops forms the recognition function and is established by the flux-signaling metabolites binding to their target TFs, creating flux sensors (the four columns in , and the upper of the three layers of arrows in ). The second half of these four loops forms the adjustment function and is established by (1) the transcriptional regulation of the four flux-sensing TFs (the middle layer of arrows in ), which causes the regulated enzymes to approach their measured steady state values, and by (2) the impact of this transcriptional regulation on metabolic operation (the lower layer of arrows in ), which, together with allosteric enzyme regulation, adjusts the metabolic fluxes.
To sum up, the adaptation of the in silico
cell arises from the global feedback loop-embedded, flux sensor-adjusted transcriptional regulation of the four TFs, with each TF performing one part of the overall adaptation. This adaptation incorporates both the influence of the metabolic on the genetic layer, achieved through TF–metabolite interactions, and of the genetic on the metabolic layer, achieved through the impact of adjusted enzyme levels on metabolic fluxes. Remarkably, the thus formed global feedback loops follow the general logic of the recently proposed consumer motif, which has been suggested to be ideal for the regulation of carbon source uptake (Krishna et al, 2007
Coherence through network topology
We have shown that the transcriptional response of the in silico cell to carbon source fluctuations is realized by four global feedback loops. As the four involved TFs are not regulated by a common transcriptional master regulator, it remains unclear how the apparently independent adjustments carried out by these TFs produce a coherent response of the overall system.
As the in silico cell can modulate its four TF activities only through the levels of the TFs' effectors, coherent TF activities can only result from coherent levels of the flux-signaling effectors. Such coherence arises on the metabolic layer, which is one step upstream of the TF regulatory layer (see ). We identified two means through which network topology encourages such coherence.
First, the responses of flux-signaling metabolites are coupled to each other because the metabolic fluxes to which they respond are connected to each other through the flux balances at network nodes. Therefore, when the local flux signaled by one of the flux-signaling metabolites changes, then the local fluxes signaled by the other metabolites are also likely to change.
Second, the responses of flux-signaling metabolites are coupled to each other because they mutually regulate each other's adjacent enzymes. Therefore, a change in one flux-signaling metabolite level propagates into changes of the other flux-signaling metabolite levels. Specifically,
- The levels of cAMP, PYR, PEP and the phosphorylation state of the EIIA protein are coupled through the phosphorylations of the PTS transporter (Bettenbrock et al, 2007). The levels of FBP and PEP are coupled through a dual-time switch, a motif that has been shown to be rapidly inducible yet robust to noise (Brandman et al, 2005). This switch ensures a high level of FBP and a low level of the downstream PEP on glucose, and the reverse behavior on acetate. The fast switch is formed by PEP and FBP mutually activating each other's consuming enzymes (Fdp, PykF, Ppc) through feed-forward loops, a motif that enables a high level of the upstream metabolite to lower the level of the downstream metabolite (Kremling et al, 2008). The slow switch is established through the transcriptional regulation of FBP-inhibited Cra on the expression of these metabolites' producing and consuming enzymes Fdp, PfkA, PckA, PykF, and PpsA and amplifies the coupling of FBP and PEP.
- The levels of PYR and GLX are coupled through GLX acting as inhibitor of the PYR-consuming Pdh reaction, and PYR acting as corepressor of the GLX shunt operon aceBAK and as effector regulating the phoshorylation of isocitrate dehydrogenase (which diverts flux from the TCA through the GLX shunt).
Through these two means, the levels of the flux-signaling metabolites become coupled, enabling a robust, coherent response of the four TFs. The coherent behavior of the overall system is therefore not established by a common transcriptional master regulator upstream of that system, but arises from the molecular interactions within the system itself.