are remarkably efficient at converting nutrient inputs into biomass. This efficiency enables estimation of many of their steady-state metabolic fluxes through linear optimization, an approach called flux balance analysis (FBA) (Edwards et al, 2002
). Although FBA is a powerful tool for flux estimation, it does not reveal the chemical events actually controlling metabolite concentrations and fluxes in cells. Here, we attempted to understand quantitatively such regulation, focusing on short-term responses to changes in nitrogen availability.
To this end, we used LC-MS/MS to measure the dynamics of the E. coli
metabolome when ammonium availability increases. Large concentration changes in α-ketoglutarate and glutamine, two of the central players in nitrogen assimilation, occurred rapidly (~10-fold changes in the first minute after upshift). Unbiased statistical identification of the major trends in the metabolome revealed two predominant characteristic response patterns, one mirroring α-ketoglutarate and one mirroring glutamine. Thus, at least among measured metabolites, those most strongly signaling nitrogen availability were species directly involved in nitrogen assimilation. This observation also conforms well to the known regulation by glutamine and α-ketoglutarate of the protein sensors of nitrogen status (e.g., PII) (Ikeda et al, 1996
). The α-ketoglutarate response is also interesting in light of evidence that α-ketoglutarate is the principal signal of nitrogen status in cyanobacteria (Forchhammer, 2004
A substantial fraction of the metabolome (~27/59) showed a muted version of the α-ketoglutarate and/or glutamine response patterns, with citric acid cycle compounds generally mirroring α-ketoglutarate and amino acids generally mirroring glutamine. Another large set of metabolites hardly changed in concentration (~30/59). Thus, despite the dramatic alterations to overall cell physiology, which lead to a two-fold increase in growth rate after ammonium upshift, much of the metabolome was effectively insulated from these changes. The homeostatic compounds included ATP and NADPH, both substrates consumed in nitrogen assimilation. Presumably, increased consumption of these compounds on ammonium upshift was offset by increased production.
The observation that co-factors involved in nitrogen assimilation remained homeostatic enabled simulation of the core reactions of nitrogen assimilation as a discrete module, with the measured cellular concentrations of the relevant carbon skeletons (e.g., α-ketoglutarate) considered as inputs to the model. The model included regulation of GS activity by a cascade of covalent modification reactions. In addition to GS modification, the model captured ammonia diffusion into the cell, its assimilation into glutamine, glutamate, and aspartate, and consumption of these species to drive biomass production. Growth rate was simulated as a function of the intracellular concentrations of glutamine and glutamate. The model thereby related environmental conditions to the growth rate through intracellular metabolite levels. To our knowledge, it is the first quantitative model to simulate the chemical steps by which environmental nutrient availability controls, through intracellular metabolite levels, cellular growth.
To the extent possible, the biochemical parameters of the model were taken from literature data. Those parameters not available in the literature (or for which biochemical estimates are generally not indicative of cellular conditions, e.g., Vmax), were determined by using a genetic algorithm to search for parameter values that resulted in the model matching the experimental results. One important conclusion of this integrated experimental-modeling effort was that, for the most part, known regulation of nitrogen assimilation is correct: it was sufficient to result in good agreement between the model and the experimental data.
Perhaps most informative, however, was the exception to this rule: all of the simulations failed to reproduce experimental results unless competition for enzyme active sites was explicitly included. Although theoretical analyses of metabolic regulation have discussed the potential importance of such competition (Fell, 1997
), concrete examples of its significance have been lacking. Here we provide two examples. One involves competition of aspartate, glutamate, and glutamine for the active site of GOGAT. Given that neither aspartate nor glutamate is a potent GOGAT inhibitor biochemically (Miller and Stadtman, 1972
), such competition was previously overlooked; however, given the high cellular concentrations of these amino acids, this ‘weak' inhibition is nevertheless physiologically critical. Interestingly, aspartate, which is not directly involved in the GOGAT reaction, is a more important active-site inhibitor than glutamate, the enyzme's product. A second example involves control of net aspartate production (by AST), which increases on nitrogen upshift. This net flux increase is achieved not by accelerating the forward reaction but by shutting off the reverse one. The decrease in the reverse flux is accomplished by glutamate out-competing α-ketoglutarate for the enzyme active site.
Our observation that active-site competition has an important function in controlling nitrogen assimilation fluxes matches nicely with the recent finding that most enzymes are substrate saturated in E. coli
(Bennett et al, 2009
). Both of these findings point to the intracellular milieu being crowded not only with macromolecules (Vazquez et al, 2008
), but also with small molecule metabolites, which greatly outnumber macromolecules on a molar basis. Flux control through active-site competition is especially valuable in vivo
given such an intracellular environment, because it provides regulation even in the regime in which substrate concentration greatly exceeds the Km
of the enzyme.
A distinguishing feature of flux control by active-site competition, relative to allostery or protein covalent modification, is that maximum enzyme activity can always be achieved if the substrate pool gets high enough. Thus, while flux control by active-site competition is efficient (not requiring expression of specific regulatory proteins or subunits), it is insufficient when reaching maximum enzyme activity might actually be dangerous to the cell. For example, it is probably critical for cells to be able to shut down GS activity in some circumstances, to save ATP and to prevent excess glutamine production (e.g., in ammonium shock of carbon-starved cells).
This work builds on a rich history of dynamic modeling of biological systems using ordinary differential equations, including in the area of metabolism (Teusink et al, 2000
; Rohwer and Botha, 2001
; Chassagnole et al, 2002
; Snitkin et al, 2008
). A distinguishing feature here is integration of systems level experiments with computational modeling to quantitatively understand a metabolic network involving multiple levels of regulation (i.e., protein covalent modification and enzyme active-site competition). We experimentally validated the model's ability to predict not only trends but time-dependent absolute cellular concentrations ().
Beyond clarifying mechanisms of cellular metabolic regulation, integrated experimental-modeling studies have the potential to generate models of intrinsic value. One potential value of these models is providing an easy way to determine properties that cannot be readily experimentally measured. Examples include dynamically changing fluxes (Supplementary Figure 8
), flux-control coefficients, and sensitivities of metabolite concentrations to enzyme parameters (). These properties, together with the measured ones, will then hopefully reveal regulatory principles. As an example, here we propose two principles relating to control of steady-state metabolite concentrations in cells:
- In nutrient-limited cells, the concentration of the growth-limiting metabolite (e.g., glutamine in wild-type cells, glutamate in ΔGOGAT ones) is determined by the sensitivity of growth rate to the metabolite's concentration (i.e., the Km of the growth function). The logic is that production of this metabolite is limited by environmental factors (e.g., the amount of ammonium). To balance production with consumption, growth must slow. The concentration in which this slowing occurs determines the metabolite's steady-state value.
- The concentrations of other metabolites are determined by the strength of the feedback control of their production. The logic is that production capacity of most metabolites exceeds demand and is brought into balance by feedback. The concentration in which balance is achieved is controlled by the Ki (or analogous parameter) of the feedback, as well as the extent of excess production capacity. This concept has been explored in depth mathematically (Hofmeyr and Cornish-Bowden, 2000).
In addition to providing insight into regulation of nitrogen assimilation in particular, and metabolite concentrations and fluxes in general, this work exemplifies the potential for using metabolomic data to drive the development of predictive metabolic models. As parameter identification for large nonlinear dynamic models is unreliable, we believe the most promising route to genome-scale dynamic simulations is through careful development of modular models such as the one presented here. If designed appropriately, these models can then be integrated to yield larger ones. For example, the nitrogen assimilation model, which takes α-ketoglutarate and oxaloacetate concentration as inputs, is well prepared for integration with a modular model of the TCA cycle, which predicts these concentrations, among others. The points in which these modular pathways meet, for example, α-ketoglutarate between the TCA cycle and nitrogen assimilation, should be particularly informative regarding metabolic integration: how information about the availability of one nutrient is communicated to pathways metabolizing others.