The multifarious short-term regulation of ammonium assimilation of Escherichia coli: dissection using an in silico replica Frank J Bruggeman1, Fred C Boogerd1 and Hans V Westerhoff1,2,3 Molecular Cell Physiology, Institute of Molecular Cell Biology, CRBCS, Vrije Universiteit, Amsterdam, the Netherlands Mathematical Biochemistry, SILS, Universiteit van Amsterdam, the Netherlands Stellenbosch Institute for Advanced Studies, Stellenbosch, South Africa Keywords ammonium assimilation; systems biology; glutamine synthetase; robustness; silicon cell Correspondence H.V Westerhoff, Molecular Cell Physiology, Institute of Molecular Cell Biology, CRBCS, Vrije Universiteit, de Boelelaan 1085, NL-1081, HV Amsterdam, the Netherlands Fax: +31 20 598 7229 Tel: +31 20 598 7230 E-mail: hw@bio.vu.nl Note The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed free of charge at http://jjj biochem.sun.ac.za/database/Bruggeman/ index.html (Received October 2004, revised 31 January 2005, accepted 23 February 2005) doi:10.1111/j.1742-4658.2005.04626.x Ammonium assimilation in Escherichia coli is regulated through multiple mechanisms (metabolic, signal transduction leading to covalent modification, transcription, and translation), which (in-)directly affect the activities of its two ammonium-assimilating enzymes, i.e glutamine synthetase (GS) and glutamate dehydrogenase (GDH) Much is known about the kinetic properties of the components of the regulatory network that these enzymes are part of, but the ways in which, and the extents to which the network leads to subtle and quasi-intelligent regulation are unappreciated To determine whether our present knowledge of the interactions between and the kinetic properties of the components of this network is complete ) to the extent that when integrated in a kinetic model it suffices to calculate observed physiological behaviour ) we now construct a kinetic model of this network, based on all of the kinetic data on the components that is available in the literature We use this model to analyse regulation of ammonium assimilation at various carbon statuses for cells that have adapted to low and high ammonium concentrations We show how a sudden increase in ammonium availability brings about a rapid redirection of the ammonium assimilation flux from GS ⁄ glutamate synthase (GOGAT) to GDH The extent of redistribution depends on the nitrogen and carbon status of the cell We develop a method to quantify the relative importance of the various regulators in the network We find the importance is shared among regulators We confirm that the adenylylation state of GS is the major regulator but that a total of 40% of the regulation is mediated by ADP (22%), glutamate (10%), glutamine (7%) and ATP (1%) The total steady-state ammonium assimilation flux is remarkably robust against changes in the ammonium concentration, but the fluxes through GS and GDH are completely nonrobust Gene expression of GOGAT above a threshold value makes expression of GS under ammoniumlimited conditions, and of GDH under glucose-limited conditions, sufficient for ammonium assimilation Many unicellular organisms exhibit enormous plasticity towards sudden changes in their physico-chemical environment Much of the adaptation capacity derives from the ‘emergent’ properties of biochemical networks composed of signal-transduction, metabolic, and gene-expression regulatory levels [1] Most of the Abbreviations a-KG, a-ketoglutarate; ATase, adenylyltransferase; GDH, glutamate dehydrogenase; GOGAT, glutamate synthase; GS, glutamine synthetase; NRI, response regulator of two-component signal transduction couple NRI ⁄ NRII; NRII, sensor of two-component signal transduction couple NRI ⁄ NRII; UTase, uridylyltransferase FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS 1965 Multifarious regulation dissected adaptation phenomena remain to be explained mechanistically in terms of the network topology and the kinetic properties of the molecular components of the network One possible approach to finding these explanations is through calculation of the properties of (parts of) such cellular networks from the experimentally determined properties of the macromolecules within them, for those cases where these properties are known sufficiently (e.g [2–5]) Such detailed kinetic models of parts of living cells have been called ‘silicon cells’ or ‘silicon replicas’ ([6], see also http://www siliconcell.net and http://www.jjj.bio.vu.nl) Silicon cells can be used: (a) to test whether the molecular-biological knowledge can account for observed physiological behaviour; (b) to analyse behaviour accounted for; and (c) to predict behaviour not observed experimentally (e.g [2–4,7]) Here, we present a silicon cell for the biochemistry underlying the metabolic regulation of ammonium assimilation in Escherichia coli A classical example of a hierarchical regulatory network is the glutamine synthetase (GS) adenylylation cascade involved in the regulation of ammonium assimilation of E coli [8–13] It is composed of two ammonium-assimilatory routes: one through GS ⁄ glutamate synthase (GOGAT) and one through GDH (glutamate dehydrogenase) Both lead to the net reductive addition of ammonium to a-ketoglutarate (KG) Whereas GDH accomplishes this in a single reaction, the GS ⁄ GOGAT pathway constitutes two reactions that additionally hydrolyse ATP The affinity of GS for ammonium (i.e % 0.1 mm) is a factor of % 10 higher than the affinity of GDH for ammonium (i.e % mm) [14,15] GS ⁄ GOGAT is essential for growth at low ( mm) ammonium concentrations, when < GDH appears to be redundant GDH might function in ammonium assimilation when free energy limits growth and sufficient ammonium is available [16,17] Furthermore, GDH has been implicated in osmotolerance and pH homeostasis [18] While growing on glucose and ammonium, as sole carbon and nitrogen source, respectively, the carbon skeleton of both glutamate (GLU) and glutamine (GLN) is derived from catabolism, i.e from a-KG (a tricarboxylic acid cycle intermediate), and the nitrogen atom is obtained directly from incorporating ammonium Glutamine (the product of GS) and GLU (the product of GDH and GOGAT) serve as precursors for the synthesis of a diverse range of metabolites, i.e (almost all) amino acids, purine and pyrimidine nucleotides, glucosamine-6-phosphate, and NAD+ [11] This central role of GLU and GLN at the intersection of catabolism and anabolism in E coli led physiologists and enzymologists to perform detailed 1966 F J Bruggeman et al studies on the regulation of the regulatory network connected to ammonium assimilation (reviewed in [11–13]) This network proved to harbour a stunning complexity, comprising at least five different regulatory mechanisms dedicated to the regulation of ammonium assimilation through direct effects on the activity of and amount of GS One mechanism resides in the difference in affinity of GS and GDH for ammonium, rendering GDH more important at high ammonium concentrations [15,19] A second mechanism operates through the cumulative feedback control of GS by various end products of the GLN- and GLU-demand pathways [20] The third mechanism involves the adenylyltransferase (ATase) catalysed inactivation of GS through a progressive adenylylation of its 12 subunits [21] The net rates of (de) adenylylation depend on: (a) the concentration of GLN [22]; and (b) the uridylylation state and the a-KG-binding state of the trimeric proteins PII [23] and GlnK [24,25] The latter two proteins act as substrates for the ambiguous enzyme uridylyltransferase (UTase) that can (de) uridylylate all three subunits of PII [26] and also those of GlnK [24,25] GlnK has recently been shown to be important under conditions of nitrogen starvation whereas PII is functional at higher concentrations of ammonium [27] All activities of UTase ⁄ UR are sensitive to the GLN concentration Additionally, PII can bind one a-KG molecule per subunit each having different effects on the signalling role of PII The fourth mechanism involves the transcriptional stimulation of the glnALG operon, which codes for GS, NRII, and NRI, by the doubly phosphorylated dimeric response-regulator NRI The dimeric protein NRII acts as the cognate sensor of the two-component regulatory system NRINRII When it binds PII complexed with one molecule of a-KG, NRII catalyses the dephosphorylation of phosphorylated NRI [12,28] The fifth mechanism is by regulation of the concentration of GS through protein turnover (reviewed in [11]) The network as a whole has been postulated to integrate and decide upon information concerning the physiological carbon and nitrogen status through its sensitivities for ammonium, a-KG, and GLN [12,22,29] A silicon cell that includes all known kinetic properties of the macromolecules involved in the five regulatory mechanisms might prove to be the only way to understand such complex regulation Provided that the kinetic properties of the molecules are represented correctly in the replica, the latter should behave in the same way as the real pathway With this challenge in mind, we now construct a silicon cell version of the regulation of the GS adenylylation cascade, based exclusively on what is known about the molecular constituents, i.e on FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al all the kinetic data We then analyse the effects of changes in the ammonium level and in the carbon status (a-KG) on the transient and short-time steady-state properties of the ammonium-assimilation flux by the network When considering such relatively short time scales, regulation through gene expression can be assumed to be negligible (e.g [30]) allowing one only to consider metabolic regulatory processes We devise and apply a method that determines the relative importance of the various regulators during transient regulation of the rate of GS Finally, we alter gene expression of GDH, GOGAT, and GS and calculate the effects on the ammonium assimilation flux We observe that the regulatory network gives rise to a number of regulatory phenomena that are not present in the constituent individual molecules, yet may exemplify much of the basis for the quasi-intelligent response of the living cell to changes in its environment The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/ database/Bruggeman/index.html free of charge Multifarious regulation dissected The three gln regulatory genes are expressed constitutively at a low level [13], suggesting that the intracellular concentrations of PII, UTase and ATase are independent of nitrogen status Accordingly, the amount of the regulatory protein PII and the activities of UTase, and ATase were fixed at levels normally encountered in wild type E coli cells The expression levels of the genes glnA, gltBD, and gdhA, encoding GS, GOGAT, and GDH, respectively, depend on the physiological state of E coli (e.g [31]) Time-dependent gene expression was not taken into account: the replica was meant to reconstruct the short-term metabolic regulation only Furthermore, the kinetics of the anabolic modules were chosen such that: (a) the net ammonium assimilation uxes (JN ẳ 2541 mmặmin)1) were consistent with intermediate specific growth rates of E coli (0.3– 0.5 h)1); and (b) the flux via the GLU demand route was approximately eight times higher than the flux via the GLN demand route [32] The maximal rates for GS, GOGAT, and GDH used in the calculations below were determined with wild type E coli growing at a specific growth rate of 0.3 h)1 in an ammonium-limited or a glucose-limited chemostat (Table 1) Results The ammonium assimilation network in silico: biochemical and physiological aspects The silicon cell version of the ammonium assimilation network in E coli was constructed from existing literature data on the kinetic and physicochemical properties of its components (Experimental procedures) The interaction network is shown in Fig The model incorporates the kinetic data known for the central proteins (GS, GOGAT, GDH, ATase, UTase, PII) The kinetic parameter values derive from in vitro measurements in cell-free extracts or with purified proteins, except for the kinetic parameters of ATase The latter parameters were obtained from fitting them to adenylylation states of GS as function of GLN and a-KG levels in a reconstituted system containing only ATase, UTase, PII and GS (with constant concentrations of a-KG and GLN) (Experimental procedures) We emphasize that we did not fit to systemic behaviour as a whole: all behaviour we calculate here results from the properties of the components rather than from a fit Also the physiological boundary conditions, e.g moiety conserved totals, were obtained from the literature The silicon cell employed simple modular kinetics for the reactions outside the ammonium assimilation pathway itself, such as amino acid synthesis of amino acids derived from GLU and GLN A detailed description of the kinetic model can be found in the Supplementary material FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS The ammonium assimilation network in silico – partial validation No comprehensive physiological studies of the ammonium assimilation network under controlled conditions that could serve as a full validation of the model could be found in the literature Therefore, we choose to compare the in silico behaviour of the wild type and mutants (obtained by removing the corresponding reactions) to the reported physiology of the corresponding real wild type and mutant strains Unfortunately, the type of physiological experiments carried out to determine the physiology of mutants is semiquantitative at best In the cases used in this section none of them included measurements of the maximal rates at the used physiological conditions This means that the physiological behaviour of the mutants in vivo and in silico can be compared in a qualitative sense only The steady states of the in silico wild type and mutants were calculated for four different ‘physiological’ conditions, i.e at a low (0.05 mm; Table 2) and at a high (1.0 mm; Table 3) intracellular ammonium concentration, each for two a-KG concentrations (0.2 and 1.0 mm) These a-KG concentrations represent the low and high end of the reported physiological range of intracellular concentrations [31] The following experimentally obtained physiological data (a–d) are qualitatively consistent with the simulated in silico data shown in Tables and (a) Under all 1967 Multifarious regulation dissected F J Bruggeman et al Fig Reaction scheme of the metabolic ammonium-assimilation network in E coli Subnetworks (UTase, ATase, metabolism), defined such that there is no mass flux between them, are enclosed in dashed boxes Metabolites are denoted in upper case letters Boundary metabolites (with concentrations held constant) are denoted by white letters in grey boxes Dashed arrows portray the regulatory interconnections between the subnetworks governed by the communicating intermediates that are displayed outside of the dashed boxes Full arrows represent the rates, which are further characterized by vj’s (where j denotes the enzyme abbreviation) Activators and inhibitors are depicted in bold and plain format below or above the process rates they regulate ATPase stands for the cellular free-energy pathways that re-phosphorylate ADP The following abbreviations were used: UT, uridylyl transfer; UR, uridylyl removal; DEAD, deadenylylation; AD, adenylylation; GS, glutamine synthetase; GDH, glutamate dehydrogenase; GOGAT, glutamate synthase; GLNDEM, glutamine demand; GLUDEM, glutamate demand; NH, ammonium; KG, a-KG; GLU, glutamate; GLN, glutamine; METGLN, metabolite derived from glutamine; and METGLU, metabolite derived from glutamate Table Measured maximal rates of GS, GOGAT and GDH determined for E coli K12 growing at a dilution rate of 0.3 h)1 in an ammonium-limited and glucose-limited chemostat All maximal rates are in mMỈmin)1 Enzyme Ammonium limited Glucose limited GS GOGAT GDH 600 85 360 110a 55 205 a Corrected experimental value (Experimental procedures) 1968 conditions, the calculated wild type steady-state GLN concentration (0.6–1.0 mm) proved to be at least one order of magnitude lower than the calculated GLU concentration (4.0–21 mm) This reproduces the concentration ranges and the relationship that has been observed frequently in vivo [31,33–35] (b) As expected for the wild type, at glucose limitation the in silico GS was adenylylated to a higher degree than for the conditions mimicking ammonium limitation Accordingly, ammonium assimilation ran predominantly via GS during ammonium limitation whereas GDH dominated during glucose limitation The ammonium assimilation FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Multifarious regulation dissected Table Calculated steady-state in silico physiology of wild type and of mutant E coli strains in the presence of 0.05 mM ammonium (ammonium-limited chemostat) and 0.2 (A) or 1.0 (B) mM a-KG The values for the maximal rates were 360 mMỈmin)1 (GDH), 600 mMỈmin)1 (GS), and 85 mMỈmin)1 (GOGAT) GLU (mM) GLN (mM) nAMP (AMPỈGS)1) JGS (mMỈmin)1) JGDH (mMỈmin)1) JN (mMỈmin)1) Genotype A B A B A B A B A B A B Wild type GS– GOGAT– GDH– Atase– Utase–a 0.6 0.0 0.1 0.6 1.5 0.0 0.9 0.0 0.4 0.8 2.5 0.0 4.0 0.3 0.1 3.5 4.3 0.6 5.3 0.6 0.2 3.9 5.3 1.3 1.2 0.0 0.0 0.7 0.0 7.0 1.5 0.0 0.0 0.4 0.0 9.1 30 0.0 2.7 31 36 4.5 30 0.0 5.2 34 37 6.0 2.8 3.7 3.8 0.0 2.6 3.6 6.5 7.3 7.4 0.0 6.4 7.2 33 3.7 7.0 31 39 8.1 37 7.3 13 34 43 13 a Initial conditions: PII ¼ 0.003 mM, PIIUMPi ¼ 0.000 mM (i ¼ 1,2,3) Table Calculated steady-state in silico physiology of wild type and of mutant E coli strains in the presence of 1.0 mM ammonium (glucose-limited chemostat) and 0.2 (A) or 1.0 (B) mM a-KG The values for the maximal rates where 205 mMỈmin)1 (GDH), 110 mMỈmin)1 (GS), and 55 mMỈmin)1 (GOGAT) GLU (mM) GLN (mM) nAMP (AMP GS)1) JGS (mM min)1) JGDH (mMỈmin)1) JN (mMỈmin)1) Genotype A B A B A B A B A B A B Wild type GS– GOGAT– GDH– ATase– UTase–a 0.6 0.0 0.6 0.0 2.1 0.0 1.0 0.0 1.0 0.0 14 0.1 6.0 3.6 1.9 0.1 5.7 4.1 21 27 14 0.2 14 24 2.1 0.0 5.2 0.0 0.0 11 0.0 10 0.0 0.0 11 18 0.0 6.3 2.1 26 3.3 12 0.0 8.0 3.0 25 3.1 17 19 21 0.0 17 19 31 28 34 0.0 34 29 35 19 27 2.1 43 22 43 28 42 3.0 59 32 a Initial conditions: PII ¼ 0.003 mM, PIIUMPi ¼ 0.000 mM (i ¼ 1,2,3) fluxes are comparable under the two conditions (this illustrates growth at comparable growth rates) (c) Experimental cells lacking GOGAT show unimpaired growth at high ammonium concentrations Only under nitrogen-limitation they grow more slowly [36] The in silico GOGAT mutant showed a similar behaviour; its ammonium flux (JN) was clearly much lower than that of the wild type at low ammonium concentrations, irrespective of the a-KG level At the higher ammonium concentration the silicon GOGAT deletion cells did assimilate ammonium at a substantial rate, again consistent with the experimental result (d) Mutants lacking GDH have no obvious growth impairment when both free energy and carbon are available in excess [17,32] In agreement with this experimental observation, the silicon GDH deletion mutant sustained a high ammonium-assimilation flux during ammonium-limited growth (e) Cells of Salmonella typhimurium devoid of ATase and induced for GS expression accumulate GLN to high levels under high ammonium conditions, even after the initially depleted GLU pool has been restored [37,38] This is indeed calculated for the in silico pathway for the case of glucose FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS limitation (f) Experimental mutants lacking UTase exhibit a high adenylylation state of GS independent of the absence or presence of ammonium in the medium [39,40]; they are not able to sense changes in the nitrogen status (they sense nitrogen all the time) Likewise, GS was adenylylated to a substantial extent in the in silico UTase mutant growing at two limitations An in silico PII mutant was not included, because the interpretation of the phenotypes of experimental PII mutants is confounded by the presence of the PII paralogue, GlnK, in these mutants [41] The in silico mutant strain deficient in GS did engage in ammonium assimilation but its GLN production flux was zero (Tables and 3) In reality such a mutation is indeed lethal due to the fact that GS is the sole enzyme capable of producing GLN Steady-state response to changes in ammonium concentration The effects of the external nitrogen and internal carbon and nitrogen status on the metabolic regulation of the ammonium assimilation flux were investigated The 1969 Multifarious regulation dissected external nitrogen and the internal carbon and nitrogen status were taken to be reflected by the ammonium, a-KG, and the GLN concentration, respectively Metabolic steady states were computed at internal ammonium concentrations ranging from 0.01 to mm, while the a-KG concentration was either set to 0.2 or to 1.0 mm The calculations were performed for cells that had expression levels of GS, GDH, and GOGAT that mimicked long exposure to ammonium limitation, i.e identical conditions to those in Table All calculations involved metabolic steady states that had been reached within minutes after cells ) incubated for generations at ammonium limitation (i.e 0.05 mm ammonium) ) had been shifted to the ammonium concentration indicated on the abscissa of Fig The computed steady states thus reflect metabolic states reached before enzyme synthesis or degradation could have had any effect The range of a-KG concentrations was again chosen to mimic the physiological concentrations range [31] The steady-state relationship between the overall ammonium-assimilation flux (JN) and the ammonium concentration for two different a-KG concentrations is shown in Fig 2A,B Irrespective of the a-KG concentrations, JN increased sharply with the ammonium concentration as long as the latter stayed below % 0.03 mm Above this ammonium concentration the dependence of the ammonium assimilation flux on the ammonium concentration changed drastically: the ammonium assimilation flux increased only slightly with a further increase in ammonium concentration Below the threshold, the metabolic regulation appeared to fail, in view of the sharp drop in JN with even a minor decrease in ammonium Our calculations suggest that the expression of the ammonium transporter AmtB may be necessary to sustain ammonium assimilation at ammonium concentrations below this threshold To investigate which regulatory mechanism acting on GS has the highest effect on the dependency of the ammonium assimilation flux on the ammonium concentration we removed three such mechanisms The ammonium assimilation flux in the insets of Fig 2A,B corresponds to the three different models in which the direct regulation of GS is ‘mutated’ by removal of the terms from the rate equation of GS that correspond to: (a) thermodynamic regulation; (b) kinetic regulation; and (c) both thermodynamic and kinetic regulation Removal of thermodynamic regulation corresponds to neglecting the inhibitory effect of the backward reaction of GS on the rate of biosynthetic ammonium assimilotion (by deleting the term [ADP][GLN][Pi] ⁄ Keq,GS from Eqn 19a) The kinetic effect was removed by abolishing both the effect of adenylylation on the maximal rate of GS (the JGS term on Eqn 19a and b 1970 F J Bruggeman et al was set to 1) and by eliminating the product inhibition terms, e.g ADP ⁄ KADP To enable a fair comparison, the maximal rate of GS in the ‘mutated’ models was corrected such that the net ammonium assimilation flux (JN) of the mutated and the original model was identical at 0.05 mm of ammonium (i.e 32 and 37 mmỈmin)1, respectively, at 0.2 and 1.0 mm a-KG) Clearly, both insets indicate that the effect of the removal of both regulatory mechanisms (but not of either alone) on the ammonium assimilation flux was drastic, i.e at 1.0 mm a-KG, JN now increased from 47 at 0.02 mm ammonium to 160 mmỈmin)1 at 1.0 mm (The value for the JN at 1.0 mm ammonium in the case for removal of the kinetic and thermodynamic regulation was 69 and 47 mmỈmin)1, respectively.) Ammonium assimilation is thought to be associated with high activities of GS and GOGAT at low concentrations of ammonium (< mm) and no activity of GDH, whereas GDH is presumed to carry the flux exclusively at higher concentrations of ammonium [11] This has been postulated to be favourable because of the additional hydrolysis of one ATP per molecule of ammonium assimilated if the GS ⁄ GOGAT pathway is used [17] To investigate whether the shift from GS ⁄ GOGAT to GDH should actually be expected on the basis of known kinetics and of metabolic regulation alone, the relative contributions of GS and GDH to the net ammonium assimilation flux were calculated as a function of the ammonium concentration, again for the two different concentrations of a-KG (Fig 2C,D) Contrary to the expectations, GDH was calculated to be active at low ammonium concentrations Even at the ammonium level that maximally supported GS activity (0.03 mm), GDH activity contributed 12% to the ammonium assimilation flux (at 1.0 mm a-KG) The relative contribution of GS increased strongly with increasing ammonium concentrations before it went through a maximum of 88% at 0.03 mm ammonium Hereafter, the contribution of GS decreased, quickly at first and then slowly, to settle to a plateau value of 20% (for 1.0 mm a-KG) for ammonium in excess of mm (data not shown) The heights of both the peak in the dependence of the variation of the relative contribution of the two enzymes on the ammonium concentration and, to a lesser extent, the minimum plateaus, decreased with an increase in the a-KG concentration Remarkably, Fig 2C shows that, at a low a-KG concentration, even at an ammonium concentration exceeding mm, GS contributed significantly to the overall ammonium assimilation (43% at 1.0 mm NH4+ and 0.2 mm KG) The strict paradigm of ammonium assimilation flux through GS at low and through GDH at high ammonium concentrations should perhaps be replaced by the FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Multifarious regulation dissected Fig Calculated, steady-state characteristics of the ammonium assimilation network as function of the ammonium concentration at two a-KG concentrations, i.e 0.2 (A, C, E, G), and 1.0 (B, D, F, H) mM; AB, overall ammonium assimilation flux (JN); CD, flux ratio of GS and GDH (JGS ⁄ JGDH); EF, apparent maximal rate of GS (VAPPGS) and the adenylylation state of glutamine synthetase (nAMP); GH, the concentration of PII with one a-KG attached to it (PIIKG1), of PII saturated with both UMP and KG (PIIUMP3KG3), and of glutamine (GLN) The numbered lines in the insets of (A) and (B) correspond to the removal of thermodynamic regulation (1), kinetic regulation (2), and both (3) In order to guarantee identical ammonium assimilation fluxes of the original and the mutated model at 0.05 mM ammonium, the fluxes in the insets were calculated with the following values for the maximal rates of GS (in mM min)1), 555 (1, inset A), 160 (2, inset A), 160 (3, inset A), 550 (1, inset B), 140 (2, inset B), 140 (3, inset B) FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS 1971 Multifarious regulation dissected subtler picture emerging from what we calculated here on the basis of the properties of the participating enzymes The general perception that all ammonium assimilation at high ammonium concentrations follows the energetically cheaper route along GDH, is not supported by the known kinetic properties of the pathway Indeed it is well known that microorganisms are not generally efficient free-energy transducers [42] The contribution of GS to the nitrogen assimilation flux was smaller at the high a-KG concentration (24% at 1.0 mm NH4+) This indicates that GS may not only play a role at low external ammonium conditions but also at low internal carbon conditions Indeed, not only does the enzyme couple GS ⁄ GOGAT have a higher affinity for ammonium than GDH, it also has a higher affinity for a-KG, i.e the KM values of GDH and GOGAT for a-KG are 0.3 mm and lm, respectively Apparently, GS ⁄ GOGAT not only senses the internal nitrogen status (GLN) but, additionally, the internal carbon status The concentrations of GLN and PIIKG1 (the form of the signalling protein PII that binds to the sensor NRII activating the phosphatase activity of the latter towards NRIP) increased steadily with the ammonium concentration above 0.03 mm The extent of the increase in the concentration of PIIKG1 depended on the a-KG concentration (Fig 2G,H) At 1.0 mm ammonium and 1.0 mm a-KG, its concentration amounted to % 22 nm, which represented 0.7% of the total amount of PII present (3 lm) An increased concentration of PIIKG1 implies an increased rate of NRII-PIIKG1-catalysed dephosphorylation of NRIP and hence a decrease in the expression level of GS The physiological concentration of NRII (assuming it is comparable to the concentration of NRI) is between and nm for cells grown in the presence of excess ammonium and it may rise to > 60 nm in cells grown at low nitrogen conditions [42a] Therefore, especially at high concentrations of a-KG, where the contribution of GS to JN was relatively low (Fig 2D), gene expression of GS may be down regulated by PIIKG1 The concentration of the other regulatory PII intermediate, i.e PIIUMP3KG3, decreased with increasing ammonium concentrations, but increased with increasing a-KG concentrations These two species reflect the decrease in the overall uridylylation state of PII as a function of increasing ammonium concentration (data not shown) Transient response to a sudden increase in ammonium availability Schutt and Holzer [43] measured a rapid decrease in the apparent maximal rate of GS (its maximal rate 1972 F J Bruggeman et al corrected for its adenylylation state) upon a sudden increase in the ammonium concentration to cells that had been adapted to growth on proline, i.e to the virtual absence of ammonium They stopped short of determining the actual composite rates of ammonium assimilation and of confirming that the system shifted between rates as effectively as often hypothesized Inspired by this work, we subjected the silicon network, adapted to ammonium limitation as reflected in the values of the maximal rates of GS, GDH and GOGAT and at the reference steady state used previously (i.e an ammonium concentration of 0.05 mm), to a sudden increase in the ammonium concentration to 1.0 mm To investigate the effect of the carbon status we performed the calculations at constant concentrations of both 0.2 and 1.0 mm of a-KG (Fig 3) At low concentrations of ammonium and a-KG, in silico ammonium assimilation ran predominantly via GS ⁄ GOGAT (Figs 3A and 2C) Upon the 20-fold increase in the ammonium concentration at time zero, the rate of GS (and GDH) initially increased rapidly, as expected from the increase in the concentration of one of their substrates After a few seconds the rates began to decrease Eventually the (steady-state) GS rate dropped to a level lower than before the addition of the ammonium, in spite of the 20-fold increased concentration of one of its substrates Figure 3C illustrates that the decrease in the rate of GS correlated with a decline in its apparent maximal rate (to % 10% of its preshift value) This in turn correlated with the (rapid) adenylylation of nearly all subunits of GS (from 1.2 to 11 AMP ⁄ GS) within Within a minute after the ammonium shift, the GLN concentration increased rapidly to finally settle down to a higher steady state than before the ammonium change (Fig 3E) The progressive adenylylation of GS resulted from two effects both caused by the rapid increase of the GLN concentration Firstly, GLN itself may have directly stimulated the ATase-catalysed adenylylation reaction Secondly, GLN interacts with UTase and may hereby have increased the level of PIIKG1 and decreased the level of PIIUMP3KG3 (Fig 3E), giving rise to both a further stimulation of the ATase-catalysed adenylylation reaction and a release of the stimulation of the ATase-catalysed deadenylylation reaction Effects of mutations on the transient response of the network To obtain a more detailed picture of the contribution of the different proteins involved in the regulation of the shift from GS- to GDH-dominated ammonium assimilation upon an increase in the ammonium concentration, FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Multifarious regulation dissected Fig Calculated transient response to a sudden increase in the ammonium concentration from 0.05 to 1.0 mM at time zero The a-KG concentration was 0.2 mM (panels A, C, and E), or 1.0 mM (panels B, D and F) continuously A, B: rates of glutamine synthetase (vGS), glutamate synthase (vGOGAT) and glutamate dehydrogenase (vGDH) C, D: adenylylation state of glutamine synthetase (nAMP) and the ‘apparent’ maximal rate of glutamine synthetase (VAPPGS) E, F: concentrations of glutamine (GLN), PII with one a-KG attached to it (PIIKG1), and PII saturated with UMP and a-KG (PIIUMP3KG3) we removed ATase, UTase, and PII from the model We performed these in silico experiments at an a-KG concentration of 1.0 mm, i.e the conditions where the shift was most appreciable (Supplementary Figs S1– S3) These ‘deletions’ took place at the moment of the addition of ammonium to make sure that the initial conditions at the moment of the addition were similar to those in Fig 3B This illustrates the potential power of silicon cells; here we calculate the outcome of an FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS experiment not achievable in the laboratory The removal of ATase caused an accumulation of GLN (to 67 mm within after the pulse) (Supplementary Fig S1) Most importantly, in this simulated absence of the regulation through ATase, GS contributed 44% to the ammonium assimilation rate mins after the addition of ammonium Similarly, in order to investigate the role of UTase in regulating the maximal rate of ATase we removed UTase from the model (Supplementary 1973 Multifarious regulation dissected Fig S2) Removal of UTase led to (relative to the wild type): (a) an increased steady-state concentration of GLN; (b) a similar adenylylation state and apparent maximal rate of GS; and (c) comparable rate changes in GS, GOGAT and GDH Apparently, GLN can take over the regulatory role of PIIKG1 and PIIUMP3KG3 after the pulse (Of course, removal of UTase is likely to have important effects on the regulation of ammonium assimilation due to its second regulatory role, i.e hierarchical regulation of the activity of the two-component signalling network NRI ⁄ NRII through its directs effect on the concentration of PIIKG1, but gene expression regulation is not considered here) Do these results hint at PII being redundant for metabolic ammonium assimilation: can GLN substitute for PII? This we investigated by removing PII from the model at the moment the mm ammonium was added (Supplementary Fig S3) PII turned out to be of major importance; its removal led to an accumulation of GLN and to total deadenylylation of GS (causing its apparent maximal rate to rise to its maximal value of 600 mmỈmin)1) As in the case of the removal of ATase, PII removal interfered with the shift from GS ⁄ GOGAT- to GDH-dominated ammonium assimilation This may have been due to the synergistic effect of PIIKG1, PIIUMP3KG3 and GLN on the rate of ATase (Eqns 15b and 16b) These results indicate that the interplay between GS ⁄ GOGAT and GDH critically depends on the signalling cascade composed of both ATase and PII, UTase being perhaps more important as a hierarchical regulatory mediator Additionally, the calculated results of PII removal indicated that ATase alone may be insufficient for regulating the level of ammonium assimilation upon an ammonium pulse Analysis of regulation of the transient response of the GS rate The decrease in the rate of GS upon the sudden addition of ammonium at time zero (Fig 3A,B) is a result of the regulatory network as a whole For, in the metabolic subnetwork alone, the rate of GS should have increased upon the addition of ammonium (as exemplified by the results obtained in silico after the removal of ATase (Supplementary Fig S1) The change in the rate of GS could be caused by the changes in: its state of covalent modification (nAMP), and the concentrations of substrates (GLU; ATP) and products (GLN; ADP) There was no method available yet however, to analyse the relative importance of these various regulatory routes These regulatory influences could well depend on time, making such an analysis even more complicated 1974 F J Bruggeman et al To test whether the adenylylation of GS is indeed the most important regulatory event to downregulate the flux of GS upon a rise in the ammonium level, we set out to develop an in silico method that should enable us to quantify the relative strengths of parallel regulatory pathways as a function of time To this aim we wrote the fractional change in the rate of GS at time t as follows: 5 X @ lnvGS X v dlnvGS dlnXi tịẳ tịẳ tị HXGS tị i dt @ lnXi dt iẳ1 iẳ1 1ị where the sum was taken over the regulatory contributions of all five regulators (denoted by Xi) The regulator with the highest regulatory contribution (HvGS for the regulatory contribution of Xi on the Xi rate of GS) at time t has the highest contribution to the change in the rate of GS at that moment in time After integrating over the entire steady-state relaxation time, one then obtains for the average regulatory  contribution of Xi ðHvGS Þ: Xi t Zt d ln vGS ðsÞ ds dt 5 X v X Z @ ln vGS d ln Xi  GS ðsÞ ds ẳ ẳ sị HXi t @ ln Xi dt iẳ1 iẳ1 t 2ị Similarly, the average absolute regulatory contribution of a regulator Xi to transient regulation of vGS over a time span to t should be given by Z   vGS t  v  H GS sịds H  ẳ 3ị Xi Xi t In Supplementary Fig S4 the regulatory contributions of the five regulators are displayed for the changes in the rate of GS that were shown in Fig Supplementary Fig S4 indicates that initially (seconds) ADP, ATP, GLN, GLU, and nAMP (in decreasing order of importance) were important regulators, after that (seconds to minute) GLU and nAMP, and at a later stage (minutes) nAMP was most important The integrated regulator contributions can be found in Table In the average regulatory contribution up- and downregulation are included: negative and positive effects are just summed up over time A more interesting variable is therefore the average absolute regulatory contribution: here negative effects are integrated, turned into positive values and summed up with positive effects It is noteworthy that the average regulatory contributions of ATP and ADP have the same sign, even though they are an activator and an inhibitor of GS, respectively This is explained by the definition of the regulatory FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Multifarious regulation dissected Table Average regulatory and average absolute regulatory contributions of the regulators of the rate of GS from to after the pulse at 0.2 mM and 1.0 mM a-KG Average absolute regulatory contribution KG (mM) Average regulatory contribution KG (mM) 0.2  HvGS GLN  HvGS GLU  HvGS ATP  HvGS ADP  HvGS nAMP 1.0 )0.019 )0.032 0.11 0.14 0.0020 0.0026 0.048 0.068 )0.45 A )0.56  vGS  H  GLN  HvGS  vGLU  H GS  ATP  HvGS  ADP  HvGS n AMP 0.2 1.0 0.079 0.077 0.12 0.14 0.016 0.017 0.26 0.26 0.69 0.61 contribution and the fact that the sum of ATP and ADP remains constant For the time-averaged absolute regulation, the contribution of the adenylylation to the regulation of GS proved most important The importance of the regulatory contributions (on basis of their magnitude) in decreasing order is nAMP, ADP, GLU, GLN, and ATP The magnitudes of the regulatory contributions depended on the a-KG concentration but their order of importance turned out to be independent of the carbon status B Steady-state analysis of ammonium assimilation flux as function of the enzyme expression levels So far, the calculations were performed for fixed expression levels of GDH, GOGAT and GS, levels that corresponded to E coli growing at a rate of 0.3 h)1 in either an ammonium-limited or a glucose-limited chemostat The proteins constituting the regulatory cascade (UTase, PII, ATase) are constitutively expressed at a low level [44] The levels of expression of the assimilatory proteins GS and GDH may vary considerably whereas that of GOGAT changes to a smaller extent [31] It is shown (Supplementary Fig S5) that if GOGAT is expressed above a threshold activity level of approximately 60 mmỈmin)1 expression of GS at a low level of ammonium and a-KG (respectively, 0.05 and 0.2 mm) is sufficient to guarantee a high ammonium-assimilation flux We calculated the implications for the ammonium assimilation flux of the above mentioned expression response of E coli by changing the maximal rate of GS (range, 50–800 mmỈmin)1) and GDH (range: 50–500 mmỈmin)1) with GOGAT fixed at either 85 mmỈmin)1 (Fig 4A: ammonium-limited chemostat) or 55 mmỈmin)1 (Fig 4B: glucose-limited chemostat) Figure 4A indicates that gene expression of GS is necessary for a high ammonium assimilation flux during FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS Fig Calculated ammonium-assimilation flux (JN) as a function of the maximal rates of GDH and GS Conditions: (A) VGOG ẳ 85 mMặmin)1, NH ẳ 0.05 mM, and KG ¼ 0.2 mM and B VGOG ¼ 55 mMỈmin)1, NH4+ ¼ 1.0 mM, and KG ¼ 1.0 mM, respectively, mimicking ammonium-limited and glucose-limited chemostat The dots in the figures resemble the conditions of the models used in the text [JN value was taken from A: Table (3rd row, 12th column), and B: Table (3rd row, 13th column)] ammonium-limited growth The effects of expression of GDH on ammonium assimilation are negligible (It makes the dependence of JN on VGS slightly less sigmoidal and the VGS value at which JN achieves its halfmaximal value shifts slightly to lower VGS values.) At parameter values mimicking glucose-limited growth the effects of the expression of GS and GDH are only evident at low values for VGS and VGDH 1975 Multifarious regulation dissected Discussion The approach taken here started from the contemporary knowledge on the interactions between the components and their kinetic properties as documented in the literature All the kinetic parameters were taken as such, with one exception; the kinetic parameters of ATase had to be obtained via a fitting procedure Importantly, this was done only at the level of a reconstituted subnetwork, i.e not at the entire system level Consequently, any system behaviour that arose in the subsequent calculations of the entire network resulted from the properties of and the interactions between its components This type of models aims at in silico replica of biochemical systems This method of biochemical calculations has been successful in a number of cases [2–4,7] (cf http://www.jjj.bio.vu.nl) Unfortunately, no studies could be found in the literature that contained sufficiently large data sets containing transient or steady-state measurements of the ammonium assimilation network suitable to truly validate the model Therefore, we aimed at partial validation The kinetic model was demonstrated to exhibit realistic behaviour as witnessed by the good qualitative match between calculated and known physiological features of wild type and mutant strains of E coli (Tables and and associated text) Despite the scarcity of physiological data, the model allows for an insight into the general features of the network and their underlying regulatory mechanisms that are presently predictable on the basis of what is known experimentally We tested the model behaviour regarding some frequently posed hypotheses about the physiological features of the ammonium-assimilation network The hypotheses are mostly based upon qualitative experimentation carried out in vitro And even though they are widely accepted to capture the functioning of the network, they have hardly been confirmed in vivo The lack of confirmation is partially explained by the complicated nature of such experiments With the silicon cell model at hand, we can determine to what extent the model behaviour is consistent with these hypotheses We considered the following hypotheses [11–13,23] (a) At low ammonium concentrations, GS carries most of the ammonium assimilation flux, while GDH takes over at high concentrations (> 1.0 mm) (b) A sudden change in the ammonium concentration brings about a short-term (metabolic regulation) redistribution of the flux over GS and GDH caused by (de-)adenylylation of GS (c) The degree of adenylylation of GS is the most important regulator of GS (d) Upon a downshift in ammonium availability, extra GS expression is necessary to sustain growth In a qualitat1976 F J Bruggeman et al ive sense, the model confirmed all of these hypotheses; hence, they may be considered an additional validation of the model In addition, and more importantly, the quantitative nature of the model allows us to make detailed predictions on the behaviour of the network Comparison of the predictions with the relevant data from the literature, if available, may give us clues about further experimentation and modelling The following predictions stood out most conspicuously in the model calculations (a) Either the KM of GS for ammonium is much lower than the reported value of 100 lm or a free energy-dependent transporter for ammonium uptake is mandatory when the intracellular ammonium concentration falls below 30 lm This prediction is based on the in silico observation that the ammonium assimilation flux collapses below 30 lm ammonium (Fig 2) The observation indirectly supports one (or both) of the above alternative predictions, as can be argued as follows It has been claimed that the AmtB transport protein facilitates the diffusion of ammonia (NH3) across the cytoplasmic membrane; it would not actively transport the ammonium ion [45] Furthermore, at neutral pH, the ammonium transporter appeared to be required only at very low (< 10 lm) external ammonium concentrations [46] Taken together, the implication would be that, given a cytoplasmic pH of 7.5, the concentration of intracellular ammonium should then be even lower (< lm) Still growth was not affected [46] In contrast, our model indicates that at an intracellular ammonium concentration < lm the ammonium assimilation rate would not be sufficient to sustain normal growth of E coli In principle, this interesting discrepancy could be reconciled by either one of the two predictions (b) The high affinity for ammonium of GS (KM ¼ 100 lm) relative to that of GDH (KM ¼ 1100 lm) is considered to be essential for the activity of the GSGOGAT route at low ammonium concentrations However, the network behaviour of our replica indicates that the relatively high affinity for a-KG of GOGAT (KM ¼ lm) compared to that of GDH (KM ¼ 300 lm) is on the basis of a similar argument indicative for the activity of GS-GOGAT at a low carbon status In other words, even at relatively high ammonium concentrations and a simultaneously low level of a-KG, GS-GOGAT would be considerably active Thus, the ammonium-assimilating network not only ‘senses’ the N status but also the C status Integration of N and C signals at the metabolic level may occur in various sophisticated ways, that is, through regulatory proteins, covalent modifications, and specific binding of small molecules, but also (partly) via controlled mass action, that is, by controlling the FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al substrate and product availability (c) UTase is not so much involved in metabolic regulation of GS, and, as a consequence, is expected to be more engaged in hierarchical regulation This prediction is based upon the comparison of the calculated behaviour of our in silico ATase, PII and UTase mutants The removal of either one of the three proteins at the time of an upshift in the ammonium level, told us that UTase was not really necessary for a well-behaved transient behaviour Without ATase or PII, a metabolic explosion occurred as indicated by the excessive accumulation of GLN It is noteworthy that such experiments would be virtually impossible to carry out in reality UTase catalyses the uridylylation of PII and PII and its uridylylated forms interact not only with ATase but also with NRII, the sensor protein of two component system NRI–NRII, thereby indirectly affecting the phosphorylation degree of NRI, the transcriptional regulator (d) Upon a downshift in the ammonium availability, expression of GS is not only necessary (see hypothesis d) but also sufficient to ensure ammonium assimilation after the shift This prediction needs some introduction Upon an upshift in ammonium availability, metabolic regulation alone is sufficient to maintain ) by and large ) the ammonium assimilation flux at the level before the shift (Figs and 3) The situation is different, however, upon a downshift Our calculations show that upon an ammonium downshift, the GS expression level ) that corresponds with cells that have been grown at constant high ammonium concentrations ) would be too low to sustain an ammonium assimilation flux compatible with growth after the shift; extra expression of GS is necessary Moreover, the calculations also show that extra expression of GS alone is sufficient to arrive at an ammonium assimilation flux compatible with growth (Fig 4; Supplementary Fig S5), provided that a moderate amount of GOGAT is present (i.e Vmax > 60 mmỈmin)1 is needed) The latter condition is likely to be fulfilled GS and GOGAT are encoded by genes that are part of separate operons (glnALG and gltBDF, respectively) Expression of GOGAT, unlike that of GS, is not regulated by NRIP [47] and expression levels of GOGAT are rather condition-invariant ([31] and unpublished data) Maximal activities of GOGAT around 60 mmỈmin)1 or higher are easily achieved (e) The sum of the fluxes of GS and GDH ) the overall ammonium assimilation flux ) is held almost constant by the metabolic regulation considered in this model provided that the cells have been adapted to low levels of ammonium This partial robustness of the net ammonium assimilation flux is achieved by the active regulation of the system, which is dominated by FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS Multifarious regulation dissected the adenylylation of GS The constancy of the ammonium assimilation flux is accompanied by large changes in the GLU level and the adenylylation state of GS (not shown) The transient regulation stops when GLN is nearly restored to its level before the ammonium change (Fig 3) It is tempting to speculate that the observed robustness of the ammonium assimilation flux is one of the salient functions of the regulatory mechanisms around the GDH-GS ⁄ GOGAT system This paper reports on an example of a novel generation of computer models of parts of living cells, socalled silicon cells These ‘silicon cells’ incorporate all existing experimental information on the molecules of living cells into computer replica of parts of living cells This paper shows that biochemical calculations with such silicon cell models can serve to calculate how the network should be expected to function, on the basis of what is known about its molecules Comparison of the calculated network behaviour with what is known experimentally about physiological behaviour of the network, serves as a test of whether the molecular information suffices to understand observed function In addition, as shown in this paper, behaviour hypothesized by the physiological community, can be provided with some molecular basis, if silicon cell behaviour corresponds with the function that was hypothesized One should realize that the molecular information on which the silicon cell of this paper was based, is incomplete Only eventually, when all relevant biochemical knowledge has been obtained and incorporated in the model, silicon cells will reproduce the physiological behaviour precisely (within experimental error) We consider the construction and analysis of this first-generation silicon cell models already a challenging and productive scientific endeavour, because it may lead to the discovery of new principles and mechanisms [48,49] Because such models are an exact as possible representation of existing experimental information, these discoveries should bear more on reality than those of mainstream mathematical biology made with phenomenological models Experimental procedures The ammonium assimilation network is composed of three interacting subnetworks The network regulating ammonium assimilation in E coli at the metabolic level is depicted in Fig It consists of three subnetworks, referred to as UTase, ATase and metabolism, which are coupled by four intermediates: the two PII species, i.e PIIKG1 and PIIUMP3KG3, the adenylylation state of GS (denoted by the number of adenylyl groups 1977 Multifarious regulation dissected F J Bruggeman et al per GS dodecamer, nAMP) and GLN For a detailed discussion of the assumptions underlying the modular structure of this network the reader is referred to [50] The enzymes and metabolites will be assumed to be homogeneously distributed in the cytoplasm This allows us to describe the dynamics of the network in terms of a set of nonlinear ordinary differential equations concentration of PII and KG, while Eqn (6) gives the PIIUMP3KG3 concentration as a function of PIIUMP3 and KG The amount of KG sequestered by PII was considered negligible; under physiological conditions in E coli, the range of KG concentrations is 0.1–0.9 mm [31] and the range of PII concentrations is 1–3 lm [13,28] which maximally amounts to 9% sequestration of the total a-KG pool to the PII-species Mass-flow description of the UTase subnetwork and binding of a-KG to PII Any of the three subunits of PII can be covalently modified through (de-)uridylylation by the activity of the ambiguous [51] enzyme UTase, which possesses uridylyl-transferase (UT) and uridylyl-removing (UR) activities [26] Eqns (1–3) were used to describe the dynamics of the various uridylylated forms of PII dPIIUMP1 ẳ vUT;1 ỵ vUR;2 vUR;1 vUT;2 dt 1ị dPIIUMP2 ẳ vUT;2 ỵ vUR;3 vUR;2 vUT;3 dt 3ị 1ỵ3 KG KG ỵ K1;PII K2;PII ỵ K1;PII K2;PII K3;PII 5ị The values for the dissociation constants are: K1,PII ¼ lm, K2,PII ¼ 150 lm and K3,PII ¼ 150 lm [28] PIIUMP3 KG3 ¼ PIIUMP3 ÁKG3 K1;PIIU3 ÁK2;PIIU3 ÁK3;PIIU3 KG KG KG ỵ K1;PIIU3 ỵ K1;PIIU3 K2;PIIU3 ỵ K1;PIIU3 K2;PIIU3 K3;PIIU3  6ị PII ẳ PIItot À PIIUMP1 À PIIUMP2 À PIIUMP3 where K1,PIIU3 ¼ 25 lm, K2,PIIU3 ¼ 150 lm and K3,PIIU3 ¼ 150 lm represent the dissociation constants [28] Mass-flow description of the ATase subnetwork Each vi in the differential equations (above and below) denotes the rate at which a certain catalytic process i takes place Each rate depends on process-specific parameters (e.g KM and Vmax) and on concentrations of its substrates, products, and effectors (see below) In view of the conservation of the total pool of PII (PIItot) at the metabolic time scale, the concentration of unmodified PII was calculated from the relationship ð4Þ The uridylylated and nonuridylylated PII species are trimers [52], which can bind one molecule of ATP and one molecule of a-KG per subunit [23,26] The dissociation constant for ATP and PII (% 15 lm [26]) and the physiological concentration of ATP (% mm [53]) suggests that PII is practically saturated with ATP under physiological conditions It has been shown that PII needs to be saturated with ATP in order to be functional [26] For notational convenience PII is used, but one may read PIIATP3 whenever PII is mentioned KG was assumed to bind to PII in a rapid-equilibrium fashion, i.e the rate of (de-)uridylylation of subunits of PII was considered to be much slower than the rate of KG binding to PII The concentrations of the PIIUMPiKGj (i,j ¼ 0,…,3) species were calculated from the appropriate dissociation constants and the concentration of PIIUMPiKGj (i ¼ 0,…,3; j ¼ 0,…,2) and KG Of the 16 different forms of PII, only two species, PIIKG1 and PIIUMP3KG3, appear to play a significant physiological role [12,52] Equation (5) gives the PIIKG1 concentration as a function of the total 1978 Á PIIKG K1;PII KG K1;PII 2ị dPIIUMP3 ẳ vUT;3 vUR;3 dt PIIKG1 ¼ GS consists of 12 identical subunits, each of which can be (de) adenylylated The time dependence of the concentration of deadenylylated GS was calculated as: dGS ¼ vDEAD À vAD ð7Þ dt The rates of deadenylylation and adenylylation are given by vDEAD and vAD, respectively The total amount of GS present in the cell (GStot) was taken to be constant at the metabolic time scale for which we studied the system As deadenylylated GS was chosen as the independent variable, the concentration of GSAMP was calculated from GSAMP ¼ GStot ) GS The adenylylation state of GS was calculated using: nAMP ¼ 12 Á GSAMP GStot Mass-flow description of the metabolism subnetwork The changes in the GLU and GLN concentrations were calculated following Eqns (8) and (9), respectively: dGLU ẳ vGDH ỵ vGOGAT vGS vGLUDEM1 dt 8ị dGLN ẳ vGS vGOGAT vGLNDEM1 dt ð9Þ All products of GLN and of GLU metabolism were lumped into two generalized metabolite pools, called METGLN and METGLU, respectively Equations (10 and 11) describe the changes of these two pools: FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Multifarious regulation dissected dMETGLN ẳ vGLNDEM1 vGLNDEM2 dt 10ị dMETGLU ẳ vGLUDEM1 À vGLUDEM2 dt ð11Þ where vGLNDEM1 and vGLNDEM2 represent the rates of production and consumption of METGLN, respectively, and vGLUDEM1 and vGLUDEM2 the rates of production and consumption of METGLU, respectively ATP was produced by the reaction referred to as ATPase (which should be seen as a summary of glycolytic and oxidative phosphorylation activities; Fig 1) and consumed in the reaction catalysed by GS ATP consumption due to adenylylation of GS was neglected (see below): degree of saturation of PII with a-KG and UMP (see also [26]) Rate equations for the ATase module For the adenylylation of GS by ATase we developed a kinetic description, for lack of any published results The kinetic data for ATase published by Rhee et al [54] were not used here Their assumption that a-KG directly interacts with ATase was later shown to be incorrect by Jiang et al [23] (see also [52]) The latter authors showed that the effect of a-KG was indirect and mediated by a-KG bound to PII and to PIIUMP3 We started from irreversible product-insensitive Michaelis–Menten kinetics: vAD ¼ VAD Á 0AD dATP ẳ vATPase vGS dt 12ị The concentration of ADP was calculated from: ADP ¼ Atot – ATP The concentration of inorganic phosphate (Pi) was considered constant Rate equations for the UTase module vUT;jỵ1 ẳ 15aị where VAD ẳ 0.5 mmặmin)1 and KGS ẳ 0.0017 mm The factor JAD represents a rapid-equilibrium binding function describing the binding of the effectors of the adenylylation reaction to ATase: 0AD ¼ The uridylylation reaction of UTase (UT) follows irreversible, product-sensitive, ordered bi-bi kinetics with an inhibitory effect of GLN [26]: GS KGS ỵ GSị PIIKG1 GLN b1 PIIKG1 ỵ b2 KGLN ỵ b3 aKPIIKGGLN KPIIKG KGLN PIIKG1 GLN ỵ PIIKG1 ỵ KGLN ỵ aKPIIKGGLN KPIIKG KGLN 15bị where a ẳ 0.039, b1 ẳ 10)22, b2 ẳ 0.52, b3 ¼ 0.6, KPIIKG ¼ 10)5 mm and KGLN ¼ 0.97 mm All bi factors correct for VUT Á PIIUMPj Á UTP 2 P P Ki;PIIUMPj Á KUTP ỵ KUTP PIIUMPi ỵ KPIIUMPj UTP ỵ PIIUMPi Á UTP C   B i¼0 i¼0 C B GLN 2 ỵ KGLN B P P C A @ KPIIUMPj KUTP PIIUMPjỵ1 PIIUMPi UTPPPi iẳ0 iẳ0 ỵ ỵ KPPi KPIIUMP 13ị jỵ1 where j ẳ 0,,2, VUT ẳ 0.0822 mmặmin)1, Ki,PIIUMPj ẳ 0.0018 mm, KUTP ¼ 0.04 mm, KPIIUMPj ¼ 0.003 mm, KPIIUMPj+1 ¼ 0.0035 mm, KPPi ¼ 0.114 mm and KGLN ¼ 0.070 mm [26] The deuridylylation reaction of PIIUMPi by the UTase (UR) follows irreversible, product-insensitive, ordered uni-bi kinetics with an activating effect of GLN [26]: vUR;j ¼ À VUR PIIUMPj B P ỵ KGLN @KPIIUMPj ỵ PIIUMPi ỵ GLN jẳ1 P PIIUMPj UMP jẳ1 KUMP C A 14ị where, j ẳ 1,,3, VUR ẳ 0.0033 mmặmin)1, KGLN ẳ 0.070 mm, KPIIUMPj ẳ 0.0023 mm for all values of j and KUMP ¼ 8.4 mm [26] The affinity of UTase (UR) for the different forms of PII was taken to be independent of the FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS the different catalytic rate constants (kcat values) of the different ATase-effector complexes, whereas the deviation of a from measures the cooperativity between PIIKG1 and GLN All kinetic data in Eqns (15a and b) (and Eqns 16c and d) resulted from fitting the ATase kinetics with a model containing the Eqns (1–4 and 7) to transient and steady-state experimental data concerning GS activity and the degree of adenylylation of GS [28] using the software package Gepasi [55–57] Please note that the fitting was not to system behaviour, but to behaviour of enzyme activity The deadenylylation of GS by ATase was described similarly: GSAMP 16aị vDEAD ẳ VDEAD 0DE KGSAMP ỵ GSAMPị where VDEAD ẳ 0.5 mmặmin)1 and KGSAMP ẳ 0.0002 mm The factor JDE represents a rapid-equilibrium binding function for the binding of the effectors of the deadenylylation reaction to ATase: 1979 Multifarious regulation dissected  0DE ¼ F J Bruggeman et al A B C AÁB AÁC BÁC ABC b1 KA ỵ b2 KB ỵ b3 KC ỵ b4 a1 KA KB ỵ b5 a2 KA KC ỵ b6 a3 KB KC þ b7 Á a4 ÁKA ÁKB ÁKC   A B C AB AC BC ABC ỵ KA ỵ KB ỵ KC ỵ a1 KA KB ỵ a2 KA KC ỵ a3 KB KC ỵ a4 KA KB KC where A ¼ PIIKG1, B ¼ GLN, and C ¼ PIIUMP3KG3 Furthermore, a1 ¼ 0.023, a2 ¼ 0.88, a3 ¼ 8.49, a4 ¼ 0.88, b1 ¼ 10)22, b2 ¼ 2.77, b3 ¼ 3.23, b4 ¼ 0.0049, b5 ¼ 10)22, b6 ¼ 10)22, b7 ¼ 10)22, KPIIKG ¼ 2.2 · 10)6 mm, KGLN ẳ vGS  ỵ ATP NH4 GLU ADPGLNPi Keq  ẳ  ỵ ỵ þ NH4 GLNÁNH4 GLUÁNH4 ATP ADP Pi ADPÁPi GLN GLU ỵ KATP ỵ KADP ỵ KPi ỵ KADP KPi ỵ K ỵ ỵ KGLN ỵ KGLU ỵ KGLN K ỵ ỵ KGLU K ỵ APP VGS KATP KNHỵ KGLU  0.044 mm and KPIIUMP3KG3 ¼ 1.8 · 10)5 mm The factors and bi have the same meaning as in Eqn (15b) The kinetic parameters en bi were obtained from the same fitting session as described for the adenylylation reaction Rate equations for the metabolism module Glutamate dehydrogenase (GDH) catalyses the formation of GLU and NADP+ (NADP) from NH4+, a-KG and [NADPH + H+] (NADPH) GDH kinetics was described by:   VGDH ỵ GLUNADP KKG KNHỵ ÁKNADPH Á KG Á NH4 Á NADPH À Keq  vGDH ẳ    NH4 ỵ KG GLU NADPH NADP ỵ K ỵ ỵ KKG ỵ KGLU ỵ KNADPH ỵ KNADP 17ị where the dissociation constants are: KKG ¼ 0.32 mm, KNADPH ¼ 0.04 mm, KNH4+ ¼ 1.1 mm, KNADP ¼ 0.042 mm [15], KGLU ¼ 10 mm, and Keq ¼ 1290 mm)1 (http://xpdb nist.gov/enzyme_thermodynamics/enzyme_thermodynamics html) GOGAT catalyses the formation of two molecules of GLU and one molecule NADP+ from one molecule each of GLN, a-KG and NADPH Its kinetics is described by an irreversible rapid-equilibrium ter-ter mechanism that incorporates a noncompetitive inhibitory effect of METGLU: vGOGAT ẳ  NH 19aị NH APP with the apparent maximal rate constant as VGS ¼ 0GS Á VGS and the affinity constants KATP ¼ 0.35 mm, KGLU ¼ 4.1 mm, KNH4+ ¼ 0.1 mm, KADP ¼ 0.0585 mm, KPi ¼ 3.7 mm, and KGLN ¼ 5.65 mm (determined at adenylyation state 1.7–3.3 [58]), and the equilibrium constant Keq ¼ 460 [11] The GStot concentration is % 14 lm at physiological conditions of adaptation to low ammonium concentrations [13] The phenomenological factor JGS was obtained from a fit of the dependence of the maximal rate of GS to the adenylylation state as measured by [59] and described by: 0GS ẳ 1ỵ a1  a3 nAMP a2 1ỵ b1  b3 19bị nAMP b2 with a1 ¼ 10, a2 ¼ 2.37, a3 ¼ 1.15, b1 ¼ 0.10, b2 ¼ 10.87 and b3 ¼ 19.22 The values for en bi were obtained from fitting the apparent maximal rate of GS to its adenylylation state with Mg2+ as cofactor (Fig in [59]) Ginsburg et al [59] reported moderate cooperative effects of the rate of GS with respect to its substrates Their analysis however, was insufficient to extract allosteric kinetic information Therefore, we choose to approximate the kinetics of GS by Eqns (19a and b) The maximal rate of GS under glucoselimited chemostat culturing conditions was experimentally determined (Table 1) However, the rate is uncorrected for adenylylation; to take the effect of adenylylation into VGOGAT Á KGLNÁKGÁNADPH    GLN ÁKKG ÁKNADPH    METGLU GLN GLU KG GLU NADPH NADP ỵ KMETGLU ỵ KGLN ỵ KGLU ỵ KKG ỵ KGLU ỵ KNADPH ỵ KNADP where the dissociation constants are: KGLN ¼ 0.175 mm, KKG ¼ 0.007 mm, KNADPH ¼ 0.0015 mm, KGLU ¼ 11 mm, KNADP ¼ 0.0037 mm [19] and KMETGLU ¼ 0.65 mm (manual optimization) GS catalyses the formation of GLN, ADP and Pi from GLU, ammonium and ATP It obeys a random ter-ter 1980 ð16bÞ mechanism with a preferential ordered ter-ter pathway [58] This was approximated by a rapid-equilibrium binding mechanism The effect of adenylylation (nAMP) on the activity of GS is most pronounced on its maximal rate [59]: NH NH  ð18Þ account we deduced a correction factor of 5.5 from data published by Senior [31] The consumption of GLU, GLN, METGLU, and METGLN by the lumped enzyme systems GLUDEM1, GLNDEM1, GLUDEM2 and GLNDEM2, respectively, were all modeled with product-sensitive Michaelis-Menten kinetics: FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Multifarious regulation dissected Table Kinetic parameters of the GLN and GLU consumption reactions Reaction Vmax [mM min)1] Km,S [mM] Km,P [mM] GLUDEM1 GLUDEM2 GLNDEM1 GLNDEM2 120 30 70 20 0.3 0.5 0.5 0.25 0.5 vẳ S Vmax Km;S S P ỵ Km;S þ Km;P ð20Þ (where S and P represent the concentrations of substrate and product, respectively.) P was arbitrarily set at 0.1 mm for the GLNDEM2 and GLUDEM2 rate equations The kinetic parameters of the four lumped enzyme systems are given in Table and were chosen such that (a) the net ammonium-assimilation fluxes (JN ¼ 34–46 mm min)1 cf Table 1) were consistent with intermediate specific growth rates of E coli (0.4–0.6 h)1) and (b) the flux via the GLU demand route was approximately eight times higher than the flux via the GLN demand route [32] The kinetics for the ATP re-synthesis reaction was described with irreversible product-insensitive Michaelis– Menten kinetics, vẳ VATP ADP KADP ỵ ADP 21ị with VATP ¼ 100 mmỈmin-1 and KADP ¼ 0.5 mm Physiological conditions All the concentrations in the model (irregardless of whether they are variables or parameters) are intracellular concentrations No measurements of the intracellular ammonium concentrations could be found in the literature The internal ammonium concentration for E coli W growing in an ammonium-limited chemostat at a growth rate of 0.3 h)1 can be estimated for the data obtained by Senior [31] Assuming a 14% nitrogen content [60] and that the cytoplasmic volume equals lLỈmg)1 dry weight [13] we obtain an ammonia assimilation flux (JNH3) of 25 mmỈmin)1 Assuming that ammonia crosses the membrane by passive diffusion only, the ammonia gradient (DNH3 ¼ NH3,cult ) NH3,cyto) over the membrane in a steady state with this ammonia assimilation flux can be estimated to be DNH3 ¼ JNH3Vcell ⁄ (P Acell) (where JNH3 is in mmolỈLcyto)1Ỉmin)1, Vcell denotes the cellular volume in lcytcell)1, P equals the permeability coefficient of NH3 for E coli liposomes ) 1.2 dmỈmin)1 [61], and Acell denotes the area of the plasma membrane of E coli in dm2Ỉcell)1) If we assume E coli to be cigar shaped (perfectly spherical at the two ends) with a radius of 0.3 · 10)6 m, and a total length of · 10)6 m [62], its volume and surface area should equal FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS 0.79 · 10)18 m3 and 5.6 · 10)12 m2, respectively We calculate an ammonia gradient of 29 nm From the data of Senior [31] the ammonium concentration in the culture can be estimated to be 78 lm at 0.3 h)1 using a Monod constant of 130 lm for ammonium, and a maximal growth rate of 0.8 h)1, as obtained from a fit of the Monod equation to the growth rate as function of the ammonium concentration in the culture At a culture pH of 7.15 and using an acid dissociation constant pKa equal to 9.25, this amounts to an ammonia concentration in the culture of 0.62 lm Considering the ammonia gradient over the membrane (29 nm), the cytoplasmic ammonia and ammonium concentration become 0.59 lm and 33.2 lm, respectively (cytoplasmic pH was assumed to be 7.5) We estimated the cytoplasmic ammonium concentration of E coli K12 growing ammonium-limited in a chemostat at a growth rate of 0.3 h)1 to be somewhat higher due its smaller maximal growth rate (% 0.5 h)1, determined in our laboratory), i.e we took 50 lm for the cytoplasmic ammonium concentration when evaluating the model at ammonium-limited conditions For glucose-limited growth no values for the intracellular ammonium concentration could be found either To characterize ammonium sufficiency under these growth conditions the ammonium concentration was taken to be 1.0 mm (10 times higher than the KM of GS for ammonium and close to the KM of GDH for ammonium) The proteins and metabolites that were considered parameters in the model are listed in Table The values for the intracellular concentrations of these proteins and metabolites as used in the calculations were considered to represent ‘normal’ physiological conditions The total GS concentration (GStot) of 14 lm was chosen as a representative value for cells grown in the absence of ammonium [13] E coli contains the glnKamtB operon, which encodes a paralogue of PII, i.e GlnK, and the ammonium transporter, AmtB [24,67] This operon is under the control of NRIP and is not expressed constitutively So far it seems to be expressed only under conditions of (severe) nitrogen limitation [24,25,27] The proteins GlnK and AmtB were not included in the kinetic model Our model is therefore Table Physiological parameters used in the silicon cell Protein or metabolite Concentration (mM) Reference PIItot UTP GStot (dodecamer) UMP PPi Atot Pi NADPH NADP 0.003 0.5 0.014 0.01 0.05 5.4 10 0.15 0.05 [13] [63] [13]a [64] [65] [53] [65] [66] [66] a Determined in the absence of ammonium (growth on GLN) 1981 Multifarious regulation dissected only valid under conditions preventing the expression of the glnKamtB operon These conditions are likely to be met when E coli is growing in batch cultures with ammonium as the nitrogen source, in glucose-limited chemostat cultures, and in ammonium-limited chemostat cultures at intermediary growth rates Unfortunately, direct and quantitative measurements of the expression level of AmtB in relation to the external ammonium concentration have not been reported so far Our model did also not include the reported cumulative feedback inhibition of GS and adenylylated GS Under normal physiological conditions end product inhibition was taken to be negligible [20] Determination of maximal activities of GS, GOGAT, and GDH The dilution rate in an ammonium-limited and glucoselimited chemostat at which we determined the maximal rates of GS, GDH and GOGAT for E coli K12 (YMC10) in cell-free extract was 0.3 h)1 E coli K12 was grown aerobically (sterile air flow of 15 LỈh)1) at 37 °C in a L fermentor with a 0.5 L working volume The mineral medium contained 10 mm NaH2PO4, 10 mm KCl, 1.25 mm MgCl2, mm Na2SO4, 0.38 gỈL)1 nitrilo-tri-acetic acid, 20 mm CaCl2, 2.5 mgỈL)1 thiamine HCl, mLỈL)1 micronutrients stock solution [68], and 50 lLỈL)1 silicone antifoaming agent (BDH laboratory supplies) The glucoselimited cultures contained 14 mm NH4Cl and 15 mm glucose The ammonium-limited cultures contained 11 mm NH4Cl and 20 mm glucose Samples were taken from the chemostat and rapidly injected into )45 °C methanol (60%; diluted with 10 · Mops [69] pH 7.5 to a final volume fraction of sample ⁄ methanol ¼ : 2.5, w ⁄ v) Cell-free extract was prepared by ultrasonification after harvesting, fixation, and washing Extracts were stored at )20 °C Protein in cell-free extracts was determined with a BCA protein determination method (BCA protein assay kit, Pierce) The maximal activities of GS, GOGAT and GDH were all measured spectrophotometrically The measurements of GOGAT and GDH involved following the oxidation of NADPH The assays were performed at 37 °C by the addition of 200 lL cell-free extract to a reaction mixture (final volume 2.0 mL) of · Mops pH 7.5 containing mm a-KG, 250 lm NADPH, and either 40 mm NH4Cl (GDH assay) or mm GLN (GOGAT assay) The GS activity was measured at 37 °C in the biosynthetic direction (Mg2+-dependent) in a coupled assay containing pyruvate kinase (Sigma) and lactate dehydrogenase (Roche) The reaction was started by the addition of 100 lL cell-free extract to a 100-mm Hepes pH 7.5 solution (to a final volume of 2.0 mL) containing 128 mm NH4Cl, mm ATP, 20 mm GLU, mm phosphoenolpyruvate, 100 lgỈmL)1 lactate dehydrogenase (Roche), 25 lgỈmL)1 pyruvate kinase (Sigma), 280 lm NADH and 100 mm MgCl2 1982 F J Bruggeman et al Numerical methods The model was developed with the public domain systembiology software packages jarnac (http://www.cds.caltech edu/$hsauro/) and gepasi [55–57] The commercially available package mathematica (Wolfram Research, Inc., Mathematica, Version 4.2 & 5, Champaign, IL; 1999) was used for all calculations shown in this paper Acknowledgements The authors thank Herbert M Sauro for answering questions regarding the software package jarnac, Wally van Heeswijk for discussions about the GS regulatory network in general, Lody de Groot for performing the experiments, and Boris N Kholodenko and Jan B Hoek for discussions on the modular organization of metabolism References Westerhoff HV, Koster JG, van Workum M & Rudd KE (1989) On the control of gene expression In Control of Metabolic Processes (Cornish-Bowden A & Cardenas ML, eds), pp 399–413 Plenum Press, New York Bakker BM, Michels PAM, Opperdoes FR & Westerhoff HV (1997) Glycolysis in bloodstream form Trypanosoma brucei can be understood in terms of the kinetics of the glycolytic enzymes J Biol Chem 272, 3207–3215 Teusink B, Passarge J, Reijenga CA, Esgalhado E, van der Weijden CC, Schepper M, Walsh MC, Bakker BM, van Dam K, Westerhoff HV & Snoep JL (2000) Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry Eur J Biochem 267, 5313–5329 Rohwer JM, Meadow ND, Roseman S, Westerhoff HV & Postma PW (2000) Understanding glucose transport by the bacterial phosphoenolpyruvate: glucose phosphotransferase system on the basis of kinetic measurements in vitro J Biol Chem 275, 34909–34921 Kholodenko BN, Demin OV, Moehren G & Hoek JB (1999) Quantification of short term signaling by the epidermal growth factor receptor J Biol Chem 274, 30169–30181 Westerhoff HV (2001) The silicon cell, not dead but live! Metab Eng 3, 207–210 Hoefnagel MH, Starrenburg MJ, Martens DE, Hugenholtz J, Van Kleerebezem MSII, Bongers R, Westerhoff HV & Snoep JL (2002) Metabolic engineering of lactic acid bacteria, the combined approach: kinetic modelling, metabolic control and experimental analysis Microbiology 148, 1003–1013 FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al Shapiro BM, Kingdon HS & Stadtman ER (1967) Regulation of glutamine synthetase VII Adenylyl glutamine synthetase: a new form of the enzyme with altered regulatory and kinetic properties Proc Natl Acad Sci USA 58, 642–649 Stadtman ER (1990) Discovery of glutamine synthetase cascade Methods Enzymol 182, 793–809 10 Rhee SG, Chock PB & Stadtman ER (1989) Regulation of Escherichia coli glutamine synthetase Adv Enzymol Relat Areas Mol Biol 62, 37–92 11 Rhee SG, Chock PB & Stadtman ER (1985) Glutamine synthetase from Escherichia coli Methods Enzymol 113, 213–241 12 Ninfa AJ, Jiang P, Atkinson MR & Peliska JA (2000) Integration of antagonistic signals in the regulation of nitrogen assimilation in Escherichia coli Curr Top Cell Regul 36, 31–75 13 Heeswijk WC van (1998) The glutamine synthetase cascade: A search for its control and regulation PhD Thesis, Free University of Amsterdam, the Netherlands 14 Miller RE & Stadtman ER (1972) Glutamate synthase from Escherichia coli An iron-sulfide flavoprotein J Biol Chem 247, 7407–7419 15 Sakamoto N, Kotre AM & Savageau MA (1975) Glutamate dehydrogenase from Escherichia coli: purification and properties J Bacteriol 124, 775–783 16 Helling RB (1998) Pathway choice in glutamate synthesis in Escherichia coli J Bacteriol 180, 4571–4575 17 Helling RB (1994) Why does Escherichia coli have two primary pathways for synthesis of glutamate? J Bacteriol 176, 4664–4668 18 Booth IR & Higgins CF (1990) Enteric bacteria and osmotic stress: intracellular potassium glutamate as a secondary signal of osmotic stress? FEMS Microbiol Rev 6, 239–246 19 Rendina AR & Orme-Johnson WH (1978) Glutamate synthase: on the kinetic mechanism of the enzyme from Escherichia coli W Biochemistry 17, 5388–5393 20 Woolfolk CA & Stadtman ER (1967) Regulation of glutamine synthetase Cumulative feedback inhibition of glutamine synthetase from Escherichia coli Arch Biochem Biophys 118, 736–755 21 Kingdon HS, Shapiro BM & Stadtman ER (1967) Regulation of glutamine synthetase ATP: glutamine synthetase adenylyltransferase, an enzyme that catalyzes alterations in the regulatory properties of glutamine synthetase Proc Natl Acad Sci USA 58, 1703–1710 22 Jaggi R, van Heeswijk WC, Westerhoff HV, Ollis DL & Vasudevan SG (1997) The two opposing activities of adenylyl transferase reside in distinct homologous domains, with intramolecular signal transduction EMBO J 16, 5562–5571 23 Jiang P, Peliska JA & Ninfa AJ (1998) The regulation of Escherichia coli glutamine synthetase revisited: role of 2-ketoglutarate in the regulation of glutamine FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS Multifarious regulation dissected 24 25 26 27 28 29 30 31 32 33 34 35 36 synthetase adenylylation state Biochemistry 37, 12802–12810 van Heeswijk WC, Hoving S, Molenaar D, Stegeman B, Kahn D & Westerhoff HV (1996) An alternative PII protein in the regulation of glutamine synthetase in Escherichia coli Mol Microbiol 21, 133–146 Atkinson MR & Ninfa AJ (1999) Characterization of the GlnK protein of Escherichia coli Mol Microbiol 32, 301–313 Jiang P, Peliska JA & Ninfa AJ (1998) Enzymological characterization of the signal-transducing uridylyltransferase ⁄ uridylyl-removing enzyme (EC 2.7.7.59) of Escherichia coli and its interaction with the PII protein Biochemistry 37, 12782–12794 Blauwkamp TA & Ninfa AJ (2002) Physiological role of the GlnK signal transduction protein of Escherichia coli: survival of nitrogen starvation Mol Microbiol 46, 203–214 Jiang P, Peliska JA & Ninfa AJ (1998) Reconstitution of the signal-transduction bicyclic cascade responsible for the regulation of Ntr gene transcription in Escherichia coli Biochemistry 37, 12795–12801 Kamberov ES, Atkinson MR & Ninfa AJ (1995) The Escherichia coli PII signal transduction protein is activated upon binding 2-ketoglutarate and ATP J Biol Chem 270, 17797–17807 de la Fuente A, Snoep JL, Westerhoff HV & Mendes P (2002) Metabolic control in integrated biochemical systems Eur J Biochem 269, 4399–4408 Senior PJ (1975) Regulation of nitrogen metabolism in Escherichia coli and Klebsiella aerogenes: studies with the continuous-culture technique J Bacteriol 123, 407– 418 Reitzer LJ (1996) Ammonia assimilation and the biosynthesis of glutamine, glutamate, aspartate, asparagine, l-alanine, and d-alanine In Escherichia coli and Salmonella: cellular and molecular biology (Neidhardt EA, ed.), pp 391–407 ASM Press, Washington, D.C Lowry OH, Carter J, Ward JB & Glaser L (1971) The effect of carbon and nitrogen sources on the level of metabolic intermediates in Escherichia coli J Biol Chem 246, 6511–6521 Osorio AV, Camarena L, Salazar G, Noll-Louzada M & Bastarrachea F (1993) Nitrogen regulation in an Escherichia coli strain with a temperature sensitive glutamyl-tRNA synthetase Mol Gen Genet 239, 400– 408 Roe AJ, McLaggan D, Davidson I, O’Byrne C & Booth IR (1998) Perturbation of anion balance during inhibition of growth of Escherichia coli by weak acids J Bacteriol 180, 767–772 Goss TJ, Perez-Matos A & Bender RA (2001) Roles of glutamate synthase, gltBD, and gltF in nitrogen metabolism of Escherichia coli and Klebsiella aerogenes J Bacteriol 183, 6607–6619 1983 Multifarious regulation dissected 37 Kustu S, Hirschman J, Burton D, Jelesko J & Meeks JC (1984) Covalent modification of bacterial glutamine synthetase: physiological significance Mol Gen Genet 197, 309–317 38 Kustu S, Hirschman J & Meeks JC (1985) Adenylylation of bacterial glutamine synthetase: physiological significance, Curr Top Cell Regul 27, 201–213 39 Bancroft S, Rhee SG, Neumann C & Kustu S (1978) Mutations that alter the covalent modification of glutamine synthetase in Salmonella typhimurium J Bacteriol 134, 1046–1055 40 Bloom FR, Levin MS, Foor F & Tyler B (1978) Regulation of glutamine synthetase formation in Escherichia coli: characterization of mutants lacking the uridylyltransferase J Bacteriol 134, 569–577 41 van Heeswijk WC, Stegeman B, Hoving S, Molenaar D, Kahn D & Westerhoff HV (1995) An additional PII in Escherichia coli: a new regulatory protein in the glutamine synthetase cascade FEMS Microbiol Lett 132, 153–157 42 Westerhoff HV, Hellingwerf KJ & Van Dam K (1983) Thermodynamic efficiency of microbial growth is low but optimal for maximal growth rate Proc Natl Acad Sci USA 80, 305–309 42a Weiss V, Claverie-Martin F & Magasanik B (1992) Phosphorylation of nitrogen regulator I of Escherichia coli induces strong cooperative binding to DNA essential for activation of transcription Proc Natl Acad Sci USA 89, 5088–5092 43 Schutt H & Holzer H (1972) Biological function of the ammonia-induced inactivation of glutamine synthetase in Escherichia coli Eur J Biochem 26, 68–72 44 van Heeswijk WC, Rabenberg M, Westerhoff HV & Kahn D (1993) The genes of the glutamine synthetase adenylylation cascade are not regulated by nitrogen in Escherichia coli Mol Microbiol 9, 443–457 45 Soupene E, He L, Yan D & Kustu S (1998) Ammonia acquisition in enteric bacteria: physiological role of the ammonium ⁄ methylammonium transport B (AmtB) protein Proc Natl Acad Sci USA 95, 7030–7034 46 Soupene E, Lee H & Kustu S (2002) Ammonium ⁄ methylammonium transport (Amt) proteins facilitate diffusion of NH3 bidirectionally Proc Natl Acad Sci USA 99, 3926–3931 47 Ernsting BR, Denninger JW, Blumenthal RM & Matthews RG (1993) Regulation of the gltBDF operon of Escherichia coli: how is a leucine-insensitive operon regulated by the leucine-responsive regulatory protein? J Bacteriol 175, 7160–7169 48 Teusink B, Walsh MC, van Dam K & Westerhoff HV (1998) The danger of metabolic pathways with turbo design Trends Biochem Sci 23, 162–169 49 Bakker BM, Mensonides FI, Teusink B, van Hoek P, Michels PA & Westerhoff HV (2000) Compartmentation protects trypanosomes from the dangerous 1984 F J Bruggeman et al 50 51 52 53 54 55 56 57 58 59 60 61 62 63 design of glycolysis Proc Natl Acad Sci USA 97, 2087–2092 Bruggeman FJ, Westerhoff HV, Hoek JB & Kholodenko BN (2002) Modular response analysis of cellular regulatory networks J Theor Biol 218, 507–520 Ortega F, Acerenza L, Westerhoff HV, Mas F & Cascante M (2002) Product dependence and bifunctionality compromise the ultrasensitivity of signal transduction cascades Proc Natl Acad Sci USA 99, 1170–1175 Ninfa AJ & Atkinson MR (2000) PII signal transduction proteins Trends Microbiol 8, 172–179 Rohwer JM, Jensen PR, Shinohara Y, Postma PW & Westerhoff HV (1996) Changes in the cellular energy state affect the activity of the bacterial phosphotransferase system Eur J Biochem 235, 225–230 Rhee SG, Park R, Chock PB & Stadtman ER (1978) Allosteric regulation of monocyclic interconvertible enzyme cascade systems: use of Escherichia coli glutamine synthetase as an experimental model Proc Natl Acad Sci USA 75, 3138–3142 Mendes P (1993) GEPASI: a software package for modelling the dynamics, steady states and control of biochemical and other systems Comput Appl Biosci 9, 563–571 Mendes P (1997) Biochemistry by numbers: simulation of biochemical pathways with Gepasi Trends Biochem Sci 22, 361–363 Mendes P & Kell D (1998) Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation Bioinformatics 14, 869–883 Meek TD & Villafranca JJ (1980) Kinetic mechanism of Escherichia coli glutamine synthetase Biochemistry 19, 5513–5519 Ginsburg A, Yeh J, Hennig SB & Denton MD (1970) Some effects of adenylylation on the biosynthetic properties of the glutamine synthetase from Escherichia coli Biochemistry 9, 633–649 Buurman ET, Teixeira de Mattos MJ & Neijssel OM (1989) Nitrogen-limited behaviour of micro-organisms growing in the presence of large concentrations of ammonium ions FEMS Microbiol Lett 49, 229–232 Mathai JC, Sprott GD & Zeidel ML (2001) Molecular mechanisms of water and solute transport across archaebacterial lipid membranes J Biol Chem 276, 27266–27271 Francke C, Postma PW, Westerhoff HV, Blom JG & Peletier MA (2003) Why the phosphotransferase system of Escherichia coli escapes diffusion limitation Biophys J 85, 612–622 Landick R, Turnbough JRCL & Yanofski C (1996) Transcription attenuation In Escherichia coli and Salmonella: cellular and molecular biology (Neidhardt EA, ed.), pp 1263–1286 ASM Press, Washington, D.C FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS F J Bruggeman et al 64 Neidhardt FC & Umbarger HE (1996) Chemical composition of Escherichia coli In Escherichia coli and Salmonella: cellular and molecular biology (Neidhardt EA, ed.), pp 13–17 ASM Press, Washington, D.C 65 Wanner BL (1996) Phosphorus assimilation and control of the phosphate regulon In Escherichia coli and Salmonella: cellular and molecular biology (Neidhardt EA, ed.), pp 1357–1381 ASM Press, Washington, D.C 66 Penfound T & Foster JW (1996) Biosynthesis and recycling of NAD In Escherichia coli and Salmonella: cellular and molecular biology (Neidhardt EA, ed.), pp 721–730 ASM Press, Washington, D.C 67 Thomas G, Coutts G & Merrick M (2000) The glnKamtB operon A conserved gene pair in prokaryotes Trends Genet 16, 11–14 68 Evans CGT, Herbert D & Tempest DW (1970) The continuous culture of microorganisms Construction of a chemostat In Methods in Microbiology (Norris R & Ribbons DW, eds), pp 277–327 Academic Press, London New York 69 Neidhardt FC, Bloch PL & Smith DF (1974) Culture medium for enterobacteria J Bacteriol 119, 736–747 FEBS Journal 272 (2005) 1965–1985 ª 2005 FEBS Multifarious regulation dissected Supplementary material The following material is available from http://www blackwellpublishing.com/products/journals/suppmat/ EJB/EJB4626/EJB4626sm.htm Fig S1 Transient response of the network to a sudden increase in the ammonium concentration at time zero and the simultaneous deletion of ATase Fig S2 Transient response of the network to a sudden increase in the ammonium concentration at time zero and the simultaneous deletion of UTase Fig S3 Transient response of the network to a sudden increase in the ammonium concentration at time zero and the simultaneous deletion of PII Fig S4 Temporal dynamics of the regulatory contributors of the regulators of GS upon the sudden change in the ammonium concentration considered in Fig of the main text Fig S5 The steady-state ammonium-assimilation flux (N) as function of the maximal rate of GS and GOGAT 1985 ... conditions This means that the physiological behaviour of the mutants in vivo and in silico can be compared in a qualitative sense only The steady states of the in silico wild type and mutants were calculated... because the interpretation of the phenotypes of experimental PII mutants is confounded by the presence of the PII paralogue, GlnK, in these mutants [41] The in silico mutant strain deficient in GS... of PII saturated with both UMP and KG (PIIUMP3KG3), and of glutamine (GLN) The numbered lines in the insets of (A) and (B) correspond to the removal of thermodynamic regulation (1), kinetic regulation