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 leve
Trang 1assimilation of Escherichia coli: dissection using an
in silico replica
Frank J Bruggeman1, Fred C Boogerd1and Hans V Westerhoff1,2,3
1 Molecular Cell Physiology, Institute of Molecular Cell Biology, CRBCS, Vrije Universiteit, Amsterdam, the Netherlands
2 Mathematical Biochemistry, SILS, Universiteit van Amsterdam, the Netherlands
3 Stellenbosch Institute for Advanced Studies, Stellenbosch, South Africa
Many unicellular organisms exhibit enormous
plasti-city towards sudden changes in their physico-chemical
environment Much of the adaptation capacity derives
from the ‘emergent’ properties of biochemical works composed of signal-transduction, metabolic,and gene-expression regulatory levels [1] Most of the
net-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
Sys-tems Modelling Database and can be
accessed free of charge at http://jjj.
biochem.sun.ac.za/database/Bruggeman/
index.html
(Received 7 October 2004, revised 31
Janu-ary 2005, accepted 23 FebruJanu-ary 2005)
doi:10.1111/j.1742-4658.2005.04626.x
Ammonium assimilation in Escherichia coli is regulated through multiplemechanisms (metabolic, signal transduction leading to covalent modification,transcription, and translation), which (in-)directly affect the activities of itstwo ammonium-assimilating enzymes, i.e glutamine synthetase (GS) andglutamate dehydrogenase (GDH) Much is known about the kinetic proper-ties 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 tosubtle and quasi-intelligent regulation are unappreciated To determine whe-ther our present knowledge of the interactions between and the kinetic prop-erties of the components of this network is complete) to the extent thatwhen integrated in a kinetic model it suffices to calculate observed physiolo-gical 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 ous carbon statuses for cells that have adapted to low and high ammoniumconcentrations We show how a sudden increase in ammonium availabilitybrings about a rapid redirection of the ammonium assimilation flux fromGS⁄ glutamate synthase (GOGAT) to GDH The extent of redistributiondepends on the nitrogen and carbon status of the cell We develop a method
vari-to quantify the relative importance of the various regulavari-tors in the network
We find the importance is shared among regulators We confirm that the nylylation state of GS is the major regulator but that a total of 40% of theregulation is mediated by ADP (22%), glutamate (10%), glutamine (7%) andATP (1%) The total steady-state ammonium assimilation flux is remarkablyrobust against changes in the ammonium concentration, but the fluxesthrough GS and GDH are completely nonrobust Gene expression ofGOGAT above a threshold value makes expression of GS under ammonium-limited conditions, and of GDH under glucose-limited conditions, sufficientfor ammonium assimilation
ade-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.
Trang 2adaptation 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
experiment-ally 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-biologi-cal knowledge can account for observed physiologimolecular-biologi-cal
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
net-work 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⁄
glu-tamate synthase (GOGAT) and one through GDH
(glutamate dehydrogenase) Both lead to the net
reduc-tive 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
1 mm) [14,15] GS ⁄ GOGAT is essential for growth
at low (< 1 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
osmotoler-ance 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
ammo-nium 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
inter-section of catabolism and anabolism in E coli led
physiologists and enzymologists to perform detailed
studies on the regulation of the regulatory networkconnected to ammonium assimilation (reviewed in[11–13]) This network proved to harbour a stunningcomplexity, comprising at least five different regulatorymechanisms dedicated to the regulation of ammoniumassimilation through direct effects on the activity ofand amount of GS One mechanism resides in the dif-ference in affinity of GS and GDH for ammonium,rendering GDH more important at high ammoniumconcentrations [15,19] A second mechanism operatesthrough the cumulative feedback control of GS byvarious end products of the GLN- and GLU-demandpathways [20] The third mechanism involves the aden-ylyltransferase (ATase) catalysed inactivation of GSthrough 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 uridylyla-tion state and the a-KG-binding state of the trimericproteins PII [23] and GlnK [24,25] The latter two pro-teins act as substrates for the ambiguous enzyme uri-dylyltransferase (UTase) that can (de) uridylylate allthree subunits of PII [26] and also those of GlnK[24,25] GlnK has recently been shown to be importantunder conditions of nitrogen starvation whereas PII isfunctional at higher concentrations of ammonium [27].All activities of UTase⁄ UR are sensitive to the GLNconcentration Additionally, PII can bind one a-KGmolecule per subunit each having different effects onthe signalling role of PII The fourth mechanisminvolves the transcriptional stimulation of the glnALGoperon, which codes for GS, NRII, and NRI, by thedoubly phosphorylated dimeric response-regulatorNRI The dimeric protein NRII acts as the cognatesensor of the two-component regulatory system NRI-NRII When it binds PII complexed with one molecule
of a-KG, NRII catalyses the dephosphorylation ofphosphorylated NRI [12,28] The fifth mechanism is byregulation of the concentration of GS through proteinturnover (reviewed in [11])
The network as a whole has been postulated to rate and decide upon information concerning the phy-siological carbon and nitrogen status through itssensitivities for ammonium, a-KG, and GLN [12,22,29]
integ-A silicon cell that includes all known kinetic properties
of the macromolecules involved in the five regulatorymechanisms might prove to be the only way to under-stand such complex regulation Provided that the kin-etic 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, wenow construct a silicon cell version of the regulation
of the GS adenylylation cascade, based exclusively onwhat is known about the molecular constituents, i.e on
Trang 3all the kinetic data We then analyse the effects of
chan-ges 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
indi-vidual 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
sub-mitted to the Online Cellular Systems Modelling
Data-base and can be accessed at http://jjj.biochem.sun.ac.za/
database/Bruggeman/index.html free of charge
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
litera-ture data on the kinetic and physicochemical properties
of its components (Experimental procedures) The
inter-action network is shown in Fig 1 The model
incorpor-ates 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
recon-stituted 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
com-ponents 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
The three gln regulatory genes are expressed tively at a low level [13], suggesting that the intracellularconcentrations of PII, UTase and ATase are independ-ent of nitrogen status Accordingly, the amount of theregulatory protein PII and the activities of UTase, andATase were fixed at levels normally encountered in wildtype E coli cells The expression levels of the genesglnA, gltBD, and gdhA, encoding GS, GOGAT, andGDH, respectively, do depend on the physiological state
constitu-of E coli (e.g [31]) Time-dependent gene expressionwas not taken into account: the replica was meant toreconstruct the short-term metabolic regulation only.Furthermore, the kinetics of the anabolic modules werechosen such that: (a) the net ammonium assimilationfluxes (JN¼ 25–41 mmÆmin)1) were consistent withintermediate specific growth rates of E coli (0.3–0.5 h)1); and (b) the flux via the GLU demand routewas approximately eight times higher than the flux viathe GLN demand route [32] The maximal rates for GS,GOGAT, and GDH used in the calculations below weredetermined with wild type E coli growing at a specificgrowth rate of 0.3 h)1 in an ammonium-limited or aglucose-limited chemostat (Table 1)
The ammonium assimilation network in silico –partial validation
No comprehensive physiological studies of the nium assimilation network under controlled conditionsthat could serve as a full validation of the model could
ammo-be found in the literature Therefore, we choose tocompare the in silico behaviour of the wild type andmutants (obtained by removing the correspondingreactions) to the reported physiology of the corres-ponding real wild type and mutant strains Unfortu-nately, the type of physiological experiments carriedout to determine the physiology of mutants is semi-quantitative at best In the cases used in this sectionnone of them included measurements of the maximalrates at the used physiological conditions This meansthat the physiological behaviour of the mutants in vivoand in silico can be compared in a qualitative senseonly The steady states of the in silico wild type andmutants were calculated for four different ‘physiologi-cal’ conditions, i.e at a low (0.05 mm; Table 2) and at
a high (1.0 mm; Table 3) intracellular ammonium centration, each for two a-KG concentrations (0.2 and1.0 mm) These a-KG concentrations represent the lowand high end of the reported physiological range ofintracellular concentrations [31]
con-The following experimentally obtained physiologicaldata (a–d) are qualitatively consistent with the simula-ted in silico data shown in Tables 2 and 3 (a) Under all
Trang 4conditions, the calculated wild type steady-state GLNconcentration (0.6–1.0 mm) proved to be at least oneorder of magnitude lower than the calculated GLUconcentration (4.0–21 mm) This reproduces the con-centration ranges and the relationship that has beenobserved frequently in vivo [31,33–35] (b) As expectedfor the wild type, at glucose limitation the in silico GSwas adenylylated to a higher degree than for the condi-tions mimicking ammonium limitation Accordingly,ammonium assimilation ran predominantly via GS dur-ing ammonium limitation whereas GDH dominatedduring glucose limitation The ammonium assimilation
Fig 1 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 interconnec- tions 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) Activa- tors 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-phos- phorylate ADP The following abbreviations were used: UT, uridylyl transfer; UR, uridylyl removal; DEAD, deadenylylation; AD, ade- nylylation; GS, glutamine synthetase; GDH, glutamate dehydrogenase; GOGAT, gluta- mate synthase; GLNDEM, glutamine demand; GLUDEM, glutamate demand; NH, ammonium; KG, a-KG; GLU, glutamate; GLN, glutamine; MET GLN , metabolite derived from glutamine; and METGLU, meta- bolite derived from glutamate.
Table 1 Measured maximal rates of GS, GOGAT and GDH
deter-mined 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 m M Æmin)1.
Trang 5fluxes 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
ammo-nium 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
sus-tained 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
cal-culated for the in silico pathway for the case of glucose
limitation (f) Experimental mutants lacking UTaseexhibit a high adenylylation state of GS independent ofthe absence or presence of ammonium in the medium[39,40]; they are not able to sense changes in the nitro-gen status (they sense nitrogen all the time) Likewise,
GS was adenylylated to a substantial extent in the
in silicoUTase mutant growing at two limitations
An in silico PII mutant was not included, because theinterpretation of the phenotypes of experimental PIImutants is confounded by the presence of the PII para-logue, GlnK, in these mutants [41] The in silico mutantstrain deficient in GS did engage in ammonium assimil-ation but its GLN production flux was zero (Tables 2and 3) In reality such a mutation is indeed lethal due tothe fact that GS is the sole enzyme capable of producingGLN
Steady-state response to changes in ammoniumconcentration
The effects of the external nitrogen and internal carbonand nitrogen status on the metabolic regulation ofthe ammonium assimilation flux were investigated The
Table 2 Calculated steady-state in silico physiology of wild type and of mutant E coli strains in the presence of 0.05 m M ammonium (ammonium-limited chemostat) and 0.2 (A) or 1.0 (B) m M a-KG The values for the maximal rates were 360 m M Æmin)1(GDH), 600 m M Æmin)1(GS), and 85 m M Æmin)1(GOGAT).
Genotype
GLN
(m M )
GLU (m M )
n AMP (AMPÆGS)1)
J GS (m M Æmin)1)
J GDH (m M Æmin)1)
J N (m M Æmin)1)
a Initial conditions: PII ¼ 0.003 m M , PIIUMP i ¼ 0.000 m M (i ¼ 1,2,3).
Table 3 Calculated steady-state in silico physiology of wild type and of mutant E coli strains in the presence of 1.0 m M ammonium cose-limited chemostat) and 0.2 (A) or 1.0 (B) m M a-KG The values for the maximal rates where 205 m M Æmin)1(GDH), 110 m M Æmin)1(GS), and 55 m M Æmin)1(GOGAT).
(glu-Genotype
GLN
(m M )
GLU (m M )
n AMP (AMP GS)1)
J GS (m M min)1)
J GDH (m M Æmin)1)
J N (m M Æmin)1)
Trang 6external nitrogen and the internal carbon and nitrogen
status were taken to be reflected by the ammonium,
a-KG, and the GLN concentration, respectively
Meta-bolic steady states were computed at internal
ammo-nium concentrations ranging from 0.01 to 1 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 2 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 2 The computed steady states
thus reflect metabolic states reached before enzyme
syn-thesis 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
concentra-tions, JNincreased sharply with the ammonium
concen-tration as long as the latter stayed below 0.03 mm
Above this ammonium concentration the dependence of
the ammonium assimilation flux on the ammonium
con-centration changed drastically: the ammonium
assimil-ation 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 JNwith even a minor decrease in
ammo-nium Our calculations suggest that the expression of
the ammonium transporter AmtB may be necessary to
sustain ammonium assimilation at ammonium
concen-trations 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
concen-tration we removed three such mechanisms The
ammo-nium 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
reac-tion 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 JGSterm on Eqn 19a and b
was set to 1) and by eliminating the product inhibitionterms, e.g ADP⁄ KADP To enable a fair comparison,the maximal rate of GS in the ‘mutated’ models wascorrected such that the net ammonium assimilation flux(JN) of the mutated and the original model was identi-cal at 0.05 mm of ammonium (i.e 32 and 37 mmÆmin)1,respectively, at 0.2 and 1.0 mm a-KG) Clearly, bothinsets indicate that the effect of the removal of bothregulatory mechanisms (but not of either alone) on theammonium assimilation flux was drastic, i.e at 1.0 mma-KG, JN now increased from 47 at 0.02 mm ammo-nium to 160 mmÆmin)1at 1.0 mm (The value for the JN
at 1.0 mm ammonium in the case for removal of thekinetic and thermodynamic regulation was 69 and
47 mmÆmin)1, respectively.)Ammonium assimilation is thought to be associatedwith high activities of GS and GOGAT at low concen-trations of ammonium (< 1 mm) and no activity ofGDH, whereas GDH is presumed to carry the fluxexclusively at higher concentrations of ammonium [11].This has been postulated to be favourable because ofthe additional hydrolysis of one ATP per molecule ofammonium assimilated if the GS⁄ GOGAT pathway isused [17] To investigate whether the shift from GS⁄GOGAT to GDH should actually be expected on thebasis of known kinetics and of metabolic regulationalone, the relative contributions of GS and GDH to thenet ammonium assimilation flux were calculated as afunction of the ammonium concentration, again for thetwo different concentrations of a-KG (Fig 2C,D).Contrary to the expectations, GDH was calculated to
be active at low ammonium concentrations Even at theammonium level that maximally supported GS activity(0.03 mm), GDH activity contributed 12% to theammonium assimilation flux (at 1.0 mm a-KG) Therelative contribution of GS increased strongly withincreasing ammonium concentrations before it wentthrough a maximum of 88% at 0.03 mm ammonium.Hereafter, the contribution of GS decreased, quickly atfirst and then slowly, to settle to a plateau value of 20%(for 1.0 mm a-KG) for ammonium in excess of 1 mm(data not shown) The heights of both the peak in thedependence of the variation of the relative contribution
of the two enzymes on the ammonium concentrationand, to a lesser extent, the minimum plateaus, decreasedwith an increase in the a-KG concentration Remark-ably, Fig 2C shows that, at a low a-KG concentration,even at an ammonium concentration exceeding 1 mm,
GS contributed significantly to the overall ammoniumassimilation (43% at 1.0 mm NH4+and 0.2 mm KG).The strict paradigm of ammonium assimilation fluxthrough GS at low and through GDH at high ammo-nium concentrations should perhaps be replaced by the
Trang 7Fig 2 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) m M ; AB, overall ammonium assimilation flux (J N ); CD, flux ratio of GS and GDH (JGS⁄ J GDH ); EF, apparent maximal rate of GS (V APP
GS ) and the adenylylation state of glutamine synthetase (nAMP); GH, the concentration of PII with one a-KG attached to it (PIIKG 1 ), of PII saturated with both UMP and KG (PIIUMP 3 KG 3 ), 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 m M ammonium, the fluxes in the insets were calculated with the following values for the maximal rates of GS (in m M 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).
Trang 8subtler 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
sup-ported 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 7 lm,
respect-ively 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
concen-tration above 0.03 mm The extent of the increase in the
concentration of PIIKG1 depended on the a-KG
con-centration (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
pre-sent (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
concentra-tion of NRI) is between 1 and 2 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
relat-ively 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
corrected for its adenylylation state) upon a suddenincrease in the ammonium concentration to cells thathad been adapted to growth on proline, i.e to the vir-tual absence of ammonium They stopped short ofdetermining the actual composite rates of ammoniumassimilation and of confirming that the system shiftedbetween rates as effectively as often hypothesized.Inspired by this work, we subjected the silicon net-work, adapted to ammonium limitation as reflected inthe values of the maximal rates of GS, GDH and GO-GAT and at the reference steady state used previously(i.e an ammonium concentration of 0.05 mm), to asudden increase in the ammonium concentration to1.0 mm To investigate the effect of the carbon status
we performed the calculations at constant trations of both 0.2 and 1.0 mm of a-KG (Fig 3)
concen-At low concentrations of ammonium and a-KG,
in silico ammonium assimilation ran predominantly via
GS⁄ GOGAT (Figs 3A and 2C) Upon the 20-foldincrease in the ammonium concentration at time zero,the rate of GS (and GDH) initially increased rapidly,
as expected from the increase in the concentration ofone of their substrates After a few seconds the ratesbegan to decrease Eventually the (steady-state) GSrate dropped to a level lower than before the addition
of the ammonium, in spite of the 20-fold increasedconcentration of one of its substrates Figure 3C illus-trates that the decrease in the rate of GS correlatedwith 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 3 min Within a min-ute after the ammonium shift, the GLN concentrationincreased rapidly to finally settle down to a highersteady state than before the ammonium change(Fig 3E) The progressive adenylylation of GS resultedfrom two effects both caused by the rapid increase ofthe GLN concentration Firstly, GLN itself may havedirectly stimulated the ATase-catalysed adenylylationreaction Secondly, GLN interacts with UTase andmay hereby have increased the level of PIIKG1 anddecreased the level of PIIUMP3KG3 (Fig 3E), givingrise to both a further stimulation of the ATase-cata-lysed adenylylation reaction and a release of the stimu-lation 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 ofthe different proteins involved in the regulation of theshift from GS- to GDH-dominated ammonium assimil-ation upon an increase in the ammonium concentration,
Trang 9we 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
experiment not achievable in the laboratory Theremoval of ATase caused an accumulation of GLN (to
67 mm within 5 min after the pulse) (SupplementaryFig S1) Most importantly, in this simulated absence ofthe regulation through ATase, GS contributed 44% tothe ammonium assimilation rate 5 mins after the addi-tion of ammonium Similarly, in order to investigate therole of UTase in regulating the maximal rate of ATase
we removed UTase from the model (Supplementary
Fig 3 Calculated transient response to a sudden increase in the ammonium concentration from 0.05 to 1.0 m M at time zero The a-KG centration was 0.2 m M (panels A, C, and E), or 1.0 m M (panels B, D and F) continuously A, B: rates of glutamine synthetase (vGS), glutam- ate synthase (vGOGAT) and glutamate dehydrogenase (vGDH) C, D: adenylylation state of glutamine synthetase (nAMP) and the ‘apparent’ maximal rate of glutamine synthetase (V APP
con-GS ) E, F: concentrations of glutamine (GLN), PII with one a-KG attached to it (PIIKG1), and PII saturated with UMP and a-KG (PIIUMP3KG3).
Trang 10Fig 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
ammo-nium assimilation due to its second regulatory role, i.e
hierarchical regulation of the activity of the
two-compo-nent signalling network NRI⁄ NRII through its directs
effect on the concentration of PIIKG1, but gene
expres-sion regulation is not considered here)
Do these results hint at PII being redundant for
metabolic ammonium assimilation: can GLN
substi-tute for PII? This we investigated by removing PII
from the model at the moment the 1 mm ammonium
was added (Supplementary Fig S3) PII turned out to
be of major importance; its removal led to an
accumu-lation of GLN and to total deadenylyaccumu-lation of GS
(causing its apparent maximal rate to rise to its
max-imal value of 600 mmÆmin)1) As in the case of the
removal of ATase, PII removal interfered with the
shift from GS⁄ GOGAT- to GDH-dominated
ammo-nium 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
sig-nalling 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
sub-strates (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
To test whether the adenylylation of GS is indeedthe most important regulatory event to downregulatethe flux of GS upon a rise in the ammonium level, weset out to develop an in silico method that shouldenable us to quantify the relative strengths of parallelregulatory pathways as a function of time To this aim
we wrote the fractional change in the rate of GS attime t as follows:
dlnvGS
dt ðtÞ¼
X5 i¼1
HvGS
X i ðtÞ ð1Þ
where the sum was taken over the regulatory butions of all five regulators (denoted by Xi) Theregulator with the highest regulatory contribution(HvGS
contri-X i for the regulatory contribution of Xi on therate of GS) at time t has the highest contribution tothe change in the rate of GS at that moment in time.After integrating over the entire steady-state relaxa-tion time, one then obtains for the average regulatorycontribution of Xið HvGS
X i Þ:
1t
Zt 0
d ln vGS
dt ðsÞ ds
¼X5 i¼1
1t
Zt 0
@ln vGS
@ln XiðsÞ d ln Xi
dt ðsÞ ds ¼
X5 i¼1
HvGS
Similarly, the average absolute regulatory contribution
of a regulator Xi to transient regulation of vGS over atime span 0 to t should be given by
H
vGS
Xi ¼1t
Z t 0
HvGS
Xi ðsÞ
In Supplementary Fig S4 the regulatory contributions
of the five regulators are displayed for the changes inthe rate of GS that were shown in Fig 3 Supplement-ary Fig S4 indicates that initially (seconds) ADP,ATP, GLN, GLU, and nAMP (in decreasing order ofimportance) were important regulators, after that (sec-onds to minute) GLU and nAMP, and at a later stage(minutes) nAMP was most important The integratedregulator contributions can be found in Table 4 In theaverage regulatory contribution up- and downregula-tion are included: negative and positive effects are justsummed up over time A more interesting variable istherefore the average absolute regulatory contribution:here negative effects are integrated, turned into posit-ive values and summed up with positive effects It isnoteworthy that the average regulatory contributions
of ATP and ADP have the same sign, even though theyare an activator and an inhibitor of GS, respectively.This is explained by the definition of the regulatory