From the
Department of Chemical Engineering and
School of Biosciences and Bioengineering, Indian Institute of Technology,
Bombay, Powai, Mumbai 400 076, India
Received for publication, January 7, 2003 , and in revised form, March 28, 2003.
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ABSTRACT |
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INTRODUCTION |
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Covalent modification cycles and allosteric interactions are important mechanisms involved in signal transduction (9). Interconverting enzymes are covalently modified and demodified by independent converter enzymes or by a same bifunctional (ambiguous) enzyme in a covalent modification cycle. Theoretical analyses of these interconvertible enzyme cascades have shown that enzyme cascades exhibit a potential for signal amplification, flexibility, and ultrasensitivity (57, 1012). Multicyclic enzyme cascades are shown to sense and integrate the fluctuations in intracellular concentration of metabolites and, accordingly, adjust the specific activity of converter enzymes with allosteric effectors (11, 12). Recent studies reveal the behavior of enzyme cascades in presence of noise (13) and demonstrate how these enzyme cascades help to reduce the signal fluctuations (14). Such theoretical analyses help in developing hypothesis, which can be verified experimentally in biological systems (1520).
The regulation of glutamine synthetase enzyme in Escherichia coli, a well characterized bicyclic cascade system, is attributed to interconvertible enzymes, bifunctional modifying enzymes, and allosteric interactions on these enzymes. Here, we have developed a steady state model of this system to generate stimulus/response curves for fractional modification of glutamine synthetase to varying input stimuli. The stimulus/response curve of a typical Michaelis-Menten enzyme is hyperbolic and requires an 81-fold change in the input stimulus for a 1090% change in the output response. Ultrasensitive enzyme requires <81-fold change in the input stimulus for a 1090% change in the output response; thus, stimulus/response curve is steeper than hyperbolic curve. A subsensitive enzyme requires >81-fold increase in the input stimulus for the same effect (58, 12). Ferrell and co-workers (17, 20) have used the Hill coefficient as a sensitivity quantification parameter to indicate Michaelis-Menten sensitivity (nH = 1), ultrasensitivity (nH > 1), and subsensitivity (nH < 1).
Most often in nature, the physiological responses are known to be ultrasensitive (21). The existence of ultrasensitivity in covalent modification cycles is the result of operation of enzymes in a region of saturation with respect to their substances termed as zero order sensitivity (58), involvement of the same effector in multiple steps of a pathway (7, 12), and presence of stoichiometric inhibitors (16). Functional significance of ultrasensitivity has been reviewed previously (6, 7, 16, 22, 23), and conditions for existence of ultrasensitivity in interconvertible enzyme cascades have been uncovered (24, 25).
Glutamine synthetase (GS)1 of Escherichia coli plays a vital role in nitrogen assimilation under nitrogen starvation conditions (9). This enzyme catalyzes the formation of glutamine from glutamate and ammonia. Its activity is regulated by reversible covalent modification cycles and by cumulative feedback inhibition (9, 2628). Reversible covalent adenylylation and biosynthesis of GS share a common mechanism for sensing intracellular nitrogen status (29). Because of these multiple regulation mechanisms, GS activity is highly controlled and rapidly adjustable to different environmental stimuli (28). Therefore, GS has been a prototype of signal transduction by enzyme cascades since four decades (27).
Glutamine synthetase covalent modification is a closed bicyclic cascade of two protein nucleotidylylation cycles (reviewed in Refs. 26 and 28). In one cycle, glutamine synthetase is reversibly adenylylated to an inactive form (in absence of Mn(II)) and deadenylylated to active form by a bifunctional enzyme adenylyltransferase/adenylyl-removing enzyme (ATase/AR). While in a second cycle, regulatory protein PII is reversibly uridylylated and deuridylylated by another bifunctional enzyme uridylyltransferase/uridylyl-removing enzyme (UTase/UR). These two cycles are connected in a manner that the unmodified protein PII activates adenylylation of GS and uridylylated PII (PII-UMP) activates deadenylylation of GS, thus converting it to a more active form.
Stadtman and co-workers (29, 30) have shown by theoretical analysis of GS regulatory cascade that the interconvertible enzyme cascade is endowed with remarkable flexibility, rate amplification, signal amplification potential, and sensitivity. In addition to theoretical analysis, it has been proved experimentally that covalent modification of dodecameric enzyme GS is not an all-or-none process (28, 29). GS subunits are adenylylated/deadenylylated independently, and under most physiological conditions, GS activity is inversely proportional to the number of adenylylated subunits per dodecamer. The steady state level of GS adenylylation varies from 0 to 12, and this depends upon the nutritional state of the organism, primarily on glutamine and 2-ketoglutarate concentrations as confirmed by in situ experiments (31) and in vivo studies (32). Thus, the steady state GS activity can be achieved by modulating the concentration of the known carbon and nitrogen effectors (3033).
Recently, Ortega et al. (18) challenged the zero order ultrasensitivity mechanism in covalent modification cycles by showing that zero order ultrasensitivity is lost if the modifying enzyme is strongly product-sensitive and ambiguous (bifunctional). They correlated these results with in vivo experiments of GS cascade sensitivity (34) where a change in concentration of regulatory protein PII did not affect the nonadenylylated glutamine synthetase concentration. In subsequent work, Ortega et al. (35) clarified that the degree of modification of target molecule can exhibit ultrasensitivity to change in total rather than free effector concentration that decide whether a bifunctional enzyme acts as a modifier or demodifier. Product inhibition per se has not been demonstrated experimentally in vivo in E. coli glutamine synthetase cascade, but allosteric regulation to control the glutamine synthetase activity has been well documented (2628, 36, 37).
The main objective of this paper is to investigate the effect of bifunctionality and allosteric interaction of effectors, glutamine, and 2-ketoglutarate on the response of GS bicyclic cascade at steady state using new insights from recent experimental work on reconstituted GS enzyme system. We solved the steady state equations for GS cascade numerically and found the predicted dose/response curve for GS adenylylation to be sigmoidal and represented by the Hill equation. From the theoretical analysis, we show that the GS system responds with robust ultrasensitivity to a varying concentration of modifying and interconvertible enzymes of GS bicyclic cascade. Furthermore, we investigate the reason for robustness of the system toward varying parameters. We conclude from our analysis that bifunctional modifying enzymes and allosteric interactions on modifying and interconvertible enzymes with closed loop cascade structure render robustness to the ultrasensitive performance of GS system.
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MATERIALS AND METHODS |
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PII is a homotrimeric protein and has been found to act as a sensor of the carbon signal, 2KG, by directly binding to it (38, 39). We have assumed that free PII without the binding of 2KG cannot be uridylylated, and furthermore, three molecules of 2KG can bind to PII with negative cooperativity (39, 40). 2KG-bound PII species (i.e. PII-2KG, PII-(2KG)2, and PII-(2KG)3) can go through the uridylylation/deuridylylation cycle. PII bound with only one 2KG molecule is active in terms of activation of ATase for adenylylation of GS.
The deadenylylation of GS by ATase requires 2KG-bound PII-UMP, whereas glutamine inhibits deadenylylation of GS by inactivating ATase-PII-UMP-2KG complex. Studies have indicated that PII can be uridylylated to PII-UMP and can form a combination of PII-(UMP)2 and PII-(UMP)3 species bound with 13 numbers of 2KG molecules depending on 2KG concentration (37, 40, 41). Here, we have assumed that all of these species can activate ATase to deadenylylate GS-AMP.
It can also be noted from Fig. 1 that in the case of cells under rich carbon and poor nitrogen sources, PII will mainly exist as the uridylylated form of PII-2KG, PII-(2KG)2, and PII-(2KG)3, which would further activate deadenylylation of GS-AMP, resulting in active GS. In the case of cells under poor carbon and rich nitrogen sources, PII will mainly exist as unmodified PII-2KG and will activate adenylylation of GS. Thus, the structure shown in Fig. 1 representing GS regulation qualitatively correlates with known response to carbon and nitrogen status.
Supplemental Table 1 lists the steady state equations for covalent
modification cycles, equilibrium relationships for allosteric interactions,
and mass balance equations for total species. These equations were solved
numerically using Fsolve program of MATLAB (The Math-Works Inc.). The accuracy
of the simulation was verified by numerically checking the mass balance of all
of the species. The simulations were carried out for estimating the fractions
of GS-AMP formed for particular glutamine and fixed 2KG concentration. We
found that the predicted dose/response curves for adenylylation of GS are
sigmoidal on semilogarithmic plots. These predicted curves of fractional
output response (f) to a given input (I) are similar in
shape to those given by the Hill type equation of the form as shown in
Equation 1,
![]() | (Eq. 1) |
![]() | (Eq. 2) |
Supplemental Table 1 also lists the parameters used in the simulations, and most of the kinetic/equilibrium constants were taken from the literature (32, 3841). Estimated reaction rate parameters were individually varied over a wide range, and the system response was analyzed. Reaction rate constants were screened to get a best fit to the half-saturation constant for GS adenylylation from the data taken from literature (39). The enzyme concentrations are referred from the work of Ninfa et al. (37) and Rhee et al. (30). The data taken from the literature consider Mg2+ as sole divalent metal ion in the reaction. We compared our simulation results with the dose/response curves of GS adenylylation at various total glutamine concentrations reported by Ninfa et al. (37) on reconstituted GS enzyme system. In this work, we have assumed that the total glutamine concentration is nearly equal to its free concentration; hence, we can validate the sensitivity of the response using Hill coefficient.
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RESULTS |
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Besides Hill coefficient, the half-saturation constant (K0.5) quantifies the response by indicating the concentration of glutamine required for 50% adenylylation of GS. K0.5 increases with an increase in 2KG concentration, and the results are in agreement with reported in vitro studies by Jiang et al. (41) on reconstituted GS system (Fig. 2B). The value of K0.5 was invariant with varying PII, GS, and ATase concentrations. However, K0.5 increased with an increase in UTase/UR concentration but to a much lower extent than that of the 2KG (results not shown). Although the sensitivity was invariant to system parameters, K0.5 was highly dependent on changes in parameter values.
Fig. 3A shows the
dose/response curves for effect of 2KG concentration on GS adenylylation at
various glutamine concentrations. A higher concentration of 2KG was required
to activate the GS system with increasing glutamine concentration. At a low
concentration of glutamine (50 µM), GS was active even at a
very low 2KG concentration. Fig.
3B shows the performance of uridylylation cycle at
various glutamine and 2KG concentrations when complete bicyclic cascade of GS
was simulated. The uridylylated form of PII was largely insensitive to 2KG
concentration and more dependent on glutamine. However, the unmodified PII
concentration was sensitive to both glutamine as well as 2KG concentration. At
high concentrations of both glutamine and 2KG, PII will mainly exist as
inactive PII-(KG)2 and PII-(KG)3 as indicated by
Fig. 3B, curves
a and e. Thus, in such an instance, our analysis shows that the
signals of carbon and nitrogen status are not transmitted to the second GS
cycle. It can also be noted from Fig.
3B that a specific ratio of unmodified PII to
uridylylated PII (i.e. PII/PII-UMP) exists at a given 2KG and
glutamine concentration. This ratio was found to be mainly dependent on
glutamine.
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From our studies, it appears that the GS system responds strongly to the
carbon and nitrogen status of the cell and is invariant to the system
variables/parameters. What is the reason for such a robust response of GS
cascade to changes in enzyme concentrations and system parameters? To
understand this behavior, we have analyzed a simple monocyclic cascade with
allosteric interactions, representative of the second cascade in the GS system
as shown in Fig. 4. The steady
state equations are given in Supplemental Table 2 and were solved using
parameters given in Supplemental Table 1 as explained for the GS cascade. If
the total concentrations of B and P (converting enzymes in the cycle) are
altered independently, the fractional modification of interconvertible enzyme
(G) demonstrates zero order sensitivity
(Fig. 4, curves
ac). This is a well known result as illustrated by Koshland and
co-workers (5,
6,
12). When we consider that B
and P are related through an effector such as PII and PII-UMP in GS cascade
related through glutamine, the zero order effect is compromised as shown by
Fig. 4, curve d). At
steady state, the rate expression for the modification and demodification of
enzyme cascade given in Fig. 4
is shown in Equation 3.
![]() | (Eq. 3) |
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Simplifying for Bx in terms of its dissociation constant
(K5), the free glutamine concentration (x) can be
given as shown in Equation 4,
![]() | (Eq. 4) |
![]() | (Eq. 5) |
For simplicity, if Gt = G + H, then for f =
H/Gt we obtain
Equation 6.
![]() | (Eq. 6) |
In such a case, using Equation 2, we obtain a Hill coefficient of 2, irrespective of the parameter values embedded in n1 and n2. Also, the sensitivity in this case is independent of the total enzyme concentrations, Gt and Bt. The half-saturation constant K0.5 in this case can be given as xt(f=0.5) = (n1 x n2)0.5 and is therefore related to the system parameter values present in n1 and n2. Thus, by linking the ratio of B to P through an effector, the response is rendered ultrasensitive and robust.
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DISCUSSION |
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As compared with ATase, another bifunctional enzyme UTase/UR was not under
the influence of closed loop. Therefore, the GS system response shows zero
order effects at higher concentration of UTase/UR. Such a high concentration
of UTase/UR may not be relevant in vivo. It is noteworthy that for
E. coli grown under derepressed conditions, UTase/UR concentration is
400-fold less than GS concentration under similar conditions. This
represents the pyramidal relationship of enzyme concentration (GS, 411; PII,
42; ATase, 2.6; UTase/UR, 1) in GS cascade system known to be responsible for
efficient performance of the cascade
(29). The robust
ultrasensitive response of GS can thus be quantified by
Equation 7,
![]() | (Eq. 7) |
The genetic regulation of GS synthesis is also regulated by PII and 2KG (26, 29, 37). Our analysis has shown that the response of GS adenylylation was insensitive to total GS concentration. We postulate that even the response of the GS synthesis cycle may depend only on the effector concentration. Thus, the synthesis and activity of GS may depend on the carbon (2KG) and nitrogen (glutamine) status of the cell alone.
Our results are consistent with reported experimental observations.
(i) According to Jiang et al.
(41) and Rhee et al.
(30), the effect of glutamine
on GS adenylylation shows approximately a linear change in half-saturation
constant at various 2KG concentrations. (ii) According to Rhee et
al. (30), the GS
adenylylation dose response curves for glutamine as input show
cooperative-like behavior with a Hill coefficient of 1.5. (iii)
As analyzed by van Heeswijik
(34), the variation of total
PII concentration did not influence the adenylylation of GS. Ortega et
al. (18) have argued that
this insensitivity is because of product inhibition and bifunctionality. Here
we have shown that this effect is attributed to specific allosteric
interactions, bifunctionality, and closed loop bicyclic cascade structure. We
have extended this result and shown that adenylylation of GS is not influenced
by the variation, not only in the total PII but also in total GS, ATase, and
UTase/UR under in vivo conditions. (iv) As presented under
"Results," our model correlates well with various hypothetical
observations made by Ninfa et al.
(37).
Robustness is an important issue in sensitivity analysis of biological system, because it provides an in depth understanding of the response of the system to internal failures and environmental changes. Various biological systems have been shown to respond with robustness to system parameters and environmental perturbations (reviewed in Refs. 3 and 4) because of feed forward control and redundancy in system components. In this work, we have used the term "robustness" to describe the constant output response of GS system to various system parameters (such as kinetic constants and so on) and change in concentration of system components (PII, ATase, and GS). Although the system does respond with a constant Hill coefficient, the half-saturation constant K0.5 was sensitive to changes. It can be emphasized that the ultrasensitive robust response of GS system is the result of cascade network topology and regulatory architecture. Does this ultrasensitive robust response of GS system exist inside the cell? The significance of this behavior of enzyme cascade has to be studied further. From available details, it can be postulated that GS cascade has the necessary components for exhibiting robustness and ultrasensitivity. As explained above, allosteric regulation of ambiguous and interconverting enzymes impart structural stability to the GS cascade. GlnK, a PII-like protein, has been shown to exist in E. coli and appears to be designed to function under the condition of nitrogen starvation (4345). It is possible that this protein may provide redundancy, a property of robustness to GS cascade system.
The ultrasensitive robust response of E. coli GS cascade shown by our simulations for glutamine and 2KG as inputs may be important under nitrogen starvation conditions, because E. coli do not require dedicated response of all-or-none as also shown by the experiments (26, 29) (see Addendum), whereas Huang and Ferrell (17) and Ferrell and Machleder (20) demonstrate that in a mitogen-activated protein kinase cascade system, a dedicated response is essential for the oocyte to decide on the question of maturation. In such cases, a switch-like ultrasensitive response from a cascade system is necessary.
System level understanding and quantification are vital for analyzing signal transduction pathways (3, 47). The mathematical and computational modeling by integrating different formalisms can help in uncovering the behavioral complexity of biological systems. Through such an analysis, we have demonstrated that the likely function of enzyme cascades might be to provide robustness other than imparting ultrasensitivity toward environmental perturbations.
AddendumBatchelor and Goulian (46) have recently reported robustness in EnvZ/OmpR (covalent modification cycle, two-component regulatory) system of E. coli. They found that when EnvZ concentration is lower than OmpR, steady state level of phosphorylated OmpR is insensitive to variation in the EnvZ and OmpR concentration. This work not only supports our work presented here but also suggests that two-component regulatory system of GS synthesis (i.e. NRI/NRII cycle) may also respond with robustness to change in component enzyme concentrations.
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FOOTNOTES |
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The on-line version of this article (available at
http://www.jbc.org)
contains Supplemental Tables 1 and 2.
To whom correspondence should be addressed. E-mail:
venks{at}che.iitb.ac.in.
1 The abbreviations used are: GS, glutamine synthetase; ATase,
adenylyltransferase; AR, adenylyl-removing enzyme; PII, signal transduction
protein PII; UTase, uridylyltransferase; UR, uridylyl-removing enzyme; 2KG,
2-ketoglutarate; GLN, glutamine.
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REFERENCES |
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