Converter Enzymes Research Articles

Operating regimes of covalent modification cycles at high enzyme concentrations

The Goldbeter–Koshland model has been a paradigm for ultrasensitivity in biological networks for more than 30 years. Despite its simplicity the validity of this model is restricted to conditions when the substrate is in excess over the converter enzymes – a condition that is easy to satisfy in vitro, but which is rarely satisfied in vivo. Here, we analyze the Goldbeter-Koshland model by means of the total quasi-steady state approximation which yields a comprehensive classification of the steady state operating regimes under conditions when the enzyme concentrations are comparable to or larger than that of the substrate. Where possible we derive simple expressions characterizing the input-output behavior of the system. Our analysis suggests that enhanced sensitivity occurs if the concentration of at least one of the converter enzymes is smaller (but not necessarily much smaller) than that of the substrate and if that enzyme is saturated. Conversely, if both enzymes are saturated and at least one of the enzyme concentrations exceeds that of the substrate the system exhibits concentration robustness with respect to changes in that enzyme concentration. Also, depending on the enzyme’s saturation degrees and the ratio between their maximal reaction rates the total fraction of phosphorylated substrate may increase, decrease or change nonmonotonically as a function of the total substrate concentration. The latter finding may aid the interpretation of experiments involving genetic perturbations of enzyme and substrate abundances.

Reciprocal regulation as a source of ultrasensitivity in two-component systems with a bifunctional sensor kinase.

Two-component signal transduction systems, where the phosphorylation state of a regulator protein is modulated by a sensor kinase, are common in bacteria and other microbes. In many of these systems, the sensor kinase is bifunctional catalyzing both, the phosphorylation and the dephosphorylation of the regulator protein in response to input signals. Previous studies have shown that systems with a bifunctional enzyme can adjust the phosphorylation level of the regulator protein independently of the total protein concentrations – a property known as concentration robustness. Here, I argue that two-component systems with a bifunctional enzyme may also exhibit ultrasensitivity if the input signal reciprocally affects multiple activities of the sensor kinase. To this end, I consider the case where an allosteric effector inhibits autophosphorylation and, concomitantly, activates the enzyme's phosphatase activity, as observed experimentally in the PhoQ/PhoP and NRII/NRI systems. A theoretical analysis reveals two operating regimes under steady state conditions depending on the effector affinity: If the affinity is low the system produces a graded response with respect to input signals and exhibits stimulus-dependent concentration robustness – consistent with previous experiments. In contrast, a high-affinity effector may generate ultrasensitivity by a similar mechanism as phosphorylation-dephosphorylation cycles with distinct converter enzymes. The occurrence of ultrasensitivity requires saturation of the sensor kinase's phosphatase activity, but is restricted to low effector concentrations, which suggests that this mode of operation might be employed for the detection and amplification of low abundant input signals. Interestingly, the same mechanism also applies to covalent modification cycles with a bifunctional converter enzyme, which suggests that reciprocal regulation, as a mechanism to generate ultrasensitivity, is not restricted to two-component systems, but may apply more generally to bifunctional enzyme systems.

Sensitivity and Robustness in Covalent Modification Cycles with a Bifunctional Converter Enzyme

Regulation by covalent modification is a common mechanism to transmit signals in biological systems. The modifying reactions are catalyzed either by two distinct converter enzymes or by a single bifunctional enzyme (which may employ either one or two catalytic sites for its opposing activities). The reason for this diversification is unclear, but contemporary theoretical models predict that systems with distinct converter enzymes can exhibit enhanced sensitivity to input signals whereas bifunctional enzymes with two catalytic sites are believed to generate robustness against variations in system’s components. However, experiments indicate that bifunctional enzymes can also exhibit enhanced sensitivity due to the zero-order effect, raising the question whether both phenomena could be understood within a common mechanistic model. Here, I argue that this is, indeed, the case. Specifically, I show that bifunctional enzymes with two catalytic sites can exhibit both ultrasensitivity and concentration robustness, depending on the kinetic operating regime of the enzyme’s opposing activities. The model predictions are discussed in the context of experimental observations of ultrasensitivity and concentration robustness in the uridylylation cycle of the PII protein, and in the phosphorylation cycle of the isocitrate dehydrogenase, respectively.

Reciprocal enzyme regulation as a source of bistability in covalent modification cycles

Covalent modification cycles (CMCs) are the building blocks of many regulatory networks in biological systems. Under proper kinetic conditions such mono-cyclic enzyme systems can show a higher sensitivity to effectors than enzymes subject to direct allosteric regulation. Using methods from reaction network theory it has been argued that CMCs can potentially exhibit multiple steady states if the converter enzymes are regulated in a reciprocal manner, but the underlying mechanism as well as the kinetic requirements for the emergence of such a behavior remained unclear. Here, we reinvestigate CMCs with reciprocal regulation of the converter enzymes for two common regulatory mechanisms: allosteric regulation and covalent modification. To analyze the steady state behavior of the corresponding mass-action equations, we derive reduced models by means of a quasi-steady state approximation (QSSA). We also derive reduced models using the total QSSA which often better reproduces the transient dynamics of enzyme-catalyzed reaction systems. Through a steady state analysis of the reduced models we show that the occurrence of bistability can be associated with the presence of a double negative feedback loop. We also derive constraints for the model parameters which might help to evaluate the potential significance of the mechanisms described here for the generation of bistability in natural systems. In particular, our results support the view of a possible bistable response in the metabolic PFK1/F1,6BPase cycle as observed experimentally in rat liver extracts, and it suggests an alternative view on the origin of bistability in the Cdk1–Wee1–Cdc25 system.

On sensitivity amplification in intracellular signaling cascades

Sensitivity amplification has long been regarded as a virtually universal property of signal transduction cascades, yet a comprehensive parameter analysis remains a challenge even for relatively simple networks. We use a fast and accurate method to compute properties of multilevel cascades of activation–inactivation cycles and show that the monocyclic cascades amplify sensitivity only under specific conditions. In particular, it is found that efficient sensitivity amplification in a cascade, relative to the sensitivities of individual cycles, requires asymmetry in saturation of converter enzymes, with inhibitors much more saturated than activators.

Comparación en el manejo de pacientes con degeneración mixomatosa mitral con enalapril o con la combinación enalapril-espironolactona

El comportamiento de 45 pacientes caninos con degeneración valvular mixomatosa mitral, manejados con una combinación enalapril- espironolactona (20) o enalapril (25) fueron evaluados en tres ocasiones durante 12 meses, realizando un seguimiento de sobrevivencia, niveles séricos de aldosterona (marcador), creatinina, nitrógeno ureico en sangre, sodio y potasio.Se observó que la aldosterona tiene una reducción en los niveles séricos posterior al tratamiento con enalapril y espironolactona muy superior a los tratados únicamente con enalapril, pero en la última evaluación, aumentan los niveles por encima de los valores iniciales, lo que sugiere que ya se han activado otras vías diferentes para la síntesis de la aldosterona, que no están mediados por la angiotensina II y que por tal motivo no responden adecuadamente a las enzimas convertidoras de angiotensina. El beneficio de la combinación con espironolactona se basa en que ésta, es un bloqueador selectivo de los receptores para aldosterona, lo que disminuiría su acción letal sobre el miocardio y los vasos sanguíneos.

Allosteric Interactions and Bifunctionality Make the Response of Glutamine Synthetase Cascade System of Escherichia coli Robust and Ultrasensitive

Glutamine synthetase (GS) regulation in Escherichia coli by reversible covalent modification cycles is a prototype of signal transduction by enzyme cascades. Such enzyme cascades are known to exhibit ultrasensitive response to primary stimuli and act as signal integration systems. Here, we have quantified GS bicyclic cascade based on steady state analysis by evaluating Hill coefficient. We demonstrate that adenylylation of GS with glutamine as input is insensitive to total enzyme concentrations of GS, uridylyltransferase/uridylyl-removing enzyme, regulatory protein PII, and adenylyltransferase/adenylyl-removing enzyme. This robust response of GS adenylylation is also observed for change in system parameters. From numerical analyses, we show that the robust ultrasensitive response of bicyclic cascade is because of allosteric interactions of glutamine and 2-ketoglutarate, bifunctionality of converter enzymes, and closed loop bicyclic cascade structure. By system level quantification of the GS bicyclic cascade, we conclude that such a robust response may help the cell in adapting to different carbon and nitrogen status.

Fluctuations and Quality of Control in Biological Cells: Zero-Order Ultrasensitivity Reinvestigated

Living cells differ from most other chemical systems in that they involve regulation pathways that depend very nonlinearly on chemical species that are present in low copy numbers per cell. This leads to a variety of intracellular kinetic phenomena that elude macroscopic modeling, which implicitly assumes that cells are infinitely large and fluctuations negligible. It is of particular importance to assess how fluctuations affect regulation in cases where precision and reliability are required. Here, taking finite cell size and stochastic aspects into account, we reinvestigate theoretically the mechanism of zero-order ultrasensitivity for covalent modification of target enzymes (Goldbeter and Koshland (1981) Proc. Natl. Acad. Sci. USA. 78:6840–6844). Macroscopically, this mechanism can produce a very sharp transition in target concentrations for very small changes in the activity of the converter enzymes. This study shows that the transition is much more gradual in a finite cell or a population of finite cells. It also demonstrates that the switch is exactly analogous to a thermodynamic phase transition and that ultrasensitivity is inevitably coupled to random ultravariation. As a consequence, the average response in a large population of cells will often be much more gradual than predicted from macroscopic descriptions.

Arresting the mitotic oscillator and the control of cell proliferation: insights from a cascade model for cdc2 kinase activation.

We consider a minimal cascade model previously proposed for the mitotic oscillator driving the embryonic cell division cycle. The model is based on a bicyclic phosphorylation-dephosphorylation cascade involving cyclin and cdc2 kinase. By constructing stability diagrams showing domains of periodic behavior as a function of the maximum rates of the kinases and phosphatases involved in the two cycles of the cascade, we investigate the role of these converter enzymes in the oscillatory mechanism. Oscillations occur when the balance of kinase and phosphatase rates in each cycle is in a range bounded by two critical values. The results suggest ways to arrest the mitotic oscillator by altering the maximum rates of the converter enzymes. These results bear on the control of cell proliferation.

Enzyme Sharing in Phosphorylation-Dephosphorylation Cascades: The Case where One Protein Kinase (or Phosphatase) Acts on Two Different Substrates

In several metabolic cascades, distinct phosphorylation-dephosphorylation cycles share the same protein kinase or phosphatase. To deal with such a situation, the analysis of covalent modification cycles is extended to the case where one converter enzyme acting on two different substrates is shared by two cycles of protein covalent modification. The steady-state behavior of such a bicyclic cascade is determined as a function of the activity of the common converter enzyme; while the latter may be a kinase or a phosphatase, the model also applies to other modes of covalent modification. The analysis indicates that thresholds in phosphorylation owing to zero-under ultrasensitivity may still occur in this bicyclic system, as in the case of a single cycle of covalent modification or of multiple cycles possessing distinct converter enzymes. As the activity of the common kinase is progressively increased, the phosphorylation of the two substrates occurs at the same threshold or at distinct thresholds, depending on the values of the parameters. Approximate expressions for these thresholds are obtained. When the phosphorylation of the substrate in one cycle is caused by the inhibition of the associated phosphatase by some effector, rebound phosphorylation of the substrate of the second cycle is observed, even if the converter enzymes of the latter cycle are not controlled by the effector.

Mitochondrial rhodanese: membrane-bound and complexed activity.

We have proposed that phosphorylated and dephosphorylated forms of the mitochondrial sulfurtransferase, rhodanese, function as converter enzymes that interact with membrane-bound iron-sulfur centers of the electron transport chain to modulate the rate of mitochondrial respiration (Ogata, K., Dai, X., and Volini, M. (1989) J. Biol. Chem. 204, 2718-2725). In the present studies, we have explored some structural aspects of the mitochondrial rhodanese system. By sequential extraction of lysed mitochondria with phosphate buffer and phosphate buffer containing 20 mM cholate, we have shown that 30% of the rhodanese activity of bovine liver is membrane-bound. Resolution of cholate extracts on Sephadex G-100 indicates that part of the bound rhodanese is complexed with other mitochondrial proteins. Tests with the complex show that it forms iron-sulfur centers when incubated with the rhodanese sulfur-donor substrate thiosulfate, iron ions, and a reducing agent. Experiments on the rhodanese activity of rat liver mitochondria give similar results. Taken together, the findings indicate that liver rhodanese is in part bound to the mitochondrial membrane as a component of a multiprotein complex that forms iron-sulfur centers. The findings are consistent with the role we propose for rhodanese in the modulation of mitochondrial respiratory activity.

Experimental Evidence for a zero-order ultrasensitivity in a simple substrate cycle

It was shown [ Goldbeter & Koshland (1981), Proc. Natl. Acad. Sci. USA, 78, 6840–6844] that amplified sensitivity may arise in reversible covalent modification systems, when the converter enzymes operate in their zero-order region. we show that “zero-order ultrasensitivity” may also occur in simple substrate cycles. The experimental study deals with the Formate/Lactic dehydrogenases model cycle, interconverting the reduced and oxidized forms of NAD. For NAD(H) concentrations high enough (with respect to the enzyme K M's), abrupt changes in the steady-state substrate concentrations may result from small variations in the ratio of maximal enzyme activities. The amplification factors are measured. Implications in metabolic regulation are also taken up.

Energy expenditure in the control of biochemical systems by covalent modification.

Regulation by reversible, covalent modification of proteins requires a continuous expenditure of energy, even in a steady-state situation. The cost of this energy drain is evaluated for the case of an effector controlling the modifying enzyme and an effector controlling the demodifying enzyme and for the case of dual control in which an effector activates one of these enzymes and inhibits the other. Energy consumption is determined when the converter enzymes are functioning in the first-order and zero-order domains. The profile of energy expenditure versus fractional protein modification at steady state varies both as a function of the mechanism of control of the converter enzymes and of the kinetic domain in which they operate. This theory allows one to predict the strategies that would minimize energy costs. Dual control appears to provide maximum sensitivity with minimal energy expenditure. The analysis is applied to two experimental systems. Comparison of ATP turnover rates with rates for individual modification enzymes in living systems shows that a significant fraction of the total energy expenditure of an organism is required for the large number of reactions which involve covalent modification of proteins. It is concluded that there will be selection pressure for energy-efficient control of covalent regulation.

Comparative properties of bovine heart and liver rhodaneses and the regulatory role of the rhodaneses in energy metabolism

In previous studies on the rhodanese activity of bovine liver mitochondria, we have shown that in addition to activity observed in the soluble protein fraction, there is rhodanese activity that is bound to the mitochondrial membrane. The latter activity accounts for as much as 40% of the total and, in situ, is associated in a multiprotein complex that forms iron-sulfur centers. In the present studies, we have investigated the rhodanese activity of bovine heart muscle. We have found that the major part of this enzyme activity is localized in the mitochondria and, further, that at least 25% of the total rhodanese activity of heart mitochondria is membrane-bound. As in liver tissue, the heart activity at least in part is associated in a multiprotein complex that forms iron-sulfur centers. Upon purification of the heart rhodanese in the soluble protein fraction, there is a 10- to 30-fold decrease inKm values for the standard assay substrates thiosulfate and cyanide ions. These observations are consistent with the interpretation that there are activated and deactivated (low activity) forms of the heart enzyme in crude extracts, but only the activated form survives purification. The present results, together with our recent finding that liver mitochondrial rhodanese is subject to phosphorylation, lend support to our proposal that the rhodaneses serve as converter enzymes which regulate the rate of electron transport through sulfuration of respiratory chain components. The rhodaneses, in turn, are controlled by protein kinases and the local ATP concentration.

The Role of Adenylyltransferase and Uridylyltransferase in the Regulation of Glutamine Synthetase in Escherichia coli

The regulation of GS activity involves two nucleotidylation cycles, the uridylylation cycle of PII and the adenylylation cycle of GS, which are catalyzed by two converter enzymes, uridylyltransferase and adenylyltransferase, respectively. The converter enzymes sense the fluctuation in the availability of nitrogen and accordingly regulate the activity of GS. On the other hand, the posttranslational modification of GS is tightly coupled to the transcriptional regulation of the glnA gene by unmodified PII protein acting as a repressor in the GS synthesis. Therefore, metabolic signals perceived by uridylyltransferase are transmitted through PII to two different levels of the regulation, namely, the posttranslational level and transcriptional level. In order to study the converter enzymes which exist in extremely low concentration, the glnD and glnE genes were cloned into a plasmid vector carrying the strong, regulatable lambda phage promoter. In this way, uridylyltransferase and adenylyltransferase were overproduced to the levels approaching 800- and 500-fold, respectively. The recombinant DNA technology also enabled us to examine the transcriptional regulation of the glnD and glnE genes. The expression of these genes was slightly repressed under nitrogen-excess conditions and the repressions were more pronounced under excess nitrogen plus carbon-limiting conditions. It was found that variations of the concentration of uridylyltransferase and adenylyltransferase also affect the rate of GS synthesis. Studies with strains harboring a multicopy plasmid, pglnD or pglnE, indicate that the elevated synthesis of the converter enzymes causes the enhancement of GS synthesis. In addition, the absence of one of the converter enzymes reduces the expression of the glnA gene. The parallel relationship between the converter enzymes and GS seems to derive from the binding capacity of the converter enzymes for the unbound PII, which is a repressor for the glnA gene. Therefore, it is believed that the metabolic regulation of the glnD and glnE genes is ultimately linked to the expression of the glnA operon.

Ultrasensitivity in biochemical systems controlled by covalent modification. Interplay between zero-order and multistep effects.

A previous analysis of covalent modification systems (Goldbeter, A., and Koshland, D. E., Jr. (1981) Proc. Natl. Acad. Sci. U. S. A. 78, 6840-6844) showed that steep transitions in the amount of modified protein can occur when the converter enzymes are saturated by their protein substrate. This "zero-order ultrasensitivity" can further be amplified when an effector acts at more than one step in a monocyclic or multicyclic cascade of covalent modification. We analyze the limitations of the latter "multistep ultrasensitivity" and show how it can combine with the zero-order effect to enhance the sensitivity of biochemical systems controlled by covalent modification.

Energy consumption in a cyclic phosphorylation/dephosphorylation cascade.

Cyclic phosphorylation/dephosphorylation cascade systems are responsible for regulating numerous metabolic pathways. The capacity of a cyclic cascade system to maintain a steady-state level of phosphorylation and, hence, a specific biological activity of a phosphorylatable protein is dependent upon a constant supply of metabolic energy (ATP). Quantification of the extent of ATP consumption in a cyclic cascade was examined experimentally with the model in vitro phosphorylation/dephosphorylation system described in detail in the previous paper (Shacter, E., Chock, P. B., and Stadtman, E. R. (1984) J. Biol. Chem. 259, 12252-12259). The results indicate that (a) when the concentrations of converter enzymes and interconvertible substrate are held constant and the fractional phosphorylation of the substrate is varied by changing the allosteric effector concentrations, the rate of ATP consumption in the monocyclic cascade is directly proportional to the steady-state level of phosphorylation being maintained. (b) Attainment of a particular steady-state level of phosphorylation is determined by the net ratio of the protein kinase and phosphatase activities and is independent of the absolute concentrations of these enzymes. (c) Whereas the time required to reach a given steady state is inversely proportional to the converter enzyme concentrations, the amount of ATP consumed in maintaining that steady state is directly proportional to the kinase and phosphatase concentrations. In addition, a theoretical analysis based upon experimentally determined parameters for two in vivo cyclic cascade systems (pyruvate kinase and glycogen phosphorylase) revealed that under normal conditions, cyclic phosphorylation/dephosphorylation cascades consume only a small proportion (less than 0.02%) of the total cellular energy flux.

Regulation through phosphorylation/dephosphorylation cascade systems.

The cyclic interconversion of enzymes between phosphorylated and unphosphorylated forms comprises a major mechanism of cellular regulation. A theoretical analysis of reversible covalent modification systems (Stadtman, E.R., and Chock, P.B. (1977) Proc. Natl. Acad. Sci. U.S.A. 74, 2761-2765) revealed that they are endowed with extraordinary regulatory capacities; they may exhibit smooth, flexible responses to changes in single and multiple metabolite levels, signal amplification, and apparent positive cooperativity. To test qualitatively and quantitatively the theories and equations involved in this analysis, a model in vitro phosphorylation/dephosphorylation cyclic cascade was developed in which the converter enzymes catalyzing the covalent modifications were cAMP-dependent protein kinase (EC 2.7.1.37; type II) and phosphoprotein phosphatase (EC 3.1.3.16; Mr = 38,000), both purified to near homogeneity from bovine heart. The kinetic constants for both enzymes were fully characterized using the nanopeptide Leu-Arg-Arg-Ala-Ser-Val-Ala-Gln-Leu as the interconvertible substrate, cAMP as an activator for the kinase, and Pi as an inhibitor for the phosphatase. In the presence of a nearly constant concentration of ATP, a steady-state level of phosphorylation of the peptide was attained which was determined by the relative concentrations of the kinase, phosphatase, and effectors. As predicted by the cyclic cascade model, this monocyclic cascade exhibited both signal amplification and an increase in sensitivity to variations in multiple effector concentrations. In addition, the data show that the steady-state level of phosphorylation obtained in the presence of an activator of the kinase (e.g. cAMP) and an inhibitor of the phosphatase (e.g. Pi) is a function of the product of the relative effector concentrations. Finally, the results reveal that when the concentration of enzyme-substrate complex is not negligible, cyclic cascades are potentially more sensitive to variations in effector concentrations and can achieve even greater signal amplification than predicted previously.

19] Identification of N-terminal myristyl blocking groups in proteins

This chapter illustrates the identification of N-terminal myristyl blocking groups in proteins. The catalytic subunit of cyclic-AMP-dependent protein kinase (C subunit) and the regulatory subunit of protein phosphatase 2B contain myristic acid covalently attached to their amino-terminus. The discovery of myristic acid at the N-terminus of a protein phosphatase and a protein kinase suggests that this unusual blocking group may be involved in the interaction of converter enzymes with their protein substrates. The myristyl group could also play a role in maintaining the subunit-subunit interactions between the regulatory (B) and catalytic (A) subunits of calcineurin and between the regulatory and catalytic subunits of cyclic-AMP-dependent protein kinase. The myristyl group may be possibly involved in the translocation of the C subunit from the cytoplasm to the nucleus, across the nuclear membrane. Fast atom bombardment (FAB) mass spectrometry is considered the most useful mass spectrometric technique for identification of myristic acid in blocked peptides. Involatile and thermally labile compounds can be studied by this method and very small amounts of material can be used.

Phosphorylation of isocitrate dehydrogenase as a demonstration of enhanced sensitivity in covalent regulation.

The sensitivity to regulation of proteins undergoing covalent modification can be greatly increased when the substrates saturate the converter enzymes. This phenomenon, termed zero-order ultrasensitivity, has been found to occur in the reversible phosphorylation of isocitrate dehydrogenase. The possibility that this enhanced sensitivity is a common feature of covalent regulatory systems is discussed.