Maintenance of the monomeric structure of glucokinase under reacting conditions

Characterization of Glucokinase Catalysis from a Pseudo-Dimeric View

Glucose phosphorylation by glucokinase exhibits a sigmoidal dependency on substrate concentration regardless of its simple structure. Dimorph mechanism suggested the existence of two enzymatic states with different catalytic properties, which has been shown to be plausible by structural analysis. However, the dimorph mechanism gives rise to a complicated or non-explicit non-closed mathematical form. It is neither feasible to apply the dimorph mechanism in effector characterizations. To improve the area of glucokinase study with stronger theoretical support and less complication in computation, we proposed the investigation of the enzyme from a pseudo-dimeric angle. The proposed mechanism started from the idealization of two monomeric glucokinase as a dimeric complex, which significantly simplified the glucose phosphorylation kinetics, while the differences in enzyme reconfiguration caused by variable substrates and effectors have been successfully characterized. The study presented a simpler and more reliable way in studying the properties of glucokinase and its effectors, providing guidelines of effector developments for hyperglycemia and hypoglycemia treatment.

Advances in the Computational Identification of Allosteric Sites and Pathways in Proteins

With the increasing difficulty to develop new drugs and the emergence of resistance to traditional orthosteric-site inhibitors, the search for alternatives is finally approaching the focus on allosteric sites. Allosteric sites offer opportunities to regulate many pharmacologically targeted pathways by inhibition or activation. In addition, allosteric sites tend to be less conserved than the functional site, which may facilitate the design of specific effectors in the protein families for which specific orthosteric inhibitors have proved difficult to design. Furthermore, recent evidence suggests that all proteins might be susceptible of allosteric regulation, increasing the space of druggable targets. Computational identification of allosteric sites has therefore become an active field of research. The problem can be approached from two sides: (1) the identification of allosteric-communication pathways between the functional site and potential allosteric sites and (2) the functional-site-independent identification of allosteric sites. While the first approach tends to be more laborious and thus restricted to a single protein, the second tends to be more amenable to larger-scale analysis, thus providing tools for the two drug discovery scenarios: the analysis of known targets and the screening for new potential targets. Here, I show some basic concepts and methods useful to the identification of allosteric sites and pathways, in line with these two approaches. I describe them in some detail to build a clear framework, at the risk of losing the interest of experts. Examples of recent studies involving these methods are also illustrated, focusing on the techniques rather than on their findings on allosterism.

A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions

Kinetic models provide the means to understand and predict the dynamic behaviour of enzymes upon different perturbations. Despite their obvious advantages, classical parameterizations require large amounts of data to fit their parameters. Particularly, enzymes displaying complex reaction and regulatory (allosteric) mechanisms require a great number of parameters and are therefore often represented by approximate formulae, thereby facilitating the fitting but ignoring many real kinetic behaviours. Here, we show that full exploration of the plausible kinetic space for any enzyme can be achieved using sampling strategies provided a thermodynamically feasible parameterization is used. To this end, we developed a General Reaction Assembly and Sampling Platform (GRASP) capable of consistently parameterizing and sampling accurate kinetic models using minimal reference data. The former integrates the generalized MWC model and the elementary reaction formalism. By formulating the appropriate thermodynamic constraints, our framework enables parameterization of any oligomeric enzyme kinetics without sacrificing complexity or using simplifying assumptions. This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled. Uniform sampling of the kinetics space enabled dissecting enzyme catalysis and revealing the impact of thermodynamics on reaction kinetics. Our analysis distinguished three reaction elasticity regions for common biochemical reactions: a steep linear region (0> ΔGr >-2 kJ/mol), a transition region (-2> ΔGr >-20 kJ/mol) and a constant elasticity region (ΔGr <-20 kJ/mol). We also applied this framework to model more complex kinetic behaviours such as the monomeric cooperativity of the mammalian glucokinase and the ultrasensitive response of the phosphoenolpyruvate carboxylase of Escherichia coli. In both cases, our approach described appropriately not only the kinetic behaviour of these enzymes, but it also provided insights about the particular features underpinning the observed kinetics. Overall, this framework will enable systematic parameterization and sampling of enzymatic reactions.

Role of connecting loop I in catalysis and allosteric regulation of human glucokinase

Glucokinase (GCK, hexokinase IV) is a monomeric enzyme with a single glucose binding site that displays steady-state kinetic cooperativity, a functional characteristic that affords allosteric regulation of GCK activity. Structural evidence suggests that connecting loop I, comprised of residues 47-71, facilitates cooperativity by dictating the rate and scope of motions between the large and small domains of GCK. Here we investigate the impact of varying the length and amino acid sequence of connecting loop I upon GCK cooperativity. We find that sequential, single amino acid deletions from the C-terminus of connecting loop I cause systematic decreases in cooperativity. Deleting up to two loop residues leaves the kcat value unchanged; however, removing three or more residues reduces kcat by 1000-fold. In contrast, the glucose K0.5 and KD values are unaffected by shortening the connecting loop by up to six residues. Substituting alanine or glycine for proline-66, which adopts a cis conformation in some GCK crystal structures, does not alter cooperativity, indicating that cis/trans isomerization of this loop residue does not govern slow conformational reorganizations linked to hysteresis. Replacing connecting loop I with the corresponding loop sequence from the catalytic domain of the noncooperative isozyme human hexokinase I (HK-I) eliminates cooperativity without impacting the kcat and glucose K0.5 values. Our results indicate that catalytic turnover requires a minimal length of connecting loop I, whereas the loop has little impact upon the binding affinity of GCK for glucose. We propose a model in which the primary structure of connecting loop I affects cooperativity by influencing conformational dynamics, without altering the equilibrium distribution of GCK conformations.

Small-Molecule Allosteric Activation of Human Glucokinase in the Absence of Glucose

Synthetic allosteric activators of human glucokinase are receiving considerable attention as potential diabetes therapeutic agents. Although their mechanism of action is not fully understood, structural studies suggest that activator association requires prior formation of a binary enzyme-glucose complex. Here, we demonstrate that three previously described activators associate with glucokinase in a glucose-independent fashion. Transient-state kinetic assays reveal a lag in enzyme progress curves that is systematically reduced when the enzyme is preincubated with activators. Isothermal titration calorimetry demonstrates that activator binding is enthalpically driven for all three compounds, whereas the entropic changes accompanying activator binding can be favorable or unfavorable. Viscosity variation experiments indicate that the k_cat value of glucokinase is almost fully limited by product release, both in the presence and absence of activators, suggesting that activators impact a step preceding product release. The observation of glucose-independent allosteric activation of glucokinase has important implications for the refinement of future diabetes therapeutics and for the mechanism of kinetic cooperativity of mammalian glucokinase.

Homotropic allosteric regulation in monomeric mammalian glucokinase

Glucokinase catalyzes the ATP-dependent phosphorylation of glucose, a chemical transformation that represents the rate-limiting step of glycolytic metabolism in the liver and pancreas. Glucokinase is a central regulator of glucose homeostasis as evidenced by its association with two disease states, maturity onset diabetes of the young (MODY) and persistent hyperinsulinemia of infancy (PHHI). Mammalian glucokinase is subject to homotropic allosteric regulation by glucose-the steady-state velocity of glucose-6-phosphate production is not hyperbolic, but instead displays a sigmoidal response to increasing glucose concentrations. The positive cooperativity displayed by glucokinase is intriguing since the enzyme functions as a monomer under physiological conditions and contains only a single binding site for glucose. Despite the existence of several models of kinetic cooperativity in monomeric enzymes, a consensus has yet to be reached regarding the mechanism of allosteric regulation in glucokinase. Experimental evidence collected over the last 45 years by a number of investigators supports a link between cooperativity and slow conformational reorganizations of the glucokinase scaffold. In this review, we summarize advances in our understanding of glucokinase allosteric regulation resulting from recent X-ray crystallographic, pre-equilibrium kinetic and high-resolution nuclear magnetic resonance investigations. We conclude with a brief discussion of unanswered questions regarding the mechanistic basis of kinetic cooperativity in mammalian glucokinase.

Cooperativity in monomeric enzymes with single ligand-binding sites

Cooperativity is widespread in biology. It empowers a variety of regulatory mechanisms and impacts both the kinetic and thermodynamic properties of macromolecular systems. Traditionally, cooperativity is viewed as requiring the participation of multiple, spatially distinct binding sites that communicate via ligand-induced structural rearrangements; however, cooperativity requires neither multiple ligand binding events nor multimeric assemblies. An underappreciated manifestation of cooperativity has been observed in the non-Michaelis-Menten kinetic response of certain monomeric enzymes that possess only a single ligand-binding site. In this review, we present an overview of kinetic cooperativity in monomeric enzymes. We discuss the primary mechanisms postulated to give rise to monomeric cooperativity and highlight modern experimental methods that could offer new insights into the nature of this phenomenon. We conclude with an updated list of single subunit enzymes that are suspected of displaying cooperativity, and a discussion of the biological significance of this unique kinetic response.

Global fit analysis of glucose binding curves reveals a minimal model for kinetic cooperativity in human glucokinase

Human pancreatic glucokinase is a monomeric enzyme that displays kinetic cooperativity, a feature that facilitates enzyme-mediated regulation of blood glucose levels in the body. Two theoretical models have been proposed to describe the non-Michaelis-Menten behavior of human glucokinase. The mnemonic mechanism postulates the existence of one thermodynamically favored enzyme conformation in the absence of glucose, whereas the ligand-induced slow transition model (LIST) requires a preexisting equilibrium between two enzyme species that interconvert with a rate constant slower than turnover. To investigate whether either of these mechanisms is sufficient to describe glucokinase cooperativity, a transient-state kinetic analysis of glucose binding to the enzyme was undertaken. A complex, time-dependent change in enzyme intrinsic fluorescence was observed upon exposure to glucose, which is best described by an analytical solution comprised of the sum of four exponential terms. Transient-state glucose binding experiments conducted in the presence of increasing glycerol concentrations demonstrate that three of the observed rate constants decrease with increasing viscosity. Global fit analyses of experimental glucose binding curves are consistent with a kinetic model that is an extension of the LIST mechanism with a total of four glucose-bound binary complexes. The kinetic model presented herein suggests that glucokinase samples multiple conformations in the absence of ligand and that this conformational heterogeneity persists even after the enzyme associates with glucose.

23-Residue C-terminal alpha-helix governs kinetic cooperativity in monomeric human glucokinase

Human glucokinase is a monomeric enzyme that displays a sigmoidal steady-state kinetic response toward increasing glucose concentrations. The allosteric regulation produced by glucose is postulated to arise from the slow interconversion of multiple enzyme conformations during the course of catalysis. Crystallographic data suggest that structural rearrangements linked to glucokinase cooperativity involve a substrate-induced repositioning of an alpha-helix (alpha13) located at the C-terminus of the polypeptide. Here, we show that removal of helix alpha13 abolishes cooperativity and restores Michaelis-Menten kinetics, while reducing the k(cat) value of the wild-type enzyme by 160-fold. The impaired catalytic activity of the truncated enzyme is not rescued by the trans addition of a synthetic alpha13 peptide. Unexpectedly, the K(m glucose) value of a glucokinase variant lacking alpha13 is equivalent to the K(0.5 glucose) value of the full-length enzyme. Glucokinase steady-state kinetics is unaffected by the elongation of alpha13 via the addition of a C-terminal polyalanine tail. To explore the link between cooperativity and the primary sequence of alpha13, we randomized seven residues within the helix core. Genetic selection experiments in a glucokinase-deficient bacterium identified a variety of hyperactive alpha13 variants that display lower K(0.5 glucose) values, Hill coefficients near unity, and enhanced equilibrium binding affinities for glucose. The present results demonstrate that alpha13 plays an essential role in facilitating cooperativity. Our findings also establish a link between the primary amino acid sequence of helix alpha13 and the functional dynamics of the glucokinase scaffold that are required for allostery.

Molecular physiology of mammalian glucokinase

The glucokinase (GCK) gene was one of the first candidate genes to be identified as a human “diabetes gene". Subsequently, important advances were made in understanding the impact of GCK in the regulation of glucose metabolism. Structure elucidation by crystallography provided insight into the kinetic properties of GCK. Protein interaction partners of GCK were discovered. Gene expression studies revealed new facets of the tissue distribution of GCK, including in the brain, and its regulation by insulin in the liver. Metabolic control analysis coupled to gene overexpression and knockout experiments highlighted the unique impact of GCK as a regulator of glucose metabolism. Human GCK mutants were studied biochemically to understand disease mechanisms. Drug development programs identified small molecule activators of GCK as potential antidiabetics. These advances are summarized here, with the aim of offering an integrated view of the role of GCK in the molecular physiology and medicine of glucose homeostasis.

Structural Basis for Allosteric Regulation of the Monomeric Allosteric Enzyme Human Glucokinase

Glucokinase is a monomeric enzyme that displays a low affinity for glucose and a sigmoidal saturation curve for its substrate, two properties that are important for its playing the role of a glucose sensor in pancreas and liver. The molecular basis for these two properties is not well understood. Herein we report the crystal structures of glucokinase in its active and inactive forms, which demonstrate that global conformational change, including domain reorganization, is induced by glucose binding. This suggests that the positive cooperativity of monomeric glucokinase obeys the "mnemonical mechanism" rather than the well-known concerted model. These structures also revealed an allosteric site through which small molecules may modulate the kinetic properties of the enzyme. This finding provided the mechanistic basis for activation of glucokinase as a potential therapeutic approach for treating type 2 diabetes mellitus.

Analysis of the cooperativity of human beta-cell glucokinase through the stimulatory effect of glucose on fructose phosphorylation

Using overexpressed Escherichia coli sorbitol-6-phosphate dehydrogenase to monitor fructose 6-phosphate formation, we found that the stimulation of fructose phosphorylation by glucose was reduced in two human beta-cell glucokinase mutants with a low Hill coefficient or when the activity of wild type glucokinase was decreased by replacing ATP with poorer nucleotide substrates. Mutation of two other residues, neighboring glucose-binding residues in the catalytic site, also reduced the affinity for glucose as a stimulator of fructose phosphorylation. Among a series of glucose analogs, only 3, all substrates of glucokinase, stimulated fructose phosphorylation; other analogs were either inactive or inhibited glucokinase. Glucose increased the apparent affinity for inhibitors that are glucose analogs but not for the glucokinase regulatory protein or palmitoyl-CoA. These data indicate that the stimulatory effect of glucose on fructose phosphorylation reflects the positive cooperativity for glucose and is mediated by binding of glucose to the catalytic site. They support models involving the existence of two slowly interconverting conformations of glucokinase that differ through their affinity for glucose and for glucose analogs. We show by computer simulation that such a model can account for the kinetic properties of glucokinase, including the differential ability of mannoheptulose and N-acetylglucosamine to suppress cooperativity (Agius, L., and Stubbs, M. (2000) Biochem. J. 346, 413-421).

Dissociation of enzyme oligomers: a mechanism for allosteric regulation

Most enzymes exist as oligomers or polymers, and a significant subset of these (perhaps 15% of all enzymes) can reversibly dissociate and reassociate in response to an effector ligand. Such a change in subunit assembly usually is accompanied by a change in enzyme activity, providing a mechanism for regulation. Two models are described for a physical mechanism, leading to a change in activity: (1) catalytic activity depends on subunit conformation, which is modulated by subunit dissociation; and (2) catalytic or regulatory sites are located at subunit interfaces and are disrupted by subunit dissociation. Examples of such enzymes show that both catalytic sites and regulatory sites occur at the junction of 2 subunits. In addition, for 9 enzymes, kinetic studies supported the existence of a separate regulatory site with significantly different affinity for the binding of either a substrate or a product of that enzyme. Over 40 dissociating enzymes are described from 3 major metabolic areas: carbohydrate metabolism, nucleotide metabolism, and amino acid metabolism. Important variables that influence enzyme dissociation include: enzyme concentration, ligand concentration, other cellular proteins, pH, and temperature. All these variables can be readily manipulated in vitro, but normally only the first two are physiological variables. Seven of these enzymes are most active as the dissociated monomer, the others as oligomers, emphasizing the importance of a regulated equilibrium between 2 or more conformational states. Experiments to test whether enzyme dissociation occurs in vivo showed this to be the case in 6 out of 7 studies, with 4 different enzymes.

2-Deoxyglucose stimulates the release of insulin and somatostatin from the perfused catfish pancreas

Glucokinase was proposed to function as a glucose sensor in pancreatic B-cells, acting possibly as a pacemaker of the rate of glycolysis. Glucose, mannose, and 2-deoxyglucose are good substrates of glucokinase which are easily taken up into B-cells. Glucose and mannose are well-known stimuli of insulin release in mammals and fish. I report here that 2-deoxyglucose is also a strong stimulus of insulin and somatostatin release from the in vitro perfused pancreas (i.e., splenic Brockmann body) of channel catfish (Ictalurus punctatus). This is surprising because the product of the glucokinase-catalyzed phosphorylation of 2-deoxyglucose. 2-deoxyglucose-6-phosphate, cannot be metabolized further at an appreciable rate. 3-O-Methylglucose, which does not bind appreciably to mammalian glucokinase, stimulated neither insulin nor somatostatin release. Glucosamine, which binds tightly to glucokinase but is phosphorylated only at a very low rate, did not stimulate insulin release either, but did cause a small amount of somatostatin to be released. The results suggest that glucose-activated glucokinase itself may serve as a signal molecule in glucose recognition by B- and D-cells.

Separate effects of Mg2+, MgATP, and ATP4- on the kinetic mechanism for insulin receptor tyrosine kinase

The separate effects of the equilibrium species Mg2+, MgATP substrate, and ATP4- on the reaction catalyzed by insulin receptor tyrosine kinase were examined. The separated kinetic constants show that the K0.5 value for Mg2+ decreased from 23 to 0.43 mM and the Hill coefficient for Mg2+ (hMg2+) decreased from 1.43 to 0.668 when the concentration of ATPT (MgATP + ATP4-) was increased from 50 to 1000 microM. The apparent Ki for ATP4- increased from 0.20 to 136 microM and the Hill coefficient for ATP4- (hATP4-) decreased from 1.41 to 0.82 as the concentration of total ATP (ATPT) increased. These findings suggest that the [ATP4-]/[Mg2+] ratio modulates the shift from positive to negative cooperativity. It was also shown that the apparent affinity of the kinase for MgATP increased as the concentration of free Mg2+ increased and that the apparent affinity of the kinase for free Mg2+ increased as the concentration of MgATP substrate increased. Thus, Mg2+ and MgATP interact with the kinase in a mutually inclusive manner which leads to an increase in the ratio of the enzyme (E) rate-limiting species, [Mg-E-MgATP]/[E-MgATP]. Free ATP4- not only acts as a competitive inhibitor of the substrate but also decreases the relative concentration of Mg-E-MgATP. ATPT-dependent activation of the kinase is, therefore, a result of MgATP's increasing the affinity of the kinase for Mg2+, thereby leading to saturation of the enzyme with Mg2+ at lower concentrations of the divalent metal. This results in an increase in the [Mg-E-MgATP]/[E-MgATP] ratio, and therefore decreases saturation of the kinase with ATP4- inhibitor, not only at the active site but also at a kinetically distinct regulatory site. This kinetic relationship allows not only for the mutually inclusive interaction between Mg2+ and MgATP, but also for the mutually exclusive interaction toward ATP4-, hence indicating that the effect of Mg2+ will be to form an enzyme complex (Mg-E) which will have a higher affinity for MgATP substrate and a lower affinity for ATP4- than E alone. The role of the equilibrium concentrations of Mg-E,E, and ATP-E on the activation of insulin receptor tyrosine kinase is discussed which may account, at least in part, for modulation of cooperativity and the metal-dependent increase in turnover (VM).

Inhibition of hexokinase activity by a fructose 2,6-bisphosphate-dependent cytosolic protein from liver

Mammalian and yeast hexokinases were found to be reversibly inhibited by fructose 2,6-bisphosphate, an effect requiring the presence of a cytosolic protein factor. Experimental evidence suggests that this factor (inhibitor) is a regulatory protein, the interactions of which with hexokinases are modulated by fructose 2,6-bisphosphate. The Vmax of hexokinase D was decreased, and no changes on other kinetic parameters were observed. The inhibitor was present in fresh liver cytosol filtered through Sephadex G-25 and was partially isolated by negative absorption on DEAE-cellulose followed by ammonium sulfate fractionation. The inhibitor was also present in brain and kidney, but not in muscle. A molecular mass of 200,000 was determined by gel filtration. The inhibition was dependent on the concentrations of both the inhibitory protein and fructose 2,6-bisphosphate. No delay in fructose 2,6-bisphosphate inhibition was observed. Several other hexose phosphates were tested and were not effective. In the presence of amounts of inhibitor sufficient to produce complete inhibition of hexokinase D, the concentration of fructose 2,6-bisphosphate required to produce 50% inhibition was about 0.5 microM. The inhibitor was unstable and was stabilized by the presence of fructose 2,6-bisphosphate.

Co-operativity in monomeric enzymes

It has been known for at least 20 years that monomeric enzymes can in principle show kinetic behaviour similar in appearance to the binding of ligands to oligomeric proteins in which there are co-operative interactions between multiple binding sites. However, the initial lack of experimental examples of kinetic co-operativity suggested that in nature co-operativity always arose from interactions between binding sites. Now, however, several examples are known, most of which cannot be explained in terms of multiple binding sites on one polypeptide chain. All current theoretical models for monomeric co-operativity postulate that it arises from the presence in the mechanism of parallel pathways for substrate binding that are slow compared with the possible rate of the catalytic reaction. Rapid removal of the intermediates produced in the slow steps prevents them from approaching equilibrium and allows the appearance of kinetic properties that would not be possible in systems at equilibrium.

Effect of glycerol on glucokinase activity: loss of cooperative behavior with respect to glucose

Glucose phosphorylation catalyzed by rat liver glucokinase measured at saturating concentrations of MgATP2- shows a cooperative response with respect to glucose in the concentration range 0.25-5 mM with a Hill coefficient of 1.6. In this range of glucose concentrations, the degree of cooperativity was dependent on the presence of glycerol in the assay mixture, and it decreased progressively and disappeared completely as the glycerol concentration reached about 20% (v/v) glycerol. If attention was confined to concentrations above 5 mM, no cooperativity could be detected either in the absence or in the presence of glycerol. The limiting velocity of the glucokinase reaction (measured at saturating concentrations of glucose and MgATP2-), and the half-saturation concentration for glucose and MgATP2- were all decreased by about 50-60% as the glycerol concentration was raised from zero to 30% (v/v). The presence of glycerol had no effect on the qualitative inhibition patterns of MgADP2-, glucose 6-phosphate, or N-acetylglucosamine, and only slight effects on the quantitative half-saturation values and inhibition constants. All of these effects caused by glycerol were fully reversible by decreasing the concentration of glycerol by dilution. Simulation studies based on the "mnemonical" model of glucokinase action proposed earlier [A. C. Storer and A. Cornish-Bowden (1977) Biochem. J. 165, 61-69] show that the effects of glycerol on glucokinase-catalyzed glucose phosphorylation can simply be explained assuming the glycerol favors the existence of the conformation of the enzyme with a higher affinity for glucose and thus supports the model.

Suppression of kinetic cooperativity of hexokinase D (glucokinase) by competitive inhibitors. A slow transition model

Hexokinase D ('glucokinase') displays positive cooperativity with mannose with the same h values (1.5-1.6) as with glucose but with higher K0.5 values (8 mM at pH 8.0 and 12 mM at pH 7.5). In contrast, fructose and 2-deoxyglucose exhibit Michaelian kinetics [Cárdenas, M. L., Rabajille, E., and Niemeyer, H. (1979) Arch. Biol. Med. Exp. 12, 571-580; Cárdenas, M. L., Rabajille, E., and Niemeyer, H. (1984) Biochem. J. 222, 363-370]. Mannose, fructose, 2-deoxyglucose and N-acetylglucosamine acted as competitive inhibitors of glucose phosphorylation and decreased the cooperativity with glucose. Their relative efficiency for reducing the value of h to 1.0 was: fructose greater than mannose greater than 2-deoxyglucose greater than N-acetylglucosamine. Galactose, which is not a substrate nor an inhibitor, was unable to change the cooperativity. The competitive inhibition of glucose phosphorylation by N-acetylglucosamine or mannose was cooperative at very low glucose concentrations (less than 0.5 K0.5), suggesting the interaction of the inhibitors with more than one enzyme form. These and previously reported results are discussed on the basis of a slow transition model, which assumes that hexokinase D exists mainly in one conformation state (E1) in the absence of ligands and that the binding of glucose (or mannose) induces a conformational transition to EII. This new conformation would have a higher affinity for the sugar substrates and a higher catalytic activity than EI. Cooperativity would emerge from shifts of the steady-state distribution between the two enzyme forms as the sugar concentration increase. The inhibitors would suppress cooperativity with glucose by inducing or trapping the EII conformation. In addition, the model postulates that the different kinetic behaviour of hexokinase D with the different sugar substrates, cooperative with glucose and mannose and Michaelian with 2-deoxyglucose and fructose, is the consequence of differences in the velocities of the conformational transitions induced by the sugar substrates.

Fructose is a good substrate for rat liver 'glucokinase' (hexokinase D)

Rat liver 'glucokinase' (hexokinase D) catalyses the phosphorylation of fructose with a maximal velocity about 2.5-fold higher than that for the phosphorylation of glucose. The saturation function is hyperbolic and the half-saturation concentration is about 300 mM. Fructose is a competitive inhibitor of the phosphorylation of glucose with a Ki of 107 mM. Fructose protects hexokinase D against inactivation by 5,5'-dithiobis-(2-nitrobenzoic acid), and the apparent dissociation constants are about 300 mM in the presence of different concentrations of the inhibitor. The co-operativity of the enzyme in the phosphorylation of glucose can be abolished by addition of fructose to the reaction medium. Fructose appears to be no better as a substrate for the other mammalian hexokinases than it is for hexokinase D. It is proposed that the name 'glucokinase' ought to be reserved for enzymes that are truly specific for glucose, such as those of micro-organisms and invertebrates, and that liver glucokinase must be called hexokinase D (or hexokinase IV) within the classification EC 2.7.1.1.

All hexokinase isoenzymes coexist in rat hepatocytes

The cellular distribution of hexokinase isoenzymes, N-acetylglucosamine Kinase and pyruvate kinases in rat liver was studied. Hepatocytes and non-parenchymal cells with high viability and almost no cross-contamination were obtained by perfusion in situ of the liver with collagenase, with the use of an enriched cell-culture medium in all steps of cell isolation. Separation of hexokinase isoenzymes was done by DEAE-cellulose chromatography, and enzyme activities were measured by a specific radioassay. Cytosol from isolated hepatocytes contained high-affinity hexokinases A, B and C, in addition to hexokinase D. The last-mentioned represented about 95% of total glucose-phosphorylating activity. Only hexokinase A was found associated t the particulate fraction. Isolated non-parenchymal cells contained only hexokinases A, B and C. N-Acetylglucosamine kinase was measured with a specific radioassay and was found as a single enzyme form in both hepatocytes and non-parenchymal cells, with higher activities in the former. Pyruvate kinase isoenzyme L was present only in the hepatocytes and isoenzyme K only in the non-parenchymal liver cells, confirming that they are good cellular markers.

Solvent isotope effects on the glucokinase reaction. Negative co-operativity and a large inverse isotope effect in 2H2O

The solvent isotope effects on the reaction catalysed by rat-liver glucokinase have been studied. At low concentrations of glucose and high concentrations of MgATP2- there is an inverse solvent isotope effect of 3.5. At high glucose concentrations there is a normal solvent isotope effect of 1.3. In 1H2O there is positive co-operativity with respect to glucose [ Storer , A.C. and Cornish - Bowden , A. (1976) Biochem. J. 159, 7-14], but this is changed to negative co-operativity in 2H2O. The half-saturation points for both glucose and MgATP2- are decreased in 2H2O compared with those in 1H2O. Explanations of these effects in terms of the mnemonical model proposed by Storer and Cornish - Bowden [Biochem. J. 65, 61-69 (1977)] were considered in computer simulation. Two interpretations could account for the results, either a decrease in the rate of interconversion of the two forms of free enzyme postulated in the model, or an increase in the affinity for glucose of the enzyme form with the lower affinity in 1H2O. The results of a proton-inventory analysis were consistent with either of these interpretations. The solvent isotope effects thus provide additional evidence for the mnemonical model as an explanation of glucokinase co-operativity.

Kinetic, chromatographic and electrophoretic studies on glucose-phosphorylating enzymes of rat intestinal mucosa

The number and nature of glucose-phosphorylating enzymes of rat intestinal mucosa were investigated by chromatographic, electrophoretic, and kinetic methods. Three fractions with glucose-phosphorylating activity were obtained from the supernatant fluid of mucosa homogenate by means of DEAE-cellulose chromatography, corresponding to hexokinases A and B (EC 2.7.1.1.), and N-acetyl-D-glucosamine kinase (EC 2.7.1.59). Although the latter uses N-acetylglucosamine as the main substrate, it is also able to phosphorylate glucose. Electrophoresis in polyacrylamide and in cellulose acetate gels showed the same three enzyme activities. None of these procedures revealed the presence of either hexokinase D ("glucokinase") or hexokinase C in the intestinal mucosa. In the sediment fractions hexokinase A and B, but not N-acetylglucosamine kinase, were found. The Km values for glucose of partially purified hexokinases A and B were 0.025 and 0.174 mM, respectively, and their substrate specificity was the same as that of hexokinases A or B from other tissues. Partially purified N-acetylglucosamine kinase showed hyperbolic saturation functions for N-acetylglucosamine and ATP, with Km values of 0.021 and 0.38 mM, respectively. This enzyme also phosphorylated glucose, mannose, fructose, 2-deoxyglucose, and glucosamine. The dependence of velocity on glucose concentrations was complex, mimicking negative cooperativity. The molecular weight of both hexokinases A and B was 98,000 and that of N-acetylglucosamine kinase was 59,000. The kinetic properties, as well as the chromatographic and electrophoretic mobilities, of N-acetylglucosamine kinase may serve to confuse it with hexokinase D, and thus several criteria should be applied for correct identification.

Interconversions between different sulfhydryl-related kinetic states in glucokinase

Rat liver glucokinase (EC 2.7.1.2) undergoes two distinct sulfhydryl-related reversible kinetic transitions. During normal assays in the presence of both substrates but without added reducing agents, the activity decays ("kappa" decay) over time to a new steady-state rate. The half-time for this decay is essentially constant at glucose levels from 2 to 200 mM and averages 6.2 +/- 2 min. Glucokinase in this kappa steady state displays an increased Km for glucose but has the same Vmax as normal, sulfhydryl-activated glucokinase. The kappa form does not itself exhibit kinetic cooperativity with glucose. In contrast, glucokinase incubated with neither glucose nor sulfhydryl reagents decays (mu decay) to a form whose Vmax is near zero. The t 1/2 for this transition is about 0.5 min at 0 or very low (0.5 mM) glucose concentrations. For both decays, incubations of enzyme with intermediate levels of reducing agents give steady-state mixtures of activated and either kappa and/or mu forms, depending on conditions during the decay. Enzyme at intermediate stages of the kappa decay displays an unchanged Vmax, intermediate (increased relative to activated enzyme) glucose S0.5 values, and diminished glucose cooperativity. In contrast, enzyme at intermediate steady-state mixtures of activated and mu forms has a normal glucose S0.5 and cooperativity but a diminished Vmax from the activated states. The enzyme at any stage of each decay may be fully reactivated by the addition of sulfhydryl reducing agents such as dithiothreitol, dithioerythritol, glutathione, or mercaptoethanol. A model is proposed to account for this complex behavior in glucokinase kinetics which proposes different enzymatic states (kappa and mu) locked in by sulfhydryl oxidation of different conformations dictated by glucose concentration. These sulfhydryl-related transitions may be important in regulation of glucokinase activity, since glucokinase is very sensitive (at least 20-fold differential activity) to concentrations of glutathione within the physiological range, perhaps allowing the normally variable glutathione levels or cytosolic redox potential to modify the rate of uptake and storage of blood glucose through control of glucokinase activity.

The stereochemical course of phosphoryl transfer catalysed by glucokinase

Adenosine 5'-[gamma(S)-16O,17O,18O]triphosphate has been used to determine the stereo-chemical course of phosphoryl transfer catalysed by rat liver glucokinase. The chirality of the product, D-glucose 6-[16O,17O,18O]phosphate was analysed by 31P n.m.r. spectroscopy. The reaction proceeds with inversion of configuration at phosphorus. The simplest interpretation of this result, which is the same as that observed with yeast hexokinase [Lowe & Potter (1981) Biochem. J. 199, 277-233], is that the phosphoryl group is transferred between MgATP2- and glucose in the ternary complex by an 'in-line' mechanism. It accords with the veiw that the kinetic differences between glucokinase and the other hexokinases arise from differences in rate constants and not from any fundamental differences in chemical mechanism.

The comparative isozymology of vertebrate hexokinases

1. Multiple hexokinase isozymes have been found in most vertebrates. Since each isozyme displays distinctive structural, kinetic and regulatory characteristics, the system qualifies as a useful probe for studies on molecular evolution. 2. At least seven types of chromatographic patterns of liver hexokinases have been observed in mammals. In contrast, each Class of lower vertebrates present only two or three distinct profiles. 3. Aves and higher Reptiles do not have the same hexokinase isozymes as other vertebrates. The nature of the differences is poorly understood. 4. Ontogenetic changes of liver hexokinase profiles are quite different in rat, chick and frog. 5. Structural comparisons of three vertebrate hexokinases having a molecular weight of approximately 100,000 suggest that those isozymes originated from a pre-vertebrate ancestor through gene duplication followed by fusion and further duplication events. Another hexokinase (the so-called glucokinase), with half the molecular weight, may have arisen either as the result of subsequent even splitting of the fused gene or, less probably, by divergence from a duplicated gene before the fusion event.

Exponential model for a two-ligand, regulatory enzyme. Part 3: Performance tests of INDEXP computer programs for determination of model constants from initial velocity data. 2. Experimental data

The exponential model for a regulatory enzyme describes the relationship between the initial velocity of the catalysed reaction and the concentration of two ligands. A program, entitled 'INDEXP' has been devised to analyse rate data in terms of the model (Kinderlerer et al., 1981) and, in this report, its performance is examined when presented with experimental initial velocity data taken from the literature. It is shown that the two-ligand exponential model can satisfactorily rationalise experimental data with five linked constants (Ainsworth and Gregory, 1978); as a result the influence of ligand concentrations on the catalysed reactions can be described in rather simple terms.