The theoretical analysis of kinetic behaviour of kinetic behaviour of "hysteretic" allosteric enzymes. III. Dissociating and associating enzyme systems in which the rate of installation of equilibrium between the oligomeric forms in comparable to that of enzymatic reaction

Single-Molecule Mechanistic Study of Enzyme Hysteresis

Hysteresis is an important feature of enzyme-catalyzed reactions, as it reflects the influence of enzyme regulation in the presence of ligands such as substrates or allosteric molecules. In typical kinetic studies of enzyme activity, hysteretic behavior is observed as a "lag" or "burst" in the time course of the catalyzed reaction. These lags and bursts are due to the relatively slow transition from one state to another state of the enzyme molecule, with different states having different kinetic properties. However, it is difficult to understand the underlying mechanism of hysteresis by observing bulk reactions because the different enzyme molecules in the population behave stochastically. In this work, we studied the hysteretic behavior of mutant β-glucuronidase (GUS) using a high-throughput single-molecule array platform and investigated the effect of thermal treatment on the hysteresis.

Allostery and Hysteresis Are Coupled in Human UDP-Glucose Dehydrogenase

Human UDP-glucose dehydrogenase (hUGDH) is regulated by an atypical allosteric mechanism in which the feedback inhibitor UDP-xylose (UDP-Xyl) competes with the substrate for the active site. Binding of UDP-Xyl triggers the T131-loop/α6 allosteric switch, which converts the hexameric structure of hUGDH into an inactive, horseshoe-shaped complex (EΩ). This allosteric transition buries residue A136 in the protein core to produce a subunit interface that favors the EΩ structure. Here we use a methionine substitution to prevent the burial of A136 and trap the T131-loop/α6 switch in the active conformation. We show that hUGDHA136M does not exhibit substrate cooperativity, which is strong evidence that the methionine substitution prevents the formation of the low-UDP-Glc-affinity EΩ state. In addition, the inhibitor affinity of hUGDHA136M is reduced 14-fold, which most likely represents the Ki for competitive inhibition in the absence of the allosteric transition to the higher-affinity EΩ state. hUGDH also displays a lag in progress curves, which is caused by a slow, substrate-induced isomerization that activates the enzyme. Stopped-flow analysis shows that hUGDHA136M does not exhibit hysteresis, which suggests that the T131-loop/α6 switch is the source of the slow isomerization. This interpretation is supported by the 2.05 Å resolution crystal structure of hUGDHA136M, which shows that the A136M substitution has stabilized the active conformation of the T131-loop/α6 allosteric switch. This work shows that the T131-loop/α6 allosteric switch couples allostery and hysteresis in hUGDH.

Hysteresis and negative cooperativity in human UDP-glucose dehydrogenase

Human UDP-α-d-glucose 6-dehydrogenase (hUGDH) forms a hexamer that catalyzes the NAD(+)-dependent oxidation of UDP-α-d-glucose (UDG) to produce UDP-α-d-glucuronic acid. Mammalian UGDH displays hysteresis (observed as a lag in progress curves), indicating that the enzyme undergoes a slow transition from an inactive to an active state. Here we show that hUGDH is sensitive to product inhibition during the lag. The inhibition results in a systematic decrease in steady-state velocity and makes the lag appear to have a second-order dependence on enzyme concentration. Using transient-state kinetics, we confirm that the lag is in fact due to a substrate and cofactor-induced isomerization of the enzyme. We also show that the cofactor binds to the hUGDH:UDG complex with negative cooperativity. This suggests that the isomerization may be related to the formation of an asymmetric enzyme complex. We propose that the hysteresis in hUGDH is the consequence of a functional adaptation; by slowing the response of hUGDH to sudden increases in the flux of UDG, the other biochemical pathways that use this important metabolite (i.e., glycolysis) will have a competitive edge.

Hysteretic behavior of proprotein convertase 1/3 (PC1/3)

The proprotein convertases (PCs) are calcium-dependent proteases responsible for processing precursor proteins into their active forms in eukariotes. The PC1/3 is a pivotal enzyme of this family that participates in the proteolytic maturation of prohormones and neuropeptides inside the regulated secretory pathway. In this paper we demonstrate that mouse proprotein convertase 1/3 (mPC1/3) has a lag phase of activation by substrates that can be interpreted as a hysteretic behavior of the enzyme for their hydrolysis. This is an unprecedented observation in peptidases, but is frequent in regulatory enzymes with physiological relevance. The lag phase of mPC1/3 is dependent on substrate, calcium concentration and pH. This hysteretic behavior may have implications in the physiological processes in which PC1/3 participates and could be considered an additional control step in the peptide hormone maturation processes as for instance in the transformation of proinsulin to insulin.

Control of the glycolytic flux in Saccharomyces cerevisiae grown at low temperature: a multi-level analysis in anaerobic chemostat cultures

Growth temperature has a profound impact on the kinetic properties of enzymes in microbial metabolic networks. Activities of glycolytic enzymes in Saccharomyces cerevisiae were up to 7.5-fold lower when assayed at 12 degrees C than at 30 degrees C. Nevertheless, the in vivo glycolytic flux in chemostat cultures (dilution rate: 0.03 h(-1)) grown at these two temperatures was essentially the same. To investigate how yeast maintained a constant glycolytic flux despite the kinetic challenge imposed by a lower growth temperature, a systems approach was applied that involved metabolic flux analysis, transcript analysis, enzyme activity assays, and metabolite analysis. Expression of hexose-transporter genes was affected by the growth temperature, as indicated by differential transcription of five HXT genes and changed zero trans-influx kinetics of [(14)C]glucose transport. No such significant changes in gene expression were observed for any of the glycolytic enzymes. Fermentative capacity (assayed off-line at 30 degrees C), which was 2-fold higher in cells grown at 12 degrees C, was therefore probably controlled predominantly by glucose transport. Massive differences in the intracellular concentrations of nucleotides (resulting in an increased adenylate energy charge at low temperature) and glycolytic intermediates indicated a dominant role of metabolic control as opposed to gene expression in the adaptation of glycolytic enzyme activity to different temperatures. In evolutionary terms, this predominant reliance on metabolic control of a central pathway, which represents a significant fraction of the cellular protein of the organism, may be advantageous to limit the need for protein synthesis and degradation during adaptation to diurnal temperature cycles.

Kinetic study on the dimer-tetramer interconversion of glycogen phosphorylase a

Kinetic theory of dissociating enzyme systems has been applied to a study of the dimer-tetramer interconversion of glycogen phosphorylase a. All kinetic constants for the dissociating-associating reaction of phosphorylase a have been determined. The results indicate that (a) the presence of glucose-1-phosphate has no influence on either the rate of dissociation or the rate of association, and hence does not shift the dimer-tetramer equilibrium of phosphorylase a; (b) the binding og glycogen to the enzyme decreases the association rate of the dimer to form the tetramer, but has no effect on the dissociation rate of the tetramer; (c) both the dimeric and tetrameric form of phosphorylase a can bind glycogen, but the tetrameric form has a lower affinity for glycogen and is catalytically inactive.

A novel method for determining kinetic parameters of dissociating enzyme systems

The theoretical analysis has been presented for the kinetics of dissociating-associating enzyme-catalyzed reactions. On the basis of the kinetic equation of substrate reaction, a general procedure is developed for determining the kinetic constants of dissociating-associating enzyme reactions. By analyzing the experimental data of initial velocity and steady-state velocity as functions of enzyme and substrate concentration, all unknown kinetic parameters can be determined from several simple, sequential calculations. This method is simple and rigorous, and the required experiments may also not be difficult for most dissociating enzyme systems. Therefore, the present method should be a useful addition to the available methods for studying subunit dissociation of enzymes. In comparison to other physical methods, the advantage of this method is not only its usefulness in the study of self-associating reactions at very low protein concentration but its convenience in the study of substrate effects on subunit-subunit interactions.

Hysteresis of cytosolic NADP-malic enzyme II from Trypanosoma cruzi

NADP-malic enzyme II, one of two isoenzymes of NADP-malic enzyme (EC 1.1.1.40) in Trypanosoma cruzi epimastigotes, presents hysteretic behavior that results in a kinetic lag in the reaction progress curve. The lag is affected by the malate, aspartate and oxaloacetate concentrations in the assay mixture. This dependence suggests that hysteresis is due to an association-dissociation process influenced by the binding of these ligands to the enzyme. The enzyme was separated from NADP-malic enzyme I and purified 43-fold from a cell homogenate by a procedure involving column chromatography on DEAE-Sephacel and Cibacron-blue Sepharose. The molecular mass of the highly purified enzyme was determined as 126 kDa.

The dimeric form of phosphoenolpyruvate carboxylase isolated from maize: physical and kinetic properties

Phosphoenolpyruvate carboxylase purified from maize was a homodimer of molecular weight 200 kDa and was readily converted to a tetrameric form in the presence of Mg2+ plus PEP or Mg2+ alone. During the assay, the enzyme activity increased with time, reaching a steady state after a discernible lag, suggesting its hysteretic nature. The hystereses was not due to oligomerization of the enzyme as the lag time tau was independent of the enzyme concentration and the lag was not abolished on preincubation with 25 mM Mg2+, the condition under which the enzyme existed in tetrameric form. Nevertheless, the lag could be abolished on preincubating the enzyme with PEP plus Mg2+, indicating that the hystereses is due to a PEP plus Mg2(+)-induced slow transition of the enzyme to an activated state during the catalysis. During steady state, the enzyme showed cooperative kinetics for PEP and Mg2+ at pH 7. It had two binding sites with nearly 10-fold difference in affinities for PEP and Mg2+.

Pre-steady-state kinetics of beef heart mitochondrial ATPase

The pre-steady-state kinetics of beef heart mitochondrial ATPase (F1) were examined. F1 was found to exhibit hysteretic behavior when hydrolyzing ATP. The hysteretic property was expressed as an activation process which occurred when the enzyme was mixed with its substrate, MgATP. Many catalytic turnovers were required before the activation was complete. The lag in hydrolysis increased hyperbolically as the concentration of enzyme increased. Passage of F1 through Sephadex G25 eliminated the activation process. Several kinetically distinct possibilities for explaining these data, including multiple nucleotide dissociations, enzyme conformational changes, and regulatory site interactions, are discussed. The enzyme was apparently able to recognize nucleotide in a noncatalytic manner, as evidenced by the fact that F1 preincubated with ADP in the absence of substrate achieved partial activation (smaller lag times) before being introduced to substrate. ADP is also a time-dependent inhibitor, exhibiting a slow hysteretic inhibition in addition to immediate competitive inhibition.

Characterization of ligand-induced states of maize homoserine dehydrogenase

The threonine-sensitive homoserine dehydrogenase (L-homoserine: NAD(P)+ oxido-reductase), isolated from seedlings of Zea mays L., is characterized by variable kinetic and regulatory properties. Previous analysis of this enzyme suggested that it is capable of ligand-mediated interconversions among four kinetically distinct states (S. Krishnaswamy and J. K. Bryan (1983) Arch. Biochem. Biophys. 222, 449-463). These forms of the enzyme have been identified and found to differ in oligomeric configuration and conformation. In the presence of KCl and threonine a rapid equilibrium among three species of the enzyme (B, T, and K) is established. Each of these species can undergo a unique slow transition to a steady-state form under assay conditions. Results obtained from gel-filtration chromatography and sucrose density centrifugation indicate that the B and steady-state forms are tetramers and the T and K states are dimers. Evidence is presented to indicate that the rapid conversion from one dimeric species to the other can only occur via formation of the tetrameric B state. Chromatography under reacting-enzyme conditions provides direct support for the slow formation of a common steady-state species from any one of the other forms of the enzyme. The rate of transition is influenced by threonine, homoserine, NAD+, and, for transitions involving association reactions, by enzyme concentration. Small, reproducible differences in the apparent size of the T and K forms, and the B and steady-state species, are attributed to changes in conformation. This conclusion is supported by differential susceptibility of the enzymic states to proteolytic inactivation, by different rates of inactivation by dithio-bis-nitrobenzoate, and by alterations in their thermal stability. In addition, the B, T, and K states of the enzyme exhibit unique intrinsic fluorescence spectra. Spectral changes are shown to closely parallel changes in kinetic and hysteretic properties of the enzyme. The results of diverse methods of analysis are internally consistent, and provide considerable support for the conclusion that this pleiotropic regulatory enzyme can exist in any of several physically distinct states.

Purification, properties and assay of D-ribulose 5-phosphate 3-epimerase from human erythrocytes

A direct assay procedure is described for D-ribulose 5-phosphate 3-epimerase (EC 5.1.3.1) which exploits differences in the c.d. spectra of substrate and product. The enzyme has been purified from human erythrocytes and was resolved by gel filtration and sucrose-density-gradient centrifugation into a major component of apparent Mr 45 000 and a minor component of Mr 23 000. Electrophoresis in sodium dodecyl sulphate gave a single component corresponding to Mr 23 000. Kinetic and sucrose-density-gradient centrifugation data indicate dissociation of the dimeric form of the enzyme into monomers of low specific activity; substrate favours the active dimeric form of the enzyme. At concentrations of the enzyme where both forms of the enzyme are present initial velocity data yielded a Hill plot with an interaction coefficient of approx. 2.0, indicating co-operative binding of substrate under these conditions.

Ligand-induced interconversions of maize homoserine dehydrogenase among different states

The threonine-sensitive homoserine dehydrogenase has been isolated and extensively purified from shoots of Zea mays L. var. earliking. This enzyme is shown to be hysteretic under certain conditions. Progress curves of the NAD-dependent reaction catalyzed by the maize enzyme can be characterized by distinct lags prior to achievement of steady state velocities, reflecting transitions from less active species to a more active steady state form of the enzyme. Incubation of the enzyme for 1 min at 25 degrees C prior to initiation of the reaction profoundly influences the properties of the less active enzyme and the nature of the subsequent slow transitions during assay. When the feedback modifier, L-threonine, or KCl is included in the preincubation mixture, the transitions involve biomolecular association reactions. In the absence of either ligand, or in the presence of an appropriate mixture of both, a unimolecular transition occurs during assay. Three unique preincubation states of the enzyme have been identified on the basis of their response to substrates and effectors; whereas, the kinetic and regulatory properties of the steady state form of the enzyme are independent of preincubation conditions. Steady state can thus be achieved by three different transitions. Each transition is retarded by threonine and favored by substrates and potassium, although the effects of these compounds differ quantitatively. Under the conditions tested, monovalent cations have no effect on the steady state velocity of the enzyme. A model describing the relationships among the four unique states of the enzyme which is consistent with the present results and supported by previous observations is proposed.

Human eosinophil arylsulfatase B. Structure and activity of the purified tetrameric lysosomal hydrolase

Arylsulfatase B from human eosinophils was purified free of contaminating proteins by gel filtration and sequential affinity chromatography on Affi-Gel Blue and zinc chelate Sepharose. 50 micrograms of the purified enzyme presented as a single stained band on alkaline disc gel electrophoresis. In both goats and rabbits, the purified enzyme elicited monospecific antisera that yielded single precipitation arcs on Ouchterlony analysis with a human eosinophil extract and the purified enzyme; the immunoprecipitation lines fused in a pattern of identity, providing immunochemical evidence for the homogeneity of the purified enzyme. On sodium dodecyl sulfate (SDS)-polyacrylamide gel electrophoresis, a dominant lower molecular weight protein and three other bands with molecular weights approximately two, three, and four times that of the major protein band were resolved. The prominence of the less rapidly migrating protein bands increased relative to the major band if the enzyme was maintained under acidic conditions or was reacted with the cross-linking agent dimethyl suberimidate under alkaline conditions before SDS-polyacrylamide gel electrophoresis, supporting the conclusion that the enzyme consists of four subunits. Two stained bands were present on acid disc gel electrophoresis; they were composed of oligomeric forms of enzyme on analysis by SDS-polyacrylamide gel electrophoresis in a second dimension. A minimum molecular weight of 70,190 was determined from amino acid composition analysis for the tetrameric form of the enzyme. The specific functional activity of the purified arylsulfatase B was concentration and time dependent, compatible with its association or dissociation into subunit forms with differing specific activities. Factors that govern subunit interactions of arylsulfatase B, including local enzyme concentration and pH, provide mechanisms for regulating the enzymatic activity of this lysosomal hydrolase.

The binding of NADH to succinic semialdehyde dehydrogenase

The enzyme succinic semialdehyde dehydrogenase from pig brain is a tetramer composed of identical subunits of molecular weight 41000. Fluorometric titrations conducted on samples of enzyme in pyrophosphate buffer (pH 8.4) reveal the presence of two NADH binding sites characterized by a dissociation constant of 4 microM. The unusual stoichiometry of binding of NADH, i.e. two moles NADH/enzyme tetramer, as demonstrated by emission anisotropy measurements is not due to reversible association-dissociation of the oligomeric structure at pH 8.4. The results of the fluorometric titrations are consistent with a model of extreme negative cooperativity, i.e. the affinity of NADH for the enzyme is influenced by interactions between the protomers. The reaction catalyzed by succinic semialdehyde dehydrogenase is inhibited by the substrate succinic semialdehyde with a Ki of 0.09 microM which is fivefold greater than the Km value. The binding of excess substrate to the catalytic site provides a direct and simple mechanism for regulation of the rate of product formation.

New relations for activity analysis of associating enzymes

New relations for catalytic-activity analysis are proposed for simple association/dissociation equilibria between the mono- and oligo-meric forms of enzymes in the case where these equilibria evolve very slowly in comparison with the binding of the substrates. This analysis of activity versus total enzyme concentration leads rapidly to information, complementary to that given by physico-chemical methods, on specific activities, the degree of polymerization of the enzyme forms and on their dissociation constants.

Slow association-dissociation equilibrium of NADP-linked isocitrate dehydrogenase from beef liver in relation to catalytic activity

In this paper experiments are reported which show evidence for a relation between quaternary structure and catalytic activity of cytoplasmic NADP-linked isocitrate dehydrogenase from beef liver. The inactivation of the enzyme occurring upon dilution and the plots of the catalytic activity versus the enzyme concentration indicate that the monomeric species is catalytically inactive and that the monomer-dimer equilibrium is shifted towards the dimer upon binding of the substrate magnesium isocitrate complex. The association of the enzyme following binding of the substrate takes place at a rate comparable with that of the enzymatic reaction, which results in a 'hysteretic' behaviour of the enzyme. The possibility is discussed that slow changes in quaternary structure can give rise to a physiological regulation of the enzymatic activity.