Studies of substrate-induced conformational changes in human cytomegalovirus protease using optical biosensor technology

The interaction between human cytomegalovirus (HCMV) protease and a peptide substrate was studied using a surface plasmon resonance (SPR)-based biosensor. Immobilization of the enzyme to the sensor chip surface by amine coupling resulted in an active enzyme with a higher catalytic efficiency than the enzyme in solution, primarily due to a lower K(m) value. The interaction between immobilized protease and substrate was characterized by a biphasic SPR signal. Rate constants for the formation of the initial enzyme-substrate complex could be determined from the sensorgrams. Simulated binding curves based on the determined k(cat) and the rate constants indicated that the complex binding signal did not originate from the accumulation of intermediates in the catalytic reaction. By chemical crosslinking of the immobilized HCMV protease, which was shown to limit the enzyme's structural flexibility, it was revealed that the obtained sensorgrams were composed of a signal caused by substrate binding and considerable structural alterations in the immobilized enzyme. Furthermore, HCMV protease was inactivated by chemical crosslinking, indicating that structural flexibility is essential for this enzyme. Parallel experiments with immobilized alpha-chymotrypsin revealed that it does not undergo similar conformational changes on peptide binding and that crosslinking did not inactivate the enzyme. The simultaneous detection of binding and conformational changes using optical biosensor technology is expected to be of importance for further characterization of the enzymatic properties of HCMV protease and for identification of inhibitors of this enzyme. It can also be of use for studies of other flexible proteins.     

Structural features of ring C of 20-oxo steroids and the interaction with cortisone reductase

Kinetic measurements were made with cortisone reductase (20-dihydrocortisone-NAD(+) oxidoreductase, EC 1.1.1.53) and a series of substrates which differed in shape, size and electronic character in the region adjacent to C-11, C-14 and C-18. Structural changes at C-11 in these substrates resulted in up to 660-fold changes in the apparent K(m) value, up to 200-fold changes in the apparent V(max.) value and up to 800-fold changes in the ratio of these kinetic constants. It is suggested that interactions important for substrate function normally occur between the enzyme and the C ring in the region of C-11, that these interactions arise from so-called hydrophobic forces between the generally hydrophobic C ring portion of the substrate and a hydrophobic region of the enzyme, but that when the substrate contains a polar substituent in this portion of the molecule, then polar interactions with polar moieties of the enzyme can also be important. It is further suggested that the part of the enzyme that interacts with the region of C-11 in the substrate is flexible, and that substrate binding involves at least some degree of induced fit.     

Catalytic activity of rabbit skeletal muscle aldolase in the crystalline state

The monoclinic crystalline form of aldolase from rabbit skeletal muscle grown at 29 degrees C is catalytically active in the direction of aldol cleavage. Activity was assayed for in a crystallization buffer containing 45% saturated ammonium sulfate using chemically unmodified single crystals cut to precise dimensions. Diffusion effects on velocities from assays employing aldolase crystals do not appear to be limiting when cut single crystals are crushed. Assays of crushed crystals are linear with respect to both time and enzyme concentration. Kinetic constants are reported for both substrates fructose 1-phosphate and fructose 1,6-phosphate. Maximal velocities and binding constants determined differ by no more than a factor of 2 between the crystalline and the soluble state of the enzyme. Analysis of the kinetic constants for fructose 1-phosphate as substrate shows that binding of substrate does not change in going to the crystalline state. Release of product is reduced roughly 2-fold in the crystalline state. A similar conclusion can be reached in the case of fructose 1,6-phosphate as substrate provided the "on" steps of substrate and product are only diffusion limited but independent of the physical state of the enzyme. It is not possible to distinguish between a more sluggish conformational change during catalysis or simply tighter product binding in the crystalline state as compared to the soluble enzyme state.     

Substrate activation of porcine pancreatic kallikrein by N alpha derivatives of arginine 4-nitroanilides

Hydrolysis of several N alpha-substituted L-arginine 4-nitroanilides with porcine pancreatic kallikrein was studied under different conditions of pH, temperature, and salt concentration. At high substrate concentrations a deviation from Michaelis-Menten kinetics was observed with a significant increase in the hydrolysis rates of almost all substrates. Kinetic data were analyzed on the assumption that porcine pancreatic kallikrein presents an additional binding site with lower affinity for the substrate. Binding to this auxiliary site gives rise to a modulated enzyme species which can hydrolyze an additional molecule of the substrate through a second catalytic pathway. The values of both Michaelis-Menten and catalytic rate constants were higher for the modulated species than for the free enzyme, suggesting a mechanism of enzyme activation by substrate. Kinetic data indicated similar substrate requirements for binding at the primary and auxiliary sites of the enzyme. Tris(hydroxymethyl)aminomethane hydrochloride and NaCl were shown to alter the kinetic parameters of the hydrolysis of N alpha-acetyl-L-Phe-L-Arg 4-nitroanilide by porcine pancreatic kallikrein but not the enzyme activation pattern (ratio of the catalytic constants for the activated and the free enzyme forms). Similar observations were made when the hydrolysis of D-Val-L-Leu-L-Arg 4-nitroanilide was studied under different pH and temperature conditions.     

Kinetic model of ethopropazine interaction with horse serum butyrylcholinesterase and its docking into the active site.

The action of a potent tricyclic cholinesterase inhibitor ethopropazine on the hydrolysis of acetylthiocholine and butyrylthiocholine by purified horse serum butyrylcholinesterase (EC 3.1.1.8) was investigated at 25 and 37 degrees C. The enzyme activities were measured on a stopped-flow apparatus and the analysis of experimental data was done by applying a six-parameter model for substrate hydrolysis. The model, which was introduced to explain the kinetics of Drosophila melanogaster acetylcholinesterase [Stojan et al. (1998) FEBS Lett. 440, 85-88], is defined with two dissociation constants and four rate constants and can describe both cooperative phenomena, apparent activation at low substrate concentrations and substrate inhibition by excess of substrate. For the analysis of the data in the presence of ethopropazine at two temperatures, we have enlarged the reaction scheme to allow primarily its competition with the substrate at the peripheral site, but the competition at the acylation site was not excluded. The proposed reaction scheme revealed, upon analysis, competitive effects of ethopropazine at both sites; at 25 degrees C, three enzyme-inhibitor dissociation constants could be evaluated; at 37 degrees C, only two constants could be evaluated. Although the model considers both cooperative phenomena, it appears that decreased enzyme sensitivity at higher temperature, predominantly for the ligands at the peripheral binding site, makes the determination of some expected enzyme substrate and/or inhibitor complexes technically impossible. The same reason might also account for one of the paradoxes in cholinesterases: activities at 25 degrees C at low substrate concentrations are higher than at 37 degrees C. Positioning of ethopropazine in the active-site gorge by molecular dynamics simulations shows that A328, W82, D70, and Y332 amino acid residues stabilize binding of the inhibitor.     

Tryptophan fluorescence monitors multiple conformational changes required for glutamine phosphoribosylpyrophosphate amidotransferase interdomain signaling and catalysis.

Single tryptophan residues were incorporated into each of three peptide segments that play key roles in the structural transition of ligand-free, inactive glutamine phosphoribosylpyrophosphate (PRPP) amidotransferase to the active enzyme-substrate complex. Intrinsic tryptophan fluorescence and fluorescence quenching were used to monitor changes in a phosphoribosyltransferase (PRTase) "flexible loop", a "glutamine loop", and a C-terminal helix. Steady state fluorescence changes resulting from substrate binding were used to calculate binding constants and to detect the structural rearrangements that coordinate reactions at active sites for glutamine hydrolysis and PRTase catalysis. Pre-steady state kinetics of enzyme.PRPP and enzyme.PRPP.glutamine complex formation were determined from stopped-flow fluorescence measurements. The kinetics of the formation of the enzyme.PRPP complex were consistent with a model with two or more steps in which rapid equilibrium binding of PRPP is followed by a slow enzyme isomerization. This isomerization is ascribed to the closing of the PRTase flexible loop and is likely the rate-limiting step in the reaction of PRPP with NH(3). The pre-steady state kinetics for binding glutamine to the binary enzyme. PRPP complex could also be fit to a model involving rapid equilibrium binding of glutamine followed by an enzyme isomerization step. The changes monitored by fluorescence account for the interconversions between "end state" structures determined previously by X-ray crystallography and define an intermediate enzyme.PRPP conformer.     

The effects of modification with N-bromosuccinimide on the binding of ligands to dihydrofolate reductase.

The binding constants of substrate, inhibitors and coenzymes to native Lactobacillus casei dihydrofolate reductase and to the enzyme modified (at Trp-21) by N-bromosuccinimide have been determined using fluorimetric and spectrophotometric methods. The modification leads to only modest decreases (factors of 2-4) in the binding of substrate or substrate analogues, but the effects of coenzyme binding are much larger. The binding of NADPH is decreased by a factor of 200, but that of NADP+ by only a factor of 4, indicating a clear difference in their mode of interaction with the enzyme. The nature of this difference is discussed in the light of crystallographic and n.m.r. studies of the enzyme.     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Toward the elucidation of the catalytic mechanism of the mono-ADP-ribosyltransferase activity of Pseudomonas aeruginosa exotoxin A

The catalytic mechanism for the mono-ADP-ribosyltransferase activity of Pseudomonas aeruginosa exotoxin A was investigated by steady-state and stopped-flow kinetic analyses. The rate constants for binding of the NAD(+) substrate to the enzyme were found to be 4.7 +/- 0.4 microM(-1) s(-1) and 194 +/- 15 s(-1) for k(on) and k(off), respectively. The k(on) and k(off) rate constants for the eEF-2 substrate binding to the enzyme were 320 +/- 39 microM(-1) s(-1) and 131 +/- 22 s(-1), respectively. A potent, competitive inhibitor against the enzyme, 1,8-naphthalimide, bound the enzyme with k(on) and k(off) rates of 82 +/- 9 microM(-1) s(-1) and 51 +/- 6 s(-1), respectively. Furthermore, the binding on and off rates for the reaction products, ADP-ribose and nicotinamide, were too rapid for detection with the stopped-flow technique. Investigation of the pre-steady-state kinetics for the ADP-ribose transferase activity of the toxin-enzyme showed that there is no pre-steady-state complex formed during the catalytic cycle. Binding of NAD+ and smaller compounds representing the various parts of this substrate were investigated by the fluorescence quenching of the intrinsic toxin fluorescence. The binding data revealed a significant structural change in the enzyme upon NAD+ binding that could not be accounted for on the basis of the sum of the structural changes induced by the various NAD+ constituents. Product inhibition studies were conducted with nicotinamide and eEF-2-ADP-ribose, and the results indicate that the reaction involves a random-order ternary complex mechanism. Detailed kinetic analysis revealed that the eEF-2 substrate shows sigmoidal kinetic behavior with the enzyme, and fluorescence resonance energy transfer measurements indicated that wheat germ eEF-2 is oligomeric in solution.     

Nucleotide regulation of Escherichia coli glycerol kinase: initial-velocity and substrate binding studies

Substrate binding to Escherichia coli glycerol kinase (EC 2.7.1.30; ATP-glycerol 3-phosphotransferase) was investigated by using both kinetics and binding methods. Initial-velocity studies in both reaction directions show a sequential kinetic mechanism with apparent substrate activation by ATP and substrate inhibition by ADP. In addition, the Michaelis constants differ greatly from the substrate dissociation constants. Results of product inhibition studies and dead-end inhibition studies using 5'-adenylyl imidodiphosphate show the enzyme has a random kinetic mechanism, which is consistent with the observed formation of binary complexes with all the substrates and the glycerol-independent MgATPase activity of the enzyme. Dissociation constants for substrate binding determined by using ligand protection from inactivation by N-ethylmaleimide agree with those estimated from the initial-velocity studies. Determinations of substrate binding stoichiometry by equilibrium dialysis show half-of-the-sites binding for ATP, ADP, and glycerol. Thus, the regulation by nucleotides does not appear to reflect binding at a separate regulatory site. The random kinetic mechanism obviates the need to postulate such a site to explain the formation of binary complexes with the nucleotides. The observed stoichiometry is consistent with a model for the nucleotide regulatory behavior in which the dimer is the enzyme form present in the assay and its subunits display different substrate binding affinities. Several properties of the enzyme are consistent with negative cooperativity as the basis for the difference in affinities. The possible physiological importance of the regulatory behavior with respect to ATP is considered.     

Structural determinants of substrate binding to Bacillus cereus metallo-beta-lactamase

Binding and hydrolysis of the beta-lactams cefotaxime, cephapirin, imipenem, and benzylpenicillin by the metallo-beta-lactamase from Bacillus cereus were studied by presteady state kinetic measurements. In all cases, the substrate was unmodified in the most populated reaction intermediate, and no chemically modified substrate species accumulated to a detectable amount. The cephalosporins tested showed similar formation rate constants for this intermediate, and they differed mostly in their decay rates. Formation of a non-productive enzyme.substrate complex was detected for imipenem. The substrate binding differences can be accounted for by considering the structural features of each substrate. The apoenzyme could not bind any of the substrates, but binding was restored when the apoenzyme was reconstituted with Zn(II), revealing that the metal ions are the main determinants of substrate binding. This evidence is in line with the lack of an optimized substrate recognition patch in B1 and B3 metallo-beta-lactamases that provides a broad substrate spectrum.     

Kinetic studies on the reaction of p-hydroxybenzoate hydroxylase. Agreement of steady state and rapid reaction data.

p-Hydroxybenzoate hydroxylase (EC 1.14.13.2) from Pseudomonas fluorescens is a NADPH-dependent, FAD-containing monooxygenase catalyzing the hydroxylation of p-hydroxybenzoate to form 3,4-dihydroxybenzoate in the presence of NADPH and molecular oxygen. The mechanism of this three-substrate reaction was investigated in detail at pH 6.6, 4 degrees C, by steady state kinetics, stopped flow spectrophotometry, and equilibrium binding experiments. The initial velocity patterns are consistent with a ping-pong type mechanism which involves two ternary complexes between the enzyme and substrates. The first ternary complex is formed by random addition of p-hydroxybenzoate and NADPH to the enzyme, followed by the release of the first product (NADP+). The reduced enzyme . p-hydroxybenzoate complex now reacts with oxygen, the third substrate, to form the second ternary complex. The enzyme-bound p-hydroxybenzoate then reacts with the activated oxygen to give 3,4-dihydroxybenzoate which is released regenerating the oxidized enzyme for the next cycle. The binding of p-hydroxybenzoate to the oxidized enzyme to form a 1:1 complex causes large, characteristic spectral perturbations and fluorescence quenching. The dissociation constant for the enzyme . substrate complex was obtained by titrations in which absorbance and/or fluorescence quenching was measured. The binding constants of NADPH to the enzyme with and without p-hydroxybenzoate were determined kinetically by measuring the rate of reduction of the enzyme at different concentrations of NADPH. The reduction of the enzyme proceeds extremely slowly in the absence of p-hydroxybenzoate. The presence of the substrate causes a dramatic stimulation (140,000-fold) in the rate of enzyme reduction. The anaerobic reduction of the enzyme by NADPH in the presence of p-hydroxybenzoate produces a transient charge-transfer intermediate. On the basis of the proposed mechanism, the dissociation constants for p-hydroxybenzoate and NADPH as well as the Michaelis constants for all the three substrates were calculated from the initial velocity data. The agreement obtained between various kinetic parameters from the initial rate measurements and those calculated from the individual rate constants determined in rapid reactions, strongly supports the proposed mechanism for the p-hydroxybenzoate hydroxylase reaction.     

The N-terminal region of cystatin A (stefin A) binds to papain subsequent to the two hairpin loops of the inhibitor. Demonstration of two-step binding by rapid-kinetic studies of cystatin A labeled at the N-terminus with a fluorescent reporter group

The three-dimensional structures of cystatins, and other evidence, suggest that the flexible N-terminal region of these inhibitors may bind to target proteinases independent of the two rigid hairpin loops forming the remainder of the inhibitory surface. In an attempt to demonstrate such two-step binding, which could not be identified in previous kinetics studies, we introduced a cysteine residue before the N-terminus of cystatin A and labeled this residue with fluorescent probes. Binding of AANS- and AEDANS-labeled cystatin A to papain resulted in approximately 4-fold and 1.2-fold increases of probe fluorescence, respectively, reflecting the interaction of the N-terminal region with the enzyme. Observed pseudo-first-order rate constants, measured by the loss of papain activity in the presence of a fluorogenic substrate, for the reaction of the enzyme with excess AANS-cystatin A increased linearly with the concentration of the latter. In contrast, pseudo-first-order rate constants, obtained from measurements of the change of probe fluorescence with either excess enzyme or labeled inhibitor, showed an identical hyperbolic dependence on the concentration of the reactant in excess. This dependence demonstrates that the binding occurs in two steps, and implies that the labeled N-terminal region of cystatin A interacts with the proteinase in the second step, subsequent to the hairpin loops. The comparable affinities and dissociation rate constants for the binding of labeled and unlabeled cystatin A to papain indicate that the label did not appreciably perturb the interaction, and that unlabeled cystatin therefore also binds in a similar two-step manner. Such independent binding of the N-terminal regions of cystatins to target proteinases after the hairpin loops may be characteristic of most cystatin-proteinase reactions.     

Effects of general anesthetics on the bacterial luciferase enzyme from Vibrio harveyi: an anesthetic target site with differential sensitivity

The effects of a diverse range of 36 general anesthetics and anesthetic-like compounds on a highly purified preparation of the bacterial luciferase enzyme from Vibrio harveyi have been investigated. Under conditions where the flavin site was saturated, almost all of the anesthetics inhibited the peak enzyme activity and slowed the rate of decay. However, a small number of the more polar agents only inhibited at high concentrations, while stimulating activity at lower concentrations. The inhibition was found to be competitive in nature, with the anesthetics acting by competing for the binding of the aldehyde substrate n-decanal. The anesthetic binding site on the enzyme could accommodate only a single molecule of a large anesthetic but more than one molecule of a small anesthetic, consistent with the site having circumscribed dimensions. The homologous series of n-alcohols and n-alkanes exhibited cutoffs in inhibitory potency, but these cutoffs occurred at very different chain lengths (about C10 for the n-alkanes and C15 for the n-alcohols), mimicking similar cutoffs observed for general anesthetic potencies in animals. Binding constants determined from peak height measurements showed that the inhibitor binding site was predominantly hydrophobic (with a mean delta delta G CH2 of -5.0 kJ/mol), but fluctuations in the binding constants with chain length revealed regions in the binding site with polar characteristics. Binding constants to an intermediate form of the enzyme (intermediate II) were also determined, and these confirmed the principal features of the binding site deduced from the peak height measurements. The long-chain compounds, however, bound considerably tighter to the intermediate II form of the enzyme, and this was shown to account for the biphasic decay kinetics that were observed with these compounds. Overall, there was poor agreement between the EC50 concentrations for inhibiting the luciferase enzyme from V. harveyi and those which induce general anesthesia in animals, with bulky compounds being much less potent, and moderately long chain alcohols being much more potent, as luciferase inhibitors than as general anesthetics.     

Conformational aspects of inhibitor design: enzyme-substrate interactions in the transition state.

The theory of absolute reaction rates suggests that enzymes, like other catalysts, can enhance the rate of a reaction only to the extent that they bind the altered substrate in the transition state (S++) more tightly than they bind the substrate in the ground state (S). ES dissociation constants commonly fall in the physiological range, but recent kinetic studies indicate that formal ES++ dissociation constants of less than 10(-20) M are achieved by enzymes of several classes. Studies with stable analogues suggest that these remarkable powers of discrimination involve a tendency of the enzyme to close around S++ in such a way as to maximize binding contacts; that several parts of the substrate contribute to S++ binding; and that their contributions to binding affinity can be strongly synergistic.     

Catalytic properties and active-site structural features of immobilized horse liver alcohol dehydrogenase

Alcohol dehydrogenase from horse liver was immobilized by covalent attachment to CNBr-Sepharose and by adsorption to octyl-Sepharose CL-4B, a hydrophobic analog of Sepharose. In each case, rate constants for the binding and release of coenzyme and for the oxidation of substrates were measured based on the concentration of accessible active-site zinc atoms determined by titration with a paramagnetic inhibitor. All rate constants were substantially reduced upon immobilization; however, the rate constant of immobilized enzyme for ethanol oxidation was independent of the immobilization method, whereas the rate constant for cyclohexanol oxidation was lower for enzyme immobilized to octyl-Sepharose. Consequently, the substrate specificity of the two immobilized enzyme samples differed by an order of magnitude. Moreover, EPR spectroscopy studies and computer graphic analyses of spin labels occupying three defined regions of the active-site domain indicated that the active-site conformation adjacent to the catalytic zinc atom was similar in the two samples while the conformation slightly further from the zinc atom was different. This result may explain why the two immobilized enzyme preparations exhibited the same rate constant toward a small substrate (ethanol) yet different rate constants toward a larger substrate (cyclohexanol), whose rate constant is expected to be sensitive to a larger portion of the active site.     

The magnitude of enzyme transition state analog binding constants

Transition state binding theory utilizes non-enzymic and enzymic rate ratios to predict the ratio of transition state analog dissociation constants to substrate dissociation constants. In this paper we show that enzyme rate accelerations due solely to lessened entropy requirements, arising from the juxtaposition of a catalytic group and a substrate binding site at an enzyme active site, will result in a ratio of transition state and substrate dissociation constants which is different, in general, from the ratio of non-enzymic and enzymic rate constants. The arguments presented in this paper provide a possible explanation for the frequently observed large discrepancy between the measured and predicted values for transition state analog dissociation constants.     

Role of the ribose residue of substrates in reactions catalyzed by ribonuclease

The rate constants and Km for the hydrolysis of the optically active nonglycosidic analogues of the CpA and C greater than p catalysed by RNase A and RNase BS-I were measured. The rate of hydrolysis of the model substrates in 10(5) and 10(3) slower that for the appropriate dinucleoside phosphate and nucleoside cyclophosphate. However, substitution of the relatively rigid ribofuranose ring with flexible alifatic chains is accompanied by little variation in binding constants. The analyses based on the single substrate system indicate that the observed difference in rate constants must be accounted for by a difference between the binding of the substrates in the transition state to the RNase active site. Consequently, the "rigidity" of the ribose rings in RNA leads to large decreases in the free energy of activation for the reactions catalysed by RNases.     

Negative cooperativity of substrate binding but not enzyme activity in wild-type and mutant forms of CTP:glycerol-3-phosphate cytidylyltransferase

CTP:glycerol-3-phosphate cytidylyltransferase (GCT) catalyzes the synthesis of CDP-glycerol for teichoic acid biosynthesis in certain Gram-positive bacteria. This enzyme is a model for a cytidylyltransferase family that includes the enzymes that synthesize CDP-choline and CDP-ethanolamine for phosphatidylcholine and phosphatidylethanolamine biosynthesis. We have used quenching of intrinsic tryptophan fluorescence to measure binding affinities of substrates to the GCT from Bacillus subtilis. Binding of either CTP or glycerol-3-phosphate to GCT was biphasic, with two binding constants of about 0.1-0.3 and 20-40 microm for each substrate. The stoichiometry of binding was 2 molecules of substrate/enzyme dimer, so the two binding constants represented distinctly different affinities of the enzyme for the first and second molecule of each substrate. The biphasic nature of binding was observed with the wild-type GCT as well as with several mutants with altered Km or kcat values. This negative cooperativity of binding was also seen when a catalytically defective mutant was saturated with two molecules of CTP and then titrated with glycerol-3-phosphate. Despite the pronounced negative cooperativity of substrate binding, negative cooperativity of enzyme activity was not observed. These data support a mechanism in which catalysis occurs only when the enzyme is fully loaded with 2 molecules of each substrate/enzyme dimer.     

Some equilibrium and nonequilibrium properties of the allosteric interactions in enzymes. II. Allosteric effect in the absence of a rapid quilibrium between substrate and enzyme

The existence of allosteric interactions in enzymes was determined even in the absence of a rapid equilibrium between enzyme and substrate. The ratio between the rate constants was found at which the K allosteric effect was possible. Rate equations were formulated in which the two-stage substrate binding was taken into account. The conditions for the existence of allosteric interactions were verified by means of theoretical curves. The calculations were made with the help of rate equations taking into account the two stages in substrate binding.