Kinetic mechanism of the type II calmodulin-dependent protein kinase: studies of the forward and reverse reactions and observation of apparent rapid-equilibrium ordered binding

The kinetic reaction mechanism of the type II calmodulin-dependent protein kinase was studied by using its constitutively active kinase domain. Lacking regulatory features, the catalytic domain simplified data collection, analysis, and interpretation. To further facilitate this study, a synthetic peptide was used as the kinase substrate. Initial velocity measurements of the forward reaction were consistent with a sequential mechanism. The patterns of product and dead-end inhibition studies best fit an ordered Bi Bi kinetic mechanism with ATP binding first to the enzyme, followed by binding of the peptide substrate. Initial-rate patterns of the reverse reaction of the kinase suggested a rapid-equilibrium mechanism with obligatory ordered binding of ADP prior to the phosphopeptide substrate; however, this apparent rapid-equilibrium ordered mechanism was contrary to the observed inhibition by the phosphopeptide which is not supposed to bind to the kinase in the absence of ADP. Inspection of product inhibition patterns of the phosphopeptide with both ATP and peptide revealed that an ordered Bi Bi mechanism can show initial-rate patterns of a rapid-equilibrium ordered system when a Michaelis constant for phosphopeptide, Kip, is large relative to the concentration of phosphopeptide used. Thus, the results of this study show an ordered Bi Bi mechanism with nucleotide binding first in both directions of the kinase reaction. All the kinetic constants in the forward and reverse directions and the Keq of the kinase reaction are reported herein. To provide theoretical bases and diagnostic aid for mechanisms that can give rise to typical rapid-equilibrium ordered kinetic patterns, a discussion on various sequential cases is presented in the Appendix.     

Analysis of the mechanism of chloramphenicol acetyltransferase by steady-state kinetics. Evidence for a ternary-complex mechanism.

The mechanism of the enzymic reaction responsible for chloramphenicol resistance in bacteria was examined by steady-state kinetic methods. The forward reaction catalysed by chloramphenicol acetyltransferase leads to inactivation of the antibiotic. Use of alternative acyl donors and acceptors, as well as the natural substrates, has yielded data that favour the view that the reaction proceeds to the formation of a ternary complex by a rapid-equilibrium mechanism wherein the addition of substrates may be random but a preference for acetyl-CoA as the leading substrate can be detected. Chloramphenicol and acetyl-CoA bind independently, but the correlation between directly determined and kinetically derived dissociation constants is imperfect because of an unreliable slope term in the rate equation. The reverse reaction, yielding acetyl-CoA and chloramphenicol, was studied in a coupled assay involving citrate synthase and malate dehydrogenase, and is best described by a rapid-equilibrium mechanism with random addition of substrates. The directly determined dissociation constant for CoA is in agreement with that derived from kinetic measurements under the assumption of an independent-sites model.     

Uridine phosphorylase from Escherichia coli B.: kinetic studies on the mechanism of catalysis

Using a highly purified enzyme preparation of uridine phosphorylase from Escherichia coli B, we have performed detailed kinetic studies which include initial-velocity and product-inhibition experiments in the forward and reverse directions of the reaction. These studies indicate a rapid-equilibrium random mechanism for this enzyme with the formation of an enzyme . uracil phosphate abortive complex. Lack of formation of the enzyme . uridine . ribose-1-phosphate abortive complex suggests that the ribosyl moiety of the two ligands compete for the same binding site. The random mechanism is different from the ordered addition of substrates found for uridine phosphorylase from other sources. All the kinetic constants in the forward and reverse directions and the Keq of reaction for E. coli uridine phosphorylase are reported herein.     

An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.     

Kinetic analysis and design of experiments to identify the catalytic mechanism of the monocarboxylate transporter isoforms 4 and 1

Transport of lactate, pyruvate, and other monocarboxylates across the sarcolemma of skeletal and cardiac myocytes occurs via passive diffusion and by monocarboxylate transporter (MCT) mediated transport. The flux of lactate and protons through the MCT plays an important role in muscle energy metabolism during rest and exercise and in pH regulation during exercise. The MCT isoforms 1 and 4 are the major isoforms of this transporter in skeletal and cardiac muscle. The current consensus on the mechanism of these transporters, based on experimental measurements of labeled lactate fluxes, is that monocarboxylate-proton symport occurs via a rapid-equilibrium ordered mechanism with proton binding followed by monocarboxylate binding. This study tests ordered and random mechanisms by fitting experimental measurements of tracer exchange fluxes from MCT1 and MCT4 isoforms to theoretical predictions derived using relationships between one-way fluxes and thermodynamic forces. Analysis shows that: 1), the available kinetic data are insufficient to distinguish between a rapid-equilibrium ordered and a rapid-equilibrium random-binding model for MCT4; 2), MCT1 has a higher affinity to lactate than does MCT4; 3), the theoretical conditions for the so-called trans-acceleration phenomenon (e.g., increased tracer efflux from a vesicle caused by increased substrate concentration outside the vesicle) do not necessarily require the rate constant for the lactate and proton bound transporter to reorient across the membrane to be higher than that for the unbound transporter; and finally, 4), based on model analysis, additional experiments are proposed to be able to distinguish between ordered and random-binding mechanisms.     

Rapid-equilibrium rate equations for the enzymatic catalysis of A+B=P+Q over a range of pH

This article shows how pKs for the enzymatic site and enzyme-substrate complexes can be obtained from kinetic experiments on the reaction A+B=P+Q, with and without the consumption of hydrogen ions. The rapid-equilibrium rate equation makes it possible to obtain the pKs and chemical equilibrium constants involved in the mechanism, the apparent equilibrium constant K' for the catalyzed reaction, and the number of hydrogen ions consumed in the rate-determining reaction. Experimentally-determined Michaelis constants can be adjusted for the pKs of the substrates A, B, P, and Q so that it is easier to obtain the pKs of E, EA, EB, EAB, EQ, and EPQ, and the chemical equilibrium constants. Reaction rates are discussed for the forward reaction ordered A+B=ordered P+Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction and for random A+B=ordered P+Q with zero, one, or two hydrogen ions consumed in the rate-determining reaction. When hydrogen ions are consumed in the rate-determining reaction, there is a new factor 10(n)(pH) in the rate equation, where n is the number of hydrogen ions consumed in the rate-determining reaction for the forward reaction. The integer n can be obtained from rate measurements over a range of pH, but it cannot be determined from thermodynamic measurements.     

Three mechanisms and rapid-equilibrium rate equations for a type of reductase reaction

Rapid-equilibrium rate equations for enzyme-catalyzed reactions are especially useful when the mechanism involves a number of pKs, but they are also useful when some reactants have stoichiometric numbers greater than one or hydrogen ions are produced or consumed in the rate-determining step. The pH dependencies of limiting velocities, Michaelis constants, and reaction velocities for the forward reaction are discussed for two examples of reductase reactions of the type mR + O -> products, where R is the reductant and O is the oxidant. For the nitrate reductase reaction (EC 1.9.6.1), m = 2 and two hydrogen ions are consumed. For the nitrite-ferredoxin reductase reaction (EC 1.7.7.1), m = 6 and eight hydrogen ions are consumed. The expressions for the limiting velocities, Michaelis constants, and rate equations for the forward reaction are derived for two ordered mechanisms and the random mechanism. Three Mathematica programs are used to make plots of kinetic parameters as functions of pH and three-dimensional plots of rapid-equilibrium velocities as functions of [O] and [R] for arbitrary sets of input parameters.     

Comparison of the kinetic specificity of subtilisin and thiolsubtilisin toward n-alkyl p-nitrophenyl esters.

The p-nitrophenyl esters of straight-chain fatty acids were used as substrates of the enzyme subtilisin Novo (EC 3.4.4.16) and its chemically produced artificial enzyme thiolsubtilisin. Subtilisin and thiolsubtilisin pH--activity profiles were determined, and kinetic effects of the active site O-S substitution were observed. Among the substrates tested, both enzymes show highest specificity with p-nitrophenyl butyrate. It was also found that subtilisin is more sensitive to changes in substrate chain length than is thiolsubtilisin. Second-order acylation rate constants (k2/Ks) are remarkably similar for both enzymes. However, thiolsubtilisin deacylation rate constants and Km values are lower than analogous subtilisin constants. While thiolsubtilisin deacylation rate constants give a pH profile identical with that of subtilisin, the pH profile of thiolsubtilisin acylation rate constants shows an active site pK value lowered from the subtilisin pK of 7.15 and exhibits an inflection point at pH 8.45, which is absent in subtilisin.     

The role of glutamate 87 in the kinetic mechanism of Thermus thermophilus isopropylmalate dehydrogenase.

The kinetic mechanism of the oxidative decarboxylation of 2R,3S-isopropylmalate by the NAD-dependent isopropylmalate dehydrogenase of Thermus thermophilus was investigated. Initial rate results typical of random or steady-state ordered sequential mechanisms are obtained for both the wild-type and two mutant enzymes (E87G and E87Q) regardless of whether natural or alternative substrates (2R-malate, 2R,3S-tartrate and/or NADP) are utilized. Initial rate data fail to converge on a rapid equilibrium-ordered pattern despite marked reductions in specificity (kcat/Km) caused by the mutations and alternative substrates. Although the inhibition studies alone might suggest an ordered kinetic mechanism with cofactor binding first, a detailed analysis reveals that the expected noncompetitive patterns appear uncompetitive because the dissociation constants from the ternary complexes are far smaller than those from the binary complexes. Equilibrium fluorescence studies both confirm the random binding of substrates and the kinetic estimates of the dissociation constants of the substrates from the binary complexes. The latter are not distributed markedly by the mutations at site 87. Mutations at site 87 do not affect the dissociation constants from the binary complexes, but do greatly increase the Michaelis constants, indicating that E87 helps stabilize the Michaelis complex of the wild-type enzyme. The available structural data, the patterns of the kinetics results, and the structure of a pseudo-Michaelis complex of the homologous isocitrate dehydrogenase of Escherichia coli suggest that E87 interacts with the nicotinamide ring.     

Vitamin K-dependent carboxylase from calf liver: studies on the steady-state kinetic mechanism

The steady-state kinetic mechanism of vitamin K-dependent carboxylase from calf liver has been investigated by initial-velocity measurements with varying concentrations of two carboxylase substrates and constant, nonsaturating concentrations of the other two substrates. With all combinations of the varied substrates tested linear kinetics were obtained with lines intersecting on the left side of the 1/v axis in double-reciprocal plots. Thus the carboxylase has a sequential reaction mechanism which includes the quinternary complex of the enzyme with its four substrates. A mechanism with the ordered steady-state addition of all substrates to the enzyme accords well with the results. A totally random mechanism was excluded but the alternative possibility remained that part of the substrates are added in a rapid-equilibrium random reaction. Experiments with saturating constant concentrations of sodium bicarbonate and varying concentrations of the other substrates suggest that bicarbonate (CO2) is either the first or, more probably, the last substrate bound to the enzyme.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.     

Recombinant human glucose-6-phosphate dehydrogenase. Evidence for a rapid-equilibrium random-order mechanism.

Cloning and over-expression of human glucose 6-phosphate dehydrogenase (Glc6P dehydrogenase) has for the first time allowed a detailed kinetic study of a preparation that is genetically homogeneous and in which all the protein molecules are of identical age. The steady-state kinetics of the recombinant enzyme, studied by fluorimetric initial-rate measurements, gave converging linear Lineweaver-Burk plots as expected for a ternary-complex mechanism. Patterns of product and dead-end inhibition indicated that the enzyme can bind NADP+ and Glc6P separately to form binary complexes, suggesting a random-order mechanism. The Kd value for the binding of NADP+ measured by titration of protein fluorescence is 8.0 microm, close to the value of 6.8 microm calculated from the kinetic data on the assumption of a rapid-equilibrium random-order mechanism. Strong evidence for this mechanism and against either of the compulsory-order possibilities is provided by repeating the kinetic analysis with each of the natural substrates replaced in turn by structural analogues. A full kinetic analysis was carried out with deaminoNADP+ and with deoxyglucose 6-phosphate as the alternative substrates. In each case the calculated dissociation constant upon switching a substrate in a random-order mechanism (e.g. that for NADP+ upon changing the sugar phosphate) was indeed constant within experimental error as expected. The calculated rate constants for binding of the leading substrate in a compulsory-order mechanism, however, did not remain constant when the putative second substrate was changed. Previous workers, using enzyme from pooled blood, have variously proposed either compulsory-order or random-order mechanisms. Our study appears to provide unambiguous evidence for the latter pattern of substrate binding.     

Mechanistic studies with solubilized rat liver steroid 5 alpha-reductase: elucidation of the kinetic mechanism

A solubilized preparation of steroid 5 alpha-reductase (EC 1.3.1.30) from rat liver has been used in studies focused toward an understanding of the kinetic mechanism associated with enzyme catalysis. From the results of analyses with product and dead-end inhibitors, a preferentially ordered binding of substrates and release of products from the surface of the enzyme is proposed. The observations from these experiments were identical with those using the steroid 5 alpha-reductase activity associated with rat liver microsomes. The primary isotope effects on steady-state kinetic parameters when [4S-2H]NADPH was used also were consistent with an ordered kinetic mechanism. Normal isotope effects were observed for all three kinetic parameters (Vm/Km for both testosterone and NADPH and Vm) at all substrate concentrations used experimentally. Upon extrapolation to infinite concentration of testosterone, the isotope effect on Vm/Km for NADPH approached unity, indicating that the nicotinamide dinucleotide phosphate is the first substrate binding to and the second product released from the enzyme. The isotope effects on Vm/Km for testosterone at infinite concentration of cofactor and on Vm were 3.8 +/- 0.5 and 3.3 +/- 0.4, respectively. Data from the pH profiles of these three steady-state parameters and the inhibition constants (1/Ki) of competitive inhibitors versus both substrates indicate that the binding of nicotinamide dinucleotide phosphate involves coordination of its anionic 2'-phosphate to a protonated enzyme-associated base with an apparent pK near 8.0. From these results, relative limits have been placed on several of the internal rate constants used to describe the ordered mechanism of the rat liver steroid 5 alpha-reductase.     

The use of chromogenic reference substrates for the kinetic analysis of penicillin acylases.

Determination of kinetic parameters of penicillin acylases for phenylacetylated compounds is complicated due to the low K(m) values for these substrates, the lack of a spectroscopic signal, and the strong product inhibition by phenylacetic acid. To overcome these difficulties, a spectrophotometric method was developed, with which kinetic parameters could be determined by measuring the effects on the hydrolysis of the chromogenic reference substrate 2-nitro-5-[(phenylacetyl)amino]benzoic acid (NIPAB). To that end, spectrophotometric progress curves with NIPAB in the absence and presence of the phenylacetylated substrates and their products were measured and analyzed by numerical fitting to the appropriate equations for competing substrates with product inhibition. This analysis yielded kinetic constants for phenylacetylated substrates such as penicillin G, which are in close agreement with those obtained in independent initial velocity experiments. Using NIPAB analogs with lower k(cat)/K(m) values, kinetic parameters for the hydrolysis of cephalexin and penicillin V were determined. This method was suitable for determining the kinetic constants of penicillin acylases in periplasmic extracts from Escherichia coli, Alcaligenes faecalis, and Kluyvera citrophila. The use of chromogenic reference substrates thus appears to be a rapid and reliable method for determining kinetic constants with various substrates and enzymes.     

The mechanism of regulation of actomyosin subfragment 1 ATPase

The mechanism of regulation of actin-subfragment 1 nucleoside triphosphatase is described in terms of the rate and equilibrium constants of a relatively simple kinetic scheme: (Formula: see text) where T, D, and Pi are nucleoside triphosphate, nucleoside diphosphate, and inorganic phosphate, respectively; Ka, Kb, and Kc are association constants; the ki are first-order rate constants; A is regulated actin (actin-tropomyosin-troponin); and M is subfragment 1. Calcium binding to regulated actin had little effect on step 2; k2 was almost unaffected, and k-2 increased, at most, 2-fold. k-1 and k3 increased 10-20-fold for ATP and 3-5-fold for 1-N6-ethenoadenosine triphosphate as substrates. Kb and Kc increased by less than 50%, whereas Ka increased 6-10-fold. The primary effect in regulation is on the rate of a conformational change which determines the rate of dissociation of ligands bound to the active site. The measurements probably underestimate the ratio of rate constants of product dissociation for active and relaxed states of actin because of heterogeneity. The kinetic evidence can be explained by a partial steric blocking mechanism or by a conformational (nonsteric) mechanism.     

Rat liver cytoplasmic glucose-6-phosphate dehydrogenase. Steady-state kinetic properties and circular dichroism.

Steady-state kinetic studies including initial velocity, NADPH product inhibition, dead-end inhibition, and combined dead-end and product inhibition measurements with purified rat liver glucose-6-phosphate dehydrogenase indicate a sequential and obligatory addition of substrates in the order of NADP+, glucose-6-P for the catalytic pathway at pH 8.0. Although instability of 6-phosphoglucono-delta-lactone precluded product inhibition experiments which might directly exclude an enzyme-6-phosphoglucono-delta-lactone complex, the absence of an enzyme-glucose-6-P complex suggests that the enzyme-lactone product is unlikely and the release of products is also ordered, with NADPH released last. Consideration of the kinetic constants (Ka = 2.0 muM, Kiq = 13 muM) and cellular concentration of the substrates and products suggests extensive inhibition of the enzyme in vivo and control by the NADPH/NADP+ ratios. Circular dichroism spectra of the enzyme in 20 mM phosphate buffer at pH 7.0 and 25 degrees C indicate 51% helix and 33% pleated sheet structures which is considerably different from results (14% helix) with yeast enzymes.     

The amino terminus regulates binding to and activation of cGMP-dependent protein kinase

The allosteric regulation of binding to and the activation of cGMP-dependent protein kinase (cGMP kinase) was studied under identical conditions at 30 degrees C using three forms of cGMP-kinase which differed in the amino-terminal segment, e.g. native cGMP kinase, phosphorylated cGMP kinase which contained 1.4 +/- 0.4 mol phosphate/subunit and constitutively active cGMP kinase which lacked the amino-terminal dimerization domain. These three enzyme forms have identical kinetic constants, e.g. number of cGMP-binding sites, Km values for MgATP and the heptapeptide kemptide, and Vmax values. In the native enzyme, MgATP decreases the affinity for binding site 1. This effect is abolished by 1 M NaCl. In contrast, high concentrations of Kemptide increase the affinity of binding site 2 about fivefold. Under the latter conditions, identical Kd values of 0.2 microM were obtained for sites 1 and 2. Salt, MgATP and Kemptide do not affect the binding kinetics of the phosphorylated or the constitutively active enzyme, suggesting that allosteric regulation depends solely on the presence of a native amino-terminal segment. Cyclic GMP activates the native enzyme at Ka values which are identical with the Kd values for both binding sites. The activation of cGMP-dependent protein kinase is noncooperative but the Ka value depends on the substrate peptide concentration. These results show that the activity of cGMP kinase is primarily regulated by conformational changes within the amino-terminal domain.     

Interpretation of V/K isotope effects for enzymatic reactions exhibiting multiple isotopically sensitive steps

Formulations of an enzyme mechanism where only a single step is presumed to be isotopically sensitive can be written in terms of forward and reverse commitments to catalysis. These commitments provide a natural and intuitive way of interpreting the observed isotope effects. Unfortunately, when multiple isotopically sensitive steps are present in the mechanism, including effects associated with pre-equilibria of the unbound substrate, the observed V/K kinetic isotope effect is expressed as a complicated expression of the intrinsic rate constants for each step, the interpretation of which is not always immediately obvious. We show here that V/K isotope effects from unbranched or rapid-equilibrium random Michaelis-Menten systems containing multiple isotopically sensitive steps can be written as a weighted average of the intrinsic isotope effects on each step, where this intrinsic isotope effect from each step is the product of the equilibrium isotope effect on the formation of the reacting intermediate for that step and the intrinsic kinetic effect on the forward rate constant for that step, and the weighting factors are simply the reciprocal sum of the forward and reverse commitments for each step i plus unity, 1/(C(fi)+C(ri)+1), equivalent to the sensitivity index [Ray, W.J., 1983.     

Mechanism of an insect glutathione S-transferase: kinetic analysis supporting a rapid equilibrium random sequential mechanism with housefly I1 isoform

The steady-state kinetics of glutathione S-transferase I1 (GST I1) from housefly Musca domestica expressed in Escherichia coli were investigated with glutathione (GSH) and 1-chloro-2,4-dinitrobenzene (CDNB). Concentrations of the varied substrates were from 0.03 to 1 mM for GSH and 0.05 to 1 mM for CDNB. Within this range, Michaelis-Menten behaviour was observed and convergent straight lines in double reciprocal plots excluded a ping-pong kinetic mechanism. Instead, data were consistent either with rapid-equilibrium random or with steady-state ordered sequential mechanisms because of abscissa convergence. Discrimination was achieved by studying the reaction with another electrophilic partner, p-nitrophenyl-acetate (PNPA). Concentrations of PNPA and GSH varied within the ranges 0.5 to 10 mM and 0.03 to 0.6 mM, respectively. The complete set of data supports the proposal of a rapid-equilibrium random-sequential model with strictly independent sites for GSH and CDNB or PNPA. Kinetic parameters are thus true dissociation equilibrium constants with values of 0.15 mM for GSH, 0.15 mM for CDNB, and 7 mM for PNPA. Analysis of the inhibition by the product (S-(2,4-dinitrophenyl)-glutathione, 10 to 100 microM), on the coupling reaction between GSH and CDNB with either GSH (0.05 to 0.5 mM, CDNB 0.2 mM) or CDNB (0.05 to 0.5 mM, GSH 0.2 mM) varied, consistent with the proposed mechanism. Binding of product to the free enzyme excludes GSH (competitive inhibition pattern with Kp = 12 microM) but only slightly hinders binding of CDNB. Binding free energies, together with the inhibition pattern, suggest that the non-peptidic moiety of product interacts with an alternative sub-site within the large open pocket accommodating the various electrophilic substrates. These results lead us to propose a model for intra-pocket shifting of the non-peptidic moiety upon product formation which contributes to the product release.