Internal thermodynamics of enzymes determined by equilibrium quench: values of Kint for enolase and creatine kinase

The equilibrium constant (Kint) for the enzyme-bound substrate and product of a one substrate/one product enzyme (enolase) and for those of a two substrate/two product enzyme (creatine kinase) have been determined. The values of Kint were determined by the rapid quenching of equilibrium mixtures of enzyme and radiolabeled substrate and product, under conditions where all of the marker substrate and product are bound. The scope and limitations of this method are discussed. Values of Kint have been collected from the literature, and it is shown that these data are consistent with the theory for kinetically optimized enzymes that is developed in the preceding paper.     

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.     

Energy metabolism during insect flight: biochemical design and physiological performance

Flying insects achieve the highest known mass-specific rates of O(2) consumption in the animal kingdom. Because the flight muscles account for >90% of the organismal O(2) uptake, accurate estimates of metabolic flux rates (J) in the muscles can be made. In steady state, these are equal to the net forward flux rates (v) at individual steps and can be compared with flux capacities (V(max)) measured in vitro. In flying honeybees, hexokinase and phosphofructokinase, both nonequilibrium reactions in glycolysis, operate at large fractions of their maximum capacities (i.e., they operate at high v/V(max)). Phosphoglucoisomerase is a reversible reaction that operates near equilibrium. Despite V(max) values more than 20-fold greater than the net forward flux rates during flight, a close match is found between the V(max) required in vivo (estimated using the Haldane relationship) to maintain near equilibrium and this net forward flux rate and the V(max) measured in vitro under simulated physiological conditions. Rates of organismal O(2) consumption and difference spectroscopy were used to estimate electron transfer rates per molecule of respiratory chain enzyme during flight. These are much higher than those estimated in mammalian muscles. Current evidence indicates that metabolic enzymes in honeybees do not display higher catalytic efficiencies than the homologous enzymes in mammals, and the high electron transfer rates do not appear to be the result of higher enzyme densities per unit cristae surface area. A number of possible mechanistic explanations for the higher rates of electron transfer are proposed.     

Kinetic studies of thymidine phosphorylase from mouse liver

Initial velocity and product inhibition studies of thymidine phosphorylase from mouse liver revealed that the basic reaction mechanism of this enzyme is a rapid equilibrium random bi-bi mechanism with an enzyme-phosphate-thymine dead-end complex. Thymine displayed both substrate inhibition and nonlinear product inhibition, i.e., slope and intercept replots vs. 1/[thymine] were nonlinear, indicating that there is more than one binding site on the enzyme for thymine and that when thymine is bound to one of these sites, the enzyme is inhibited. Furthermore, both thymidine and phosphate showed "cooperative effects" in the presence of thymine at concentrations above 60 microM, suggesting that the enzyme may have multiple interacting allosteric and/or catalytic sites. The deoxyribosyl transferase reaction catalyzed by this enzyme is phosphate-dependent, requires nonstoichiometric amounts of phosphate, and can proceed by an "enzyme-bound" 2-deoxyribose 1-phosphate intermediate. These findings are in accord with the rapid equilibrium random bi-bi mechanism and demonstrate that deoxyribosyl transfer by this enzyme involves an indirect-transfer mechanism. These results strongly suggest that phosphorolysis and deoxyribosyl transfer are catalyzed by the same site on thymidine phosphorylase.     

The catalytic power of enzymes: conformational selection or transition state stabilization?

The mechanism by which enzymes produce enormous rate enhancements in the reactions they catalyze remains unknown. Two viewpoints, selection of ground state conformations and stabilization of the transition state, are present in the literature in apparent opposition. To provide more insight into current discussion about enzyme efficiency, a two-state model of enzyme catalysis was developed. The model was designed to include both the pre-chemical (ground state conformations) and the chemical (transition state) components of the process for the substrate both in water and in the enzyme. Although the model is of general applicability, the chorismate to prephenate reaction catalyzed by chorismate mutase was chosen for illustrative purposes. The resulting kinetic equations show that the catalytic power of enzymes, quantified as the k(cat)/k(uncat) ratio, is the product of two terms: one including the equilibrium constants for the substrate conformational states and the other including the rate constants for the uncatalyzed and catalyzed chemical reactions. The model shows that these components are not mutually exclusive and can be simultaneously present in an enzymic system, being their relative contribution a property of the enzyme. The developed mathematical expressions reveal that the conformational and reaction components of the process perform differently for the translation of molecular efficiency (changes in energy levels) into observed enzymic efficiency (changes in k(cat)), being, in general, more productive the component involving the transition state.     

Organization of enzymes on subcellular structures: relay at the surface

There is a large body of evidence that soluble cytoplasmic enzymes of eukaryotic cells, e.g., glycolytic enzymes and proteins of the translational machinery, are organized in some way in space and in time. The following features of such organization emerge from the experimental data: (1) metabolites are transferred between enzymes directly "from hand to hand" in short-living enzyme-enzyme complexes rather than by diffusion in aqueous media; (2) enzymes show a tendency to be absorbed on surfaces of subcellular structures, such as membranes, cytoskeleton and polyribosomes; (3) enzymes are desorbed from a surface of a subcellular structure after binding specific metabolites, i.e., substrates and/or products of the reactions catalyzed by these enzymes. These features are suggestive of a relay mechanism for the enzyme systems functioning in a cell; an enzyme adsorbed on a surface of a subcellular structure is desorbed after binding its substrate or in the course of the catalytic act. Within a complex with its product the enzyme diffuses into the environment, until it reaches the next enzyme adsorbed on the same surface; then a short-living enzyme-enzyme complex is formed, and a direct "from hand to hand" transfer of the metabolite takes place. As a result, the overall metabolic process appears to be localized near the surface. We termed this mechanism as a "relay at the surface".     

Calcium and magnesium dependence of phospholipase A2-catalyzed hydrolysis of phosphatidylcholine small unilamellar vesicles.

The Ca2+ requirement for lipid hydrolysis catalyzed by phospholipase A2 from Agkistrodon piscivorus piscivorus (App-D49) and porcine pancreas has been examined using small, unilamellar vesicles of dipalmitoylphosphatidylcholine (DPPC SUV). Hydrolysis was affected by product inhibition even at early times, and the extent of this inhibition depended on the concentration of divalent cations. The Ca2+ requirement for half-maximal rates of hydrolysis reflected, in part, this non-catalytic role of divalent cations. The presence of 10 mM Mg2+, a cation which does not support catalysis, reduced the Ca2+ required for half-maximal rates of hydrolysis from millimolar concentrations to 40 microM for App-D49. Since the dissociation constant of the enzyme for Ca2+ in solution is 2 mM, these results indicate a change in the interaction of the enzyme with Ca2+ under catalytic conditions. The kinetic dissociation constant of Ca2+ for the pancreatic enzyme was 20 microM which is substantially lower than the dissociation constant in solution, 0.35 mM. The similarity of apparent kinetic dissociation constants for these enzymes suggests that structurally similar features determine the affinity for Ca2+ under catalytic conditions. Evidence is presented that the affinity of phospholipase A2 for Ca2+ changes subsequent to the initial interaction of the enzyme with the substrate interface. However, the apparent Michaelis constant, KMapp, for App-D49, 0.03-0.06 mM, is independent of [Ca2+] and is about the same as the equilibrium dissociation constant for DPPC SUV, 0.14 mM. We thus suggest that KMapp is a steady-state constant.     

Reaction mechanism of the membrane-bound ATPase of submitochondrial particles from beef heart

Submitochondrial particles from beef heart, washed with dilute solutions of KCl so as to activate the latent, membrane-bound ATPase, F1, may be used to study single site catalysis by the enzyme. [gamma-32P]ATP, incubated with a molar excess of catalytic sites, a condition which favors binding of substrate in only a single catalytic site on the enzyme, is hydrolyzed via a four-step reaction mechanism. The mechanism includes binding in a high affinity catalytic site, Ka = 10(12)M-1, a hydrolytic step for which the equilibrium constant is near unity, and two product release steps in which Pi dissociates from catalytic sites about 10 times more rapidly than ADP. Catalysis by the membrane-bound ATPase also is characterized by a 10(6)-fold acceleration in the rate of net hydrolysis of [gamma-32P]ATP, bound in the high affinity catalytic site, that occurs when substrate is made available to additional catalytic sites on the enzyme. These aspects of the reaction mechanism of the ATPase of submitochondrial particles closely parallel the reaction mechanism determined for solubilized, homogeneous F1 (Grubmeyer, C., Cross, R. L., and Penefsky, H. S. (1982) J. Biol. Chem. 257, 12092-12100). The finding that removal of the enzyme from the membrane does not significantly alter the properties of single site catalysis lends support to models of ATP synthesis in oxidative phosphorylation, catalyzed by membrane-bound F1, that have been based on the study of the soluble enzyme.     

Further theoretical refinement on the internal thermodynamics of perfect enzymes.

By solving simultaneously the equation for ''uniform binding'' [Albery & Knowles (1976) Biochemistry 15, 5631-5640] and the equation for ''differential binding'' [Chin (1983) J. Am. Chem. Soc. 105, 6502-6503], I derived the following simple equation for perfect enzymes (with single substrate and single product) under irreversible conditions: K2 = beta(1 + Rs)/1-beta(1 + Rs) where K2 is the internal equilibrium constant and beta is the Brönsted coefficient of the elementary catalytic step, and Rs is defined as [S]0/Ks, with [S]0 being the physiological substrate concentration and Ks being the substrate dissociation constant. The equation suggests that the perfect enzyme can have different internal thermodynamic properties depending on physiological conditions.     

Effect of metal ions and adenylylation state on the internal thermodynamics of phosphoryl transfer in the Escherichia coli glutamine synthetase reaction.

Experiments were conducted to study the differences in catalytic behavior of various forms of Escherichia coli glutamine synthetase. The enzyme catalyzes the ATP-dependent formation of glutamine from glutamate and ammonia via a gamma-glutamyl phosphate intermediate. The physiologically important metal ion for catalysis is Mg2+; however, Mn2+ supports in vitro activity, though at a reduced level. Additionally, the enzyme is regulated by a covalent adenylylation modification, and the metal ion specificity of the reaction depends on the adenylylation state of the enzyme. The kinetic investigations reported herein demonstrate differences in binding and catalytic behavior of the various forms of glutamine synthetase. Rapid quench kinetic experiments on the unadenylylated enzyme with either Mg2+ or Mn2+ as the activating metal revealed that product release is the rate-limiting step. However, in the case of the adenylylated enzyme, phosphoryl transfer is the rate-limiting step. The internal equilibrium constant for phosphoryl transfer is 2 and 5 for the unadenylylated enzyme with Mg2+ or Mn2+, respectively. For the Mn2(+)-activated adenylylated enzyme the internal equilibrium constant is 0.1, indicating that phosphoryl transfer is less energetically favorable for this form of the enzyme. The factors that make the unadenylylated enzyme most active with Mg2+ are discussed.     

Energetic limits of phosphotransfer in the catalytic subunit of cAMP-dependent protein kinase as measured by viscosity experiments.

Viscosogenic agents were used to test the diffusion limits of the reaction catalyzed by the catalytic subunit of the cAMP-dependent protein kinase. The effects of glycerol and sucrose on the maximum rate (kcat) and the apparent second-order rate constants (kcat/Kpeptide) for the phosphorylation of four peptidic substrates were measured at their pH optima. The agents were found to have moderate to no effect on kcat/Kpeptide for good and poor substrates, respectively. Conversely, kcat was highly sensitive to solvent viscosity for three of the four peptides at high concentrations of ATP. Taken together, these data indicate that enzymatic phosphorylation by the catalytic subunit proceeds with rapid or near rapid equilibrium binding of substrates and that all steps following the central substrate complex (i.e., chemical and conformational events) are fast relative to the rate-determining dissociation of product, ADP, when ATP levels are high. Under saturating concentrations of peptide I, LRRASLG, an unproductive form of the enzyme is populated. The observed phosphorylation rate from this complex is involved in rate limitation owing to a slow step separating unproductive and productive enzyme forms. The data are used to establish a kinetic mechanism for the catalytic subunit that predicts initial reaction velocities under varying concentrations of ATP and substrate.     

A common speed limit for RNA-cleaving ribozymes and deoxyribozymes

It is widely believed that the reason proteins dominate biological catalysis is because polypeptides have greater chemical complexity compared with nucleic acids, and thus should have greater enzymatic power. Consistent with this hypothesis is the fact that protein enzymes typically exhibit chemical rate enhancements that are far more substantial than those achieved by natural and engineered ribozymes. To investigate the true catalytic power of nucleic acids, we determined the kinetic characteristics of 14 classes of engineered ribozymes and deoxyribozymes that accelerate RNA cleavage by internal phosphoester transfer. Half approach a maximum rate constant of approximately 1 min(-1), whereas ribonuclease A catalyzes the same reaction approximately 80,000-fold faster. Additional biochemical analyses indicate that this commonly encountered ribozyme "speed limit" coincides with the theoretical maximum rate enhancement for an enzyme that uses only two specific catalytic strategies. These results indicate that ribozymes using additional catalytic strategies could be made that promote RNA cleavage with rate enhancements that equal those of proteins.     

Purification and characterization of a pyridine nucleotide glycohydrolase from rabbit spleen

A particulate NMN glycohydrolase of rabbit spleen was solubilized with Triton X100 and purified approximately 100-fold. The enzyme was shown to have a pH maximum of 6.5, a Km of 0.25 mM, a Vmax of 5.3 mumol/min/mg protein, an activation energy of 7.9 kcal/mol, and a molecular weight of approximately 400,000. Both of the purified and the particulate enzymes exhibited identical catalytic properties with respect to substrate specificity, activation energy, pH profile and exchange reaction with nicotinic acid, except that the purified enzyme was highly activated with Triton X100 as compared with the particulate enzyme; it appears that the purified enzyme possesses the same catalytic properties as the enzyme present in the tissue and that solubilization does not significantly alter the native protein. In addition to catalytic activity with NMN, the rabbit spleen enzyme catalyzed an irreversible hydrolysis with NAD and NADP, exhibiting catalyzing activity ratios of NMN:NAD:NADP = 1.00:1.45:0.44 and Vmax/Km ratios of 1.00:1.7:2.3, respectively. These ratios of activity remained constant throughout purification of the enzyme and no separation of these activities was detected. Mutually competitive inhibition of the enzyme with Ki values similar to Km, and identical rates of thermal denaturation of the enzyme and activity-pH profiles with NMN or NAD indicated the hydrolysis of the C-N glycosidic linkage of the pyridine nucleotides to be catalyzed by the same enzyme. The enzyme was less specific for the purine structure of the substrate dinucleotides but was stereospecific for the glycosidic linkage cleaved. Nicotinamide riboside, the nicotinic acid analogs and the reduced forms were not hydrolyzed. A linear noncompetitive inhibition of NMN hydrolysis with nicotinamide indicated an ordered Uni-Bi mechanism in which nicotinamide was the first product released from the enzyme. A property that the rabbit spleen enzyme appears to share with other NAD glycohydrolases is the transglycosidation reaction. The ratio of transglycosidation reaction vs. hydrolysis catalyzed by the enzyme in the presence of NMN and nicotinic acid indicated that the enzyme could function as a primary transglycosidase rather than a hydrolytic enzyme in vivo.     

Michaelis-Menten equation for an enzyme in an oscillating electric field.

The electric charges on an enzyme may move concomitantly with a conformational change. Such an enzyme will absorb energy from an oscillating electric field. If in addition the enzyme has a larger association constant for substrate than for product, as is often true, it can use this energy to drive the catalyzed reaction away from equilibrium. Approximate analytical expressions are given for the field-driven flux, electrical power absorbed, free-energy produced per unit time, thermodynamic efficiency, and zero-flux concentrations. The field-driven flux is written as a generalized Michaelis-Menten equation.     

Adenosine kinase from human erythrocytes: kinetic studies and characterization of adenosine binding sites

The reaction catalyzed by adenosine kinase purified from human erythrocytes proceeds via a classical ordered sequential mechanism in which adenosine is the first substrate to bind to and AMP is the last product to dissociate from the enzyme. However, the interpretation of the steady-state kinetic data is complicated by the finding that while AMP acts as a classical product inhibitor at concentrations greater than 5 mM, at lower concentrations AMP can act as an apparent activator of the enzyme under certain conditions. This apparent activation by AMP is proposed to be due to AMP allowing the enzyme mechanism to proceed via an alternative reaction pathway that avoids substrate inhibition by adenosine. Quantitative studies of the protection of the enzyme afforded by adenosine against both spontaneous and 5,5'-dithiobis(2-nitrobenzoic acid)-mediated oxidation of thiol groups yielded "protection" constants (equivalent to enzyme-adenosine dissociation constant) of 12.8 microM and 12.6 microM, respectively, values that are more than an order of magnitude greater than the dissociation constant (Kia = 0.53 microM) for the "catalytic" enzyme-adenosine complex. These results suggest that adenosine kinase has at least two adenosine binding sites, one at the catalytic center and another quite distinct site at which binding of adenosine protects the reactive thiol group(s). This "protection" site appears to be separate from the nucleoside triphosphate binding site, and it also appears to be the site that is responsible for the substrate inhibition caused by adenosine.     

Specific immobilization of in vivo biotinylated bacterial luciferase and FMN:NAD(P)H oxidoreductase.

Bacterial bioluminescence, catalyzed by FMN:NAD(P)H oxidoreductase and luciferase, has been used as an analytical tool for quantitating the substrates of NAD(P)H-dependent enzymes. The development of inexpensive and sensitive biosensors based on bacterial bioluminescence would benefit from a method to immobilize the oxidoreductase and luciferase with high specific activity. Toward this end, oxidoreductase and luciferase were fused with a segment of biotin carboxy carrier protein and produced in Escherichia coli. The in vivo biotinylated luciferase and oxidoreductase were immobilized on avidin-conjugated agarose beads with little loss of activity. Coimmobilized enzymes had eight times higher bioluminescence activity than the free enzymes at low enzyme concentration and high NADH concentration. In addition, the immobilized enzymes were more stable than the free enzymes. This immobilization method is also useful to control enzyme orientation, which could increase the efficiency of sequentially operating enzymes like the oxidoreductase-luciferase system.     

Nonequilibrium linear behavior of biological systems. Existence of enzyme-mediated multidimensional inflection points.

The linear phenomenological equations of nonequilibrium thermodynamics are limited theoretically to near equilibrium although a number of biological systems have been shown to exhibit a "linear" relationship between steady-state flows and conjugate thermodynamic forces outside the range of equilibrium. We have found a multidimensional inflection point which can exist well outside the range of equilibrium around with enzyme-catalyzed reactions exhibit "linear" behavior between the logarithm of reactant concentrations and enzyme catalyzed flows. A set of sufficient conditions has been derived which can be applied to any enzyme mechanism to determine whether a multidimensional inflection point exists. The conditions do not appear overly restrictive and may be satisfied by a large variety of coupled enzyme reactions. It is thus possible that the linearity observed in some biological systems may be explained in terms of enzyme operating near this multidimensional point.     

Moritella cold-active dihydrofolate reductase: are there natural limits to optimization of catalytic efficiency at low temperature?

Adapting metabolic enzymes of microorganisms to low temperature environments may require a difficult compromise between velocity and affinity. We have investigated catalytic efficiency in a key metabolic enzyme (dihydrofolate reductase) of Moritella profunda sp. nov., a strictly psychrophilic bacterium with a maximal growth rate at 2 degrees C or less. The enzyme is monomeric (Mr=18,291), 55% identical to its Escherichia coli counterpart, and displays Tm and denaturation enthalpy changes much lower than E. coli and Thermotoga maritima homologues. Its stability curve indicates a maximum stability above the temperature range of the organism, and predicts cold denaturation below 0 degrees C. At mesophilic temperatures the apparent Km value for dihydrofolate is 50- to 80-fold higher than for E. coli, Lactobacillus casei, and T. maritima dihydrofolate reductases, whereas the apparent Km value for NADPH, though higher, remains in the same order of magnitude. At 5 degrees C these values are not significantly modified. The enzyme is also much less sensitive than its E. coli counterpart to the inhibitors methotrexate and trimethoprim. The catalytic efficiency (kcat/Km) with respect to dihydrofolate is thus much lower than in the other three bacteria. The higher affinity for NADPH could have been maintained by selection since NADPH assists the release of the product tetrahydrofolate. Dihydrofolate reductase adaptation to low temperature thus appears to have entailed a pronounced trade-off between affinity and catalytic velocity. The kinetic features of this psychrophilic protein suggest that enzyme adaptation to low temperature may be constrained by natural limits to optimization of catalytic efficiency.     

Isomerization of delta 1-piperideine-2-carboxylate to delta 2-piperideine-2-carboxylate on complexation with flavoprotein D-amino acid oxidase.

The 1,646 cm-1 band in a resonance Raman spectrum obtained with excitation in the charge-transfer band of the complex of oxidized D-amino acid oxidase (DAO) with the oxidation product of D-lysine catalyzed by DAO shifted to 1,617 cm-1 upon 2-13C substitution of lysine. Thus, the band is assigned to a C(2) = C(3) stretching mode of the enamine, delta 2-piperideine-2-carboxylate (En). In the enzyme-free solution, the product is preferentially in the cyclic imine form, delta 1-piperideine-2-carboxylate (Im). Thus, DAO has a higher affinity for the enamine form than for the imine form. The pH effects on the affinity of DAO for the product and on the molar absorption coefficient at 630 nm in the charge-transfer band, suggest that the enzyme-bound product is En in the neutral form at the N atom. As the value of observed rate constant between DAO and the product was constant at high product concentrations, the binding mechanism can be explained as follows; E + Im in equilibrium with EIm in equilibrium with EEN: rapid bimolecular and slow unimolecular processes. The isomerization of the imine form to the enamine form proceeds in the slow process. The low affinity of Im for DAO may be due to a steric repulsion of the hydrogen atoms of Im at C(3) in the active site. The hydrogen atoms of a substrate D-amino acid at C(3), which correspond to the C(3) hydrogens of Im, may act repulsively in the active site and the repulsive energy may induce strain or distortion of the substrate and the enzyme, accelerating the catalytic reaction.