The use of steady-state rate equations to analyse progress curve data

On the reducible character of Haldane-Radić enzyme kinetics to conventional and logistic Michaelis-Menten models

The conceptual and practical issues regarding the reduction of the Haldane-Radić enzymic mechanism, specific for cholinesterase kinetics, to the consecrated or logistically modified Michaelis-Menten kinetics, specific for some mutant enzymes, are here clarified as due to the limited initial substrate concentration, through detailed initial rate and progress curve analysis, even when other classical conditions for such equivalence are not entirely fulfilled.

Rapid determination of enzyme kinetics from fluorescence: overcoming the inner filter effect

Fluorescence change is convenient for monitoring enzyme kinetics. Unfortunately, it loses linearity as the absorbance of the fluorescent substrate increases with concentration. When the sum of absorbance at excitation and emission wavelengths exceeds 0.08, this inner filtering effect (IFE) alters apparent initial velocities, K(m), and k(cat). The IFE distortion of apparent initial velocities can be corrected without doing fluorophore dilution assays. Using the substrate's extinction coefficients at excitation and emission wavelengths, the inner filter effect can be modeled during curve fitting for more accurate Michaelis-Menten parameters. A faster and simpler approach is to derive k(cat) and K(m) from progress curves. Strategies to obtain reliable and reproducible estimates of k(cat) and K(m) from only two or three progress curves are illustrated using matrix metalloproteinase 12 and alkaline phosphatase. Accurate estimates of concentration of enzyme-active sites and specificity constant k(cat)/K(m) (from one progress curve with [S]<<K(m)) confer accuracy, freedom of choices of [S], and robustness to k(cat) and K(m) globally fitted to a few progress curves. The economies of the progress curve approach make accurate k(cat) and K(m) more accessible from fluorescence measurements.

Analysis of wild-type and mutant aspartate aminotransferases using integrated rate equations

A general integrated rate equation was fit to reaction progress curves catalyzed by wild-type E. coli aspartate aminotransferase and the site-specific mutant enzymes, H193Q and Y70F. A nonlinear step-regression code, revised for this study selected from all kinetic constants in a general integrated rate equation for all unbranched enzyme mechanisms with stoichiometries upto two substrates and two products including terms for substrate inhibitions and that of an exogenous inhibitor. For each aspartate aminotransferase enzyme studied only kinetic constants consistent with a substituted enzyme mechanism were found statistically significant, thus the enzyme mechanism and sources of inhibition were determined objectively by statistics. The kinetic constants for wild-type and Y70F aspartate aminotransferase were similar to those previously reported indicating the validity of the integrated rate equation analysis. Minor changes in kinetic constants were observed for the H193Q mutant enzyme suggesting that the catalytic effects of the electrostatic hydrogen bonding network extending from the pyridine nitrogen of the cofactor through Asp-222, His-189 ends prior to His-193.

Analysis of progress curves for enzyme-catalysed reactions. Automatic construction of computer programs for fitting integrated rate equations

The computer analysis of progress curves for enzyme-catalysed reactions involves a series of mathematical and computational tasks. The three most daunting of these are the derivation of an integrated rate equation, solving this equation so that the amount of product formed by the reaction at any time can be calculated, and incorporating this solution into a non-linear-regression computer program. This paper describes the basis of a computer program that greatly simplifies the problem. The proposed mechanism is specified in the familiar kinetic constant form, which is automatically translated into a program capable of fitting this mechanism to a series of experimental progress curves. The approach is illustrated for a reversible reaction with one substrate and one product, and tested with some data obtained for the fumarase reaction. A copy of the program has been deposited as Supplementary Publication SUP 50148 (13 pages) at the British Library Document Supply Centre, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1989) 257, 5.

Uptake and efflux of copper-64 in Menkes'-disease and normal continuous lymphoid cell lines

The accumulation of copper over 2 h by normal lymphoid cells and those from Menkes'-disease patients (Menkes' cells) was found to be biphasic, with an initial phase of rapid uptake, an approach to steady state at around 40-60 min, followed by a further accumulation phase. The accumulation of copper was not diminished by the addition of a variety of metabolic inhibitors, suggesting that copper uptake is not an active process. The presence of carbonyl cyanide m-chlorophenylhydrazone in the culture medium stimulated the uptake and accumulation of copper in both normal and Menkes' cells to the same absolute level. This effect appeared to be specific for copper, since the accumulation of Zn and Cd was unaffected. Menkes' cells did not differ from normal in their initial rate of copper uptake. Analysis of the uptake curve suggested that the membrane transport of copper involves both passive and facilitated diffusion. Initial rate of efflux from the cells was approximated by two methods. Menkes' cells did not appear to be affected in this function. It seems likely that the basic defect in Menkes' disease involves a step in intracellular copper transport rather than the membrane transport of copper.

Chorismate mutase-prephenate dehydrogenase from Escherichia coli: cooperative effects and inhibition by L-tyrosine

The effects of a variety of structural analogs of L-tyrosine on the mutase and dehydrogenase activities of hydroxyphenylpyruvate synthase have been investigated. From these studies it is concluded that the alpha-NH3+ alpha-COO-, and the 4-OH groups are essential for binding of L-tyrosine as an inhibitor of the dehydrogenase and that the L configuration is also essential. Dixon plots for inhibition of the dehydrogenase activity by some of these analogs were nonlinear and could be described by a velocity equation that is the ratio of quadratic polynomials (a 2/1 function). Dixon plots for inhibition of the mutase by prephenate at low concentrations of chorismate could also be described by a 2/1 function, but at low concentrations of prephenate chorismate acts as an apparent hyperbolic activator of the dehydrogenase activity. Up to concentrations of 300 microM, L-tyrosine activates the mutase but acts as a potent inhibitor of the dehydrogenase. Such data for the dehydrogenase could not be described by a 2/1 function in 1/[prephenate] but could be fitted to the Hill equation with increasing concentrations of L-tyrosine in the presence of 1.0 mM NAD yielding increasing values for the Hill number (n): in the absence of L-tyrosine, n = 1.6 +/- 0.1; at 150 microM L-tyrosine, n = 2.1 +/- 0.1; at 300 microM L-tyrosine, n = 2.3 +/- 0.4. L-Tyrosine bears a close structural resemblance to both prephenate and hydroxyphenylpyruvate, and evidence is presented which is consistent with L-tyrosine acting as a competitive inhibitor with respect to prephenate of the dehydrogenase.

Estimation of the initial velocity of enzyme-catalysed reactions by non-linear regression analysis of progress curves

Most methods for studying the kinetic properties of an enzyme involve the determination of initial velocities. When the reaction progress curve shows significant curvature due to depletion of the substrate, accumulation of inhibitory products or instability of the enzyme, estimation of the initial velocity is a subjective and inexact process. Two methods have been suggested [Cornish-Bowden (1975) Biochem. J. 144, 305-312; Boeker (1982) Biochem J. 203, 117-123] that attempt to eliminate this subjective element. The present study offers a third alternative, which is based on fitting a reparameterized form of the integrated Michaelis-Menten equation to the progress curves by non-linear regression. This method yields estimates and standard errors of the initial velocity and of the time to reach 50% reaction. No prior knowledge of the apparent product concentration at zero time or infinite time is required, since both of these quantities are also estimated from the data. It is shown that this method yields reliable estimates of the initial velocity under a wide range of circumstances, including those where the two previously published methods perform poorly.

Regulation of hamster carbamoyl-phosphate synthase II by 5-phospho-alpha-D-ribosyl 1-diphosphate and uridine 5'-triphosphate

In mammals, carbamoyl phosphate for utilization in pyrimidine biosynthesis is synthesized by a glutamine-dependent carbamoyl-phosphate synthase II which is subject to regulation by 5-phospho-alpha-D-ribosyl 1-diphosphate (PRib-PP), a positive effector, and MgUTP, a negative effector [Mori, M., Ishida, H. and Tatibana, M. (1975) Biochemistry 14, 2622-2630]. We have found that Lineweaver-Burk plots of carbamoyl phosphate synthase activity versus 1/[MgATP] are described by a velocity equation which is a ratio of quadratic polynomials, consistent with a positive homotropic interaction between two catalytic sites for the binding of MgATP (Ks = 16.6 +/- 3.1 mM, interaction factor a = 0.00538 +/- 0.00245). The activating effect of PRib-PP upon carbamoyl-phosphate synthase is consistent with PRib-PP binding at an allosteric site (Ka = 31.4 +/- 6.4 microM) and promoting the binding of a first molecule of MgATP as substrate (interaction factor l = 0.0437 +/- 0.0063). Thus MgATP and PRib-PP bind to the E X MgATP complex with respective dissociation constants of a X Ks = 0.089 mM and l X Ka = 1.4 microM while MgATP binds to the E X PRib-PP complex with a dissociation constant of l X Ks = 0.73 mM. Data for the inhibitory effect of MgUTP upon carbamoyl-phosphate synthase indicate that MgUTP competes with MgATP for binding at the catalytic site (Ki = 0.203 +/- 0.016 mM). A computer model has recently been developed which enables quantitative stimulation of the time-dependent effects of blockade of the pyrimidine pathway by a tight-binding enzyme inhibitor [Duggleby, R.G. and Christopherson, R.I. (1984) Eur. J. Biochem. 143, 221-226]. The velocity equation derived in the present paper provides a quantitative basis for predicting changes in the flux through the de novo pyrimidine pathway in growing cells.

Kinetic studies of fructokinase I of pea seeds

Fructokinase I of pea seeds has been purified to homogeneity and the enzyme shown to be monomeric, with a molecular weight of 72,000 +/- 4000. The reaction mechanism was investigated by means of initial velocity studies. Both substrates inhibited the enzyme; the inhibition caused by MgATP was linear-uncompetitive with respect to fructose whereas that caused by D-fructose was hyperbolic-noncompetitive against MgATP. The product D-fructose 6-phosphate caused hyperbolic-noncompetitive inhibition with respect to both substrates. MgADP caused noncompetitive inhibition, which gave intercept and slope replots that were linear with D-fructose but hyperbolic with MgATP. Free Mg2+ caused linear-uncompetitive inhibition when either substrate was varied. L-Sorbose and beta, gamma-methyleneadenosine 5'-triphosphate were used as analogs of D-fructose and MgATP, respectively. Inhibition experiments using these compounds indicated that substrate addition was steady-state ordered, with MgATP adding first. The product inhibition experiments were found to be consistent with a steady-state random release of products. The substrate inhibition caused by MgATP was most likely due to the formation of an enzyme-MgATP-product dead-end complex, whereas that caused by D-fructose was due to alternative pathways in the reaction mechanism. The inhibition caused by Mg2+ can be explained in terms of a dead-end complex with either a central complex or an enzyme-product complex.

The pH-dependence of the binding of dihydrofolate and substrate analogues to dihydrofolate reductase from Escherichia coli

The interaction of dihydrofolate reductase (EC 1.5.1.3) from Escherichia coli with dihydrofolate and folate analogues has been studied by means of binding and spectroscopic experiments. The aim of the investigation was to determine the number and identity of the binary complexes that can form, as well as pKa values for groups on the ligand and enzyme that are involved with complex formation. The results obtained by ultraviolet difference spectroscopy indicate that, when bound to the enzyme, methotrexate and 2,4-diamino-6,7-dimethylpteridine exist in their protonated forms and exhibit pKa values for their N-1 nitrogens of above 10.0. These values are about five pH units higher than those for the compounds in free solution. The binding data suggest that both folate analogues interact with the enzyme to yield a protonated complex which may be formed by reaction of ionized enzyme with protonated ligand and/or protonated enzyme with unprotonated ligand. The protonated complex formed with 2,4-diamino-6,7-dimethylpteridine can undergo further protonation to form a protonated enzyme-protonated ligand complex, while that formed with methotrexate can ionize to give an unprotonated complex. A group on the enzyme with a pKa value of about 6.3 is involved with the interactions. However, the ionization state of this group has little effect on the binding of dihydrofolate to the enzyme. For the formation of an enzyme-dihydrofolate complex it is essential that the N-3/C-4 amide of the pteridine ring of the substrate be in its neutral form. It appears that dihydrofolate is not protonated in the binary complex.

Determination of the kinetic properties of enzymes catalysing coupled reaction sequences

In a coupled system of two enzyme-catalysed reactions the concentration of the final product follows a sigmoidal progress curve. The shape of this curve is dependent on the concentrations and kinetic properties of both enzymes in the system; provided that the activities of the two enzymes are similar, the kinetic properties of both enzymes may be determined simultaneously by analysis of such curves. The value of this approach is substantiated using a model system consisting of pyruvate kinase (EC 2.7.1.40) and lactate dehydrogenase (EC 1.1.1.27). Analysis of the data by a combination of numerical integration and nonlinear regression yielded values for the kinetic parameters which are in excellent agreement with those determined from measurements of steady-state rates. Appropriate experimental designs for this type of progress curve analysis are considered. The analysis is compared with, and is shown to be of much greater generality than, published procedures involving measurements of the early stages of progress curves.

The action of thrombin on peptide p-nitroanilide substrates. Substrate selectivity and examination of hydrolysis under different reaction conditions

Kinetic parameters for the action of bovine alpha-thrombin on 24 commercially available peptide p-nitroanilides have been determined. The selectivity constant, kcat/Km, ranges from 3.3 X 10(1) to 1.1 X 10(8) M-1 X S-1 for the poorest and the best substrates, respectively. The best substrates for thrombin were identified as those with arginine in the P1 position, proline or a proline homolog in the P2 position, and an apolar amino acid in the P3 position. Quantitative distinction between lysine and arginine in the P1 position and other amino acids in the P2-P4 positions of the substrate is reported from the changes in the kinetic parameters for substrates differing in only a single amino acid in these positions. Effects of NaCl, CaCl2 and poly(ethylene glycol) concentrations, pH and temperature on the action of thrombin on selected substrates have been assessed. A source of large systematic error in thrombin concentration estimates was identified as resulting from adsorption losses. These losses were eliminated by inclusion of poly(ethylene glycol) in dilution and reaction buffers.

Kinetic mechanism of the reaction catalyzed by dihydrofolate reductase from Escherichia coli

The kinetic mechanism of the reaction catalyzed by dihydrofolate reductase from Escherichia coli has been investigated by using progress curve, initial velocity, product inhibition, and dead-end inhibition studies as well as isotope effects. The results indicate that the reaction conforms to a random mechanism involving two dead-end complexes, viz., enzyme-DHF-THF and enzyme-NADP-DHF. At higher concentrations, DHF causes substrate inhibition by combining at the NADPH binding site on the enzyme. The steady-state velocity data can be analyzed adequately on the basis that rapid-equilibrium conditions apply. However, this can be only an approximate description of the reaction since the isotope effects observed with NADPD demonstrate clearly that catalysis cannot be rate limiting at pH 7.4. The choice of conditions for analysis of progress-curve data is discussed in the Appendix.