Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

A sensitive genetic assay for the detection of cytosine deamination: determination of rate constants and the activation energy

Previously it has not been possible to determine the rate of deamination of cytosine in DNA at 37 degrees C because this reaction occurs so slowly. We describe here a sensitive genetic assay to measure the rate of cytosine deamination in DNA at a single cytosine residue. The assay is based on reversion of a mutant in the lacZ alpha gene coding sequence of bacteriophage M13mp2 and employs ung- bacterial strains lacking the enzyme uracil glycosylase. The assay is sufficiently sensitive to allow us to detect, at a given site, a single deamination event occurring with a background frequency as low as 1 in 200,000. With this assay, we determined cytosine deamination rate constants in single-stranded DNA at temperatures ranging from 30 to 90 degrees C and then calculated that the activation energy for cytosine deamination in single-stranded DNA is 28 +/- 1 kcal/mol. At 80 degrees C, deamination rate constants at six sites varied by less than a factor of 3. At 37 degrees C, the cytosine deamination rate constants for single- and double-stranded DNA at pH 7.4 are 1 x 10(-10) and about 7 x 10(-13) per second, respectively. (In other words, the measured half-life for cytosine in single-stranded DNA at 37 degrees C is ca. 200 years, while in double-stranded DNA it is on the order of 30,000 years.) Thus, cytosine is deaminated approximately 140-fold more slowly when present in the double helix. These and other data indicate that the rate of deamination is strongly dependent upon DNA structure and the degree of protonation of the cytosine. The data suggest that agents which perturb DNA structure or facilitate direct protonation of cytosine may induce deamination at biologically significant rates. The assay provides a means to directly test the hypothesis.     

Enzyme kinetics in mammalian cells. II. Simultaneous determination of rate constants for the first three steps of galactose metabolism in red cells

The method for simultaneous measurement of the first two sequential enzymes of galactose metabolism of red cells has been extended to include the third step of the chain, epimerization of uridine diphosphogalactose to uridine diphosphoglucose. The method is rapid and precise and is applicable to a variety of genetic-biochemical problems.     

Perspectives of data analysis of enzyme inhibition and activation,part 4: Equations for calculation of constants of enzyme activation and inhibition

Equations for calculation of constants of enzyme activation and nontrivial types of enzyme inhibition, which are not reported in the literature, have been deduced. Examples of using these equations are also presented. © 2010 Wiley Periodicals, Inc. J Biochem Mol Toxicol 24:145–154, 2010; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/jbt.20316     

Evaluation of rate constants for enzyme-catalysed reactions by the jackknife technique. Application to liver alcohol dehydrogenase.

Steady-state measurements of enzyme-catalysed reactions are capable of providing more information about the rate constants of the individual steps than is commonly obtained. We have applied a combination of the jackknife and non-linear regression techniques to measurements of the rate of oxidation of ethanol by NAD+, catalysed by alcohol dehydrogenase from horse liver. This has permitted values and confidence intervals to be assigned to the eight rate constants that characterize the binding of ethanol and NAD+ in random order to the enzyme, and to the net rate constant kcat. for the breakdown of the ternary complex.     

Efficiencies of singlet oxygen production and rate constants for oxygen quenching in the S1 state of dicyanonaphthalenes and related compounds.

The quantum yield of singlet oxygen ((1)O(2) ((1)Delta(g))) production (Phi(Delta)) in the oxygen quenching of photoexcited states for 1,2-dicyanonaphthalene (1,2-DCNN), 1,4-dicyanonaphthalene (1,4-DCNN) and 2,3-dicyanonaphthalene (2,3-DCNN) in cyclohexane, benzene, and acetonitrile was measured using a time-resolved thermal lens (TRTL) technique, in order to determine the efficiency of singlet oxygen ((1)Delta(g)) production in the first excited singlet state (S(1)), (f(Delta)(S)). The efficiencies of singlet oxygen ((1)Delta(g)) production from the lowest triplet state (T(1)), (f(Delta)(T)), were nearly unity for all DCNNs in all the solvents. The values of f(Delta)(S) were fairly large for 1,2-DCNN (0.33-0.57) and 1,4-DCNN (0.33-0.66), but were close to zero for 2,3-DCNN. Rate constants for oxygen quenching in the S(1) state (k(q)(S)) obtained for these compounds were significantly smaller than diffusion-controlled rate constants. The kinetics for processes leading to production and no production of singlet oxygen is discussed on the basis of the values of f(Delta)(S) and k(q)(S). The results obtained regarding phenanthrene (PH), 9-cyanophenanthrene (9-CNPH), pyrene (PY) and 1-cyanopyrene (1-CNPY) are also discussed.     

Application of the median method to the determination of kinetic constants for competitive enzyme inhibition

A procedure was developed to determine kinetic constants for competitive inhibition (Km, Ki, Vmax) by the median method. Simulated experiments were used to compare the accuracy and precision of kinetic constants determined by the median method with unweighted and weighted least-squares analysis. The median method was superior to unweighted least-squares analysis. The weighted least-squares method was superior to the median method when the error was normally distributed but the median method was superior when two or more outliers were present. The dependence of the accuracy and precision of kinetic constants obtained by the median method on several experimentally important parameters, including the number of experimental points, the number and range of substrate concentrations, and the number and range of inhibitor concentrations, was determined.     

Effective rate models for the analysis of transport-dependent biosensor data.

Optical biosensors, including the BIACORE, provide an increasingly popular method for determining reaction rates of biomolecules. In a flow chamber, with one reactant immobilized on a chip on the sensor surface, a solution containing the other reactant (the analyte) flows through the chamber. The time course of binding of the reactants is monitored. Scientists using the BIACORE to understand biomolecular reactions need to be able to separate intrinsic reaction rates from the effects of transport in the biosensor. For a model to provide a useful basis for such an analysis, it must reflect transport accurately, while remaining simple enough to couple with a routine for estimating reaction rates from BIACORE data. Models have been proposed previously for this purpose, consisting of an ordinary differential equation with 'effective rate coefficients' incorporating reaction and transport parameters. In this paper we investigate both the theoretical basis and numerical accuracy of these and related models.     

Fourth-derivative spectrophotometry analysis of tryptophan environment in proteins. Application to melittin, cytochrome c and bacteriorhodopsin

Fourth-derivative spectrophotometry is applied to the analysis of solvent effects on the spectral transitions of N-acetyl-L-tryptophan amide, as well as of its mixtures with N-acetyl-L-tyrosine ethyl ester. These compounds were analyzed in different media. It was found that the position of the longest-wavelength minimum of the fourth-derivative spectrum is mainly determined by the nature of the Trp environment, with a minor contribution from that of Tyr. A geometrical parameter is also defined, which depends on both Trp and Tyr environments. The simultaneous consideration of both parameters allows an estimation to be made of the Trp environment. The method is applied to the study of conformational changes of three well-characterized proteins: melittin from bee venom, cytochrome c from horse heart and bacteriorhodopsin from Halobacterium halobium. The results obtained are found to be in accordance with the known conformational properties of these proteins. In addition, the fourth-derivative operation completely eliminates the interference from the near-ultraviolet bands of the prosthetic groups.     

Rapid and simple method for the determination of tryptophan in cereal grains.

Alkaline extracts of cereal proteins are treated in the prescribed sequence: Glacial acetic acid-ferric chloride and 25.8 n H₂SO₄ solutions. Specified amounts of these solutions and the sample are added in order to obtain the required sulfuric acid concentration in the reaction mixture. The reaction mixture is heated at 60°C for 45 min (cereal proteins) or 110 min (standard tryptophan). The absorbance of the resulting violet solution is read at 545 nm. Results are highly precise and agree quite favorably with those of the modified Spies and Chambers method using Pronase hydrolyzates. As little as 6–7 μg of tryptophan in cereal proteins may be determined reliably in samples with negligible blank corrections.The factors affecting color development and the accuracy and precision of the method are discussed.     

Exponential model for a two-ligand,regulatory enzyme. Part 1: Computer programs for the determination of the model constants from initial velocity data

The exponential model for a regulatory enzyme with two ligands (either two substrates or one substrate and an effector) provides an expression for the initial velocity of the catalysed reaction in terms of the fractional saturation of the enzyme by each ligand. This paper describes a program which determines the constants of the model from velocity data, measured with respect to the concentrations of the two ligands, when the corresponding fractional saturations are unknown. Listings of the essential routines, written in BASIC, are provided.     

Comparison of the specificity, stability and individual rate constants with respective activation parameters for the peptidase activity of cruzipain and its recombinant form, cruzain, from Trypanosoma cruzi.

The Trypanosoma cruzi cysteine protease cruzipain contains a 130-amino-acid C-terminal extension, in addition to the catalytic domain. Natural cruzipain is a complex of isoforms, because of the simultaneous expression of several genes, and the presence of either high mannose-type, hybrid monoantennary-type or complex biantenary-type oligosacharide chains at Asn255 of the C-terminal extension. Cruzipain and its recombinant form without this extension (cruzain) were studied comparatively in this work. S2 to S2' subsite specificities of these enzymes were examined using four series of substrates derived from the internally quenched fluorescent peptide Abz-KLRFSKQ-EDDnp (Abz, ortho-aminobenzoic acid; EDDnp, N-(2,4-dinitrophenyl)-ethylenediamine). Large differences in the kinetic parameters were not observed between the enzymes; however, Km values were consistently lower for the hydrolysis of most of the substrates by cruzain. No difference in the pH-activity profile between the two enzymes was found, but in 1 m NaCl cruzipain presented a kcat value significantly higher than that of cruzain. The activation energy of denaturation for the enzymes did not differ significantly; however, a negative entropy value was observed for cruzipain denaturation whereas the value for cruzain was positive. We determined the individual rate constants (k1, substrate diffusion; k-1, substrate dissociation; k2, acylation; k3, deacylation) and the respective activation energies and entropies for hydrolysis of Abz-KLRFSKQ-EDDnp determining the temperature dependence of the Michaelis-Menten parameters kcat/Km and kcat as previously described [Ayala, Y.M. & Di Cera, E. (2000) Protein Sci. 9, 1589-1593]. Differences between the two enzymes were clearly detected in the activation energies E1 and E-1, which are significantly higher for cruzipain. The corresponding DeltaS1 and DeltaS-1 were positive and significantly higher for cruzipain than for cruzain. These results indicate the presence of a larger energy barrier for cruzipain relating to substrate diffusion and dissociation, which could be related to the C-terminal extension and/or glycosylation state of cruzipain.     

Simultaneous determination of 76As, 122Sb and 153Sm in Chinese medicinal herbs by epithermal neutron activation analysis

Optimal conditions for the simultaneous determination of As, Sb and Sm in Chinese medicinal herbs using epithermal neutron activation analysis were investigated. The minimum detectable concentrations of 76As, 122Sb and 153Sm in lichen and medicinal herbs depended on the weight of the irradiated sample, and irradiation and decay durations. Optimal conditions were obtained by wrapping the irradiated target with 3.2 mm borated polyethylene neutron filters, which were adopted to screen the original reactor fission neutrons and to reduce the background activities of 38Cl, 24Na and 42K. Twelve medicinal herbs, commonly consumed by Taiwanese children as a diuretic treatment, were analysed since trace elements, such as As and Sb, in these herbs may be toxic when consumed in sufficiently large quantities over a long period. Various amounts of medicinal herbs, standardised powder, lichen and tomato leaves were weighed, packed into polyethylene bags, irradiated and counted under different conditions. The results indicated that about 350 mg of lichen irradiated for 24 h and counted for 20 min following a 30-60 h decay period was optimal for irradiation in a 10(11)n/cm s epithermal neutron flux. The implications of the content of the studied elements in Chinese medicinal herbs are discussed.     

Diffusion-limited forward rate constants in two dimensions. Application to the trapping of cell surface receptors by coated pits.

A variety of receptors are known to aggregate in specialized cell surface structures called coated pits, prior to being internalized when the coated pits close off. At 37 degrees C on human fibroblasts, as well as on other cell types, a recycling process maintains a constant number of coated pits on the cell surface. In this paper, we explore implications for receptor aggregation and internalization of the two types of recycling models that have been proposed for the maintenance of the coated pit concentration. In one model, coated pits alternate between accessible and inaccessible states at fixed locations on the cell surface, while in the other model, coated pits recycle to random locations on the cell surface. We consider receptors that are randomly inserted in the membrane, move by pure diffusion with diffusion coefficient D, and are instantly and irreversibly trapped when they reach a coated pit boundary (the diffusion limit). For such receptors, we calculate for each of the two models: the mean time tau to reach a coated pit, the forward rate constant k+ for the interaction of a receptor with a coated pit, and the fraction phi of receptors aggregated in coated pits. We show that for the parameters that characterize coated pits on human fibroblasts, the way in which coated pits return to the surface has a negligible effect on the values of tau, k+, and phi for mobile receptors, D greater than or equal to 1.0 X 10(-11) cm2/s, but has a substantial effect for "immobile" receptors, D much less than 1 X 10(-11) cm2/s. We present numerical examples to show that it may be possible to distinguish between these models if one can monitor slowly diffusing receptors (D less than 1 X 10(-11) cm2/s) on cells whose coated pits have relatively short lifetimes (less than or equal to 1 min). Finally, we show that for the low-density lipoprotein (LDL) receptor on human fibroblasts (D = 4.5 X 10(-11) cm2/s), the predicted and observed values of K+ and phi are in close agreement. Therefore, even for slowly diffusing LDL receptor, unaided diffusion as the transport mechanism of receptors to coated pits is consistent with measured rates of LDL internalization.     

Kinetics of formation of 8-oxy-2'-deoxyguanosine-5'-monophosphate under the effect of heat: determination of rate constants and activation energy]

Rate constants of 8-oxy-dGMP (8-hydroxy-dGMP) formation upon incubating dGMP in H2O solutions at different temperatures were determined with differential UV-spectroscopy. Extrapolation of rate constant values obtained at elevated temperatures to 37 degrees C gives k = 5.8 x 10(-10) s-1.M-1. The activation energy for the process was estimated to be 24 kcal/mole. In D2O solutions essential lowering of the activation energy (13 kcal/mole) and rising of rate constant (k = 3.7 x 10(-9) s-1.M-1 at 37 degrees C) were observed. The strong influence of D2O on the process points to the possible participation of singlet oxygen in a heat-induced formation of 8-oxy-dGMP. The obtained values of rate constants and activation energy induced by heat show that of all types of DNA damages currently known such as single strand scission, depurination, cytosine deamination and oxidation of guanyl residues to the 8-oxo-derivatives- the last process seems to be the strongest damage of DNA resulting in such biological consequences as mutagenesis, carcinogenesis and aging.     

Determination of the orientations of tryptophan analogues bound to the trp repressor and the relationship to activation.

The antirepressor indole 3-propanoate has been shown by X-ray crystallography to bind in a different orientation compared with the natural corepressor for the tryp repressor, L-tryptophan (Lawson, C.L. & Sigler, P. B. (1988) Nature 333, 869-871). This suggests a simple difference between what constitutes a corepressor versus an antirepressor. We have used visible absorption and 1H-NMR spectroscopy to characterise the nature of several ligand-repressor complexes and DNA-binding assays to assess the relative operator binding affinities. 5-Fluorotryptophan binds with similar affinity and in the same orientation as L-tryptophan, and is an equally effective corepressor. In contrast, the tight-binding antirepressor indole 3-acrylate binds in the same orientation as indole 3-propanoate. Indole, also an antirepressor, also binds in the indole-3-propanoate orientation. 5-Methyltryptamine, a corepressor, shows spectroscopic characteristics of both tryptophan and indoleacrylate, though NOEs indicate that the tryptophan orientation is preferred. These results indicate that the ammonium group in the side chain is essential both for activation and binding in the L-tryptophan orientation. Antirepressors, lacking the ammonium group, bind in the more favourable indole-3-propanoate orientation. Differences in the NMR signatures of the different repressor-ligand complexes indicate that the details of the conformations depend on the nature of the ligands and their orientation within the binding site. Despite any conformational rearrangement of the protein on binding, dissociation of ligands is facile: 5-fluorotryptophan dissociates rapidly at 313 K. These findings complement and extend the X-ray and thermodynamic analyses of ligand binding.