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Convenient method for studying enzyme kinetics.

A convenient method for enzyme kinetic studies is introduced. The method includes identification of reaction mechanism and estimation of the associated kinetic constants with a minimum number of experiments. The application of the method is illustrated by using literature data. Factors limiting the application of this method are also discussed.

Binding, Competitive

A new procedure to derive weighting factors for nonlinear regression analysis applied to enzyme kinetic data.

The experimental variance of enzymic steady-state kinetic experiments depends on velocity as approximated by a power function (Var(v) = K1 . valpha (Askelöf, P., Korsfeldt, M. and Mannervik, B. (1976) Eur. J. Biochem. 69, 61--67). The values of the constants (K1, alpha) can be estimated by making replicate measurements of velocity, and the inverse of the function can then be used as a weighting factor. In order to avoid measurement of a large number of replicates to establish the error structure of a kinetic data set, a different approach was tested. After a preliminary regression using a 'good model', which satisfies reasonable goodness-of-fit criteria, the residuals were taken to represent the experimental error. The neighbouring residuals were grouped together and the sum of their mean squared values was used as a measure of the variance in the neighbourhood of the corresponding measurements. The values of the constants obtained in this way agreed with those obtained by replicates.

Enzymes

Enzyme kinetic studies and inhibition by oligopeptides of LH-RH degradation in rat hypothalamus and pituitary.

The enzyme kinetic parameters of the degradation of luteinizing hormone-releasing hormone (LH-RH) and L-cystine-bis-(4-nitroanilide) (Cys-NA) by rat hypothalamic (HYP) and pituitary (PIT) extracts and the effect of various oligopeptides on the rate of LH-RH inactivation were investigated in vitro. The 105,000 x g supernatant of 1 rat HYP inactivated 57 microgram LH-RH during a 30 min incubation (Km = 12.4 microM, V max = 2.33 microgram LH-RH/mg protein/min), and of one rat anterior PIT, 48 microgram LH-RH during 30 min of incubation (Km = 12.2 microM, V max = 8.0 microgram LH-RH/mg protein/min). The synthetic substrate Cys-NA competitively inhibited LH-RH degradation with a Ki of 8.5 microM in the HYP and 6 microM in the PIT enzyme preparation. Vice versa, LH-RH also competitively inhibited the cleavage of Cys-NA with inhibition constants of 14 microM (HYP) and 15 microM (PIT) indicating that the 2 substrates are probably cleaved by the same enzyme. The most effective inhibitors of LH-RH degradation were found to be angiotensin-related peptides, neurotensin, bradykinin, and bacitracin. A relatively weak effect was obtained with oxytocin, enkephalin and puromycin. It is concluded that endogenous oligopeptides such as angiotensins, neurotensin, bradykinin, etc., may possibly influence H-RH degradation in the PIT and the HYP. The synthetic substrate Cys-NA may be an appropriate substrate for measuring the activity of an LH-RH-degrading peptidase, which therefore could be classified as arylamidase.

Aminopeptidases

Computer simulation of leukemia therapy: combined pharmacokinetics, intracellular enzyme kinetics, and cell kinetics of the treatment of L1210 leukemia by cytosine arabinoside.

An integrated mathematic computer-based model of the pharmacokinetics, intracellular enzyme kinetics, and cell kinetics of the treatment of L1210 leukemia by cytosine arabinoside (ara-C) is described. The compartment model of Bischoff and Dedrick is extended to the intracellular level by inclusion of equations describing the phosphorylation, dephosphorylation, and deamination of ara-C with enzymatic feedback control. The activities of kinase, deaminase, and phosphatase are explicitly included in the models and are estimated from relevant data. Cell proliferation is described by a continuous-flow mathematic model in which cellular maturation and cell-to-cell variability in maturation rates are key variables. Cell proliferation is related to intracellular biochemistry through mathematic expressions which relate cell lethality and progression delay to the time course of intracellular ara-CTP. In vitro and in vivo experiments performed in a number of laboratories are compared by simulation. The most sensitive parameters in dose-response and cell-survival simulations are deoxycytidine kinase activity, ara-CTP half-life, renal clearance of ara-C, and cell-kinetic parameters for proliferation and cell killing. Progression delay is vital to the realistic simulation of divided-dose schedules. By comparative simulation we have identified areas of uncertainty which can be classified by a few additional measurements. The applications of simulations combining pharmacokinetic, biochemical, and cell-kinetic data in vitro and in vivo are discussed, exploring consistency among different measurements, and relating experimental protocols to clinical treatment.

Animals

The use of an oscillating-tube densitometer as a tool in enzyme kinetics. Determination of the influence of sodium ascorbate on invertase, dextransucrase and dextranase.

The use of a commercial oscillating-tube densitometer with an accuracy of 4 . 10(-7) g/cm3 for the determination of enzyme-kinetics constants is tested. This method is applied to the investigation of the influence of vitamin C (sodium ascorbate) on the glycolytic enzymes invertase, dextransucrase and dextranase. Invertase is inhibited uncompetitively, dextransucrase non-competitively. There is no significant effect of the vitamin on dextranase. The comparison of the mechanisms of the three enzymes suggests that only those reaction steps are inhibited by vitamin C in which fructose is released from the enzyme.

Ascorbic Acid

Enzyme kinetics shapes the growth response of metabolic networks.

Microbes adjust their metabolism to environmental challenges by changing protein expression levels, metabolite concentrations, and reaction rates. Average expression levels in large proteome sectors change coherently, while individual proteins show divergent shifts even within the same pathway. Here, we establish a metabolic model that integrates local enzyme kinetics and global network architecture to predict the joint growth response of proteins and metabolites. Under nutrient limitation, we predict a remarkably simple pattern of proteome reallocation with growth rate: protein expression levels change linearly but heterogeneously. For a given enzyme, the direction of change is determined by its local kinetic constants - catalytic rate and substrate affinity - and by the degree of nutrient restriction affecting its embedding pathway. This double-graded growth response of the proteome is mediated by restriction-dependent metabolite levels, which are predicted to decrease with growth rate in a nonlinear way. The model establishes three specific growth laws: protein expression changes of individual enzymes are negatively correlated with their expression and with their substrate saturation at high growth; average changes of pathways and larger functional sectors are correlated with their internal variance. These predictions are in quantitative agreement with measured system-wide proteomics and metabolomics data of E. coli. Enzyme-specific response patterns are a starting point for model-guided interventions into bacterial metabolism.

Kinetics

Biomathematical enzyme kinetics model of prebiotic autocatalytic RNA networks: degenerating parasite-specific hyperparasite catalysts confer parasite resistance and herald the birth of molecular immunity.

Catalysis and specifically autocatalysis are the quintessential building blocks of life. Yet, although autocatalytic networks are necessary, they are not sufficient for the emergence of life-like properties, such as replication and adaptation. The ultimate and potentially fatal threat faced by molecular replicators is parasitism; if the polymerase error rate exceeds a critical threshold, even the fittest molecular species will disappear. Here we have developed an autocatalytic RNA early life mathematical network model based on enzyme kinetics, specifically the steady-state approximation. We confirm previous models showing that these second-order autocatalytic cycles are sustainable, provided there is a sufficient nucleotide pool. However, molecular parasites become untenable unless they sequentially degenerate to hyperparasites (i.e. parasites of parasites). Parasite resistance-a parasite-specific host response decreasing parasite fitness-is acquired gradually, and eventually involves an increased binding affinity of hyperparasites for parasites. Our model is supported at three levels; firstly, ribozyme polymerases display Michaelis-Menten saturation kinetics and comply with the steady-state approximation. Secondly, ribozyme polymerases are capable of sustainable auto-amplification and of surmounting the fatal error threshold. Thirdly, with growing sequence divergence of host and parasite catalysts, the probability of self-binding is expected to increase and the trend towards cross-reactivity to diminish. Our model predicts that primordial host-RNA populations evolved via an arms race towards a host-parasite-hyperparasite catalyst trio that conferred parasite resistance within an RNA replicator niche. While molecular parasites have traditionally been viewed as a nuisance, our model argues for their integration into the host habitat rather than their separation. It adds another mechanism-with biochemical precision-by which parasitism can be tamed and offers an attractive explanation for the universal coexistence of catalyst trios within prokaryotes and the virosphere, heralding the birth of a primitive molecular immunity.

Kinetics

Computer-based modeling in the teaching of steady-state enzyme kinetics.

Equations are derived for the steady-state treatment of enzyme reactions with one type of inhibitor, consisting of one reaction cycle or two connected cycles. Computerized stimulation programs are described which are designed to acquaint the student thoroughly with the behavior of enzyme systems. The user has freedom in the choice of parameters for the system, including up to three product-producing rate constants for the two-cycle system.

Computer-Assisted Instruction

Deuterium and tritium exchange in enzyme kinetics.

The theory of the isotopic exchange of deuterium and tritium between an enzyme-substrate complex and the solvent is derived for 16 different types of experiment involving measurements of initial velocities and of the isotopic content of the reactants and products as a function of the extent of reaction. It is shown how the data from these experiments can be analyzed to obtain the rate constants for the individual steps and thereby the Gibbs free energies of the intermediates and transition states in the reaction. The effects of isotopic substitution on each intermidiate and transition state are also found and this allows conclusions to be drawn as to the extent to which a proton is in flight in a particular transition state. Neither substrate handling (that is, on-off steps), nor the isotopic exchange with the solvent, is assumed to be rapid.

Deuterium

Postproline cleaving enzyme: kinetic studies of size and stereospecificity of its active site.

Postproline cleaving enzyme [EC 3.4.21.-] has recently been purified from lamb kidney and tentatively identified as a serine endopeptidase with a high specificity for proline-containing peptides. The interaction of postproline cleaving enzyme with peptide substrates and competitive inhibitors has been studied in an effort to explore the size and stereospecificity of the active site of the protease. The substrates and inhibitors included proline-containing peptide amides, p-nitrophenyl esters, and free acids with increasing numbers of amino acid residues and residues of L and D configuration. Oligopeptides of alanine, which can also be recognized by the protease, were also tested as substrates. This series included Ala3, Ala-D-Ala-Ala, Ala-Ala-D-Ala,Z-(Ala)3, Ala4 through Ala6. The contribution of each of the three amino acid residues flanking the primary specificity site (S1) of postproline enzyme to such kinetic parameters as Km, Kcat, and Kcat/Km in the case of substrates and Ki with inhibitors was determined. The results suggest that postproline cleaving enzyme has an extended substrate binding region in addition to the primary specificity site, S1. It seems to be comprised of three sites located at the amino-terminal site (S1, S2, and S3) and two sites at the carboxyl site from the catalytic point (S1', S2'). High stereospecificity was observed for subsites S1, S2, and S1'.

Animals