An on-line method for the collection and analysis of quasi-steady-state kinetic data for enzyme-catalyzed reactions.

A special mixing device for initiating enzyme-catalyzed reactions is used to rapidly achieve an unperturbed quasi-steady state. An on-line computer is employed to sample the initial conditions, the mixing time, and concentrations that change as a function of time during this quasi-steady state phase. A statistical method for estimating initial, quasi-steady state rates from the time course of the enzyme-catalyzed reaction is described. Practical considerations for using this parameter estimation system lead to the conclusion that for the enzyme-catalyzed reaction tested, the extent overall reaction should be above .2% for high initial substrate concentrations, and above 1% for initial substrate concentrations in the range of the Michaelis constant. Application of this method to a typical enzyme-catalyzed reaction suggests that objective estimates of initial rates from a given set of concentrations and corresponding times can be obtained with a standard error in the range of 2–3%, but that reproducibility is not better than about 10%. When this procedure was used to estimate initial rates for the glycerol dehydrogenase-catalyzed oxidation of glycerol by NAD, it was found that this enzyme did not behave according to the classical “Michaelis-Menten” mechanism of enzyme action.     

Determination of Fructose in the Presence of a Large Excess of Glucose

Some factors affecting the skatole-hydrochloric acid reaction for fructose were studied. Especially, the stability of the chromogen to light, the effect of the amount of chloroform for complete extraction of the chromogen from the aqueous phase, and the time course of color development at various temperatures were studied in some detail. The time course of color development in the β-indolylacetic acid-hydrochloric acid reaction for fructose was also investigated. Based on the results obtained from these observations, some modifications to both the skatole-hydrochloric acid and β-indolylacetic acid-hydrochloric acid reactions were proposed.

A modification of the resorcinol-thiourea-hydrochloric acid method of Roe et al.⁷⁾ for the determination of fructose is described. The modification is based on the observation that by lowering the incubation temperature to 70°C, a greater color intensity ratio (fructose color/glucose color) is obtained, thus increasing the specificity of the method for fructose. By applying the principle of the two-point determination of Mokrasch¹²⁾ to the modified procedure, fructose in the presence of 100-fold excess of glucose can be determined with an error of about 10%.

A modified procedure of the cysteine-carbazole reaction for the determination of fructose is described. By incubating the components of the color reaction at 40°C for 1 hr, fructose is determined with good sensitivity (the millimolar absorbance value of 29.3) and specificity (the color intensity ratio of fructose to glucose is about 240). When the principle of the two-point determination is applied to this modified procedure (1 hr and 3 hr at 40°C), fructose as small an amount as 0.4 μg in the presence of 250-fold excess of glucose can be determined with an error of about 10 %.     

Enzyme-catalyzed and binding reaction kinetics determined by titration calorimetry

BackgroundIsothermal calorimetry allows monitoring of reaction rates via direct measurement of the rate of heat produced by the reaction. Calorimetry is one of very few techniques that can be used to measure rates without taking a derivative of the primary data. Because heat is a universal indicator of chemical reactions, calorimetry can be used to measure kinetics in opaque solutions, suspensions, and multiple phase systems and does not require chemical labeling. The only significant limitation of calorimetry for kinetic measurements is that the time constant of the reaction must be greater than the time constant of the calorimeter which can range from a few seconds to a few minutes. Calorimetry has the unique ability to provide both kinetic and thermodynamic data.Scope of reviewThis article describes the calorimetric methodology for determining reaction kinetics and reviews examples from recent literature that demonstrate applications of titration calorimetry to determine kinetics of enzyme-catalyzed and ligand binding reactions.Major conclusionsA complete model for the temperature dependence of enzyme activity is presented. A previous method commonly used for blank corrections in determinations of equilibrium constants and enthalpy changes for binding reactions is shown to be subject to significant systematic error.General significanceMethods for determination of the kinetics of enzyme-catalyzed reactions and for simultaneous determination of thermodynamics and kinetics of ligand binding reactions are reviewed. This article is part of a Special Issue entitled Microcalorimetry in the BioSciences — Principles and Applications, edited by Fadi Bou-Abdallah.     

Applications of graph theory to enzyme kinetics and protein folding kinetics. Steady and non-steady-state systems

Graphic methods have proved to be very useful in enzyme kinetics, as reflected in both raising the efficiency of performing calculations and aiding in the analysis of catalytic mechanisms. The kinetic relations among protein folding states are very similar to those between enzyme-catalyzed species. Therefore, it should be equally useful to provide a visually intuitive relation between kinetic calculations and folding mechanisms for protein folding kinetics, as manifested by the graphic rules in enzyme kinetics. It can actually be anticipated that, due to increasing interest in protein folding, the graphic method will become an important tool in folding kinetics as well. Based on the recent progress made in graphic methods of enzyme kinetics, in this review four graphic rules are summarized, which can be used to deal with protein folding systems as well as enzyme-catalyzed systems. Rules 1-3 are established for deriving the kinetic equations for steady-state processes and Rule 4 for those in the case of non-steady-state processes. In comparison with conventional graphic methods, which can only be applied to a steady-state system, the current rules have the following advantages: (1) Complicated and tedious calculations can be greatly simplified. (2) A lot of wasted labor can be turned away. (3) Final results can be double-checked by a formula provided in each of the graphic rules. (4) Transient kinetic systems can also be treated. The mathematical proof of Rules 1-4 is given in appendices A-D, respectively.     

New relations for steady-state enzyme kinetics and their application to rapid equilibrium assumption

With the use of graph theory, new relations for steady-state enzyme kinetics are derived and strictly proved for an arbitrary mechanism of enzyme-catalyzed reaction containing a reversible segment. Using these relations, a general principle for rapid equilibrium assumption is formulated and proved: the reversible bound segment can be considered as an equilibrium segment only when the values of the base trees that are not proper to this segment can be neglected (within prescribed accuracy) in relation to the values of the base trees that belong to this segment. In contrast with the foreign base trees, the base trees that are proper to the segment have the following properties: the tree that is directed to the base within this segment does not contain edges leaving this segment; and the tree that is directed to the base outside the segment contains only one edge leaving this segment. Equilibrium variations are assessed for steady-state concentrations of intermediates in the equilibrium segment, numerical expressions are obtained for the accuracy of determination of intermediate concentrations as well as for the accuracy of determination of the rate of enzyme-catalyzed reaction under rapid equilibrium assumption.     

Kinetic analysis of enzymatic chiral resolution by progress curve evaluation

The present study deals with kinetic modeling of enzyme-catalyzed reactions by integral progress curve analysis, and shows how to apply this technique to kinetic resolution of enantiomers. It is shown that kinetic parameters for both enantiomers and the enantioselectivity of the enzyme may be obtained from the progress curve measurement of a racemate only.A parameter estimation procedure has been established and it is shown that the covariance matrix of the obtained parameters is a useful statistical tool in the selection and verification of the model structure. Standard deviations calculated from this matrix have shown that progress curve analysis yields parameter values with high accuracies.Potential sources of systematic errors in (multiple) progress curve analysis are addressed in this article. Amongst these, the following needed to be dealt with: (1) the true initial substrate concentrations were obtained from the final amount of product experimentally measured (mass balancing); (2) systematic errors in the initial enzyme concentration were corrected by incorporating this variable in the fitting procedure as an extra parameter per curve; and (3) enzyme inactivation is included in the model and a first-order inactivation constant is determined.Experimental verification was carried out by continuous monitoring of the hydrolysis of ethyl 2-chloropropionate by carboxylesterase NP and the alpha-chymotrypsin-catalyzed hydrolysis of benzoylalanine mathyl ester in a pH-stat system. Kinetic parameter values were obtained with high accuracies and model predictions were in good agreement with independent measurements of enantiomeric excess values or literature data. (c) 1994 John Wiley & Sons, Inc.     

Quinone methides—and not dehydrodopamine derivatives—as reactive intermediates of β-sclerotization in the puparia of flesh fly Sarcophaga bullata

Cuticular phenoloxidase(s) from Sarcophaga bullata larvae oxidized a variety of o-diphenolic compounds. While catechol, 3,4-dihydroxybenzoic acid, dopa, dopamine, and norepinephrine were converted to their corresponding quinone derivatives, other catechols such as 3,4-dihydroxyphenylacetic acid, 3,4-dihydroxyphenethyl alcohol, 3,4-dihydroxyphenyl glycol, 3,4-dihy-droxymandelic acid, and N-acetyldopamine were oxidized to their side-chain oxygenated products. In addition, the enzyme-catalyzed oxidation of the latter group of compounds accompanied the formation of colorless catecholcuticle adducts consistent with the operation of β-sclerotization. Radioactive trapping experiments failed to support the participation of 1,2-dehydro-N-acetyldopamine as a freely formed intermediate during phenoloxidase-mediated oxidation of N-acetyldopamine. When specifically tritiated substrates were provided, cuticular enzyme selectively removed tritium from [7-³H]N-acetyldopamine and not from either [8-³H] or [ring-³H]N-acetyldopamine during the initial phase of oxidation. The above results are consistent with the generation and subsequent reactions of quinone methides as the initial products of enzyme-catalyzed N-acetyldopamine oxidation and confirm our hypothesis that quinone methides and not 1,2-dehydro-N-acetyldopamine are the reactive intermediate of β-sclerotization of sarcophagid cuticle. Quinone methide sclerotization resolves a number of conflicting observations made by previous workers in this field.     

Inactivation of alanine racemase by beta-chloro-L-alanine released enzymatically from amino acid and peptide C10-esters of deacetylcephalothin

The reactions of a set of amino acid and peptidyl C10-esters of deacetylcephalothin (1-5) have been examined with purified enzymes in vitro. Each of the compounds examined is a substrate for the Escherichia coli TEM-2 beta-lactamase, and enzyme-catalyzed hydrolysis of the lactam bond gives release of an amino acid or a peptidyl fragment from a cephem nucleus. 7 beta-(2-Thienylacetamido)-3-[[(beta-chloro-L-alanyl)oxy]methyl]-3- cephem-4-carboxylate (4) gives time-dependent inactivation of E. coli JSR-O alanine racemase in a process that requires beta-lactamase for the initial liberation of beta-chloro-L-alanine from the cephalosporin. Alanine racemase is similarly inactivated by 7 beta-(2-thienylacetamido)-3-[[[(beta-chloro-L-alanyl)-beta-chloro- L- alanyl]oxy]methyl]-3-cephem-4-carboxylate (1), but this inhibition requires the sequential action of both beta-lactamase and alanine aminopeptidase. Analysis of the enzymatic transformations of 7 beta-(2-thienylacetamido)-3-[[[(beta-chloro-L-alanyl)-L- alanyl]oxy]methyl]-3-cephem-4-carboxylate (3), monitored by high-field 1H NMR, reveals that (1) beta-lactamase releases the dipeptide beta-chloro-L-alanyl-L-alanine from 3 and (2) leucine aminopeptidase effects stoichiometric hydrolysis of the dipeptide to beta-chloro-L-alanine and L-alanine. These biochemical findings are discussed with reference to the mechanism of antibacterial action of 1 against beta-lactamase-producing, penicillin-resistant microorganisms [Mobashery, S., Lerner, S. A., & Johnston, M. (1986) J. Am. Chem. Soc. 108, 1685].     

Diversity of Archaea Communities within Contaminated Sand Samples from Johnston Atoll

A molecular 16S rRNA gene (SSU rDNA) analysis was performed for the determination of Archaea communities in polycyclic aromatic hydrocarbon (PAH)- and polychlorinated biphenyl (PCB)-contaminated sand samples obtained from Johnston Atoll. The objective of this study was to investigate Archaea community structure and phylogenetic diversity in a PAH- and PCB-contaminated marine environment that may potentially be intrinsically bioremediating these compounds. The clones obtained from this analysis were equally represented between the Crenarchaeota and Euryarchaeota phyla. This isolated marine environment is predominantly reef habitat, suggesting that the xenobiotic compounds introduced over time influenced the community structure of autochthonous Archaea. Phylogenetic diversity within these samples suggests that the resident Archaea populations were only distantly related to cultivated taxa and cloned sequences found in the public domain from both marine and terrestrial origins.     

A response-adaptive randomization procedure for multi-armed clinical trials with normally distributed outcomes

We propose a novel response-adaptive randomization procedure for multi-armed trials with continuous outcomes that are assumed to be normally distributed. Our proposed rule is non-myopic, and oriented toward a patient benefit objective, yet maintains computational feasibility. We derive our response-adaptive algorithm based on the Gittins index for the multi-armed bandit problem, as a modification of the method first introduced in Villar et al. (Biometrics, 71, pp. 969-978). The resulting procedure can be implemented under the assumption of both known or unknown variance. We illustrate the proposed procedure by simulations in the context of phase II cancer trials. Our results show that, in a multi-armed setting, there are efficiency and patient benefit gains of using a response-adaptive allocation procedure with a continuous endpoint instead of a binary one. These gains persist even if an anticipated low rate of missing data due to deaths, dropouts, or complete responses is imputed online through a procedure first introduced in this paper. Additionally, we discuss how there are response-adaptive designs that outperform the traditional equal randomized design both in terms of efficiency and patient benefit measures in the multi-armed trial context.     

Kinetics of protease hydrolysis of extended peptide substrates: measurement by flow-injection analysis

A flow-injection analysis (FIA) system was developed to study the enzyme-catalyzed hydrolysis of synthetic peptides, each of which contained one scissile bond. The concentrations of alpha-amino groups in reactions mixtures were determined by FIA with o-phthalaldehyde as a fluorescence reagent. The method allows a rapid, precise, and sensitive determination of kinetic constants for proteases acting on extended peptide substrates.     

Application of a graphic method for analyzing the kinetics of multienzyme reactions

A new graphic method is proposed to solve kinetic equations for polyenzymic reactions. Each graph apex is corresponded by the transmitting function deduced from kinetic equations by means of Laplas transformation. Application of this procedure allows to simplify the solution of kinetic equations and its analysis. The procedure suggested makes it possible to use the methods of automatic control when solving theoretical problems of enzymology.     

A quantitative method for the determination of the activities of mushroom tyrosinase

A sensitive, rapid, quantitative method for the determination of the activities of the bifunctional enzyme, mushroom tyrosinase (o-diphenol: O₂ oxido-reductose, EC 1.10.3.1) has been developed. The spectrophotometric method utilizes p-cresol and 4-methyl catechol as substrates at pH 4.8. By maintaining this low pH value, the rates of the nonenzymic reactions are negligible during the course of the assay. Preliminary analysis of the rates of enzyme-catalyzed reactions gave typical results for both substrates: Lineweaver-Burk plots yielded straight lines and the initial velocities for the reactions were proportional to enzyme concentration. Tyrosinase preparations judged to be as pure as those previously reported could be assayed to enzyme concentrations as low as 1 mg/liter with p-cresol while catechol allowed lower concentrations to be assayed (0.3 mg/liter). The precise specific activities towards p-cresol and 4-methyl catechol were found to vary between enzyme solutions and were used to characterize enzyme preparations.     

A Parameter-Elimination Method for Nonlinear Regression with Linear Parameters and Autocorrelated Errors

In this study, we are interested in the problem of estimating the parameters in a nonlinear regression model when the error terms are correlated. Throughout this work, we restrict ourselves to the special case when the error terms follow a pth order stationary autoregressive model (AR(p)). Following the idea of LAWTON and SYLVESTRE (1971) and GALLANT and GOEBEL (1976), a parameter-elimination method is proposed, which has the advantages that it is not sensitive to the initial values and convergence of the procedure may be more stable because of the reduced dimension of the problem. The parameter-elimination method is compared with the methods by GALLANT and GOEBEL (1976) and GLASBEY (1980) by Monte Carlo Simulation, and the results of applying the first two methods to the real data obtained from the Environmental Protection Administration of the Executive Yuan of the Republic of China are presented.     

Controlling the false discovery rate with constraints: the Newman-Keuls test revisited

The Newman-Keuls (NK) procedure for testing all pairwise comparisons among a set of treatment means, introduced by Newman (1939) and in a slightly different form by Keuls (1952) was proposed as a reasonable way to alleviate the inflation of error rates when a large number of means are compared. It was proposed before the concepts of different types of multiple error rates were introduced by Tukey (1952a, b; 1953). Although it was popular in the 1950s and 1960s, once control of the familywise error rate (FWER) was accepted generally as an appropriate criterion in multiple testing, and it was realized that the NK procedure does not control the FWER at the nominal level at which it is performed, the procedure gradually fell out of favor. Recently, a more liberal criterion, control of the false discovery rate (FDR), has been proposed as more appropriate in some situations than FWER control. This paper notes that the NK procedure and a nonparametric extension controls the FWER within any set of homogeneous treatments. It proves that the extended procedure controls the FDR when there are well-separated clusters of homogeneous means and between-cluster test statistics are independent, and extensive simulation provides strong evidence that the original procedure controls the FDR under the same conditions and some dependent conditions when the clusters are not well-separated. Thus, the test has two desirable error-controlling properties, providing a compromise between FDR control with no subgroup FWER control and global FWER control. Yekutieli (2002) developed an FDR-controlling procedure for testing all pairwise differences among means, without any FWER-controlling criteria when there is more than one cluster. The empirica example in Yekutieli's paper was used to compare the Benjamini-Hochberg (1995) method with apparent FDR control in this context, Yekutieli's proposed method with proven FDR control, the Newman-Keuls method that controls FWER within equal clusters with apparent FDR control, and several methods that control FWER globally. The Newman-Keuls is shown to be intermediate in number of rejections to the FWER-controlling methods and the FDR-controlling methods in this example, although it is not always more conservative than the other FDR-controlling methods.     

An estimation method for the semiparametric mixed effects model

A semiparametric mixed effects regression model is proposed for the analysis of clustered or longitudinal data with continuous, ordinal, or binary outcome. The common assumption of Gaussian random effects is relaxed by using a predictive recursion method (Newton and Zhang, 1999) to provide a nonparametric smooth density estimate. A new strategy is introduced to accelerate the algorithm. Parameter estimates are obtained by maximizing the marginal profile likelihood by Powell's conjugate direction search method. Monte Carlo results are presented to show that the method can improve the mean squared error of the fixed effects estimators when the random effects distribution is not Gaussian. The usefulness of visualizing the random effects density itself is illustrated in the analysis of data from the Wisconsin Sleep Survey. The proposed estimation procedure is computationally feasible for quite large data sets.     

ATP regeneration using immobilized carbamyl phosphokinase

A simple and efficient system for continuous ATP regeneration is described. The procedure is based on the enzyme-catalyzed reaction between carbamyl phosphate and ADP. The carbamyl phosphate was generated in situ by reaction between potassium cyanate and potassium phosphate. The enzyme, carbamyl phosphokinase, was isolated from extracts of Streptococcus faccalis and partially purified. Immobilization of the enzyme was achieved using glutaraldehyde-treated alkylamine glass giving 200–250 units of activity per gram of glass. A column of carbamyl phosphokinase on glass was used to form ATP continuously from ADP, phosphate, and cyanate and lost approximately 16% of the initial activity after 14 days operation at room temperature.     

Use and misuse of the reduced major axis for line‐fitting

Many investigators use the reduced major axis (RMA) instead of ordinary least squares (OLS) to define a line of best fit for a bivariate relationship when the variable represented on the X‐axis is measured with error. OLS frequently is described as requiring the assumption that X is measured without error while RMA incorporates an assumption that there is error in X. Although an RMA fit actually involves a very specific pattern of error variance, investigators have prioritized the presence versus the absence of error rather than the pattern of error in selecting between the two methods. Another difference between RMA and OLS is that RMA is symmetric, meaning that a single line defines the bivariate relationship, regardless of which variable is X and which is Y, while OLS is asymmetric, so that the slope and resulting interpretation of the data are changed when the variables assigned to X and Y are reversed. The concept of error is reviewed and expanded from previous discussions, and it is argued that the symmetry‐asymmetry issue should be the criterion by which investigators choose between RMA and OLS. This is a biological question about the relationship between variables. It is determined by the investigator, not dictated by the pattern of error in the data. If X is measured with error but OLS should be used because the biological question is asymmetric, there are several methods available for adjusting the OLS slope to reflect the bias due to error. RMA is being used in many analyses for which OLS would be more appropriate. Am J Phys Anthropol, 2009. © 2009 Wiley‐Liss, Inc.     

Evaluation of extraction methods for recovery of fatty acids from Botryococcus braunii LB 572 and Synechocystis sp. PCC 6803

Microalgae are a very diverse group of organisms that consist in both prokaryotic and eukaryotic forms. Some species of microalgae can be induced to overproduce particular fatty acids through simple manipulations of the physical and chemical properties of the culture medium. In this paper, the effect of different extraction techniques on the recovery of fatty acids from the freeze-dried biomass from two lipid-producing microalgal strains: Botryococcus braunii LB 572 (green algae) and Synechocystis sp. PCC 6803 (cyanobacteria) was examined. Five procedures were used: after conversion of the lipid material into the corresponding fatty acid methyl esters (FAMEs) via suitable derivatization reactions (extraction-transesterification) and direct transesterification of biomass to produce FAMEs (without the initial extraction step) that used differential types of catalysts and processing conditions. This study has shown that procedure 3, a one step practical procedure for lipid extraction and in situ methyl ester derivation could be used successfully for the determination of the fatty acid compositions of microalgae and cyanobacteria.     

Simplified approach for developing the rate expressions for enzyme-catalyzed reactions

A Simplified version of rate equations for enzyme-catalyzed reactions has been developed in which the rate equation is analyzed with two different mechanisms: ordered bi–ter and Ping-Pong bi–bi mechanisms. This procedure is able to develop the rate expressions accurately. Random sequential order mechanism can be effectively explained by this approach.