Enzymatic assays of L-ornithine and L-delta 1-pyrroline-5-carboxylate in tissues, and orniathine-load test in human subjects

The efficiencies of estimates obtained from the direct linear plot (A. Cornish-Bowden and R. Eisenthal, 1978, Biochem. Biophys, Acta, 523, 268) are shown to be dependent on the spacing of substrate concentrations. When substrate values are harmonically spaced, the direct linear plot should not be used. The nonparametric confidence limits based on the direct linear plot are accurate in their confidence coefficient, but their efficiencies are shown to be dependent on substrate spacing. Harmonic spacing is, in general, a more efficient experimental design for estimating K_m than arithmetic spacing when the appropriate estimation methods are used. If assumptions about the error structure cannot be made, the best procedure for estimating K_m is to have harmonic spacing of substrate values and use weighted least squares for estimation. The most accurate and precise estimation of enzyme kinetic parameters requires knowledge of the error structure and utilization of the appropriate nonlinear regression.     

Determination of enzyme kinetic parameters by continuous addition of substrate to a single reaction mixture and analysis by a tangent-slope procedure: I. Analysis of the method using computed progress curves

A new method has been developed which provides reliable estimates of enzyme kinetic constants from single reaction progress curves recorded under conditions of continuously increasing substrate concentration. Equally spaced data points simulating such progress curves and containing known amounts of superimposed random noise were fit to the Hill equation by (i) direct nonlinear curve-fitting of raw data, and (ii) a tangent-slope technique in which the raw data are numerically differentiated, transformed into substrate versus velocity data, and then analyzed as linear plots. Both integral and differential procedures provided accurate and precise estimates of the Hill parameters (S_0.5, V, and n) from single reaction mixtures. However, the tangent-slope method was at least 10-fold faster to compute and was not dependent on accurate initial guesses of the Hill parameters or integration of the rate equation. With the tangent-slope method, the optimal number of data points used in calculating tangent slopes was found to be 9 or 11. The reliability of the Hill parameters determined with the tangent-slope method was relatively insensitive to the maximum substrate concentration over a range of $\text{S}{}_{\mathrm{<mtext>max</mtext>}}\text{S}{}_{0.5}$ of 1.5 to 10; the optimal value was 3. Through further analysis of simulated data, it was found that slow enzyme inactivation (<4% loss during the assay), or product competitive inhibition (maximum product concentration < 30% of the inhibitor dissociation constant) does not produce serious errors in the Hill parameters. Methods are presented to detect and distinguish enzyme inactivation and product competitive inhibition. It is suggested that continuous addition methodology combined with tangent-slope analysis provides the basis for a flexible system for kinetic characterization of enzymes which has wider applicability and other advantages over multicuvette or conventional progress curve methodology. A major advantage in contrast to the progress curve approach is that product accumulation and associated product effects are lowest at lower substrate concentrations.     

A different approach to generating the data for parameter estimation with the heterotrophic activity method

This paper outlines a different approach to generating the data for V_max and T_t estimation with the Wright-Hobbie [1] method of measuring heterotrophic activities in aquatic environments. To be certain that the incubation times chosen are appropriate for all concentrations of substrate tested, and to increase the precision of the kinetic parameter estimates, we have adopted the approach of using kinetic plots derived from independent time-course studies performed at each concentration of substrate and analyzed by non-linear regression analysis. In keeping with our interest in the impact of acidification on aquatic microbial activities, we have applied this approach to the sediments and water column of the acid-stressed Silver Lake.     

Fed-batch propionic acid production by Propionibacterium acidipropionici

The batch fermentations were conducted using lactose as the substrate at pH 6.5 and temperature 30°C. Average batch kinetic data was eventually used to develop an unstructured mathematical model. The kinetic parameters of the model were determined by non-linear regression technique using the batch experimental results. Parametric sensitivity analysis showed the maximum specific substrate consumption rate (r_S^max) and the maintenance energy constant (m_S) to be the most sensitive parameters. The experimental observations in batch fermentation were close to the model predictions. The batch model was extrapolated to identify nutrient feeding strategies, which were tested successfully for two different fed-batch fermentations. It demonstrated enhanced propionic acid productivity. The developed model was found suitable for the design of feeding strategies to increase propionic acid production in fed-batch mode of reactor operation.     

Simultaneous estimation ofV max,Km, and the rate of endogenous substrate production (R) from substrate depletion data

The nonlinear and 3 linearized forms of the integrated Michaelis-Menten equation were evaluated for their ability to provide reliable estimates of uptake kinetic parameters, when the initial substrate concentration (S₀) is not error-free. Of the 3 linearized forms, the one where t/(S₀–S) is regressed against ln(S₀/S)/(S₀–S) gave estimates ofV _max and K_m closest to the true population means of these parameters. Further, this linearization was the least sensitive of the 3 to errors (±1%) in S₀. Our results illustrate the danger of relying on r² values for choosing among the 3 linearized forms of the integrated Michaelis-Menten equation. Nonlinear regression analysis of progress curve data, when S₀ is not free of error, was superior to even the best of the 3 linearized forms. The integrated Michaelis-Menten equation should not be used to estimateV _max and K_m when substrate production occurs concomitant with consumption of added substrate. We propose the use of a new equation for estimation of these parameters along with a parameter describing endogenous substrate production (R) for kinetic studies done with samples from natural habitats, in which the substrate of interest is an intermediate. The application of this new equation was illustrated for both simulated data and previously obtained H₂ depletion data. The only means by whichV _max, K_m, and R may be evaluated from progress curve data using this new equation is via nonlinear regression, since a linearized form of this equation could not be derived. Mathematical components of computer programs written for fitting data to either of the above nonlinear models using nonlinear least squares analysis are presented.     

Kinetics of hydrogen peroxide decomposition by catalase: hydroxylic solvent effects

The effect of water–alcohol (methanol, ethanol, propan-1-ol, propan-2-ol, ethane-1,2-diol and propane-1,2,3-triol) binary mixtures on the kinetics of hydrogen peroxide decomposition in the presence of bovine liver catalase is investigated. In all solvents, the activity of catalase is smaller than in water. The results are discussed on the basis of a simple kinetic model. The kinetic constants for product formation through enzyme–substrate complex decomposition and for inactivation of catalase are estimated. The organic solvents are characterized by several physical properties: dielectric constant (D), hydrophobicity (log P), concentration of hydroxyl groups ([OH]), polarizability (α), Kamlet-Taft parameter (β) and Kosower parameter (Z). The relationships between the initial rate, kinetic constants and medium properties are analyzed by linear and multiple linear regression.     

Pseudo-Second-Order Kinetic Model for Biosorption of Methylene Blue onto Tamarind Fruit Shell: Comparison of Linear and Nonlinear Methods

In this study, the sorption of methylene blue, a basic dye, onto tamarind fruit shell was studied by performing batch kinetic sorption experiments. The equilibrium kinetic data were analyzed using the pseudo-second-order kinetic model. A comparison between linear least squares method and nonlinear regression method of estimating the kinetic parameters was examined. Four pseudo-second-order kinetic linear equations were discussed. The coefficient of determination (r ²), and the chi-square (χ²) test were employed as error analysis methods to determine the best-fitting equation. Kinetic parameters obtained from four kinetic linear equations using the linear method differed but they were the same when nonlinear method was used. Present investigation showed that by linear method a Type 1 expression very well represent the kinetic uptake of methylene blue onto tamarind fruit shell. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Nonlinear regression method was found to be the more appropriate method to determine the rate kinetic parameters.     

Two simple programs for the analysis of data from enzyme-linked immunosorbent (ELISA) assays on a programmable desk-top calculator

We have designed two programs for use with an inexpensive programmable calculator which rapidly and accurately convert raw data generated from enzyme-linked immunosorbent assays directly into antigen concentration. The first program computes and compares effective doses (ED₅₀)'s between a standard and each unknown sample assayed. The ED₅₀ from the unknown sample is then multiplied by a concentration factor which yields the unknown concentration. The second program linearizes the sigmoidal enzyme-linked immunosorbent assay titration curve using a logit-log transformation of the data in order to compute unknown concentration values. Both programs employ stringent limit conditions to decrease “nonsense” calculations. Data are then processed by a least-squares best-fit linear regression analysis.     

Evaluation of methanogenic kinetics in an anaerobic fluidized bed reactor (AFBR)

A kinetic study of the methanogenic phase was carried out on a pilot lab scale anaerobic fluidized bed reactor (AFBR) in batch mode. An examination of the effect of initial acetate concentration, bed expansion and bed segregation is presented.Experimental data observed for the acetate removal against time were adjusted to a zero-order kinetic equation, over the chemical oxygen demand (COD) range studied (1430–5340 mg litre⁻¹), independently of the bed expansion (11–37%). The kinetic constant was calculated using robust regression analysis. The zero-order kinetic constant, K₀ was between 1180–1380 mg COD litre⁻¹ h⁻¹ on the fixed bed volume basis, and the maximum specific substrate utilization rate, k, was between 145–198 mg COD g VS⁻¹ h⁻¹.The kinetic behaviour was found to be different throughout the reactor, on the fixed bed volume basis and the activity at the bottom of the bed was lower than the activity in the upper region. However, on an attached volatile solids basis, the activity at the bottom level was the greatest.     

Estimation of kinetic parameters for substrate and inhibitor in a reaction with an enzyme sample containing different types of inhibitor

The method of kinetic analysis is developed to obtain the maximum velocity (V_m), the Michaelis constant (K_m) and the parameters characterizing the inhibitors in an impure enzyme reaction, contaminated with one of four types of inhibitor (competitive, noncompetitive, uncompetitive and mixed-type). Although the reaction rate decreases with the increasing concentration of the enzyme sample containing an inhibitor, the double-reciprocal plot of the rate against the sample concentration becomes linear. The slopes of these linear plots at several different concentrations of substrate provide K_m and the specific enzyme activity, which is proportional to V_m, in the sample. These linear straight lines intersect in a point, of which the coordinates give the unique parameters for the inhibitor. To prove the validity of this kinetic method, the model experiments were carried out with acetylcholinesterase and its inhibitors, phenyltrimethylammonium and trimethylammonium. The present method was applied to the measurement of the specific activity of galactosylceramide galactosidase in the mouse cerebral homogenate. In addition, a kinetic method is indicated for the inhibition of an enzymatic reaction by a contaminant which binds the substrate to reduce the fraction available to the enzyme.     

A minicomputer program for rapid graphical and statistical analysis of laboratory data

The utility of a FORTRAN program package, which enables the scientific investigator to make a rapid assessment of laboratory data is described. Data are submitted from the keyboard or specified disk files in the form of coordinate pairs. The program includes routines for plotting values as a series of X-Y pairs on the computer video monitor or for comparing the X and Y arrays via paired differences and Student's t-test. A least squares linear regression of plotted data may also be called. Data modification, curve fitting, and I/O are easily handled in either single pair or column format. Examples of both statistical and graphical data analysis are presented.     

A free derivate program for non-linear regression analysis of enzyme kinetics to be used on small computers

A non-linear regression program, written in BASIC, is describe. The program uses the Marquardt's algorithm as modified by Reich et al. (Eur. J. Biochem., 26 (1972) pp.368–379). The user only supplies the expression to fit, since the program uses numerical differentiation. It is possible to fit models of 1 substrate, 2 substrates, 1 substrates and 1 inhibitor, and 2 substrates and 1 inhibitor. Likewise, several weighting patterns, as well as a simple or robust regression, can be selected.     

Computerized analysis of enzyme cascade reactions using continuous rate data obtained with an ELISA reader

Two programs have been written which permit analysis of multiple continuous-rate enzyme-cascade assays conducted with the use of an ELISA spectrophotometer and a synthetic chromogenic substrate. Because the product of the first reaction functions as the enzyme in the second reaction, production of chromophore continuously accelerates and it is the rate of acceleration which serves to measure the rate of the initial reaction in the system. The first program determines the rate of acceleration using linear regression to analyze the reaction curves as a function of the square of time. The second program, using a Simplex algorithm, determines the parameters which establish the assay standard curve by fitting the rate data to the Hill equation. Used together, these programs facilitate the analysis of many kinetic experiments conducted simultaneously.     

Weighted regression analysis for comparing varietal adaptation

Summary The normally used joint linear regression analysis (OLS) is not appropriate for comparing estimates of stability parameters of varieties when the error variances of site means are heterogeneous. Weighted regression analysis (WLS), in these situations, yields more precise estimates of stability parameters. A comparison of the two analytical methods using the grain yield (kg ha^–1) data of 12 varieties and one hybrid of pearl millet [Pennisetum typhoides (Burm.) S. & H.], tested at 26 sites in India, revealed that the weighted regression analysis yields more efficient estimates of regression coefficients (b _i ) than the ordinary regression analysis, and that the standard errors of b _i values were reduced by up to 43%. The estimated b _i differed with the two procedures. The number of varieties with b _i ssignificantly deviating from unity was not only more (five varieties) with weighted regression analysis than the ordinary regression analysis (one variety), but the classification of varieties as possessing general or specific adaptation differed with the two procedures.     

A comparison of methods for determining compartmental analysis parameters

The traditional method for determining compartmental analysis parameters relies on a visual selection of data points to be used for regression of data from each cellular compartment. This method is appropriate when the compartments are kinetically discrete and are easily discernible. However, where treatment effects on compartment parameters are being evaluated, a more objective method for determining initial parameters is desirable.

Three methods were examined for determining initial isotopic contents and half-times of ⁸⁶Rb elution from cellular compartments using theoretical data with known parameters. Experimental data from roots of Douglas fir (Pseudotsuga menziesii [Mirb.] Franco) and barley (Hordeum vulgare L.) intact seedlings were also used. The three methods were a visually assisted, linear regression on data of semilog plot of isotope elution versus time, a microcomputer-assisted, linear regression on semilog plot where maximization of the square of the correlation coefficient (r²) was the criterion to determine data points needed for each regression and a mainframe computer-assisted, direct nonlinear regression on elution data using a model of the sum of three exponential decay functions. The visual method resulted in the least accurate estimates of compartmental analysis parameters. The microcomputer-assisted and nonlinear regression methods calculated the parameters equally well.

     

Logistic regression for clustered data from environmental monitoring programs

Large-scale surveys, such as national forest inventories and vegetation monitoring programs, usually have complex sampling designs that include geographical stratification and units organized in clusters. When models are developed using data from such programs, a key question is whether or not to utilize design information when analyzing the relationship between a response variable and a set of covariates. Standard statistical regression methods often fail to account for complex sampling designs, which may lead to severely biased estimators of model coefficients. Furthermore, ignoring that data are spatially correlated within clusters may underestimate the standard errors of regression coefficient estimates, with a risk for drawing wrong conclusions. We first review general approaches that account for complex sampling designs, e.g. methods using probability weighting, and stress the need to explore the effects of the sampling design when applying logistic regression models. We then use Monte Carlo simulation to compare the performance of the standard logistic regression model with two approaches to model correlated binary responses, i.e. cluster-specific and population-averaged logistic regression models. As an example, we analyze the occurrence of epiphytic hair lichens in the genus Bryoria; an indicator of forest ecosystem integrity. Based on data from the National Forest Inventory (NFI) for the period 1993–2014 we generated a data set on hair lichen occurrence on  >100,000 Picea abies trees distributed throughout Sweden. The NFI data included ten covariates representing forest structure and climate variables potentially affecting lichen occurrence. Our analyses show the importance of taking complex sampling designs and correlated binary responses into account in logistic regression modeling to avoid the risk of obtaining notably biased parameter estimators and standard errors, and erroneous interpretations about factors affecting e.g. hair lichen occurrence. We recommend comparisons of unweighted and weighted logistic regression analyses as an essential step in development of models based on data from large-scale surveys.     

Identification of an Active Site-bound Nitrile Hydratase Intermediate through Single Turnover Stopped-flow Spectroscopy

Stopped-flow kinetic data were obtained for the iron-type nitrile hydratase from Rhodococcus equi TG328-2 (ReNHase) using methacrylonitrile as the substrate. Multiple turnover experiments suggest a three-step kinetic model that allows for the reversible binding of substrate, the presence of an intermediate, and the formation of product. Microscopic rate constants determined from these data are in good agreement with steady state data confirming that the stopped-flow method used was appropriate for the reaction. Single turnover stopped-flow experiments were used to identify catalytic intermediates. These data were globally fit confirming a three-step kinetic model. Independent absorption spectra acquired between 0.005 and 0.5 s of the reaction reveal a significant increase in absorbance at 375, 460, and 550 nm along with the hypsochromic shift of an Fe³⁺←S ligand-to-metal charge transfer band from 700 to 650 nm. The observed UV-visible absorption bands for the Fe³⁺-nitrile intermediate species are similar to low spin Fe³⁺-enzyme and model complexes bound by NO or N₃⁻. These data provide spectroscopic evidence for the direct coordination of the nitrile substrate to the nitrile hydratase active site low spin Fe³⁺ center.     

Rational polynomial equation as an unbiased approach for the kinetic studies of Drosophila melanogaster acetylcholinesterase reaction mechanism

The hydrolysis of substrates by cholinesterases does not follow the Michaelis–Menten reaction mechanism. The well-known inhibition by excess substrate is often accompanied by an unexpectedly high activity at low substrate concentrations. It appears that these peculiarities are the consequence of an unusual architecture of the active site, which conducts the substrate molecule over many stages before it is cleaved and released. Structural and kinetic data also suggest that two substrate molecules can attach at the same time to the free, as well as to the acetylated, enzyme. We present a procedure which provides an unbiased framework for mathematical modelling of such complex reaction mechanisms. It is based on regression analysis of a rational polynomial using classical initial rate data. The determination of polynomial degree reveals the number of independent parameters that can be evaluated from the available information. Once determined, these parameters can substantially facilitate the construction and evaluation of a kinetic model reflecting the expected molecular events in an enzymic reaction. We also present practical suggestions for testing the postulated kinetic model, using an original thermodynamic approach and an isolated effect in a specifically mutated enzyme.     

A simple computer program with statistical tests for the analysis of enzyme kinetics.

A simple computer program that calculates the kinetic parameters of enzyme reactions is described. Parameters are determined by nonlinear, least-squares regression using either Marquardt-Levenberg or Gauss-Newton algorithms to find the minimum sum of squares. Three types of enzyme reactions can be analyzed: single substrate reactions (Michaelis-Menten and sigmoidal kinetics), enzyme activation at a fixed substrate value or enzyme inhibition at a fixed substrate value. The user can monitor goodness of fit through nonparametric statistical tests (performed automatically by the computer) and through visual examination of the pattern of residuals. The program is unique in providing equations for activator and inhibition analysis as well as in enabling the user to fix some of the parameters before regression analysis. The simplicity of the program makes it extremely useful for quickly determining kinetic parameters during the data-gathering process.