The comparison of the estimation of enzyme kinetic parameters by fitting reaction curve to the integrated Michaelis-Menten rate equations of different predictor variables

Soil phosphatase assay to evaluate arsenic toxicity should be performed at the soil's actual pH

Soil phosphatase is considered an indicator to assess soil arsenic (As) pollution. In the phosphatase activity determination, a fixed buffer value (pH 5-10) is commonly used for all soils, ignoring the soil's actual pH. Here, we determined the soil phosphatase activity of 20 soils under As stress at the soils' pH, and the As inhibition mechanism was also explored by the enzyme kinetics. Our results show that soil phosphatase activity was significantly inhibited under As stress. The inhibition rate in acid soils (39.2 %) was considerably higher than in alkaline soils (25.4 %) when As concentration was 600 mg kg^-1. For alkaline soils, As inhibited phosphatase by competitive inhibition or linear mixed inhibition, while for acid soils, it was more complex, including linear mixed inhibition, non-competitive inhibition, and anti-competitive inhibition. Simultaneously, our results showed that the ecological dose (ED10) described by the partial inhibition model was far below than the complete inhibition model. According to the partial inhibition model, the ED₁₀ of As ranged from 2.66 to 164.07 mg kg^-1 for alkaline soils and 0.11 to 89.95 mg kg^-1 for acid soils. Moreover, V_max/K_m of phosphatase is a more sensitive index for evaluating As contamination than V_max in partial inhibition models. The ED₁₀ obtained based on the relationship between V_max/K_m and As concentration was 0.64-34.75 mg kg^-1 for acid soils and 8.48 to 20.16 mg kg^-1 for alkaline soils. This also confirms V_max/K_m as a sensitive and ideal index for assessing As pollution under soils' actual pH. Furthermore, soil pH and cation exchange capacity are dominant factors affecting As inhibition on soil phosphatase. The above kinetic studies indicate that performing the assay by adjusting the buffer pH to the soil pH is essential for more accurately evaluating arsenic toxicity.

Model discrimination in dynamic molecular systems: application to parotid de-differentiation network

In modern systems biology the modeling of longitudinal data, such as changes in mRNA concentrations, is often of interest. Fully parametric, ordinary differential equations (ODE)-based models are typically developed for the purpose, but their lack of fit in some examples indicates that more flexible Bayesian models may be beneficial, particularly when there are relatively few data points available. However, under such sparse data scenarios it is often difficult to identify the most suitable model. The process of falsifying inappropriate candidate models is called model discrimination. We propose here a formal method of discrimination between competing Bayesian mixture-type longitudinal models that is both sensitive and sufficiently flexible to account for the complex variability of the longitudinal molecular data. The ideas from the field of Bayesian analysis of computer model validation are applied, along with modern Markov Chain Monte Carlo (MCMC) algorithms, in order to derive an appropriate Bayes discriminant rule. We restrict attention to the two-model comparison problem and present the application of the proposed rule to the mRNA data in the de-differentiation network of three mRNA concentrations in mammalian salivary glands as well as to a large synthetic dataset derived from the model used in the recent DREAM6 competition.

Comparison of activity indexes for recognizing enzyme mutants of higher activity with uricase as model

Background

For screening a library of enzyme mutants, an efficient and cost-effective method for reliable assay of enzyme activity and a decision method for safe recognition of mutants of higher activity are needed. The comparison of activity concentrations of mutants in lysates of transformed Escherichia coli cells against a threshold is unsafe to recognize mutants of higher activity due to variations of both expression levels of mutant proteins and lysis efficiency of transformed cells. Hence, by a spectrophotometric method after verification to measure uricase activity, specific activity calculated from the level of total proteins in a lysate was tested for recognizing a mutant of higher activity.

Results

During uricase reaction, the intermediate 5-hydroxyisourate interferes with the assay of uric acid absorbance, but the measurement of absorbance at 293 nm in alkaline borate buffer was reliable for measuring uricase initial rates within a reasonable range. The level of total proteins in a lysate was determined by the Bradford assay. Polyacrylamide gel electrophoresis analysis supported different relative abundance of uricase mutant proteins in their lysates; activity concentrations of uricase in such lysates positively correlated with levels of total proteins. Receiver-operation-curve analysis of activity concentration or specific activity yielded area-under-the-curve close to 1.00 for recognizing a mutant with > 200% improvement of activity. For a mutant with just about 80% improvement of activity, receiver-operation-curve analysis of specific activity gave area-under-the-curve close to 1.00 while the analysis of activity concentration gave smaller area-under-the-curve. With the mean plus 1.4-fold of the standard deviation of specific activity of a starting material as the threshold, uricase mutants whose activities were improved by more than 80% were recognized with higher sensitivity and specificity.

Conclusion

Specific activity calculated from the level of total proteins is a favorable index for recognizing an enzyme mutant with small improvement of activity.

Spectrophotometric-dual-enzyme-simultaneous assay in one reaction solution: chemometrics and experimental models

Spectrophotometric-dual-enzyme-simultaneous assay in one reaction solution (SDESA) is proposed. SDESA requires the following: (a) Enzyme A acts on Substrate A to release Product A bearing the longest difference absorbance peak (λ(A)) much larger than that of Product B (λ(B)) formed by Enzyme B action on Substrate B; λ(B) is close to the longest isoabsorbance wavelength of Product A and Substrate A (λ(0)); (b) absorbance at λ(A) and λ(0) is quantified via swift alternation of detection wavelengths and corrected on the basis of absorbance additivity; (c) inhibition/activation on either enzyme by any substance is eliminated; (d) Enzyme A is quantified via an integration strategy if levels of Substrate A are lower than the Michaelis constant. Chemometrics of SDESA was tested with γ-glutamyltransferase and lactate-dehydrogenase of complicated kinetics. γ-Glutamyltransferase releases p-nitroaniline from γ-glutamyl-p-nitroaniline with λ(0) at 344 nm and λ(A) close to 405 nm, lactate-dehydrogenase consumes reduced nicotinamide dinucleotide bearing λ(B) at 340 nm. Kinetic analysis of reaction curve yielded lactate-dehydrogenase activity free from inhibition by p-nitroaniline; the linear range of initial rates of γ-glutamyltransferase via the integration strategy, and that of lactate-dehydrogenase after interference elimination, was comparable to those by separate assays, respectively; the quantification limit of either enzyme by SDESA at 25-fold higher activity of the other enzyme remained comparable to that by a separate assay. To test potential application, SDESA of alkaline phosphatase (ALP) and β-D-galactosidase as enzyme-linked-immunoabsorbent assay (ELISA) labels were examined. ALP releases 4-nitro-1-naphthol from 4-nitronaphthyl-1-phosphate with λ(0) at 405 nm and λ(A) at 458 nm, β-D-galactosidase releases 4-nitrophenol from β-D-(4-nitrophenyl)-galactoside with λ(B) at 405 nm. No interference from substrates/products made SDESA of β-galactosidase and ALP simple for ELISA of penicillin G and clenbuterol in one well, and the quantification limit of either hapten was comparable to that via a separate assay. Hence, SDESA is promising.

Integration of kinetic analysis of reaction curve with a proper classical approach for enzymatic analysis

For enzymatic analysis to quantify a substrate or enzyme, kinetic analysis of reaction curve can be integrated with a proper classical approach. For their integration, they should have consistent slopes and intercepts of linear response and an overlapped region of analyte quantities measurable under optimized conditions. To quantify a substrate after optimizations of tool enzyme activity and reaction duration, the equilibrium method works when the reaction is completed within the reaction duration; otherwise, kinetic analysis of reaction curve applies providing at least seven data with sufficient consumption of substrate. To quantify an enzyme after optimizations of initial substrate concentration and reaction duration, the classical initial rate method works when an estimated initial rate locates within the linear range; otherwise, kinetic analysis of reaction curve applies after the conversion of the quantification index with optimized parameters. This integration strategy has ideal linear ranges and practical efficiency for quantifying an enzyme at moderate substrate levels and for quantifying a substrate at moderate cost on tool enzyme; it has promise to simultaneous assays of multiple enzymes in one reaction vessel each time and ,thus, potential applications to concurrently quantify multiple serum enzymes, screen inhibitors against multiple enzyme targets, and detect multiple serum components by enzymeimmunoassay.

Classification of difference between inhibition constants of an inhibitor to facilitate identifying the inhibition type

To identify the common inhibition types, the putative decision system is unsatisfactory. In a new decision system, Michaelis-Menten constants and maximal reaction rates were plotted versus inhibitor concentrations for deriving K(ik) and K(iv) as the inhibition constants, respectively; their difference was quantified as the ratio of the larger one to the smaller one. Such ratios below 2.0 suggested uncompetitive inhibitors, over 5.0 suggested noncompetitive or competitive inhibitors, and from 2.0 to 5.0 suggested mixed inhibitors. By the new decision system, (i) the simulation recovery of uncompetitive inhibitors under CVs of 2% or 5% was improved by four times, but that of competitive or noncompetitive inhibitors was improved slightly; (ii) the recovery of L-phenylalanine as an uncompetitive inhibitor of intestinal alkaline phosphatase reached 38%, while the putative decision system lost all; the recovery of xanthine as a competitive inhibitor of uricase was improved slightly. Therefore, the new decision system was better.

Uricases as therapeutic agents to treat refractory gout: Current states and future directions

Treatment of refractory gout remains a challenge on drug development. While pegloticase, a recombinant mammalian uricase modified with monomethoxyl-poly(ethylene glycol) (mPEG) is effective in treating refractory gout, after continued treatment for three months biweekly at a therapeutic dose of 0.14 mg/kg body weight, it elicits an immune response against mPEG in nearly 20% of patients. For continued treatment of refractory gout PEGylated uricases at monthly therapeutic doses below 4 μg/kg body weight have promise. To formulate uricases to achieve monthly therapeutic regimens requires pharmacodynamics simulation and experimentation including: (a) molecular engineering of uricases based on rational design and evolution biotechnology in combination to improve their inherent catalytic efficiency, thermostability and selectivity for urate over xanthine and; (b) optimization of the number and distribution of accessible reactive amino acid residues in native uricases for site-specific PEGylation with PEG derivatives with lower of immunogenicity than mPEG to retain activity, minimize immunogenicity and enhance the pharmacokinetics of the PEGylated uricase. These issues are briefly reviewed as a means to stimulate the development of safer uricase formulations for continued treatment of refractory gout.

Kinetic analysis of γ-glutamyltransferase reaction process for measuring activity via an integration strategy at low concentrations of γ-glutamyl p-nitroaniline

At 0.12 mmol/L γ-glutamyl p-nitroaniline (GGPNA), an improved integrated method was developed for kinetic analysis of γ-glutamyltransferase (GGT) reaction process and the integration with the classical initial rate method to measure serum GGT. For the improved integrated method, an integrated rate equation, which used the predictor variable of reaction time and considered inhibitions by both GGPNA and products, was nonlinearly fit to GGT reaction processes. For the integration strategy, classical initial rates were estimated when GGPNA consumption percentages were below 50%; otherwise, maximal reaction rates of GGT were estimated by the improved integrated method and converted into initial rates according to the differential rate equation at 0.11 mmol/L GGPNA. The integration strategy was validated using optimized GGT kinetic parameters and 10-s intervals to record reaction curves within 8.0 min. By the integration strategy, there was a linear response from 0.9 to 32.0 U/L GGT, coefficients of variation were below 3.5% for GGT from 8.0 to 32.0 U/L (n=5), and GGT activities in clinical sera responded linearly to their classical initial rates at 2.00 mmol/L GGPNA with an expected slope. Therefore, the integration strategy was successful in measuring GGT at 0.12 mmol/L GGPNA.

Kinetic analysis of the lactate-dehydrogenase-coupled reaction process and measurement of alanine transaminase by an integration strategy

Kinetic analyses of lactate-dehydrogenase (LD)-coupled alanine transaminase (ALT) reaction processes were investigated for measuring ALT by an integration strategy. For measuring ALT by a kinetic analysis of an LD-coupled ALT reaction curve, candidate reaction curves were calculated via iterative numerical integration of the differential velocity equations to execute a weighted nonlinear-least-square-fitting. To realize the integration strategy, the conventional initial-velocity method was used if the ALT activities were below 25 U/L; otherwise, kinetic analyses of the reaction curves were employed. Of the reaction curves recorded at 10-s intervals, kinetic analyses gave ALT activities resistant to deviations in the LD kinetic parameters. The integration strategy yielded a higher value of the lower limit, but an upper limit of over 100 U/L by simulations and over 75 U/L with purified ALT. Also, its intra-run relative standard deviations were below 9% for 0.50 U/L ALT and below 5% for final 1 to 65 U/L ALT. The integration strategy gave consistent ALT activities in clinical sera. Hence, this new approach for kinetic analyses of ALT reaction processes and the integration strategy were effective to measure ALT.

Effects of modification of amino groups with poly(ethylene glycol) on a recombinant uricase from Bacillus fastidiosus

After modification with monomethoxyl-poly(ethylene glycol)-5000, a recombinant intracellular uricase from Bacillus fastidiosus ATCC 29604 showed residual activity of about 65%, a thermo-inactivation half-life >85 h, a circulating half-life about 20 h in rats in vivo, consistent effects of common cations, and consistent optima for reaction temperature and pH. Thus, this uricase can be formulated via modification with monomethoxyl-poly(ethylene glycol).

A method to describe enzyme-catalyzed reactions by combining steady state and time course enzyme kinetic parameters

BACKGROUND

Complete analysis of single substrate enzyme-catalyzed reactions has required a separate use of two distinct approaches. Steady state approximations are employed to obtain substrate affinity and initial velocity information. Alternatively, first order exponential decay models permit simulation of the time course data for the reactions. Attempts to use integrals of steady state equations to describe reaction time courses have so far met with little success.

METHODS

Here we use equations based on steady state approximations to directly model time course plots.

RESULTS

Testing these expressions with the enzyme beta-galactosidase, which adheres to classical Michaelis-Menten kinetics, produced a good fit between observed and calculated values.

GENERAL SIGNIFICANCE

This study indicates that, in addition to providing information on initial kinetic parameters, steady state approximations can be employed to directly model time course kinetics. Integrated forms of the Michaelis-Menten equation have previously been reported in the literature. Here we describe a method to directly apply steady state approximations to time course analysis for predicting product formation and simultaneously obtain multiple kinetic parameters.

The measurement of cyclic nucleotide phosphodiesterase 4 activities via the quantification of inorganic phosphate with malachite green

A spectrometric method was investigated to measure the activities of recombinant human cyclic nucleotide phosphodiesterase 4 (PDE4), based on the use of malachite green (MLG) to quantify phosphate released from adenosine-5'-monophosphate (AMP) by the action of calf intestinal alkaline phosphatase (CIAP). Glycerol at 2% stabilized the complex between MLG and phosphomolybdate, whose absorbance at 630nm was proportional to phosphate concentrations with resistance to common substances in PDE4 reaction mixtures except papaverine. CIAP had the Michaelis-Menten constant (K(m)) of (12.0+/-2.1)microM (n=3) for AMP at pH 7.4, and was resistant to EDTA below 0.20mM. By the coupled end-point assay at 30.0UL(-1) CIAP with reaction durations within 30min, the rates to release phosphate in PDE4 reaction mixtures containing 10.0mM MgCl(2) and 0.10mM EDTA linearly responded to the amounts of PDE4 over wide ranges. Meanwhile, K(m) of PDE4 was (8.8+/-0.2)microM (n=2), zinc ion inhibited PDE4 and rolipram had the inhibition constant about 10nM. These results supported that by the coupled end-point assay, this method was promising to screen of PDE inhibitors that had no interference with the MLG assay of phosphate.

Development of a fluorescent substrate to measure hyaluronidase activity

A novel fluorescent substrate (termed FRET-HA) to quantitatively assess hyaluronidase activity was developed. Hyaluronan (HA), the major substrate for hyaluronidase, was dual labeled with fluorescein amine and rhodamine B amine. The fluorescein amine fluorescence signal was significantly quenched and the rhodamine B amine signal was significantly enhanced due to fluorescence resonance energy transfer (FRET). In the presence of bovine testes hyaluronidase, cleavage of HA disrupted FRET, resulting in a loss of the fluorescein amine quenching that was dependent on both enzyme concentration and time. Increase in the fluorescein amine signal could be conveniently monitored in both noncontinuous and continuous fashions. The K(m) value for bovine testes hyaluronidase was determined using FRET-HA in a continuous fluorescent assay. Importantly, the estimated K(m) value for bovine testes hyaluronidase using FRET-HA as the substrate was in excellent agreement with K(m) values reported previously for this enzyme using native (i.e., unlabeled) HA. Therefore, FRET-HA is a reliable substrate for quantitatively assessing the HA/hyaluronidase molecular interaction. The simplicity, sensitivity, and versatility of the FRET-HA substrate suggest that it will have utility in a variety of assay platforms and should be a new tool for assessing hyaluronidase activity.

Correlation of serum arylesterase activity on phenylacetate estimated by the integrated method to common classical biochemical indexes of liver damage

The correlation of serum arylesterase (PON1) activity on phenylacetate determined by an integrated method to classical biochemical indexes of liver damage was investigated for the use of PON1 activity to evaluate liver damage. PON1 reaction curve as absorbance at 270 nm for 0.20 mmol/L phenylacetate hydrolysis was analyzed by the integrated method to determine maximal PON1 reaction rate. Classical biochemical indexes of liver damage were determined routinely. The 95% confidence threshold of PON1 activity in sera from healthy individuals was 2.12 mkat/L [(4.73+/-1.31) mkat/L, n=105]. PON1 activity in clinical sera was closely correlated to serum albumin, total protein and the ratio of albumin to globulins, but was weakly correlated to both direct and total bilirubin in serum. There were no correlations of PON1 activity to gamma-glutamyltransferase, alkaline phosphatase, alanine aminotransferase and aspartate aminotransferase. Among 127 clinical sera with PON1 activity>2.12 mkat/L, there were 92% healthy individuals examined by albumin, 90% healthy individuals examined by total protein, 88% healthy individuals examined by total bilirubin, 86% healthy individuals examined by direct bilirubin and 64% healthy individuals examined by the ratio of albumin to globulins, respectively. In each group of healthy individuals judged by classical biochemical indexes of close correlation to PON1 activity, percentage of healthy individuals examined by PON1 activity was always >80%. These results suggested PON1 activity on phenylacetate estimated by the integrated method was also suitable for the evaluation of liver damage.

Integrated rate equation considering product inhibition and its application to kinetic assay of serum ethanol

Kinetic assay of serum ethanol was investigated by predicting maximal product absorbance at 340 nm (A(mk)) through fitting to the yeast alcohol dehydrogenase reaction curve with the integrated rate equation, taking into account product inhibition in the presence of semicarbazide. Predicted A(mk) linearly responded to the preset constant of steady-state concentration of acetaldehyde (C(ald)). An exponential correlation function was established between desired C(ald) and putative A(mk) for authentic ethanol. For unknown samples, iterative fitting to reaction curve till preset constant C(ald) and resultant A(mk) satisfied this exponential correlation function yielded A(mk) with variation coefficient <4.3%. Variations in enzyme activity, data range and kinetic parameters showed negligible effects. The recovery was consistent to 100% with resistance to methanol and isopropanol. The upper limit of linear response for A(mk) was about 40 times of the lower limit. These results indicated that this kinetic method was reliable for serum ethanol assays with obvious advantages.

Evaluation of a kinetic uricase method for serum uric acid assay by predicting background absorbance of uricase reaction solution with an integrated method

A patented kinetic uricase method was evaluated for serum uric acid assay. Initial absorbance of the reaction mixture before uricase action (A(0)) was obtained by correcting the absorbance at 293 nm measured before the addition of uricase solution, and background absorbance (A(b)) was predicted by an integrated method. Uric acid concentration in reaction solution was calculated from A, the difference between A(0) and A(b), using the absorptivity preset for uric acid. This kinetic uricase method exhibited CV<4.3% and recovery of 100%. Lipids, bilirubin, hemoglobin, ascorbic acid, reduced glutathione and xanthine <0.32 mmol/L in serum had no significant effects. A linearly responded to 1.2 to 37.5 micromol/L uric acid in reaction solution containing 15 microl serum. The slope of linear response was consistent with the absorptivity preset for uric acid while the intercept was consistent with that for serum alone. Uric acid concentrations in clinic sera by different uricase methods positively correlated to each other. By Bland-Altman analysis, this kinetic uricase method accorded with that by quantifying the total change of UV absorbance on the completion of uricase reaction. These results demonstrated that this kinetic uricase method is reliable for serum uric acid assay with enhanced resistance to both xanthine and other common errors, wider range of linear response and much lower cost.