Estimation of parameters in double uptake systems.

A method is presented for estimating the kinetic parameters describing the cellular uptake of a single molecular species mediated by two independent transport processes. Two cases are considered: first, uptake by two carrier-mediated transport systems, and second, uptake by a single carrier-mediated system and diffusion. Unweighted and weighted least-squares estimations are described; the unweighted estimation is noniterative and provides excellent first approximations for the iterative weighted estimation procedure.     

The influence of signal noise on the accuracy of kinetic constants measured by surface plasmon resonance experiments.

An analysis is carried out to investigate the accuracy of kinetic parameters obtained using surface plasmon resonance methodology with a BIAcore instrument. The Cramer Rao lower bound for the least possible variance of an estimator of the kinetic parameters is determined. Using simulations it is shown that the standard least-squares estimation technique provides estimates that achieve this bound. The theoretical and simulation results are compared with experimental data obtained from an analysis of the interaction of the myc peptide with the anti-myc antibody, 9E10. This investigation indicates that the accuracy of the results depends on the signal level which has particular relevance to the design of experiments with low signal levels. It is shown how the accuracy of the estimates of the kinetic constants depends on the kinetic constants themselves and how the accuracy of the association constants depends on the concentration of the analyte that is used in the experiment. In addition, the effects of increasing the number of data points in the analysis of dissociation data on the accuracy of the estimates are quantitated. It is also demonstrated that signal averaging of data derived from repeat sensorgrams can result in a significant decrease in the standard deviation of the estimates.     

The 48 kDa Ca2+-binding protein of bovine brain.

The integrated rate equation for reactions with stoichiometry A----P + Q is: e0t = -Cf . ln(1-delta P/A0) + C1 delta P + 1/2C2(delta P)2 where the coefficients C are linear or quadratic functions of the kinetic constants and the initial substrate and product concentrations. I have used the 21 progress curves described in the accompanying paper [Cox & Boeker (1987) Biochem. J. 245, 59-65] to develop computer-based analytical and statistical techniques for extracting kinetic constants by fitting this equation. The coefficients C were calculated by an unweighted non-linear regression: first approximations were obtained from a multiple regression of t on delta P and were refined by the Gauss-Newton method. The procedure converged in six iterations or less. The bias in the coefficients C was estimated by four methods and did not appear to be significant. The residuals in the progress curves appear to be normally distributed and do not correlate with the amount of product produced. Variances for Cf, C1 and C2 were estimated by four resampling procedures, which gave essentially identical results, and by matrix inversion, which came close to the others. The reliability of C2 can also be estimated by using an analysis-of-variance method that does not require resampling. The final kinetic constants were calculated by standard multiple regression, weighting each coefficient according to its variance. The weighted residuals from this procedure were normally distributed.     

Combining probability from independent tests: the weighted Z-method is superior to Fisher's approach

The most commonly used method in evolutionary biology for combining information across multiple tests of the same null hypothesis is Fisher's combined probability test. This note shows that an alternative method called the weighted Z-test has more power and more precision than does Fisher's test. Furthermore, in contrast to some statements in the literature, the weighted Z-method is superior to the unweighted Z-transform approach. The results in this note show that, when combining P-values from multiple tests of the same hypothesis, the weighted Z-method should be preferred.     

UDP-glucuronosyltransferase: fluorometric determination and microcomputer method for bisubstrate kinetics analysis

A method for analysing UDP-glucuronosyltransferase activity in rainbow trout hepatic microsomes is described, using 1-naphthol as a substrate and fluorometric determination of glucuronide. Kinetic constants are computed with a classical plot in a weighted regression. The computer uses the least-squares method for each value of a variable which is set and incremented. To get confidence intervals, the computer generates random values around experimental data (in a confidence interval they determine), and then computes again. With each simulation, a weighted regression with classical secondary plots gives simulated kinetic parameters. From each population of simulated values, an interval containing a given percentage of the population is determined.     

Analysis of progress curves by simulations generated by numerical integration.

A highly flexible computer program written in FORTRAN is presented which fits computer-generated simulations to experimental progress-curve data by an iterative non-linear weighted least-squares procedure. This fitting procedure allows kinetic rate constants to be determined from the experimental progress curves. Although the numerical integration of the rate equations by a previously described method [Barshop, Wrenn & Frieden (1983) Anal. Biochem. 130, 134-145] is used here to generate predicted curves, any routine capable of the integration of a set of differential equations can be used. The fitting program described is designed to be widely applicable, easy to learn and convenient to use. The use, behaviour and power of the program is explored by using simulated test data.     

Determination of active concentrations and association and dissociation rate constants of interacting biomolecules: an analytical solution to the theory for kinetic and mass transport limitations in biosensor technology and its experimental verification

Accurate determination of kinetic rate constants for interacting biomolecules requires knowledge of the active concentrations of the participating molecules. Also, in other biomedical and clinical applications, sensitive, precise and accurate methods are needed to determine the concentration of biologically active molecules, which frequently constitute only a fraction of the total molecular pool. Here we report a novel development of the approach to determining active concentrations based on surface plasmon resonance (SPR) technology. The method relies on changes in binding rates with varying flow rates under conditions of partial mass transport, and does not require standards of known concentrations, given that the molecular mass of the molecule of interest is known. We introduce an analytical solution to the differential equations describing the formation of a 1:1 bimolecular complex, taking into account both the association and dissociation reactions, under partial mass transport limitations. This solution can be used in global fitting to binding curves obtained at different flow rates. The accuracy, precision, and sensitivity of this approach were determined in experiments involving binding of tyrosine-phosphorylated recombinant proteins to anti-phosphotyrosine antibodies, where the active concentration could be determined independently by in vitro phosphorylation with (33)P. There was an excellent agreement between the active concentrations determined by the analytical SPR-based method and by determination of the level of radioactivity of the phosphorylated protein. The SPR-based method allows determination of protein concentrations at picomolar levels. A procedure for accurate determinations of association and dissociation rate constants, based on the analytical solution of the mass transport and binding theory, is outlined.     

Average nucleotide diversity should be weighted by per-site sample size

Konopiński (2022) suggests that when averaging nucleotide diversity over a sequence, ignoring per-site sample size variation (i.e., using an unweighted mean) offers an improvement in precision (lower variation) and accuracy (reduced bias). Here, I argue that preserving uncertainty due to variation in sample size is in line with best statistical practices, and that the increase in accuracy observed is not a general feature of the unweighted mean proposed by Konopiński (2022). As such, I conclude that the use of a weighted mean, as employed by (Korunes & Samuk, 2020), remains the preferred method for averaging nucleotide diversity over multiple sites.     

Pyrolysis characteristics and kinetics of oak trees using thermogravimetric analyzer and micro-tubing reactor

In this work, pyrolysis characteristics were investigated using thermogravimetric analysis (TGA) at heating rates of 5-20 degrees C/min. Most of the materials were decomposed between 330 degrees C and 370 degrees C at each heating rate. The average activation energy was 236.2 kJ/mol when the pyrolytic conversion increased from 5% to 70%. The pyrolysis kinetics of oak trees was also investigated experimentally and mathematically. The experiments were carried out in a tubing reactor at a temperature range of 330-370 degrees C with a reaction time of 2-8 min. A lump model of combined series and parallel reactions for bio-oil and gas formation was proposed. The kinetic parameters were determined by nonlinear least-squares regression from the experimental data. It was found from the reaction kinetic constants that the predominant reaction pathway from the oak trees was to bio-oil formation rather than to gas formation at the investigated temperature range.     

Parameter estimation for ligand binding systems kinetics applied to 1,25-dihydroxycholecalciferol

A mathematical analysis of the kinetics of the hormone-receptor interaction was applied to the 1,25-dihydroxycholecalciferol-intestinal receptor system. The exact analytical solution and the numerical integration of the kinetic equation were installed in a Statistical Analysis System (SAS) computer program to estimate the rate constants of the reaction. Estimates of the parameters obtained by these two methods are similar, demonstrating that the numerical integration can be combined with the nonlinear regression procedure for least-squares parameter fitting using a simple SAS program. This enables estimation of kinetics rate constants when the kinetic equation cannot be solved analytically. The ratio of the rate constants (ka/kd) found by the nonlinear procedure is close to the independently determined equilibrium (Scatchard) constant in the nonlinear analysis.     

Determination of rate constants for the reaction of hydroxyl radicals with some purines and pyrimidines using sunlight

Sunlight mediated hydroxyl radical production from aqueous ferric perchlorate at low pH has been investigated using deoxyribose-thiobarbituric acid assay. The rate of production of hydroxyl radical was found to be dependent on the time of irradiation. Hydroxyl radical scavengers can compete with deoxyribose for hydroxyl radicals produced in the system leading to a decreased yield of thiobarbituric acid chromogen. The second-order rate constants of the added scavengers can be determined using a simple competition kinetic method. The rate constants for the reaction of hydroxyl radical with a number of purine and pyrimidine derivatives were determined using this method. The rate constants obtained (1-7 x 10(9) dm(3) mol(-1) s(-1)) were found to be in good agreement with those reported using pulse radiolysis technique. The rate constants of dimethyluracil, xanthosine, amino and methyl substituted pyrimidines, cytidine monophosphate and uridine monophosphate were also determined by this method. It is proposed that sunlight mediated production of hydroxyl radical coupled with deoxyribose-thiobarbituric acid assay is a simple and efficient method for the determination of rate constants for the reaction of hydroxyl radical with a wide range of biomolecules.     

Canonical sensitivities: a useful tool to deal with large perturbations in metabolic network modeling

The dynamic range of metabolic models can be extended to deal with large perturbations by introducing the related concepts of "generalized" kinetic order and "canonical" sensitivities. Generalized kinetic orders are built as a well-defined non linear combination of the canonical sensitivities coefficients, which in turn are obtained by a least-squares regression on central composite factorial design data. In a such way, the whole domain of the operating variables is mapped without need to determine locally neither the first nor the second order model derivatives. The method was validated through numerical simulations, its predictions being compared with those coming from a Michaelis-Menten formalism taken as reference. In parallel, two variants of the Power-law formalism (S-system, least-squares GMA) also were tested. The canonical sensitivities method produced the widest range to predict metabolite concentrations and metabolic fluxes at the steady states. In addition, the variation pattern for the logarithmic gains and for the characteristic eigenvalues have been accurately determined from a unique overall model, being both required to make realistic analysis in metabolic engineering. The achieved information also can be expressed in terms of those typical coefficients derived from the Metabolic Control Analysis (MCA). Even if current first order Power-law or MCA formalisms were used, the canonical sensitivities approach provides a significant advantage, since complete sets of homologous, accurate, locally valid metabolic coefficients can be simultaneously recovered from the array proposed, being representative of the whole range of the operating variables instead of a unique nominal condition as is usual.     

Development and validation of a sensitive liquid chromatography/tandem mass spectrometry method for the determination of exemestane in human plasma

Exemestane, irreversible steroidal aromatase inhibitor, acts as a false substrate for aromatase enzyme and significantly lowers circulating estrogen concentrations in postmenopausal women with hormone-sensitive breast cancer. A sensitive bioanalytical method was developed and validated to study pharmacokinetics of exemestane. The method was based on liquid-liquid extraction of exemestane with methyl t-butyl ether followed by reversed-phase liquid chromatography. Positive electrospray ionization tandem mass spectrometry in multiple reaction monitoring mode was applied for detection of exemestane. Anastrozole was used as internal standard. Calibration curve, fitted to 1/x2 weighted linear regression model, was linear in the range of 0.1-40.0 ng/mL. Intra-run precision and accuracy were 1.80-3.17% and 103.4-111.5%, respectively. Inter-run precision and accuracy measured within 3 days were 3.37-4.19% and 101.8-109.6%, respectively. Extraction recoveries of exemestane and internal standard were 79.7-86.2% and 82.9-83.6%, respectively. The method was fully validated and may be applied to pharmacokinetic studies in humans after a single dose administration of 25mg exemestane tablets.     

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.     

An evolutionary approach to enzyme kinetics: Optimization of ordered mechanisms

A theoretical investigation is presented which allows the calculation of rate constants and phenomenological parameters in states of maximal reaction rates for unbranched enzymic reactions. The analysis is based on the assumption that an increase in reaction rates was an important characteristic of the evolution of the kinetic properties of enzymes. The corresponding nonlinear optimization problem is solved taking into account the constraint that the rate constants of the elementary processes do not exceed certain upper limits. One-substrate-one-product reactions with two, three and four steps are treated in detail. Generalizations concern ordered uni-uni-reactions involving an arbitrary number of elementary steps. It could be shown that depending on the substrate and product concentrations different types of solutions can be found which are classified according to the number of rate constants assuming in the optimal state submaximal values. A general rule is derived concerning the number of possible solutions of the given optimization problem. For high values of the equilibrium constant one solution always applies to a very large range of the concentrations of the reactants. This solution is characterized by maximal values of the rate constants of all forward reactions and by non-maximal values of the rate constants of all backward reactions. Optimal kinetic parameters of ordered enzymic mechanisms with two substrates and one product (bi-uni-mechanisms) are calculated for the first time. Depending on the substrate and product concentrations a complete set of solutions is found. In all cases studied the model predicts a matching of the concentrations of the reactants and the corresponding Michaelis constants, which is in good accordance with the experimental data. It is discussed how the model can be applied to the calculation of the optimal kinetic design of real enzymes.     

Kinetic determinations of molecular interactions using Biacore--minimum data requirements for efficient experimental design

Reliable kinetic estimates can be obtained from significantly less data than is commonly used today, particularly in the characterization of 1:1 interactions involving low molecular weight compounds and proteins. We have designed a rational and cost-effective strategy to determine kinetic constants using Biacore's surface plasmon resonance-based biosensors and show that the number of measurements necessary for accurate kinetic determinations can be greatly reduced, increasing sample throughput and saving sample material. Simulated and measured data for a range of possible 1:1 interactants were studied to find the minimum requirements of a data set for kinetic analysis. The results showed that kinetic constants in the region 10(4) < k(a) < 10(7) M(-1) s(-1) (association) and 10(-4) < k(d) < 10(-1) s(-1) (dissociation) could easily be determined in a 1:1 interaction model. Owing to the information-dense nature of Biacore data, only two sample concentrations were necessary to reliably determine the kinetics. A standard sample concentration series consisting of 10-fold dilutions between approximately 10 microM and approximately 1 nM consistently provided at least two concentrations with sufficient information about the interaction in this region. Determinations of the constants became increasingly unreliable outside this region. If the rate constants prove to be outside the specified region or the data fits poorly to the 1:1-MTL model, more experiments are required. General recommendations for the design of a cost-effective assay to deliver reliable kinetic measurements are provided.     

Is the weighted z‐test the best method for combining probabilities from independent tests?

Through simulation, Whitlock showed that when all the alternatives have the same effect size, the weighted z-test is superior to both unweighted z-test and Fisher's method when combining P-values from independent studies. In this paper, we show that under the same situation, the generalized Fisher method due to Lancaster outperforms the weighted z-test.     

Quasi-equilibrium assumption for arbitrary mechanism of enzymatic reaction. criteria for existence of equilibrium segments

The possible application of the quasi-equilibrium assumption for an arbitrary mechanism of enzymatic reaction is considered. It is shown at what ratios of kinetic constants a segment consisting of two, three, and four intermediates may be considered as an equilibrium one. Expressions for evaluation of accuracy of distribution of intermediate concentrations inside the equilibrium segment and accuracy of determination of intermediate concentrations inside and outside the equilibrium segment as a function of the ratio of kinetic constants are derived. A method for determination of the limitations on the ratio of rate constants for an equilibrium segment of arbitrary structure is suggested.     

Quantitative label-free screening for antibodies using scattering biophotonic microarray imaging

A biophotonic array based on gold nanoparticles functionalized with antigen proteins has been used to determine the concentrations of the respective antibodies in solution. Four proteins—fibrinogen, bovine serum albumin, transferrin, and C-reactive protein—were used to construct a test array with the assay repeated a number of times. The antibody-antigen association and dissociation rate constants were determined for the antibody assays from a series of calibration experiments. The label-free determination of the unknown antibody concentrations was performed using two related kinetic analyses. From these results, the current array assay sensitivity is 250 ng ml^-1 with an accuracy of 15% using an 8-min kinetic measurement and a 16-spot averaged assay.