A calculator program for clinical application of the Bayesian method of predicting plasma drug levels

A pharmacokinetic program that allows individualization of drug dosage regimens through the Bayesian method is described. The program, which is designed for the Hewlett-Packard HP-41 CV calculator, is based upon the one-compartment open model with either instantaneous or zero-order absorption. Individualized estimation of the patient's kinetic parameters (clearance and volume of distribution) is performed by analyzing the plasma levels measured in the patient as well as considering the population data of the drug. After estimating the individual kinetic parameters by the Bayesian method, the program predicts the dosage regimen that will elicit the desired peak and trough plasma levels at steady state. For comparison purposes, the least-squares estimates for clearance and volume of distribution are calculated, and dosage prediction can also be made on the basis of the least-squares estimates. The least-squares estimates can be used to calculate population pharmacokinetic parameters according to the Standard Two-Stage method. Several examples of clinical use of the program are presented. The examples refer to patients with classic hemophilia who were treated with Factor VIII concentrates. In these patients, the Bayesian kinetic parameters of Factor VIII have been estimated through the calculator program. The Bayesian parameter estimates generated by the HP-41 have been compared with those determined by a Bayesian program (ADVISE) designed for microcomputers.     

Microcomputer simulation of steady-state enzyme kinetics for educational purposes

A BASIC program to assist the instruction of steady-state enzymekinetics has been developed for the IBM PC microcomputer. Itspurpose is to simulate laboratory experiments in order to minimizethe time required to obtain kinetic data from which studentsdeduce kinetic mechanisms and determine kinetic constants ofenzyme-catalyzed reactions. The program randomly selects a kineticscheme from various sequential, ping pong, and iso reactionsequences as well as values for the kinetic constants. The schemeand kinetic constants are unknown to the student at this time;the only thing he or she knows is the stoichiometry of the catalyzedreaction which can have two or three substrates and products.The student is prompted to enter values for concentrations ofsubstrates and products; several different concentrations foreach substrate and product can be entered in a single experiment.The program then calculates, displays and prints (if desired)the corresponding initial steadystate velocities. The studentcan perform as many experiments as desired until enough informationis obtained to determine the kinetic mechanism and to calculatevalues for the kinetic constants. Received on March 10, 1986; accepted on May 6, 1986     

MIR: a versatile program for the statistical analysis of enzyme kinetic data

We have developed a package program for the estimation of Michaelis-Menten parameters for enzymes that conform to different kinetic mechanisms. Data from different experimental schemes can be fitted with appropriate weighing factors to any of 6 mathematical models, corresponding to 5 kinetic mechanisms: ordered bi-bi, Theorell-Chance, rapid equilibrium random bi-bi, rapid equilibrium ordered bi-bi and ping pong bi-bi. The program also performs a significance test to discriminate between different candidate models. To illustrate the performance of the program, real data from kinetic experiments with glucose 6-phosphate from Leuconostoc mesenteroides have been fitted to different mathematical models, and the results are discussed. The program can be easily implemented for the fitting of kinetic data to any other model.     

Some Formal Approaches to the Analysis of Kinetic Data in Terms of Linear Compartmental Systems

A formal approach to the routine analysis of kinetic data in terms of linear compartmental systems is presented. The methods of analysis are general in that they include much of the theory in common use, such as direct solution of differential equations, integral equations, transfer functions, fitting of data to sums of exponentials, matrix solutions, etc. The key to the formalism presented lies in the fact that a basic operational unit—called “compartment”—has been defined, in terms of which physical and mathematical models as well as input and output functions can be expressed. Additional features for calculating linear combinations of functions and for setting linear dependence relations between parameters add to the versatility of this method. The actual computations for the values of model parameters to yield a least squares fit of the data are performed on a digital computer. A general computer program was developed that permits the routine fitting of data and the evolution of models.     

Kinetic analysis of the mechanism of action of beta-glucosidase from Botryodiplodia theobromae Pat.

1. The kinetic mechanism of beta-glucosidase (beta-D-glucoside glucohydrolase, EC 3.2.1.21) of Botryodiplodia theobromae Pat. has been studied in the presence of competing glucosyl acceptors. 2. Glycerol, fructose, sucrose, cellobiose and to a much lesser extent, maltose can act as glucosyl acceptors, apart from water. 3. Evidence confirming and supporting the kinetic mechanism previously postulated (Umezurike, G.M. (1971) Biochim. Biophys. Acta. 250, 182-191) is presented. 4. A theoretical kinetic analysis of the behaviour of the enzyme in the presence of two alternative glucosyl acceptors in addition to water is found to be consistent with experimental observation, suggesting a system in which both donor and acceptors bind to the enzyme in a random fashion to form ternary complexes. 5. The results are discussed in terms of the mechanism of group-transfer reactions.     

A biokinetic model to describe consequences of inhibition/stimulation in DNA-proofreading and repair-1. Development of the model

A biokinetic model is described which deals with the mathematical consequences of the inhibition or stimulation of DNA proofreading. It demonstrates the development of the number of DNA mismatch-dependent cells (e.g. cells with a malignant phenotype), where such mismatches arise by the in situ interaction of various substances with nucleotides of the DNA. The model can test for consequences by a logic gating on an "if-then" type of analysis in relation to the separate and consecutive processes of proofreading and repair. In particular, the consequences are considered in cases where either (i) the efficacy of proofreading and repair are reduced/prevented (inhibited) or (ii) are increased by some form of stimulation. On the chosen kinetic parameters, the model is accessible to manipulation as new data arising from further investigations become available and are introduced. The model is based on recently published data which show that an increased "mutant fraction" (see note on terms) arises in DNA replication when intracellular nucleotide pools show "asymmetries" (see note on terms). Extraordinarily high mutant fractions can be predicted/have been recorded in the presence of proofreading inhibitors. The model expresses data in mathematical terms of the competition between the development of mismatch-dependent cells and those with authentic genetic information. (Feedback and metastasis-effects and those of wild-type replicates are included.) A computerized (numerical) integration of the corresponding set of differential equations is offered. (A diskette with the program CANCER.xls is available upon request.)     

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.     

Fitting kinetic data for two independent saturable terms by MULTIFIT II, a general purpose curve fitting program in FORTRAN IV

The present report describes multifit ii, a fortran program for fitting data to non-linear equations and its application to biphasic kinetic data. Biphasic plots are encountered, e.g. in cases of enzymatic reactions and in the area of amino acid transport across biological membranes. This program gives a least squares fit of an equation to data, and obviates the need for non-statistical approximations, with their inherent bias. Equations to be fit are written in the form (numerator)/(denominator), where each may contain up to four terms, and each term may be a maximum of fourth order, including up to four independent variables. Data may be fit by the present program in either direct or reciprocal form. The approach taken is an iterative procedure (Newton's method). Scaling and weighting of data are incorporated. Parameters used to generate ideal test data in biphasic kinetic plots were recovered to four significant figures. The utility of the program in fitting real biphasic data obtained from amino acid transport experiments is demonstrated.     

Mathematical analysis of cancer chemotherapy: The effects of chemotherapeutic agents on the cell cycle traverse

For the tumor model of Skipper and Zubrod, which has been analyzed previously for the theoretical FLM function and the effect of chemotherapy against tumors of known or assumed kinetic characteristics, the theoretical continuous labeling (CL) function is derived by considering an equivalent tumor (in terms of unlabeled cell populations) in which the density function of phase duration of cells inS-phasef ₂(a ₂)=δ(a ₂−∞) and the loss functionL ₂(t)=0. This mathematical concept of blocking is applied to the analysis of synchronization in tumor growth and blocking effects in cancer chemotherapy. These effects of chemical agents on the cell cycle progression are being incorporated into a previously written computer simulation program for cancer chemotherapy. Whereas, a program is written and used to simulate the CL functions for L1210 leukemia, and primary and metastatic Lewis lung carcinoma.     

Rapid simulation and analysis of isotopomer distributions using constraints based on enzyme mechanisms: an example from HT29 cancer cells

MOTIVATION: Addition of labeled substrates and the measurement of the subsequent distribution of the labels in isotopomers in reaction networks provide a unique method for assessing metabolic fluxes in whole cells. However, owing to insufficiency of information, attempts to quantify the fluxes often yield multiple possible sets of solutions that are consistent with a given experimental pattern of isotopomers. In the study of the pentose phosphate pathways, the need to consider isotope exchange reactions of transketolase (TK) and transaldolase (TA) (which in past analyses have often been ignored) magnifies this problem; but accounting for the interrelation between the fluxes known from biochemical studies and kinetic modeling solves it. The mathematical relationships between kinetic and equilibrium constants restrict the domain of estimated fluxes to the ones compatible not only with a given set of experimental data, but also with other biochemical information. METHOD: We present software that integrates kinetic modeling with isotopomer distribution analysis. It solves the ordinary differential equations for total concentrations (accounting for the kinetic mechanisms) as well as for all isotopomers in glycolysis and the pentose phosphate pathway (PPP). In the PPP the fluxes created in the TK and TA reactions are expressed through unitary rate constants. The algorithms that account for all the kinetic and equilbrium constant constraints are integrated with the previously developed algorithms, which have been further optimized. The most time-consuming calculations were programmed directly in assembly language; this gave an order of magnitude decrease in the computation time, thus allowing analysis of more complex systems. The software was developed as C-code linked to a program written in Mathematica (Wolfram Research, Champaign, IL), and also as a C++ program independent from Mathematica. RESULTS: Implementing constraints imposed by kinetic and equilibrium constants in the isotopomer distribution analysis in the data from the cancer cells eliminated estimates of fluxes that were inconsistent with the kinetic mechanisms of TK and TA. Fluxes measured experimentally in cells can be used to estimate better the kinetics of TK and TA as they operate in situ. Thus, our approach of integrating various methods for in situ flux analysis opens up the possibility of designing new types of experiments to probe metabolic interrelationships, including the incorporation of additional biochemical information. AVAILABILITY: Software is available freely at: http://www.bq.ub.es/bioqint/selivanov.htm CONTACT: martacascante@ub.edu     

Thermodynamic non-ideality as an alternative source of the effect of sucrose on the thrombin-catalyzed hydrolysis of peptide p-nitroanilide substrates

The inhibitory effect of sucrose on the kinetics of thrombin-catalyzed hydrolysis of the chromogenic substrate S-2238 (D-phenylalanyl-pipecolyl-arginoyl-p-nitroanilide) is re-examined as a possible consequence of thermodynamic non-ideality-an inhibition originally attributed to the increased viscosity of reaction mixtures. However, those published results may also be rationalized in terms of the suppression of a substrate-induced isomerization of thrombin to a slightly more expanded (or more asymmetric) transition state prior to the irreversible kinetic steps that lead to substrate hydrolysis. This reinterpretation of the kinetic results solely in terms of molecular crowding does not signify the lack of an effect of viscosity on any reaction step(s) subject to diffusion control. Instead, it highlights the need for development of analytical procedures that can accommodate the concomitant operation of thermodynamic non-ideality and viscosity effects.     

HERSIM: a microcomputer program designed to compute the limits of conversion for real homogeneous isothermal enzymic reactors

HERSIM is a program written in BASIC designed to aid the investigatorinterested in determining the substrate conversion in a realhomogeneous isothermal enzymic reactor, for various kineticequations. The program runs after tracer data relative to aDirac impulse to the reactor have been entered, and computesthe two limits of real conversion: total segregation and maximummixedness. The kinetic constants of the reacting system areinput as data, and the variation of conversion with reactortemperature between given limits is computed as accurately asrequested. Received on November 6, 1986; accepted on March 4, 1987     

Analysis of Ter-Ter enzyme kinetic mechanisms by computer simulation of isotope exchange at chemical equilibrium: development and application of ISOTER, a personal-computer-based program

A convenient, personal-computer-based program has been developed that allows simulation of isotopic exchange kinetics at chemical equilibrium catalyzed by a three reactant-three product (TerTer) enzyme system: A + B + C integral of P + Q + R. This program, ISOTER, utilizes a rapid algebraic method to calculate the exchange rate between any reactant-product pair as a function of the substrate concentration and avoids altogether the necessity of deriving an explicit (but cumbersome and impractical) equation for exchange rate. ISOTER was used to generate model saturation patterns for 16 different TerTer kinetic mechanisms, varying different combinations of reactant-product pairs in constant ratio at equilibrium: [all substrates], [A, P], [B, Q], and [C, R], while holding the nonvaried components constant. These model studies indicate that virtually every one of these mechanisms can be distinguished from the others. In addition, ISOTER has been used to fit multiple sets of experimental data for Escherichia coli glutamine synthetase, which produced a set of rate constants consistent with the previously proposed "preferred order random" kinetic mechanism.     

Evaluation of the kinetic energy of the torso by magneto-inertial measurement unit during the sit-to-stand movement

Sit-to-stand tests are used in geriatrics as a qualitative issue in order to evaluate motor control and stability. In terms of measured indicators, it is traditionally the duration of the task that is reported, however it appears that the use of the kinetic energy as a new quantitative criterion allows getting a better understanding of musculoskeletal deficits of elderly subjects. The aim of this study was to determine the feasibility to obtain the measure of kinetic energy using magneto-inertial measurement units (MIMU) during sit-to-stand movements at various paces. 26 healthy subjects contributed to this investigation. Measured results were compared to a marker-based motion capture using the correlation coefficient and the normalized root mean square error (nRMSE). nRMSE were below 10% and correlation coefficients were over 0.97. In addition, errors on the mean kinetic energy were also investigated using Bland-Altman 95% limits of agreement (0.63 J–0.77 J), RMSE (0.29 J–0.38 J) and correlation coefficient (0.96–0.98). The results obtained highlighted that the method based on MIMU data could be an alternative to optoelectronic data acquisition to assess the kinetic energy of the torso during the sit-to-stand test, suggesting this method as being a promising alternative to determine kinetic energy during the sit-to-stand movement.     

Kinetic study of the reduction mechanism for Desulfovibrio gigas cytochrome c3.

The kinetic aspects of the reduction process in cytochrome c3 from Desulfovibrio gigas have been investigated over a wide range of pH values ranging between pH 5.8 and pH 9.8. The data have been analyzed in the framework of an I2H4 interaction network coupled to a proton-linked equilibrium between two tertiary structures (Cornish-Bowden, A. & Koshland, D.E. Jr (1970) J. Biol. Chem. 245, 6241-6250). The kinetic rate constants for the reduction of the four hemes for the two tertiary conformations have been characterized in the framework of the thermodynamic network obtained from the equilibrium analysis (Coletta, M., Catarino, T., LeGall, J.J. & Xavier, A.V. (1991) Eur. J. Biochem. 202, 1101-1106). The intrinsic reduction rate constants determined by reaction with sodium dithionite for two hemes (namely heme 4 and heme 1) are significantly faster than those for the other two heme residues. In view of the equilibrium redox properties, heme 4 (with the fastest reduction rate) may then work as the kinetic electron-capturing site for the electrons from sodium dithionite. The transfer to hemes 2 and 3 then occurs by virtue of their free-energy levels at equilibrium. At our experimental conditions, there is also transfer of electrons to hemes 2 and 3 from heme 1, which is reduced at a slower rate than heme 4, thus contributing to the biphasic kinetics observed for the overall process. The kinetic parameters obtained are discussed in terms of the mechanism proposed for the coupling between the electron and proton transfer, as induced by the heme/heme cooperativity network.     

Characterization of alternate reductant binding and electron transfer in the dopamine beta-monooxygenase reaction

The steady-state limiting kinetic parameters Vmax, V/KDA, and V/KO2, together with deuterium isotope effects on these parameters, have been determined for the dopamine beta-monooxygenase (D beta M) reaction in the presence of structurally distinct reductants. The results show the one-electron reductant ferrocyanide to be nearly as kinetically competent as the presumed in vivo reductant ascorbate. Further, a reductant system of ferricyanide plus substrate dopamine yields steady-state kinetic parameters and isotope effects very similar to those measured solely in the presence of ferrocyanide, indicating a role for catecholamine in the rapid recycling of oxidized ferrocyanide. Use of substrate dopamine as the sole reductant is found to lead to a highly unusual kinetic independence of oxygen concentration, as well as significantly reduced values of Vmax and V/KDA, and we conclude that dopamine reduces enzymic copper in a rate-limiting step that is 40-fold slower than with ascorbate. The near-identical kinetic parameters measured in the presence of either ascorbate or ferrocyanide, together with markedly reduced rates with dopamine, are interpreted in terms of a binding site for reductant that is physically distinct from the substrate binding site. This view is supported by molecular modeling, which reveals ascorbate and ferrocyanide to possess an unexpected similarity in potential sites for interaction with enzymic residues. With regard to electron flux, identical values of V/KO2 have been measured with [2,2-2H2]dopamine as substrate both in the presence and in the absence of added ascorbate.(ABSTRACT TRUNCATED AT 250 WORDS)     

Iteration model of starch hydrolysis by amylolytic enzymes.

An elaborate computer program to simulate the process of starch hydrolysis by amylolytic enzymes was been developed. It is based on the Monte Carlo method and iteration kinetic model, which predict productive and non-productive amylase complexes with substrates. It describes both multienzymatic and multisubstrate reactions simulating the "real" concentrations of all components versus the time of the depolymerization reaction the number of substrates, intermediate products, and final products are limited only by computer memory. In this work, it is assumed that the "proper" substrate for amylases is the glucoside linkages in starch molecules. Dynamic changes of substrate during the simulation adequately influence the increase or decrease of reaction velocity, as well as the kinetics of depolymerization. The presented kinetic model, can be adapted to describe most enzymatic degradations of a polymer. This computer program has been tested on experimental data obtained for alpha- and beta-amylases.     

Physico-chemical study of the heterogeneous population of opioid receptors

A physico-chemical analysis of the heterogenous population of opioid receptors was carried out. A new difference approach to the analysis of heterogenous receptor systems was developed. This procedure permits to estimate even in high stringency conditions of parameters of three or more types of receptors from the binding isotherms or competitive replacement curves as well as to determine the total receptor concentration in the system. A DELTA computer program based on this difference approach has been developed. The experimental results obtained through the use of the difference technique led to a kinetic model of interaction between morphine and D-Ala2, D-Leu5-enkephalin with rat brain receptors. This model based on the interaction of each ligand with three types of specific binding sites can be used for the determination of kinetic and thermodynamic parameters.     

Biosynthesis of heparin/heparan sulfate: kinetic studies of the glucuronyl C5-epimerase with N-sulfated derivatives of the Escherichia coli K5 capsular polysaccharide as substrates

The D-glucuronyl C5-epimerase involved in the biosynthesis of heparin and heparan sulfate was investigated with focus on its substrate specificity, its kinetic properties, and a comparison of epimerase preparations from the Furth mastocytoma and bovine liver, which synthesize heparin and heparan sulfate, respectively. New substrates for the epimerase were prepared from the capsular polysaccharide of Escherichia coli K5, which had been labeled at C5 of its D-glucuronic and N-acetyl-D-glucosamine moieties by growing the bacteria in the presence of D-[5-(3)H]glucose. Following complete or partial ( approximately 50%) N-deacetylation of the polysaccharide by hydrazinolysis, the free amino groups were sulfated by treatment with trimethylamine.SO(3)complex, which yielded products that were recognized as substrates by the epimerase and released tritium from C5 of the D-glucuronyl residues upon incubation with the enzyme. Comparison of the kinetic properties of the two substrates showed that the fully N-sulfated derivative was the best substrate in terms of its K(m)value, which was significantly lower than that of its partially N-acetylated counterpart. The V(max)values for the E.coli polysaccharide derivatives were essentially the same but were both lower than that of the O-desulfated [(3)H]heparin used in our previous studies. Surprisingly, the apparent K(m)values for all three substrates increased with increasing enzyme concentration. The reason for this phenomenon is not entirely clear at present. Partially purified C5-epimerase preparations from the Furth mastocytoma and bovine liver, respectively, behaved similarly in terms of their reactivity towards the various substrates, but the variation in apparent K(m)values with enzyme concentration precluded a detailed comparison of their kinetic properties.