Integrated rate equations for irreversible enzyme-catalysed first-order and second-order reactions.
Ontology highlight
ABSTRACT:
SUBMITTER: Boeker EA
PROVIDER: S-EPMC1144673 | biostudies-other | 1985 Feb
REPOSITORIES: biostudies-other
Similar Datasets
Project description:Generalized rate equations covering all mechanisms giving hyperbolic initial-rate kinetics with stoichiometry A in equilibrium P, A in equilibrium P + Q, A + B in equilibrium P and A + B in equilibrium P + Q were integrated. The results are regular and reasonably economical.
| S-EPMC1144258 | biostudies-other
Project description:The computer analysis of progress curves for enzyme-catalysed reactions involves a series of mathematical and computational tasks. The three most daunting of these are the derivation of an integrated rate equation, solving this equation so that the amount of product formed by the reaction at any time can be calculated, and incorporating this solution into a non-linear-regression computer program. This paper describes the basis of a computer program that greatly simplifies the problem. The proposed mechanism is specified in the familiar kinetic constant form, which is automatically translated into a program capable of fitting this mechanism to a series of experimental progress curves. The approach is illustrated for a reversible reaction with one substrate and one product, and tested with some data obtained for the fumarase reaction. A copy of the program has been deposited as Supplementary Publication SUP 50148 (13 pages) at the British Library Document Supply Centre, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1989) 257, 5.
| S-EPMC1138375 | biostudies-other
Project description:We have used an integrated rate equation to analyse the reaction catalysed by the inducible arginine decarboxylase from Escherichia coli B. The stoichiometry Arginine----agmatine + CO2 is the simplest of the multiple-substrate/multiple-product cases. Twenty-one time courses were carried out at various initial concentrations of arginine and agmatine, and were then fitted to the integrated equation by using appropriate analytical procedures. Values were obtained for six of the seven possible kinetic constants, corresponding to kcat, KArg, the terms for competitive inhibition by agmatine, by CO2 and by agmatine and CO2 together, and the term for uncompetitive inhibition by agmatine. The uncompetitive constant for CO2 was indeterminate. Our results indicate that it is both practical and experimentally economical to obtain kinetic constants from full time courses.
| S-EPMC1148082 | biostudies-other
Project description:The rate equation for a tight-binding inhibitor of an enzyme-catalysed first-order reversible reaction was used to derive two integrated equations. One of them covers the situations in which competitive, uncompetitive or non-competitive inhibition occurs and the other refers to the special non-competitive case where the two inhibition constants are equal. For these equations, graphical and non-linear regression methods are proposed for distinguishing between types of inhibition and for calculating inhibition constants from progress-curve data. The application of the non-linear regression to the analysis of stimulated progress curves in the presence of a tight-binding inhibitor is also presented. The results obtained are valid for any type of 'dead-end'-complex-forming inhibitor and can be used to characterize an unknown inhibitor on the basis of progress curves.
| S-EPMC1133683 | biostudies-other
Project description:Progress curves of enzyme-catalysed reactions are described by equations of a type that precludes direct calculation of the extent of reaction at any time. Previously, such equations have been solved by the Newton-Raphson method, but this procedure may fail when based upon the usual formulae. An alternative formulation is proposed that is both quicker and more robust.
| S-EPMC1146728 | biostudies-other
Project description:Elastic materials are ubiquitous in nature and indispensable components in man-made devices and equipments. When a device or equipment involves composite or multiple elastic materials, elasticity interface problems come into play. The solution of three dimensional (3D) elasticity interface problems is significantly more difficult than that of elliptic counterparts due to the coupled vector components and cross derivatives in the governing elasticity equation. This work introduces the matched interface and boundary (MIB) method for solving 3D elasticity interface problems. The proposed MIB elasticity interface scheme utilizes fictitious values on irregular grid points near the material interface to replace function values in the discretization so that the elasticity equation can be discretized using the standard finite difference schemes as if there were no material interface. The interface jump conditions are rigorously enforced on the intersecting points between the interface and the mesh lines. Such an enforcement determines the fictitious values. A number of new techniques has been developed to construct efficient MIB elasticity interface schemes for dealing with cross derivative in coupled governing equations. The proposed method is extensively validated over both weak and strong discontinuity of the solution, both piecewise constant and position-dependent material parameters, both smooth and nonsmooth interface geometries, and both small and large contrasts in the Poisson's ratio and shear modulus across the interface. Numerical experiments indicate that the present MIB method is of second order convergence in both L∞ and L2 error norms for handling arbitrarily complex interfaces, including biomolecular surfaces. To our best knowledge, this is the first elasticity interface method that is able to deliver the second convergence for the molecular surfaces of proteins..
| S-EPMC4404754 | biostudies-literature
Project description:Heat capacity changes are emerging as essential for explaining the temperature dependence of enzyme-catalysed reaction rates. This has important implications for enzyme kinetics, thermoadaptation and evolution, but the physical basis of these heat capacity changes is unknown. Here we show by a combination of experiment and simulation, for two quite distinct enzymes (dimeric ketosteroid isomerase and monomeric alpha-glucosidase), that the activation heat capacity change for the catalysed reaction can be predicted through atomistic molecular dynamics simulations. The simulations reveal subtle and surprising underlying dynamical changes: tightening of loops around the active site is observed, along with changes in energetic fluctuations across the whole enzyme including important contributions from oligomeric neighbours and domains distal to the active site. This has general implications for understanding enzyme catalysis and demonstrating a direct connection between functionally important microscopic dynamics and macroscopically measurable quantities.
| S-EPMC5862990 | biostudies-literature
Project description:Pericyclic reactions-which proceed in a concerted fashion through a cyclic transition state-are among the most powerful synthetic transformations used to make multiple regioselective and stereoselective carbon-carbon bonds. They have been widely applied to the synthesis of biologically active complex natural products containing contiguous stereogenic carbon centres. Despite the prominence of pericyclic reactions in total synthesis, only three naturally existing enzymatic examples (the intramolecular Diels-Alder reaction, and the Cope and the Claisen rearrangements) have been characterized. Here we report a versatile S-adenosyl-l-methionine (SAM)-dependent enzyme, LepI, that can catalyse stereoselective dehydration followed by three pericyclic transformations: intramolecular Diels-Alder and hetero-Diels-Alder reactions via a single ambimodal transition state, and a retro-Claisen rearrangement. Together, these transformations lead to the formation of the dihydropyran core of the fungal natural product, leporin. Combined in vitro enzymatic characterization and computational studies provide insight into how LepI regulates these bifurcating biosynthetic reaction pathways by using SAM as the cofactor. These pathways converge to the desired biosynthetic end product via the (SAM-dependent) retro-Claisen rearrangement catalysed by LepI. We expect that more pericyclic biosynthetic enzymatic transformations remain to be discovered in naturally occurring enzyme 'toolboxes'. The new role of the versatile cofactor SAM is likely to be found in other examples of enzyme catalysis.
| S-EPMC5679075 | biostudies-literature
Project description:Design and analysis of cluster randomized trials must take into account the intraclass correlation coefficient (ICC), which quantifies the correlation among outcomes from the same cluster. Second-order generalized estimating equations (GEE2) provides a statistically robust way in estimating this quantity and other association parameters. However, GEE2 becomes computationally infeasible as cluster sizes grow. This paper proposes a stochastic variant to fitting GEE2 which alleviates reliance on parameter starting values and provides substantially faster speeds and higher convergence rates than the widely used deterministic Newton-Raphson method. We also propose new estimators for the ICC which account for informative missing outcome data through the use of GEE2, for which we incorporate a "second-order" inverse probability weighting scheme and "second-order" doubly robust (DR) estimating equations that guard against partial model misspecification. Our proposed methods are evaluated through simulations and applied to data from a cluster randomized trial in Bangladesh evaluating the effect of different marketing interventions on the use of hygienic latrines.
| S-EPMC7540735 | biostudies-literature
Project description:A method is presented for fitting the pairs of values product formed-time taken from progress curves to the integrated rate equation. The procedure is applied to the estimation of the kinetic parameters of the adenosine deaminase system. Simulation studies demonstrate the capabilities of this strategy. A copy of the FORTRAN77 program used can be obtained from the authors by request.
| S-EPMC1150168 | biostudies-other