Algebraic methods for deriving steady-state rate equations. Practical difficulties with mechanisms that contain repeated rate constants.
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ABSTRACT:
SUBMITTER: Cornish-Bowden A
PROVIDER: S-EPMC1164051 | biostudies-other | 1976 Oct
REPOSITORIES: biostudies-other
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Project description:A method is described for systematically deriving steady-state rate equations. It is based on the schematic method of King & Altman [J. Phys. Chem. (1956) 60, 1375-1378], but is expressed in purely algebraic terms. It is suitable for implementation as a computer program, and a program has been written in FORTRAN IV and deposited as Supplementary Publication SUP 50078 (12 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1977) 161, 1-2.
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Project description:The scope and limitations of a simple and satisfactory method of deducing steady-state rate equations is described. This method (called the Flux Method) consists in writing down the flux in successive steps of the reaction, and calculating the relative concentration of enzyme forms and thence the turnover time. Kinetic mechanisms for linear and branched pathways are used as examples of this method.
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Project description:A schematic method for the derivation of steady-state enzyme rate equations by using the Wang algebra is described. The method is simple, easy to learn and offers a substantial decrease in analytical effort over previously published algorithms. Being essentially an algebraic procedure the method can be readily computerized. Computer programs in BASIC and ALGOL languages have been deposited as Supplementary Publication SUP 50065 (19 pages) at the British Library (Lending Division), Boston Spa, Wetherby, W. Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1976). 153, 5.
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Project description:Methods are given whereby the steady-state kinetic characteristics of multienzyme reactions consisting of individual single-enzyme reactions linked by freely diffusible intermediates can be determined quantitatively from the experimentally determined complete algebraic rate equations for the individual reactions. The approach is based on the fact that a valid steady-state rate equation for such a multienzyme reaction, in terms of the rate equations for the individual reactions, can be obtained simply from knowledge of the relative rates of the individual reactions when the multienzyme reaction is in the steady state. A number of model multienzyme reactions, which differ as to structural arrangement of the individual reactions, are examined by this approach. Simple mathematical methods which are applicable to most of these models are given for direct calculation of dependent variables. It is either pointed out or demonstrated with Mathematica that the rate equations for all of these models can be handled very easily with the aid of a personal computer equipped with appropriate equation-solving software. Since the approach permits evaluation of all dependent variables for any specific combination of values for the kinetic parameters and independent variables, numerical values for the flux control coefficients of the individual enzymes can be obtained by direct calculation for a wide variety of conditions and can be compared with those obtained according to the methods of Metabolic Control Analysis. Several such comparisons have been made and in all cases identical results were obtained. The intuitive notion that the individual enzymes of a multienzyme reaction would be equally rate limiting if the total amount of enzyme were being used with maximum efficiency is tested and shown to be incorrect. In the course of this test the flux control coefficient for the individual enzymes were found to be appropriate indicators of relative rate limitation or control by the enzymes and to account properly for differences in specific activity among the enzymes.
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Project description:A FORTRAN 77 program is described for the derivation of steady-state rate equations for enzyme kinetics. Input is very simple and consists of the two enzyme forms and the two rate constants for each step in the mechanism. The program may be run interactively or off-line. The results are produced after collecting together the algebraic coefficients of like concentration terms, taking account of sign. A fully interactive BASIC version running on a BBC Microcomputer is also available. Details of the programs have been deposited as Supplementary Publication SUP 50126 (45 pages) with the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies may be obtained as indicated in Biochem. J. (1984) 217, 5.
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