scholarly journals Computer program for the expression of the kinetic equations of enzyme reactions as functions of the rate constants and the initial concentrations

1990 ◽  
Vol 270 (3) ◽  
pp. 825-828 ◽  
Author(s):  
R Varón ◽  
B H Havsteen ◽  
M García ◽  
F García Cánovas ◽  
J Tudela
Keyword(s):  
Computer Program ◽  
Time Dependence ◽  
Kinetic Parameters ◽  
Rate Constants ◽  
Mathematical Theory ◽  
Kinetic Equations ◽  
British Library ◽  
Enzyme Reactions ◽  
Input Method

A versatile computer program with an easy input method has been developed for the construction of the terms in kinetic equations of enzyme reactions. It allows the expression of the time-dependence of the concentrations of all of the species involved as functions of the kinetic parameters. The mathematical theory used in this paper, the program and examples of its use have been deposited as Supplementary Publication SUP 50159 (41 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. (1990) 265, 5.

scholarly journals Computer program for the kinetic equations of enzyme reactions. The case in which more than one enzyme species is present at the onset of the reaction

1991 ◽  
Vol 278 (1) ◽  
pp. 91-97 ◽  
Author(s):  
R Varón ◽  
B H Havsteen ◽  
M García ◽  
F García-Canóvas ◽  
J Tudela
Keyword(s):  
Steady State ◽  
Computer Program ◽  
Enzyme System ◽  
Kinetic Equations ◽  
British Library ◽  
Transient Phase ◽  
Enzyme Reactions ◽  
Steady State Kinetic ◽  
State Kinetic ◽  
Enzyme Species

This paper presents an extension of the program developed by Varón, Havsteen, García, García-Cánovas & Tudela [(1990) Biochem. J. 270, 825-828] for the expression of the transient-phase and steady-state kinetic equations of a general enzyme system in which the only enzyme species present at the onset of the reaction is the free enzyme. The program has been extended to situations in which more than one enzyme species may be present at the onset of the reaction. The program is given in Supplementary Publication SUP50165 (5 pages), which has been deposited 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. (1991) 273, 5.

scholarly journals The computerized derivation of rate equations for enzyme reactions on the basis of the pseudo-steady-state assumption and the rapid-equilibrium assumption

1988 ◽  
Vol 251 (1) ◽  
pp. 175-181 ◽  
Author(s):  
H Ishikawa ◽  
T Maeda ◽  
H Hikita ◽  
K Miyatake
Keyword(s):  
Steady State ◽  
Rate Equation ◽  
Rate Equations ◽  
British Library ◽  
Enzyme Reactions ◽  
Input Method ◽  
Steady State Assumption ◽  
Rapid Equilibrium Assumption ◽  
Rapid Equilibrium ◽  
State Assumption

A computer program is developed for the derivation of the rate equation for enzyme reactions on the basis of the pseudo-steady-state assumption and the combination of the pseudo-steady-state and the rapid-equilibrium assumptions. The program not only has an easy input method, but also can obtain a complete rate equation in itself on only one run. The usefulness of the program is demonstrated by deriving the rate equations for some typical enzyme reactions. Details of the program have been deposited as Supplementary Publication SUP 50141 (42 pages) at the British Library Lending Division, Boston Spa, Wetherby, West Yorkshire LS23 7QB, U.K., from whom copies may be obtained as indicated in Biochem. J. (1988), 249, 5.

Kinetic equations and mechanisms for activation and inhibition in enzyme systems

1983 ◽  
Vol 61 (11) ◽  
pp. 1208-1218 ◽  
Author(s):  
Keith J. Laidler
Keyword(s):  
Rational Function ◽  
Rate Constants ◽  
Substrate Concentration ◽  
Kinetic Equations ◽  
Quadratic Polynomials ◽  
Enzyme Reactions ◽  
Enzyme Systems ◽  
Linear Kinetics ◽  
Positive Coefficients ◽  
Substrate Concentrations

The rates of enzyme reactions that are activated or inhibited by added modifiers can in some cases be expressed as a rational function of the first degree, v = (α0 + α1[Q])/(β0 + β1[Q] where [Q] is the concentration of the modifier and α0, α1, β0, and β1 are functions of rate constants and sometimes of the enzyme and substrate concentrations; the behaviour is then said to be linear. Three simple mechanisms that give rise to linear kinetics are examined, and the conditions under which there is activation or inhibition are determined. Sometimes there is a transition from activation to inhibition as the substrate concentration is varied. Definitions of competitive, uncompetitive, and noncompetitive activation are suggested, by analogy with the generally accepted definitions for inhibition. In second-degree activation or inhibition the rate can be expressed as the ratio of two quadratic polynomials with positive coefficients. Ten patterns are then possible for plots of v against [Q], and they may be classified with respect to (i) overall activation or inhibition, (ii) initial (at [Q] → 0) activation or inhibition, (iii) terminal (at [Q] → ∞) activation or inhibition, and (iv) whether there is an initial inflexion. The general case of an n:n rational function is also discussed.

scholarly journals Contribution of the intra- and intermolecular routes in autocatalytic zymogen activation: application to pepsinogen activation.

2006 ◽  
Vol 53 (2) ◽  
pp. 407-420 ◽  
Author(s):  
Ramón Varón ◽  
Matilde E Fuentes ◽  
Manuela García-Moreno ◽  
Francisco Garcìa-Sevilla ◽  
Enrique Arias ◽  
...  
Keyword(s):  
Kinetic Parameters ◽  
Rate Constants ◽  
Time Course ◽  
Initial Conditions ◽  
Reaction Scheme ◽  
Complete Analysis ◽  
Zymogen Activation ◽  
Relative Contribution ◽  
Starting Point ◽  
Definition Of

Taking as the starting point a recently suggested reaction scheme for zymogen activation involving intra- and intermolecular routes and the enzyme-zymogen complex, we carry out a complete analysis of the relative contribution of both routes in the process. This analysis suggests the definition of new dimensionless parameters allowing the elaboration, from the values of the rate constants and initial conditions, of the time course of the contribution of the two routes. The procedure mentioned above related to a concrete reaction scheme is extrapolated to any other model of autocatalytic zymogen activation involving intra- and intermolecular routes. Finally, we discuss the contribution of both of the activating routes in pepsinogen activation into pepsin using the values of the kinetic parameters given in the literature.

KINETIC EQUATIONS FOR ENZYME REACTIONS IN THE PRESENCE OF POWERFUL INHIBITORS

1959 ◽  
Vol 37 (8) ◽  
pp. 1268-1271 ◽  
Author(s):  
Richard M. Krupka ◽  
Keith J. Laidler
Keyword(s):  
Steady State ◽  
Kinetic Equations ◽  
Competitive Inhibitor ◽  
Graphical Analysis ◽  
Rate Data ◽  
State Equations ◽  
Enzyme Reactions ◽  
Simple Addition

Steady-state equations are worked out for the case of a competitive inhibitor that is present in concentrations comparable with that of the enzyme; allowance is made for the inhibitor attached to the enzyme. Two cases are considered: in case 1 the enzyme and inhibitor form a simple addition complex, while in case 2 a molecule is split off. Methods of graphical analysis of rate data are described.

DELAYED RESPONSE IN TRACER EXPERIMENTS AND FRAGMENT-CARRIER APPROACH TO TRANSIT TIME DISTRIBUTIONS IN NONLINEAR CHEMICAL KINETICS

2002 ◽  
Vol 12 (11) ◽  
pp. 2599-2618 ◽  
Author(s):  
MARCEL O. VLAD ◽  
JOHN ROSS ◽  
FEDERICO MORAN ◽  
YOEL RODRIGUEZ
Keyword(s):  
Time Dependence ◽  
Transit Time ◽  
Evolution Equations ◽  
Kinetic Equations ◽  
Mass Action ◽  
Rate Coefficients ◽  
Delayed Response ◽  
Linear Superposition ◽  
Highly Nonlinear ◽  
Kinetics Of

A delayed response tracer experiment is suggested, based on the following constraints: (1) The kinetics of the process can be expressed by local evolution equations without delays, for example by the mass action law. (2) The kinetic isotope effect can be neglected, that is, the rate coefficients for labeled and unlabeled chemicals are the same. (3) The total fluxes of the various chemicals are generally time dependent, but are not modified by the presence of the labeled compounds. (4) The experiment consists in the measurement of the time dependence of the fractions βu, u = 1, 2,… of labeled chemicals in the output fluxes as functionals of the time dependence of the fractions αu, u = 1, 2,… of labeled chemicals in the input fluxes, which are controlled by the researcher. We show that the output fluxes are related to the input fluxes by a linear delayed superposition theorem: βu(t) = ∑u′ ∫ χuu′(t,t′)αu′(t′)dt′, where χuu′(t,t′), is a delayed susceptibility function, which is related to the probability density of the transit time, that is, the time necessary for a molecular fragment to cross the system. This linear superposition law is not the result of a linearization procedure and holds even if the underlying kinetic equations are highly nonlinear. We establish a relationship between the transit time probability densities and the lifetime distributions of the various species in the system. The law permits extracting information about the mechanism and kinetics of chemical processes from response experiments.

Synthesis of highly reactive polyisobutylene by catalytic chain transfer in hexanes at elevated temperatures; determination of the kinetic parameters

2017 ◽  
Vol 8 (18) ◽  
pp. 2852-2859 ◽  
Author(s):  
Tota Rajasekhar ◽  
Jack Emert ◽  
Rudolf Faust
Keyword(s):  
Kinetic Parameters ◽  
Rate Constants ◽  
Chain Transfer ◽  
Elevated Temperatures ◽  
Polymerization Rate ◽  
Carbenium Ions ◽  
Catalytic Chain Transfer ◽  
Highly Reactive Polyisobutylene ◽  
Increasing Temperature

The rate constants of activation/deactivation for dormant oxonium/active carbenium ions have been measured and related to the increasing polymerization rate with increasing temperature.

scholarly journals Extended Rate Constants Distribution (RCD) Model for Sorption in Heterogeneous Systems: 2. Importance of Diffusion Limitations for Sorption Kinetics on Cryogels in Batch

Gels ◽  
2020 ◽  
Vol 6 (2) ◽  
pp. 15 ◽  
Author(s):  
Irina Malakhova ◽  
Alexey Golikov ◽  
Yuliya Azarova ◽  
Svetlana Bratskaya
Keyword(s):  
Kinetic Parameters ◽  
Diffusion Model ◽  
Residence Time ◽  
Rate Constants ◽  
Heterogeneous Systems ◽  
Sorption Kinetics ◽  
Sorption Rate ◽  
Kinetic Curves ◽  
Dynamic Conditions ◽  
Diffusion Limitations

Here we address the problem of what we can expect from investigations of sorption kinetics on cryogel beads in batch. Does macroporosity of beads indeed help eliminate diffusion limitations under static sorption conditions? Are sorption rate constants calculated using phenomenological kinetic models helpful for predicting sorption properties under dynamic conditions? Applying the rate constants distribution (RCD) model to kinetic curves of Cu(II) ions sorption on polyethyleneimine (PEI) cryogel and gel beads and fines, we have shown that diffusion limitations in highly swollen beads are very important and result in at least ten-fold underestimation of the sorption rate constants. To account for intraparticle diffusion, we have developed the RCD-diffusion model, which yields “intrinsic” kinetic parameters for the sorbents, even if diffusion limitations were important in kinetic experiments. We have shown that introduction of a new variable—characteristic diffusion time—to the RCD model significantly improved the reliability of sorption kinetic parameters and allowed prediction of the minimal residence time in column required for efficient uptake of the adsorbate under dynamic conditions. The minimal residence time determined from kinetic curves simulated using the RCD-diffusion model was in good agreement with experimental data on breakthrough curves of Cu(II) ion sorption on monolith PEI cryogel at different flow rates.

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