scholarly journals Progress-curve analysis in enzyme kinetics. Numerical solution of integrated rate equations

1986 ◽  
Vol 235 (2) ◽  
pp. 613-615 ◽  
Author(s):  
R G Duggleby
Keyword(s):  
Numerical Solution ◽  
Enzyme Kinetics ◽  
Direct Calculation ◽  
Curve Analysis ◽  
Rate Equations ◽  
Alternative Formulation ◽  
Progress Curve ◽  
Newton Raphson ◽  
Raphson Method

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.

Steady-state kinetics

2000 ◽  
Author(s):  
Athel Cornish-Bowden
Keyword(s):  
Steady State ◽  
Enzyme Kinetics ◽  
Single Molecule ◽  
Transient State ◽  
Curve Analysis ◽  
Rate Equations ◽  
Progress Curve ◽  
Steady State Kinetics ◽  
Time Regime ◽  
Time Courses

All of chemical kinetics is based on rate equations, but this is especially true of steady-state enzyme kinetics: in other applications a rate equation can be regarded as a differential equation that has to be integrated to give the function of real interest, whereas in steady-state enzyme kinetics it is used as it stands. Although the early enzymologists tried to follow the usual chemical practice of deriving equations that describe the state of reaction as a function of time there were too many complications, such as loss of enzyme activity, effects of accumulating product etc., for this to be a fruitful approach. Rapid progress only became possible when Michaelis and Menten (1) realized that most of the complications could be removed by extrapolating back to zero time and regarding the measured initial rate as the primary observation. Since then, of course, accumulating knowledge has made it possible to study time courses directly, and this has led to two additional subdisciplines of enzyme kinetics, transient-state kinetics, which deals with the time regime before a steady state is established, and progress-curve analysis, which deals with the slow approach to equilibrium during the steady-state phase. The former of these has achieved great importance but is regarded as more specialized. It is dealt with in later chapters of this book. Progress-curve analysis has never recovered the importance that it had at the beginning of the twentieth century. Nearly all steps that form parts of the mechanisms of enzyme-catalysed reactions involve reactions of a single molecule, in which case they typically follow first-order kinetics: . . . v = ka . . . . . . 1 . . . or they involve two molecules (usually but not necessarily different from one another) and typically follow second-order kinetics: . . . v = kab . . . . . . 2 . . . In both cases v represents the rate of reaction, and a and b are the concentrations of the molecules involved, and k is a rate constant. Because we shall be regarding the rate as a quantity in its own right it is not usual in steady-state kinetics to represent it as a derivative such as -da/dt.

Axisymmetric flow near the critical point on the moving boundary

2010 ◽  
Vol 7 ◽  
pp. 182-190
Author(s):  
I.Sh. Nasibullayev ◽  
E.Sh. Nasibullaeva
Keyword(s):  
Fluid Flow ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Axial Velocity ◽  
Moving Boundary ◽  
Axisymmetric Flow ◽  
Boundary Motion ◽  
Newton Raphson ◽  
Raphson Method

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

Application of progress curve analysis to in situ enzyme kinetics using 1H NMR spectroscopy

1986 ◽  
Vol 155 (1) ◽  
pp. 38-44 ◽  
Author(s):  
Jamie I. Vandenberg ◽  
Philip W. Kuchel ◽  
Glenn K. King
Keyword(s):  
Nmr Spectroscopy ◽  
Enzyme Kinetics ◽  
1H Nmr ◽  
1H Nmr Spectroscopy ◽  
Curve Analysis ◽  
Progress Curve

scholarly journals Numerical Solution of Nonlinear Equations in Maple

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Qani Yalda
Keyword(s):  
Numerical Methods ◽  
Numerical Solution ◽  
Numerical Method ◽  
Nonlinear Equations ◽  
Secant Method ◽  
Bisection Method ◽  
Real Roots ◽  
Newton Raphson ◽  
Root Analysis ◽  
Raphson Method

The main purpose of this paper is to obtain the real roots of an expression using the Numerical method, bisection method, Newton's method and secant method. Root analysis is calculated using specific, precise starting points and numerical methods and is represented by Maple. In this research, we used Maple software to analyze the roots of nonlinear equations by special methods, and by showing geometric diagrams, we examined the relevant examples. In this process, the Newton-Raphson method, the algorithm for root access, is fully illustrated by Maple. Also, the secant method and the bisection method were demonstrated by Maple by solving examples and drawing graphs related to each method.

scholarly journals A NEW SECOND ORDER DERIVATIVE FREE METHOD FOR NUMERICAL SOLUTION OF NON-LINEAR ALGEBRAIC AND TRANSCENDENTAL EQUATIONS USING INTERPOLATION TECHNIQUE

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Sanaullah Jamali
Keyword(s):  
Numerical Analysis ◽  
Numerical Solution ◽  
Bisection Method ◽  
Derivative Free ◽  
Interpolation Technique ◽  
Derivative Free Method ◽  
Newton Raphson ◽  
Transcendental Equations ◽  
Regula Falsi Method ◽  
Raphson Method

Its most important task in numerical analysis to find roots of nonlinear equations, several methods already exist in literature to find roots but in this paper, we introduce a unique idea by using the interpolation technique. The proposed method derived from the newton backward interpolation technique and the convergence of the proposed method is quadratic, all types of problems (taken from literature) have been solved by this method and compared their results with another existing method (bisection method (BM), regula falsi method (RFM), secant method (SM) and newton raphson method (NRM)) it’s observed that the proposed method have fast convergence. MATLAB/C++ software is used to solve problems by different methods.

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