Michaelis-Menten graphical methods

It is very useful to transform the Michaelis-Menten equation into a linear form for analyzing data graphically and detecting deviations from the ideal behavior. One of the best known methods is the double-reciprocal or Lineweaver-Burk plot. Inverting both sides of equation 3.1 and substituting equation 3.2 gives the Lineweaver-Burk plot 4... 

Yang, S. T. and M. R. Okos, "A New Graphical Method for Determining Parameters in Michaelis-Menten Type Kinetics for Enzymatic Lactose Hydrolysis "Biotechnol. Bioeng. 34 (1989) 763 - 773. 

If we set up the same enzyme assay with a fixed amount of enzyme but vary the substrate concentration we will observe that initial velocity (va) will steadily increase as we increase substrate concentration ([S]) but at very high [S] the va will asymptote towards a maximal value referred to as the Vmax (or maximal velocity). A plot of va versus [S] will yield a hyperbola, that is, v0 will increase until it approaches a maximal value. The initial velocity va is directly proportional to the amount of enzyme—substrate complex (E—S) and accordingly when all the available enzyme (total enzyme or E j) has substrate bound (i.e. E—S = E i -S and the enzyme is completely saturated ) we will observe a maximal initial velocity (Pmax)- The substrate concentration for half-maximal velocity (i.e. the [S] when v0 = Vmax/2) is termed the Km (or the Michaelis—Menten constant). However because va merely asymptotes towards fT ax as we increase [S] it is difficult to accurately determine Vmax or Am by this graphical method. However such accurate determinations can be made based on the Michaelis-Menten equation that describes the relationship between v() and [S],... 

In former days, before electronic caelulations came into existance all calibrations and evaluations had to be carried out manually by graphical methods Linearized solutions had been used instead of nonlinear regression. Lineweaver and Burk 73) derived the linearized equation (19). It was introduced for calibration purposes to TLC by Kufner and Schlegel74). Kaiserf,3), Hulpke and Stegh 64) also used calibration techniques with reciprocal transformations of R and m without reference to the Michaelis-Menten transformation. 

Another method to obtain estimates for Km and is the rearrangement of the Michaelis-Menten equation to a linear form. The estimation for the initial velocities, Vo, from progress curves is not a particularly reliable method. A better way to estimate Vn is by the integrated Michaelis-Menten equation (Cornish-Bowden, 1975). Nevertheless, the graphical methods are popular among enzymolo-gists. The three most common linear transformations of the Michaelis-Menten equation are the Lineweaver-Burk plot of 1/Vo vs. 1/[S] (sometimes called the double-reciprocal plot), the Eadie-Hofstee plot, i.e. v vs. vo/[S], and the Hanes plot, i.e., [SJ/vo vs. [S] (Fig. 9.3). 

Although computer software is now readily available to fit enzyme kinetic data to the Michaelis-Menten and related equations, it can be instructive to use simple graphical methods in some cases. The most convenient of these (though not necessarily the most accurate) are based on doublereciprocal methods that convert the hyperbolic rate equations into much simpler linear forms for plotting. 

If Steady states (i.e., dose-concentration pairs) are reached by two subsequent doses and desired target concentration has not been reached, it is possible to solve the Michaelis-Menten equation algebraically by using simultaneous equations or by use of a graphical method to determine the patient s and V. ... 

Yang S T, Okos M R (1989), A new graphical method for determining parameters in Michaelis-Menten-type kinetics for enzymatic lactose hydrolysis , Biotechnol. 

Rat equation in Enzyme kinetics (see), an equation expressing the rate of a reaction in terms of rate constants and the concentrations of enzyme spedes, substrate and product. When it is assumed that steady state conditions obtain, the Michaelis-Menten equation (see) is a suitable approximation. R.e. are represented graphically (see Enzyme graph) they may be derived by the King-Altman method (see). 

Hofstee plot A graphical method used in enzyme kinetics to obtain a straight line fiom experimental data. It involves forming aplotofV/SversusVinwhichSis the substrate concentration at which the velocity v is observed. The gradient of the line is equal to -K and the intercept on the y-axis is equal to the maximum velocity V. Also known as the Eadie-Hofstee plot, it is named after Canadian biochemist George Sharp Eadie (1895-1976) and B. H. J. Hofstee who developed the plot in 1942 and 1959, respectively. See michaelis-MENTEN KINETICS. 

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