Determining Rate Parameters

Michaelis-Menten Parameters. In designing assays it is useful to know the maximum rate obtainable with a given amount of enzyme, Vmax, and the concentration of substrate that gives half that rate, KM. These are the fundamental parameters in the Michaelis-Menten (M-M) rate

Figure 1. Nonlinearity of product formation with time, due to various factors. Initial rate for the theoretical reaction is 0.5. Fitting the nonlinear rates with a second degree polynomial, the calculated initial rates are: Substrate depletion, 0.51; Product inhibition, 0.51; Enzyme denaturation, 0.44. If the curves are fitted to a third degree polynomial, the calculated rates are 0.50,0.50, and 0.49, respectively. Source: Ref. 1, p. 93.

Figure 1. Nonlinearity of product formation with time, due to various factors. Initial rate for the theoretical reaction is 0.5. Fitting the nonlinear rates with a second degree polynomial, the calculated initial rates are: Substrate depletion, 0.51; Product inhibition, 0.51; Enzyme denaturation, 0.44. If the curves are fitted to a third degree polynomial, the calculated rates are 0.50,0.50, and 0.49, respectively. Source: Ref. 1, p. 93.

equation: v = Vmax[S]/(iCM + [S]>, where [S] is substrate concentration and v is the actual rate d[P]/dt. The usual procedure is to measure v at several concentrations [S] and then calculate Vmax and KM, either by applying a computer program (9) such as HYPER (Fig. 2a) or by fitting a straight line to one of the linear transforms of the M-M equation. The usual transform is the double reciprocal or Lineweaver-Burk plot: Uv = Wmax + (#M/VmaJ(l/[S]), where Uv is plotted versus 1/[S] (Fig. 2b). From statistical considerations, this is the least desirable transform to use (11).

A better plot is the Hanes plot of [S]/i> versus [S] (Fig. 2c): = KM/Vmax + (l/Vmax)[S]. The points are spaced along the x axis at the same intervals as in the M-M plot rather than being crowded together near the y axis. The larger experimental errors inherent in the smaller values of v (at low [S]) have less influence on the linear least squares regression line. The Hanes plot should be used in treating v, [S] data graphically; the use of the unsatisfactory Lineweaver-Burk plot should be discontinued.

The M-M equation is a differential equation, that is, v equals d[P]/dt at the instantaneous value of [¿>], usually taken as the initial substrate concentration. If v is only available as [P]/£ from a fixed-time assay, then the value taken for [S] for the above calculations should be the average of the substrate concentration at the beginning and end of the incubation period, ([S]0 + [Sj^/2. This approximation gives estimates of Vmax and KM that are much closer to the true values than if the initial value of [S] is used (12).

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Homemade Pet Food Secrets

Homemade Pet Food Secrets

It is a well known fact that homemade food is always a healthier option for pets when compared to the market packed food. The increasing hazards to the health of the pets have made pet owners stick to containment of commercial pet food. The basic fundamentals of health for human beings are applicable for pets also.

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