## Experimental determination of K and V

A m max

Plotting the graph of rate of reaction against substrate concentration, as in Figure 2.8, permits only an approximate determination of the values of K and V , and a

number of methods have been developed to convert this hyperbolic relationship into a linear relationship, to permit more precise fitting of a line to the experimental points, and hence more precise estimation of K and V .

m max

The most widely used such linearization of the data is the Lineweaver—Burk double-reciprocal plot of 1/rate of reaction versus 1/[substrate], as shown in Figure 2.9. This has an intercept on the y (1/v) axis = 1/Vmax when 1/s = 0 (i.e. at an infinite concentration of substrate), and an intercept on the x (1/s) axis = —1/Km.

Experimentally, the values of Km and Vmax are determined by incubating the enzyme (at optimum pH) with a range of concentrations of substrate, plotting the graph shown in Figure 2.9 and extrapolating back from the experimental points to determine the intercepts.

The Michaelis—Menten equation that describes the dependence of rate of reaction on concentration of substrate is:

max m

One of the underlying assumptions of the Michaelis—Menten model is that there is no change in the concentration of substrate — this means that what should be measured is the initial rate of reaction. This is usually estimated by determining the amount of product formed at a series of short time intervals after the initiation of the reaction, then plotting a rate curve (product formed versus time incubated) and estimating the tangent to this curve as the initial rate of reaction.

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