Case Study: Enzyme Kinetics Data for new statin drug (inhibits HMG CoA reductase): 1 Substrate (UM) ● 0.5 1.0 1.5 2.5 3.5 || Rate of reaction (mm/min) 23.5 32.2 36.9 41.8 44 • What are the Kms of the uninhibited and inhibited reactions? ||| Rate of reaction in presence of 5.0 nM statin Using the above date, create a double-reciprocal (Lineweaver Burk) plot. What type of inhibition is shown by the new statin? What are the Vmax of the uninhibited and inhibited reactions? 16.67 25.25 30.49 37.04 38.91

For a one-substrate enzyme-catalyzed reaction, the Michaelis-Menton equation shows the quantitative relationship between the initial velocity (v_o), maximum velocity(v_max), the initial substrate concentration ([S]) and enzyme's affinity(Km).

Michaelis Menton equation --> $v o space equals space fraction numerator v m a x space times space open square brackets S close square brackets over denominator K m space plus space open square brackets S close square brackets end fraction$

Values for v_o and substrate concentration can be obtained experimentally but values like Vmax and Km cannot be obtained experimentally.

To obtain these values, we plot the v_o vs [S] on a graph, which is called a MM plot. From the graph, we can easily determine the value of Km.

Theoretically, when Km = [S], v_o= v_max /2

But since the MM plot is a curve, the value of Km obtained from the graph is only an approximation.

To obtain a more accurate value of Km, we plot what is called a double reciprocal plot. This double reciprocal plot is also called the Lineweaver Burk Plot.

Lineweaver Burk Plot

MM equation can be transformed into an equation that is much easier to plot experimentally. We simply take the reciprocal on both sides.

$v o space equals space fraction numerator v m a x space times space open square brackets S close square brackets over denominator K m space plus space open square brackets S close square brackets end fraction$ becomes $fraction numerator 1 over denominator v o end fraction space equals space open parentheses fraction numerator K m over denominator v m a x end fraction times fraction numerator 1 over denominator open square brackets S close square brackets end fraction close parentheses space plus space fraction numerator 1 over denominator v m a x end fraction$ which looks very similar to y = mx +c (the straight line equation)

where y is 1/vo,

x is 1/[S]
m, the slope is Km/Vmax
c, the y-intercept is 1/vmax

$fraction numerator 1 over denominator v o end fraction space equals space open parentheses fraction numerator K m over denominator v m a x end fraction times fraction numerator 1 over denominator open square brackets S close square brackets end fraction close parentheses space plus space fraction numerator 1 over denominator v m a x end fraction$ is called the Lineweaver Burk Equation

When we plot 1/Vo on the y-axis vs 1/[S] on the x-axis, the plot is called a Lineweaver Burk Plot.

Lineweaver Burk Plot enables us to accurately determine the Km and Vmax values.

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