Problem

Solutions For An Introduction to Medicinal Chemistry Chapter 7 Problem 6Q

Step-by-Step Solution

Solution 1

Michaelis-Menten equation was given by Leonor Michaelis and Maud Menton. They proposed an equation that can be used to determine the rate of reactions catalyzed by enzymes or inhibited by inhibitors. The equation comprising of reaction rate (ν), substrate concentration (S), Michaelis constant (K_M) and maximum rate of reaction (V_max) is described as follows:

Step #2 of 7

The reciprocals of the reaction rate and the substrate concentration are plotted with and without an inhibitor being present. This generates straight lines with the equation, where the slop (m) corresponds to K_M/V_maxand the intersection with the y-axis corresponds to 1/V_max. This plot is known as Lineweaver-Burk Plot.

To determine whether the inhibitor is competitive, uncompetitive or non-competitive the Line weaver-Burk plot is used. The reciprocals of the reaction rate and the substrate concentration are plotted, with and without an inhibitor being present.

This generates straight lines with the equation where the slop (m) corresponds to K_M/rate_maxand the intersection with the y-axis (c) corresponds to 1/rate_max:

Step #3 of 7

The two following tables show the rate of reaction at different concentrations:

Without Inhibitor
Substrate Concentration (10^-2mole decimeter^-3)	5	10	25	50	100
1/[S]	0.2	0.1	0.04	0.02	0.01
Initial Rate (10^-1 mol dm^-3 second^-1)	28.6	51.5	111	141	145
Initial Rate (mol dm^-3 s^-1)	2.86	5.15	11.1	14.1	14.5
1/rate (up to 3 decimals)	0.349	0.194	0.090	0.070	0.068

EM-1745 inhibitor (4nM)
Substrate Concentration (10^-2mol dm^-3)	5	10	20	40	83.3
1/[S]	0.2	0.1	0.05	0.025	0.012
Initial Rate (mol dm^-3 s^-1)	1.0	2.0	3.45	6.25	10
1/rate (up to 3 decimals)	1	0.5	0.289	0.16	0.1