Solutions For An Introduction to Medicinal Chemistry Chapter 3 Problem 5Q

Lineweaver-Burk equation is a derivative of the Michaelis-Menten equation. It is a relation between 1/V and 1/[S]. It is denoted by the following equation as follows:

The data given in the question is of [S] and the corresponding V readings. From that 1/V and 1/[S] could be calculated easily, and one would arrive at the following data table as follows:

Plotting a Michaelis-Menten plot (V vs [S]) is as follows:

Figure: Michaelis Menten plot depicting V vs [S].

It can be seen from the plot, the V_max can be observed to be approximately equal to 14.5 mol L^-1 s^-1 (moles per liter per seconds) and the K_m (corresponding to the V_max/2) is approximately equal to 0.20mol L^-1.

The Lineweaver-Burk plot is shown below as follows (1/V vs 1/[S]):

Figure: Lineweaver-Burk plot depicting 1/V_max vs 1/[S].

Here, the plot intersecting at y-axis gives 1/V_max and the point, where the plot intersects at x-axis gives -1/K_m. Here, 1/V_max is 0.045; therefore, V_max is 22.2mol L^-1 s^-1. The value of -1/K_m is -1.2; therefore, K_m is 0.83mol L^-1.

Compared with the Michaelis-Menten plot, the Lineweaver-Burk plot gives a highly unreliable estimation of the values for K_m and V_max. The reason behind this is, the use of double reciprocal variables used in the Lineweaver-Burk equation, which totally distorts the error distribution structure of the data.

Therefore, it can be used for accurate estimation of K_m and V_max; however, it can swiftly give an estimation of the nature of inhibition of the reaction. The reactions could be competitive, non-competitive, and uncompetitive.