Question

An investigator plots 1/v as a function of 1/(concentration of substrate) for data collected with and without an inhibitor. The best-fit line of the data collected in the absence of the inhibitor had a slope of 0.12 (arbitrary units of time) and a y-intercept of 0.05 (arbitrary units of time per concentration). The best-fit line of the data collected in the presence of the inhibitor had a slope that was 2.9-times as steep (arbitrary units of time) and a y-intercept of 0.05 (arbitrary units of time per concentration). If the concentration of inhibitor was 60 nM, what is the value of the inhibition constant Ki in terms of nM to the nearest tenth?

Answer 1

Ans. Lineweaver-Burk plot gives an equation in from of y = mx + c

where, y = 1/ Vo, x = 1/ [S],

Intercept, c = 1/ Vmax ,

Slope, m = Km/ Vmax

#Step 1. Un-inhibited enzyme:

Given,

Slope of un-inhibited enzyme kinetics, m₁ = 0.12

            y-intercept of un-inhibited enzyme kinetics = 0.05

Now,

            Vmax = 1 / y-intercept = 1 / 0.05 = 20.0

Hence, Vmax = 20.0

# Km = slope x Vmax = 0.12 x 20 = 2.4

            Hence, Km = 2.4

#Step 2: In presence of inhibitor:

Given,

y-intercept of un-inhibited enzyme kinetics = 0.05

Slope of inhibited enzyme kinetics = 2.9 times steeper than that of m₁

                                                = 2.9 x 0.12

                                                = 0.348

Note: The slope in presence of inhibitor is either equal to or greater than (but never less than) that of uninhibited enzyme in the LB plot. So, multiply m₁ by 2.9 to get the slope in presence inhibitor (but do not divide).

Again,

            Vmax = 1 / y-intercept = 1/ 0.5 = 20.0

            Km,app = slope in presence of inhibitor x Vmax

                                    = 0.348 x 20.0

                                    = 6.96

#Step 3: Determine the type of inhibition: The KI of an inhibitor depend on the type of inhibitor. So, determine the type of inhibitor first.   

# Vmax remains almost the same whereas Km is increased. It is the characteristic of competitive inhibitor. Therefore, Inhibitor is a competitive inhibitor.

# Ki of completive inhibition is given by-

                        KI = [I] / [(Km,app / Km) – 1]      - equation 1

Putting the values in equation 1-

            KI = 60 nM / [ (6.96 / 2.4) -1)

            Or, KI = 60 nM / (2.9 – 1)

            Or, KI = 60 nM / 1.9 = 31.58 nM

Hence, KI = 31.58 nM