The effect of an inhibitor on an enzyme was tested and the experiment gave the r

Question

The effect of an inhibitor on an enzyme was tested and the experiment gave the results below. Plot the data and determine, by inspection of the graph, what type of inhibition is involved. 10. [S] uM V (umol/min) V (umol/min) V (umol/min) with 0.0 nM Inhibitor with 25 nM Inhibitor with 50 nM Inhibitor 0.4 0.67 1.00 2.00 0.22 0.29 0.32 0.40 0.21 0.26 0.30 0.36 0.20 0.24 0.28 0.32 (a) What type of inhibitor is in this problem and explain how the inhibitor inhibits the activity of the enzyme (b) Calculate Km and Vmax in the absence of inhibitors and calculate the K, constants for the this inhibitor

Explanation / Answer

Lineweaver- burk plot can be written as

1/V= (KM/Vmax)*1/S+1/Vmax

so a plot of 1/V vs 1/S gives straight line whose slope is KM/Vmax and intercept is 1/Vmax. This is the case when there is no inhibitor.

When there ins no inhibitor, 1/V = (Kmapp/Vmaxapp)*1/S+1/Vmaxapp

a plot of 1/V vs 1/S also gives straight line whose slope is KMapp/Vmaxapp and intercept of 1/Vmaxapp

all the three plots are generated and shown below along with the data points.

for the case of no inhibitor from the equation of best fit , 1/V=0.9997+2.032*1/S, 1/Vmax= 2.032, Vmax= 1/2.032= 0.4921umol/min, slope is Km/Vmax=0.9997

Km= 0.9997*0.4921=0.492uM

for the case of 25nM inhibitor, equation of best fit is 1/V= 0.9865*1/S+2.3252, 1/Vmaxapp= 1/2.3252= 0.431 umol/min, Kmapp/Vmax= 0.9865, Kmapp =0.9865*0.431= 0.4252 uM

for the case of 50nM inhibitor, equation of best fit is 1/V= 0.9474*1/S+2.6649, 1/Vmaxapp =1/2.6649=0.375 and Kmapp/vmax= 0.9474, Kmapp =0.375*0.9474=0.35553

since both Km and Vmax are decreased as seen by the Kmapp and Vmaxapp values, this type of inhibiton is uncompetitive inhibition, in this type, inhibitor binds to the enzyme and enhances the binding of substrate which leas to reducing Km) but the resultant enzyme-inhibitor-substrate complex slowly undergoes reaction and hence Vmax is also reduced:

Vmax app = Vmax/(1+I/Ki) and Kmapp = Km/(1+I/Ki)

for 25nM inhibitor, 0.431= 0.492/(1+I/KI)

1+I/Ki=0.492/0.431, I/KI=0.1415, Ki= 1/0.1415= 25/0.1415=177 nM

for 50 nm inhibitor, 0.375= 0.492/(1+I/KI)

1+I/Ki= 0.492/0.375

Ki= 50/0.312= 160.3 nM

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