Well, let's calculate this in a more amusing way. Brace yourself for some enzyme comedy!
So, we have a substrate concentration of 1.5x10-3 M and a Km of 2.9x10-4. That's quite a challenge for the enzyme!
Now, the Ki value of the competitive inhibitor is 2x10-5. This inhibitor is a sneaky little antagonist trying to ruin the enzyme's day!
To calculate the concentration needed for 75% inhibition, let's use a formula. But don't worry, this won't be as complicated as an algebra equation!
The formula is:
[(Inhibitor) / (substrate)] = (1 + [I] / Ki)
We rearrange this to:
[(Inhibitor) / (substrate)] - 1 = [I] / Ki
Now, to find the concentration of the inhibitor, we multiply both sides by Ki:
[(Inhibitor) / (substrate)] - 1 x Ki = [I]
Putting in the values we have:
[(Inhibitor) / (1.5x10-3)] - 1 x 2x10-5 = [I]
Now, let's solve this equation and unmask the concentration of the competitive inhibitor! Drum roll, please...
[(Inhibitor) / (1.5x10-3)] - 1 x 2x10-5 = [I]
[(Inhibitor) / (1.5x10-3)] - 1 = [I] / 2x10-5
[(Inhibitor) / (1.5x10-3)] - 1 = 75% (because 75% inhibition is what we're after)
[(Inhibitor) / (1.5x10-3)] = 1 + 0.75
[(Inhibitor) / (1.5x10-3)] = 1.75
Now, let's isolate the concentration of the inhibitor:
(Inhibitor) = 1.75 x 1.5x10-3
(Inhibitor) = 2.625x10-3
Ta-da! The concentration of the competitive inhibitor required to yield 75% inhibition is 2.625x10-3 M!
Remember, this is a laughing matter, so don't let those numbers give you a frown. Just imagine the enzyme and the inhibitor dancing in a wild circus routine!