What concentration of competitive inhibitor is required to yield 75% inhibition at a substrate concentration of 1.5x10-3 if Km=2.9x10-4 and Ki=2x10-5?
To determine the concentration of a competitive inhibitor required to achieve a specific inhibition percentage, we need to use the relationship between the inhibition constant (Ki), the substrate concentration ([S]), and the enzyme's Michaelis-Menten constant (Km).
In a competitive inhibition scenario, the inhibitor competes with the substrate for the enzyme's active site, thereby reducing the enzyme-substrate complex formation. The degree of inhibition depends on the inhibitor's concentration, as well as its affinity for the enzyme (Ki).
To calculate the concentration of the competitive inhibitor required for 75% inhibition, we first need to find the fraction of enzyme activity that remains uninhibited (25%). We can express this as a ratio:
Fraction of uninhibited enzyme activity (A) = 1 - Fraction of inhibition (I) = 1 - 0.75 = 0.25
Next, we use the definition of the Michaelis-Menten constant (Km) to find the enzyme-substrate complex concentration ([ES]) at the given substrate concentration ([S]):
Km = ([E] + [I])/[ES] (1)
Since this is a competitive inhibition case, the concentration of the enzyme-substrate complex is given by:
[ES] = [E] × [S] / (Km × (1 + ([I]/Ki))) (2)
Where:
[E] is the total enzyme concentration
[I] is the inhibitor concentration
[Ki] is the inhibition constant
We need to rearrange equation (1) to solve for the combination of [E] and [I]:
[Km × (1 + ([I]/Ki))] = ([E] + [I])/[ES]
We can substitute the expression for [ES] from equation (2):
Km × (1 + ([I]/Ki)) = ([E] + [I]) × Km × (1 + ([I]/Ki)) / ([E] × [S])
Some algebraic simplification yields:
1 + ([I]/Ki) = 1 / [S]
Finally, we solve for [I] by isolating it on one side of the equation:
[I]/Ki = 1 / [S] - 1
[I] = (1 / [S] - 1) × Ki
Now, substitute the given values:
[S] = 1.5 x 10^(-3)
Ki = 2 x 10^(-5)
[I] = (1 / 1.5 x 10^(-3) - 1) × 2 x 10^(-5)
Calculating the value in the parentheses:
1 / 1.5 x 10^(-3) - 1 = 666.67 - 1 = 665.67
Substituting the value into the equation:
[I] = 665.67 × 2 x 10^(-5)
Calculating:
[I] = 0.0133134
So, the concentration of the competitive inhibitor required to yield 75% inhibition at a substrate concentration of 1.5 x 10^(-3) is approximately 0.0133.