In: Chemistry

# Suppose an enzyme has Km = 0.1mM and kcat = 10^3 s-1, and you perform an...

Suppose an enzyme has Km = 0.1mM and kcat = 10^3 s-1, and you perform an experiment in which [E]tot = 10-7M. Suppose that adding 0.1 µM of an inhibitor results in a Kmeff= 0.5 mM, and has no effect on kcat. Determine the substrate concentation that would be necessary to achieve a reaction velocity v of 5*10^-5Ms-1

## Solutions

##### Expert Solution

Ans. Given, Kcat = 103 s-1

[E]tot = 0.1 uM = 1.0 x10-7 M                                   ; [1 uM = 10-6 M]

# Now,

Kcat = Vmax / [E]tot

Or, 103 s-1 x (1.0 x 10-7 M) = Vmax

Hence, Vmax = 1.0 x 10-4 M s-1

# In presence of Inhibitor-

Given, Kmeff = Km,app = 0.5 mM = 5.0 x 10-4 M                        ; [1 mM = 10-3 M]

We have, Vmax = 1.0 x 10-4 M s-1                        - remains unaffected of inhibitor

Vo = 5.0 x 10-5 M s-1

Now, Using Michaelis- Menten equation- Vo = Vmax [S] / (Km + [S])

(5.0 x 10-5 M s-1) = (1.0 x 10-4 M s-1) x [S] / (5.0 x 10-4 M + [S])

Or, (5.0 x 10-5 M s-1) / (1.0 x 10-4 M s-1) =[S] / (5.0 x 10-4 M + [S])

Or, 0.1 x (5.0 x 10-4 M + [S]) = [S]

Or, 5.0 x 10-5 M + 0.1[S] = [S]

Or, 5.0 x 10-5 M = [S] – 0.1[S]

Or, [S] = 5.0 x 10-5 M / 0.9

Hence, [S] = 5.56 x 10-5 M

Therefore, required [S] = 5.56 x 10-5 M

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