You have asked three questions here. As per Chegg Q&A Guidelines I am answering the first question since you haven't specified which question to answer.
We are given that:
Now, the reaction involves protonation and deprotonation steps. These reactions are very fast and hence all these acid-base reactions are considered to be in equilibrium.
The total enzyme concentration in the protonated/deprotonated state is given by:
From the equilibrium constants mentioned above, we have,
where,
Similarly, the total enzyme-substrate concentration in the protonated/deprotonated state is given by:
where,
And the total enzyme concentration in any form is given by:
Now, assuming steadu-state condition, we have, the rate of change of [ESH] is 0.
Now, let
Therefore, we have,
Now, the initial rate is given by
Let
and
where,
Thus, substituting back into the above equation gives the modified Michaelis-Menten equation as follows:
8. Enzymes often exhibit pH-dependent activity due to protonation/deprotonation of key amino acids. A general schematic...