Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

1. Kase Ceenum, a scientist working for Cullen Biosciences, has isolated a novel

ID: 45721 • Letter: 1

Question

1. Kase Ceenum, a scientist working for Cullen Biosciences, has isolated a novel viral protease Intimidase. Assuming that Intimidase follows the two-step sequential kinetic model described below, derive the velocity of product formation. Please note that the equilibrium constants have been defined for the reverse reaction. I have already provided the assumptions needed, no additional ones are necessary. a. Substrate binding and dissociation steps occur much more rapidly than the catalytic steps. b. [S} > > > ET (Total enzyme concentration) Derive the equation based on the assumption(s). Note that pre-equilibria have been defined for you. Hint: From assumption a, you can approx ST to [S].

Explanation / Answer

From the definitions of the two dissociation constants, we have:

KD1=[E][S]/[ES] so [ES]=[E][S]/KD1

KD2=[E][S]/[ESS] so [ESS]=[ES][S]/KD2

On putting the value of [ES] in this eqation we will get, [ESS]=[E][S]2/KD1KD2

Relative to the total enzyme concentration, ET:

[ES]/[ET]=[ES]/[E]+[ES]+[ESS]

In this equation we will put the value of [ES] and [ESS] so it will become:

[ES]/[ET]= {[E][S]/KD1}/{[E]+([E][S]/KD1)+[E][S]2/KD1KD2}

On solving this reaction we will get

[ESS]/[ET]= ([S]2/KD1KD2)/{1+[S]/KD1+[S]2/KD1KD2}

The total reaction velocity for this system is given by (where Vmax1 = kcat1[ET] and Vmax2 = kcat2[ET]):

?={Vmax1[S]/KD1+Vmax2[S]2/KD1KD2}/1+([S]/KD1)+([S]2/KD1KD2)