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