1 inhibit5.mcd. Product Inhibition. Instructor: Nam Sun Wang

Transcription

1 Product Inhibition. Intructor: Nam Sun Wang inhibit5.mcd Mechanim. nzyme combine with a ubtrate molecule for form a complex, which lead to product. The product can alo combine with an enzyme in a reerible manner. Thi i decribed chematically a follow. 2 S + S P + r 2r Deriation of Reaction Rate xpreion with quilibrium & Quai-Steady State Aumption. Gien. dp/dt=rate= 2 S. 2r P 2. Coneration of enzyme pecie S 3. quilibrium and Quai-Steady State Aumption for S:. S. 2r P r S 2 S We hae three equation, and we can chooe to ole for any of the three unnown --, S, and. Find the analytical expreion (ia Math SmartMath ) ). r 2 S 2r P r 2. S 2r P S 2r P r 2.. S 2. 2r P r S 2r P r 2 Thu, the lat row i the analytical expreion for... r 2r... S. 2 S.. P 2 2r P r S 2r P r 2 r 2 2r S. P Thu, the aboe form i tranformed into the Michaeli-Menten form by defining:. r 2r m 2. r 2 2.r mp K m K p. m. mp p K m. K p p The reaction rate expreion how product inhibition. More pecifically, thi i competitie inhibition, a the apparent alue of K m arie without a change in max. Phyically, thi i competitie inhibition becaue product P compete with ubtrate S for actie ite.

2 2 inhibit5.mcd Note #: A P, m /(K m +), we get bac claical Michaeli-Menten inetic. Note #2: For, m. > p mp Note #3: At equilibrium, =.. m eq. mp p.eq p eq m 2 K m. eq K p p eq eq. mp r 2r p eq At equilibrium, we hae the equilibrium contant K eq. eq Thu, m mp K eq e ΔG RT Plot of Product Inhibition Rate xpreion Model parameter m mp K m K p Product inhibition rate expreion. m. mp p '(, p) K m. K p p Normal Rate Plot,... K eq Ue thermodynamic to obtain ome of the inetic data. Alternate form:. p m K eq K m K. p p The entire cure i depreed with increaing p. '(, ) '(, ) '(, 2).5 5 Lineweaer-Bur Plot.,... 3 '(, ) 4 A we increae p, the Lineweaer-Bur plot ha the ame intercept with the coordinate axi but an increaing lope. 2 '(,.5 ) '(,.7 ) 5

3 3 inhibit5.mcd Sole with an equilibrium aumption for the firt tep only. -- Incorrect. Gien. dp/dt=rate= 2 S. 2r P 2. Coneration of enzyme pecie S r. S 3. quilibrium Aumption for the firt tep: S r r S ).. S r. S.. S 2. 2r P r r S.. 2 S. 2r P r r S.. r 2r 2 S. P r S Thu, the aboe form i tranformed into the Michaeli-Menten form by defining:. r 2r m 2. r mp K m. m. mp p ''(, p) K m Normal Rate Plot,... Thi equation, capturing only part of the product dependence, i not the ame for a before! Thu, it i not a general. Lineweaer-Bur Plot., ''(, ) ''(, ) ''(, 2).5 5 ''(, ) 2 ''(,.5 ) ''(,.7 ) The general behaior of the plot are imilar, but not quite identical, to that deried from the quai-teady tate aumption. 5

4 4 inhibit5.mcd Sole with an equilibrium aumption for the econd tep only. -- Incorrect. Gien. dp/dt=rate= 2 S. 2r P 2. Coneration of enzyme pecie S 3. quilibrium Aumption for the econd tep: ) 2 2r P 2.. 2r P 2r P 2 2r 2 Hmm... Thi reult i expected, if the product formation tep i in equilibrium, =dp/dt= automatially. Thu, an equilibrium aumption for the product formation tep lead to nonene. Now, we change the definition of to be =-d/dt Gien. -d/dt=rate=. S 2 S 2. Coneration of enzyme pecie S 3. quilibrium Aumption for the econd tep: 2 2r P 2 2r 2 S. P S. P ).. 2r P 2r P 2. S 2r P 2 2r P S 2r P 2. 2r P.. 2r 2 S. P 2 2r. P Thu, the aboe form i tranformed into the Michaeli-Menten form by defining:. 2r m r mp K m K p '''(, p). m. mp p K m. K p p Thi equation, capturing only part of the product dependence, i not the ame for a before! Furthermore, at equilibrium, = lead to p/= m / mp = 2 / 2r, which i incorrect.

5 5 inhibit5.mcd Mechanim: A Serie of Reerible Reaction. 2 3 S + S P P + r 2r 3r Gien. dp/dt=rate= 2 S 2r P 2. Coneration of enzyme pecie S P 3. quilibrium and Quai-Steady State Aumption for S:. S 2r P r S 2 S quilibrium and Quai-Steady State Aumption for P: 2 S. 3r P 2r P 3 P We hae four equation, and we can chooe to ole for four unnown --, S, P, and.. 2r r 3 r 3 2. S. 2 2r 3r P. 3r P. r 3r P. 2 2r S 2r. r 3 S P, ).. 3 S. 2r 3r P. 2r S. S. 2 2r 3r P. 3r P. r 3r P. 2 2r S 2r. r 3 S.. S. 2 3r P. r 3r P 2. S. 2 2r 3r P. 3r P. r 3r P. 2 2r S S.. r 2r 3r P. S. 2 2r 3r P. 3r P. r 3r P. 2 2r S 2r. r 3 S Thu, the lat row i the analytical expreion for S.. r 2r 3r P. 2 S. 2r 3r P. 3r P. r 3r P. 2 2r S 2r. r 3 S 3 r 3 2 After collecting lie-term and ome rearrangement, we hae: r 2r 3r S P 2r 2 3 2r r 2r r r r 2 2r S. P 2 3 2r 2 3 2r 2r Thu, the aboe form i tranformed into the Michaeli-Menten form by defining: r 2r 3r m. mp 2 3 2r 2 3 2r r 2r r K m K p 2 3 2r 3r r 2 2r K eq 2 3 2r r 2r 3r. m. mp p K m. K p p or. p m K eq K m K. p p xactly the ame form a before.

6 5 inhibit5.mcd 3 r r 3 2. r r. 3 S 3 r r. 3 2