Review lecture 2 Michaelis-Menten kinetics E+S、仝ES>E+P k d[s=,[EIS+KES dt d[日 -k1日[S+(k1+k2)ES dt des dt K,EIIS-(k_1+k2IES dP KIES dt
Review Lecture 2 Michaelis-Menten kinetics E + S ES E + P k 1 k-1 k 2 d [S ] dt = − k 1 [ E][S ] + k − 1 [ES] d [ E] dt = − k 1 [ E][ S] + ( k − 1 + k 2)[ES] d [ES] dt = k 1 [ E][ S] − ( k − 1 + k 2)[ES] dP dt = k 2 [ES] ≡ v
E。=[E+[ES dIs k1毛[S+(kS+k1E§ dt dEs dt K,E[S-(K,S+k_1+k2[ES 工ni七 ial condi tions: [S] t=0 [E] LESI [P] t=0
Eo = [E] +[ES] d[S] dt = −k 1Eo [S] + (k 1[S] +k −1 )[ES] d[ES] dt = k1Eo[S] − (k1[S] + k −1 + k 2)[ES] Initial conditions: [S]t=0 = So [E]t=0 = Eo [ES]t=0 = 0 [P]t=0 = 0
1.0H transient quasi steady state i substrate depletion 0.8 0.6 0.4 0.2 ES 0.0 0.1 10 100 time(s)
0÷maxo K +s m Good approximation if s >>e in this case So w [s] at the start of quasi-steady state
m o max o 0 K S v S v + = Good approximation if So >> Eo in this case S0 ~ [S] at the start of quasi-steady state
Review lecture 2 Equilibrium binding and cooperativity S+P,<>P, j-1 Adair′ s Equation: K1[S]+2K1K2s]+31K2K2{s]+…+nK1K2…K[S 1+K,[s]+K,K[s]+..+K,KK[s P macroscopic association constant K [P. ][s] for transitions between state j-1 and j
Review Lecture 2 Equilibrium binding and cooperativity jP j 1 S P ↔ − + n n n n ...K [S] 2K1 ... K 2 [S] 2K1 [S] K 1 1 K ...K [S] 2K1 ... nK 3 [S] 3K2K1 3K 2 [S] 2K1 [S] 2K 1K r + + + + + + + + = Adair’s Equation: ][S] j 1 [P ]j [P jK − = macroscopic association constant for transitions between state j-1 and j
Note #1 Detailed balance k +1 k k tn P、P1 p 1 dip i k,[P][S]+k[P1] dt +1 d[P1] k [P1][S]+k2[P]+k,1[P][S] +211 1 k1[P1] dt k,[P,][S]+k[ +2 etc k [P.] K≡-+j [P [S] 1
Note #1 Detailed balance P o P 1 P 2 ... Pn-1 P n k+1 k-1 k+2 k-2 k+n k-n ] 2 [P 2 ][S] k 1 [P 2 k ] 1 [P 1 ][S] k o [P 1 ] k 2 [P 2 ][S] k 1 [P 2 k dt ] 1 d[P 0 ] 1 [P 1 ][S] k o [P 1 k dt ] o d[P 0 − + + = − = − − + + − + + = = − − + + = = − ][S] j 1 [P ] j [P j k j k j K − = − + ≡ etc
I Identical and independent binding sites k k k k K=k/k K1=2K K2=K/2 2K[S]+2K4[S 2K[S] use Adair: r 1+2K[S]+K4[S 1+K[S]
I Identical and independent binding sites k + S k + k - k - S S k + k + k - S k - K=k +/k - K 1=2K K 2=K/2 1 K[S] 2K[S] 2 [S] 2 1 2K[S] K 2 [S] 2 2K[S] 2K r + = + + + use Adair: =
II Non-identical and independent binding sites k k k K=k/k K=kA/k KISI K IS] Independent binding: r 1+K[S]1+K[S]
II Non-identical and independent binding sites S S S k + k - k + * k - * Independent binding: [S] * 1 K [S] * K 1 K[S] K[S] r + + + = K=k +/k - K *=k + */k - * S k + * k - * k + k -
iii Identical and interacting binding sites k k k K=k/k K1=2K K2=K*/2 K*=k*/k_ 2K [S]+2KK [S use Adair r 1+2K[S]+KK[S]
III Identical and interacting binding sites S k + * k - * k + k - K=k +/k - K 1=2K K 2=K */2 K *=k + */k - * S S S k + k - k + * k - * 2 [S] * 1 2K[S] KK 2 [S] * 2K[S] 2KK r + + + use Adair: =
Cooperativity 2KIS]+2KK [S 1+2KS]+KK [S x(1+βx) Y 1+2x+βx β=K大/K X KISI B>1: positive cooperativity β>2: sigmoidal1 cur ve B< 1: negative cooperativity (always: dY/dx2< 0)
Cooperativity 2 1 2x βx x(1 βx) Y 2 [S] * 1 2K[S] KK 2 [S] * 2K[S] 2KK r + + + = + + + = β = K*/K x = K[S] β > 1: positive cooperativity β > 2: sigmoidal curve β < 1: negative cooperativity (always: d2Y/dx2 < 0)
