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l3_notes - Review Lecture 2 Michaelis-Menten kinetics E + S...

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Unformatted text preview: 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 o = [ E ] + [ ES ] d [ S ] dt = − k 1 E o [ S ] + ( k 1 [ S ] + k − 1 )[ ES ] d [ ES ] dt = k 1 E o [ S ] − ( k 1 [ S ] + k − 1 + k 2 )[ ES ] Initial conditions: [S] t=0 = S o [E] t=0 = E o [ES] t=0 = 0 [P] t=0 = 0 o m o max S K S v v + = Good approximation if S o >> E o in this case S ~ [S] at the start of quasi-steady state Review Lecture 2 Equilibrium binding and cooperativity j P 1 j P S ↔ − + n n n n [S] ...K 2 K 1 K ... 2 [S] 2 K 1 K [S] 1 K 1 [S] ...K 2 K 1 nK ... 3 [S] 3 K 2 K 1 3K 2 [S] 2 K 1 2K [S] 1 K r + + + + + + + + = Adair’s Equation: ][S] 1 j [P ] j [P j K − = macroscopic association constant for transitions between state j-1 and j Note #1 Detailed balance P o P 1 P 2 ... P n-1 P n k +1 k-1 k +2 k-2 k +n k-n ] 2 [P 2 k ][S] 1 [P 2 k ] 1 [P 1 k ][S] o [P 1 k ] 2 [P 2 k ][S] 1 [P 2 k dt ] 1 d[P ] 1 [P 1 k ][S] o [P 1 k dt ] o d[P − + + − = = − − + + − + + − = = − + + − = = ][S] 1 j [P ] j [P j k j k j K − = − + ≡ etc. I Identical and independent binding sites S k + k + k- k- S S k + k + k- S k- K 1 =2K K 2 =K/2 K=k + /k- K[S] 1 2K[S] 2 [S] 2 K 2K[S] 1 2 [S] 2 2K 2K[S] r + = + + + = use Adair: II Non-identical and independent binding sites S S S k + k- k + * k- * Independent binding: [S] * K 1 [S] * K K[S] 1 K[S] r + + + = K=k + /k- K * =k + * /k- * S k + * k- * k + k- III Identical and interacting binding sites...
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This note was uploaded on 11/11/2011 for the course BIO 7.344 taught by Professor Bobsauer during the Spring '08 term at MIT.

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l3_notes - Review Lecture 2 Michaelis-Menten kinetics E + S...

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