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

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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
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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
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o m o max 0 S K S v v + = Good approximation if S o >> E o in this case S 0 ~ [S] at the start of quasi-steady state
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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
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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 0 ] 1 [P 1 k ][S] o [P 1 k dt ] o d[P 0 + + = = + + + + = = + + = = ][S] 1 j [P ] j [P j k j k j K = + etc.
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