Lecture 22.Enzyme And Catalysis 21 Derivation of Michaelis-Menten Equation We need one more condition,that is,the total enzyme concentration,[E is the sum of that of enzyme-substrate complex,[ES],and that of free enzyme,[E]: [E,]=[ES]+[E]v,=k,[EIS]=k ([E,]-[ES)IS] At steady state,the forward rate should equal to the reverse rate: k ([E,]-[ES)IS]=(k+k)ES]k [E,JS]-k [ESIS]=(k+k2)ES] k[E,]=k;[ES]S]+(k+k)[ES]k [E,IS]=[ESKk [S]+(k+k2)) →eG时 kE,IS] [E,IS] [E,IS] [S+(k1+k2) [S]+Km Rate of production formation (rate law),v[ES].So: E可 =+K Derivation of Michaelis-Menten Equation • We need one more condition, that is, the total enzyme concentration, [Et ] is the sum of that of enzyme-substrate complex, [ES], and that of free enzyme, [E]: • At steady state, the forward rate should equal to the reverse rate: • Rate of production formation (rate law), v = k2 [ES]. So: Lecture 22. Enzyme And Catalysis 21                                                  m k t k k K t t t t t t S K E S ES k k k S E S k S k k k E S ES k E k ES S k k ES k E S ES k S k k k E ES S k k ES k E S k ES S k k ES m + ⎯⎯⎯⎯⎯→ = + + = + +  =  = + +  = + +  − = +  − = + + = − − − − − − − 1 1 2 ( ) 1 1 1 2 1 2 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 2 ( ( )) ( ) ( ) ( ( )) ( ) ( ) ( ) E  ES E t = + v k ES k E  ES S f t ( ) = 1 = 1 −      m t S K k E S v + = 2