Basics of Biochemistry Enzymes Kinetics Ashish Kr Dwivedi, PhD
Enzymes - Michaelis-Menton Equation What was Michaelis' and Menton' s contribution? Since the enzyme and substrate must form the ES complex before a reaction can take place, they proposed that the rate of the reaction depended upon the concentration of ES: -2 They also proposed that at the beginning of the reaction, very little product returned to form ES. Therefore, k2 was extremely small and could be ignored: 2 E +S ES E + P
k+1 E+SSES k-1 where k +1 and k1 are the rate constants for the forward and reverse reactions. At equilibrium, the rates of the forward and reverse reactions are equal and the Law of Mass Action can be applied to the reversible process: k+1 [E] [S] = k-1 [ES] hence: EIS k-1 1 where Ka is the association (or affinity) constant.
k+2 ESEP In some cases the conversion of ES to E and P may involve several stages and may not necessarily be essentially irreversible. The rate constant k2 is generally smaller than both k1 and k-1 and in some cases very much smaller. In general, therefore, the conversion of ES to products is the rate-limiting step such that the concentration of ES is essentially constant but not necessarily the equilibrium concentration. Under these conditions the Michaelis constant, Km, is given by +2 +1 =K,+ +1
The rate (Velocity) of the appearance of product, depends on [ES]: ES has two fates: 1. Go to product 2. Reverse back enzyme substrate When the catalyzed reaction is running smoothly and producing product at a constant rate, the concentration of ES is constant at we say that the reaction has reached a steady state." Therefore, we may say that the rates for formation of ES and the breakdown of ES are equal: Rate of ES Formation d[ES]/dtk[E][S] Rate of ES Breakdown -d[ES]/dtk.[ES] +k2ES] At the "steady state:" d[ES]/dt 0 k[EJ[S] - (k.1+k2)IIES] Rearranging: k1[E][S] (k-1+k2)IIES]
k1 k2 k-1 Rate of ES formation = k1([E]-[ES])[S] Rate of ES breakdown-k-1ES]k2ES]
k1[S]+ k-1 + k2 E J[S] [ES] EJIS] JI .es . .. Vo kEIrS
Enzymes - Michaelis-Menton Equation V- Vmax [SI IS1 + Km What does this equation describe? It describes the velocity of an enzyme-catalyzed reaction at different concentrations of substrate [S]. . It helps determine the maximum velocity of the catalyzed reaction. . It assigns a value for Km, the "Michaelis constant," that is inversely proportional to the affinity of the enzyme for its substrate.
max The Michaelis-Menton equation was a pivotal contribution to understandingg max 2 how enzymes functioned However, during routine use in the laboratory, it was difficult to estimate Vmax. Everyone had different ideas the actual value for Vmax. Since it is impossible to actually make a solution with infinite concentration of substrate, a different equation was needed. Substrate concentration [S]
Comparision of these two methods of plotting the same data: Michaelis-Menton Equation Linewaver-Burke Equation max 1/V Slope KM/Vmax max Intercept 1/KM max Intercept = 1/1/max KM Substrate concentration [S] 1/[S]
Ashish Kr Dwivedi
Former Scientist (IIT Kanpur), Authored 10+ Peer Reviewed International Publications, PhD (IITK) Chief Mentor Triyambak Life Sciences