- Vmax 6 Single Turnover Of Substrate When E S 20 Points The Three Step Mechanism Illustrated Below Has Been Pr 1 (141.42 KiB) Viewed 73 times
Vmax 6. Single turnover of substrate when [E]. >>[S]. (20 points) The three step mechanism illustrated below has been proposed to describe the kinetics of several proteolytic enzymes, such as papain, which forms an acyl-enzyme intermediate. By using nitrophenyl esters as substrates, the product Preleased in the reaction is nitrophenol, which can be easily monitored spectrophotometrically. Alternative substrates which show a large change in absorption when the acyl enzyme is formed permit observation of ES'. E+SES →ES' + P E + P2 ki, k. 1, K2, K3 By writing the mass balances in a well-mixed batch reactor for all the species present, use the simplification that [El. >> [S], to derive a second order differential equation for the time course of ES in terms of the kinetic constants and the initial enzyme concentration. Show that the assumption that kz [Eo>>k2 permits the solution of this equation to be simplified to yield the following solutions for [ES] and [P]: [5).x.-(keh )] 601-6 (PJ= 5- {1-exo-(KLEI ?] k[E] [ES] = - s] k[ kat KE + K + K₂ K, Eb+k+k₂ k[E] kat KE + K + K₂ (10 points) Find the corresponding solutions for [ES'] and [P2]. (10 points) Show that observation of ES or P1 permits the apparent first order rate constant to be found. (10 points) How may kz and kz be determined? (10 points) If the first reaction can be considered to be at equilibrium, with Ks being the dissociation constant for the reaction E+SES, show that the apparent first order rate constant is given by: (10 points) kobs = K[E]. K +[E] help