Mechanisms of enzyme inhibition MichaelisMenten mechanism E S

Mechanisms of enzyme inhibition • Michaelis-Menten mechanism E + S → ES ES →E + S ES →P + E k 1 k 2 k 3 • Competitive inhibition: the inhibitor (I) binds only to the active site. EI ↔ E + I • Non-competitive inhibition: binds to a site away from the active site. It can take place on E and ES EI ↔ E + I ESI ↔ ES + I • Uncompetitive inhibition: binds to a site of the enzyme that is removed from the active site, but only if the substrates already present. ESI ↔ ES + I

• The efficiency of the inhibitor (as well as the type of inhibition) can be determined with controlled experiments

Autocatalysis • Autocatalysis: the catalysis of a reaction by its products A + P → 2 P The rate law is = k[A][P] To find the integrated solution for the above differential equation, it is convenient to use the following notations [A] = [A]0 - x; [P] = [P]0 + x One gets = k([A]0 - x)( [P]0 + x) integrating the above ODE by using the following relation gives or rearrange into with a=([A]0 + [P]0)k and b = [P]0/[A]0

• Exercise 23. 12 a The p. Ka of NH 4+ is 9. 25 at 25. 0 o. C for the reaction of NH 4+ and OH- to form aqueous NH 3 is 4. 0 x 1010 dm 3 mol-1 s-1. Calculate the rate constant for proton transfer to NH 3. What relaxation time would be observed if a temperature jump was applied to a solution of 0. 15 mol dm-3 NH 3(aq) at 25. 0 o. C? • Solution: p. Ka corresponds: NH 4+ + H 2 O(l) ↔ NH 3(aq) + H 3 O+(aq) The rate constant to be calculated is from NH 3 + H 2 O(l) ↔ NH 4+(aq) + OH-(aq) Utilizing the relationship p. Ka + p. Kb = p. Kw • Time constant and relaxation time

• 22. 14 a The rate constant for the decomposition of a certain substance is 2. 8 x 10 -3 dm 3 mol-1 s-1 at 30 o. C and 1. 38 x 10 -2 dm 3 mol-1 s-1 at 50 o. C. Evaluate the Arrhenius parameters of the reaction. • Hint: Arrhenius parameters include A and Ea k = A e(-Ea/RT), where R is the universal constant

• Numerical Problem 25. 1 (7 th edition) The data below applies to the formation of urea from ammonium cyanate NH 4 CNO → NH 2 CONH 2. Initially 22. 9 g of ammonium cyanate was dissolved in enough water to prepare 1. 00 L of solution. Determine the order of the reaction, the rate constant, and the mass of ammonium cyanate left after 300 min. t/min 0 20. 0 50. 0 65. 0 150. 0 M(urea)/g 0 7. 0 12. 1 13. 8 17. 7 • Solution

• Discussion problem: Bearing in mind distinctions between the mechanisms of stepwise and chain polymerization, describe ways in which it is possible to control the molar mass of a polymer by manipulating the kinetic parameters of poltmerization. • Answers: For stepwise polymerization the degree of polymerization is given by <n> = 1 + kt[A]0 For chain polymerization the kinetic chain length is calculated through <n> = kp(f ki/kt)-1/2 [M] [I]-1/2

• Distinguish between competitive, noncompetitive, and uncompetitive inhibition of enzymes. Discuss how these modes of inhibition may be detected experimentally. • Hint: Using Lineweaver-burk plot, look for differences in the intercept with y-axis and changes in the slope.

• Exercise 26. 6 b (7 th edition) or 23. 2 b (8 th edition) Consider the following mechanism for thermal decomposition of R 2 (1) R 2 → R + R (k 1) (2) R + R 2 → PB + R’ (k 2) (3) R’ → PA + R (k 3) (4) R + R → PA + PB (k 4) Where R 2, PA and PB are stable hydrocarbons and R’ are radicals. Find the dependence of the rate of decomposition of R 2 on the concentration of R 2. • Solution