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Mechanisms of enzyme inhibition. Michaelis-Menten mechanism E + S → ES k 1 ES → E + S k 2 ES → P + E k 3 Competitive inhibition: the inhibitor (I) binds only to the active site. EI ↔ E + I
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Mechanisms of enzyme inhibition • Michaelis-Menten mechanism E + S → ES k1 ES → E + S k2 ES → P + E k3 • 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 → 2P 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 23.12a The pKa of NH4+ is 9.25 at 25.0 oC for the reaction of NH4+ and OH- to form aqueous NH3 is 4.0 x 1010 dm3 mol-1 s-1. Calculate the rate constant for proton transfer to NH3. What relaxation time would be observed if a temperature jump was applied to a solution of 0.15 mol dm-3 NH3(aq) at 25.0 oC? • Solution: pKa corresponds: NH4+ + H2O(l) ↔ NH3(aq) + H3O+(aq) The rate constant to be calculated is from NH3 + H2O(l) ↔ NH4+(aq) + OH-(aq) Utilizing the relationship pKa + pKb = pKw • Time constant and relaxation time
22.14a The rate constant for the decomposition of a certain substance is 2.8 x 10-3 dm3 mol-1 s-1 at 30 oC and 1.38 x 10-2 dm3 mol-1 s-1 at 50 oC. 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 (7th edition) The data below applies to the formation of urea from ammonium cyanate NH4CNO → NH2CONH2. 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(fki/kt)-1/2 [M] [I]-1/2
Distinguish between competitive, non-competitive, 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 26.6b (7th edition) or 23.2b (8th edition) Consider the following mechanism for the thermal decomposition of R2 (1) R2→ R + R (k1) (2) R + R2 → PB + R’ (k2) (3) R’ → PA + R (k3) (4) R + R → PA + PB (k4) Where R2, PA and PB are stable hydrocarbons and R and R’ are radicals. Find the dependence of the rate of decomposition of R2 on the concentration of R2. • Solution