ENZYME KINETICS A MODERN APPROACH – PART 1 pps

[...]... xi 11 .2 .1 Early Stages of the Reaction / 13 4 11 .2.2 Late Stages of the Reaction / 13 5 11 .3 Relaxation Techniques / 13 5 12 CHARACTERIZATION OF ENZYME STABILITY 14 0 12 .1 Kinetic Treatment / 14 0 12 .1. 1 The Model / 14 0 12 .1. 2 Half-Life / 14 2 12 .1. 3 Decimal Reduction Time / 14 3 12 .1. 4 Energy of Activation / 14 4 12 .1. 5 Z Value / 14 5 12 .2 Thermodynamic Treatment / 14 6 12 .3 Example / 15 0 12 .3 .1 Thermodynamic... −kr [A] 2 dt (1. 15) Integration of Eq (1. 15) for the boundary conditions A = A0 at t = 0 and A = At at time t, At d [A] t = −kr dt (1. 16) 2 A0 [A] 0 yields the integrated rate equation for a second-order reaction: 1 1 = + kr t [At ] [A0 ] (1. 17) [A0 ] 1 + [A0 ]kr t (1. 18) or [At ] = For a second-order reaction, a plot of 1/ At against time yields a straight line with positive slope kr (Fig 1. 5) For a second-order... rate equation for a thirdorder reaction can be expressed as d [A] = −kr [A] 3 dt (1. 22) Integration of Eq (1. 22) for the boundary conditions A = A0 at t = 0 and A = At at time t, At d [A] t = −kr dt (1. 23) 3 A0 [A] 0 yields the integrated rate equation for a third-order reaction: 1 1 = + kr t 2 2[At ] 2 [A0 ]2 (1. 24) ELEMENTARY RATE LAWS or [At ] = [A0 ] 9 (1. 25) 1 + 2 [A0 ]2 kr t For a third-order reaction,... reaction, A → products, is shown in Fig 1. 1 (a) The rate equation for a zero-order reaction can be expressed as d [A] = −kr [A] 0 dt (1. 5) Since [A] 0 = 1, integration of Eq (1. 5) for the boundary conditions A = A0 at t = 0 and A = At at time t, At A0 d [A] = −kr t dt 0 (1. 6) ELEMENTARY RATE LAWS 5 10 0 [At] 80 slope=−kr 60 40 20 0 0 10 20 30 t 40 50 60 Figure 1. 2 Changes in reactant concentration as a function... Thermodynamic Characterization of Stability / 15 1 12 .3.2 Kinetic Characterization of Stability / 15 6 13 MECHANISM-BASED INHIBITION 15 8 Leslie J Copp 13 .1 Alternate Substrate Inhibition / 15 9 13 .2 Suicide Inhibition / 16 3 13 .3 Examples / 16 9 13 .3 .1 Alternative Substrate Inhibition / 16 9 13 .3.2 Suicide Inhibition / 17 0 14 PUTTING KINETIC PRINCIPLES INTO PRACTICE Kirk L Parkin 14 .1 Were Initial Velocities Measured?... 1. 2) 1. 2.4.2 First-Order Integrated Rate Equation The reactant concentration–time curve for a typical first-order reaction, A → products, is shown in Fig 1. 1 (a) The rate equation for a first-order reaction can be expressed as d [A] = −kr [A] dt (1. 8) Integration of Eq (1. 8) for the boundary conditions A = A0 at t = 0 and A = At at time t, At d [A] t = −kr dt (1. 9) A0 [A] 0 yields the integrated rate equation... reaction, a plot of 1/ (2[At ]2 ) versus time yields a straight line with positive slope kr (Fig 1. 6) 1. 2.4.5 Higher-Order Reactions For any reaction of the type nA → products, where n > 1, the integrated rate equation has the general form 1 1 = + kr t n 1 (n − 1) [At ] (n − 1) [A0 ]n 1 or [At ] = [A0 ] n 1 (1. 26) (1. 27) 1 + (n − 1) [A0 ]n 1 kr t For an nth-order reaction, a plot of 1/ [(n − 1) [At ]n 1 ] versus... reactants A, B, and C 1. 2.3 Rate Constant The rate constant (kr ) of a reaction is a concentration-independent measure of the velocity of a reaction For a first-order reaction, kr has units of (time) 1 ; for a second-order reaction, kr has units of (concentration) 1 (time) 1 In general, the rate constant of an nth-order reaction has units of (concentration)−(n 1) (time) 1 1. 2.4 Integrated Rate Equations... reactant molecules participating in a simple reaction consisting of a single elementary step Reactions can be unimolecular, bimolecular, and trimolecular Unimolecular reactions can include isomerizations (A → B) and decompositions (A → B + C) Bimolecular reactions include association (A + B → AB; 2A → A2 ) and exchange reactions (A + B → C + D or 2A → C + D) The less common termolecular reactions can... dt (1. 1) Experimentally, one also finds that the rate of a reaction is proportional to the amount of reactant present, raised to an exponent n: rate ∝ [A] n (1. 2) ELEMENTARY RATE LAWS 3 where n is the order of the reaction Thus, the rate equation for this reaction can be expressed as − d [A] = kr [A] n dt (1. 3) where kr is the rate constant of the reaction As stated implicitly above, the rate of a reaction . Reaction / 13 4 11 .2.2 Late Stages of the Reaction / 13 5 11 .3 Relaxation Techniques / 13 5 12 CHARACTERIZATION OF ENZYME STABILITY 14 0 12 .1 Kinetic Treatment / 14 0 12 .1. 1 The Model / 14 0 12 .1. 2 Half-Life. Interfacial Enzyme Coverage / 12 7 11 TRANSIENT PHASES OF ENZYMATIC REACTIONS 12 9 11 .1 Rapid Reaction Techniques / 13 0 11 .2 Reaction Mechanisms / 13 2 CONTENTS xi 11 .2 .1 Early Stages of the Reaction. ENZYMES 12 1 10 .1 The Model / 12 2 10 .1. 1 Interfacial Binding / 12 2 10 .1. 2 Interfacial Catalysis / 12 3 10 .2 Determination of Interfacial Area per Unit Volume / 12 5 10 .3 Determination of Saturation