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Enzyme Catalysis and Enzyme Kinetics Student Edition 5/23/13 Version Enzyme Catalysis and Enzyme Kinetics Student Edition 5/23/13 Version Pharm. 304 Biochemistry.

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Presentation on theme: "Enzyme Catalysis and Enzyme Kinetics Student Edition 5/23/13 Version Enzyme Catalysis and Enzyme Kinetics Student Edition 5/23/13 Version Pharm. 304 Biochemistry."— Presentation transcript:

1 Enzyme Catalysis and Enzyme Kinetics Student Edition 5/23/13 Version Enzyme Catalysis and Enzyme Kinetics Student Edition 5/23/13 Version Pharm. 304 Biochemistry Fall 2014 Dr. Brad Chazotte 213 Maddox Hall chazotte@campbell.edu Web Site: http://www.campbell.edu/faculty/chazotte http://www.campbell.edu/faculty/chazotte Original material only ©2005-14 B. Chazotte

2 Goals- Catalysis Understand the nomenclature of enzymes. Understand the roles of cofactors and coenzymes and be familiar with examples of each. Understand the meaning of activation energy and the concepts of transition state theory & catalytic rate enhancement. Be generally familiar with the types of enzyme catalytic mechanisms. Learn the biologically important electrophiles & nucleophiles.

3 Enzymes Lehninger 2005 Figure p.191 Protein molecules that utilize the chemical and physical properties of their component amino acids to facilitate biochemical reactions that otherwise would be difficult to accomplish under physiological conditions. An enzyme provides a specific environment that allows the biochemical reaction to occur more rapidly. The distinguishing feature of an enzyme-catalyzed reaction is that it occurs within a pocket on the protein. This pocket is termed the active site and the molecule(s) that binds to the active site and is converted is called the substrate. productThe molecule(s) produced by the reaction is called the product.

4 Enzymes: General Properties Enzymatically catalyzed reactions: are typically 10 6 to 10 12 times more rapid than the corresponding uncatalyzed reactions. occur under relatively mild conditions under 100° C, 1 Atm, and ~pH 7.0. occur with a high degree of specificity with respect to both the reactants and the products. can be controlled by non-substrate molecules, i.e. allosteric control, covalent enzyme modification; or the synthesis or degradation of the enzyme (amount of enzyme present). Voet, Voet & Pratt 2002 p. 282

5 Lehninger 2000 Table 8.3 International Classification on Enzymes (OTHLIL) Enzymes are commonly named by adding the suffix –ase to the substrate the enzyme converts or a phase that describes the reaction catalyzed by the enzyme. To be systematic the IUMBMB developed a numerical coding and naming system. Here are the 6 major classes

6 Enzyme Commission Number An example: 1.9.3.1Cytochrome c oxidoreductase trivial (common) names : cytochrome oxidase, Complex IV 1.ClassOxidoreductases 1.9.Subclass Acting on a heme group of donors 1.9.3Sub-subclassWith oxygen as an acceptor See enzyme classification website @ http://expasy.ch/sprot/enzyme.html The four-part enzyme classification number is a series of 4 numbers separated by periods.

7 Specificity of Enzymes Geometric complementarity – the enzyme’s binding site has a structure complementary to the substrate it needs to bind. Electronic complementarity – amino acids that form the enzyme’s binding site are arranged to specifically interact and attract the substrate molecule. Stereospecificity – binding of chiral substrates and the catalysis of their reactions is highly specific due in large part to the inherent chirality of the L -amino acids that comprise the enzyme.

8 Enzyme- Substrate Complex Illustration Voet, Voet & Pratt 2013 Fig 11.1

9 Cofactors and Coenzymes Help can be in the form cofactors which are either one or more inorganic ions or a complex organic or metalloorganic molecules called a coenzyme. Some enzymes require some help.

10 Lehninger 2000 Table 8.2 Cofactors table Holoenzyme: catalytically active complete enzyme together with its bound coenzyme and/or metal ions. Apoenzyme (aproprotein): protein part of such an enzyme. Prosthetic group: a coenzyme or metal ion that is covalently or very tightly bound to the protein.

11 Coenzymes as Transient Carriers Table Beriberi Megaloblastic anemia Pellagra Perncious anemia Human Deficiency Disease

12 What do enzymes do? Enzymes as catalysts change the rate of a chemical reaction but do not alter the equilibrium.

13 Transition State Theory, Activation Energy (E a ), & The Reaction Coordinate Thermodynamics Again? Transition state theory was developed to describe chemical reactions by applying thermodynamic equilibrium concepts.

14 Transition State Diagram Voet, Voet & Pratt 2013 Fig 11.5 Consider the bimolecular R x (a) : H A – H B + H C  H A + H B -- H C Consider the generic bimolecular R x (b) : A + B  X ‡  P + Q rate = k ~ e -ΔG‡/RT ; ΔG ‡ = E a

15 A catalyst functions by lowering the activation energy of a reaction, the energy barrier for the reactants to become products. Transition State Diagram: Effect of Catalyst Voet, Voet & Pratt 2013 Fig 11.7

16 Catalytic Rate Enhancement * : a ΔG ‡ Calculation The enhancement of catalyzed vs uncatalyzed is given by: k= e ΔΔG‡/RT ln k = ΔΔG ‡ /RT RT ln k = ΔΔG ‡ for a 100-fold change in rate at 25 ºC (8.314514 J ºK -1 mol -1 x 298.15 ºK) x ln(100) = ΔΔG ‡ (2478.97 J mol -1 ) x (4.605) = ΔΔG ‡ 11,416 J mol -1 =11.42 kJ mol -1 = ΔΔG ‡ 10-fold: 5.71 kJ mol -1 compare H-bond ~20 kJ mol -1 1,000,000-fold:34.25 kJ mol -1 covalent bond ~300-500 kJ mol -1 * Enhancement meaning the absolute value – hence the omitted “-” sign Voet, Voet & Pratt 2013 Chap 11

17 Effect of ΔG ‡ versus ΔG Important Concepts! ΔG ‡ effects the likelihood of reactants going to products AND products to reactants - speeds up both reactions! ΔG effects the likelihood of reactant going to products OR products going to reactants based on the free energy difference between reactants and products. thermodynamics ΔG < 0 forward reaction favored A + B  P + Q A + B  P + Q

18 CATALYTIC MECHANISMS Enzymes are effective as catalysts due to: 2)their ability to specifically bind the substrate molecule in an enzyme-substrate complex and to use noncovalent interactions for binding to significantly lower the free energy. 1) their ability to rearrange covalent bonds using their various amino acid side chains, metal ions and coenzymes.

19 Types of Enzyme Catalytic Mechanisms 1.Acid-Base Catalysis 2.Covalent Catalysis 3.Metal Ion Catalysis 4.Electrostatic Catalysis 5.Proximity and Orientation Effects 6.Preferential Binding of the Transition State Complex

20 Acid-Base Catalysis Mechanism: Keto-Enol Tautomerization Voet, Voet & Pratt 2013 Fig 11.8 Uncatalyzed General Acid Catalyzed General Base Catalyzed base acid “ene” Hydroxyl “ol” ketone δ ≡ partial charge

21 Types of Acid-Bases Catalysis Specific Acid-Base Catalysis: Non-enzymatic reactions: Uses only the H + on OH - ions present in water. (No other molecules involved) Ions are transferred between water and the intermediate faster than the intermediate breaks down to reactants. General Acid Catalysis: A process in which partial proton transfer from an acid lowers ΔG‡ and accelerates the reaction. General Base Catalysis: A process in which partial proton extraction by a base lowers ΔG‡ and accelerates the reaction.

22 Amino Acids in General Acid-Base Catalysis Lehninger 2005 Figure 6.9

23 pH and Enzyme Activity Lehninger 2005 Figure 6.17

24 RNase A Mechanism: An Acid-Base Catalysis Voet, Voet & Pratt 2013 Fig 11.10 Base catalysis Acid catalysis 2’,3’Cyclic ribonucleotide intermediate

25 Typical Stages: 1.Nucleophilic R x between catalyst & substrate to form covalent bond. 2.Withdrawal of electrons from reaction center by the (now) electrophilic catalyst. 3.Elimination of the catalyst (reverse of first step) Covalent Catalysis: Decarboxylation of Acetoacetate Voet, Voet & Pratt 2013Fig 11.11 uncatalyzed carbonyl electron withdrawal decarboxylation covalent bond elimination Transition state

26 Covalent Catalysis Covalent Catalysis (nucleophilic catalysis) definition: accelerates the reaction via the transient formation of a catalyst-substrate covalent bond. The typical way this happens is a nucleophile group on the enzyme forms a covalent bond with an electrophile group on the substrate. Important – The more stable the covalent bond formed in the transition state, the less easily it can degrade. Therefore good candidates for covalent catalysis like imidazoles and thiols have high polarizability (mobile electrons) have high nucleophilicity and also can form good leaving groups.

27 Biologically Important Electrophiles & Nucleophiles Voet, Voet & Pratt 2013 Fig 11.12 “The nucleophilicity of a substance is closely related to its basicity”

28 Metal Ion Catalysis: Carbonic Anhydrase Voet, Voet & Pratt 2008 Fig 11.13 Participate in catalytic process by: Binding to substrates to properly orient them for R x Mediating redox R x via reversible metal ion oxidation state changes. Electrostatic stabilization or neg. charge shielding CO 2 + H 2 O  HCO 3 - + H + Active site opening Nearly 1/3 of all enzymes utilize a metal ion for their catalytic function.

29 Electrostatic Catalysis The charge distribution around enzyme active sites appears to be arranged to stabilize the transition state of the catalyzed reactions.

30 Proximity & Orientation Effects Voet, Voet & Pratt 2006 p. 328 Enzymes tend to be catalytically efficient. They bring substrate into contact with catalytic groups & multiple substrates with each other. ~ 5-fold boost They bind their substrates in the proper orientation to promote the reaction ~100-fold boost They freeze out relative translational and rotational motion of catalytic groups and substrates – in transition state little relative motion of catalytic groups ~10 7 -fold boost

31 Lehninger 2013 Figure 11.15 Preferential Transition State Binding “An enzyme may bind the transition state with greater affinity than the substrates or products” This increases the molecules in the transition state, thus proportionally increasing the reaction rate ES S

32 Kinetics The study of reaction rates

33 Goals -Kinetics Know the difference between 1 st and 2 nd order reactions and their half-lives. Know the nomenclature for enzyme kinetics. Understand the difference between rapid-equilibrium and steady-state approaches to enzyme kinetics. Know the Michaelis-Menten equation and how to plot it. Understand the concepts of K m and V max. Understand the Lineweaver-Burke Plot, be able to plot it and extract kinetic constants. Be aware that there are other types of kinetic plots Understand enzyme reaction reversibility and how that affects the kinetic equation. Understand basic types of multisubstrate enzymes (sequential and random, BiBi and ping-pong) and how that effects their kinetic equations. Know the various types of enzyme inhibition, how their L-B plots look, and how to get quantitative information from those plots. Understand how pH and temperature (Arrhenius eq.) affect enzyme activity

34 Setting Up A Kinetic Analysis 1.Write differential equations for each enzyme species. 2.Write the velocity equations. 3.Substitute in the differential equations the expression for the enzyme species.

35 Internet Explorer Demonstration

36 Chemical Kinetics – Elementary R x s Reaction Stoichiometry A → P substance A; product P A → I 1 → I 2 → P intermediates I n Rate Constant k The proportionality constant at constant temperature describing the rate of an elementary reaction. k is proportional to the frequency at which the reacting molecules come together. Reaction Velocity The instantaneous rate of product appearance or reactant disappearance. Reaction Order The number of molecules that must simultaneously come together (collide) to generate a product, i.e. the molecularity

37 Reaction Order – First Order

38 First Order Reaction A → P Voet, Voet & Pratt 2013 Fig 12.1 First Order Equation: d[P] d[A] v = dt = - dt = k[A] The reaction at time t is proportional to the concentration of A. A o is the initial reactant concentration k is in s -1 units For first order: The half-life is independent of [A 0 ], i.e. it is a constant

39 Determining order & rate constant for Irreversible 1 st order Rx Matthews et al.1999 Figure 11.1

40 Second Order Reactions ( 2A → P Second Order Reactions (Bimolecular) 2A → P Second Order Equation: d[A] v = dt = k[A] 2 k is in M -1 S -1 units A + B → P Second Order Equation: d[A] d[B] v = - dt = - dt = k[A][B] k is in M -1 S -1 units Pseudo first order (for B if [A] >>[B] & vice versa) 1 [A] =[A o ] + kt Half-life : t ½ = 1/k[A o ]

41 Rate Equation Describes reaction progress as a function of time. Derivation: (where t = time) d[A] [A] = d ln[A] = - k dt Integrate from [A o ] to [A] ⌠ [A] ⌠t ⌡ [ Ao] d ln [A] = - k ⌡ 0 dt ln [A] = ln[A o ] – kt or [A] = [A o ] e -kt

42 Half Life Calculation First Order Second Order k t ½ = ln [A 0 ]/2 [A o ] t ½ = ln 2/k =0.693 / k Half Life: t ½ t ½ = 1/(k [A o ])

43 Enzyme Kinetics The study of enzyme reaction rates Lehninger 205 Figure 8.6

44 Enzyme Kinetic Definitions: E Enzyme;[E] enzyme concentration:[E] T total enzyme ES enzyme substrate complex[ES] complex concentration P, Q, R,… “products” A, B, C …. “substrates” I, J, K… “inhibitors” k rate constant k 1 forward rate constant k -1 reverse rate constant k p the catalytic rate constant. v = reaction velocity v o = initial reaction velocity, when [P] ~ 0

45 Two Approaches to Enzyme Kinetics Rapid Equilibrium (Henri-Michaelis-Menten) Early components of the reaction are at equilibrium. Permits one to express [ES] in terms of [E], [S], & K s, i.e. an equilibrium expression. One still needs a velocity equation to insert expression for [ES]. Steady-State (Briggs-Haldane) {most used approach} Shortly after the reaction starts [ES] would reach a steady-state and this would be close to the equilibrium level. Problem: One does not know the concentration of ES during a reaction. Therefore, one has to make certain assumptions for calculations Lehninger 2005 Figure p.203

46 Henri-Michaelis-Menten I Unireactant Enzyme E + S k1 k-1 ES k2 E + P E, S, and ES equilibrate very rapidly compared to formation of E + P Instantaneous velocity depends on [ES]  v = k 2 [ES] (1) The total enzyme is written: [E] T = [E] + [ES] (2) Divide equation (1) by [E] T v = k 2 [ES] [E] T [E] + [ES] (3)

47 Henri-Michaelis-Menten II E + S k1 k-1 ES k2 E + P With rapid equilibrium assumption [ES] can be expressed in terms of [S], [E] and K s (the dissociation constant of the ES complex) K s = [E] [S] = k- 1  [ES] = ([S]/ K s ) [E] (4, 5) [ES] k 1 Substitute for [ES] into eq. 3 using eq 5. v = k 2 ([S]/K s )[E] [E] T [E] + ([S]/K s )[E](6)

48 Henri-Michaelis-Menten III E + S k1 k-1 ES k2 E + P Cross multiple by k 2 and cancel out [E] (on right side) If v = k p [ES] then k p [E] T = V max (enzyme is saturated)(7) v = ([S]/K s ) k 2 [E] T 1 + ([S]/K s )(6) v = ([S]/K s ) V max 1 + ([S]/K s )(8) v = [S] V max K s + [S](9)

49 A Simple Enzyme Reaction and the Steady-State (Progress Curves) Voet, Voet & Pratt 2013 Fig 12.2

50 Steady-State (Briggs-Haldane) I Unireactant Enzyme E + S k1 k-1 ES k2 E + P If the rate ES forms E + P is >> the rate ES goes back to E + S (K 2 > k -1) and [S] >> [E] T then E, S, and ES will not be in equilibrium. Instantaneous velocity isv = k 2 [ES] (1) v = k 2 [ES] [E] T [E] + [ES](from before) (2) If [ES] is constant, i.e. d[ES]/dt = 0, then the rate that ES forms is equal to the rate that ES decomposes.

51 Steady-State (Briggs-Haldane) II E + S k1 k-1 ES k2 E + P If [ES] is constant, i.e. d[ES]/dt = 0, then the rate that ES forms is equal to the rate that ES decomposes. ES formation: E + S → ES (3) ES decomposition: ES → E + P andES → E + S (4) k1k1 kpkp k -1 rate of ES formation: = k 1 [E][S] (5) rate of ES decomposition: = k -1 [ES] + k 2 [ES] (6) = (k -1 + k 2 ) [ES](6a)

52 Steady-State (Briggs-Haldane) III E + S k1 k-1 ES kp E + P At steady-state. d[ES]/dt = 0, (7) rate of ES formation = rate of ES decomposition k 1 [E][S] = (k -1 + k p ) [ES](8) Solve eq. 8 for [ES] k 1 [E][S] (9) [ES]= (k -1 + k p ) define Michaelis constant k -1 + k p [S] (for above reaction)k m = k 1  [ES] = k m [E]

53 Steady-State (Briggs-Haldane) IV E + S k1 k-1 ES k2 E + P v = ([S]/K m ) = v = [S] V max 1 + ([S]/K m ) Vmax K m + [S] (10a,b) Can rearrange ES expression k -1 + k 2 [S] [E] K m = k 1  = [ES] When [S] = K m K m v = K m + K m V max = ½V max V max = k 2 [E] T the highest velocity when all of the enzyme is [ES], i.e. saturated.

54 Steady-State (Briggs-Haldane) V Differential Equations for Unireactant Enzyme E + S k1 k-1 ES k2 E + P d[E] dt = (k -1 + k 2 ) [ES] - k 1 [E] [S](11) d[ES] dt = k 1 [E] [S] - (k -1 + k 2 ) [ES] (12) d[S] dt = (k -1 ) [ES] - k 1 [E] [S](13) d[P] dt = (k 2 ) [ES] (14) Also know that: [E] T =[E] + [ES](15) One can write 4 differential equations to describe the above reaction Segal Enzyme Kinetics 1975 p. 28

55 Steady-State Kinetic Plot

56 Initial Velocity vs Substrate [ ] in a Simple Enzyme Reaction Voet, Voet & Pratt 2013 Fig 12.3 Lehninger 2000 Figure 8.12 o Michaelis-Menten equation

57 HTML DISPLAY Michaelis-Menten Kinetics 12-1b_MichaelisMenten\MichaelisMenten.htm

58 Significance of K m 1.It establishes an approximate value for the intracellular level of a substrate. 2.Since it is constant for a given enzyme/substrate, its numerical value provides a means of comparing enzymes from different organisms or from different tissues of the same organism, or from the same tissue at different developmental stages (V max is not a constant but depends on k p and [E] T.) K m will vary with temperature and pH. 3.K m can be altered by ligand binding – one mode of enzyme regulation. 4.If K m is known the assay conditions can be altered so that [S] >> K m so that V max can be determined which is a measure of [E] T. 5.It indicates the relative “suitability” of alternate substrates for an enzyme. The substrate with the lowest K m has the highest affinity for the enzyme. The “best” substrate has the highest V max /K m ratio. Segal Biochemical Calculations 1976 p. 218 Operational Definition: The substrate concentration at which the reaction velocity is half maximal, i.e. when K m = [S] then v o = ½V max

59 Catalytic Efficiency & Turnover Number Define the catalytic constant: k cat = V max /[E] T This is also known as the turnover number – the number of reaction processes (number of moles of substrate transformed per minute per mole of catalytic site under optimal conditions - turnovers) that each active site catalyzes per unit time (Note: some enzymes have more than one active site) However, more complex enzymes have a more complicated expression for k cat, i.e. more rate constants. When [S] << K m very little ES is formed and then [E] ≈ [E] T V o ≈ (k 2 /K m )[E] T [S] ≈ (k cat /K m ) [E] [S] Under these conditions (k cat /K m ) is a measure of the enzyme’s catalytic efficiency since this apparent second order rate constant (depends on BOTH [E] and [S]) the rate of the reaction depends on how often E and S encounter each other in solution. Most efficient enzymes have this ratio near the diffusion-controlled limit: 10 8 – 10 9 M -1 s -1 k cat /K m ≤ k 1

60 Kinetic Data Analyses Michaelis-Menten equation o

61 Lineweaver-Burke Plot Voet, Voet & Pratt 2013 Fig 12.4 1 K m 1 + 1 v o V max [S] V max y = (m) x + b

62 Eadie-Hofstee Plot Matthews et al.1999 Figure 11.17 v V max [S] K m Km* v+ y = m * x + b

63 Reversibility I Effect of Product on Forward Reaction E +SESEPE + P k1k1 k2k2 k3k3 k- 1 k- 2 k- 3 When [P] = 0 V maxf [S] (initial)K ms + [S] When [S] = 0 V maxr [P] (final)K mp + [P] vf =vf = vr =vr = The direction of the reaction will depend upon the ratio of [P]/[S] relative to K eq

64 Reversibility II Effect of Product on Forward Reaction E +SESEPE + P k1k1 k2k2 k3k3 k- 1 k- 2 k- 3 From rapid equilibrium assumptions set up net velocity eqs. v net = k 2 [ES] - k -2 [EP] v net k 2 [ES] - k -2 [EP] [E] t [E] + [ES] + [EP] Know [ES] = ([S]/K s ) [E] and [EP] = ([P]/K p ) [E]; substitute in v net k 2 ([S]/K s ) [E] - k -2 ([P]/K p ) [E] [E] t [E] + ([S]/K s ) [E] + ([P]/K p ) [E] Factor [E] out 

65 Reversibility III Effect of Product on Forward Reaction E +SESEPE + P k1k1 k2k2 k3k3 k- 1 k- 2 k- 3 k 2 [E] t ([S]/K s ) - k -2 [E] t ([P]/K p ) 1 + ([S]/K s )] + ([P]/K p ) v net V maxf ([S]/K ms ) - V maxr ([P]/K mp ) 1 + ([S]/K ms )] + ([P]/K mp ) v net Final equation in terms of steady-state Multiply right side by [E] t

66 Multisubstrate Enzymes Voet, Voet & Pratt 2013 Figure 12.5

67 Sequential Reaction Mechanisms “Reactions in which all substrates must combine with the enzyme before a reaction can occur and products are released” A+ BP+ Q E

68 Sequential Mechanisms: Types Ordered Bi-Bi Random Bi-Bi Voet, Voet & Pratt 2013 p. 367

69 Lehninger 2000 Figure 8.14a Bisubstrate Rx Steady-State Kinetic Analysis: Random BiBi

70 Ping-Pong Non-Sequential Reaction Mechanisms “Group transfer reactions in which one or more products are released before all susbtrates have been added.”

71 Non-Sequential Mechanism Ping- Pong Bi-Bi Voet, Voet & Pratt 2013 p. 367 V [A][B] V max K ma [A] + K mb [B] + [A][B] MgATPMgADPglucoseGlucose-6-P

72 Lehninger 2000 Figure 8.14b Bisubstrate Rx Steady-State Kinetic Analysis: BiBi Ping Pong

73 King-Altman Diagrams

74 Enzyme Inhibition Reversible Types: Competitive Uncompetitive Mixed (Noncompetitive) Inhibitor - Any substance that reduces the velocity of an enzyme-catalyzed reaction. Inactivator - Any substance that irreversibly binds to an enzyme. (appears similar to noncompetitive inhibition.)

75 Competitive Inhibition K I = [E][I] / [EI] v = k 2 [ES] v max = k 2 [E] T v k 2 [ES] [E] T [E] + [ES] + [EI] v ([S]/K m ) [E] k 2 [E] T [E] + ([S]/K m ) [E] + ([I]/K I ) [E] v ([S]/K m ) [S] [S] V max 1 + ([S]/K m ) + ([I]/K I )K m (1 + ([I]/K I )) +[S]αK m + [S] K mapp = K m [1 + ([I]/K i )] Voet, Voet & Pratt 20 Figure 12.8

76 Competitive Inhibition Matthews et al.1999 Figure 11.20Voet, Voet & Pratt 2013 Figure 12.7

77 Uncompetitive Inhibition: M-M enzyme in L-B Plot Voet, Voet & Pratt 2013 Fig 12.9 k2k2 k -1 k1k1 K I = [ES][I] / [ESI] v = k 2 [ES] v max = k 2 [E] T v k 2 [ES] [E] T [E] + [ES] + [ESI] v ([S]/K m ) [E] k 2 [E] T [E] + ([S]/K m ) [E] + ([S][I]/K m K I ) [E] v ([S]/K m ) v [S] [S] V max 1 + ([S]/K m ) + ([S][I]/K m K I ) V maxI (Km/(1 + ([I]/K I )) +[S]αK m + [S] v maxI = v max / /(1 + ([I]/K I ))

78 Mixed Inhibition: M-M enzyme in L-B Plot Voet, Voet & Pratt 2013 Fig 12.10 K I = [E][I]/[EI] and K’ I = [ES][I]/[ESI] v k 2 [ES] [E] T [E] + [ES] +[EI] + [ESI] v [S] v [S] V max K m (1+ ([I]/K I )) + [S] (1+ ([I]/K ’ I )) V maxI αK m + α’ [S]

79 Michaelis-Menten Equations: Effects of Inhibitors Table Voet, Voet & Pratt 2013 Table 12.2 Lehninger 2005 Table 6.9 An example for competitive inhibitor the X intercept is: 1/K m app =1/αK m = 1 /(1+[I]/K i )K m

80 Temperature Effects Enzyme Activity

81 Kinetics, Thermodynamics, and Transition State Theory I A + B X ‡ P + Q K‡K‡ k’ dP/dt = k [A][B] = k’ [X ‡ ] under rapid equilibrium assumption write: K ‡ = [X ‡ ] / [A][B] equilibrium constant expression ΔG ‡ = -RT ln K ‡ relate equil. const. to free energy (thermodynamics) dP/dt = k’ e -ΔG‡/RT [A] [B] substituting into the first equation k’ =  define  vibra. freq. bond breaks as X‡ to products and  prob. X goes to products rather than reactant. (0 -1) ν = ε/h h is Planck’s const. ε is the avg. energy of the vibration for the decomposition on X ‡

82 Kinetics, Thermodynamics, and Transition State Theory II A + B X ‡ P + Q K‡K‡ k’ ε = k B T from Stat. Mech. The energy of a classical oscillator at T. (the available thermal energy) where k B = Boltzman constant 6.6261 x 10 -34 J s k’ = k B T/h via substitution k = (k B T/h) e -ΔG‡/RT = A e -ΔG‡/RT

83 Arrhenius Equation Matthews et al.1999 Figure 11.3 k = Ae -Ea/RT ln k = ln A –E a /RT or log k = log A –E a /2.303RT Slope -E a /2.303R log A

84 pH Effects Enzyme Activity Lehninger 2004 Figure 6.17

85 Enzyme Regulation Control of Enzyme availability Cells control the rate of enzyme synthesis and degradation and thus can control the amount of enzyme present. Control of Enzyme activity via binding of small molecule “allosteric effectors” that alter catalytic activity. via covalent modification of an enzyme, e.g. phosphorylation and dephosphorylation Voet, Voet & Pratt 2013 0.381

86 Allosteric Effect 0.4 mM 2.0 mM Voet, Voet & Pratt 2013 Fig 12.11

87 Kinetics and Mechanism The steady-state kinetic analysis of a reaction cannot unambiguously establish the reaction’s mechanism

88 Bisubstrate Rx: Examples Voet, Voet & Pratt 2008 Fig 12.5 Transferase Redox

89 Cytochrome P450 & Drug Metabolism “Differences in reactions to drugs arise from genetic differences among individuals as well as differences in their disease states, other drugs they are taking, age, sex, and environmental factors” Cytochromes P450: a major function is to detoxify xenobiotics – involved in metabolic clearance of a many of drugs in use today. Cytochromes P450: superfamily of enzymes – occur in nearly all living organisms. Human genome has 57 isoforms -33% of isoforms are in liver Nomenclature: P450 isozymes are named by the letters CYP followed by a number designating its family, an uppercase letter designating its subfamily, and another number, e.g. CYP2D6 Voet, Voet & Pratt 2012 p.389

90 Cytochrome P450 & Drug Metabolism II Typical reaction type: RH + O 2 + 2 H + + 2e - → ROH + H 2 O Different Cyt P450 are SPECIFIC for particular types of a wide variety of typically lipophilic compounds, RH. PAH polycyclic aromatic hydrocarbons (carcinogenic – in smoke, broiled meat) PCB polycyclic biphenyls (electrical insulators; plasticizers) steroids (P450s also involved in their biosynthesis) drugs (many types) Convert Xenobiotics to a more water soluble form to facilitate excretion New hydroxyl group can be enzymatically conjugated to glucuronic acid, glycine, sulfate & acetate – further increases water solubility Good: Allow xenobiotics to be detoxified and/or cleared. Bad: Sometimes converts an innocuous compound to a toxic agent, e.g. acetaminophen metabolism at high dosages

91 Cytochrome P450 & Drug Metabolism III Cyt P450s often mediate drug-drug interactions. Text Example: Two drugs A & B. Case 1: Drug A metabolized by or inhibits Cyt P450 isozyme. Same isozyme metabolizes drug B. Both drugs given together – Bioavailability of drug B increases. Why? What if drug B has a low therapeutic index? Case 2: Drug A induces increased expression of the particular isozyme of Cyt P450 Both drugs given together – Bioavailability of Drug B decreases. Why? Case 3: Additionally Drug B is metabolized to a toxic product. Both drugs given together. What happens to rate of Drug B metabolism? Why? What is the resultant problem?

92 End of Lectures


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