Enzyme Catalysis and Enzyme Kinetics 9/15/11 Version

Enzyme Catalysis and Enzyme Kinetics 9/15/11 Version

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

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. Enzymes 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. The molecule(s) produced by the reaction is called the product. Lehninger 2005 Figure p.191 Enzymes: General Properties Enzymatically catalyzed reactions: are typically 106 to 1012 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 International Classification on Enzymes (OTHLIL) To be systematic the IUMBMB developed a numerical coding and naming system. Here are the 6 major classes

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. Lehninger 2000 Table 8.3 Enzyme Commission Number An example: The four-part enzyme classification number is a series of 4 numbers separated by periods. Cytochrome c oxidoreductase trivial (common) names : cytochrome oxidase, Complex IV 1. Class

Oxidoreductases 1.9. Subclass Acting on a heme group of donors 1.9.3 Sub-subclass With oxygen as an acceptor See enzyme classification website @ http://expasy.ch/sprot/enzyme.html Specificity of Enzymes Geometric complementarity the enzymes binding site has a structure complementary to the substrate it needs to bind.

Electronic complementarity amino acids that form the enzymes 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. EnzymeSubstrate Complex Illustration Voet, Voet & Pratt 2013 Fig 11.1 Cofactors and Coenzymes Some enzymes require some help. 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. 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. Lehninger 2000 Table 8.2 Coenzymes as Transient Carriers Table Human Deficiency Disease Perncious anemia

Pellagra Megaloblastic anemia Beriberi What do enzymes do? Enzymes as catalysts change the rate of a chemical reaction but do not alter the equilibrium. Transition State Theory, Activation Energy (Ea), & The Reaction Coordinate Thermodynamics Again? Transition state theory was developed to describe chemical reactions by applying thermodynamic equilibrium concepts.

Transition State Diagram Consider the bimolecular Rx (a) : HA HB + HC HA + HB-- HC Consider the generic bimolecular Rx (b) : A + B X P + Q rate = k ~ e-G/RT G/RT ; G/RT G = Ea Voet, Voet & Pratt 2013 Fig 11.5 Transition State Diagram: Effect of Catalyst

A catalyst functions by lowering the activation energy of a reaction, the energy barrier for the reactants to become products. Voet, Voet & Pratt 2013 Fig 11.7 Catalytic Rate Enhancement*: a GG Calculation The enhancement of catalyzed vs uncatalyzed is given by: k= eG/RT G/RT G/RT ln k = G/RT G/RT G/RT RT ln k = G/RT G/RT G for a 100-fold change in rate at 25 C (8.314514 J K-1 mol-1 x 298.15 K) x ln(100) = G/RT G/RT G (2478.97 J mol-1 ) x (4.605) = G/RT G/RT G 11,416 J mol-1 = 11.42 kJ mol-1 = GGG

10-fold: 5.71 kJ mol -1 1,000,000-fold: compare H-bond ~20 kJ mol-1 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 Effect of GG versus GG Important Concepts!

A+B P+Q GG effects the likelihood of reactants going to products AND products to reactants - speeds up both reactions! GG effects the likelihood of reactant going to products OR products going to reactants based on the free energy difference between reactants and products. thermodynamics G/RT G < 0 forward reaction favored A+ B P+ Q CATALYTIC MECHANISMS Enzymes are effective as catalysts due to: 1) their ability to rearrange covalent bonds using their various amino acid side chains, metal ions and coenzymes. 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. 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 Acid-Base Catalysis Mechanism: Keto-Enol Tautomerization Uncatalyzed

ketone Hydroxyl ol ene acid General Acid Catalyzed General Base Catalyzed base partial charge

Voet, Voet & Pratt 2013 Fig 11.8 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 G/RT G and accelerates the reaction. General Base Catalysis: A process in which partial proton extraction by a base lowers G/RT G and accelerates the reaction. Amino Acids in General Acid-Base Catalysis

Lehninger 2005 Figure 6.9 pH and Enzyme Activity Lehninger 2005 Figure 6.17 RNase A Mechanism: An Acid-Base Catalysis Base catalysis 2,3Cyclic ribonucleotide intermediate Acid catalysis

Voet, Voet & Pratt 2013 Fig 11.10 Covalent Catalysis: Decarboxylation of Acetoacetate uncatalyzed carbonyl elimination decarboxylation covalent bond electron withdrawal Transition state Typical Stages: 1.

Nucleophilic Rx 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) Voet, Voet & Pratt 2013Fig 11.11 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. Biologically Important Electrophiles & Nucleophiles The nucleophilicity of a substance is closely related to its basicity Voet, Voet & Pratt 2013 Fig 11.12 Metal Ion Catalysis: Carbonic Anhydrase

Participate in catalytic process by: Binding to substrates to properly orient them for Rx Mediating redox Rx via reversible metal ion oxidation state changes. CO2 + H2O HCO3- + H+ Active site opening Electrostatic stabilization or neg. charge shielding Nearly 1/3 of all enzymes utilize a metal ion for their catalytic function. Voet, Voet & Pratt 2008 Fig 11.13

Electrostatic Catalysis The charge distribution around enzyme active sites appears to be arranged to stabilize the transition state of the catalyzed reactions. Proximity & Orientation Effects 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 ~107-fold boost

Voet, Voet & Pratt 2006 p. 328 Preferential Transition State Binding S ES 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 Lehninger 2013 Figure 11.15 Kinetics The study of reaction rates Goals -Kinetics

Know the difference between 1st and 2nd 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 Km and Vmax. 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 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. Internet Explorer Demonstration Chemical Kinetics Elementary Rxs Reaction Stoichiometry A P substance A; product P A I1 I2 P intermediates In 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 Reaction Order First Order First Order Reaction A P First Order Equation: d[P] v= dt = - d[A]

dt = k[A] The reaction at time t is proportional to the concentration of A. Ao is the initial reactant concentration k is in s-1 units For first order: The half-life is independent of [A0], i.e. it is a constant Voet, Voet & Pratt 2013 Fig 12.1 Determining order & rate constant for Irreversible 1st order Rx Matthews et al.1999 Figure 11.1 Second Order Reactions (Bimolecular)

2A P Second Order Equation: d[A] v= dt = 1 1 [A] = k[A]2

[Ao] + kt k is in M-1 S-1 units Half-life : t = 1/k[Ao] A+BP 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)

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

[A] = [Ao] e-kt Half Life Calculation First Order k t = ln [A0]/2 [Ao] t = ln 2/k = 0.693 / k Second Order t = 1/(k [Ao]) Half Life: t Enzyme Kinetics The study of enzyme reaction rates Lehninger 205 Figure 8.6

Enzyme Kinetic Definitions: E Enzyme; [E] enzyme concentration: ES enzyme substrate complex P, Q, R, products [E]T total enzyme [ES] complex concentration A, B, C . substrates I, J, K inhibitors k rate constant k1 forward rate constant k-1 reverse rate constant

kp the catalytic rate constant. v = reaction velocity vo = initial reaction velocity, when [P] ~ 0 Two Approaches to Enzyme Kinetics Problem: One does not know the concentration of ES during a reaction. Therefore, one has to make certain assumptions for calculations Rapid Equilibrium (Henri-Michaelis-Menten) Early components of the reaction are at equilibrium. Permits one to express [ES] in terms of [E], [S], & Ks, 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. Lehninger 2005 Figure p.203 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 = k2 [ES] (1) The total enzyme is written: [E]T = [E] + [ES] (2) Divide equation (1) by [E]T v [E]T =

k2 [ES] [E] + [ES] (3) 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 Ks (the dissociation constant of the ES complex) Ks = [E] [S] = k-1 [ES] = ([S]/ Ks) [E] (4, 5) [ES] k1 Substitute for [ES] into eq. 3 using eq 5. v [E]T = k2 ([S]/Ks)[E] [E] + ([S]/Ks)[E] (6)

Henri-Michaelis-Menten III E + S k1 k-1 ES E + P k2 Cross multiple by k2 and cancel out [E] (on right side) v = ([S]/Ks) k2 [E]T

1 + ([S]/Ks) (6) If v = kp [ES] then kp [E]T = Vmax (enzyme is saturated) (7) v Vmax v Vmax = ([S]/Ks) 1 + ([S]/Ks) (8) = [S]

Ks + [S] (9) A Simple Enzyme Reaction and the Steady-State (Progress Curves) Voet, Voet & Pratt 2013 Fig 12.2 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 (K2 > k-1) and [S] >> [E]T then E, S, and ES will not be in equilibrium. Instantaneous velocity is v [E]T = v = k2 [ES] (1)

k2 [ES] [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. 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. k1 ES formation: E + S ES (3) kp k-1 ES decomposition: ES E + P andES E + S rate of ES formation: = k1 [E][S] rate of ES decomposition: = k-1 [ES] + k2 [ES] =

(k-1 + k2) [ES] (4) (5) (6) (6a) Steady-State (Briggs-Haldane) III E + S k1 k-1 ES E + P

kp At steady-state. d[ES]/dt = 0 , (7) rate of ES formation = rate of ES decomposition k1 [E][S] = (k-1 + kp) [ES] (8) Solve eq. 8 for [ES] k1[E][S] [ES]

(9) = (k-1 + kp) define Michaelis constant (for above reaction) k-1 + kp km = k1 [S] [ES] = km [E]

Steady-State (Briggs-Haldane) IV E + S v Vmax = ES k1 k-1 ([S]/Km) 1 + ([S]/Km) = v Vmax

k2 = [S] Km + [S] E + P (10a,b) Can rearrange ES expression k-1 + k2 Km = [S] [E] k1 When [S] = Km

v= = [ES] Km Km + Km Vmax = Vmax Vmax = k2 [E]T the highest velocity when all of the enzyme is [ES], i.e. saturated. Steady-State (Briggs-Haldane) V Differential Equations for Unireactant Enzyme E + S

k1 k-1 ES k2 E + P One can write 4 differential equations to describe the above reaction d[E] dt = (k-1 + k2) [ES] - k1 [E] [S] d[ES] dt = k1 [E] [S] - (k-1 + k2) [ES]

d[S] dt = (k-1) [ES] - k1 [E] [S] d[P] dt = (k2) [ES] (14) Also know that: [E]T = [E] + [ES] (15) (11) (12) (13) Segal Enzyme Kinetics 1975 p. 28

Steady-State Kinetic Plot Initial Velocity vs Substrate [ ] in a Simple Enzyme Reaction o Michaelis-Menten equation Voet, Voet & Pratt 2013 Fig 12.3 Lehninger 2000 Figure 8.12 HTML DISPLAY Michaelis-Menten Kinetics 12-1b_MichaelisMenten\MichaelisMenten.htm

Significance of Km Operational Definition: The substrate concentration at which the reaction velocity is half maximal, i.e. when Km = [S] then vo = Vmax 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 (Vmax is not a constant but depends on kp and [E]T.) Km will vary with temperature and pH. 3.

Km can be altered by ligand binding one mode of enzyme regulation. 4. If Km is known the assay conditions can be altered so that [S] >> Km so that Vmax 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 Km has the highest affinity for the enzyme. The best substrate has the highest Vmax/Km ratio. Segal Biochemical Calculations 1976 p. 218 Catalytic Efficiency & Turnover Number Define the catalytic constant: kcat = Vmax/[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 kcat, i.e. more rate constants. When [S] << Km very little ES is formed and then [E] [E]T Vo (k2/Km)[E]T [S] (kcat/Km) [E] [S] Under these conditions (kcat/Km) is a measure of the enzymes 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: 108 109 M-1s-1 kcat/Km k1

Kinetic Data Analyses Michaelis-Menten Michaelis-Mentenequation equation o Lineweaver-Burke Plot y = (m) x + b 1 Km 1 + 1 vo Vmax [S] Vmax Voet, Voet & Pratt 2013 Fig 12.4

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

Reversibility I Effect of Product on Forward Reaction E +S k1 k-1 ES When [P] = 0 (initial) When [S] = 0 (final) k2 EP

k-2 E+P Vmaxf [S] vf = Kms + [S] Vmaxr [P] vr = Kmp + [P] k3 k-3

The direction of the reaction will depend upon the ratio of [P]/[S] relative to Keq Reversibility II Effect of Product on Forward Reaction E +S k1 k-1 ES k2 EP

k-2 k3 E+P k-3 From rapid equilibrium assumptions set up net velocity eqs. vnet = k2 [ES] - k-2 [EP] vnet [E]t k2 [ES] - k-2 [EP] [E] + [ES] + [EP]

Know [ES] = ([S]/Ks) [E] vnet [E]t and [EP] = ([P]/Kp) [E]; substitute in k2 ([S]/Ks) [E] - k-2 ([P]/Kp) [E] [E] + ([S]/Ks) [E] + ([P]/Kp) [E] Factor [E] out Reversibility III Effect of Product on Forward Reaction E +S

vnet vnet k1 k-1 k2 ES EP k-2 k3

E+P k-3 k2 [E]t([S]/Ks) - k-2 [E]t ([P]/Kp) 1+ ([S]/Ks)] + ([P]/Kp) Vmaxf ([S]/Kms) - Vmaxr ([P]/Kmp) 1+ ([S]/Kms)] +

([P]/Kmp) Final equation in terms of steady-state Multiply right side by [E]t Multisubstrate Enzymes Voet, Voet & Pratt 2013 Figure 12.5 Sequential Reaction Mechanisms Reactions in which all substrates must combine with the enzyme before a reaction can occur and products are released A+ B

E P + Q Sequential Mechanisms: Types Ordered Bi-Bi Random Bi-Bi Voet, Voet & Pratt 2013 p. 367 Bisubstrate Rx Steady-State Kinetic Analysis: Random BiBi

Lehninger 2000 Figure 8.14a Ping-Pong Non-Sequential Reaction Mechanisms Group transfer reactions in which one or more products are released before all susbtrates have been added. Non-Sequential Mechanism MgATP MgADP glucose Glucose-6-P

PingPong Bi-Bi V Vmax [A][B] Kma[A] + Kmb[B] + [A][B] Voet, Voet & Pratt 2013 p. 367 Bisubstrate Rx Steady-State Kinetic Analysis: BiBi Ping Pong Lehninger 2000 Figure 8.14b King-Altman Diagrams KING-ALTMAN DIAGRAM EXAMPLE PART A

k1[bc1ox] Qr k4 k-4 QO k-1 Qrbc1ox k -2 k -3[bc1ox] k2

QObc1r k3 Qr QT = k2k3k4 +k-1k3k4 + k-3[bc1r]k-2k-4 + k-2k-1k4 D Qrbc1ox QT = k3k4k1[bc1ox] +k4k1[bc1ox]k-2 + k-2k-3[bc1r]k1[bc1ox] + k-4 k-3k-2

D Qobc1r QT = k4k1[bc1ox] +k1[bc1ox]k2k-3[bc1r] + k2k-4k-3[bc1r] + k-1 k-4 k-3[bc1r] D Qo QT = KING-ALTMAN DIAGRAM EXAMPLE PART B k1[bc1ox] +k2k3k-4 + k3k--4k-1 + k-2k-1k-4

D Velocity Equation : v ET = v= k1[Qr] [bc1ox] - k-1 [Qbc1ox] k1k2k3k4 [bc1ox] - k-1k-2k-3k-4 [bc1r] k4(k2k3+k-1k3+k-1k-2) + k-4(k2k3+k3k-1+k-1k-2) + k1(k3k4+k4k-2+k2k4+k2k3)[bc1ox] + k-3(k1k2+k-1k-2)[bc1ox] [bc1r] + k-3(k1k-2+k-2k-4+ k-1k-4)[bc1r] Enzyme Inhibition Inhibitor - Any substance that reduces the velocity of an enzyme-catalyzed reaction. Reversible Types:

Competitive Uncompetitive Mixed (Noncompetitive) Inactivator - Any substance that irreversibly binds to an enzyme. (appears similar to noncompetitive inhibition.) Competitive Inhibition Kmapp = Km [1 + ([I]/Ki)] KI = [E][I] / [EI] v = k2 [ES] v vmax = k2[E]T k2 [ES]

[E]T [E] + [ES] + [EI] v ([S]/Km) [E] k2[E]T [E] + ([S]/Km) [E] + ([I]/KI) [E] v ([S]/Km) Vmax 1 + ([S]/Km) + ([I]/KI) [S] [S] Km(1 + ([I]/KI)) +[S]

Voet, Voet & Pratt 20 Figure 12.8 Km + [S] Competitive Inhibition Matthews et al.1999 Figure 11.20 Voet, Voet & Pratt 2013 Figure 12.7 k1 k-1 Uncompetitive Inhibition: M-M enzyme in L-B Plot k 2

KI = [ES][I] / [ESI] v = k2 [ES] v [E]T vmax = k2[E]T k2 [ES] [E] + [ES] + [ESI] Voet, Voet & Pratt 2013 Fig 12.9 vmaxI = vmax / /(1 + ([I]/KI)) v ([S]/Km) [E]

k2[E]T [E] + ([S]/Km) [E] + ([S][I]/KmKI) [E] v ([S]/Km) v [S] Vmax 1 + ([S]/Km) + ([S][I]/Km KI) VmaxI [S] (Km/(1 + ([I]/KI)) +[S] Km + [S] Mixed Inhibition: M-M enzyme in L-B Plot

KI = [E][I]/[EI] and KI = [ES][I]/[ESI] v k2 [ES] [E]T [E] + [ES] +[EI] + [ESI] v [S] (1+ ([I]/KI)) v VmaxI [S] Km + [S]

Vmax Km (1+ ([I]/KI)) + [S] Voet, Voet & Pratt 2013 Fig 12.10 Michaelis-Menten Equations: Effects of Inhibitors Table An example for competitive inhibitor the X intercept is: 1/Km app =1/KKm = 1 /(1+[I]/Ki)Km Lehninger 2005 Table 6.9 Voet, Voet & Pratt 2013 Table 12.2 Temperature Effects Enzyme Activity Kinetics, Thermodynamics, and

Transition State Theory I A+B K X k P+Q dP/dt = k [A][B] = k [X] under rapid equilibrium assumption write: K = [X] / [A][B] G/RT G = -RT ln K equilibrium constant expression relate equil. const. to free energy (thermodynamics)

dP/dt = k e-G/RTG/RT [A] [B] k = substituting into the first equation define vibra. freq. bond breaks as X to products and prob. X goes to products rather than reactant. (0 -1) = /h h is Plancks const. is the avg. energy of the vibration for the decomposition on X Kinetics, Thermodynamics, and Transition State Theory II A+B = k BT

K X k P+Q from Stat. Mech. The energy of a classical oscillator at T. (the available thermal energy) where kB = Boltzman constant 6.6261 x 10-34 J s k = kBT/h via substitution k = (kBT/h) e-G/RTG/RT = A e -G/RTG/RT

Arrhenius Equation log A k = Ae-Ea/RT Slope ln k = ln A Ea/RT or -Ea/2.303R log k = log A Ea/2.303RT Matthews et al.1999 Figure 11.3 pH Effects Enzyme Activity

Lehninger 2004 Figure 6.17 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 Allosteric Effect 2.0 mM 0.4 mM Voet, Voet & Pratt 2013 Fig 12.11 Kinetics and Mechanism The steady-state kinetic analysis of a reaction cannot unambiguously establish the reactions mechanism Bisubstrate Rx: Examples Transferase

Redox Voet, Voet & Pratt 2008 Fig 12.5 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 Cytochrome P450 & Drug Metabolism II Typical reaction type: RH + O2 + 2 H+ + 2e- ROH + H2O 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 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? End of Lectures

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