Biochemistry 304 2014 Student Edition Enzymes and Enzyme

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Transcript Biochemistry 304 2014 Student Edition Enzymes and Enzyme

Enzyme Catalysis and Enzyme Kinetics

Student Edition

5/23/13 Version

Dr. Brad Chazotte 213 Maddox Hall [email protected]

Web Site: http://www.campbell.edu/faculty/chazotte

Pharm. 304 Biochemistry Fall 2014

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 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

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.

1.9.3.1

Cytochrome c oxidoreductase trivial (common) names : cytochrome oxidase, Complex IV 1.

1.9.

1.9.3

Class Subclass Oxidoreductases Acting on a heme group of donors Sub-subclass With oxygen as an acceptor

See enzyme classification website @ http://expasy.ch/sprot/enzyme.html

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

-amino acids that comprise the enzyme.

Enzyme Substrate 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 (E

), & 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 R x (a) :

H A – H B + H C



H A + H B -- H C

Consider the generic bimolecular R x (b) :

A + B

rate = k ~

-ΔG‡/RT ; ΔG ‡ =

E a



X ‡



P + Q

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 ΔG

‡

Calculation

The enhancement of catalyzed

uncatalyzed is given by: k=

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 10-fold: -1 =

11.42 kJ mol -1 = ΔΔG ‡

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

Effect of ΔG

‡

versus ΔG Important Concepts!

A + B



P + Q ΔG ‡

effects the likelihood of reactants going to products

D products to reactants - speeds up both reaction

ΔG

effects the likelihood of reactant going to products

products going to reactants based on the free energy difference between reactants and products. thermodynamics ΔG < 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

ketone Uncatalyzed Hydroxyl “ol” “ene” acid General Acid Catalyzed General Base Catalyzed base δ ≡ partial charge Voet, Voet & Pratt 2013 Fig 11.8

Types of Acid-Bases Catalysis

• • •

Specific Acid-Base Catalysis

: reactions: Uses only the H + Non-enzymatic 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

proton transfer from an acid lowers ΔG‡ and accelerates the reaction.

: A process in which partial

General Base Catalysis:

proton extraction by a base lowers ΔG‡ and accelerates the reaction.

A process in which partial

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’,3’Cyclic ribonucleotide intermediate Acid catalysis Voet, Voet & Pratt 2013 Fig 11.10

Covalent Catalysis: Decarboxylation of Acetoacetate

carbonyl covalent bond uncatalyzed electron withdrawal decarboxylation elimination Transition state

Typical Stages:

Nucleophilic R x between catalyst & substrate to form covalent bond.

Withdrawal of electrons from reaction center by the (now) electrophilic catalyst.

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 good leaving groups

and also can form

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 R x •Mediating redox R x reversible metal ion via oxidation state changes.

•Electrostatic stabilization or neg. charge shielding Active site opening CO 2 + H 2 O  HCO 3 + H + 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 ~

10 7

-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 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

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 R

s

Reaction Stoichiometry A → P substance A; product P A → I 1 → I 2 → P intermediates I n Rate Constant

The proportionality constant at constant temperature describing the rate of an elementary reaction.

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:

[P]

[A] v =

= -

[A] The reaction at time t is proportional to the concentration of A. A o is the initial reactant concentration

is in s -1 units For first order: The half-life is

independent

of [A 0 ], i.e. it is a constant Voet, Voet & Pratt 2013 Fig 12.1

Determining order & rate constant for Irreversible 1 st order Rx

Matthews

et al.

1999 Figure 11.1

Second Order Reactions (Bimolecular) 2A → P

Second Order Equation:

[A] v =

[A] 2

is in M -1 S -1 units 1 1 [A] =

A + B → P

[A o ] +

Half-life : t ½ = 1/

[A o ] Second Order Equation:

[A]

[B] v = -

= -

[A][B]

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)

[A] [A] =

ln[A] = -

k dt

⌠ [A] ⌠t Integrate from [A o ] to [A] ⌡ [ Ao] d ln [A] = -

⌡ 0

ln [A] = ln[A o ] –

t or [A] = [A o ]

e -kt

Half Life Calculation

First Order

t ½ = ln [A 0 ]/2 [A o ] t ½ = ln 2/

k =

0.693 /

Second Order t ½ = 1/(

[A o ]) Half Life: t ½

Enzyme Kinetics

The study of enzyme reaction rates Lehninger 205 Figure 8.6

Enzyme Kinetic Definitions:

E ES Enzyme; [E] enzyme concentration enzyme substrate complex : [E] T total enzyme [ES] complex concentration P, Q, R,… “products” A, B, C ….

“substrates” I, J, K… “inhibitors”

k p

rate constant

k 1

forward rate constant

-1 the catalytic rate constant . reverse rate constant

= reaction velocity

v o

= initial reaction velocity, when [P] ~ 0

Two Approaches to Enzyme

Problem:

Kinetics

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], & 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.

Lehninger 2005 Figure p.203

Henri-Michaelis-Menten I

Unireactant Enzyme

E + S

k1 k-

1 ES

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)

Henri-Michaelis-Menten II

E + S

k1 k-

1 ES

E + P With rapid equilibrium assumption [ES] can be expressed in terms of [S], [E] and K

K s

s (the dissociation constant of the ES complex) = [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)

Henri-Michaelis-Menten III

E + S

k1 k-

1 ES

E + P Cross multiple by

k 2

and cancel out [E] (on right side) v = ([S]/

K s

)

k 2

[E] T 1 + ([S]/

K s

) (6) If v =

k p

[ES] then

k p

[E] T = V max (enzyme is saturated ) (7) v = ([S]/

K s

) V max 1 + ([S]/

K s

) v = [S] V max

K s

+ [S] (8) (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

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 is v =

k 2

[ES] (1) v =

k 2

[ES] [E] T [E] + [ES] (from before) (2) If [ES] is constant, i.e.

[ES]/

= 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

E + P If [ES] is constant, i.e.

[ES]/

= 0 ,

then the rate that ES forms is equal to the rate that ES decomposes.

ES formation:

k 1

E + S → ES ES decomposition:

ES → E + P and (3)

ES → E + S (4) rate of ES formation: =

k 1

[E][S] rate of ES decomposition: =

k -1

[ES] +

k 2

[ES] = (

k -1

k 2

) [ES] (5) (6) (6a)

Steady-State (Briggs-Haldane) III

E + S

k1 k-

1 At steady-state.

[ES]/

= 0 , E + P rate of ES formation = rate of ES decomposition

k 1

[E][S] = (

k -1

k p

) [ES] Solve eq. 8 for [ES] [ES]

k 1

[E][S] = (

k -1

k p

) define Michaelis constant (for above reaction) (7) (8) (9)

k m

k -1

k p

[S]

k 1

 [ES] =

k m

[E]

Steady-State (Briggs-Haldane) IV

E + S

k1 k-

1 ES

E + P v = ([S]/

K m

) V max 1 + ([S]/

K m

) = v = [S] Vmax

K m

+ [S] (10a,b) Can rearrange ES expression

K m

= When [S] =

K m k -1

k 2

[S] [E]

k 1

 = [ES]

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.

Steady-State (Briggs-Haldane) V

Differential Equations for Unireactant Enzyme

E + S

k1 k-

1 ES

E + P One can write 4 differential equations to describe the above reaction

[E]

= (

k -1

k 2

) [ES] -

k 1

[E] [S]

[ES]

k 1

[E] [S] - (

k -1

k 2

) [ES]

[S]

= (

k -1

) [ES] -

k 1

[E] [S]

[P]

= (

k 2

) [ES] Also know that: [E] T = [E] + [ES] (11) (12) (13) (14) (15) 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 K

Operational Definition: The substrate concentration at which the reaction velocity is half maximal, i.e. when

K m

= [S] then v o = ½

V max

It establishes an approximate value for the intracellular level of a substrate.

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. K m can be altered by ligand binding – one mode of enzyme regulation. If

K m

V max is known the assay conditions can be altered so that [S] >> can be determined which is a measure of [E] T.

K m

so that 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

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 o

≈ (

k 2 /K m

)[E] T very little ES is formed and then [E] ≈ [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

Kinetic Data Analyses

Lineweaver-Burke Plot

y = (m) x + b 1

K m

1 + 1

v o V max

[S]

V max

Voet, Voet & Pratt 2013 Fig 12.4

Eadie-Hofstee Plot

y = m * x + b

v V max Km

[S]

K m

Matthews

et al.

1999 Figure 11.17

Reversibility I

Effect of Product on Forward Reaction

k 1 k 2

E +S ES

k 1 k 2

When [P] = 0

V maxf v f

(initial)

K ms

[S] + [S] EP When [S] = 0

V maxr v r

(final)

K mp

[P] + [P]

k 3 k 3

E + P The direction of the reaction will depend upon the ratio of [P]/[S] relative to K eq

Reversibility II

Effect of Product on Forward Reaction

k 1 k 2 k 3

E +S ES EP

k 1 k 2 k 3

From rapid equilibrium assumptions set up net velocity eqs.

v net

k 2

[ES] -

k -2

[EP] E + P

v net

[E]

t k 2

[ES] -

k -2

[EP] [E] + [ ES ] + [ EP ] Know [ ES ] = ([S]/

K s

) [E] and [ EP ] = ([P]/

K p

) [E]; substitute in

v net

[E]

t k 2

([S]/

K s

) [E] -

k -2

([P]/

K p

) [E] [E] + ([S]/

K s

) [E] + ([P]/

K p

) [E] Factor [E] out 

E +S

v net

Reversibility III

Effect of Product on Forward Reaction

k 1 k 1

k 2 k 2

k 3 k 3 k 2

[E]

([S]/

K s

) -

k -2

[E]

([P]/

K p

) 1 + ([S]/

K s

)] + ([P]/

K p

) E + P Multiply right side by [E] t

v net

V maxf ([S]/

K ms

) V maxr ([P]/

K mp

) 1 + ([S]/

K ms

)] + ([P]/

K mp

) Final equation in terms of steady-state

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

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

MgADP

Ping Pong Bi-Bi

MgATP glucose Glucose-6-P V

V max

[A][B]

K ma

[A] +

K mb

[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

Q r k 1 [bc 1ox ] Q r bc 1ox k -1 k 4 k-4 k -2 k 2 k -3 [bc 1ox ] Q O Q O bc 1r Q r Q T = Q r bc 1ox Q T = Q o bc 1r Q T = k 3 k 2 k 3 k 4 +k -1 k 3 k 4 + k -3 [bc 1r ]k -2 k -4 + k -2 k -1 k 4

k 3 k 4 k 1 [bc 1ox ] +k 4 k 1 [bc 1ox ]k -2 + k -2 k -3 [bc 1r ]k 1 [bc 1ox ] + k -4 k -3 k -2

k 4 k 1 [bc 1ox ] +k 1 [bc 1ox ]k 2 k -3 [bc 1r ] + k 2 k -4 k -3 [bc 1r ] + k -1 k -4 k -3 [bc 1r ]

D KING-ALTMAN DIAGRAM EXAMPLE PART B

Q o Q T = k 1 [bc 1ox ] +k 2 k 3 k 4 + k 3

k --4 k -1 + k -2 k -1 k -4 Velocity Equation :

k 1 [Q r ] [bc 1ox ] - k -1 [Qbc 1ox ]

k 1 k 2 k 3 k 4 [bc 1ox ] - k 1 k 2 k 3 k 4 [bc 1r ]

E T =

k 4 (k 2 k 3 +k -1 k 3 +k -1 k -2 ) + k 4 (k 2 k 3 +k 3 k -1 +k -1 k -2 ) + k 1 (k 3 k 4 +k 4 k -2 +k 2 k 4 +k 2 k 3 )[bc 1ox ] + k -3 (k 1 k 2 +k -1 k -2 )[bc 1ox ] [bc 1r ] + k -3 (k 1 k 2 +k -2 k -4 + k -1 k -4 )[bc 1r ]

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

K mapp

K m

[1 + ([I]/

K i

)]

K I = [E][I] / [EI]

v = k 2

[ES]

v max

k 2

[E] T

v k 2

[ES] [E] T [E] + [ES] + [ EI ]

k 2 [E] T ([S]/

K m

) [E] [E] + ([S]/

K m

) [E] + ([I]/

K I

) [E]

([S]/

K m

)

V max

1 + ([S]/

K m

) + ([I]/

K I

) [S]

K m

(1 + ([I]/

K I

)) +[S] Voet, Voet & Pratt 20 Figure 12.8

αK

[S] + [S]

Competitive Inhibition

Matthews

et al.

1999 Figure 11.20

Voet, Voet & Pratt 2013 Figure 12.7

k 1 k -1

Uncompetitive Inhibition: M-M enzyme in L-B Plot

k 2

K I = [ES][I] / [ESI]

v = k 2

[ES]

v max

k 2

[E] T

v k 2

[ES] [E] T

k 2 [E] T [E] + [ES] + [ ESI ] ([S]/

K m

[E] + ([S]/ ) [E]

K m

) [E] + ([S][I]/

K m K I

) [E]

([S]/

K m

)

V max

1 + ([S]/

K m

) + ([S][I]/

K m K I

) v

V max I

Voet, Voet & Pratt 2013 Fig 12.9

max I =

max / /(1 + ([I]/

K I

)) [S] (Km/(1 + ([I]/

K I

)) +[S]

αK

[S] + [S]

Mixed Inhibition: M-M enzyme in L-B Plot

K v I

= [E][I]/[EI]

k 2

and

K’ I

[ES] [E] T = [ES][I]/[ESI] [E] + [ES] +[ EI ] + [ ESI ]

[S]

V max K m

(1+ ([I]/

K I

)) + [S] (1+ ([I]/

K ’ I

)) v

V maxI

[S] αK

+ α’ [S]

Voet, Voet & Pratt 2013 Fig 12.10

Michaelis-Menten Equations: Effects of Inhibitors Table

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 Voet, Voet & Pratt 2013 Table 12.2

Temperature Effects Enzyme Activity

Kinetics, Thermodynamics, and Transition State Theory I

K ‡

A + B X ‡

k’

P + Q

t =

[A][B] =

k’

[X ‡ ]

K ‡

= [X ‡ ] / [A][B] under rapid equilibrium assumption write: equilibrium constant expression ΔG ‡ = -RT ln K

‡

ν = ε

relate equil. const. to free energy (thermodynamics)

k’ e -ΔG‡/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)

is Planck’s const. ε is the avg. energy of the vibration for the decomposition on X ‡

Kinetics, Thermodynamics, and Transition State Theory II

K ‡

A + B X ‡

k’

P + Q 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 B T/h

)

e -ΔG‡/RT

A e

-ΔG‡/RT

Arrhenius Equation

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 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 reaction’s 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”

• Cytochrome s 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 + 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

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?