biochemistry 304 2014 student edition enzymes and enzyme kinetics

Enzyme Catalysis and Enzyme Kinetics

Student Edition 5/23/13 Version

Pharm. 304 Biochemistry

Fall 2014

Dr. Brad Chazotte 213 Maddox Hall

[email protected]

Web Site:

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

Original material only ©2005-14 B. Chazotte

http://www.campbell.edu/faculty/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

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.

• The molecule(s) produced by the reaction is called the product.

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

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

Enzyme Commission NumberAn example:

1.9.3.1 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

The four-part enzyme classification number is a series of 4 numbers separated by periods.

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.

Enzyme-Substrate Complex

Illustration

Voet, Voet & Pratt 2013 Fig 11.1

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.

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.

Coenzymes as Transient Carriers Table

BeriberiMegaloblastic anemia

Pellagra

Perncious anemia

Human Deficiency Disease

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-ΔG‡/RT ; ΔG‡ = Ea

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


Catalytic Rate Enhancement*: a ΔG‡ Calculation

The enhancement of catalyzed vs uncatalyzed is given by: k= eΔΔG‡/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 “-” signVoet, Voet & Pratt 2013 Chap 11

Effect of ΔG‡ versus ΔGImportant 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

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.

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 CatalysisMechanism: Keto-Enol Tautomerization


Uncatalyzed

General Acid Catalyzed

General Base Catalyzed base

acid

“ene”

Hydroxyl “ol”

ketone

δ ≡ partial charge

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.

Amino Acids in General Acid-Base Catalysis

Lehninger 2005 Figure 6.9

pH and Enzyme Activity


RNase A Mechanism: An Acid-Base Catalysis


Base catalysis

Acid catalysis

2’,3’Cyclic ribonucleotide intermediate

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)

Covalent Catalysis: Decarboxylation of Acetoacetate

Voet, Voet & Pratt 2013Fig 11.11

uncatalyzedcarbonyl

electron withdrawal

decarboxylation

covalent bond

elimination

Transition state

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”

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.

• Electrostatic stabilization or neg. charge shielding

CO2 + H2O HCO3- + H+

Active site opening

Nearly 1/3 of all enzymes utilize a metal ion for their catalytic function.

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


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

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 RxsReaction 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] d[A]

v = dt = - 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

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 = k[A]2 k is in M-1 S-1 units

A + B → PSecond 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 1

[A] = [Ao] + kt Half-life : t½ = 1/k[Ao]

Rate Equation

Describes reaction progress as a function of time.

Derivation: (where t = time)

d[A]

[A] = d ln[A] = - k dt Integrate from [Ao] to [A]

⌠ [A] ⌠t

⌡ [ Ao] d ln [A] = - k ⌡0 dt

ln [A] = ln[Ao] – kt or [A] = [Ao] e-kt

Half Life Calculation

First Order

Second Order

k t½ = ln [A0]/2

[Ao]

t½ = ln 2/k = 0.693 / k Half Life: t½

t½ = 1/(k [Ao])

Enzyme Kinetics

The study of enzyme reaction rates


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 k1 forward rate constant k-1 reverse rate constantkp the catalytic rate constant.

v = reaction velocity

vo = initial reaction velocity, when [P] ~ 0

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], & 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.

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

Henri-Michaelis-Menten IUnireactant Enzyme

E + S k1k-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 = k2 [ES]

[E]T [E] + [ES] (3)

Henri-Michaelis-Menten II

E + S k1k-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 = k2 ([S]/Ks)[E]

[E]T [E] + ([S]/Ks)[E] (6)

Henri-Michaelis-Menten III

E + S k1k-1 ES k2 E + P

Cross multiple by k2 and cancel out [E] (on right side)

If v = kp [ES] then kp [E]T = Vmax (enzyme is saturated) (7)

v = ([S]/Ks)

k2 [E]T 1 + ([S]/Ks) (6)

v = ([S]/Ks)

Vmax 1 + ([S]/Ks) (8) v = [S]

Vmax Ks + [S] (9)

A Simple Enzyme Reaction and the Steady-State (Progress Curves)


Steady-State (Briggs-Haldane) IUnireactant Enzyme

E + S k1k-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 = k2 [ES] (1)

v = k2 [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.

Steady-State (Briggs-Haldane) II

E + S k1k-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 and ES → E + S (4)

k1

kp k-1

rate of ES formation: = k1 [E][S] (5)

rate of ES decomposition: = k-1 [ES] + k2 [ES] (6)

= (k-1 + k2) [ES] (6a)

Steady-State (Briggs-Haldane) III

E + S k1k-1 ES kp E + P

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] (9)

[ES] = (k-1 + kp)

define Michaelis constant k-1 + kp [S]

(for above reaction) km = k1 [ES] = km [E]

Steady-State (Briggs-Haldane) IV

E + S k1k-1 ES k2 E + P

v = ([S]/Km) = v = [S]Vmax 1 + ([S]/Km) Vmax Km + [S] (10a,b)

Can rearrange ES expression

k-1 + k2 [S] [E]

Km = k1 = [ES]

When [S] = Km Km

v = Km + Km Vmax = ½Vmax

Vmax = k2 [E]T the highest velocity when all of the enzyme is [ES], i.e. saturated.

Steady-State (Briggs-Haldane) VDifferential Equations for Unireactant Enzyme

E + S k1k-1 ES k2 E + P

d[E]

dt = (k-1 + k2) [ES] - k1 [E] [S] (11)d[ES] dt = k1 [E] [S] - (k-1 + k2) [ES] (12)d[S] dt = (k-1) [ES] - k1 [E] [S] (13)d[P] dt = (k2) [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

Steady-State Kinetic Plot

Initial Velocity vs Substrate [ ] in a Simple Enzyme Reaction

Voet, Voet & Pratt 2013 Fig 12.3Lehninger 2000 Figure 8.12

oMichaelis-Menten equation

HTML DISPLAYMichaelis-Menten Kinetics

12-1b_MichaelisMenten\MichaelisMenten.htm

Significance of Km

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

Operational Definition: The substrate concentration at which the reaction velocity is half maximal, i.e. when Km = [S] then vo = ½Vmax

Catalytic Efficiency & Turnover NumberDefine 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 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: 108 – 109 M-1s-1 kcat/Km ≤ k1

Kinetic Data Analyses

Michaelis-Menten equationo

Michaelis-Menten equation

Lineweaver-Burke Plot


1 Km 1 + 1

vo Vmax [S] Vmax

y = (m) x + b

Eadie-Hofstee Plot


v Vmax

[S] Km Km* v +

y = m * x + b

Reversibility IEffect of Product on Forward Reaction

E +S ES EP E + Pk1 k2 k3

k-1 k-2 k-3

When [P] = 0 Vmaxf [S]

(initial) Kms + [S]

When [S] = 0 Vmaxr [P]

(final) Kmp + [P]

vf =

vr =

The direction of the reaction will depend upon the ratio of [P]/[S] relative to Keq

Reversibility IIEffect of Product on Forward Reaction


k-1 k-2 k-3

From rapid equilibrium assumptions set up net velocity eqs.

vnet = k2 [ES] - k-2 [EP]

vnet k2 [ES] - k-2 [EP]

[E]t [E] + [ES] + [EP]

Know [ES] = ([S]/Ks) [E] and [EP] = ([P]/Kp) [E]; substitute in

vnet k2 ([S]/Ks) [E] - k-2 ([P]/Kp) [E]

[E]t [E] + ([S]/Ks) [E] + ([P]/Kp) [E]

Factor [E] out

Reversibility IIIEffect of Product on Forward Reaction


k-1 k-2 k-3

k2 [E]t([S]/Ks) - k-2 [E]t ([P]/Kp)

1 + ([S]/Ks)] + ([P]/Kp)vnet

Vmaxf ([S]/Kms) - Vmaxr ([P]/Kmp)

1 + ([S]/Kms)] + ([P]/Kmp)vnet

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 P + QE

Sequential Mechanisms: TypesOrdered Bi-Bi

Random Bi-Bi


Lehninger 2000 Figure 8.14a

Bisubstrate Rx Steady-State Kinetic Analysis: Random BiBi

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

Ping-Pong Bi-Bi


V [A][B]

Vmax Kma[A] + Kmb[B] + [A][B]

MgATP MgADP glucose Glucose-6-P

Lehninger 2000 Figure 8.14b

Bisubstrate Rx Steady-State Kinetic Analysis: BiBi Ping Pong

King-Altman Diagrams KING-ALTMAN DIAGRAM EXAMPLE PART A

k1[bc1ox] Qr Qrbc1ox

k-1

k4 k-4 k-2 k2

k-3[bc1ox] QO QObc1r

k3 Qr k2k3k4 +k-1k3k4 + k-3[bc1r]k-2k-4 + k-2k-1k4 QT = D Qrbc1ox k3k4k1[bc1ox] +k4k1[bc1ox]k-2 + k-2k-3[bc1r]k1[bc1ox] + k-4 k-3k-2 QT = D Qobc1r k4k1[bc1ox] +k1[bc1ox]k2k-3[bc1r] + k2k-4k-3[bc1r] + k-1 k-4 k-3[bc1r] QT = D

KING-ALTMAN DIAGRAM EXAMPLE PART B Qo k1[bc1ox] +k2k3k-4 + k3k--4k-1 + k-2k-1k-4 QT = D Velocity Equation : v= k1[Qr] [bc1ox] - k-1 [Qbc1ox] v k1k2k3k4 [bc1ox] - k-1k-2k-3k-4 [bc1r] ET = 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

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.)

Competitive Inhibition

KI = [E][I] / [EI]

v = k2 [ES] vmax = k2[E]T

v k2 [ES]

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

v ([S]/Km) [E] k2[E]T [E] + ([S]/Km) [E] + ([I]/KI) [E]

v ([S]/Km) [S] [S]Vmax 1 + ([S]/Km) + ([I]/KI) Km(1 + ([I]/KI)) +[S] αKm + [S]

Kmapp = Km [1 + ([I]/Ki)]

Voet, Voet & Pratt 20 Figure 12.8

Competitive Inhibition

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

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


k2k-1

k1

KI = [ES][I] / [ESI]

v = k2 [ES] vmax = k2[E]T

v k2 [ES]

[E]T [E] + [ES] + [ESI]

v ([S]/Km) [E] k2[E]T [E] + ([S]/Km) [E] + ([S][I]/KmKI) [E]

v ([S]/Km) v [S] [S]

Vmax 1 + ([S]/Km) + ([S][I]/Km KI) VmaxI (Km/(1 + ([I]/KI)) +[S] αKm + [S]

vmaxI = vmax / /(1 + ([I]/KI))

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


KI = [E][I]/[EI] and K’I = [ES][I]/[ESI]v k2 [ES][E]T [E] + [ES] +[EI] + [ESI]

v [S] v [S]

Vmax Km (1+ ([I]/KI)) + [S] (1+ ([I]/K’I)) VmaxI αKm + α’ [S]

Michaelis-Menten Equations: Effects of Inhibitors Table

Voet, Voet & Pratt 2013 Table 12.2Lehninger 2005 Table 6.9

An example for competitive inhibitor the X intercept is:

1/Km app =1/αKm = 1 /(1+[I]/Ki)Km

Temperature Effects Enzyme Activity

Kinetics, Thermodynamics, and Transition State Theory I

A + B X‡ P + QK‡ 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‡

Kinetics, Thermodynamics, and Transition State Theory II

A + B X‡ P + QK‡ k’

ε = kBT 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-ΔG‡/RT = A e -ΔG‡/RT

Arrhenius Equation


k = Ae-Ea/RT

ln k = ln A –Ea/RT or

log k = log A –Ea/2.303RT

Slope

-Ea/2.303R

log A

pH Effects Enzyme Activity


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

0.4 mM

2.0 mM


Kinetics and Mechanism

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

Bisubstrate Rx: Examples


Transferase

Redox

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

biochemistry 304 2014 student edition enzymes and enzyme kinetics

Education

enzyme catalysis

enzymecatalyzed reaction

enzyme present

enzymes othlil enzymes

voet pratt

enzyme classification

active complete enzyme

enzymes lehninger