chem 40 enzyme kinetics

8/3/2019 Chem 40 Enzyme Kinetics

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Catalysis

Enzymes catalysts that allow biological reactions tooccur at a faster rate

Ea energy input required to initiate the reaction


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Properties of A True Catalyst

Increases the rate of reaction by lowering theactivation energy barrier

Not

used up

or permanently changed during thecatalytic process

Does not change the position of equilibrium, only the

rate at which equilibrium is attained

Usually acts by forming a transient complex with the

reactant, thus stabilizing the transition state


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Enzyme

Cofactor may be an organic or organometallicmolecule (coenzyme) or a metal ion ( Zn2+, Mg2+,

Cu2+)

Holoenzyme complete molecular package, proteinand cofactor

Apoenzyme protein component


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Naming Enzyme

Common names for enzymes are usually formed byadding the suffix ase to the name of the reactant Tyrosinase catalyzes the oxidation of tyrosine

Cellulase catalyzes the hydrolysis of cellulose to produceglucose

Some early enzyme names are less descriptive and

give no clue of their function or substrates Trypsin, chymotrypsin


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Enzyme nomenclature

6 major classes, each w/ subsclasses according torxn catalyzed

Each is assigned with a 4-digit number andsystematic name which identifies the rxn catalyzed.


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Enzyme nomenclature

4-digit official number

1st

digit: class name 2nd digit: subclass

3rd digit: accepting functional group

4th digit: accepting molecule


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EC 1 Oxidoreductases

EC 1.1 Acting on CH-OH group of donors

EC 1.2 Acting on aldehyde or oxo group of

donors EC 1.3 Acting on CH-CH group of donors

EC 1.4 Acting on CH-NH2 group of donors

EC 1.5 Acting on CH-NH group of donors

EC 1.6 Acting on NADH or NADPH


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Kinetics

In a reaction of the form A + B P, the rate can beexpressed in terms of the rate of disappearance ofone of the reactants or in terms of the rate ofappearance of the product

Rate of disappearance of A = -[A]/t where symbolizes thechange on [A] and t is time

Rate of appearance of P = [P]/t

So we can express rate in terms of any of these :

Rate = -[A]/t = -[B]/t = [P]/t


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Kinetics

It is established that Rate [A]f[B]g Rate = k [A]f[B]g

Where k is the rate constant (proportionality factor that accountsfor how well the reacting molecules oriented during collisions)

Exponents f and g usually small whole numbers 1 or 2 or in somecases 0 must be determined experimentally

The overall order of the reaction is the sum of all the

exponents

Rate = k[A]1 first order reaction w/ respect to A and firstorder overall


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Kinetics

First order reaction rate depends only on onereactant

Second order reaction the rate of reaction dependson the two reactants Rate = k[A]1[B]1 first order wrt A and first order wrt B and

second order overall

Zero order reaction rate is constant depends not onconcentrations of reactants but on other factors(presence of catalyst)

A

B, Rate = k[A]0


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Kinetic Properties of Enzymes

Initial rate (0) determined during the first fewminutes of the reaction

Maximum velocity(Vmax)


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Michaelis-Menten Equation

Leonor Michaelis and Maud Menten explain thehyperbolic rate curve Proposed that enzyme molecules, E, and substrate molecules,

S, combine in a fast and reversible step to form an ES complex

E + S k1k2

ES k3k4

E + P where k are rate constants

Assumptions:1. Neglect the reaction that reverts product P and free enzyme to

the ES complex defined by k4

2. ES complex is a steady-state intermediate

After mixing E and S, a certain level of ES is formed and itsconcentration remain constant because it is produced at the

same rate as it breaks down


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Time course of Sconsumption, P

formation andestablishment ofsteady state level ofES

Bottom curve: detailof early stage of timecourse


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M-M equation

][

][max0

SK

SV

M


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Km

Km Michaelis constant In E + S

k1

k2ES

k3E + P, Km is expressed as:

Let Km = [S]

][

][max0

SK

SV

m

][][

][max

0

SS

SV

][2

][max

0

S

SV

2

max0

V

1

32

k

kkKm


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Km

Remember:

Km becomes:

This is equal to the equilibrium constant for the dissociation ofthe ES complex

ESk2

k1E + S

So when k2>>k3, Km is simply the dissociation

constant for the ES complex

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k

kkKm

1

2

k

kKm

1

2

][]][[

kk

ESSEKeq


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Km

Km measure of how tightly the substrate is boundto the enzyme

The greater the value of Km, the higher is k2 than k1

Km is the inverse measure of the affinity of theenzyme for the substrate


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Vmax and K3

If the substrate concentration is so high so that E iscompletely saturated : [ES] = [ET] and V= Vmax

From this part of the enzyme equation:

ES

k3

k4 E + P

Turnover number, k3 (kcat or kp) number of molesof substrate transformed to product per mole ofenzyme in a defined time period

][

max

3

TE

Vk

][3ESkV

][3max TEkV


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KM, Kcat

Carbonic anhydrase -CO2:

Kcat = 1 x 106s-1;

KM = 1.2 x 10-2M

Carbonic anhydrase -HCO3-:

Kcat = 4 x 105s-1

KM = 2.6 x 10-2M

Which is better substrate for the enzyme?


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KM, Kcat

Carbonic anhydrase - CO2:

Kcat = 1 x 106s-1;

KM = 1.2 x 10-2M

Carbonic anhydrase - HCO3-

Kcat = 4 x 105s-1

KM = 2.6 x 10-2

M

Kcat/KM = 8.3 X107M-1s-1

Kcat

/KM

= 1.5 X107M-1s-1


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Lineweaver-Burk Equation

Double reciprocal plot allows one to plotexperimental enzyme rate data in the form of astraight line

y = m x + b

][][1

max0 SV

SKM

maxmax

0

1][

11VSV

KM

][][

][1

maxmax0 SV

SSV

KM ][

][max0SKSV

M


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maxmax

0

1

][

11

VSV

KM


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Other Methods of Km and VmaxDetermination

Eadie-Hofstee Plot The Michaelis-Menten equation is rearranged to

This is a graph of0 vs 0/[S] where:

Slope = -Km

Y-intercept = Vmax X-intercept = Vmax/Km

max

0

0

][

V

S

Km


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Eadie-Hofstee


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Other Methods of Km and VmaxDetermination

Hanes-Woolf Plot The Michaelis-Menten equation is rearranged to

This is a graph of [S]/0 vs [S] where:

Slope = 1/Vmax

Y-intercept = Km/Vmax X-intercept = -Km

maxmax0

][1][

V

KmS

V

S


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Hanes-Woolf


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Characteristics of Enzyme Reactions

1. Enzyme

2. pH enzymes have an optimal pH at which they

function most effectively (pH 6-8)


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Characteristics of Enzyme Reactions

1. Enzyme

2. pH enzymes have an optimal pH at which they

function most effectively (pH 6-8)

3. Temperature enzymes are sensitive totemperature changes

For most enzymes, the rate decline begins in the temp.range of 50C to 60 C


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Binding of Substrate to Enzyme

Active site specific region in the enzyme where thesubstrate specifically binds

Pocket or crevice in the 3-D structure of the enzyme Consists of certain amino acids that may be involved with the

noncovalent interaction with the substrate


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Characteristics of The Active Site

1. Specificity it is able to discriminate amongpossible substrate molecules

Two Types

1. Absolute accept only one type of molecule (can evendiscriminate between a D or L isomer)

2. Group Specificity accept a number of closely relatedsubstances as long as the reactive functional group ispresent


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Characteristics of The Active Site

2. Relatively small, 3-D region within the enzyme aaresidues need not be contiguous in the linearprotein chain

3. Holds substrate through weak, noncovalent,reversible interactions hydorphobic, ionic and H-

bonding


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First Step

Binding of substrate to the enzyme

Three Models Lock and key model

Induced-fit model

Transition-state model


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Lock-and-Key model


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Induce-fit model


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Transition state model


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Increase in Reaction Rate

1. Entropy loss in the ES formation

2. Destabilization of ES due to strain, desolvation or

electrostatic effect


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Loss of Entropy

G = H - TS

ES complex is highly organized compared to E and S

in solution

E and S have translational entropy (freedom tomove in 3-D) as well as rotational entropy (freedom

to rotate or tumble about in an axis)


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Destabilization of ES Complex

By strain or distortion consequence of the fact thatthe enzyme is designed to bind the transition statemore strongly than the substrate

By desolvation of charged groups in the substrate charged groups are highly stabilized in water

By electrostatic destabilization when a substrateenters the active site, charged groups may be forcedto interact with groups with same charge resulting torepulsion and destabilization


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2nd Step

The transition state is formed and catalysis can occur

Proximity and orientation speed up the reaction in

the transition state, the substrate is bound close toatoms with which it is to react and also placed in thecorrect orientation wrt those atoms

M h i ti F t f E


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Mechanistic Features of Enzymes General Acid-Base

Catalysis

Step 1 H+ is added tothe carbonyl group

Step 2 formation of

the tetrahedralintermediate

Step 3 a proton istransferred from O to

N Step 4 a base will

assist by accepting theproton from the

intermediate


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Mechanistic Features of Enzymes

Metal-ion Catalysis alkali metal ions (Na+, K+)and transition metals (Mg2+, Mn2+, Cu2+, Zn2+,Fe2+,

Fe3+,Ni2+,and others)

1. Holds a substrate properly oriented by coordinatecovalent bonds


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Metal-ion Catalysis

2. Enhance reaction by polarizing the scissile bond or

by stabilizing a negatively charged intermediate


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Metal-ion Catalysis

3. Participate in biological oxidation-reduction

reactions by reversible electron transfer betweenmetal ions and substrate

Acts as a Lewis acid by accepting electrons


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Covalent Catalysis nucleophilic substitutionreaction A nucleophilic, (electron-rich) functional group attacks an

electron-deficient group

Nucleophile Leavinggroup


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Active Site Events

Functional groups in the active site that can havecatalytic roles:

Imidazole ring of histidine

Hydorxyl group of serine

Carboxyl side chain of aspartate and glutamate

Sulfhydryl group of cysteine

Amine group of lysine

Phenol group of tyrosine


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Mechanism of Chymotrypsin Action

Serine residue at position 195 is required for activity Another critical aa in chymotrypsin is His 57

Ser 195

His 57

Asp 102


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l


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Enzyme Activity Regulation

Irreversible inhibitor forms covalent or very strongnoncovalent interactions with the enzyme

E-H + R-X E-R + HX

(active) (inactive)

Example: aspirin (acetylsalicylic acid) Acts by blocking synthesis of pain-producing prostaglandins

ibl hibi


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Reversible Inhibitors

Can readily combine with and dissociate from anenzyme and render the enzyme inactive only when

bound

EI is held by weak, noncovalent interactions similarto ES complex

i i hibi i


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Competitive Inhibition

Inhibitor usually resembles the structure of normalsubstrate and is capable of binding to the active siteof the enzyme

Transition state analogs modeled after thestructures of substrate in presumed transition states

N i i I hibi i


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Noncompetitive Inhibition

Inhibitor can bind to the enzyme at a site other thanthe active site of the enzyme

Binding of inhibitor causes a change in the structureof the enzyme especially around the active site

U i i I hibi i


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Uncompetitive Inhibition

Inhibitor binds only to the ES complex but not withthe free enzyme

Influence the activity of the enzyme only when [S] ishigh and, in turn, the ES concentrations are high

Ki i f I hibi i


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Kinetics of Inhibition

Competitive inhibition slope and x-intercept ofLineweaver-Burk plot change but the y-interceptdoes not

Km increase more substrate is needed to get the velocity of

half the maximum velocity

Ki ti f I hibiti


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Pure noncompetitive inhibition - slope and y-intercept of Lineweaver-Burk plot change but the x-intercept does not

Pure - Vmax decreases but Km remains the same because the

inhibitor does not interfere with the binding of substrate to theactive site

Mixed Vmax decreases and Km increase because the

inhibitor affects the binding of the substrate to the active site

Ki ti f I hibiti


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Uncompetitive inhibition Vmax and Km bothdecrease

Reversal of inhibition is not achieved by increase in[S]


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All t i E


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Allosteric Enzymes

Concentration of final products (feedback inhibition) Concentration of the beginning substrate

Concentration of an intermediate formed in the

sequence Concentration of external factors (hormones)

Eff t


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Effectors

Biomolecules that influence the action of anallosteric enzyme Positive effectors stimulants

Negative effectors - inhibitors

C t l ti d R l t Sit


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Catalytic and Regulatory Sites

Catalytic site where substrate binds

Regulatory site the binding of effector molecules

changes the conformation of the protein in a waythat tells the other subunits that it is bound

Ch i l Alt ti


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Chemical Alterations

1. Phosphorylation of hydroxyl groups of serine,threonine or tyrosine

2. Attachment of an adenosyl monophosphate to ahydroxyl group

3. Reduction of cysteine disulfide bonds


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Catalyzed by phosphorylase kinase


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Catalyzed by phosphorylase kinase

Catalyzed by phosphorylase phosphatase


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Glutamine synthetase


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Proteolytic Cleavage


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Proteolytic Cleavage

Zymogen inactive protein precursor Cleaved at one or a few specific peptide bonds to produce the

active form of the enzyme


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Regulation by Isoenzyme


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Regulation by Isoenzyme

Isoenzymes multiple forms of enzymes that havesimilar but not identical amino acid sequences

May demonstrate the same enzyme activity but the may differ

in kinetics (Km and Vmax), differ in effectors, differ in theform of coenzyme needed and cellular distribution

chem 40 enzyme kinetics

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