enzyme lab

Fundamentals of Enzyme Kinetics

Department of Biochemistry

History of Enzymes

-Enzymes are biological catalysts.-Each enzyme has a genetically determined and unique primary sequences.

History of enzyme researches-In 1700s, studies of meat digestion by stomach secretions-In 1800s, studies of conversion of starch into sugar by saliva and plant extract-In 1850s, Louis Pasteur concluded that the fermentation of sugar into alcohol is catalyzed by ‘ferments’.-In 1897s, Buchner discovered that yeast extract could ferment sugar into alcohol and proved that the fermentation can be promoted by molecules that continued to function when it was separated from the cells.

History of enzyme researches-In 1897s, Kuhne called these molecules that can catalyst the biological reaction as enzymes.-In 1926, Sumner isolated and crystallized urease and found that enzymes are proteins.-Northrop and Kunitz isolated pepsin and found to be also a protein.-Haldane wrote a treatise entitled ‘Enzyme’ and made remarkable suggestion about the interaction between enzyme and substrate. -In the twentieth century, research on enzymes has been intensive in purification of thousand enzymes leading to elucidate the structure and chemical mechanism.

History of Enzymes

Enzymes

-All enzymes are proteins, with exception of some RNA molecules.-Catalytic RNA molecules are called ‘ribozyme’ (self-splicing intron and spliceosome, protein-RNA complex)-Some antibodies can catalyze reaction called ‘abzymes’.

Enzymes

Function without additional chemical Components (only proteins)

Function with additional chemical components

Enzymes

-Some enzymes require both cofactors and coenzymes.-Some enzymes require either cofactor or coenzyme.-Some enzymes contain many kinds of either cofactors or coenzymes.

Additional chemical components for enzyme function

Cofactors Coenzymes

One or more metal ions-Fe2+

-Mg2+

-Mn2+

-Zn2+

Complex organic ormetalloorganic molecules-NAD+

-PLP-Lipoate-FAD

Enzymes

Holoenzyme = Apoenzyme + Cofactor or Coenzymes

Coenzymes or cofactors covalently linked to enzymes arecalled prosthetic groups.

Classification of Enzymes

Many enzymes have been named by adding the suffix ‘-ase’.

Enzyme Catalysis of Reactions

-Enhancement of the reaction rate is important to living system.

-Enzyme can catalyze reaction by providing a specific environment within which a given reaction can occur more rapidly.

-An enzyme-catalyzed reaction take places at the defined areas called active site.

-The molecules that can bind to the active site are called substrate.

-The active site of enzyme is lined with amino acid residues with side chains that can bind the substrate and catalyze its reaction.


-The function of enzymes is a catalyst by affecting on the rate of reaction but they do not affect on chemical equilibrium.-The effect of enzyme catalysis is an decrease in activation energy (G#).

-Transition state is the highest energy state of compound undergoing to product or returning to substrate.


Principles of enzyme in lowering activation energy

-The binding energy (GB) between enzyme and substrate is released from weak interactions to lower activation energy (G#).-The weak interactions are optimized substrate in transition state: active sites of enzyme are complementary to transition intermediate of substrate facilitating the conversion to product.

Bcat GGG #

Weak interaction between enzyme and substrate in transition state

Enzyme Kinetics

-Enzyme kinetic is the study of enzyme action.-Enzyme action: chemical mechanism of an enzyme catalyze reaction, determining the rate of reaction and responses to changes experimental parameters, substrate concentration, inhibition, temperature and pH.

Methods of measuring enzyme activity

-Monitoring enzyme activity = Enzyme assay-Selection of a suitable physical and chemical technique for following the appearance of product or disappearance of substrate by widely used techniques, optical properties (light absorption or fluorescence).

Methods of Measuring Enzyme Activity

H3C C

O

C

O

+ NADH+H3C CH

OH

C

O

O-O- + NAD+

Lactate Dehydrogenase

Lactate Pyruvate

dt

Pd

dt

Sdr

][][

-[S]: lactate or NAD+ has no absorption in visible range.-[P]: NADH has absorption at 340 nm.-It is possible to monitor the reaction by assay at 340 nm for product formation.

A340

Time

Approximation of Reaction Rate

-Substrate concentration is not constant at a time during enzyme reaction.

A0

time

At

ktt eAA 0

The measurement of reaction rateat the initial period can be approximatedthat the substrate is not changed significantly when it is compared to thestarting concentration.

-At the initial time 0~ AAt

][

][

0Ak

Akdt

dAr t

-The velocity of initial period is dependent on initial concentration of substrate called initial velocity.-Initial velocity is useful to measure the rate at defined concentration of substrate.

Time Course of Reaction

[P]

[S]

S PC

once

ntra

tion

Uni

t

TimeThe time course reaction will be curved; as the concentration of substrates decrease, and products accumulate, the net forward rate decreases reaching to equilibrium.

Con

cent

ratio

n

Time

Slope of the tangent at time zero is initial rate.

Equilibrium state

Initial Rate

-Tangents to an experimentally obtained curve are not easy to draw accurately.-The suitable condition is to minimize the curvature by decreasing the concentration of enzyme.

Time

Con

cent

ratio

n

High [E]

Low [E]: more accurate initial velocity

Enzyme activity 1 unit = A mount of enzyme which converts one mole of substrate per minute.

One-substrate Kinetics

The Michaelis-Menten equation (Rapid-equilibrium assumption)

I. Concentration of [E]<<[S], therefore the all enzyme molecules are in [ES] complex and [S]~[S0].II. The initial rate is not affected by reverse reaction from product accumulation because the initial period the product is not significant.III. The binding and dissociation of enzyme to substrate is very fast (rapid-equilibrium assumption), so the rate-limiting step becomes the product-releasing step.


E + S ES E + Pk1

k2

k3

k4

At initial period, the product formation is not significant (k4~0).

E + S ES E + Pk1

k2

k3

Rapid-equilibrium assumption 32 kk

][]][[ 21 ESkSEk

Because the rate-limiting step is product releasing-step.

][3 ESkv

][][ ESEe

][][ ESEe e = total enzyme concentration

(Rapid-equilibrium assumption)

1

2

k

kKm Michaelis-Menten constant

][3max ekV Maximum velocity


(Rapid-equilibrium assumption)

12

3

/][

][

kkS

Sekv

mKS

SVv

][

][max

Km is also referred to dissociation constant (Kd = k2/k1)


Steady-state assumption

-In 1926, Briggs and Haldane showed that the rapid-equilibrium is not restrictive in all enzyme mechanism.

-They assume instead a steady state that the concentrations of E and ES remained constant over the period of the rate measurement.



E + S ES E + Pk1

k2

k3

The steady-state treatment

Rate formation of ES

Rate decay of ES

0][

dt

ESd

][][ 32 ESkESk

][

)(][][

])[(]][[

1

32

321

Sk

kkESE

ESkkSEk



1

32

3

][

][

kkk

S

Sekv

Because the rate-limiting step is product releasing-step.

][3 ESkv

][][ ESEe e = total enzyme concentration

mKS

SVv

][

][max

1

32

k

kkKm

Michaelis-Menten constant

][3max ekV Maximum velocity

Comparison between Rapid-equilibrium and Steady-state Assumption

E + S ES E + Pk1

k2

k3

Rapid-equilibrium assumption


32 kk

Not restrictive

1

2

k

kKm

1

32

k

kkKm

-In case of rapid-equilibrium, k2 >> k3, k2 + k3 ~ k2, so Km k2/k1.-Michaelis-Menten assumption is only one case of steady-state assumption.

Experimental Basis: Michealis-Menten Equation

-The relationship between initial rate and substrate concentration is always hyperbolically depenent.

][

][max

SK

SVv

m

At very low substrate

mmm KSKKS ~][;][

mK

SVv

][max

At substrate saturation

ekV catmax

The Meaning of Kinetic Parameters

I. kcat: catalytic constant (turnover number)

-The value of kcat is nearly to the rate-limiting step.

E + S ES E + Pk1

k2

k3EP

k4

k5

fast fast slow

-The overall rate in enzyme-catalyzed reaction is not faster than step of kcat (k5).

][EPkv cat

totalcat EkV ][max -At saturated concentration of substrate ([EP] = [E]total).

I. kcat: catalytic constant (turnover number)


-kcat is also referred to the number of cycles that enzyme can catalyze the reaction.-The reciprocal of kcat is referred to the time the enzyme used since it binds to substrate until it releases of product becoming free enzyme.

-In case of rapid equilibrium that k2 is much more than other steps, the Km can be referred to dissociation constant.


II. Km: Michaelis-Menten constant

-In all case, Km is the substrate concentration at which

2maxV

v

1

2

k

kKm

-In case of steady state assumption that k2 is not necessary to be much more than other steps, the Km is a complex of many rate constants.

1

32

k

kkKm

Enzyme inhibition

-Inhibitors: some substances alter the activity of an enzyme by combining with it influencing on substrate binding or its turnover number in reducing enzyme activity.-Most inhibitors are structurally resemble substrate but not react or react slowly to enzyme.

Types of inhibitorI Reversible inhibitors-Inhibitors can bind and dissociate from enzyme active siteII Irreversible inhibitors-Inhibitors that can not be removed from enzyme after bindingto enzyme

E + S E:S E:P E + P+I

E:I

Competitive inhibition

-Substances that can compete directly with a normalsubstrate for an enzymatic binding site.-A competitive inhibitor acts by reducing the concentration of free enzyme available for substrate binding.

E + S E:S E + P+I

E:I

k1

k-1

k-2 k2

k3

Derivations

Rapid equilibrium for inhibitor binding

][

]][[

EI

IEK I

][][][][ ESEIEE T

Initial rate (v) ][3 ESkv

Maximal velocity (Vmax) TEkV ][3max

E + S E:S E + P+I

E:I

k1

k-1

k-2 k2

k3

Derivations

Define [E] and [EI] in term of [ES]


])[(]][[ 311 ESkkSEk

Available of [E] in term of [ES]

][

]][[

EI

IEK I Substitution of [E] into KI

Available of [EI] in term of [ES]

][][][][ ESEIEE T

Derivations

Initial rate (v) ][3 ESkv

E + S E:S E + P+I

E:I

k1

k-1

k-2 k2

k3

TEkV ][3max

][)][

1(

][][3

SKI

K

SEkv

Im

T

][)][

1(

][max

SKI

K

SVv

Im

Analysis of the kinetic parameters

Primary plot; reciprocal plot of v versus [S]

][)][

1(

][max

SKI

K

SVv

Im

maxmax

1

][

1)

][1(

1

VSK

I

V

K

v I

m

v

1

][

1

S

Slope varies depending on inhibitor concentration.

Intercept = max

1

V

Slope = )][

1(max I

m

K

I

V

K

Secondary plot; Plot of any term functioning withinhibitor concentration versus inhibitor concentrations

Analysis of the kinetic parameters

Slope = )][

1(max I

m

K

I

V

K

Slope

[I]

maxV

KmIntercept =

Slope = I

m

KV

K

max

Secondary plot


E:S:I

Uncompetitive inhibition

-Uncompetitive inhibitors bind only enzyme-substrate complex and not to free enzyme-Substrate binding could cause an enzyme conformationalchange suitable for inhibitor binding.

maxmax

1)

][1(

][

1)(

1

VK

I

SV

K

v I

m


Intercept is dependent on inhibitor concentration.

v

1

][

1

S

Primary plot

Slope = maxV

Km

Intercept = max

1)

][1(

VK

I

I


Intercept = max

1)

][1(

VK

I

I

Intercept

Intercept = max

1

V

[I]

Slope = max

1

VK I

Secondary plot


E:S:I

+I

E:I

Non-competitive inhibition

-Non-competitive inhibitor can combine with both enzyme Form, ES or E molecule to produce dead-end complex.-KI for E KI for ES, mixed inhibition

KI for E KI for ES


maxmax

1)

][1(

][

1)

][1(

1

VK

I

SK

I

V

K

v II

m

v

1

][

1

S

Primary plot

Both slope and intercept vary depending on inhibitor concentration.

Slope =

Intercept =

)][

1(max I

m

K

I

V

K

max

1)

][1(

VK

I

I


Secondary plot

Slope Intercept

[I] [I]

maxV

Km

I

m

KV

K

max

max

1

V

max

1

VK I

Slope = )][

1(max I

m

K

I

V

K Intercept =

max

1)

][1(

VK

I

I

Effect of inhibitor on kinetic parameters

Competitive inhibitor)

][1(

][max

Im K

IK

SVv

Uncompetitive inhibitor

][)

][1(

][)

][1(

max

S

KI

K

S

KI

V

v

I

m

I

Noncompetitive inhibitor][

][)

][1(

max

SK

S

KI

V

vm

I

Two-substrate Kinetics

A + B P + QEnz

-For one substrate reaction, there is no argument about the order of addition of reactants.-For more than one substrate, there are possibilities of order of substrate in a reaction.

I. Ternary complex (Sequential mechanism)

-Reaction can not be occurred until both substrates are bound at enzyme active site.

A + B + E P + QEAB



E EA EAB EPQ EP E

Compulsory-order mechanism

- Substrate B can not bind to free enzyme, but only to binary complex of EA.

Random-order mechanism

E

EA

EAB EPQ

EB

EP

E

EQ

-An either pathway in binding substrate A and B to enzyme forming a central complex (EAB).


II. Ping-Pong mechanism

-Substrate A and B do not meet at the enzyme active site, no EAB complex.-One substrate must leave something on the enzyme to be passed on to the other substrate.

E

A

E'

B

EA

P

E'B

Q

E

-E can be referred to reducing equivalent, chemical group such as phosphate group, acyl group and amino group. (enzyme substitution mechanism or double displacement mechanism)



Alcohol:NAD+:Enz Acetalehyde:NADH:Enz

Reaction of enzyme alcohol dehydrogenase requires ternary complex.


Glucose + E-FAD 1-ketoglucose + E-FADH2

E-FADH2 + O2 E-FAD + H2O2

Reaction of enzyme glucose oxidase. Enzyme is in eitherreduced and oxidized form during catalysis.


General equation of two-substrate kinetics (Dalziels equation)


]][[][][0 BABAv

e ABBA


][][0 BAv

e BA

At high concentration of A and B 0max

V

eekV catmax

10catk

Kinetic study of Two-substrate Reaction-Determining of initial velocity (v) by fixing one concentration of substrate [B] with varied concentrations of [A]-Determining the reaction mechanism by primary plot, e/v versus reciprocal values of substrate concentrations -Determining of all Dalziels parameters from primary and secondary plot

e/v

1/[A]

[B]

[B][B]

[B]

Ternary complex (Sequential mechanism)

e/v

1/[A]

[B][B][B][B]

Ping-Pong mechanism

enzyme lab

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