enzyme kinetics and catalysis

M.Prasad NaiduMSc Medical Biochemistry,Ph.D.Research Scholar

•Diverse and widespread proteolytic enzymes

•Involved in digestion, development, clotting,

inflammation…

•Common catalytic mechanism

P-Nitrophenolate is very

yellow while the acetate is

colorless. This is an example

of an artificial substrate!

The kinetics show

1. A “burst phase” where the product is rapidly formed with amounts stoichiometric with the enzyme.

2. Slower steady state that is independent of substrate concentration.

A covalent bond between a Serine and the substrate

suggests an “active Serine”. These Serines can be

labeled with inhibitors such as diidopropyl

phosphofluoridate specifically killing the enzyme.

Ser 195 is specifically labeled

DIPF is extremely toxic because other active Serines

can be labeled. Such as acetylcholine esterase.

Nerve gases, serin gas,

are very toxic!! Many

insecticides also work

this way.

His 57 is a second important catalytic residue. A

substrate containing a reactive group binds at the

active site of the enzyme and reacts with a nearby

reactive amino acid group. A Trojan horse effect.

Tosyl-L-phenylalanine chloromethyl ketone (TPCK)

The reaction of TPCK with His 57 of chymotrypsin

Bovine

Trypsin

Bovine trypsin catalytic triad

Catalytic mechanism

1. After the substrate binds Ser 195 nucleophilically

attacks the scissile peptide bond to form a transition state

complex called the tetrahedral intermediate (covalent

catalysis) the imidazole His 52 takes up the proton Asp 102

is hydrogen bonded to His 57. Without Asp 102 the rate of

catalysis is only 0.05% of wild-type.

2. Tetrahedral intermediate decomposes to the acyl-

enzyme intermediate. His 57 acts as an acid donating a

proton.

3. The enzyme is deacylated by the reverse of step 1 with

water the attacking nucleophile and Ser 195 as the leaving

group.

1. Conformational distortion forms the tetrahedral

intermediate and causes the carboxyl to move close to the

oxyanion hole

2. Now it forms two hydrogen bonds with the enzyme that

cannot form when the carbonyl is in its normal conformation.

3. Distortion caused by the enzyme binding allows the

hydrogen bonds to be maximal.

Triad charge transfer complex stabilization

Rates of Enzyme Reactions

How fast do reactions take place

•Reaction rates

Thermodynamics says I know the difference between

state 1 and state 2 and DG = (Gf - Gi)

But

Changes in reaction rates in response to differing conditions is related to path followed by the reaction

and

is indicative of the reaction mechanism!!

1. Substrate binding constants can be measured as well as inhibitor strengths and maximum catalytic rates.

2. Kinetics alone will not give a chemical mechanism but combined with chemical and structural data mechanisms can be elucidated.

3. Kinetics help understand the enzymes role in metabolic pathways.

4. Under “proper” conditions rates are proportional to enzyme concentrations and these can be determine “ metabolic problems”.

Chemical kinetics and Elementary

Reactions

A simple reaction like A B may proceed through several

elementary reactions like A I1 I2 B Where I1 and I2 are

intermediates.

The characterization of elementary reactions comprising an

overall reaction process constitutes its mechanistic

description.

Rate Equations

Consider aA + bB + • • • + zZ. The rate of a reaction is

proportional to the frequency with which the reacting

molecules simultaneously bump into each other

zbaZBAk Rate

The order of a reaction = the sum of exponents

Generally, the order means how many molecules have to bump into

each other at one time for a reaction to occur.

A first order reaction one molecule changes to

another

A B

A second order reaction two molecules react

A + B P + Q

or

2A P

3rd order rates A + B + C P + Q + R rarely occur

and higher orders are unknown.

Let us look at a first order rate

A B

dt

Pd

dt

Ad v

n = velocity of the reaction

in Molar per min.

or

moles per min per volume

k = the rate constant of the

reaction

Adt

Adkv

Instantaneous rate: the rate of reaction at any specified

time point that is the definition of the derivative.

We can predict the shape of the curve if we know the

order of the reaction.

A second order reaction: 2A P

2A

Ak

dt

dv

Or for A + B P + Q

BA

BAk

dt

d

dt

dv

Percent change in A (ratio ) versus time in first and

second order reactions

It is difficult to determine if the reaction is either first or

second order by directly plotting changes in

concentration.

A

dt

Ad k

dtd

kA

A

t

0

A

A

dtk-A

A

o

d to kAlnAln

-kt

o eA A

However, the natural log of the concentration is

directly proportional to the time.

- for a first order reaction-

The rate constant for the

first order reaction has

units of s-1 or min-1 since

velocity = molar/sec

and v = k[A] : k = v/[A]

Gather your data and plot

ln[A] vs time.

2

A A o Plugging in

to rate equation

2

1

o

A

2

A

ln kt

kk

693.02lnt

2

1

The half-life of a first order reaction can be used to

determine the amount of material left after a length

of time.

The time for half of the reactant which is initially

present to decompose or change.

32P, a common radioactive isotope, emits an

energetic b particle and has a half-life of 14 days. 14C has a half life of 5715 years.

A second order reaction such like 2A P

t

dtk0

A

oA

2

o

A

Ad-

kt

oA

1

A

1

When the reciprocal of the concentration is plotted verses time a

second order reaction is characteristic of a straight line.

The half-life of a second order reaction is

and shows a dependents on the initial concentration o2

1A

1t

k

A bimolecular reaction A + B C A B + C at some point

in the reaction coordinate an intermediate ternary complex will exist

A B C

This forms in the process of bond formation and bond breakage

and is called a transition state.

Ha + Hb Hc Ha Hb + Hc

This is a molecule of H2 gas reforming by a collision

An energy contour of

the hydrogen reaction

as the three molecules

approach the transition

state at location c.

This is called a saddle

point and has a higher

energy than the

starting or ending

point.

Energy diagrams for the

transition state using the

hydrogen molecule

Transition state diagram

for a spontaneous reaction.

X‡ is the symbol for the

species in the transition

state

Xk'BAk

dt

Pd

Q P B A For the reaction

‡ Where [X] is the

concentration of the

transition state species

BA

X K

‡‡

G RTlnK - D‡ ‡

DG‡ is the Gibbs free energy of the activated

complex.

k' = rate constant for the decom-

position of the activated complex

BAek'

t

PRT

G-D

d

d

‡The greater the DG‡, the more unstable the transition

state and the slower the reaction proceeds.

This hump is the activation barrier or kinetic barrier for a reaction.

The activated complex is held together by a weak bond that would

fly apart during the first vibration of the bond and can be

expressed by k' = kn where n is the vibrational frequency of the

bond that breaks the activated complex and k is the probability

that it goes towards the formation of products.

Now we have to define n. E = hn and n = E/h where h

is Planks constant relating frequency to Energy. Also

through a statistical treatment of a classical

oscillator E= KbT where Kb is Boltzmann constant.

By putting the two together

h

TK k b

RT

G

b

h

TK k

D

eAnd

The rate of reaction decreases as its free energy of

activation, DG‡ increases

or

the reaction speeds up when thermal energy is added

‡

Consider PA 21 kk

I

If one reaction step is much slower than all the rest this step

acts as a “bottleneck” and is said to be the rate-limiting step

Catalysts act to lower the activation barrier of the reaction being

catalyzed by the enzyme.

Where DDG‡cat = DG‡

uncat- DG‡cat

The rate of a reaction is increased by RT

GcateDD

DDG‡cat = 5.71 kJ/mol is a ten fold increase in rate.

This is half of a hydrogen bond!!

DDG‡cat = 34.25 kJ/mol produces a million fold

increase in rate!!

Rate enhancement is a sensitive function of DDG‡cat