Enzyme Kinetics and Catalysis

1
Enzyme Kinetics and Catalysis

• 3/19/2003

2
Serine proteases

• Diverse and widespread proteolytic enzymes
• Involved in digestion, development, clotting,
  inflammation
• Common catalytic mechanism

3
Use of an Artificial Substrate
P-Nitrophenolate is very yellow while the acetate
is colorless. This is an example of an
artificial substrate!
4
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.
5
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
6
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.
7
Affinity labeling
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)
8
The reaction of TPCK with His 57 of chymotrypsin
9
Bovine Trypsin
10
The catalytic triad
11
Bovine trypsin catalytic triad
12
(No Transcript)
13
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.
14
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.
15
Triad charge transfer complex stabilization
16
Enzyme Kinetics

• 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!!

17
Enzyme kinetics are important for many reasons
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.
18
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
19
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
20
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
n velocity of the reaction in Molar per
min. or moles per min per volume k the rate
constant of the reaction
21
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
Or for A B ? P Q
22
Percent change in A (ratio ) versus time in first
and second order reactions
23
It is difficult to determine if the reaction is
either first or second order by directly plotting
changes in concentration.
24
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 kA k v/A
Gather your data and plot lnA vs time.
25
The half-life of a first order reaction
Plugging in to rate equation
26
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.
27
A second order reaction such like 2A ? P
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
28
The Transition State
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
29
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.
30
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
31
For the reaction
Where X is the concentration of the transition
state species


k' rate constant for the decom-position of the
activated complex



DG is the Gibbs free energy of the activated
complex.
32

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.
33
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

And
The rate of reaction decreases as its free energy
of activation, DG increases or the reaction
speeds up when thermal energy is added
34
Multi-step reactions have rate determining steps
Consider
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
35
Catalysis lowers the activation energy
36
Catalysts act to lower the activation barrier of
the reaction being catalyzed by the enzyme.
Where DDGcat DGuncat- DGcat
The rate of a reaction is increased by
DDGcat 5.71 kJ/mol is a ten fold increase in
rate. This is half of a hydrogen bond!! DDGcat
34.25 kJ/mol produces a million fold increase
in rate!! Rate enhancement is a sensitive
function of DDGcat