Enzyme kinetics and associated reactor design:

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CP504 Lecture 3
Enzyme kinetics and associated reactor design
Introduction to enzymes, enzyme catalyzed
reactions and simple enzyme kinetics

• learn about enzymes
• learn about enzyme catalyzed reactions
• study the kinetics of simple enzyme catalyzed
  reactions

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What is an Enzyme?
Enzymes are mostly proteins, and hence they
consists of amino acids. Enzymes are present
in all living cells, where they help converting
nutrients into energy and fresh cell material.
Enzymes breakdown of food materials into
simpler compounds. Examples - pepsin,
trypsin and peptidases break down proteins
into amino acids - lipases split fats into
glycerol and fatty acids - amylases break down
starch into simple sugars
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What is an Enzyme?
Enzymes are very efficient (biological)
catalysts. Enzyme catalytic function is very
specific and effective. Enzymes bind temporarily
to one or more of the reactants of the reaction
they catalyze. By that means, they lower the
amount of activation energy needed and thus speed
up the reaction. Enzymes does not get consumed
in the reaction that it catalyses.
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Enzyme classification
Oxidoreductase transfer oxygen atoms or
electron Transferase transfer a group (amine,
phosphate, aldehyde, oxo, sulphur,
etc) Hydrolase hydrolysis Lyase transfer
non-hydrolytic group from substrate Isomerase
isomerazion reactions Ligase bonds synthesis,
using energy from ATPs
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Examples of Enzyme Catalysed Reactions
Examples of enzyme catalyzed reactions
Example 1
Carbonic anhydrase
CO2 H2O
H2CO3
Carbonic anhydrase is found in red blood cells.
It catalyzes the above reaction enabling red
blood cells to transport carbon dioxide from the
tissues (high CO2) to the lungs (low CO2). One
molecule of carbonic anhydrase can process
millions of molecules of CO2 per second.
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Examples of enzyme catalyzed reactions
Example 2
Catalase
2H2O2 2H2O
O2
Catalase is found abundantly in the liver and in
the red blood cells. One molecule of catalase
can breakdown millions of molecules of hydrogen
peroxide per second. Hydrogen peroxide is a
by-product of many normal metabolic processes.
It is a powerful oxidizing agent and is
potentially damaging to cells which must be
quickly converted into less dangerous substances.

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Industrial use of catalase
- in the food industry for removing hydrogen
peroxide from milk prior to cheese production -
in food-wrappers to prevent food from oxidizing
- in the textile industry to remove hydrogen
peroxide from fabrics to make sure the material
is peroxide-free - to decompose the hydrogen
peroxide which is used (in some cases) to
disinfect the contact lens
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Examples of Industrial Enzymes
See the hand out on the same topic
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More on enzymes
Enzymes are very specific. Absolute specificity
- the enzyme will catalyze only one
reaction Group specificity - the enzyme will act
only on molecules that have specific functional
groups, such as amino, phosphate or methyl groups
Linkage specificity - the enzyme will act on a
particular type of chemical bond regardless of
the rest of the molecular structure Stereochemica
l specificity - the enzyme will act on a
particular steric or optical isomer
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Source http//waynesword.palomar.edu/molecu1.htm
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E S ES
Source http//waynesword.palomar.edu/molecu1.htm
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Lock Key Theory Of Enzyme Specificity (postulate
d in 1894 by Emil Fischer)
E S ES
E P
Source http//waynesword.palomar.edu/molecu1.htm
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(No Transcript)
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Active Site Of Enzyme Blocked By Poison Molecule
Source http//waynesword.palomar.edu/molecu1.htm
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Induced Fit Model (postulated in 1958 by Daniel
Koshland )
E S ES
E P
Binding of the first substrate induces a
conformational shift that helps binding of the
second substrate with far lower energy than
otherwise required. When catalysis is complete,
the product is released, and the enzyme returns
to its uninduced state.
Source http//www.mun.ca/biology/scarr/Induced-Fi
t_Model.html
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Simple Enzyme Kinetics
k1
k3
E S ES
E P
k2
which is equivalent to
E
P
S
S for substrate (reactant)
E for enzyme
ES for enzyme-substrate complex
P for product
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Michaelis-Menten approach to the rate equation
k1
k3
E S ES
E P
k2

• Assumptions
• Product releasing step is slower and it
  determines the reaction rate
• 2. ES forming reaction is at equilibrium
• 3. Conservation of mass (CE0 CE CES)

Initial concentration of E
Concentration of E at time t
Concentration of ES at time t
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Michaelis-Menten approach to the rate equation
k1
k3
E S ES
E P
k2
Product formation ( substrate utilization) rate
rP - rS k3 CES
(1)
Since ES forming reaction is at equilibrium, we
get
k1 CE CS k2 CES
(2)
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Michaelis-Menten approach to the rate equation
k1
k3
E S ES
E P
k2
Using CE0 CE CES in (2) to eliminate CE, we
get
k1 (CE0 CES) CS k2 CES
which is rearranged to give
CE0CS
CES
(3)
k2/k1 CS
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Michaelis-Menten approach to the rate equation
k1
k3
E S ES
E P
k2
Using (3) in (1), we get
k3CE0CS
rmaxCS
(4)
rP

- rS
KM CS
k2/k1 CS
where rmax k3CE0 and KM k2 / k1
(5)
(6)
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Briggs-Haldane approach to the rate equation
k1
k3
E S ES
E P
k2
Assumptions 1. Steady-state of the
intermediate complex ES 2. Conservation of mass
(CE0 CE CES)
Initial concentration of E
Concentration of E at time t
Concentration of ES at time t
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Briggs-Haldane approach to the rate equation
k1
k3
E S ES
E P
k2
Product formation rate
rP k3 CES
(7)
Substrate utilization rate
rs - k1 CECS k2 CES
(8)
Since steady-state of the intermediate complex ES
is assumed, we get
k1 CECS k2 CES k3 CES
(9)
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Briggs-Haldane approach to the rate equation
k1
k3
E S ES
E P
k2
Combining (7), (8) and (9), we get
rP - rS k3 CES
(10)
Using CE0 CE CES in (9) to eliminate CE, we
get
k1 (CE0 - CES)CS (k2 k3)CES
which is rearranged to give
CE0CS
CES
(11)
(k2k3)/k1 CS
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Briggs-Haldane approach to the rate equation
k1
k3
E S ES
E P
k2
Combining (10) and (11), we get
k3CE0CS
rmaxCS
- rS

(12)
rP
KM CS
(k2k3)/k1 CS
where rmax k3CE0 and KM (k2
k3) / k1
(5)
(13)
When k3 ltlt k2 (i.e. product forming step is
slow), KM k2 / k1
(6)
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Simple Enzyme Kinetics (in summary)
E
P
S
rmaxCS

- rS
rP
KM CS
where rmax k3CE0 and KM f(rate constants)
rmax is proportional to the initial concentration
of the enzyme KM is a constant