Download The Kinetics of Enzyme Catalyzed Reactions

CHAPTER 1
ENZYME KINETICS AND APPLICATIONS
CHAPTER 1
ENZYME KINETICS AND
APPLICATIONS
Kinetics of Enzyme
Catalyzed Reactions
Applied Enzyme
Catalysis
Chapter 1.1
The Kinetics of Enzyme
Catalyzed Reactions
Introduction
Classification of enzymes according to the
reaction catalyzed and how enzymes work.
Enzymes



There are many chemical compounds in the living cell.
How they are manufactured and combined at sufficient
reaction rates under relatively mild temperature and
pressure?
How does the cell select exactly which reactants will be
combined and which molecule will be decomposed?
Catalysis by ENZYME
Enzymes
•Enzymes are biological catalysts that are protein molecules in
nature- react in mild condition
•They are produced by living cells (animal, plant, and
microorganism) and are absolutely essential as catalysts in
biochemical reactions.
•Almost every reaction in a cell requires the presence of a specific
enzyme– related to its particular protein structure.
•A major function of enzymes in a living system is to catalyze
the making and breaking of chemical bonds.
•Therefore, like any other catalysts, they increase the rate of
reaction without themselves undergoing permanent chemical
changes.
•The catalytic ability of enzymes is due to its particular
protein structure.
•A specific chemical reaction is catalyzed at a small
portion of the surface of an enzyme, which is known as
the active site.
•Some physical and chemical interactions occur at this
site to catalyze a certain chemical reaction for a certain
enzyme.
Catalysts




A catalyst is unaltered during the course of a reaction and
functions in both the forward and reverse directions.
In a chemical reaction, a catalyst increases the rate at
which the reaction reaches equilibrium.
For a reaction to proceed from starting material to
product, the chemical transformations of bond-making and
bond-breaking require a minimal threshold amount of
energy, termed activation energy.
Generally, a catalyst serves to lower the activation energy
of a particular reaction.
Enzyme
Enzyme is protein or nucleic acid.
 Catalyze biochemical reactions
 breaking, forming and rearranging bonds.
 Specificity
 Dictated by the enzyme active site.
 Some active sites allow for multiple substrates.
 Cofactors/Coenzyme (Non protein group)
 Vitamin derivatives, metals (minerals) can bind as cosubstrates or remain attached through multiple catalytic
cycles
 Cofactors: metal ions, Mg, Zn, Mn, Fe.
 Coenzyme: complex organic molecule, NAD, FAD, CoA or
some vitamins
Holoenzyme = apoenzyme + cofactor
Enzymes

Proteins that assist in chemical reactions may be Enzymes


Enzymes are catalysts



Specific because of conformational shape
Catalyst: chemical that changes the rate of a reaction without
being consumed
Recycled (used multiple times)
Enzymes reduce the activation energy of a reaction

Amount of energy that must be added to get a reaction to
proceed
The activation
energy for the
decomposition of
hydrogen peroxide
varies depending on
the type of catalysis.
Type of
catalysis
Activatio
n energy
Uncatalyzed
reaction at
20°C
18
kcal/mol
Enzymatically
catalyzed
(catalase)
7 kcal/mol
Chemically
catalysed (by
collodial
platinum)
13
kcal/mol
Enzyme lower the activation energy of the reaction by binding
the substrate and forming an enzymes-substrate complex.
Important terms (Enzyme)



active site - a region of an enzyme comprised of different
amino acids where catalysis occurs or a small portion of
the surface of an enzyme which a specific chemical
reaction is catalyzed
substrate - the molecule being utilized and/or modified
by a particular enzyme at its active site
co-factor - organic or inorganic molecules that are
required by some enzymes for activity. These include Mg2+,
Fe2+, Zn2+ and larger molecules termed co-enzymes like
nicotinamide adenine dinucleotide (NAD+), coenzyme A,
and many vitamins.
Important terms (Enzyme)



holoenzyme - a complete, catalytically active enzyme
including all co-factors OR an enzyme containing a
nonprotein group
apoenzyme - the protein portion of a holoenzyme
minus the co-factors OR the protein part of holoenzyme
(holoenzyme=apoenzyme+cofactor)
isozyme - (or iso-enzyme) an enzyme that performs the
same or similar function of another enzyme that occur in
several different molecular forms.
Nomenclature of enzyme
Originally enzymes were given nondescriptive names such as:
rennin : curding of milk to start cheese-making processor
pepsin : hydrolyzes proteins at acidic pH
trypsin : hydrolyzes proteins at mild alkaline pH
The nomenclature was later improved by adding the suffix ase to the name of the substrate with which the enzyme
functions, or to the reaction that is catalyzed, for example:
Nomenclature of enzyme
Alcohol dehydrogenase
Glucose isomerase
Glucose oxidase
Lactic acid
dehydrogenase
Enzyme reactions are different from chemical
reactions, as follows:
1. An enzyme catalyst is highly specific, and catalyzes only one
or a small number of chemical reactions. A great variety of
enzymes exist, which can catalyze a very wide range of
reactions.
2. The rate of an enzyme-catalyzed reaction is usually much
faster than that of the same reaction when directed by
nonbiological catalysts at mild reaction condition.
3. A small amount of enzyme is required to produce a desired
effect.
4. Enzymes are comparatively sensitive or unstable molecules
and require care in their use.
Enzymatic Reaction Principles


Biochemically, enzymes are highly specific for their
substrates and generally catalyze only one type of reaction
at rates thousands and millions times higher than nonenzymatic reactions.
Two main principles to remember about enzymes are
a)
b)
they act as CATALYSTS (they are not consumed in a
reaction and are regenerated to their starting state) and
they INCREASE the rate of a reaction towards
equilibrium (ratio of substrate to product), but they do not
determine the overall equilibrium of a reaction.
Reaction Rates




The rate of the reaction is determined by several factors
including the concentration of substrate, temperature and
pH.
For most standard physiological enzymatic reactions, pH
and temperature are in a defined environment (pH 6.9-7.4,
37oC).
This enzymatic rate relationship has been described
mathematically by combining the equilibrium constant, the
free energy change and first or second-order rate theory.
Keq = e−∆Go/RT
The net result for enzymatic reactions is that the lower
the activation energy, the faster the reaction rate, and vice
versa.
Specificity

Most synthetic catalyst are not specific i.e., they will
catalyze similar reactions involving many different kinds of
reactants. While enzymes are specific. They will catalyze
only one reaction involving only certain substances.
Binding Energy



The interaction between enzyme and its substrate is
usually by weak forces.
In most cases, van der Waals forces and hydrgen
bonding are responsible for the formation of ES
complexes.
The substrate binds to a specific site on the enzyme
known as the active site.
Classification of Enzyme

Enzymes fall into 6 classes based on function
5.
Oxidoreductases: which are involved in oxidation,
reduction, and electron or proton transfer reactions
Transferases : catalysing reactions in which groups are
transferred
Hydrolases : which cleave various covalent bonds by
hydrolysis
Lyases : catalyse reactions forming or breaking double
bonds
Isomerases : catalyse isomerisation reactions
6.
Ligases : join substituents together covalently.
1.
2.
3.
4.
SIMPLE ENZYME KINETICS
•Enzyme kinetics deals with the rate of enzyme
reaction
•Kinetic studies of enzymatic reactions provide
information about :
(1)the basic mechanism of the enzyme reaction and
(2) other parameters that characterize the properties of the
enzyme.
•The rate equations developed from the kinetic
studies can be applied in :
(1)calculating reaction time,
(2) yields, and
(3) optimum economic condition, which are important in the
design of an effective bioreactor.
Assume that a substrate (S) is converted to a product (P)
with the help of an enzyme (E) in a reactor as:
If you measure the concentrations of substrate and
product with respect to time, the product concentration
will increase and reach a maximum value, whereas the
substrate concentration will decrease as shown in
Figure 2.1
The rate of reaction can be expressed in terms of either
the change of the substrate Cs or the product
concentrations CP as follows:
Brown (1902) proposed that an enzyme forms a complex
with its substrate. The complex then breaks down to the
products and regenerates the free enzyme. The mechanism
of one substrate-enzyme reaction can be expressed as:
One of the original theories to account for the formation of the enzymesubstrate complex is the "lock and key" theory. The main concept of this
hypothesis is that there is a topographical, structural compatibility between an
enzyme and a substrate which optimally favors the recognition of the
substrate as shown in Figure 2.3.
The reaction rate equation can be derived from the preceding mechanism
based on the following assumptions:
1. The total enzyme concentration stays constant during the reaction,
2. The amount of an enzyme is very small compared to the amount of
substrate. Therefore, the formation of the enzyme substrate complex does
not significantly deplete the substrate.
3. The product concentration is so low that product inhibition may be
considered negligible.
The simplest model describing this interaction is the lockand-key model, in which the enzyme represents the lock
and substrate represents the key.
In multisubstrate, enzyme-catalyzed reactions, enzymes
can hold substrates such that reactive regions of
substrates are close to each other and to the
enzyme’s active site, which is known as the proximity
effects (nearest in distance).
Also, enzymes can hold substrates at certain positions
and angles to improve the reaction rate, which is
known as the orientation effect.
Multisubstrate
enzyme catalyst
reaction
Alteration of active site
by activator
Enzyme Kinetics



Enzymes are protein catalysts that, like all catalysts,
speed up the rate of a chemical reaction without being
used up in the process.
A mathematical model of the kinetics of single –
substrate-enzyme-catalyzed reaction was first developed
by V.C.R. Hendry (1902), and by L. Michaelis and M.L.
Menten (1913).
Kinetics of simple enzyme catalyzed reaction are often
refered to Michaelis-Menten or saturation kinetics.
This model are based on data from batch
reactors with constant liquid volume in which the
the initial substrate,[S0], and enzyme [E0],
concentration are known.
An enzyme solution has a fixed number of active
sites to which substrate can bind. At high
substrate concentrations, all these sites may be
occupied by substrates or the enzyme is
saturated.
Two major approaches used in developing a rate
expression for enzyme catalyzed reactions are ,
(1) rapid-equilibrium approach and (2) quasisteady-state approach.
Both quasi-steady state approximation and the assumption
of rapid equilibrium share the same few steps in deriving a
rate expression,
Rate of product formation:
Rate of variation of the ES complex:
Since the enzyme is not consumed, the conservation equation yields,
An assumption is required to achieve an analytical
solution
Vm = k2[Eo]
Quasi-steady-state Approximation


Briggs and Haldane first proposed Quasi-steadystate assumption
In a batch reactor at closed system, [E0] is considered
very small compared S
Therefore, d(ES)/dt ≈0
From equation
d ES 
 k1 [ S ][ E ]  k 1  k 2 ES  ----1
dt
k1 [ E ][ S ]
ES  
k1  k2 
----2
Quasi-steady-state Approximation
•
Substituting ,
[ES],
, and solve equation 2 for
[ S ][ E0 ]
ES   k  k
1
2
[S]
k1
----3
Production formation kinetics,
d[ S ] d[ P]
v

 k 2 [ ES ] ----4
dt
dt
•
Substitute equation 3 into 4,
k 2 [ E0 ][ S ]
v
k1  k2  / k1   [ S ]
----5
Quasi-steady-state Approximation
Substituting,
Vm  k2 [ E0 ] and
Vm [ S ]
v
Km  [ S ]
k 1  k 2
Km 
k1
----6
There is difference between Michaelis-Menten and Quasisteady-state constant. [K’m=k-1/k1]
Since Km results from the more general derivation, we
will use it in the rest of our discussion
Enzyme-catalysed reactions display saturation
kinetic
Determination of Rate Parameters for
Michaelis-Menten Type Kinetics
 Lineweaver-Burk plot
 Eadie- Hofstee plot
 Hanes-Woolf plot
 Batch kinetics
Lineweaver-Burk plot

From equation 6,

Double reciprocal plot
Vm [ S ]
v
Km  [ S ]
slope
Y-intercept
Lineweaver-Burk plot gives good estimates on Vm but
not necessarily on Km (error relates with substrate conc)
Eadie–Hofstee plot
Vm [ S ]
From equation 6, v 
Km  [ S ]
Rearranged equation 6,
plot v versus v/[S] gives a
line of slope –Km and y-axis
intercept of Vm
 Can be subject to large errors since both coordinates
contain v, but less bias on points at low [S]
Hanes–Woolf plot
Rearrangement of equation 6 yields,
slope
intercept

This plot is used to
determine Vm more
accurately.
Batch kinetics

Integration of equation 6 and rearranged yields,
1 [ So ]
1  [ So ]  [ S ]  Vm
ln




t
[S]
Km 
t
 Km
slope
Y-intercept
1 [ So ]
ln
t [S]
 [ So ]  [ S ] 


t


Models for More Complex Enzyme
Kinetics
Allosteric Enzymes
Allostery @ cooperative binding
 The binding of one substrate to enzyme facilitates binding
of other substrate molecules
Vm [ S ] n
v
K" m  [ S ] n
Where,
n = cooperativity coefficient
Modulation and Regulation of Enzyme
Activity



enzyme-substrate inhibitors systems classify by their
influence on the Michaelis-Menten equation parameters
Vm and Km
Reversible inhibitors are termed competitive if their
presence increases the value of Km but does not alter Vm.
On the other hand, by rendering the enzyme or the
enzyme-substrate complex inactive, a noncompetitive
inhibitor decreases the Vm of the enzyme but does not
alter the Km value.
Inhibited enzyme kinetic
•Certain compound may bind to enzymes and reduce their
activities ~ enzyme inhibitors
•Enzyme inhibitions may be irreversible ( heavy metal: lead,
cadium, mercury–form a stable complex with enzyme and
reduce enzyme activity) or reversible (EDTA and citrate)
•Three major class of reversible enzyme inhibitioncompetitive, noncompetitive and uncompetitive
inhibitions.
•Competitive- compete with substrate for active site of the
enzyme
Competitive enzyme inhibition scheme can be described as:
K’m,app
The effect of such inhibitors can be countered or
reversed by increasing the substrate concentration.
•Noncompetitive inhibitors bind on site other than the active site,
reduce enzyme affinity to the substrate
• Can be described by:
Rate equation:
Overcome by adding reagents to block binding of inhibitor
Uncompetitive inhibition
Inhibitors binds to the ES complex only and have no
affinity for the enzyme itself
Rate of reaction,
v
Vm, app [ S ]
K ' m ,app  [ S ]
The net effect is reduction in both Vm and K’m values.
Substrate inhibition

High substrate concentrations may cause inhibition in
some enzymatic reaction
Effect of pH and temperature
-Enzyme are active only over small range of pH due to:
 the active site functional group charges (ionic form)
 the three dimensional shape of enzyme are pHdependent
-these ionic group on active sites must be in a suitable
form (acid or base) to function.
-Variation in pH of medium result in changes of:
Ionic form of the active site
Activity of enzyme, hence the reaction rate
Affect the maximum reaction rate, Km and enzyme
stability
-Scheme to describe pH dependence of the enzymatic
reaction rate for ionizing enzymes.
-
Variation of enzyme activity
with pH for 2 different
enzymes
-Some cases, the substrate may contain ionic groups,
and the pH of medium affects the affinity of substrate to
enzyme.
(How to determine pH optimum?)
-Refer to Eq. 3.44& Eq. 3.45
ascending
descending
The rate varies
according to
Arrhenius equation
Thermal
denaturation
occurred
Variation of reaction rate with temperature
The rate,
v  k2 [ E ]
k2  Ae
 Ea / RT
 kd is the denaturation constant,
k d  Ad e
 Ea / RT
Enzyme denaturation is much faster than enzyme
activation.
Variation in T affect both Vm and Km