Models for More Complex Enzyme
Kinetics
• Allosteric enzymes
- Some enzymes have more than one
substrate binding site.
- Allostery or cooperative binding:
the binding of one substrate to the
enzyme facilitates binding of other
substrate molecules.
Models for More Complex Enzyme
Kinetics
The rate expression in this case is
Vm[S ]n
d[ S ]
v

dt
K m"[S ]n
n is cooperativity coefficient;
n>1 indicates positive cooperativity;
n can be determined by rearranging the above equation as
v
''
ln
 n ln[S ]  ln K m
Vm  v
v
And plotting ln V  v
m
versus ln[S].
Models for More Complex Enzyme
Kinetics
• Insoluble substrate
wood chips, cellulosic residues
-Access to the active site on these biopolymers
by enzyme is limited by enzyme diffusion.
-The number of reaction sites exceeds the number
of enzyme molecules.
-This is opposite that of the typical situation with
soluble substrates, where access to the
enzyme’s active site by substrate limits reaction.
Models for More Complex Enzyme
Kinetics
• Insoluble substrate
If considering
- the initial product formation rate and
- the reaction is first order in terms of
the enzyme-substrate complex concentration,
yields,
v
V max,S [ E ]
K eq  [ E ]
Vmax,S  k 2[ S 0 ]
K eq  k des / k ads
Factors Affecting Enzyme Kinetics
• pH effects
- on enzymes
- enzymes have ionic groups on their active sites.
- Variation of pH changes the ionic form of the active
sites.
- pH changes the three-Dimensional structure of
enzyme.
- on substrate
- some substrates contain ionic groups
- pH affects the ionic form of substrate
affects the affinity of the substrate to the
enzyme
Factors Affecting Enzyme Kinetics
• Temperature
- on the rate enzyme catalyzed reaction
d[P]
v
 k [ES]
2
dt
k2=A*exp(-Ea/R*T)
T
k2
v
- enzyme denaturation
d[ E ]

 kd [ E]
Denaturation rate:
T
dt
kd=Ad*exp(-Ea/R*T)
kd: enzyme denaturation rate constant;
Ea: deactivation energy
Immobilized Enzyme Systems
• Enzyme immobilization:
To restrict enzyme mobility in a fixed space.
Advantages:
- Easy separation from reaction mixture, providing the
ability to control reaction times and minimize the
enzymes lost in the product.
- Re-use of enzymes for many reaction cycles, lowering the
total production cost of enzyme mediated reactions.
- Ability of enzymes to provide pure products.
- Possible provision of a better environment for enzyme
activity
- Study of the action of membrane-bound intracellular
enzyme
Immobilized Enzyme Systems
• Methods of Enzyme Immobilization:
- Entrapment
- Surface immobilization
- Cross-linking
Immobilized Enzyme Systems
Entrapment immobilization is based on the
localization of an enzyme within the lattice
of a polymer matrix or membrane.
- to retain enzyme
- allow the penetration of substrate.
It can be classified into matrix and micro
capsule types.
Immobilized Enzyme Systems
Entrapment
- matrix entrapment
- membrane entrapment
(microencapsulation)
Immobilized Enzyme Systems
- matrix entrapment
Matrix materials:
organics: polysaccharides, proteins, carbon, vinyl and allyl
polymers, and polyamides. e.g. Ca-alginate, agar,
K-carrageenin, collagen
Enzyme + polymer solution → polymerization
→ extrusion/shape the particles
inorganics: activated carbon, porous ceramic and
diatomaceous earth.
Shapes:
- particle
- membrane
- fiber
Immobilized Enzyme Systems
- membrane entrapment
- Regular semipermeable membrane: nylon,
cellulose, polysulfone and polyacrylate.
- Microencapsulation:
Microscopic hollow sphere are formed.
The sphere contain the enzyme solution
and
is enclosed within a porous membrane.
Immobilized Enzyme Systems
Entrapment
challenges:
- enzyme leakage into solution
- diffusional limitation
- reduced enzyme activity and stability
- lack of control micro-environmental
conditions.
It could be improved by modifying matrix or
membrane.
Immobilized Enzyme Systems
Surface immobilization
According to the binding mode of the enzyme,
this method can be further sub-classified
into:
- Physical Adsorption
- Ionic Binding
- Covalent Binding
Immobilized Enzyme Systems
Surface immobilization
Physical Adsorption is based on the physical
adsorption of enzyme protein on the surface
of water-insoluble carriers.
- If a suitable carrier is found, this method can be both
simple and cheap.
- The active sites and activity of enzymes are less affected.
- Desorption of enzyme takes place because of weak
attraction.
- Non-specific of other protein or substances will affect the
properties of enzyme.
Immobilized Enzyme Systems
Physical Adsorption:
Weak forces: Van der Waals or dispersion
Materials:
Inorganic: almumina, silica, porous glass,
ceramics.
Organic: e.g. cellulose, starch, activated
carbon.
Carbon nano-tube (Kim, Jeong Yun, Special
Publication - Royal Society of Chemistry, 2004)
Immobilized Enzyme Systems
Ionic binding:
Interaction forces: ionic bonds.
Features: similar to that of physical adsorption.
Polysaccharides and synthetic polymers
having ion-exchange centers are usually
used as carriers.
Immobilized Enzyme Systems
Covalently binding is the formation of covalent
bonds between the enzyme and the support
matrix.
Interaction forces: covalent bonds.
Features:
- may alter the conformational structure and active
center of the enzyme, resulting in major loss of
activity and/or changes of the substrate.
- the binding force between enzyme and carrier is
so strong that no leakage of the enzymes occurs.
Immobilized Enzyme Systems
Covalent binding:
To select the type of reaction for enzyme
covalent immobilization:
- do not cause loss of enzymatic activity.
- the active site of the enzyme must be
unaffected by the reagents used.
Immobilized Enzyme Systems
Covalent binding:
The functional groups on the supports that
may take part in this binding are listed
below:
e.g. amino group, carboxyl group,
sulfhydryl group, hydroxyl group, phenolic
group etc.
Immobilized Enzyme Systems
Cross-linking: to cross link enzyme
molecules with each other using agents
such as glutaraldehyde.
Features: similar to covalent binding.
Several methods are combined.
Summary of Immobilization
Methods
Methods of Enzyme immobilization:
- Entrapment
- matrix
- membrane (microencapsulation)
- Surface immobilization
- physical adsorption
- ionic binding
- covalent binding
- Cross-linking
Immobilized Enzyme Reactors
Recycle packed column reactor:
- allow the reactor to operate at high fluid velocities.
- a substrate that cannot be completely processed on a single pass
Fluidized Bed Reactor:
- a high viscosity substrate solution
- a gaseous substrate or product in a continuous reaction system
- care must be taken to avoid the destruction and
decomposition of immobilized enzymes
- An immobilized enzyme tends to decompose
upon physical stirring.
- The batch system is generally suitable for the production
of rather small amounts of chemicals.