Lecture – 4
The Kinetics of Enzyme-Catalyzed
Reactions
Dr. Saleha Shamsudin
Effect of pH and temperature
-Enzyme are active only over small range of pH due to
the active site functional group charges (ionic form) and
the three dimensional shape of enzyme are pHdependent
-Certain enzyme have ionic group on their active sites,
and these ionic group 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
-stability
of enzyme
-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.
-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
Restriction of enzyme mobility
in a fixed space = enzyme
immobilization
Allowing small MW
compound access to
enzyme
Retain high MW
compound
Prior to
Functional groups on support material are usually
activated by using chemical reagent such as
cyanogen bromide, carbodiimide and
glutaraldehyde
Chemical reagent
Support
materials
with
functional
group
Cross-linking of enzyme molecule
The agent used are: ____________,
____________, ________________
Cross-linking can be achieved in several ways:
1)
2)
3)
The disadvantages of cross-linking:
1)
2)
Quiz
This is the schematic diagram of enzyme
immobilization methods:
Suggest the method of (a), (b), (c) and (d)?
Diffusional Limitation in Immobilized
Enzyme System
• Immobilized enzyme system normally includes
- insoluble immobilized enzyme
- soluble substrate, or product
• They are heterogeneous systems
Substrate
external diffusion
Immobilized
Enzyme
HIGH
Sb
Low S concentration
DIFFUSION
DRIVING FORCE
external diffusion
Immobilized
Enzyme
HIGH
Sb
REACTION
PRODUCT
DIFFUSION
DRIVING FORCE
HIGH
Immobilized
Enzyme
Sb
DIFFUSION
DRIVING FORCE
HIGH
Immobilized
Enzyme
Sb
REACTION
PRODUCT
Diffusional Limitation in
Immobilized Enzyme Systems
In immobilized enzyme systems,
the overall production rate is determined
by
- liquid film mass transfer (external diffusion)
substrate, product
- intraparticle mass transfer (internal diffusion)
substrate, product in porous supports
- enzyme catalysis reaction
Mass transfer coefficient
(cm/s)
Substrate
conc.
(g/cm3)
Diffusional Limitation in
Immobilized Enzyme System
Diffusion Effects in Surface-bound Enzymes
on Nonporous Support Materials
Ss
E+S
Sb
k2
ES  P  E
Assume the enzyme catalyzed
reaction rate follows Michaelis-Menten
type kinetics.
Enzyme
Liquid Film Thickness, L
Ss: substrate concentration at the surface;
Sb: substrate concentration in bulk solution.
Diffusion Effects in Surface-bound Enzymes
on Nonporous Support Materials
Assume:
Ss
Sb
-Enzyme are evenly distributed on the
surface of a nonporous support
material.
-All enzyme molecules are equally
active.
Enzyme
-Substrate diffuses through a thin
liquid film surrounding the support
surface to reach the reactive surface.
Liquid Film Thickness, L
No intraparticle diffusion
-The process of immobilization has not altered the enzyme
structure and the intrinsic parameters (Vm, Km) are unaltered.
Enzyme
are bound
on surface
At steady state, the reaction
rate=mass transfer rate
Diffusion Effects in Surface-bound Enzymes
on Nonporous Support Materials
The external diffusion rate
Js
(g/cm2-s):
J s  k L ([Sb ]  [S s ])
kL
is the liquid mass transfer coefficient (cm/s).
If the product formation rate is :
Vm '[ S s ]
v 
K m  [S s ]
'
Vm ' the maximum reaction rate per unit surface area.
(g/cm2-s)
Graphical solution for reaction rate per unit of surface area
for enzyme immobilized on a non-porous support
Diffusion Effects in Surface-bound Enzymes
on Nonporous Support Materials
When the system is strongly external diffusion
(liquid film mass-transfer) limited, [Ss]≈0,
the overall reaction rate is equal to the rate:
v  k L [ Sb ]
Da>>1
The system behaves as pseudo first order.
The rate is a linear function of bulk substrate concentration.
Diffusion Effects in Surface-bound Enzymes
on Nonporous Support Materials
When the system is strongly reaction limited,
[Sb] ≈ [Ss]
the overall reaction rate is equal to the rate:
Vm '[ Sb ]
v
K m, app  [ Sb ]
Da << 1
where


Vm'
K m,app  K m 1 

 k L ([ Sb ]  K m ) 
Km,app is increased. It is a function of mixing speed and Sb.
Diffusion Effects in Enzymes
Immobilized in a Porous Matrix
- Substrate diffuses through the tortuous
pathway within the porous support to reach
the enzyme.
- Substrate reacts with enzyme on the pore
surface.
Ex. Spherical support particles
Sr
Diffusion Effects in Enzymes
Immobilized in a Porous Matrix
Assume:
- Enzyme is uniformly distributed in a
spherical support particle.
- The reaction kinetics follows MichaelisMenten kinetics.
- There is no external diffusion limitation,
(no partitioning of the substrate between
exterior and interior of support).
A steady state: Diffusion rate =reaction rate
reaction rate with intraparticle diffusion limitation

reaction rate without diffusion limitation.
Relationship of effectiveness factor with the size of
immobilized enzyme particle and enzyme loading