Lets recall….
Chapter 1.2
Applied Enzyme Catalysis
Restriction of enzyme mobility in a fixed space = enzyme immobilization
Method of enzyme immobilization
Retain high MW compound
Allowing small MW compound access to enzyme
Functional groups on support material are usually activated by using chemical reagent such as cyanogen bromide, carbodiimide and glutaraldehyde
Support materials with functional group
Chemical reagent
Cross-linking of enzyme molecule
Agent: glutaraldehyde,bis-diazobenzidine and 2,2-disulfonic acid Cross-linking can be achieved in several ways:1) Cross linked to form insoluble aggregates2) Adsorbed enzyme may be cross-linked3) Cross-linking after impregnation of porous support material with enzyme solution.
The disadvantages of cross-linking:1) Significant changes of active site2) Severe diffusion limitation
Diffusional Limitation in Immobilized Enzyme System
Immobilized enzyme system normally includes- insoluble immobilized enzyme- soluble substrate, or product
They are heterogeneous systems
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
Substrate conc. (g/cm3)
Mass transfer coefficient (cm/s)
Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials
Ss: substrate concentration at the surface;Sb: substrate concentration in bulk solution.
Enzyme
SsSb
Liquid Film Thickness, L
EPkES 2E+S
Assume the enzyme catalyzed reaction rate follows Michaelis-Mententype kinetics.
Enzyme
SsSb
Liquid Film Thickness, L No intraparticle diffusion
Assume:-Enzyme are evenly distributed on the surface of a nonporous support material.
-All enzyme molecules are equally active.
-Substrate diffuses through a thin liquid film surrounding the support surface to reach the reactive surface.
-The process of immobilization has not altered the enzyme structure and the intrinsic parameters (Vm, Km).
Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials
At steady state, mass transfer rate = the reaction rate
]S[K]S['V])S[]S([kJsm
smsbLs
area surface external ofunit per ratereaction max 'mV
22 enzyme/cm molor enzyme/cm mgEL
EL x
m'm VV
]S[K]S[Vvsm
s'm
Since the product formation rate is :
])[]([ sSbSLksJ The mass transfer rate (g/cm2-s):sJ
'mV the maximum reaction rate per unit surface area.
(g/cm2-s or mol/cm2-s)
Lk is the liquid mass transfer coefficient (cm/s) or stirring rate.
Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials
Graphical solution for reaction rate per unit of surface area for enzyme immobilized on a non-porous support
][ bSLkv
When the system is strongly external diffusion (liquid film mass-transfer) limited, [Ss]≈0,the overall reaction rate is equal to the rate:
The system behaves as pseudo first order.
The rate is a linear function of bulk substrate concentration.
Da>>1
Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials
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:
][,
]['
bSappmKbSmVv
Da << 1
)]([1
'
,mbL
mmappm KSk
VKK
Km,app is increased. It is a function of stirring speed.
where
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.
• Diffusion and reaction are simultaneous
Example: Spherical support particles
*tortuous = full of twist and turn, lengthy and complex
Diffusion Effects in Enzymes Immobilized in a Porous Matrix
Assume:- Enzyme is uniformly distributed in a spherical support particle.- The reaction kinetics follows Michaelis-Menten 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
.limitationdiffusion without ratereaction limitationdiffusion cleintraparti with ratereaction
Relationship of effectiveness factor with the size of immobilized enzyme particle and enzyme loading
Design consideration:Vm and R
High [E] = high enzyme activity but low effective factorand vice versa.
From the plot,best condition for particle radius of 10 microns?
