1. Immobilized enzymes Enzyme kinetics and associated reactor design:
CP504 – Lecture 5
Enzyme kinetics and associated reactor design:
Immobilized enzymes
enzyme mobility gets restricted in a fixed space
Prof. R. Shanthini Sept 2011

2. Immobilized enzyme reactor (example)
Recycle packed column reactor
Prof. R. Shanthini Sept 2011

3. Advantages of immobilized enzymes:
- 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
Prof. R. Shanthini Sept 2011

4. Disadvantages of immobilized enzymes:
- Problem in diffusional mass transfer
- Enzyme leakage into solution
- Reduced enzyme activity and stability
- Lack of controls on micro environmental conditions
Prof. R. Shanthini Sept 2011

5. Methods of immobilization
Entrapment Immobilization
Surface Immobilization
Cross-linking
Prof. R. Shanthini Sept 2011

6. Entrapment Immobilization
It is the physical enclosure of enzymes in a small space.
Matrix entrapment (matrices used are polysaccharides, proteins, polymeric materials, activated carbon, porous ceramic and so on)
Membrane entrapment (microcapsulation or trapped between thin, semi-permeable membranes)
Prof. R. Shanthini Sept 2011

7. Entrapment Immobilization
Advantage is enzyme is retained.
Disadvantages are
- substrate need to diffuse in to access enzyme and product need to diffuse out
- reduced enzyme activity and enzyme stability owing to the lack of control of micro environmental conditions
Prof. R. Shanthini Sept 2011

8. 2) Surface Immobilization
Physical adsorption (Carriers are silica, carbon nanotube, cellulose, and so on; easily desorbed; simple and cheap; enzyme activity unaffected )
Ionic binding (Carriers are polysaccharides and synthetic polymers having ion-exchange centers)
Covalent binding (Carriers are polymers containing amino, carboxyl, hydroxyl, or phenolic groups; loss of enzyme activity; strong binding of enzymes)
Prof. R. Shanthini Sept 2011

9. Methods of immobilization
Prof. R. Shanthini Sept 2011

10. 3) Cross linking
is to cross link enzyme molecules with each other using agents such as glutaraldehyde.
Prof. R. Shanthini Sept 2011

11. Comparison between the methods
Characteristics
Adsorption
Covalent coupling
Entrapment
Membrane confinement
Preparation
Simple
Difficult
Cost
Low
High
Moderate
Binding force
Variable
Strong
Weak
Enzyme leakage
Yes No
Applicability
Wide
Selective
Very wide
Running problems
Matrix effects
Large diffusional barriers
Microbial protection
Prof. R. Shanthini Sept 2011

12. Immobilized enzyme reactor (example)
Recycle packed column reactor
- Allow the reactor to operate at high fluid velocities
Prof. R. Shanthini Sept 2011

13. Immobilized enzyme reactor (example)
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
Prof. R. Shanthini Sept 2011

14. Immobilized enzyme reactor (example)
- An immobilized enzyme tends to decompose upon physical stirring.
- The batch system is generally suitable for the production of rather small amounts of chemicals.
Continuous stirred
tank reactor
Prof. R. Shanthini Sept 2011

15. Effect of mass-transfer resistance in immobilized enzyme systems:
Mass transfer resistance is present
- due to the large particle size of the immobilized enzymes
- due to the inclusion of enzymes in polymeric matrix
Prof. R. Shanthini Sept 2011

16. Effect of mass-transfer resistance in immobilized enzyme systems:
Mass transfer resistance are divided into the following:
- External mass transfer resistance
(during transfer of substrate from the bulk liquid to the relatively unmixed liquid film surrounding the immobilized enzyme and
during diffusion through the relatively unmixed liquid film)
- Intra-particle mass transfer resistance
(during diffusion from the surface of the particle to the active site of the enzyme in an inert support)
Prof. R. Shanthini Sept 2011

17. Liquid film thickness, L
External mass-transfer resistance:
Assumption:
- Enzymes 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 M-M kinetic parameters (rmax, KM) are unaltered.
Enzyme Ss Sb
Liquid Film Thickness, L
CSs
CSb
Enzyme
Liquid film thickness, L
Prof. R. Shanthini Sept 2011

18. Liquid film thickness, L
External mass-transfer resistance:
Diffusional mass transfer across the liquid film:
Enzyme Ss Sb
Liquid Film Thickness, L
CSs
CSb
JS = kL (CSb – CSs) kL
liquid mass transfer coefficient (cm/s)
CSb
substrate concentration in the bulk solution (mol/cm3)
CSs
substrate concentration at the immobilized enzyme surface (mol/cm3)
Enzyme
Liquid film thickness, L
Prof. R. Shanthini Sept 2011

19. Liquid film thickness, L
External mass-transfer resistance:
At steady state, the reaction rate is equal to the mass-transfer rate:
Enzyme Ss Sb
Liquid Film Thickness, L
CSs
CSb
rmax CSs
JS = kL (CSb – CSs) =
KM + CSs
rmax
maximum reaction rate per unit of external surface area (e.g. mol/cm2.s) KM
is the M-M kinetic constant (e.g. mol/cm3)
Enzyme
Liquid film thickness, L
Prof. R. Shanthini Sept 2011

20. Example 3.4 in Shuler & Kargi:
Consider a system where a flat sheet of polymer coated with enzyme is placed in a stirred beaker. The intrinsic maximum reaction rate of the enzyme is 6 x 10-6 mols/s.mg enzyme. The amount of enzyme bound to the surface has been determined to be maximum 1 x 10-4 mg enzyme/cm2 of support. In solution, the value of KM has been determined to be 2 x 10-3 mol/l. The mass-transfer coefficient can be estimated from standard correlations for stirred vessels. We assume in this case a very poorly mixed system where kL = 4.3 x 10-5 cm/s. What is the reaction rate, when the bulk concentration of the substrate (CSb) is (a) 7 x 10-3 mol/l and (b) 1 x 10-2 mol/l?
Prof. R. Shanthini Sept 2011

21. Solution to Example 3.4 in Shuler & Kargi:
Data provided:
rmax = 6 x 10-6 x 1 x 10-4 mols/s.cm2
= 6 x mols/s.cm2
KM = 2 x 10-3 mol/l = 2 x 10-6 mol/cm3
kL = 4.3 x 10-5 cm/s
CSb = 7 x 10-3 mol/l OR 1 x 10-2 mol/l
= 7 x 10-6 mol/cm3 OR 1 x 10-5 mol/cm3
Equation to be solved:
rmax CSs
JS = kL (CSb – CSs) +
KM + CSs
where CSs should be solved for, which can then be used to calculate JS.
Prof. R. Shanthini Sept 2011

22. Solution to Example 3.4 in Shuler & Kargi:
Prof. R. Shanthini Sept 2011

23. External mass-transfer resistance:
rmax CSs
JS = kL (CSb – CSs) =
KM + CSs
Non dimensionalizing the above equation, we get
1 - C’Ss
β C’Ss =
NDa
1 + β C’Ss
where
C’Ss =
CSs / CSb
NDa =
rmax / (kL CSb )
is the Damköhler number β =
CSb / KM
is the dimensionless substrate concentration
Prof. R. Shanthini Sept 2011

24. Damköhler number (NDa)
rmax
Maximum rate of reaction
NDa = =
kL CSb
Maximum rate of diffusion
If NDa >> 1, rate of diffusion is slow and therefore the limiting mechanism
rp = JS = kL (CSb – CSs)
If NDa << 1, rate of reaction is slow and therefore the limiting mechanism
rmax CSs rp =
KM + CSs
If NDa = 1, rates of diffusion and reaction are comparable.
Prof. R. Shanthini Sept 2011

25. Effectiveness factor (η)
actual reaction rate
η =
rate if not slowed by diffusion
rmax CSs
β C’Ss
KM + CSs
1 + β C’Ss
η = =
rmax CSb β
1 + β
KM + CSb
Effectiveness factor is a function of β and C’Ss
Prof. R. Shanthini Sept 2011

26. Internal mass transfer resistance:
Assumption:
- Enzyme are uniformly distributed in spherical support particle.
Substrate diffuses through the tortuous pathway among pores to reach the enzyme
Substrate reacts with enzyme on the pore surface
Diffusion and reaction are simultaneous
Reaction kinetics are M-M kinetics
CSs
CSr2
Prof. R. Shanthini Sept 2011

27. Diffusion effects in enzymes immobilized in a porous matrix:
Under internal diffusion limitations, the rate per unit volume is
expressed in terms of the effectiveness factor as follows:
rmax’ CSs
rS = η
KM + CSs
rmax’
maximum reaction rate per volume of the support KM
M-M constant
CSs
substrate concentration on the surface of the support η
effectiveness factor
Prof. R. Shanthini Sept 2011

28. Diffusion effects in enzymes immobilized in a porous matrix:
Definition of the effectiveness factor η
reaction rate with intra-particle diffusion limitation
η =
reaction rate without diffusion limitation
For η < 1, the conversion is diffusion limited
For η = 1, the conversion is limited by the reaction rate
Effectiveness factor is a function of β and C’Ss
Prof. R. Shanthini Sept 2011

29. Diffusion effects in enzymes immobilized in a porous matrix:β η φ
Theoretical relationship between the effectiveness factor (η) and first-order Thiele’s modulus (φ) for a spherical porous immobilized particle for various values of β, where β is the substrate concentration at the surface divided by M-M constant.
Prof. R. Shanthini Sept 2011

30. Diffusion effects in enzymes immobilized in a porous matrix:
Relationship of effectiveness factor (η) with the size of
immobilized enzyme particle and enzyme loading
Prof. R. Shanthini Sept 2011