1. Chapter Three: Enzymes_ Part Four

2. Enzyme Deactivation
Enzymes are denatured by
Temperature pH

3. Temperature Effects
Higher temperatures give higher reaction rate constant, Higher corresponds to higher
The change in as a function of temperature can be obtained from The Arrhenius Equation
as follows:
Where and are the activation energy and the universal gas constant, respectively. T is the temperature in Kelvin and A is a constant.

4. Temperature Effects
If 1/T is plotted against , the relation is linear with a slope of
Assuming that the enzyme deactivation due to the temperature effect is a first order reaction, we get the following first order differential equation for active enzyme:
Integrating the above equation yields:

5. Temperature Effects
Effect on rate is a combination of the two effects

6. pH Effects
Certain enzymes have ionic groups on their active sites.
These ionic groups must be in a suitable form (acid or base) to function.
Variations in the pH of the medium result in changes in the ionic form of the active site and changes in the activity of the enzyme and hence the reaction rate.
For these reasons enzyme are only active over a certain pH range. 6

7. Effect of Enzyme Ionization
The solution pH for optimum enzyme activity
is between pK1 and pK2

8. pH-Activity Profile
The pH-activity profiles of two enzymes. (A) trypsin
and (B) cholinesterase 8

9. Immobilized Enzyme Systems

10. Introduction
Most enzymes are soluble in water. Therefore, it is very difficult or impractical to separate the enzymes for reuse.
Enzymes can be immobilized on the surface of or inside of an insoluble carrier either by chemical or physical methods. 10

11. Some Advantages of Enzyme Immobilization
There are a number of advantages for attaching enzymes to a solid support and a few of the major advantages are listed below:
Multiple or repetitive use of a single batch of enzymes.
2. The ability to stop the reaction rapidly by removing the enzyme from the reaction solution (or vice versa).
3. Enzymes are usually stabilized by immobilization
Product is not contaminated with the enzyme  (this is especially useful in the food and pharmaceutical industries). 11

12. Disadvantages of Enzyme Immobilization
Mass transfer might become limited
Generally, reduced activity of enzymes
Enzymes can leak out of solid support

13. Immobilization Methods
Membrane entrapment
Matrix entrapment
Adsorption
Covalent bonding
Physical
Chemical

14. Membranes Entrapment

15. Aqueous enzyme solution
Membrane Entrapment
Membrane entrapment: is inclosing enzymes into in a semi-permeable polymer membrane
Membrane polymerized around aqueous enzyme solution in colloidal suspension (particle sizes on the order of µm)
Add polymer
mixing
Organic solvent
Aqueous enzyme solution

16. Membrane Entrapment Advantages High surface area to volume ratio
Thin membrane
Relatively gentle attachment method
Problems
Can be easily damaged

17. Other Membrane Immobilization Methods- HFM
Hollow fiber membrane (HFM) reactors use micro- or ultra-filtration membranes to retain high molecular weight (MW) enzymes, but pass low MW compounds.
Substrate and products outside the membrane
Product diffuses out of the membrane
Enzymes or cells
Substrate diffuses through membrane

18. Matrix Entrapment

19. Matrix Entrapment
Matrix entrapment: is incorporating enzymes into the lattices of a semi-permeable gel.
  The entrapment method of immobilization is based on the localization of an enzyme within the lattice of a polymer matrix. It is done in such a way as to retain enzyme while allowing penetration of substrate. It can be classified into lattice and micro capsule types.
  This method differs from the covalent binding and cross linking in that the enzyme itself does not bind to the gel matrix.  19 19

20. Matrix Entrapment Advantages Relatively gentle attachment method
Easy to perform
Problems
Mass transfer limitations
Enzyme leakage
Enzyme deactivation

21. Adsorption 21

22. Immobilization by Adsorption
Binding forces are ionic, hydrophobic, hydrogen bonds, or Van der Waals interactions
Binding is simple (incubate solid support in enzyme solution) but is reversible.
Substrate addition can cause desorption. 22

23. Physical Adsorption
This method for the immobilization of an enzyme is based on the physical adsorption of enzyme on the surface of water-insoluble carriers.
The method causes little or no conformational changes of the enzyme.
If a suitable carrier is available, this method can be both simple and cheap.
It has the disadvantage that the adsorbed enzyme may leak from the carrier during use due to a weak binding forces between the enzyme and the carrier. 23 23

24. Typical Adsorbents Cellulose Polystyrene resins Kaolinite Glass
Alumina
Silica gel 24

25. Surface Immobilization

26. Covalent Immobilization
The covalent binding method is based on the binding of enzymes and water-insoluble carriers by covalent bonds.
Covalent bonds are the result of two atoms sharing electrons in order to fill their energy level.
The most intensely studied techniques of the immobilization is the formation of covalent bonds between the enzyme and the carrier.
When trying to select the type of reaction by which a given enzyme should be immobilized, the choice is limited by two factors:  (1) the binding reaction must be performed under conditions that do not cause loss in enzymatic activity, and (2) the active site of the enzyme must be unaffected by the reagents used. 26 26

27. Covalent Bonding
The most widely utilized method of immobilization due to high bond strength (stable immobilization)
Different carriers with different functional groups can be used

28. Covalent Immobilization
1. Aldehyde surface
2. Carboxylic acid surface
3. Epoxide surface (X is NH for lysine or S for cysteine)

29. Covalent Immobilization
4. Maleimide surface
5. Amine surface

30. Covalent Immobilization
6. Isothiocyanate surface
7. Thiol surface

31. Covalent Immobilization
8. Alcohol surface

32. Copolymerization of Enzymes
Copolymerization is performed with multifunctional bridge molecules to yield and insoluble product
Usually an inert protein is also included

33. Diffusional Limitations in Immobilized Enzyme Systems
Diffusional resistances depend on:
1. Nature of the support material ( porous , nonporous).
2. Hydrodynamical conditions surrounding the support material.
3. Distribution of the enzyme inside or on the surface of the
supporting material.
Depending on the value of the Damkohler number (Da), the rate of enzymatic reaction may be limited by:
Diffusion rate (mass transfer) if Da >> 1 the rate is limiting.
Reaction rate if Da << 1, the is limiting.
In the case when Da= 1, the diffusion and reaction resistances are comparable. 33

34. Diffusion effects in surface-bound enzymes on
nonporous support materials
Assumptions when dealing with such a system:
Enzymes are bound and evenly distributed on the
surface of a nonporous support material,
All enzyme molecules are equally active,
3. Substrate diffuses through a thin liquid film
surrounding the support surface to reach the reactive
surface,
4. The process of immobilization has not altered
the enzyme structure,
5. The kinetic parameters (Vm, Km) are unaltered. 34

35. Diffusion effects in surface-bound enzymes on
nonporous support materials
At steady state, the reaction rate is equal to the mass-transfer rate: 35

36. Diffusion effects in surface-bound enzymes on
nonporous support materials
Above equation can be solved graphically as shown in the adjacent figure. Such a plot makes it easy to visualize the effects of parameter changes such as stirring rate, changes in bulk substrate concentration, or enzyme loading on the enzymatic reaction.
Curve A represents the solution of the right side of the above equation. Lines B and B’ represent the mass transfer equation (left side). The intersections of the lines with curve A correspond to the enzymatic reaction rates at given Sb 36

37. Diffusion effects in surface-bound enzymes on
nonporous support materials
When the system is strongly mass-transfer limited (Da>>1),
[Ss]=0, since the reaction is rapid compared to mass transfer, and
the system behaves as pseudo first order. 37

38. Diffusion effects in surface-bound enzymes on
nonporous support materials
When the system is strongly reaction limited (Da<<1), [Sb] ≈ [Ss]
and the reaction rate is often expressed as:
Under these circumstances, the apparent Michaelis-Menten ( ) constant is a function of stirring speed.
Usually, is estimated experimentally as the value of [Sb], when one-half of the maximal reaction rate is acheived.
Where (with appropriate assumptions): 38

39. Example 3.4 39

40. Example 3.4 40

41. Diffusion Effects in Enzymes Immobilized
in a Porous Matrix
When enzymes are immobilized on internal pore surfaces of a porous matrix, substrate diffuses through the tortuous pathway among pores and reacts with enzyme immobilized on pore surface. Diffusion and reaction are simultaneous.
Assumptions required to deal with such a situation:
Enzyme is uniformly distributed in a spherical support particle.
The reaction kinetics are expressed by Michaelis-Menten kinetics.
The bulk [Sb] and surface [Ss] concentrations of the substrate are the same. 41

42. Diffusion Effects in Enzymes Immobilized
in a Porous Matrix
From mass balance at steady state:
Effective diffusivity of substrate within the porous matrix.
where
is diffusion coefficient,
is porosity, and
is the tortuosity
factor. 42 42

43. Diffusion Effects in Enzymes Immobilized in a Porous Matrix
The above equation can be written in dimensionless form by defining the following dimensionless variables: or
where
At steady state, the rate of substrate consumption is equal to the rate of substrate transfer through the external surface of the support particle into the sphere. 43

44. Diffusion Effects in Enzymes Immobilized
in a Porous Matrix
Under diffusion limitations, the reaction rate per unit volume is usually expressed in terms of the effectiveness factor (ɳ) as follows:
The effectiveness factor (ɳ) is defined as the ratio of the reaction rate with diffusion limitation (or diffusion rate) to the reaction rate with no diffusion limitation.
The value of the effectiveness factor (ɳ) is a measure of the extent of diffusion limitation.
For ɳ < 1, the process is diffusion limited,
For ɳ≈1, the process is limited by the reaction rate (diffusion limitation is negligible).
The effectiveness factor is a function of and β as shown in the figure on the following slide. 44

45. Diffusion Effects in Enzymes Immobilized in a Porous Matrix
The effectiveness factor (ɳ) is a function of ϕ and β as shown in the figure below.
For a zero-order reaction rate (β→0), ɳ≈1 (for a large range of Thiele modulus values such as 1< <100).
For a first-order reaction rate (β→ ∞), ɳ is approximated to the following equation (for the high values of ).
The figure represents the theoretical relationship between the effectiveness factor (ɳ) and first-order Thiele modulus ( ), for a spherical porous immobilized particle for various values of β (β is the dimensionless Michaelis constant (β=Km/Ss) ). 45

46. Example 3.5 46

47. Example 3.5
when internal diffusion limits the enzymatic reaction rate, the rate-constants Vm and Km values are not true intrinsic rate constant, but apparent values. 47

48. How to overcome Diffusional Resistance
Diffusional resistance might be overcome by:
Using small particle sizes
Increasing high degree of turbulency around the particles
Using high substrate concentrations. 48 48

49. End of Chapter Three