ENZYME IMMOBILIZATION KINETICS PTT311: ENZYME TECHNOLOGY CO2: - - PowerPoint PPT Presentation

ENZYME IMMOBILIZATION KINETICS

PTT311: ENZYME TECHNOLOGY

CO2: Ability to distinguish methods for enzyme immobilization and the characterization of immobilized enzymes kinetics.

By: Pn AinHarmiza 1

Immobilization of Enzymes

• Consider the following two designs for a

continuous enzyme process S  P

By: Pn AinHarmiza 2

What are the advantages and disadvantages of PROCESS 2 compared to PROCESS 1 ?

ADVANTAGES

• Enzyme is not lost after process

and might therefore be used for greater duration.

• Enzyme does not need to be

separated from products. (Conversely, products do not need to be separated from enzyme.)

• Higher enzyme concentrations

are attainable without sacrificing these advantages.

• Some enzymes are more stable if

they are immobilized. (Many native enzymes are “immobilized” in the cell.)

• An additional process (and cost)

is associated with enzyme immobilization.

• Enzymes may leak from

immobilized state.

• Diffusional limitations.

Substrate(s) and product(s) must transfer across a boundary to get to/from active site.

• Can be difficult to control

environment immediately affecting enzyme and its activity.

• Some enzymes are less stable if

they are immobilized. (Structural change).

By: Pn AinHarmiza 3

DISADVANTAGES

How to reduce structural changes and prevent binding at activity site:

• 1. Mix enzyme with

competitive inhibitor.

• 2. Immobilize.
• 3. Wash the competitive

inhibitor away.

By: Pn AinHarmiza 4

EFFECT OF MASS-TRANSFER RESISTANCE

• The immobilization of enzymes may introduce

a new problem which is absent in free soluble enzymes.

• It is the mass-transfer resistance due to the

large particle size of immobilized enzyme or due to the inclusion of enzymes in polymeric matrix.

By: Pn AinHarmiza 5

EFFECT OF MASS-TRANSFER RESISTANCE

• If we follow the hypothetical path of a substrate from

the liquid to the reaction site in an immobilized enzyme, it can be divided into several steps (Figure 3.2):

• 1. transfer from the bulk liquid to a relatively

unmixed liquid layer surrounding the immobilized enzyme;

• 2. diffusion through the relatively unmixed liquid

layer; and

• 3. diffusion from the surface of the particle to the

active site of the enzyme in an inert support.

By: Pn AinHarmiza 6

EFFECT OF MASS-TRANSFER RESISTANCE

• Steps 1 and 2 are the

external mass-transfer resistance.

• Step 3 is the

intraparticle mass- transfer resistance.

By: Pn AinHarmiza 7

Kinetic Properties

• There is usually a decrease in specific activity of an enzyme upon

insolubilization: denaturation caused by the coupling process

• Microenvironment after immobilization may be drastically different from

that existing in free solution: the physical and chemical character of the support matrix, or interactions of the matrix with substrates or products involved in the enzymatic reaction

– The Michaelis constant may decrease by more than one order of magnitude when substrate of opposite charge to the carrier matrix

• The diffusion of substrate can limit the rate of the enzyme reaction: the

thickness of the diffusion film determines the concentration of substrate in the vicinity of the enzyme and hence the rate of reaction

• The effect of the molecular weight of the substrate can also be large. This

may be an advantage in some cases, since the immobilized enzymes may be protected from attack by large inhibitor molecules

DIFFUSIONAL LIMITATIONS IN IMMOBILIZED ENZYME SYSTEMS

• Diffusional resistances may be observed at

different levels in immobilized enzymes.

• Immobilized enzyme system normally includes:
• insoluble immobilized enzyme
• soluble substrate, or product
• They are heterogeneous systems.

By: Pn AinHarmiza 9

DRIVING FORCE DIFFUSION HIGH

Immobilized Enzyme

Sb

Low S concentration Substrate

DRIVING FORCE DIFFUSION HIGH

Immobilized Enzyme

Sb

REACTION

PRODUCT

DRIVING FORCE DIFFUSION HIGH

Immobilized Enzyme

Sb

PRODUCT HIGH

Immobilized Enzyme

Sb

REACTION

• 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.

By: Pn AinHarmiza 14

By: Pn AinHarmiza 15

is the maximum reaction rate per unit of external surface area (e.g. g/cm2-s) To determine the significant effect of external diffusion resistance

• n the rate of enzyme catalytic reaction rate: Damköhler numbers

(Da)

] [ ' diffusion

• f

rate maximum reaction

• f

rate maximum b S L k m V Da  

' m V

L k

] [ b S

is the liquid mass transfer coefficient (cm/s) Is the substrate concentration in bulk solution (g/cm3)

By: Pn AinHarmiza 16

When Da >> 1, the external diffusion rate is limiting; Da << 1, the reaction rate is limiting; Da ≈ 1, the external diffusion and reaction resistances are comparable.

] [ ' diffusion external

• f

rate maximum reaction

• f

rate maximum b S L k m V Da  

Diffusion Effects in Surface-bound Enzymes

• n Nonporous Support Materials

By: Pn AinHarmiza 17

Ss: substrate concentration at the surface; Sb: substrate concentration in bulk solution.

Enzyme Ss Sb Liquid Film Thickness, L

E P k ES     2

E+S

Assume the enzyme catalyzed reaction rate follows Michaelis-Menten type kinetics.

By: Pn AinHarmiza 18

Enzyme Ss Sb 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) are unaltered.

By: Pn AinHarmiza 19

] [ ] [ '

' s m s m

S K S V v  

If the product formation rate is :

]) [ ] ([ s S b S L k s J  

The external diffusion rate (g/cm2-s):

s J

' m V

the maximum reaction rate per unit surface area.

(g/cm2-s)

L k

is the liquid mass transfer coefficient (cm/s).

By: Pn AinHarmiza 20

] [ ] [ ' ]) [ ] ([ s S m K s S m V s S b S L k s J    

At steady state, the reaction rate is equal to the external diffusion rate: With the equation and known Sb, KL, Vm’ or Km, to determine numerically or graphically:

• The substrate concentration at the surface.
• The reaction rate.

E P k ES     2

E+S

By: Pn AinHarmiza 21

Graphical solution for reaction rate per unit of surface area for enzyme immobilized on a non-porous support

]) [ ] ([ s S b S L k s J  

By: Pn AinHarmiza 22

] [ b S L k v 

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

By: Pn AinHarmiza 23

To increase the overall reaction rate with external diffusion limitation:

• Increase .
• Increase .

] [ ' diffusion

• f

rate maximum reaction

• f

rate maximum b S L k m V Da  

The liquid film mass transfer coefficient kL:

(H. Fogler, Elements of Chemical Reaction Engineering 1999, p705)

DAB is mass diffusivity of the substrate in the liquid phase, a function of temperature and pressure (m2/s) ν is the kinematic viscosity (m2/s), a function of temperature. U is the free-system liquid velocity (velocity of the fluid flowing past the particle) (m/s). dp is the size of immobilized enzyme particle (m). At specific T and P, increasing U and decreasing dp increase the liquid film mass transfer coefficient and the external diffusion rate.                        2 / 1 2 / 1 6 / 1 3 / 2 6 . p d U AB D L k 

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:

] [ , ] [ ' b S app m K b S m V v  

Da << 1

         ) ] ([ 1

' , m b L m m app m

K S k V K K

Km,app is increased. It is a function of mixing speed and Sb. 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.

• 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 Michaelis-

Menten kinetics.

• There is no external diffusion limitation.



is .

1  

1  

the rate is . the rate is .

. limitation diffusion without rate reaction limitation diffusion cle intraparti with rate reaction  

] [ ] [

" s m s m s

S K S V r  

Under internal diffusion limitations, the rate per unit volume is expressed in terms of the effectiveness factor as follows:

" m

V

is the maximum velocity per volume of the support.

m

K

is the M-M constant.

] [

s

S

is the substrate concentration on the surface of the support.

Relationship of effectiveness factor with the size of immobilized enzyme particle and enzyme loading

At specific conditions (T, P) for a fixed system, To increase the intra-particle mass transfer rate:

• the size of immobilized enzyme particle
• the porosity or specific surface area of the

particle

Application of immobilized enzymes

Bioreactors

Large scale production or conversion of various compounds

Application of immobilized enzymes

Biosensors

An analytical device which can detect and quantify specific analytes in complex samples

Biological Sample Detection Transducer Solution Element Signal Signal Processor Readout

Enzyme biosensors

Electrodes detecting gases such as O2, CO2, NH3 and various ionic species are commercially available

Application of immobilized enzymes

Bioremediation

• For the removal/detoxification of contaminants
• E.g. Polyphenol oxidase immobilized on chitosan coated membranes

THANK YOU

THE END

By: Pn AinHarmiza 36

By: Pn AinHarmiza 37

EXTERNAL MASS TRANSFER EFFECTS

• General Derivation:
• Enzymes are immobilized on surface of

uncharged, nonporous flat plate.

• Entire surface is uniformly accessible to

substrate in adjacent fluid

By: Pn AinHarmiza 38

• Consider S  P as immobilized enzyme reaction:
• Case I

– Enzyme reaction is very slow – Surface concentration (SSURF) is identical to bulk concentration (SBULK)

• Case II

– Enzyme reaction is very fast – Surface concentration (SSURF) is zero

By: Pn AinHarmiza 39

By: Pn AinHarmiza 40

• Case I

– Enzyme reaction is very slow – Rate of reaction is limited by enzyme and its intrinsic reaction rate

• Case II

– Enzyme reaction is very fast – Rate of reaction is limited by rate of mass transfer – At steady-state, substrate and product will not accumulate at the surface, and the rate of reaction is equal to the rate of mass transfer…

By: Pn AinHarmiza 41

rate of reaction = rate of mass transfer

By: Pn AinHarmiza 42

INTERNAL MASS-TRANSFER RESISTANCE

• In order to derive an equation that shows how the mass-transfer

resistance affects the effectiveness of an immobilized enzyme, let's make a series of assumptions as follows: 1. The reaction occurs at every position within the immobilized enzyme, and the kinetics of the reaction are of the same form as observed for free enzyme. 2. Mass transfer through the immobilized enzyme occurs via molecular diffusion. 3. There is no mass-transfer limitation at the outside surface of the immobilized enzyme. 4. The immobilized enzyme is spherical.

• The model developed by these assumptions is known as the

distributed model.

By: Pn AinHarmiza 43

• Input - Output + Generation = Accumulation
• Ds = diffusivity of the substrate in an

immobilization matrix.

• dr = shell thickness.

SHELL BALANCE FOR A SUBSTRATE IN AN IMMOBILIZED ENZYME

By: Pn AinHarmiza 44

SHELL BALANCE FOR A SUBSTRATE IN AN IMMOBILIZED ENZYME

• For a steady-state condition, the change of

substrate concentration, dCs / dt, is equal to zero.

• After opening up the brackets and simplifying

by eliminating all terms containing dr2 or dr3 we obtain the second order differential equation:

By: Pn AinHarmiza 45

SHELL BALANCE FOR A SUBSTRATE IN AN IMMOBILIZED ENZYME

• This equation can be solved by substituting a

suitable expression for rs.

• Let's solve the equation first for the simple

cases or zero-order and first-order reactions, and for the Michaelis-Menten equation.

By: Pn AinHarmiza 46

Zero-order Kinetics

• only valid when Cs > 0.
• Assume:
• The critical radius, below which Cs is zero, can be
• btained by solving:

By: Pn AinHarmiza 47

Zero-order Kinetics

• The effectiveness factor

= the ratio of the actual reaction rate to the rate if not slowed down by diffusion.

By: Pn AinHarmiza 48

First-order Kinetics

• Assume:

By: Pn AinHarmiza 49