models for more complex enzyme kinetics allosteric enzymes - some enzymes have more than one...

Models for More Complex Enzyme Kinetics

• Allosteric enzymes- Some enzymes have more than one substrate binding site.

- Allostery or cooperative binding:the binding of one substrate to the

enzyme facilitates binding of other substrate molecules.

Models for More Complex Enzyme Kinetics

The rate expression in this case is

nSmK

nSmV

dt

Sdv

]["

][][

''ln]ln[ln mKSnvmV

v

vmV

v

ln

n is cooperativity coefficient; n>1 indicates positive cooperativity;n can be determined by rearranging the above equation as

And plotting versus ln[S].

Models for More Complex Enzyme Kinetics

• Insoluble substratewood chips, cellulosic residues

-Access to the active site on these biopolymers by enzyme is limited by enzyme diffusion.

-The number of reaction sites exceeds the number of enzyme molecules.

-This is opposite that of the typical situation with soluble substrates, where access to the enzyme’s active site by substrate limits reaction.

Models for More Complex Enzyme Kinetics

• Insoluble substrate

If considering- the initial product formation rate and - the reaction is first order in terms of

the enzyme-substrate complex concentration, yields,

][

][max,

EeqK

ESVv

][2max, 0SkSV adskdeskeqK /

Factors Affecting Enzyme Kinetics • pH effects

- on enzymes

- enzymes have ionic groups on their active sites.

- Variation of pH changes the ionic form of the active sites.

- pH changes the three-Dimensional structure of enzyme.

- on substrate

- some substrates contain ionic groups

- pH affects the ionic form of substrate

affects the affinity of the substrate to the enzyme

Factors Affecting Enzyme Kinetics • Temperature

- on the rate enzyme catalyzed reaction

k2=A*exp(-Ea/R*T)

T k2

- enzyme denaturation

T

][][

2ESk

dt

Pdv

v

][][

Edkdt

Ed

Denaturation rate:kd=Ad*exp(-Ea/R*T)

kd: enzyme denaturation rate constant;

Ea: deactivation energy

Immobilized Enzyme Systems• Enzyme immobilization:

To restrict enzyme mobility in a fixed space.

Advantages:- 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

- Study of the action of membrane-bound intracellular enzyme

Immobilized Enzyme Systems

• Methods of Enzyme Immobilization:

- Entrapment

- Surface immobilization

- Cross-linking

Entrapment immobilization is based on the localization of an enzyme within the lattice of a polymer matrix or membrane.

- to retain enzyme - allow the penetration of substrate.

It can be classified into matrix and micro capsule types.

Immobilized Enzyme Systems

Immobilized Enzyme Systems

Entrapment - matrix entrapment - membrane entrapment

(microencapsulation)

Immobilized Enzyme Systems- matrix entrapment

Matrix materials:

organics: polysaccharides, proteins, carbon, vinyl and allyl polymers, and polyamides. e.g. Ca-alginate, agar,

K-carrageenin, collagenEnzyme + polymer solution → polymerization

→ extrusion/shape the particles

inorganics: activated carbon, porous ceramic and diatomaceous earth.

Shapes: - particle- membrane - fiber

Immobilized Enzyme Systems- membrane entrapment

- Regular semipermeable membrane: nylon, cellulose, polysulfone and polyacrylate.

- Microencapsulation: Microscopic hollow sphere are formed.The sphere contain the enzyme solution

and is enclosed within a porous membrane.

Immobilized Enzyme Systems

Entrapment

challenges:- enzyme leakage into solution

- diffusional limitation

- reduced enzyme activity and stability

- lack of control micro-environmental conditions.

It could be improved by modifying matrix or membrane.

Immobilized Enzyme Systems

Surface immobilization

According to the binding mode of the enzyme, this method can be further sub-classified into:

- Physical Adsorption - Ionic Binding - Covalent Binding

Immobilized Enzyme SystemsSurface immobilization

Physical Adsorption is based on the physical adsorption of enzyme protein on the surface of water-insoluble carriers.

- If a suitable carrier is found, this method can be both simple and cheap.

- The active sites and activity of enzymes are less affected.

- Desorption of enzyme takes place because of weak attraction.

- Non-specific of other protein or substances will affect the properties of enzyme.

Immobilized Enzyme SystemsPhysical Adsorption:

Weak forces: Van der Waals or dispersion

Materials:

Inorganic: almumina, silica, porous glass, ceramics.

Organic: e.g. cellulose, starch, activated carbon.

Carbon nano-tube (Kim, Jeong Yun, Special Publication - Royal Society of Chemistry, 2004)

Immobilized Enzyme Systems

Ionic binding:

Interaction forces: ionic bonds.

Features: similar to that of physical adsorption.

Polysaccharides and synthetic polymers having ion-exchange centers are usually used as carriers.

Immobilized Enzyme Systems

Covalently binding is the formation of covalent bonds between the enzyme and the support matrix.

Interaction forces: covalent bonds.

Features: - may alter the conformational structure and active

center of the enzyme, resulting in major loss of activity and/or changes of the substrate.

- the binding force between enzyme and carrier is so strong that no leakage of the enzymes occurs.

Immobilized Enzyme Systems

Covalent binding:

To select the type of reaction for enzyme covalent immobilization: 

- do not cause loss of enzymatic activity. - the active site of the enzyme must be

unaffected by the reagents used.

Immobilized Enzyme Systems

Covalent binding:

The functional groups on the supports that may take part in this binding are listed below:

e.g. amino group, carboxyl group, sulfhydryl group, hydroxyl group, phenolic

group etc.

Immobilized Enzyme Systems

Cross-linking: to cross link enzyme molecules with each other using agents such as glutaraldehyde.

Features: similar to covalent binding.

Several methods are combined.

Summary of Immobilization Methods

Methods of Enzyme immobilization:

- Entrapment - matrix- membrane (microencapsulation)

- Surface immobilization- physical adsorption- ionic binding- covalent binding

- Cross-linking

Recycle packed column reactor: - allow the reactor to operate at high fluid velocities.- a substrate that cannot be completely processed on a single pass

Immobilized Enzyme Reactors

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

- An immobilized enzyme tends to decompose upon physical stirring.

- The batch system is generally suitable for the production of rather small amounts of chemicals.