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.


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].


• 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.


• 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.



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.


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.


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)


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.


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.


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.


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.


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.

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

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