chapter 1 enzyme kinetics and applications kinetics of enzyme catalyzed reactions applied enzyme...

Lets recall….

Chapter 1.2

Applied Enzyme Catalysis

Restriction of enzyme mobility in a fixed space = enzyme immobilization

Method of enzyme immobilization

Retain high MW compound

Allowing small MW compound access to enzyme

Functional groups on support material are usually activated by using chemical reagent such as cyanogen bromide, carbodiimide and glutaraldehyde

Support materials with functional group

Chemical reagent

Cross-linking of enzyme molecule

Agent: glutaraldehyde,bis-diazobenzidine and 2,2-disulfonic acid Cross-linking can be achieved in several ways:1) Cross linked to form insoluble aggregates2) Adsorbed enzyme may be cross-linked3) Cross-linking after impregnation of porous support material with enzyme solution.

The disadvantages of cross-linking:1) Significant changes of active site2) Severe diffusion limitation

Diffusional Limitation in Immobilized Enzyme System

Immobilized enzyme system normally includes- insoluble immobilized enzyme- soluble substrate, or product

They are heterogeneous systems

Diffusional Limitation in Immobilized Enzyme Systems

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

Substrate conc. (g/cm3)

Mass transfer coefficient (cm/s)

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

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

Enzyme

SsSb

Liquid Film Thickness, L

EPkES 2E+S

Assume the enzyme catalyzed reaction rate follows Michaelis-Mententype kinetics.

Enzyme

SsSb

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).

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

At steady state, mass transfer rate = the reaction rate

]S[K]S['V])S[]S([kJsm

smsbLs

area surface external ofunit per ratereaction max 'mV

22 enzyme/cm molor enzyme/cm mgEL

EL x

m'm VV

]S[K]S[Vvsm

s'm

Since the product formation rate is :

])[]([ sSbSLksJ The mass transfer rate (g/cm2-s):sJ

'mV the maximum reaction rate per unit surface area.

(g/cm2-s or mol/cm2-s)

Lk is the liquid mass transfer coefficient (cm/s) or stirring rate.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

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

][ bSLkv

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

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

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:

][,

]['

bSappmKbSmVv

Da << 1

)]([1

'

,mbL

mmappm KSk

VKK

Km,app is increased. It is a function of stirring speed.

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.

• Diffusion and reaction are simultaneous

Example: Spherical support particles

*tortuous = full of twist and turn, lengthy and complex

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,(no partitioning of the substrate between exterior and interior of support).

A steady state: Diffusion rate =reaction rate

.limitationdiffusion without ratereaction limitationdiffusion cleintraparti with ratereaction

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

Design consideration:Vm and R

High [E] = high enzyme activity but low effective factorand vice versa.

From the plot,best condition for particle radius of 10 microns?