Lecture – 4 The Kinetics of Enzyme-Catalyzed

ReactionsDr. Saleha Shamsudin

Effect of pH and temperature

-Enzyme are active only over small range of pH due to the active site functional group charges (ionic form) and the three dimensional shape of enzyme are pH-dependent-Certain enzyme have ionic group on their active sites, and these ionic group must be in a suitable form (acid or base) to function.-Variation in pH of medium result in changes of: -Ionic form of the active site -Activity of enzyme, hence the reaction rate -Affect the maximum reaction rate, Km

-stability of enzyme

-Scheme to describe pH dependence of the enzymatic reaction rate for ionizing enzymes.

-Some cases, the substrate may contain ionic groups, and the pH of medium affects the affinity of substrate to enzyme.-Refer to Eq. 3.44& Eq. 3.45

Variation of enzyme activity with pH for 2 different enzymes

-

Variation of reaction rate with temperature

ascending

descending

The rate varies according to Arrhenius equation

Thermal Denaturation occurred

Restriction of enzyme mobility in a fixed space = enzyme immobilization

Retain high MW compound

Allowing small MW compound access to enzyme

Prior to

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

The agent used are: ____________, ____________, ________________

Cross-linking can be achieved in several ways:1)2)3)

The disadvantages of cross-linking:1)2)

This is the schematic diagram of enzyme immobilization methods:Suggest the method of (a), (b), (c) and (d)?

Quiz

Diffusional Limitation in Immobilized Enzyme System

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

• They are heterogeneous systems

CONCENTRATION D

IFFERENCE

FILM

TRANSFER

DRIVING FORCEDIFFUSION

HIGH

Immobilized Enzyme

Sb

Low S concentration

Substrate

external diffusion

CONCENTRATION D

IFFERENCE

FILM

TRANSFER

DRIVING FORCEDIFFUSION

HIGH

Immobilized Enzyme

Sb

REACTION

PRODUCT

external diffusion

FILM

TRANSFER

DRIVING FORCEDIFFUSION

HIGH

Immobilized Enzyme

Sb

INTRA-PARTICLE

TRANSFER

FILM

TRANSFER

PRODUCT

HIGH

Immobilized Enzyme

Sb

INTRA-PARTICLE

TRANSFER

REACTION

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)

Diffusional Limitation in Immobilized Enzyme System

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

Enzyme

SsSb

Liquid Film Thickness, L

EPk

ES 2E+S

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

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) are unaltered.

Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

Enzyme are bound on surface

At steady state, the reaction rate=mass transfer rate

][

][''

sm

sm

SK

SVv

If the product formation rate is :

])[]([ sSbSLksJ The external diffusion rate (g/cm2-s):sJ

'mV the maximum reaction rate per unit surface area.(g/cm2-s)

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

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 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,(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