LOGO IN THE NAME OF GOD KINETICS OF ENZYME & IMMOBILIZED ENZYMES BY SARA MADANI

Contents Enzyme Immobilized Enzymes Kinetics of immobilized enzyme Enzyme kinetics Method of Immobilization

Introduction  Enzymes are usually proteins of high molecular weight (15,000 < MW < several million daltons ) that act as catalysts.  Enzymes are specific versatile, biological catalysts, resulting in much higher reaction rates as compared to chemically catalyzed reaction under ambient condition.  Enzymes are substrate specific and are classified according to the reaction the catalyze.

Substrate & Enzyme  The substrate is a relatively small molecule and fit into a certain region on the enzyme molecule, which is a much larger molecule.  The simplest model describing this interaction is the lock-and-key model.

Immobilized Enzymes The restriction of enzyme mobility in a fixed space is known as enzyme immobilization.

Why Immobilization? ImmobilizationImmobilization Advantages Lower capital cost enzyme reutilization elimination of recovery & purification provide a better environment

METHODS OF IMMOBILIZATION D B C A Binding to Carriers Immobilization by binding Cross-linking Matrix Entrapment Membrane Enclosure Immobilization by Physical retention

Classification of enzyme immobilization method

Immobilized Enzyme Kinetics of Enzyme in Solution Enzyme Kinetics Kinetic of Immobilized Enzyme

Enzyme Kinetic Introduction  A mathematical model of the kinetics of single- substrate-enzyme-catalyzed reaction was first developed by V. C. R. Henri and by L. Michaelli and M. L. Menten. Kinetics of simple enzyme-catalysed reaction are often referred to as Michaelis-Menten kinetics.

Mechanistic Models for Simple Enzyme Kinetics Two major approaches used in developing a rate expression for the enzyme catalyzed reactions are:  rapid-equilibrium approach  quasi-study-state approach.

Mechanistic Models for Simple Enzyme Kinetics The rate of product formation: The rate of variation of ES complex: The eqn on the enzyme yields: Both of them are the same in initial steps in deriving a rate expression.

The rapid equilibrium assumption Assuming a rapid equilibriume between the enzyme & Substrate to form an [ES] complex. The equilibriume constant is: For [ES]: Finaly: where

The quasi- steady-state assumption By applying this assumption to eqn 3 we find: Subs enzyme eqn in eqn 9 yields: Subs above eqn in to eqn 2 yields Where

Kinetic of Immobilized Enyme Many factors can cause the kinetic parameters of immobilized enzymes to differ from those of soluble enzymes. 2 Electrostatic and partitioing effects 3 Diffusional,or mass- transfer effect 1 Conformational effects This factors can be classified as follows

Effects Of the Electrostatic potential The equilibrium condition requires that the electrochemical potential of the hydrogen ions in the particle equals with bulk phase The distribution of the charged substrate between the particle and the bulk phase is then:

Assume that the reaction catalyzed by the immobilized enzyme obey Michaelis-Menten kinetics The rate of reaction expressed in terms of the local substrate concentration by: the apparent Michaelis-Menten of the immobilized enzyme is: Effects Of the Electrostatic potential

Effect of External Mass Transfer Uncharged Support Suppose the enzyme is immobilized to the surface of an nonporous particle The average flux of substrate to the fluid-solid interface can be written : At steady state, the enzymatic reaction rate must be exactly balanced by the rate of substrate transport to the catalyst surface ;therefore, This eqn can be cast into dimensionless form by introducing the following dimensionless variables

Thus we can write Where Da,an important dimensionless group known as the Damköhler numbers To determine the significant effect of external diffusion resistance on the rate of enzyme catalytic reaction rate we use Da. The physical interpretation: Effect of External Mass Transfer

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. In general form the observed reaction rate is: But in the case of no diffusional limitations;that is when And hence Da << 1 Effect of External Mass Transfer

Therefore, the observed rate can be related to the rate that whould be obtained in the absence of external diffusional limitations by Where is known as the external effectivenss factor defined as In terms of dimensionless quantities Effect of External Mass Transfer

The external effectiveness factor is a numerical measure of the influence of external mass transfer resistance on the observed reaction rate. when the external mass transfer resistance is limiting. When the external mass transfer rate is not limiting Effect of External Mass Transfer

For diffusion-limited regime Therefore,the observed rate of reaction At the other extreme, we have: and Effect of External Mass Transfer

c Charged Support The steady-state molar flux of charged substrate to planar charged support can be written as : Fickian diffusion Migration due to the gradient of the electrostatic potential Effect of External Mass Transfer

 Integration and subsequent manipulation yields : and the enzymatic reaction rate yields the steady-state relation where Effect of External Mass Transfer

 We defind a modified Damköhler numbers as:  And apparent Michaelis-Menten constant,that accounts for both electrostatic and external mass transfer effect: Effect of External Mass Transfer

 Michaelis-Menten Kinetics  Enzymes are often immobilized to porous materials with larg internal surface areas,  All of the effective factor are typically incorporated into a single diffusion coefficient, the effective diffusivity, And Effects of Intraparticle Diffusion

 The general differential eqn for mass transfer is If we assume that diffusion occurs in the radial direction only,the s-s material balance becomes  And dimensionless form is Effects of Intraparticle Diffusion

We combine main factor that exist in the eqn in a dimensionless parameter,Thiele modulus, defined for Michaelis-Menten Kinetics by: Effects of Intraparticle Diffusion

And definition of effectiveness factor is Effects of Intraparticle Diffusion

Simultaneous External &Internal Mass-Transfer Resistances& Partitioning Effects  We begin by reconsidering the steady –state intraparticle mass balance for substrate in a spherical immobilized enzyme pellet:  Boundary conditions for eqn are

The new parameter appearing here is the Biot number,Bi defined as In the presence of partitioning effects,the equilibrium concentration of substrate with in the pellet wil differ from that in outside liquid. If Bi>100 the effects of external resistance are not significant Simultaneous External &Internal Mass-Transfer Resistances& Partitioning Effects

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Reference [1] Shuler,ML. and Kargi, F.”Bioprocess Engineering:Basic Concepts”2 nd Edition, 2005.prentice-Hall Inc. [2] Harvey W.Blanch. And Douglas S. Clark.”Biochemical Engineering”1996,MARCEL DEKKER,INC., New York,USA. [3] [4] Company Logo