CHAPTER 1 ENZYME KINETICS AND APPLICATIONS Kinetics of Enzyme Catalyzed Reactions Applied Enzyme Catalysis 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 aggregates 2) Adsorbed enzyme may be cross-linked 3) Cross-linking after impregnation of porous support material with enzyme solution.  The disadvantages of cross-linking: 1 ) Significant changes of active site 2) 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/cm 3 ) 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 Ss Sb Liquid Film Thickness, L E+S Assume the enzyme catalyzed reaction rate follows Michaelis-Menten type kinetics.

Enzyme Ss Sb 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 (V m, K m ). Diffusion Effects in Surface-bound Enzymes on Nonporous Support Materials

At steady state, mass transfer rate = the reaction rate

Since the product formation rate is : The mass transfer rate (g/cm 2 -s): the maximum reaction rate per unit surface area. (g/cm 2 -s or mol/cm 2 -s) 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

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

When the system is strongly reaction limited, [Sb] ≈ [Ss] the overall reaction rate is equal to the rate: Da << 1 K m,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

Relationship of effectiveness factor with the size of immobilized enzyme particle and enzyme loading Design consideration:  V m and R High [E] = high enzyme activity but low effective factor and vice versa. From the plot, best condition for particle radius of 10 microns?