prof. r. shanthini 30 sept 2011 1 enzyme kinetics and associated reactor design: immobilized enzymes...
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Enzyme kinetics and associated reactor design:
Immobilized enzymesCP504 Lecture 5enzyme mobility gets restricted in a fixed space
Immobilized enzyme reactor (example)Recycle packed column reactor
Advantages of immobilized enzymes: - 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
Disadvantages of immobilized enzymes: - Problem in diffusional mass transfer - Enzyme leakage into solution - Reduced enzyme activity and stability - Lack of controls on micro environmental conditions
Methods of immobilizationEntrapment ImmobilizationSurface ImmobilizationCross-linking
Entrapment Immobilization It is the physical enclosure of enzymes in a small space. Matrix entrapment (matrices used are polysaccharides, proteins, polymeric materials, activated carbon, porous ceramic and so on)Membrane entrapment (microcapsulation or trapped between thin, semi-permeable membranes)
Entrapment ImmobilizationAdvantage is enzyme is retained.
Disadvantages are- substrate need to diffuse in to access enzyme and product need to diffuse out - reduced enzyme activity and enzyme stability owing to the lack of control of micro environmental conditions
2) Surface Immobilization Physical adsorption (Carriers are silica, carbon nanotube, cellulose, and so on; easily desorbed; simple and cheap; enzyme activity unaffected )Ionic binding (Carriers are polysaccharides and synthetic polymers having ion-exchange centers)Covalent binding (Carriers are polymers containing amino, carboxyl, hydroxyl, or phenolic groups; loss of enzyme activity; strong binding of enzymes)
Methods of immobilization
3) Cross linking is to cross link enzyme molecules with each other using agents such as glutaraldehyde.
Comparison between the methods
CharacteristicsAdsorptionCovalent couplingEntrapmentMembrane confinementPreparationSimpleDifficultDifficultSimpleCostLowHighModerateHighBinding forceVariableStrongWeakStrongEnzyme leakageYesNoYesNoApplicabilityWideSelectiveWideVery wideRunning problemsHighLowHighHighMatrix effectsYesYesYesNoLarge diffusional barriersNoNoYesYes
Immobilized enzyme reactor (example)Recycle packed column reactor - Allow the reactor to operate at high fluid velocities
Immobilized enzyme reactor (example)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
Immobilized enzyme reactor (example)- An immobilized enzyme tends to decompose upon physical stirring.
- The batch system is generally suitable for the production of rather small amounts of chemicals. Continuous stirred tank reactor
Effect of mass-transfer resistance in immobilized enzyme systems: Mass transfer resistance is present - due to the large particle size of the immobilized enzymes- due to the inclusion of enzymes in polymeric matrix
Effect of mass-transfer resistance in immobilized enzyme systems: Mass transfer resistance are divided into the following: - External mass transfer resistance (during transfer of substrate from the bulk liquid to the relatively unmixed liquid film surrounding the immobilized enzyme andduring diffusion through the relatively unmixed liquid film) - Intra-particle mass transfer resistance (during diffusion from the surface of the particle to the active site of the enzyme in an inert support)
External mass-transfer resistance: EnzymeLiquid film thickness, LCSsCSbAssumption:- Enzymes 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 M-M kinetic parameters (rmax, KM) are unaltered.
External mass-transfer resistance: EnzymeLiquid film thickness, LCSsCSbDiffusional mass transfer across the liquid film: liquid mass transfer coefficient (cm/s)substrate concentration in the bulk solution (mol/cm3)kLCSbJS = kL (CSb CSs)substrate concentration at the immobilized enzyme surface (mol/cm3)CSs
External mass-transfer resistance: EnzymeLiquid film thickness, LCSsCSbAt steady state, the reaction rate is equal to the mass-transfer rate: JS = kL (CSb CSs)= rmax CSsKM + CSsmaximum reaction rate per unit of external surface area (e.g. mol/cm2.s)rmaxis the M-M kinetic constant (e.g. mol/cm3)KM
Example 3.4 in Shuler & Kargi:Consider a system where a flat sheet of polymer coated with enzyme is placed in a stirred beaker. The intrinsic maximum reaction rate of the enzyme is 6 x 10-6 mols/s.mg enzyme. The amount of enzyme bound to the surface has been determined to be maximum 1 x 10-4 mg enzyme/cm2 of support. In solution, the value of KM has been determined to be 2 x 10-3 mol/l. The mass-transfer coefficient can be estimated from standard correlations for stirred vessels. We assume in this case a very poorly mixed system where kL = 4.3 x 10-5 cm/s. What is the reaction rate, when the bulk concentration of the substrate (CSb) is (a) 7 x 10-3 mol/l and (b) 1 x 10-2 mol/l?
Solution to Example 3.4 in Shuler & Kargi:Data provided: rmax= 6 x 10-6 x 1 x 10-4 mols/s.cm2 = 6 x 10-10 mols/s.cm2 KM = 2 x 10-3 mol/l = 2 x 10-6 mol/cm3 kL = 4.3 x 10-5 cm/s CSb= 7 x 10-3 mol/l OR 1 x 10-2 mol/l = 7 x 10-6 mol/cm3 OR 1 x 10-5 mol/cm3
where CSs should be solved for, which can then be used to calculate JS.Equation to be solved:JS = kL (CSb CSs)+ rmax CSsKM + CSs
Solution to Example 3.4 in Shuler & Kargi:
External mass-transfer resistance: Non dimensionalizing the above equation, we get JS = kL (CSb CSs)= rmax CSsKM + CSswhere= CSs1 + CSs
1 - CSsNDarmax / (kL CSb )
CSs= = CSs / CSbNDa= CSb / KMis the Damkhler numberis the dimensionless substrate concentration
- Damkhler number (NDa)NDa = Maximum rate of reactionMaximum rate of diffusion= rmaxkL CSbIf NDa >> 1, rate of diffusion is slow and therefore the limiting mechanism If NDa
Effectiveness factor () = actual reaction raterate if not slowed by diffusion = rmax CSsKM + CSsrmax CSbKM + CSb= CSs1 + CSs1 + Effectiveness factor is a function of and CSs
Internal mass transfer resistance:Assumption:- Enzyme are uniformly distributed in spherical support particle. Substrate diffuses through the tortuous pathway among pores to reach the enzyme Substrate reacts with enzyme on the pore surface Diffusion and reaction are simultaneous Reaction kinetics are M-M kinetics CSsCSr2
Diffusion effects in enzymes immobilized in a porous matrix:Under internal diffusion limitations, the rate per unit volume is expressed in terms of the effectiveness factor as follows:rS = rmax CSsKM + CSsmaximum reaction rate per volume of the supportM-M constantsubstrate concentration on the surface of the supportrmaxKMCSs effectiveness factor
Diffusion effects in enzymes immobilized in a porous matrix: Definition of the effectiveness factor =reaction rate with intra-particle diffusion limitation reaction rate without diffusion limitation For < 1, the conversion is diffusion limitedFor = 1, the conversion is limited by the reaction rateEffectiveness factor is a function of and CSs
Diffusion effects in enzymes immobilized in a porous matrix: Theoretical relationship between the effectiveness factor () and first-order Thieles modulus () for a spherical porous immobilized particle for various values of , where is the substrate concentration at the surface divided by M-M constant.
Diffusion effects in enzymes immobilized in a porous matrix:Relationship of effectiveness factor () with the size of immobilized enzyme particle and enzyme loading