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Ind. Eng. Chem. Res. 2008, 47, 8808–8814
How Is Effective Enantioselectivity of Immobilized Enzyme in Kinetic Resolution of Racemate Affected in a Fixed-Bed Reactor? Hongwei Yu*,† and Chi Bun Ching‡ Institute of Bioengineering, College of Materials Science and Chemical Engineering, Zhejiang UniVersity, Hangzhou, P. R. China, 310027, and School of Chemical and Biomedical Engineering, Nanyang Technological UniVersity, Singapore, 637722
The purpose of this theoretical discussion is to help researchers understand how some parameters and reaction type (first-order and Michaelis-Menten kinetic) could impact effective enantioselectivity of enzyme in a fixed-bed reactor, including adsorption equilibrium constant (adsorption effect), Biot number, Peclet number, and bed length parameter. The theoretical analysis clearly derives that reaction rate is able to impact the effective enantioselectivity of enzyme through controlling the loading of enzyme on the solid support. In addition, adsorption phenomenon and reaction type have no effect on the effective enantioselectivity in a fixed-bed reactor. Among these parameters, Bi ( 1) as shown in Figure 1a. The higher reaction rate is able to cause lower effective enantioselectivity, which is not favorable to the kinetic resolution of racemates. In other words, the enzyme loading should be controlled to achieve an expected effective enantioselectivity of the enzyme. The bigger the enantioselectivity of the enzyme, the more significant the influence, as shown in Figure 1b. No matter how linear or nonlinear the reaction rate is, the effect of reaction rate on effective enantioselectivity is the same. Figure 2a,b show that the dimensionless number Rj can influence the effectiveness factor as well and the effect of the reaction rate is weakened with increasing dimensionless number. Bhatia et al.14 studied kinetic resolution of ibuprofen ester in a fixed-bed reactor shown in Figure 3 and demonstrated the effect of the Thiele modulus on effective enantioselectivity by changing enzyme loading on a solid support as shown in Table 1. With increasing enzyme loading from 0.92 to 2.85 g/m2, the Thiele modulus was increased from 0.002 to 0.65. Meanwhile, the effective enantioselectivity dropped sharply from 363 to 7. The experimental results show that the reaction rate significantly affects the effective enantioselectivity.
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Figure 4. Time courses of exit concentration of the two substrates with (K ) 30) and without considering adsorption effect (K ) 0).
Figure 5. Effect of Bi on Eeff/E. Figure 2. Effect of dimensionless number Rj on (a) effective factor η and (b) Eeff/E.
Figure 3. Lipase-catalyzed hydrolysis of racemic ibuprofen esters (CRL ) Candida rugosa lipase). Table 1. Effect of Thiele Modulus on Eeff in the Kinetic Resolution of Racemic Ibuprofen Easter in a Fixed-Bed Reactor Thiele modulus
0.002
0.011
0.65
enzyme loading (g/m2) ees conversion (C) Eeff
0.92 42.5% 30% 363
1.78 41% 32% 22
2.85 38% 36% 7
3.2. Adsorption Effect on the Time Course of Exit Concentration. Adsorption effect is not neglected in a fixed-bed reactor if the adsorbents are employed to be solid supports for enzyme immobilization. The partial substrates are delayed to be converted as they are adsorbed on the surface of the solid supports in the fixed-bed reactor. Therefore, the time to reach
steady state is prolonged. Figure 4 compares the time courses of exit concentration of the two substrates with (K ) 30) and without considering adsorption effect (K ) 0) at Dr ) 1, Pe ) 35, Bi ) 1, E ) 20, and φ12 ) 10. Without considering adsorption effect, the two substrates are able to reach steady state at τ ) 10, respectively; considering adsorption effect, the two substrates are able to reach steady state at τ ) 160 and 120, respectively. The concentrations of the two substrates at the steady state under the two situations are the same. The simulation results clearly demonstrate that the adsorption process does not affect the exit concentration of the substrates at the steady state; in other words, conversion and effective enantioselectivity are not changed, but significantly delay the outlet to reach steady state. 3.3. Parameter Studies of Steady-State Kinetic Resolution in a Fixed-Bed Reactor. Biot number, Bi, is the ratio of intraparticle diffusion resistance to external mass transfer resistance. Figure 5 presents the effect of Bi on Eeff for a firstorder reaction and Michaelis-Menten kinetics at Dr ) 1, Pe ) 35, E ) 5 and 50, and φ12 ) 1. When the intraparticle diffusion resistance is comparable with the external mass transfer resistance, Bi < 10, the Eeff is strongly influenced by Bi; when the intraparticle diffusion resistance is much more than the external mass transfer resistance, Bi > 10, the effect of Bi on Eeff is not significant. With increasing Bi, Eeff increases close to E. At different E, 5 and 50, the effect of Bi on Eeff for a first-order reaction and Michaelis-Menten kinetics exhibits the
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Figure 6. Effect of Pe on Eeff/E.
same trend. At the same operating condition, Eeff/E at a higher E, E ) 50, is smaller than that at a smaller E, E ) 5, and Eeff/E for a first-order reaction is bigger than that for Michaelis-Menten kinetics. Peclet number, Pe, is the ratio of back-mixing time to residence time. Figure 6 presents the effect of Pe for a firstorder reaction and Michaelis-Menten kinetics on Eeff at Dr ) 1, Bi ) 1, E ) 5 and 50, and φ12 ) 1. Generally, the effect of Pe on Eeff is less significant than that of Bi. At different E, 5 and 50, the effect of Pe on Eeff for a first-order reaction and Michaelis-Menten kinetics exhibits the same trend: Eeff increases slightly with increasing Pe. At the same operating condition, Eeff for a first-order reaction is bigger than that for Michaelis-Menten kinetics. Bed-length parameter, Dr, is the ratio of the residence time of the substrates in the reactor to the intraparticle diffusion time of the substrates in the porous support. The conversion C is able to be adjusted by the bed-length parameter while other operating conditions are specified. In fact, it is easy to understand that the conversion increases at the steady state when the bed length is lengthened; in other words, the retention time of the substrates in the reactor is prolonged. Figure 7a,b compare the effect of Dr on ees and conversion for a first-order reaction and Michaelis-Menten kinetics. The conversion and ees for Michaelis-Menten kinetics are smaller than those for the firstorder reaction under the same Dr. The interesting result is that the ees for the first-order reaction is almost the same as that for the Michaelis-Menten kinetics under the same conversion as shown in Figure 7b. It demonstrates that the reaction type does not affect enantioselectivity at the steady state. It is critical to overcome the mass transfer limitation for immobilized enzyme in a fixed-bed reactor. Many researchers have paid much effort to develop some approaches to solve the problem. In the past few years, Sheldon et al.27,28 developed a novel way to immobilize enzyme without any solid support, cross-linked enzyme aggregates (CLEAs). The carrier-free immobilized enzyme exhibits highly concentrated activity, high stability, and low cost. Another important advantage is that this type of immobilized enzyme is able to overcome mass transfer limitation completely because no support is applied at all. Nevertheless, we have not found any report about a fixed-bed reactor equipped with the carrier-free enzyme until now, although it could be concluded that this approach is a promising way to overcome mass transfer limitation in a fixed-bed reactor theoretically.
Figure 7. Effect of Dr on ees and conversion for a first-order reaction and Michaelis-Menten kinetics.
4. Recent Development of Technologies To Improve Enzyme Enantioselectivity It could be a very hot topic and target for many researchers to improve enzyme enantioselectivity. Conventional methods include enzyme immobilization, medium engineering, and so forth. Nevertheless, these technologies cannot change the intrinsic nature of enzyme. With the recent development of genetic engineering, it becomes possible to improve enzyme characteristics by changing the gene sequence of wild-type enzyme, in terms of activity, stability, and enantioselectivity. If the gene sequence of the enzyme is known, site-directed mutagenesis technique is often applied to change the properties of it; if it is not known, directed evolution is an option.29 The critical part of directed evolution is to develop an efficient high through screening method to pick up positive mutants. Reetz30 developed a series of high through screening methods and successfully improved enantioselectivity of lipase. These positive results demonstrate that genetic engineering is a promising way to enhance enantioselectivity of enzyme. 5. Conclusions Kinetic resolution of racemates with high enantiomeric excess of product is pursued by researchers, especially at a large scale. The purpose of the theoretical discussion is to help researchers to understand those parameters that are able to impact enantioselectivity and design a reactor efficiently when they are going
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to conduct a kinetic resolution of racemate in a fixed-bed reactor. The theoretical analysis clearly indicated the effect of some parameters on effective enantioselectivity of enzyme, including adsorption equilibrium constant (adsorption effect), Biot number, Peclet number, and bed-length parameter. We demonstrated that adsorption of substrate on the solid support must impact the effective enantioselectivity of immobilized enzyme in a batch reactor. Herein, it is derived that the adsorption has no effect on the effective enantioselectivity in a fixed-bed reactor, except delaying the outlet; in addition, reaction rate is able to impact the effective enantioselectivity of enzyme through controlling the loading of enzyme on the solid support. Among these parameters, Bi (
