Ind. Eng. Chem. Res. 2008, 47, 4251–4255
4251
Theoretical Analysis of the Adsorption Effect on Kinetic Resolution of Racemates Catalyzed by Immobilized Enzymes in a Batch Reactor Hongwei Yu*,† and Chi Bun Ching‡
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Institute of Bioengineering, College of Material and Chemical Engineering, Zhejiang UniVersity, Hangzhou, P. R. China 310027, and DiVision of Chemical and Biomolecular Engineering, Nanyang Technological UniVersity, Singapore 637722
Adsorption, a typical physical phenomenon, always neglected in the kinetic resolution of the racemate catalyzed by enzymes immobilized on the porous solid support, was theoretically analyzed. A concept that the adsorption effect plays an important role to affect the superficial performance of the enzyme which is often applied to evaluate the performance of the enzyme was described. Adsorption intensity, or so-called mass equilibrium constant (K), is the most important factor to affect the performance of the enzyme compared with adsorption rate coefficient (k) and adsorption equilibrium (adsorption isotherm) if the solid support with chiral selectivity is applied. The conclusion can be drawn that the solid support with a weak adsorption effect on the racemate may favorite the enzyme to exhibit a good performance in the kinetic resolution of the racemate. The adsorption phenomenon should be considered as an explanation to the performance changing of the enzyme after immobilized. 1. Introduction Enzymes have been widely applied in the synthesis of enantiopure intermediates and drugs due to their high activity and enantioselectivity in a mild condition. Kinetic resolution of a racemate is an important process and extensively investigated to produce pure isomers.1–3 Many resolution reactions are conducted in a simple batch reactor to investigate the reaction mechanism and the time course of conversion and enantiomeric excess of the racemate (ees) and, in addition, evaluate the performance of the enzyme in terms of activity and enantioselectivity. It is often necessary to conduct these enzymatic reactions in organic solvents in favor of improving substrate solubility and shifting the chemical equilibrium.4–6 However, the practical applications of enzymes in organic solvents have been hampered by low catalytic activity and thermal stability. To circumvent these shortcomings which appeared in enzymatic reactions and recycle the expensive enzymes for reuse, many enzymes are immobilized on porous solid supports by adsorption or covalent attachment. The effects of mass transfer resistances could significantly result in a lower enantioselectivity, which have been reported in the literature.7,8 Xiu and Jiang reported an exact solution to predict the purity and yield of the desired product for a first-order reaction coupled with the intraparticle and external mass transfers.9,10 Nevertheless, enzymatic reactions normally proceed at a low reaction rate, in which the effects of the mass transfer limitation are not significant. This means that the mass transfer limitation does not need to be taken into consideration in most enzymatic reactions. It is crucial to predict and control the purity and yield of the desired product and the optimal time to terminate the resolution process. Therefore, understanding the factors to influence the performance of the enzyme during the course of the kinetic resolution process is an essential step. Due to applications of many porous solid supports, the racemate for kinetic resolution could be adsorbed on them. Although the adsorption phenom* To whom correspondence should be addressed. E-mail: yuhongwei@ zju.edu.cn. † Zhejiang University. ‡ Nanyang Technological University.
enon is inevitable, little investigation is given when the porous solid supports are employed. The question is does the adsorption behavior of the racemate on the solid support affect the performance of the enzyme in terms of activity and enantioselectivity like the mass transfer limitation in a fast reaction? In the paper, we will investigate the adsorption effects on the performance of the enzyme to answer the above question and discuss the factors which influence the adsorption effect in the kinetic resolution of the racemate including reaction rate, adsorption intensity, adsorption rate, and adsorption equilibrium. A concept will be introduced about the adsorption effects on the kinetic resolution which will benefit the effective selection of the solid supports for enzyme immobilization. 2. Mathematical Formulation The assumptions employed in this work for the heterogeneous kinetic resolution process in a batch mixed reactor are isothermal, constant effective diffusivity of substrates inside the porous support, spherical particle shape, and homogeneously distributed enzyme activity on the surface of the solid support without considering the thickness of the enzyme film. For the reaction/ mass-transfer-controlling process, the material balance equation of an individual enantiomer i (i ) 1 and 2) in the porous support matrix is derived from Ruthven’s work11 and given by εp
( )
∂ci ∂qi 1 ∂ 2 ∂ci ) De 2 - Vi r - (1 - εp) ∂t ∂r ∂t r ∂r
(1)
For a linear driving force ∂qi ) ki ′ (q/i - qi) ∂t
(2)
Where, Vi is the special reaction rate of enantiomers. Suppose that the fast and slow reacting enantiomers compete for the same site on the enzyme, the intrinsic reacting is virtually irreversible, and there is no product inhibition. For a first order reaction VR ) (Vm1/Km1)c1
(3a)
VS ) (Vm2/Km2)c2
(3b)
10.1021/ie071300t CCC: $40.75 2008 American Chemical Society Published on Web 05/15/2008
4252 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008
Dimensionless contact time Der
τ)
R2εp
Dimensionless mass transfer coefficient R2εpki ′ ki ) De Biot number Bi )
kfR De
Thiele modulus for 1 and 2 enantiomers
φi ) R Phase ratio Figure 1. Effect of adsorption intensity on the time courses of conversion and enantiomeric excess (ees) of the racemate at φ1 ) 0.1, φ2 ) 0.4, kR ) kS ) 0.005, Bi ) 10, N ) 0.01, and F ) 1.22.
The enantioselectivity, E, of the enzyme is defined as the ratio of the specificity constants (Vm/Km) of the enzyme for the R and S enantiomers. E≡
V1max/K1m V2max/K2m
≡
k1cat/K1m
(4)
k2cat/K2m
By definition, E is an intrinsic property of the enzyme. The intrinsic E value cannot change unless the intrinsic values of Km or kcat change.12 In the dilute region, a linear isotherm was used: q/i ) Kici
(5)
( )
( ) ∂ci ∂r
r)0
)0
(7)
The mass balance equation for the substrates in the bulk phase is V
dCi 3W + k [C - (ci)r)R] ) 0 dt FpR f i ci ) 0,
Ci ) Ci0,
qi ) 0
(9)
Equations 1 and 2 and eqs 5–9 can be nondimensionalized as follows: Dimensionless concentrations Xi )
ci ; Ci0
Yi )
Ci ; Ci0
Dimensionless radial distance ξ)
r R
( )
∂Xi 1 ∂ 2 ∂Xi ∂Qi ) 2 - φi2Xi ξ -F ∂τ ξ ∂ξ ∂ξ ∂τ ∂Qi ) ki(Q/i - Qi) ∂τ The boundary conditions are as follows:
Qi )
qi Ci0
ξ)1
) Bi[Yi - (Xi)ξ)1]
( ) ∂Xi ∂τ
ξ)0
)0
Yi ) 1,
Qi ) 0,
(11)
(12) (13)
dYi + 3NBi[Yi - (Xi)ξ)1] ) 0 dτ Xi ) 0,
(10)
τ)0
(14) (15)
The calculation will be conducted by FEMLAB 3.1. 3. Results and Discussion
(8)
The initial conditions for eqs 1 and 2 and eqs 6–9 are t ) 0,
Wεp VFp
Written in dimensionless form, eqs 1 and 2 and eqs 6–9 become
(6)
Herein, we assume no temporal change in concentration in the core to simplify the simulation.
1 - εp εp
N)
∂Xi ∂ξ
) kf[Ci - (ci)r)R]
r)R
KmiDe
Ratio of the pore volume of support to that of the reactor
( )
The boundary conditions of eq 1 are ∂ci De ∂r
F)
Vmi
Most of the solid supports employed to immobilize enzymes are porous medium like macro porous resin,13 silica gel,14 porous cellulose bead,15 ceramics,16 etc. Some of these materials are applied widely in chromatographic technology to achieve enantioseparation. Due to the physical property of the porous solid supports, adsorption phenomenon appears between them and the substrates. In the subsequent discussions, the adsorption effect on the kinetic resolution of the racemate in terms of activity and enantiomeric excess of the racemate (ees) will be investigated. 3.1. Adsorption Intensity (Mass Equilibrium Constant, K1 ) K2). The porous solid support exhibits different adsorption intensity to the different substrate. The adsorption intensity may impact on the time courses of conversion and ees of the racemate in the bulk phase as shown in Figure 1, where conversion (Cs)
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4253 Table 1. Superficial Enzyme Performance at the Different Adsorption Intensities and Reaction Ratesa φR ) 0.05 φS ) 0.2
φR ) 0.1 φS ) 0.4
φR ) 0.4 φS ) 1.6
KR ) KS ) 0 KR ) KS ) 10 KR ) KS ) 30 KR ) KS ) 0 KR ) KS ) 10 KR ) KS ) 30 KR ) KS ) 0 KR ) KS ) 10 KR ) KS ) 30 time (τ) ees SRAb Eeff a
315 52.7% 1 14.4
2460 39.4% 1.28 5.66
127 18.2% 2.48 2.07
800 52.5% 1 13.9
610 39.9% 1.20 5.83
340 21.9% 2.21 2.42
60 51.2% 1 12.6
55 47.1% 1.09 12.4
50 42.8% 1.20 6.92
Bi ) 10, N ) 0.01, F ) 1.22, and Cs ) 40%.b Superficial relative activity.
is calculated as Cs ) 1 - (X1 + X2)/2 and enantiomeric excess (ees) is calculated as ees ) (X1 - X2)/(X1 + X2). In fact, the conversion and enantiomeric excess determined by the concentration of two enantiomers in the bulk phase are not true values in the whole reaction system. Therefore, we can name them as superficial conversion and superficial enantiomeric excess when adsorption effect is considered. Nevertheless, it is they that can often be determined by experiments and employed to evaluate the performance of the enzyme in the kinetic resolution of the racemate. The adsorption intensity for two isomers should be the same since the physical characteristics of the pair of isomers are not different. The superficial conversion rate for the reaction with involving strong adsorption (K1 ) K2 ) 30) is apparently more than that without involving adsorption (K1) K2 ) 0). A general trend appears that the superficial conversion rate increases with the increasing of the adsorption intensity between the solid support and the racemate. It is easy to understand that adsorbing a certain amount of substrates on the solid support surface causes the concentration of substrates in the bulk solvent to decrease; hence, the conversion rate appears to be increasing. The enantiomeric excess appears a reversed trend of conversion rate. The concentration of the slow reactant, enantiomer 1, in the bulk solvent is higher than that of the fast one, enantiomer 2. More of the former is adsorbed on the solid support based on the adsorption equilibrium to decrease its concentration in the bulk solvent; hence, the enantiomeric excess in the bulk solvent decreases. Due to the involved mass transfer limitation and adsorption effect, the enantioselectivity calculated as E ) (ln [(1 - C)(1 - ees)])/(ln [(1 - C)(1 + ees)]) is the effective enantioselectivity (Eeff). The enantiomeric excess, activity, and effective enantioselectivity at the conversion of 40% under a certain condition in the reaction with and without adsorption effect are listed in Table 1, where the activity of the enzyme without involving adsorption effect is normalized to be 1. The ees of the racemate (52.5%) and the Eeff of the immobilized enzyme (13.9) in the bulk solvent without involving the adsorption effect (K1 ) K2 ) 0) are 1.5 times and 5.54 times more than those (21.9%, 2.42) with adsorption effect (K1 ) K2 ) 30), respectively, and the superficial relative activity (2.21) of the enzyme with the adsorption effect is 2.21 times of that (1) of the enzyme without the adsorption effect. These interesting results confirm that the adsorption behavior between the porous solid support and the racemate do influence the performance of the enzyme in the kinetic resolution of the racemate and induce a new explanation for an enhanced activity of the enzyme after immobilized, beside decreasing mass transfer limitation and stabilizing the conformation of the enzyme after immobilized. A concept can be concluded that the materials with strong adsorption effect on substrates are able to make enzyme lose effective enantioselectivity, which makes us think seriously what kind of materials is suitable to immobilize enzyme. 3.2. Reaction Rate (O1 and O2). Most of enzymatic reactions proceed at a low reaction rate. In a faster reaction, the mass
transfer through external and internal films plays a main role for the performance of the enzyme in terms of activity and effective enantioselectivity; in a slower reaction, the mass transfer limitation is trivial and the adsorption effect on the performance of the enzyme appears if the enzyme is immobilized on the solid support with a strong adsorption intensity to the substrate. The results listed in Table 1 clearly show that adsorption behavior exhibits a significant effect on the time courses of ees and conversion of the racemate under a lower reaction rate (φ1 ) 0.05 φ2 ) 0.2). On the contrary, the difference of ees and conversion of the racemate between with and without involving adsorption effect under a higher reaction rate (φ1 ) 0.4, φ2 ) 1.6) is small. Table 1 gives the comparison between slower and faster reaction at the conversion of 40%. In the slower reaction (φ1 ) 0.05, φ2 ) 0.2), Eeff (2.07) and the superficial relative activity of the enzyme (2.48) involving strong adsorption are 14.4% and 2.48 times of those (14.4 and 1) without involving strong adsorption intensity (K1 ) K2 )30), respectively; however, in the faster reaction (φ1 ) 0.4, φ2 ) 1.6), the Eeff and the superficial relative activity of the enzyme with involving weak adsorption (K1 )K2 ) 10) are almost the same as those without involving adsorption, and only the Eeff (6.92) and superficial relative activity (1.2) with strong adsorption intensity (K1 ) K2 ) 30) are changed to be 54.9% and 1.2 times of those (12.6 and 1) without involving adsorption effect respectively. It is reasonable to project that the adsorption effect will be diminished with the increasing of the reaction rate. It can be concluded that the adsorption effect on the performance of the enzyme in kinetic resolution is significant and cannot be ignored as most of enzymatic reactions are of low reaction rate. 3.3. Adsorption Rate Coefficient (k1 ) k2). The adsorption rate coefficient represents the adsorption rate between the solid support and the racemtate. When the adsorption rate coefficient is large, in other words, the substrate is absorbed on the solid support very fast, the adsorption behavior is dominated by the adsorption intensity, K. This means that the adsorption rate cannot affect the superficial enzyme performance significantly. When the adsorption rate coefficient is small, in other words, the substrate is adsorbed on the solid support very slow, at the moment, the adsorption effect is not so significant that the enzyme performance is close to that without involving adsorption effect. Generally, adsorption rate does not exhibit a significant impact on the enzyme performance like adsorption intensity (K). At a conversion of 40% under different adsorption rates, apparently, when k is above 0.005 which refers to a fast adsorption, adsorption cannot show effect on the performance of the enzyme; when k is below 0.005 which refers to a slow reaction, the enantiomeric excess of the racemate and the effective enantioselectivity of the enzyme increases with the decreasing k until they approach those without involving adsorption effect. The relative reaction rate exhibits a contrary trend. Nevertheless, the effect of k on it is not significant. 3.4. Adsorption EquilibriumsAn Assumption. Almost all solid supports used to immobilize enzymes have no enantiose-
4254 Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 Table 2. Superficial Enzyme Performance while the Two Enantiomers Exhibit Different Adsorption Intensities on an Assumed Chiral Solid Support (k1 ) k2 ) 0.005, Bi ) 10, N ) 0.01, F ) 1.22, and Cs ) 40%) KR KS
KR ) 30 KS ) 30
KR ) 30 KS ) 10
KR ) 20 KS ) 10
KR ) 10 KS ) 20
KR ) 10 KS ) 30
KR ) 10 KS ) 10
time (τ) ees SRAa Eeff
340 21.9% 2.21 2.42
420 19.9% 1.90 2.22
490 28.4% 1.63 3.24
610 40.6% 1.36 5.83
590 40.7% 1.20 6.07
550 39.9% 1.45 6.08
a
Superficial relative activity.
lectivity to the racemate targeted to be separated in the kinetic resolution reaction. Assuming that the enzyme is immobilized on a chiral solid support, or CSS, the two enantiomers exhibit different adsorption behavior on the chiral solid support; therefore, the adsorption equilibrium constant (K) and adsorption rate coefficient (k) of the two isomers are different, respectively. What we want to investigate is whether the enantioselectivity of the solid support is able to improve the kinetic resolution of the racemtate in the enzymatic reaction. To simplify the problem, the mass equilibrium constant effect is discussed in the case that the adsorption rate coefficient of the two isomers are assumed to be the same, k1 ) k2 ) 0.005. The superficial enzyme performance in terms of enantiomeric excess and conversion when enantiomer 2, the fast reactant, exhibits stronger adsorption behavior is worse than that when the two enantiomers share the same adsorption intensity. In other words, the chiral solid support cannot provide a positive impact on the resolution of the racemtate in that case. The superficial enzyme performance when enantiomer 2 exhibits weaker adsorption behavior is better than that when two enaniomers share the same adsorption intensity, especially significantly better than that when two enantiomers share the same stronger adsorption behavior on the solid support. In Table 2, the superficial enzyme performance in a different case is compared. The enantioselectivity (6.07) when K1 ) 10, K2 ) 30 is 2.5 times of that (2.42) when K1 ) K2 ) 30. It seems that a chiral solid support could improve the enzyme performance. It must be noted that the enantioselectivity when K1 ) 10, K2 ) 30is almost the same as that when K1 ) K2 ) 10. This means that a weak adsorbent as a solid support is very important for enzyme to exhibit performance in kinetic resolution of the racemate. The adsorption rate coefficient effect is discussed when K1 ) 10, K2 ) 30 because the enzyme is able to exhibit a better performance than in the case discussed above. When the adsorption rate of enantiomer 2, the fast reactant, is higher than that of enantiomer 1, the slow reactant, the superficial enzyme performance is enhanced compared with the case that two enantiomers share the same adsorption rate coefficient. The fast adsorption mass transfer facilitates the fast reactant to convert to the product so that the difference of the reaction rate of the two reactants is enlarged. Therefore, the effective enantioselectivity is improved. When adsorption rate of enantiomer 2 is lower than that of enantiomer 1, the slower adsorption mass transfer offsets the fast reaction rate of enantiomer 2. Therefore, the enzyme performance is worse than that in the case that two enantiomers share the same adsorption rate coefficient. The superficial enzyme performance under different adsorption rate coefficient is compared at the conversion of 40% in Table 3. The effective enantioselectivity (19.3) and relative reaction rate (6.43) of the enzyme when k1 ) 0.005, k2 ) 0.05 are 3.2 and 5.4 times of those (6.07 and 1.2) when k1 ) 0.005, k2 ) 0.005, respectively. It should be mentioned that the conversion and enantiomeric excess in the bulk phase when k1 ) 0.005, k2 ) 0.05 increase up to a high value within a relative short time. It is very helpful to determine the time to terminate the reaction and save reaction time.
Table 3. Superficial Enzyme Performance while the Two Enantiomers Exhibit Different Adsorption Rates on an Assumed Chiral Solid Support (K1 ) 10, K2 ) 30, Bi ) 10, N ) 0.01, F ) 1.22, and Cs ) 40%) kR kS
kR ) 0.005 kS ) 0.05
kR ) 0.005 kS ) 0.005
kR ) 0.05 kS ) 0.005
Time (τ) ees SRAa Eeff
110 55.6% 6.43 19.3
590 40.7% 1.20 6.07
640 39.2% 1.11 5.60
a
Superficial relative activity.
Table 4. Experimental Results on Adsoprtion Effect app app kcat /Km
o-diphenol DL-dopa L-dopa D-dopa
E
enzyme immobilized on chiral support
enzyme immobilized on nonchiral support
free enzyme
674.73 ( 25 844.86 ( 70 411.57 ( 41 2.06
926 ( 66 1076 ( 98 610 ( 68 1.76
76.43 134.25 23.86 5.62
Generally, the selection of a chiral solid support for immobilizing enzyme applied in kinetic resolution of the racemate is complex as the integrated effect of adsorption equilibrium constant and adsorption rate coefficient does not take a significant effect on the kinetic resolution of the racemate in any case. Therefore, it is important to identify the various situations in order to reach a positive effect. 4. Experimental Validation of the Theoretical Analysis Garcia-Ruiz et al.17 described the stereospecificity of mushroom tyrosinase immobilized on a chiral and nonchiral support by adsorption. Some interesting results demonstrated the above theoretical analysis of the adsorption effect on the enantioselectivity of racemates in the kinetic resolution catalyzed by immobilized enzyme. The experimental results listed in Table 4 clearly indicated that the enantioselectivity of immobilized enzyme (1.76) is lower than that of the free enzyme (5.62), and the reaction rate of the immobilized enzyme is higher than that app of free enzyme derived from kapp cat /Km . A suitable chiral solid support to immobilize enzyme was developed and superficial enantioselevitity of enzyme immobilized on the chiral solid support (2.06) is higher than that of enzyme immobilized on nonchiral solid support. Nevertheless, the improvement is not that significant. We really appreciate the favorable results to validate our theoretical analysis. With the reference of theoretical analysis and experimental results, the concept is introduced that adsorption effect must be considered, and K, the mass equilibrium constant, should be measured as a critical parameter before trying to immobilize the enzyme to conduct kinetic resolution of racemates. 5. Conclusions Enantioselectivity is an intrinsic property of the enzyme which is not changed unless reaction temperature or the conformation
Ind. Eng. Chem. Res., Vol. 47, No. 12, 2008 4255
of the enzyme is changed. The adsorption effect, a typical physical phenomenon, always neglected, plays an important role to affect the superficial performance of the enzyme applied to evaluate the performance of the enzyme. In a fast reaction, external and internal mass transfer limitations have a significant effect on the performance of the enzyme and the adsorption effect does not appear; in a slow reaction, which most enzymatic reactions are, the adsorption behavior of the racemate on the solid support exhibits a significant effect on the performance of the enzyme in terms of superficial enantioselectivity and activity. Adsorption intensity, or so-called mass equilibrium constant K, is the most important fact to affect the performance of the enzyme compared with adsorption mass transfer coefficient k and adsorption equilibrium (adsorption isotherm) if a solid support with chiral selectivity is applied. The conclusion can be drawn that the solid support with a weak adsorption effect on the substrate may favor the enzyme to exhibit a good performance in the kinetic resolution of the racemate. Generally, the adsorption phenomenon cannot be ignored when a new solid support is considered to immobilize enzymes, and we have to revisit the issue of the change in performance of the enzyme after it is immobilized, which is possibly caused by adsorption behavior of the racemate on the solid support. Nomenclature Bi ) Biot number C ) substrate concentration in bulk phase (kg/m3) Cs ) Conversion c ) substrate concentration in liquid phase within the macropores (kg/m3) De ) effective diffusivity (m2/s) q ) substrate concentration in solid support (kg/m3) ees ) enantiomeric excess of the remaining substrate E ) enantioselectivity of the enzyme Eeff ) effective enantioselectivity of the enzyme F ) phase ratio K ) mass equilibrium constant kf ) external liquid-solid mass transfer coefficient (m/s) ki ) dimensionless adsorption rate coefficient ki′ ) adsorption rate coefficient (1/s) r ) radial coordinate inside support matrix (m) R ) particle radium (m) Ra ) superficial relative activity t ) time (s) N ) ratio of the pore volume of support to that of the reactor V ) volume of the liquid phase in the batch reactor (m3) X ) dimensionless substrate concentration in liquid phase within the macropores Y ) dimensionless substrate concentration in bulk phase Greek Letters εp ) support porosity ξ ) dimensionless radial distance τ ) dimensionless contact time φi ) Thiele modulus for 1 and 2 enantiomers
Subscripts i ) 1 and 2 0 ) initial
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ReceiVed for reView September 27, 2007 ReVised manuscript receiVed March 5, 2008 Accepted March 5, 2008 IE071300T
