not converted at all. Then the enzymatic reaction will cease automatically at
50% conversion when there is nothing left of the more reactive enantiomer
(Scheme 2.6) [38].
In practice, however, the enantioselectivity is not ideal, and the difference in – or
more precisely the ratio of – the reaction rates of the enantiomers is not infinite, but
measurable. The thermodynamic reasons for this have been discussed in Chap. 1
(Fig. 1.8). What one observes in these cases is not a complete standstill of the
reaction at 50% conversion but a marked slowdown in reaction rate at around this
point. In these numerous cases one encounters some crucial dependencies:
• The velocity of the transformation of each substrate enantiomer varies with the
degree of conversion, since their ratio does not remain constant during the
reaction.
• Therefore, the optical purity of both substrate (e.e. S ) and product (e.e. P ) becomes
a function of the conversion.
A very useful treatment of the kinetics of enzymatic resolution, describing the
dependency of the conversion (c) and the enantiomeric excess of substrate (e.e. S )
and product (e.e. P ), was developed by C.J. Sih in 1982 [39] on a theoretical basis
described by K.B. Sharpless [40] and K. Fajans [41]. The parameter describing the
selectivity of a resolution was introduced as the dimensionless ‘Enantiomeric
Ratio’ (E), which remains constant throughout the reaction and is only determined
by the ‘environment’ of the system [42–45].
3 E corresponds to the ratio of the
relative second-order rate constants (v A , v B ) of the individual substrate enantiomers
(A, B) and is related to the k cat and K M values of enantiomers A and B according to
Michaelis–Menten kinetics as follows (for the thermodynamic background see
Fig. 1.8):
R
2
R 1
X
R 3
R 2
R
1
R
3
X
R 2
R 1
Y
R
3
R 2
R
1
R
3
X
slow
fast
Hydrolase
+
racemic substrate
+
separable enantiomers
*
*
symmetry plane
*
*
Scheme 2.6 Enantiomer differentiation
3 The Enantiomeric Ratio (E) is a synonym for the so-called selectivity factor (s). Whereas E is
used more often in biocatalyzed kinetic resolutions, the s-factor is more common in chemocatalysis. In a mathematical sense, both are identical and describe the ratio of the relative
(second-order) rate constants of enantiomers. For a comprehensive discussion see [45].
2.1 Hydrolytic Reactions
39
50% conversion when there is nothing left of the more reactive enantiomer
(Scheme 2.6) [38].
In practice, however, the enantioselectivity is not ideal, and the difference in – or
more precisely the ratio of – the reaction rates of the enantiomers is not infinite, but
measurable. The thermodynamic reasons for this have been discussed in Chap. 1
(Fig. 1.8). What one observes in these cases is not a complete standstill of the
reaction at 50% conversion but a marked slowdown in reaction rate at around this
point. In these numerous cases one encounters some crucial dependencies:
• The velocity of the transformation of each substrate enantiomer varies with the
degree of conversion, since their ratio does not remain constant during the
reaction.
• Therefore, the optical purity of both substrate (e.e. S ) and product (e.e. P ) becomes
a function of the conversion.
A very useful treatment of the kinetics of enzymatic resolution, describing the
dependency of the conversion (c) and the enantiomeric excess of substrate (e.e. S )
and product (e.e. P ), was developed by C.J. Sih in 1982 [39] on a theoretical basis
described by K.B. Sharpless [40] and K. Fajans [41]. The parameter describing the
selectivity of a resolution was introduced as the dimensionless ‘Enantiomeric
Ratio’ (E), which remains constant throughout the reaction and is only determined
by the ‘environment’ of the system [42–45].
3 E corresponds to the ratio of the
relative second-order rate constants (v A , v B ) of the individual substrate enantiomers
(A, B) and is related to the k cat and K M values of enantiomers A and B according to
Michaelis–Menten kinetics as follows (for the thermodynamic background see
Fig. 1.8):
R
2
R 1
X
R 3
R 2
R
1
R
3
X
R 2
R 1
Y
R
3
R 2
R
1
R
3
X
slow
fast
Hydrolase
+
racemic substrate
+
separable enantiomers
*
*
symmetry plane
*
*
Scheme 2.6 Enantiomer differentiation
3 The Enantiomeric Ratio (E) is a synonym for the so-called selectivity factor (s). Whereas E is
used more often in biocatalyzed kinetic resolutions, the s-factor is more common in chemocatalysis. In a mathematical sense, both are identical and describe the ratio of the relative
(second-order) rate constants of enantiomers. For a comprehensive discussion see [45].
2.1 Hydrolytic Reactions
39