Enzyme Technology
Equilibria in biphasic aqueous-organic systems
Much of the theory outlining the effect of biphasic systems on
the apparent equilibria was outlined by Karel Martinek and his co-workers at
Lomonosov Moscow State University. Consider the simple reaction scheme,
involving the equilibrium between reactant (A) and product (B) with Kw
representing the equilibrium constant (Keq) in water:
[7.1]
If this
reaction is carried out in a biphasic system consisting of a mixture of an
aqueous and an organic solvent, both A and B will be partitioned between the two
solvents (with partition coefficients, PA and PB) and a
separate equilibrium (Korg) will be established between A and B in the
organic phase.
[7.2]
where:
(7.2)
(7.3)
(7.4)
(7.5)
Because of the cyclic nature of
these equilibria only three of these parameters are independent 'variables' (i.e., Korg depends on Kw,
PA and PB). It
should be noticed from the following discussion that Korg plays no
further part, although similar derivations could be made involving
Korg, PA and PB rather than Kw, PA and
PB. The apparent equilibrium constant
(Kbiphasic) of this system may be defined as
(7.6)
where the
subscripts t, org and w refer to the total
solution, the organic and water phases respectively. If V represents the
volumes involved, it follows that
(7.7)
(7.8)
(7.9)
Substituting from equations 7.7 and 7.8 into
equation 7.6,
(7.10)
(7.11)
Substituting
the partition coefficients from equations 7.3 and 7.4 gives the simplified
relationship,
(7.12)
i.e., a is the
ratio of the volumes of the organic and water phases.
(7.13)
The apparent equilibrium
constant (Kbiphasic) varies with the relative volumes of the aqueous
and organic phases; increasing when the substrate is partitioned more
efficiently out of the organic phase and into the aqueous phase relative to the
behaviour of the product (i.e., PA < PB), and decreasing
when the reverse occurs (Figure 7.3A). If there are sufficient differences in
the partition coefficients and both substrate and product are relatively
non-polar then substantial shifts in the equilibria occur even at high relative
water contents. A substantial increase in the apparent equilibrium constant may
be achieved, when both the substrate and product have partition coefficients
less than unity, when the ratio of the partition coefficients is suitable (Figure
7.3B). Clearly if a is very small Kbiphasic tends to
Kw, the equilibrium constant in aqueous solution. However, if
a is sufficiently large, equation 7.12 simplifies
to
(7.14)
Therefore,
substituting from equations 7.2 - 7.5,
(7.15)
Therefore
Kbiphasic tends to Korg, the equilibrium constant of the
reaction in the pure organic liquid.
Figure
7.3. The variation in the apparent equilibrium constants of a
one-substrate one-product reaction (A
B) with the relative
component composition of a biphasic aqueous-organic system. (A) shows the effect
of the ratio of the partition coefficients, PB/PA. The
curves have been generated using equation 7.12 and the following values for the
partition coefficients, from the top downwards; PA = 0.2, PB
= 20; PA = 0.2, PB = 2; PA = 0.2, PB =
0.6; PA = 0.6, PB = 0.2; PA = 2, PB =
0.2; PA = 20, PB = 0.2. (B) shows the effect of the polarity
of A and B, keeping the ratio of the partition coefficients constant (PB/PA = 100). The following values for the partition
coefficients have been used, from the top downwards; PB = 100, PB = 10,
PB = 1, PB = 0.1, PB = 0.01, PB = 0.001,
PB = 0.0001.
Many reactions
are bimolecular, and these are influenced in a more complex way by the biphasic
system. The processes may be represented in a manner similar to that used for
monomolecular reactions;
[7.3]
Using
similar reasoning to that outlined above, the following expression may be
obtained for the apparent equilibrium constantes
(7.16)
As in the case of monomolecular reactions, when
the relative water content is very low (i.e., a is high) the apparent
equilibrium constant tends to Korg. However, the equation (7.16) is
quadratic in terms of a and at intermediate values may produce a maximum
or minimum value for the apparent equilibrium constant that is several decades
different from either Kw or Korg (i.e., the apparent
equilibrium constant may be greater than the equilibrium constant of the same
reaction in either of the pure phases, see Figure 7.4). Under some circumstances
this may enable the reaction productivity in the biphasic system to be much
greater than that attainable in either pure phase.
Figure 7.4. The
variation in the apparent equilibrium constants of a two-substrate two-product
reaction (A + B
C + D) with the relative component composition of
a biphasic aqueous-organic system. In all cases the partition coefficients are PA = 1,
PB = 1 and PC = 100. The following values
for the partition coefficient (PD) have been used, from the top
downwards; 1, 0.1, 0.01, 0.001 and 0.0001.
A
special and relevant case of the bimolecular reaction scheme is where one of the
reactants is water (e.g., use of the hydrolases). These reactions may be written
in a way corresponding to reaction scheme
[7.3].
[7.4]
The normal direction for the
reaction in aqueous solution is the hydrolytic process from right to left.
However, the apparent equilibrium constant may be shifted in biphasic solutions,
as outlined above, and allow the hydrolase to act in a synthetic (i.e., left to
right in reaction scheme [7.4]), rather than hydrolytic, manner.
Such reactions significantly extend the processes available to the enzyme
technologist, as synthetic reactions are generally much more difficult to
achieve by classical organic chemistry than hydrolytic reactions, particularly
when a regiospecificity is required as, then, there is a choice of reactive
groups in the substrates. Two factors affect the yield of the product (C) in
such reactions: (1) the shift in apparent equilibrium constant
(Kbiphasic); and (2) the concentration of water ([(H2O)t]), as one of the participating reactants.
[(H2O)t] may be obtained from the material balance,
(7.17)
where [(H2O)w] is the molar concentration of pure water (= 1000/18
= 55.5 M). Substituting Pw for [(H2O)org]/[(H2O)w],
(7.18)
(7.19)
Substituting for
Kbiphasic from equation 7.16 (with PD set to equal
Pw) and rearranging, the terms in (1 + aPw) cancel
to give
(7.20)
This represents a
fairly complex relationship but a few generalisations may be made. If the
product (C) is less polar than either reactant (A or B) then the yield generally
increases with the relative concentration of the organic phase (a) to
reach a plateau. If the reverse occurs, then there will be a plateau at low
yield and high a in the a-yield diagram. Both minima and maxima
may occur, dependent on the parameters. Figure 7.5 shows the variation of the
apparent equilibrium constant and the yield for the enzymic synthesis of an
ester from its acid and alcohol in a biphasic system. From this it can be seen
that the use of a biphasic system can increase the yield of such reactions from
zero to nearly 100%. In order to achieve high conversions, the water produced
must be removed from the two-phase system. If it is not removed, there is a
continual drop in a which reduces the extent of the favourable
equilibrium. There are no simple ways in which this water may be removed but
reactors which allow the constant addition of fresh catalyst and organic phase
reduce the size of the problem.
Figure 7.5. The
variation in the apparent equilibrium constant and percentage yield of a reverse
hydrolytic reaction (A + B
C + H2O) with the relative
component composition of a biphasic aqueous-organic system. The reaction
portrayed is the synthesis of N-benzoyl-L-phenylalanine ethyl ester, from N-benzoyl-L-phenylalanine
and ethyl alcohol, catalysed by a-chymotrypsin in a biphasic
chloroform-water system (pH 7). ———
apparent equilibrium constant;
------- % yield (semi-logarithmic plot). The curves were calculated assuming
Kw = 0.002, PA = 0.11 (N-benzoyl-L-phenylalanine at pH 7),
PB = 0.01 (ethyl alcohol), PC = 4100 (N-benzoyl-L-phenylalanine
ethyl ester), and an equimolar mixture of reactants.
Use of biphasic
solvent systems also affect the ionisation of acid and basic groups. Consider
the ionisation of an acid HA, where only the unionised form is soluble in the
organic phase and the ionic species are only soluble in the aqueous phase,
[7.5]
(7.21)
(7.22)
The hydrogen ion
concentration, as determined, is characteristic of the aqueous phase,
(7.23)
A consideration of
material mass balances for A− and HA gives
(7.24)
(7.25)
Substituting for pH from equation
7.22 into equation 7.23 gives
(7.26)
Substituting
from equations 7.24 and 7.25 this simplifies to
give
(7.27)
Similarly, for the protonation of a base
[7.6]
(7.28)
A qualitative assessment of reaction
schemes [7.5] and [7.6] shows that increasing
the partition coefficient for the uncharged acid or base will pull the reaction
away from the formation of the ionised species. It follows from equations 7.27
and 7.28 that the apparent pKas of acids increase in biphasic systems
whereas those of bases decrease. These changes may well be several pH units,
dependent on the partition coefficients and the relative fraction of organic
solvent present. The shifts in pKa are in addition to any increase in
the pKa due to the lower dielectric constant of the aqueous phase, as
outlined in Chapter 1. This is likely to be particularly relevant under almost
anhydrous conditions (i.e., where a is high) which tend to 'freeze' the
hydrogen ions lowering their activity. The utility of the shift in the pKa can be shown using ester synthesis catalysed by
a-chymotrypsin as an
example.
[7.7]
where RCOOH and RCOO−
represent the un-ionised and ionised forms of N-benzoyl-L-phenylalanine, RCOOR'
represents N-benzoyl-L-phenylalanine ethyl ester and R'OH represents ethyl
alcohol.Although the non-ionic reaction in aqueous solution is evenly balanced
(Knonionic,w = 7), the overall reaction proceeds towards the left, in
water at neutral pH, due to the pull exerted by the acid's ionisation
(pKa = 3.4). In biphasic chloroform-water solution (a = 20,
PHA = 100), the Ka shifts by three decades to give a pKa close to 7. This, together with a shift in the equilibrium
constant due to the partition effects, outlined earlier, produces an overall
shift in the equilibrium constant of about five decades at the optimal pH (7.5) of
the enzyme (Figure 7.6). Use of the biphasic system allows reactions to be
performed at a pH that is both thermodynamically favourable to the reaction
direction required and at the optimum for the enzyme's catalytic efficiency.
Figure 7.6.
pH dependence of the apparent equilibrium constant for the synthesis of N-benzoyl-L-phenylalanine
ethyl ester, as given by the reaction scheme [7.7]. ———
reaction in aqueous solution only
(i.e., a = 0); ----------
reaction in a biphasic chloroform-water system (a = 20). The shift
upwards is due to the more significant partition of the ester into the organic
phase relative to the reactants, whereas the shift in the pH dependence to
higher pH is due to the change in the apparent pKa of the acid.
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This page was established in 2004 and last updated by Martin
Chaplin on
6 August, 2014
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