Enzyme substrate solvent interactions
A case study on serine hydrolases
Linda Fransson
Doctoral thesis
Royal Institute of Technology
School of Biotechnology
Stockholm 2008
© Linda Fransson 2008
In tihs pdf file, I have corrected
typos and layout errors present in
the printed version.
Royal Institute of Technology
School of Biotechnology
AlbaNova University Center
SE-106 91 Stockholm
Sweden
ISBN 978-91-7415-094
TRITA-BIO-Report 2008:15
ISSN 1654-2312
Printed in Stockholm, August 2008
E-PRINTAB, Lästmakargatan 24
111 44 Stockholm
ABSTRACT
Reaction rates and selectivities were measured for transacylation of fatty acid
esters in solvents catalysed by Candida antarctica lipase B and by cutinase from
Humicola insolens. With these enzymes classical water-based enzymology can be
expanded to many different solvents allowing large variations in interaction
energies between the enzymes, the substrates and the surrounding. Further,
hydrolysis reactions catalysed by Bacillus subtilis esterase 2 were investigated.
Thermodynamics analyses revealed that the enzyme contribution to
reaction rate acceleration compared to acid catalysis was purely entropic. On the
other hand, studies of differences in activation entropy and enthalpy between
enantiomers and between homologous esters showed that high substrate specificity was favoured by enthalpic stabilisation.
Solvent was found to have a profound effect on enzyme catalysis,
affecting both reaction rate and selectivity. Differences in substrate solubility will
impact enzyme specificity since substrate binding is an equilibrium between
enzyme-bound substrate and substrate in free solution. In addition, solvent
molecules were found to act as enzyme inhibitors, showing both competitive
and non-competitive behaviour.
In several homologous data series enthalpy-entropy compensation
relationships were encountered. A possible extrathermodynamic relationship
between enthalpy and entropy can easily be lost under co-varying errors
propagated from the experiments. From the data in this thesis, one instance was
found of a real enthalpy-entropy compensation that could be distinguished from
statistical errors, while other examples could not be verified.
SAMMANFATTNING
Reaktionshastighet och specificitet har uppmätts för transacylering av fettsyraestrar i lösningsmedel där lipas B från Candida antarctica och cutinas från Humicola
insolens har använts som katalysatorer. För dessa enzymer kan den traditionella
vattebaserade enzymologin utökas till att även omfatta studier i lösningsmedel,
vilket ger möjlighet att erhålla stor variation i interaktionsenergier mellan enzym,
substrat och omgivning. Vidare studerades även hydrolytiska reaktioner
katalyserade av Bacillus subtilis.
Termodynamisk analys av experimentaldata visade att enzymers bidrag till
acceleration av reaktionshastighet jämfört med motsvarande syrakatalyserade
reaktion hade ett entropiskt ursprung. Samtidigt visade studier av skillnader i
aktiveringsentropi och -entalpi mellan enantiomerer och homologa estrar att
hög substratspecificitet gynnades av entalpisk stabilisering.
Lösningsmedel hade en tydlig påverkan på såväl enzymaktivitet som
-specificitet. Skillnader i löslighet substrat emellan påverkar specificiteten då
substratbindning är en jämvikt mellan enzymbundet substrat och substrat i fri
lösning. Dessutom visade sig lösningsmedel kunna inhibera enzymer både
kompetitivt och icke-kompetitivt.
Flera homologa dataserier uppvisade en mycket god entalpi-entropikompensation. Ett eventuellt fysikaliskt innehåll dränks dock lätt av samvarierande fel. Av de kompensatoriska relationer som identifierats i den här
avhandlingen visade det sig i ett fall vara möjligt att säkerställa en relation som
inte var dominerad av statistiska fel. I övriga fall kunde ingen sådan slutsats dras.
LIST OF ARTICLES
This thesis is based on the following articles which are referred to by their
roman numerals.
I
Ottosson J, Fransson L, Hult K:
Substrate entropy in enzyme enantioselectivity: An experimental and
molecular modeling study of a lipase.
Protein Sci 2002, 11(6): 1462-1471.
II
Ottosson J, Fransson L, King JW, Hult K:
Size as a parameter for solvent effects on Candida antarctica lipase B
enantioselectivity.
Biochim Biophys Acta, Protein Struct Molec Enzym 2002, 1594(2): 325-334.
III
Graber M, Irague R, Rosenfeld E, Lamare S, Fransson L, Hult K:
Solvent as a competitive inhibitor for Candida antarctica lipase B.
Biochim Biophys Acta, Proteins Proteomics 2007, 1774(8): 1052-1057.
IV
Leonard V, Fransson L, Lamare S, Hult K, Graber M:
A water molecule in the stereospecificity pocket of Candida antarctica
lipase B enhances enantioselectivity towards pentan-2-ol.
ChemBioChem 2007, 8(6): 662-667.
V
Kourist R, Bartsch S, Fransson L, Hult K, Bornscheuer UT:
Understanding promiscuous amidase activity of an esterase from
Bacillus subtilis.
ChemBioChem 2008, 9(1): 67-69.
VI
Fransson L, Bernhardt P, Hult K:
On the benefit of an active site.
Manuscript.
TABLE OF CONTENTS
Enzyme substrate solvent interactions ........................................................................................................ 1 The origin of enzyme catalytic power........................................................................................................... 2 Proximity effects ...................................................................................................................................................... 2 The role of steric hindrance in enzyme specificity ............................................................................ 9 Structural basis for specificity maxima ....................................................................................................... 11 On solvent effects on enzymatic catalysis.............................................................................................. 15 Substrate solubility as a basis for solvent effects.................................................................................... 15 Solvent as a competitive inhibitor................................................................................................................. 18 Solvent as a non-competitive inhibitor....................................................................................................... 19 Solvent stabilisation of transition state ....................................................................................................... 23 Correlation between solvent effects and physical parameters ......................................................... 25 Enthalpy-entropy compensation .................................................................................................................... 27 Appendix A – Derivation of rate equations for dead-end and mixed-type
inhibition .............................................................................................................................................................................. 34 Dead-end (competitive) inhibition ............................................................................................................... 34 Mixed-type inhibition ......................................................................................................................................... 35 Acknowledgements .................................................................................................................................................... 37 Enzyme substrate solvent interactions
ENZYME SUBSTRATE SOLVENT INTERACTIONS
Enzymes show an intriguing ability of performing highly specific and efficient
catalysis. Their catalytic performance is governed by the interactions between
substrate, enzyme and its surrounding. With the development of enzymecatalysed synthesis enzymes have been introduced into organic solvents. This
has opened a new research area within enzymology which allows a large
variation of reaction media. In this thesis, enzyme catalytic efficiency and
specificity will be discussed in terms of molecular interactions between enzymes,
substrates and the surrounding solvent. Transacylation reactions catalysed by
Candida antarctica lipase B and Humicola insolens cutinase have been used as a
model system in all but one case, where hydrolysis reactions catalysed by Bacillus
subtilis esterase were studied. In total, the following reactions have been investigated:
Paper I
R1
O
OH
R2
+
O
CALB
6
Solvent
O
R1
R2
6
Paper II
OH
O
+
O
+
O
Hexane
R1=CH 3 or C 2H 5
R2=C 2H5, C 3HCHCH3 or C(CH 3)3
O
O
+
Solvent
O
CALB
6
Solvent
O
Solvent
6
Decaline
Cyclopentane
Tetrahydrofuran
Dichloromethane
Paper III
OH +
O
O
CALB
O
+
O
Paper IV
Effector
2-Pentanone
2-Methyl-2-pentanol
2-methylpentane
OH
O
OH
O
+
CALB
Effector
Water
O
+
O
OH
Paper V
H 2O
O2N
O
+
Water
X
Paper VI
OH
O
+
O
n
n=2-10
CALB,
cutinase or
HCl
Solvent
O2N
O
BSE2
Solvent
+
Water
HO
XH
O
X=O or NH
Solvent
+
O
n
n=2-10
1
Supercritical CO2
Hexane
1,4-Dioxane
Acetone
Carbon disulfide
OH
Hexane
Toluene
Acetonitrile
3-Pentanone
3-Methyl-3-pentanol
3-methylpentane
The origin of enzyme catalytic power
THE ORIGIN OF ENZYME CATALYTIC POWER
Several hypotheses have been put forward on how enzymes achieve their
increased reaction rate compared to uncatalysed reactions.1,2 One of the most
well-established hypotheses on enzyme catalytic ability is the concept of
transition-state stabilisation.3 It was introduced by Linus Pauling in 1948 suggesting that enzymes exert catalytic power by being complementary to the
reactant transition state. Together with Eyring´s transition state theory it
provides a relation connecting enzyme kinetic data and thermodynamics.4 The
hypothesis of transition state stabilisation is not unproblematic. Although used
as a fundament for our present reasoning about kinetics and catalysis it is
founded on an inherent simplification where an equilibrium between ground
state and transition state is present. In reality, there is no such equilibrium since
a reaction is taking place and thus acting as a driving force.5,6 It has also been
questioned whether transition state stabilisation is the main source of enzyme
catalytic power. Measurements of catalytic proficiency suggests that the change
in reaction environment going from solution to an active site is the dominating
factor in the enzymatic reaction rate accelerations: A reaction taking place in the
active site will benefit from not having to coordinate – and recoordinate solvent
molecules.7
Proximity effects
A major contribution to enzyme catalytic power is suggested to be the enzyme
active site imposing a spatial arrangement where reactants are put close together,
presumably increasing the likelihood of a reaction taking place. An early attempt
to estimate the catalytic effects of proximity was seen in the orbital steering
model from 1972. Here enzyme catalytic power is assumed to arise from their
precise arrangement of reactants making reacting orbitals immediately ready to
1
2
3
4
5
6
7
Menger FM: An alternative view of enzyme catalysis. Pure Appl Chem 2005, 77(11): 1873-1886.
Blow D: So do we understand how enzymes work? Structure Fold Des 2000, 8(4): R77-R81.
Pauling L: Nature of forces between large molecules of biological interest. Nature 1948,
161(4097): 707-709.
Eyring H: The Activated Complex in Chemical Reactions. J Chem Phys 1935, 3(2): 107-115.
Fong FK: A successor to transition-state theory. Acc Chem Res 1976, 9(12): 433-438.
The situation is analogous to the simplification of the Michaelis constant, when KM is approximated to the equilibrium constant KS.
Cannon WR, Benkovic SJ: Solvation, reorganization energy, and biological catalysis. J Biol Chem
1998, 273(41): 26257-26260.
2
The origin of enzyme catalytic power
overlap.8 A more recent variant of the idea of enzyme catalytic power originating
from its ability to bring reactants into proximity is suggested by Bruice and
Benkovic by introducing the concept of near-attack conformers: The formation
of a near-attack conformer is a necessary prerequisite for a catalytic event to take
place and the higher ratio of near-attack conformers compared to non-productive conformers formed in the enzyme active site, the faster the enzymatic
reaction will proceed.9
Proximity arguments are implicitly founded on the assumption that
enzymes benefit from having pre-organized active sites. An optimised reaction
environment as that in the active site will not only facilitate the orientation of
the participating reactants but also facilitate catalysis through a predefined electrostatic field created therein.10 The electrostatic field has been suggested to contribute to catalysis by direct electrostatic stabilisation of the transition state
structure, but also by facilitating tunnelling and the formation of extra short and
strong low-barrier hydrogen bonds.11,12,13
The effects of proximity on reaction rates have been studied by Page and
Jencks comparing intra-and intermolecular reactions, where the intramolecular
reactions are used as a model for a spatially arranged active site situation. They
attributed the intramolecular rate acceleration to entropic effects and proposed
the same driving force to be valid for enzyme-catalysed reactions.14
The hypothesis suggesting that the catalytic power of enzymes originates
from their ability to reduce entropic losses during catalysis was evaluated in
Paper VI. A transacylation reaction of nine homologous fatty acid ethyl esters
8
9
10
11
12
13
14
Storm DR, Koshland DE: Indication of the magnitude of orientation factors in esterification. J
Am Chem Soc 1972, 94(16): 5805-5814.
Bruice TC, Benkovic SJ: Chemical basis for enzyme catalysis. Biochemistry 2000, 39(21): 62676274.
Warshel A: Electrostatic origin of the catalytic power of enzymes and the role of preorganized
active sites. J Biol Chem 1998, 273(42): 27035-27038.
Cleland WW, Frey PA, Gerlt JA: The low barrier hydrogen bond in enzymatic catalysis. J Biol
Chem 1998, 273(40): 25529-25532.
Sutcliffe MJ, Scrutton NS: Enzyme catalysis: over-the-barrier or through-the-barrier? Trends
Biochem Sci 2000, 25(9): 405-408.
Benkovic SJ, Hammes-Schiffer S: Biochemistry - Enzyme motions inside and out. Science 2006,
312(5771): 208-209.
Page MI, Jencks WP: Entropic contributions to rate accelerations in enzymic and intramolecular
reactions and the chelate effect. Proc Natl Acad Sci U S A 1971, 68(8): 1678-1683.
3
C6
C7
C8
Acyl chain length
C5
C9 C10 C11 C12
0
20
40
C4
C6
C7
C8
Acyl chain length
C5
C9 C10 C11 C12
HCl
Cutinase
Hexane
n
n=2-10
O
O
OH
0
20
40
−ΤΔS‡ / kJ mol-1
60
80
100
C4
C6
C7
C8
Acyl chain length
C5
HCl
Cutinase
CALB
C9 C10 C11 C12
c) Free entropy -TΔS‡ of activation
+
4
Figure 1
Activation free energy, enthalpy and entropy for three series of transacylation reactions catalysed by HCl, Candida antarctica
lipase B and Humicola insolens cutinase, respectively. a) Activation free energies ΔG‡. b) Enthalpic contributions ΔH‡ to the activation free
energy. The difference in activation enthalpy varied between substrates as much as between catalysts, and no clear separation between catalysts
were seen. c) Entropic contributions -TΔS‡ to the activation free energy. The acid-catalysed reactions showed a significantly higher entropic
energy of activation than the enzyme-catalysed reactions. In total, the difference in reaction rates between enzymatic and non-enzymatic
reactions for the investigated series of substrates lied in an entropic penalty exerted to the acid-catalysed reactions.
0
20
C4
60
ΔH‡/ kJ mol-1
60
40
Hexane
CALB,
cutinase or
HCl
b) Free enthalpy ΔH‡ of activation
80
ΔG‡/ kJ mol-1
O
n
n=2-10
O
80
+
100
HCl
Cutinase
CALB
OH
Paper VI
100
a) Free energy ΔG‡ of activation
The origin of enzyme catalytic power
The origin of enzyme catalytic power
catalysed by HCl, Candida antarctica lipase B and Humicola insolens cutinase were
investigated, Figure 1. The activation free energies ΔG‡, Figure 1a, were clearly
separated for the three catalysts with the highest values displayed for the slow acidcatalysed reactions. For the activation enthalpies ΔH‡, Figure 1b, the separation
between catalysts disappeared, yielding values in the same range for the acid-catalysed
and the enzymatic reactions. In the activation entropy -TΔS‡, Figure 1c, the catalyst
separation was regained, again showing significantly higher energies for the nonenzymatic reactions.
The differences in activation entropies between enzymatic and non-enzymatic
reactions have several physical origins. Activation entropies are influenced by solvent
reorganisation energies both in free solution and in the active site. The entropic
penalty for the acid-catalysed reactions can also be seen as the cost for bringing –
and keeping – the reactants and catalysts oriented together during a catalytic event
without the help of a confining active site. The confining of substrates in the active
site will also in itself contribute to the activation entropy. Interestingly it has been
shown that ligand binding not only can decrease mobility and therefore the entropy
of ligand and enzyme, but it can also contribute to an increase in backbone
conformational entropy of the enzyme, making binding an overall entropically
favourable process.15,16
In Paper I, the role of entropy in selectivity was studied. The contribution to
enzymatic activation entropy from substrate conformational freedom within an
enzyme active site was investigated by molecular modelling. It was hypothesised that
the difference in entropic activation energy between enantiomers was dependent on
the difference in transition state conformational freedom. Enantioselectivities for
four secondary alcohols were measured in a transacylation reaction catalysed by
Candida antarctica lipase B, Table 1. The enzyme showed an R-preference for all four
substrates. The difference in activation enthalpy and entropy between enantiomers,
ΔΔH‡ and ΔΔS‡, are shown in Table 1.
15
16
Forman-Kay JD: The 'dynamics' in the thermodynamics of binding. Nat Struct Biol 1999, 6(12): 10861087.
Zidek L, Novotny MV, Stone MJ: Increased protein backbone conformational entropy upon
hydrophobic ligand binding. Nat Struct Biol 1999, 6(12): 1118-1121.
5
The origin of enzyme catalytic power
Table 1
Experimentally determined enantioselectivities, E, for transesterification of
four secondary alcohols together with calculated differences between enantiomers in
activation free energy ΔΔG‡, enthalpy ΔΔH‡ and entropy TΔΔS‡. ΔV is the difference
between enantiomers in explored active site volume, calculated from molecular dynamics
simulations.
Paper I
R1
R2
O
OH
+
O
sec-alcohol
3-hexanol
2-butanol
3-methyl-2-butanol
3,3-dimethyl-2-butanol
CALB
6
Solvent
E
(298 K)
340
8.3
810
460
O
R1
R
2
Solvent
O
6
‡
∆∆G
(kJ/mol)
-14.4
-5.3
-16.6
-15.2
+
Hexane
O
R1=CH 3 or C 2H 5
R2=C 2H5, C 3HCHCH3 or C(CH 3)3
‡
∆∆H
(kJ/mol)
-9.0
-10.7
-24.3
-20.4
‡
T∆∆S (298 K)
kJ/mol)
+5.5
-5.4
-7.7
-5.2
∆R-SV
(Å3)
+19
-21
-46
+27
For the three substrates 2-butanol, 3-methyl-2-butanol and 3,3-dimethyl-2butanol ΔΔH‡ and ΔΔS‡ were counteracting, with the fast enantiomer being
enthalpically favoured and entropically disfavoured. For 3-hexanol the enthalpic and
entropic contributions reinforced each other and the highest activation entropy was
seen for the fast S enantiomer. The accessible active site volume of each enantiomer
was evaluated by molecular dynamics simulations. For the three alcohols 2-butanol,
3-methyl-2-butanol and 3-hexanol the differential accumulated volume, ∆R-SV,
visited by the enantiomers during the course of the simulation where qualitatively
correlated to TΔΔS‡. For the fourth alcohol 3-3-dimethyl-2-butanol the explored
active site volumes did not correlate to the difference in activation entropy. Analyses
of the dynamics simulations revealed that both enantiomers of 3-3-dimethyl-2butanol were sterically constrained to a point were even methyl groups were found
to be rotationally restricted (results not shown). The bulky and slow-reacting alcohol
might have needed significantly longer simulation times to explore all its reachable
active site space.
From the data presented in Paper I it is seen that the fast enantiomer in three
out of four cases suffers from a higher activation entropy cost than the slow one.
The same result is seen in for transacylation reactions of fatty acid ethyl esters
catalysed by Candida antarctica lipase B in Paper VI. In Figure 2, the enthalpic and
entropic contributions to the activation free energy are shown together with a
specificity profile for the substrates. Also here the faster substrates are enthalpically
favoured and entropically disfavoured over the slower ones.
6
The origin of enzyme catalytic power
Paper VI
OH
O
+
O
CALB
O
n
n=2-10
O
Hexane
a)
+
n
n=2-10
OH
b)
45
Activation enthalpy
Rate constant
4
45
40
Activation entropy
Rate constant
4
40
3
3
35
35
30
2
ΔH ‡
-1
/ kJ mol
25
30
‡
−Τ ΔS
-1
/ kJ mol
25
k cat /K M
relative C7
2
k cat /K M
relative C7
1
1
20
20
15
15
-
C4 C5 C6 C7 C8 C9 C10 C11 C12
C4 C5 C6 C7 C8 C9 C10 C11 C12
Acyl chain length
Acyl chain length
Figure 2
a) Enthalpic and b) entropic contributions to reaction free energy of a
transacylation reaction catalysed by Candida antarctica lipase B compared to the substrate
specificities.
In conclusion, enzyme catalytic power is attributed to a stabilisation of the
reaction transition state. However, in the light of catalytic proficiency the change
from an environment consisting of a free solution to a reaction-optimised active site
is of higher importance. Besides providing a beneficial and stabilising surrounding to
the reactants, the significance of the pre-organised active site has been suggested to
lie in its ability to bring reactants in proximity of each other, limiting the entropic
cost of keeping reactants together in free solution. In literature, studies have come to
different conclusions whether to support the hypothesis of entropy as a driving force
for catalysis or not.17,18 Unfortunately, only a few substrates have been studied, and
no overall trend has been revealed. In Paper VI, the hypothesis was evaluated for
transacylation reactions catalysed by Candida antarctica lipase B and Humicola insolens
17
18
Snider MJ, Gaunitz S, Ridgway C, Short SA, Wolfenden R: Temperature effects on the catalytic
efficiency, rate enhancement, and transition state affinity of cytidine deaminase, and the
thermodynamic consequences for catalysis of removing a substrate "anchor". Biochemistry 2000,
39(32): 9746-9753.
Snider MJ, Lazarevic D, Wolfenden R: Catalysis by entropic effects: The action of cytidine deaminase
on 5,6-dihydrocytidine. Biochemistry 2002, 41(12): 3925-3930.
7
The origin of enzyme catalytic power
cutinase for a series of homologous fatty acid ethyl esters. For both enzymes, their
contribution to reaction rate acceleration compared to an acid catalyst was found to
be purely entropic. On the other hand, studies of difference in activation entropy
and enthalpy between enantiomers in Paper I and between homologous esters in
Paper VI show that high substrate specificity is achieved by enthalpic stabilisation.
Entropic contribution to activation free energy thus seems to be beneficial for
reaction rate enhancement but to have a negative impact on specificity.
8
The role of steric hindrance in enzyme specificity
THE ROLE OF STERIC HINDRANCE IN ENZYME SPECIFICITY
Rational design of enzymes is based on understanding of their interactions with the
substrate. A thorough knowledge on the impact of active site geometry on substrate
transition states is therefore of great importance. By investigating the relationship
between active site shape and substrate specificity valuable knowledge for design of
mutants can be gained. This can be investigated by comparison of specificities
between substrates differing in a single methylene group. A methylene has a binding
energy which fully developed is approximately 4 kJ/mol and an enzyme incorporating the full methylene binding energy will lower the transition state energy
by the same amount.19,20,21 Addition of a single methylene will thus contribute to a
specificity change of up to five times depending on how much of the binding energy
is being utilised.22 If the alteration in specificity between such homologous substrates
differing in one methylene deviates significantly from this value, some additional
mechanism besides pure binding for achieving specificity is present.
One example on how this can be achieved can be seen in the discrimination
between isoleucine and valine performed by isoleucine-tRNA synthethase. The low
energy available for discrimination between the amino acids raises problems in
protein synthesis, where high specificity is of outermost importance. Therefore
isoleucine-tRNA synthethase is forced to use an editing step to get its high discrimination of 1 to 40 000 towards isoleucine over the one methylene group smaller
substrate valine. A proofreading is achieved by a separate hydrolytic pocket in which
isoleucine is sterically hindered to bind and only the erroneously formed valinyltRNA will be hydrolysed. When this hydrolytic proofreading step of the enzyme is
removed, the specificity for isoleucine over valine decreases to 3.5 which is the value
expected from methylene binding energy.23
19
20
21
22
23
Linus Pauling, referenced by Nureki et al 23
Andrews PR, Craik DJ, Martin JL: Functional-group contributions to drug receptor interactions. J
Med Chem 1984, 27(12): 1648-1657.
Wear MA, Kan D, Rabu A, Walkinshaw MD: Experimental determination of van der Waals energies
in a biological system. Angew Chem, Int Ed 2007, 46(34): 6453-6456.
− ΔG
= e RT
Nureki O, Vassylyev DG, Tateno M, Shimada A, Nakama T, Fukai S, Konno M, Hendrickson TL,
Schimmel P, Yokoyama S: Enzyme structure with two catalytic sites for double-sieve selection of
substrate. Science 1998, 280(5363): 578-582.
Calculated as
k1
k2
9
The role of steric hindrance in enzyme specificity
a) Candida antarctica lipase B
b) Fusarium solani cutinase
Figure 3
a) The active site of Candida antarctica lipase B. b) The active site of Fusarium
solani cutinase. Fusarium solani cutinase has a sequence identity of 50% to the experimentally studied cutinase from Humicola insolens.24 The pictures are based on the enzyme
structures 1tca and 1xzm, respectively. 25,26
Methylene probing can be used to investigate what structural features that
might be important to enantioselectivity. In Paper I measurements of alcohol
enantioselectivity on 2-butanol and 3-hexanol were performed. According to an
earlier molecular modelling study, the two enantiomers bind in different modes.27
The fast-reacting R enantiomers bind with their medium-sized substituent of the
alcohol in the stereospecificity pocket and the large one directed towards the active
site entrance. The slow S enantiomers have a reverse binding. For both alcohols the
24
25
26
27
Ternström T, Svendsen A, Akke M, Adlercreutz P: Unfolding and inactivation of cutinases by AOT
and guanidine hydrochloride. Biochim Biophys Acta, Proteins Proteomics 2005, 1748(1): 74-83.
Uppenberg J, Öhrner N, Norin M, Hult K, Kleywegt GJ, Patkar S, Waagen V, Anthonsen T, Jones
TA: Crystallographic and molecular-modeling studies of lipase B from Candida antarctica reveal a
stereospecificity pocket for secondary alcohols. Biochemistry 1995, 34(51): 16838-16851.
Longhi S, Nicolas A, Creveld L, Egmond M, Verrips CT, deVlieg J, Martinez C, Cambillau C:
Dynamics of Fusarium solani cutinase investigated through structural comparison among different
crystal forms of its variants. Proteins 1996, 26(4): 442-458.
Haeffner F, Norin T, Hult K: Molecular modeling of the enantioselectivity in lipase-catalyzed
transesterification reactions. Biophys J 1998, 74(3): 1251-1262.
10
The role of steric hindrance in enzyme specificity
Paper VI
OH
O
O
+
n
n=2-10
O
CALB
Hexane
a) Candida antarctica lipase B
+
O
OH
n
n=2-10
b) Humicola insolens cutinase
6
500
400
4
300
kcat/KM / M -1s-1
kcat/KM / M -1s-1
200
2
100
0
0
C4
C5
C6
C7
C8
C4
C9 C10 C11 C12
C5
C6
C7
C8
C9
C10 C11 C12
Acyl chain length
Acyl chain length
Figure 4
Specificity profiles of a) Candida antarctica lipase B, CALB, and b) Humicola
insolens cutinase for transacylation of nine fatty acid ethyl esters with methanol. CALB
showed a significantly more complex specificity profile containing two maxima as compared with cutinase. Cutinase showed a considerably smoother specificity profile with
specificities declining with substrate fatty acid chain length, containing only one
maximum.
difference in size between the medium and the large substituents is a methylene and
so the maximal enantioselectivity originating from methylene binding energy would
correspond to an E-value of 5. This is close to the value seen for 2-butanol with E =
8.3. For 3-hexanol on the other hand E was 340. This suggests that steric hindrance
is a strong contributing factor to enantioselectivity for 3-hexanol.
Structural basis for specificity maxima
For enzymes catalysing the same reactions with different substrates the specificity
will depend on the shape of the active sites. Candida antarctica lipase B (CALB) and
cutinase are two enzymes belonging to the α/β -hydrolase family both capable of
catalysing transacylation reactions in organic solvents. The two enzymes have
different appearances of their active sites, Figure 3. CALB has a deep and narrow
active site, whereas that of cutinase is shallow.
11
The role of steric hindrance in enzyme specificity
a) Candida antarctica lipase B
b) Fusarium solani cutinase
Figure 5
a) The ligand Tween 80 co-crystallised with Candida antarctica lipase B
extracted from X-ray structure 1lbt.25 The deep active site forces the long acyl chain into
a staggered conformation. The alcohol part of the ligand is omitted for clarity.
b) Undecanylphosphonate methyl ester co-crystallised with cutinase from structure
1xzm.26 The acyl chain is not restricted by the active site geometry, and adopts a relatively
extended conformation.
In Paper VI, homologous unbranched fatty acid ethyl esters were used to
probe the shape of the acyl binding part of the active site of these two enzymes. In
these measurements differences in solubility between substrates influence the
specificity constants. It is therefore no longer possible to attribute energy differences
between consecutive substrates solely to methylene binding. The general patterns of
specificity between substrates will still remain unaffected. To probe the specificity
dependence on the shape of the active sites of CALB and cutinase, the specificities
for nine homologous fatty acid ethyl esters ranging from ethyl butanoate to ethyl
dodecanoate where measured in a transacylation reaction with methanol as the acyl
acceptor, Figure 4.
The specificity profile for CALB, Figure 4a, displayed two maxima, one sharp
for ethyl pentanoate and one less pronounced around ethyl nonanoate and ethyl
decanoate. Cutinase on the other hand, Figure 4b, had an overall smoother
specificity profile, containing a single specificity maximum for ethyl heptanoate. The
difference in specificity profiles between CALB and cutinase are a direct reflection of
the difference in complexity of the active site shapes for the two enzymes. The pro12
The role of steric hindrance in enzyme specificity
a) Candida antarctica lipase B
b) Fusarium solani cutinase
10
9
7
Figure 6
a) The acyl chain of the ligand Tween 80 exiting the active site of Candida
antarctica lipase B, CALB. Carbon number nine and ten at which a local specificity
maximum is found are labelled in the picture. b) The acyl chain of undecanylphosphonate methyl ester exiting the active site of cutinase. Carbon number seven is labelled. The
pictures are based on enzyme structures 1tlbt and 1xzm, respectively.25,26
nounced optimum in CALB seen for ethyl pentanoate is caused by the sharp
curvature of the deep active site. Substrates with an acyl chain consisting of up to
five carbons can be bound in an extended conformation, whereas substrates having
an acyl chain of length of six or more have to adopt an eclipsed conformation. This
caused a sharp drop in substrate specificity, Figure 5a. For cutinase on the other
hand no such conformational restriction was present, allowing also longer acyl chains
to be bound in an extended conformation, Figure 5b.
The small maxima in the CALB specificity profile around C9/C10 was reached
when the substrate displayed maximal binding to the active site. This was achieved
when the substrate chain was long enough to utilise the whole depth of the binding
site and any elongation of the chain would cause the substrate to be located partly
outside the active site, Figure 6a. The single specificity maximum in cutinase at C7
was caused by the same effect, Figure 6b.
In conclusion, substrate specificity is deeply connected with the shape of the
active site. For homologous substrates differing in methylenes, the maximal change
in specificity that can be achieved from pure binding energy is a factor of five. If
larger variations in specificity are seen, that is attributed to some kind of steric interference. This has practical consequences for rational design of enzymes. If the difference in available binding energy between two substrates is low, an efficient enzyme
13
The role of steric hindrance in enzyme specificity
cannot be designed by creating a good fit for one of them. To reach high specificity,
one of the substrates must be sterically hindered.
When specificities between non-enantiomeric substrates are compared, the
measured specificity values cannot be solely attributed to enzyme-substrate
interactions, but will also depend on substrate chemical reactivity and solubility.
Differences in solubility will also have an impact on enzyme specificity as substrate
binding is an equilibrium between bound substrate and substrate in solution. The
more favourable the enzyme environment is to a substrate, the higher specificity is
achieved. For the presented series of fatty acid acyl esters transacylated in hexane, the
active site will appear the most attractive for the shorter substrates compared to the
longer ones.
For cutinase with its relatively uncomplicated active site geometry, this
solubility trend is clearly visible. Even though the numerical values of specificities
were difficult to refine to only attribute to substrate binding, it was still possible to
draw conclusions on how specificity was achieved by the enzyme. The sharpest
specificity peak was seen for CALB when a spatial restriction of the active site was
imposed on the substrate chain, forcing it into a non-optimal conformation. Also
here, steric hindrance was the basis for substrate specificity.
14
On solvent effects on enzymatic catalysis
ON SOLVENT EFFECTS ON ENZYMATIC CATALYSIS
The introduction of organic solvents in enzymology has made it possible to achieve a
broad variation of reaction environments. The choice of reaction media will affect
both substrate and enzyme and can have a profound effect on the outcome of
enzyme-catalysed reactions. Solvent is proposed to induce enzyme conformational
changes, to affect the enzyme dynamics, to act as an enzyme inhibitor and to modify
substrates and substrate properties. These factors – and probably others as well – are
likely to cooperate in creating the complex relation seen between reaction media and
reaction outcome.28 In the following, experiments designed to reveal and study
individual solvent effects will be presented.
Substrate solubility as a basis for solvent effects
In Paper VI the effect of solvent on substrate specificity was investigated. The
specificities for transacylation of nine homologous esters were determined in hexane
and acetonitrile, respectively, Figure 7.
The specificity profiles for reactions in hexane and acetonitrile show a radically
different behaviour. In acetonitrile, the esters with longer fatty acid chains were
strongly preferred over the shorter ones. In hexane, the highest specificity was
achieved for the shorter fatty acid acyl esters. From this data, it was suggested that
the differences in specificity were related to differences in substrate solubility. In the
polar solvent acetonitrile the longer esters should favour the relatively non-polar
active site of CALB over staying in free solution, while the opposite should be valid
in hexane. The hypothesis was tested by first measuring the relative solubility of the
esters in the two solvents, and thereafter correcting the experimental specificities
accordingly. The nine substrate esters were put into a hexane - acetonitrile two-phase
system. After equilibration, the distribution of esters between the two phases were
analysed and the free energy differences for the esters between the solvents were
calculated, Figure 8.
28
Klibanov AM: Improving enzymes by using them in organic solvents. Nature 2001, 409(6817): 241246.
15
On solvent effects on enzymatic catalysis
Paper VI
O
OH
O
CALB
O
+
n
n=2-10
Solvent
+
O
OH
n
n=2-10
b) Acetonitrile
a) Hexane
4
4
3
3
kcat/KM / M -1s-1
2
k cat /K M
relative C7
kcat/KM / M -1s-1
2
k cat /K M
relative C7
1
1
0
0
C4
C5
C6
C7
C8
C9
C4
C10 C11 C12
C5
C6
C7
C8
C9
C10 C11 C12
Acyl chain length
Acyl chain length
Figure 7
The influence of the solvents hexane and acetonitrile on Candida antarctica
lipase B for nine fatty acid ethyl esters. a) Specificity in hexane. b) Specificity in acetonitrile. In each system, the specificity constants are given as fractions of the rate constant
for ethyl heptanoate.
2
O
1
O
n
n=2-10
0
Δ G hexane-AcN
/ kJ mol-1
C4
C5
C6
C7
C8
C9 C10 C11 C12
-1
-2
-3
-4
Acyl chain length
Figure 8
Free energy difference for the distribution of substrates in a two-phase
system consisting of acetonitrile and hexane. The linear behaviour in free energy is
consistent with the consecutive addition of methylenes.
16
On solvent effects on enzymatic catalysis
Paper VI
OH
O
O
CALB
O
+
n
n=2-10
+
O
n
n=2-10
Solvent
OH
4
AcN corrected
Hexane
3
2
k cat /K M
relative C7
1
0
C4
C5
C6
C7
C8
C9 C10 C11 C12
Acyl chain length
Figure 9
Substrate specificities in acetonitrile were adjusted according to solubility in
hexane together with specificities in hexane. The specificity profile adopted the same
general appearance as that seen in hexane. In each case, the specificity constants are given
as fractions of the rate constant for ethyl heptanoate.
The substrate specificity for CALB-catalysed transacylation in acetonitrile was
adjusted for the solubility-caused energy difference experienced by the esters. The
specificity profile was reverted to the same appearance as for reactions in hexane,
Figure 9. Changes in solubility between substrates has a profound effect on
specificity constants. Based only on the change of hexane to acetonitrile the
specificity of ethyl pentanoate over ethyl undecanoate changed with a factor of five.
The close relation between KM and KS suggests that the substrate solubility effect on
specificity is reflected in KM rather than in kcat, which was shown earlier in a very
similar system.29
29
Martinelle M, Hult K: Kinetics of acyl transfer reactions in organic media catalysed by Candida
antarctica lipase B. Biochim Biophys Acta, Protein Struct Molec Enzym 1995, 1251(2): 191-197.
17
On solvent effects on enzymatic catalysis
Solvent as a competitive inhibitor
To elucidate solvent effects on enzyme catalysed reactions separated from substrate solubility a precise control of solvent activity is needed. This can be achieved
in a solid/gas reactor, where substrates and effectors (“solvents”) in gas phase are
percolated over a bed of immobilized enzyme. The reactor allows precise and
independent control of individual thermodynamic activities of participating
compounds as well as a well-defined physical environment.30,31
In Paper III, the inhibitory properties of solvents were studied in a solid/gas
reactor. Six solvents: 2-pentanone, 3-pentanone, 2-methyl-2-pentanol, 3-methyl-3pentanol, 2-methylpentane and 3-methylpentane were chosen for having approximately the same size but three different chemical functionalities. A clear inhibitory
character was seen for the ketones, whereas no inhibition was detected for the
alcohols and alkanes. A molecular modelling study was performed on 2-pentanone,
2-methyl-2-pentanol and 2-methylpentane to investigate their interactions with
Candida antarctica lipase B and the molecular basis for solvent inhibition. For each
case one solvent molecule was manually positioned in the active site in a conformation utilizing available hydrogen bonding possibilities. Dynamics simulations
were undertaken and the interaction between the solvent molecules and the lipase
was studied over time, Figure 10.
During the time course of the simulation, the ketone was firmly fixed by the
oxyanion hole while the alcohol was mainly coordinated in the catalytic site. The
alkane 3-methylpentane, having no coordination to utilise, explored the active site
environment whereafter it exited trough the active site entrance. The modelling study
supported the experimental findings of inhibitory character for 2-pentanone and the
lack of the same for 2-methylpentane. For 2-methyl-2-pentanol, the experimental
and modelling results were contradictory. Earlier experimental measurements with
the smaller homologue 2-methyl-2-butanol showed inhibition and it is astonishing
that the addition of a methylene to 2-methyl-2-butanol would completely remove its
inhibitory properties.
30
31
Lamare S, Legoy MD: Working at controlled water activity in a continuous process - the gas-solid
system as a solution. Biotechnol Bioeng 1995, 45(5): 387-397.
Lamare S, Legoy MD, Graber M: Solid/gas bioreactors: powerful tools for fundamental research and
efficient technology for industrial applications. Green Chem 2004, 6(9): 445-458.
18
On solvent effects on enzymatic catalysis
Paper III
OH +
O
O
O
CALB
+
O
a)
b)
c)
d)
Effector
OH
2-Pentanone
2-Methyl-2-pentanol
2-methylpentane
3-Pentanone
3-Methyl-3-pentanol
3-methylpentane
Figure 10 a) A schematic picture of the active site of Candida antarctica lipase B. The
catalytic serine (Ser105) and histidine (His224) are shown together with Thr40 and
Gln106, which constitute the oxyanion hole. Trp104 constitutes a “floor” in the active
site cavity. b) Eight hundred sampled and superimposed structures of 2-methyl-2pentanol in the active site of Candida antarctica lipase B. c) Superimposed structures of 2pentanone. d) Superimposed structures of 2-methylpentane. There were no attraction
between the alkane and the active site, and although the 2-methylpentane molecule was
positioned in the binding site from the start of the simulation, it started exploring the
surrounding whereafter it exited through the active site entrance.
Solvent as a non-competitive inhibitor
In Paper IV, an experimental study on the effect of water on transacylation
catalysed by Candida antarctica lipase B was performed in a solid/gas reactor. It
was hypothesised that a water molecule could utilise the stereospecificity pocket
19
On solvent effects on enzymatic catalysis
Figure 11 A water molecule bound in the stereospecificity pocket of lipase B from
Candida antarctica would enantioselectively inhibit the slow S enantiomer of a secondary
alcohol, while interfering much less with the fast R enantiomer.
for binding, acting as a non-competitive inhibitor to the substrate. The hypothesis
was tested using an enantioselective reaction. Since only the slow S enantiomer of 2pentanol fills the stereospecificity pocket for binding, a gradually increase in
water activity would increase enantioselectivity by lowering the specificity for the
slow S enantiomer, Figure 11. Water activity was found to have a profound effect on
the enantioselectivity, which increased the E-value from 100 at zero water activity to
a maximum of 340 at water activity 0.2, Figure 12.
A molecular modelling study was undertaken to evaluate the possibility of
water binding in the specificity pocket. Two tetrahedral intermediate enzymesubstrate complexes were built for each enantiomer. In the first structure, a tetrahedral
intermediate was constructed starting from an empty active site. In the other, a water
molecule was first positioned in the stereospecificity pocket; whereafter the
tetrahedral intermediate was built. In all four cases, the enantiomers were oriented in
their respective productive binding mode.27 Molecular dynamics simulations were
performed on the four structures. In Figure 11, examples of structures emerging
from the dynamics simulations starting from a structure without a water molecule in
the stereospecificity pocket are shown. The stereospecificity pocket was probed for
cavities capable of harbouring a water molecule. In case of the R enantiomer, the
stereospecificity pocket had a cavity of a size large enough for a water molecule. The
corresponding cavity was absent for the S enantiomer.
20
On solvent effects on enzymatic catalysis
Paper IV
O
OH
O
+
CALB
Effector
Water
O
+
O
OH
400
300
E
200
100
0
0
0.1
0.2
0.3
0.4
0.5
0.6
aw
Figure 12
Influence of thermodynamic water activity, aw, on enantioselectivity for a
transacylation reaction catalysed by Candida antarctica lipase B.
a) R enantiomer
b) S enantiomer
Figure 11 Stick models of the tetrahedral intermediates of a) R- and b) S-2-pentyl
propanoate. The surrounding amino acids consist of the catalytic triad, (Ser105, Asp187
and His224, shown in light grey), the oxyanion hole (Thr40 and Gln106, shown in dark
grey), the specificity pocket (Thr42 and Ser47, shown in dotted dark grey), and the active
site space limiter, “the floor” (Trp104, shown in dotted light grey). Catalytically important
hydrogen bonds are marked with white dotted lines. In the stereospecificity pocket, the
available space was much larger for the alcohol of the R enantiomer; in the S enantiomer
a propyl group is pointing directly at the surface of Trp104. This difference is the cause
of the enantioselectivity.
21
On solvent effects on enzymatic catalysis
The simulations of tetrahedral intermediates built on structures already containing a bound water molecule in the specificity pocket revealed a more stabilised
binding situation for the water molecule for the fast R enantiomer. In the case of the
R enantiomer the water molecule was stabilised by more hydrogen bonds than in the
case of the S one. The structure with the S enantiomer was also subjected to
distortion in the active site region. It was concluded that the S enantiomer would not
bind in the active site at the same time as the water molecule occupied the stereospecificity pocket. The water molecule will thus act as a competitive inhibitor
towards the slow S enantiomer. The R enantiomer on the other hand will be noncompetitively inhibited, and overall a mixed-competitive behaviour should be seen
for the system.
This is in contradiction with an earlier experimental study which found that
water acts as a pure competitive inhibitor.32 The two suggested models are depicted
in Figure 12 together with their respective apparent kinetic constants. Both kinetic
models show an apparent dissociation constant K Sapp which deviates from the true
constant KS , but only the model containing non-competitive inhibition has an effect
app
. The pure competitive model instead shows an
on the apparent maximum rate Vmax
app
app
Vmax indifferent to the inhibitor concentration. From the equations of Vmax it can be
seen that he apparent contradiction between the two kinetic models is trivially solved
if β = 1. As long as the catalytic rate is the same for going from ESI complex to
product and from ES complex to product respectively, the two competitive and
mixed-competitive models will be indifferent without further studies. The scenario
with β = 1 is not unlikely, and since the R enantiomer does not utilize the full
stereospecificity pocket there is no reason why it would be substantially influenced
by the water molecule. In the limiting case where the interaction of the R enantiomer
with the active site is independent of the presence of the water molecule, a pure
competitive inhibition is achieved.
32
Bousquet-Dubouch MP, Graber M, Sousa N, Lamare S, Legoy MD: Alcoholysis catalyzed by Candida
antarctica lipase B in a gas/solid system obeys a Ping Pong Bi Bi mechanism with competitive
inhibition by the alcohol substrate and water. Biochim Biophys Acta-Protein Struct Molec Enzym 2001,
1550(1): 90-99.
22
On solvent effects on enzymatic catalysis
b) Competitive and non-competitive (mixedtype) inhibition
a) Pure competitive (dead-end) inhibition
Figure 12 Kinetic models and apparent rate constants for a) competitive (dead-end)
inhibition and b) mixed type competitive and non-competitive inhibition. The kinetic
constants are derived under rapid-equilibrium assumptions. For derivations, see Appendix A.
Solvent stabilisation of transition state
In Paper V, the promiscuous amidase activity shown by Bacillus subtilis esterase 2
was investigated in a molecular modelling study. It revealed a water network
stabilising the amide proton, and it was hypothesised that the removal of this stabilising network would decrease the amidase activity relative to the esterase activity,
23
On solvent effects on enzymatic catalysis
Paper V
H 2O
O2N
O
+
X
O
BSE2
Water
O2N
Solvent
+
HO
Water
XH
X=O or NH
b) B. subtilis esterase 2. Glu188Phe mutant
a) B. subtilis esterase 2. Wild-type
Substrate
Substrate
Figure 13 Snapshots from molecular-dynamics studies of the tetrahedral intermediate
of amide in a) wild-type BS2 esterase and b) the mutant Glu188Phe. The hydrogen-bond
network that stabilises the substrate amide hydrogen in the wild-type enzyme is marked
with an arrow. This stabilization was lost in the Glu188Phe mutant.
Figure 13. The water network had its basis in Glu188 and four mutants, Glu188Asp,
Glu188Asn, Glu188Ala and Glu188Phe, were designed. The mutants Glu188Asp,
and Glu188Asn were predicted to be relatively indifferent regarding their promiscuous amidase activity, since their side-chains retain the ability of anchoring a water
bridge. The mutants Glu188Ala and Glu188Phe on the other hand were predicted to
decrease the amidase activity compared to the esterase activity. In accordance to the
hypotheses, the mutants Glu188Asp and Glu188Asn were indifferent to the wild
type in relative promiscuous activity. The promiscuous activity was only affected
with a factor of two, which in activation free energy ΔΔG‡ corresponds to a
difference of 1.4 kJ/mol. The mutants Glu188Ala and Glu188Phe both decreased
the promiscuous behaviour with energy differences of 5 and 7 kJ/mol, respectively.
24
On solvent effects on enzymatic catalysis
Paper II
OH
O
O
+
CALB
O
6
O
Solvent
Solvent
6
+
Decaline
Cyclopentane
Tetrahydrofuran
Dichloromethane
O
Supercritical CO2
Hexane
1,4-Dioxane
Acetone
Carbon disulfide
1000
cis-Decalin
Cyclopentane
Hexane
800
E
Tetrahydrofurane
Acetone
Carbon
disulfide
600
1,4-Dioxane
Dichloromethane
400
Supercritical
carbon dioxide
200
0
0
50
100
150
200
3
Volume / Å
Figure 14
Enantioselectivity for a transacylation reaction ran in nine different solvents.
Correlation between solvent effects and physical parameters
Several attempts have been made to correlate enantioselectivity to different physical
characteristics of solvents, such as dielectric constant, logP and polarisation
properties.33 In Paper II the influence of solvent on enantioselectivity in condensed
phase was measured for nine solvents for a transacylation reaction at water activity
0.1. The enantioselectivity varied between 250 and 870, and for this system the best
correlation with enantioselectivity was found for the molecular volume of the
solvent, Figure 14.
The variation of enantioselectivity with solvent cannot be due to substrate
solvation effects, unless the enzyme concentration is high enough to make the bulk
appear chiral to the substrate molecules. In all solvents, the specificity pocket of the
lipase has identical water occupancy, since the water activity is kept fixed between
33
Wescott CR, Klibanov AM: The solvent dependence of enzyme specificity. Biochim Biophys Acta,
Protein Struct Molec Enzym 1994, 1206(1): 1-9.
25
On solvent effects on enzymatic catalysis
experiments. The change in enantioselectivity can stem from either enantioselective
solvent inhibition as found in Paper III or from effects related to the enzyme
structure or dynamics. From Paper III it is known that purely hydrophobic solvents
do not inhibit the active site of Candida antarctica lipase B. Therefore enantioselective
inhibition cannot be the explanation to the difference seen between non-polar
solvents such as CS2 and hexane. A remaining factor is that the solvent affects the
enzyme in itself. The enzyme could be modified either in structure, folding or in
dynamics. It is shown in a modelling study on Candida antarctica lipase B that the
solvent dielectricity constant has a strong influence on enzyme flexibility.34
34
Trodler P, Pleiss J: Modeling structure and flexibility of Candida antarctica lipase B in organic solvents.
BMC Struct Biol 2008, 8: 10.
26
Enthalpy-entropy compensation
ENTHALPY-ENTROPY COMPENSATION
Enthalpy-entropy compensation is a phenomenon often observed in thermodynamic
analyses of kinetic data. It describes a situation where reactions favoured in activation
enthalpy simultaneously is penalised by a compensating and unfavourable activation
entropy. The meaning of an enthalpy-entropy compensation is intuitively straightforward: an increased “fit” between molecules is paid for with a corresponding restriction in freedom of motion. Many experimental systems showing enthalpy-entropy
compensation have been shown in the literature.35,36 Unfortunately, analyses of
enthalpy-entropy compensations often suffers from severe methodological and
statistical drawbacks.37 Even in cases where a compensatory trend based on experimental data is showing an excellent linearity between ΔH‡ and ΔS‡, the findings can
still be reduced to be pure artefacts of propagating experimental errors.38
Consider a chemical reaction characterised by a rate constant k determined at
temperatures T1 and T2 from which the reaction activation enthalpy ΔH‡ and
entropy ΔS‡ is deduced. If ΔH‡ and ΔS‡ are calculated from the same single experimental data set their errors will be interrelated. It can be shown that a sufficient
condition for errors not to dominate in a presumed enthalpy-entropy compensation
is achieved when the total range of activation enthalpy, ΔH‡, and the relative experimental error α of rate constants fulfils the relation39
35
36
37
38
39
Krug RR, Hunter WG, Grieger RA: Enthalpy-entropy compensation .1. some fundamental statistical
problems associated with analysis of vant Hoff and Arrhenius data. J Phys Chem 1976, 80(21): 23352341.
Krug RR, Hunter WG, Grieger RA: Enthalpy-entropy compensation .2. separation of chemical from
statistical effect. J Phys Chem 1976, 80(21): 2341-2351.
Cornish-Bowden A: Enthalpy-entropy compensation: a phantom phenomenon. J Biosci 2002, 27(2):
121-126.
Petersen RC, Markgraf JH, Ross SD: Solvent Effects in the Decomposition of 1,1´Diphenylazoethane and 2,2´-Azobis-(2-methylpropionitrile). J Am Chem Soc 1961, 83(18): 3819-3823.
Let k1 and k2 be two rate constants measured for a reaction at temperatures T1 and T2, respectively.
The reaction activation enthalpy, ΔH‡, and entropy ΔS‡ be calculated using the Eyring equation
‡
ki =
‡
H
k BT ΔRS − ΔRT
e e
h
yielding
‡
ΔH = R
T1T2
kT
ln 2 1
T2 − T1 k1T2
‡
and
‡
ΔS =
ΔH
k T
+ R ln B
T
hk1
where kB is the Bolzmann constant, h
the Planck constant and R the general gas constant. Let α be the maximal relative error in
determination of ki so that ki, measured = ki (1+α), and assume that the error in temperature
determination is negligible comparison to α. The error α will then propagate to an absolute error δ in
ΔH and an absolute error σ in ΔS according to: (continued in the footer of next page)
27
Enthalpy-entropy compensation
‡
ΔΔH >> 4 R
T2T1
α
T2 − T1
1
In Figure 15 the relation between activation enthalpies and entropies for a
transacylation reaction performed in different solvents (Paper II) is shown.
Equation 1 was used to estimate whether the compensatory trend was of
extrathermodynamic origin or a statistical artefact. The calculated enthalpies of activation ΔH ‡ covered a span of 7 kJ/mol, which then should be much larger than
4R
T2T1
α.
T2 − T1
The temperature interval used in the kinetics measurements varied
between experiments, but was mostly in the region 283 to 323 K. If a relative error
of 5% was used for the measurements of rate constants, the right hand side of
equation 1 yielded only 4 kJ/mol. The linear compensation seen for entropy as a
function of enthalpy determined from reaction rates measured in different solvents
can therefore not be distinguished from propagated experimental errors and no
conclusions could be drawn regarding the presence of an enthalpy-entropy compensation based on physical grounds.
Besides the problem of propagating errors, another complicating statistical
factor in evaluation of enthalpy-entropy compensations is present. An inherent property of the transformation going from a kinetic to a thermodynamic space is that
geometrical shapes are compressed and elongated along the compensation line in the
process. Consequently, they are perceived as more or less linear regardless of their
initial appearance.40,41 Furthermore, practical limitations on measurements of kinetics
‡
ΔH + δ = R
σ =δ
T1T2
(1 + α )k2T1
ln
T2 − T1 (1 − α )k1T2
3T2 − T1
2T1T2
41
ΔS ‡ + σ =
(ΔH ‡ + δ )
k (1 + α )h1
+ R ln 1
T1
kBT1
When α <<1,
δ = 2R
T1T2
α.
T2 − T1
and
. If the errors δ and σ dominate over the true variation in ΔS‡ versus ΔH‡, a straight line
with the slope
40
, and
3T2 − T1
2T1T2
will be achieved in the compensation plot. An enthalpy-entropy compensation
curve must thus show an interval of measured activation enthalpies much larger than twice the
propagated maximal error δ (the absolute error can be both positive and negative) to with certainty
contain compensation information not only caused by experimental errors. The derivation is
according to reference 38.
Krug RR, Hunter WG, Grieger RA: Statistical interpretation of enthalpy-entropy compensation.
Nature 1976, 261(5561): 566-567.
McBane GC: Chemistry from telephone numbers: The false isokinetic relationship. J Chem Educ 1998,
75(7): 919-922.
28
Enthalpy-entropy compensation
Paper II
OH
O
O
+
O
CALB
O
Solvent
6
Solvent
6
+
Decaline
Cyclopentane
Tetrahydrofuran
Dichloromethane
O
Supercritical CO2
Hexane
1,4-Dioxane
Acetone
Carbon disulfide
0
-2
-4
‡
O
O
O
O
S C S
-1
T ΔS / kJ mol
O C O
Cl
-6
Cl
-8
-10
-26
-24
-22
‡
-20
-18
-16
-1
ΔH / kJ mol
Figure 15 Activation entropy ΤΔS‡ as a function of activation enthalpy ΔH‡ for a
transacylation reaction catalysed by Candida antarctica lipase B performed in nine different
solvents. Clear enthalpy-entropy compensation was seen with an R2 of 0.94. If the outlier,
supercritical CO2, was removed, R2 increased to 0.98. Molecular structures of the
solvents are depicted in the graph.
will also contribute to an apparent linear enthalpy-entropy compensation curve.
Measurements of kinetic parameters are often limited to a few orders of magnitude,
so the outcome will be a data set displaying only small variations in ΔG‡. Since
ΔG‡ = ΔH ‡ - TΔS‡ a data set where the differences in activation free energy between
different species is small, enthalpy and entropy will automatically appear to follow a
linear compensating pattern.42
In close relation to enthalpy-entropy compensations are isokinetic relations.
They are present if there exists a temperature such that all analysed reactions proceed
at the same reaction rate. Graphically this can be seen as a common point of intersection in a plot of activation free energy ΔG‡ versus temperature. A plot of ΔG‡
versus temperature for the solvent data set in Figure 15 is presented in Figure 16. No
common intersection point for the reactions was seen, and thus no isokinetic relation
was present.
42
Liu L, Guo QX: Isokinetic relationship, isoequilibrium relationship, and enthalpy-entropy
compensation. Chem Rev 2001, 101(3): 673-695.
29
Enthalpy-entropy compensation
Paper II
OH
O
O
+
O
CALB
O
Solvent
6
Solvent
6
+
Decaline
Cyclopentane
Tetrahydrofuran
Dichloromethane
O
Supercritical CO2
Hexane
1,4-Dioxane
Acetone
Carbon disulfide
O C O
-13
O
Cl
Cl
-14
S C S
O
-15
ΔG
‡
/ kJ mol
O
O
-1
-16
-17
-18
270
320
370
420
T /K
Figure 16 Activation free energy ΔG‡ as a function of temperature for a transacylation
reaction catalysed by Candida antarctica lipase B performed in nine different solvents. The
reactions, lacking a common intersection, did not fulfil an isokinetic relationship.
Molecular structures of the solvents are depicted in the graph.
As a contrast, data from a series of transacylation reactions (Paper VI) are
shown in Figure 17. Also in this case enthalpy-entropy compensation is seen, but as
opposed to the previous data set, an isokinetic relationship was also present.
Enthalpy-entropy compensations and isokinetic relations are often confused as
being different expressions of the same phenomenon, but are actually independent
of each other.42 A data set showing an enthalpy-entropy compensation pattern does
not necessarily show an isokinetic relationship, exemplified above in Figure 15 and
Figure 16. Neither does a data set displaying an isokinetic relation by necessity show
an enthalpy-entropy compensation curve.42
30
Enthalpy-entropy compensation
Paper VI
OH
O
O
+
n
n=2-10
CALB,
cutinase or
HCl
O
Solvent
+
O
n
n=2-10
Solvent
a)
Hexane
Toluene
Acetonitrile
OH
b)
69
C8
C4
C12
45
C11
C7
C9
C10
‡
T ΔS / kJ mol
65
C4
-1
ΔG ‡ / kJ mol-1
63
C6
35
C9
67
61
C5
59
25
-30
-25
-20
‡
-1
ΔH / kJ mol
-15
57
270
320
370
420
T/K
Figure 17 a) Activation entropy ΔS‡ as a function of activation enthalpy ΔH‡ for
transacylation reaction catalysed by Candida antarctica lipase B of nine homologous esters.
Clear enthalpy-entropy compensation was seen with an R2 of 0.99. Data labels indicate
acyl chain lengths. b) The reactions showed an isokinetic relationship, with C4 and C9 as
outliers.
The physical meaning of isokinetic relationships is not clear. It has been suggested that isokinetic behaviour displayed by a set of reactions implies the reactions
to proceed with the same reaction mechanism, and that reactions lacking an isokinetic
behaviour will proceed through different transition states. This interpretation of the
isokinetic relationship has though been questioned.42
As a third example of enthalpy-entropy compensation, data from solubility
measurements for fatty acid esters as partitioned between hexane and acetonitrile
(Paper VI) is shown in Figure 18. The data showed an excellent compensation, and
analysis according to equation 1 shows at hand a reasonable likelihood for it to
contain compensatory pattern not governed only by experimental errors.43
43
The data set was acquired using three measurements over a temperature interval of 310-340 K. The
only source of experimental error comes from the gc analyses, estimated to be less than 2%. The
propagating error can then be calculated to 3.5 kJ/mol which is a factor 3 smaller than the measured
range of enthalpies.
31
Enthalpy-entropy compensation
4
O
C3
O
2
C4
-6
-4
-2
C5
0
0
n
n=2-10
-1
T ΔS / kJ mol
-1
ΔH / kJ mol
C6 2
4
6
8
10
C7
-2
C8
C9
-4
C10
C11
C12
-6
Figure 18 Entropy ΤΔS as a function of enthalpy ΔH for the distribution of substrates
in a two-phase system consisting of acetonitrile and hexane. Data labels indicate acyl
chain lengths.
The compensation between ΔH and ΔS was no longer linear, but instead displayed a hyperbolic appearance. This general shape of enthalpy-entropy compensation curve has been predicted by Westwell, and others.44,45 The origin of the curved
shape can be understood from the physical meaning of ΔH and ΔS: In any process,
there is a limit on the entropy change achievable – it is impossible to lose more than
all degrees of freedom, while the change in enthalpy is not subjected to the same
strong cut-off. Reasons to why this compensation curve shape is not always seen
could be, besides statistical problems, that the experimental enthalpy measurements
are performed under a too narrow interval. It could also depend on that factors other
than direct molecular interactions between the reacting species such as solvent
reorganisation processes are exerting a stronger influence on the reaction thermodynamics.
To conclude, investigations of enthalpy-entropy compensation relationships
demands experimental data of high quality covering several orders of magnitudes. If
this is not fulfilled, a possible extrathermodynamic relationship between enthalpy and
entropy can easily be lost under co-varying errors propagated from the experiments.
44
45
Westwell MS, Searle MS, Klein J, Williams DH: Successful predictions of the residual motion of
weakly associated species as a function of the bonding between them. J Phys Chem 1996, 100(39):
16000-16001.
Dunitz JD: Win some, lose some - enthalpy-entropy compensation in weak intermolecular
interactions. Chem Biol 1995, 2(11): 709-712.
32
Enthalpy-entropy compensation
Further, there is no implicit reason for the compensation to be linear. Instead, for a
situation where molecular interactions between reacting molecules dominate over
other contributions to the thermodynamic parameters a hyperbolic compensation
curve is suggested. From the work presented in this thesis, one instance of data
showed enthalpy-entropy compensation likely not to be governed by statistical
errors, and in that case a hyperbolic compensation pattern was also seen.
33
Appendix A – Derivation of rate equations for dead-end and mixed-type inhibition
APPENDIX A – DERIVATION OF RATE EQUATIONS FOR DEADEND AND MIXED-TYPE INHIBITION
All rates are initial and in the absence of product. One-substrate rapid-equilibrium
conditions are assumed.
Dead-end (competitive) inhibition
An inhibitor I competes with the substrate S for the free enzyme.
dissociation constants for the inhibitor and substrate, respectively.
and
are the
where
and
The reaction rate is given as:
Divide both sides with
Divide the right hand side with [E]
Simplify using the equilibrium constant
definitions
Reformulate to
Identification with the Michaelis-Menten
equation yields
34
Appendix A – Derivation of rate equations for dead-end and mixed-type inhibition
In dead-end inhibition, the inhibitor concentration will affect the apparent substrate
dissociation constant KS but not the apparent maximal rate Vmax.
Mixed-type inhibition
An inhibitor I acts both as a dead-end (competitive) inhibitor and as a noncompetitive inhibitor. The dead-end inhibitor associates with the free enzyme E and
prohibits further binding. The non-competitive inhibition allows binding in binding
site other than the one used for the dead-end inhibition, such that substrate
binding – and reaction – still is allowed. The substrate dissociation constant towards
the enzyme-inhibitor complex will differ from its dissociation constant towards the
free enzyme with a factor β. Analogously, the substrate turnover number from the
enzyme-inhibitor-substrate complex has changed a factor α from the one without
bound inhibitor.
,
where
,
,
and
The total reaction rate is given as
Divide both sides with
35
Appendix A – Derivation of rate equations for dead-end and mixed-type inhibition
The rate can be formulated as
Identification yields
In the mixed-type inhibition, both Vmax and KS will vary with inhibitor
,
will equal
. That happens
concentration. In the special case where
when the turnover number going from the ESI complex to product is the same as
for going from ES to product.
36
Acknowledgements
ACKNOWLEDGEMENTS
Den här avhandlingen har endast ett författarnamn, men hade inte
kommit till stånd utan många andras medverkan.
Först och främst vill jag rikta ett varmt tack till min handledare
Kalle Hult. Jag är glad och tacksam over att ha fått doktorera för dig.
Tack för att jag fått dela ditt genuina intresse för vetenskap och
undervisning, och tack för all roliga diskussioner vi haft. Det har varit
en bra tid!
I also want to thank all my co-authors, for nice collaborations and
interesting projects.
Ett stort tack till er som var med och hjälpte till i det intensiva
skrivkaoset (och innan det började…): Marianne, Jenny, Joke, Fredrik
och Maria. Tack för coachning, planering, glada tillrop, vänliga ord,
morötter och piskor, textläsning och layout. Ni är sanna hjältar!
Tack till alla nuvarande och tidigare gruppmedlemmar. Jag är glad
att ha fått jobba med er och önskar er lycka till i framtiden. Nu skriver
jag inte ner vad ni heter, men jag tänker på er allihop.
Slutligen, tack till er som finns i mitt liv utanför KTH. Mina kära
vänner Hanna, Johanna, Pirjo och Daniel. Mina föräldrar Ninnie och
Leif, mina systrar Hillevi och Linnea med familjer. Snart ses vi lite mer!
37