Enzyme Substrate Solvent Interactions

Home , Solvent effects, Substrate (chemistry)

Enzyme substrate solvent interactions

A case study on serine hydrolases

Linda Fransson

Doctoral thesis

Royal Institute of Technology School of Biotechnology Stockholm 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 fettsyra- estrar 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-entropi- kompensation. Ett eventuellt fysikaliskt innehåll dränks dock lätt av samvarier- ande 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 enzyme- catalysed 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 O Solvent R1 O R1 CALB Hexane OH O + O 2 + O 1 R 6 Solvent R2 6 R =CH3 or C2H5 2 R =C2H5, C3HCHCH3 or C(CH3)3 Paper II O Solvent O Supercritical CO2 OH CALB + O + Decaline Hexane O Solvent O Cyclopentane 1,4-Dioxane 6 6 Tetrahydrofuran Acetone Dichloromethane Carbon disulfide Paper III O CALB O Effector OH + + 2-Pentanone OH 3-Pentanone O O 2-Methyl-2-pentanol 3-Methyl-3-pentanol 2-methylpentane 3-methylpentane Paper IV O Effector OH Water O CALB O + + O OH

Paper V O N O N Solvent 2 O BSE2 O 2 H2O + + Water Water X HO XH X=O or NH

Paper VI O CALB, O Solvent cutinase or + Hexane O HCl O OH + n n OH Toluene n=2-10 Solvent n=2-10 Acetonitrile

1 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 Menger FM: An alternative view of enzyme catalysis. Pure Appl Chem 2005, 77(11): 1873-1886. 2 Blow D: So do we understand how enzymes work? Structure Fold Des 2000, 8(4): R77-R81. 3 Pauling L: Nature of forces between large molecules of biological interest. Nature 1948, 161(4097): 707-709. 4 Eyring H: The Activated Complex in Chemical Reactions. J Chem Phys 1935, 3(2): 107-115. 5 Fong FK: A successor to transition-state theory. Acc Chem Res 1976, 9(12): 433-438. 6 The situation is analogous to the simplification of the Michaelis constant, when KM is approxi- mated to the equilibrium constant KS. 7 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 Storm DR, Koshland DE: Indication of the magnitude of orientation factors in esterification. J Am Chem Soc 1972, 94(16): 5805-5814. 9 Bruice TC, Benkovic SJ: Chemical basis for enzyme catalysis. Biochemistry 2000, 39(21): 6267- 6274. 10 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. 11 Cleland WW, Frey PA, Gerlt JA: The low barrier hydrogen bond in enzymatic catalysis. J Biol Chem 1998, 273(40): 25529-25532. 12 Sutcliffe MJ, Scrutton NS: Enzyme catalysis: over-the-barrier or through-the-barrier? Trends Biochem Sci 2000, 25(9): 405-408. 13 Benkovic SJ, Hammes-Schiffer S: Biochemistry - Enzyme motions inside and out. Science 2006, 312(5771): 208-209. 14 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 The origin of enzyme catalytic power

Paper VI O CALB, O cutinase or + O HCl O OH + n n OH n=2-10 Hexane n=2-10

a) Free energy ΔG‡ of activation b) Free enthalpy ΔH‡ of activation c) Free entropy -TΔS‡ of activation 100 100 100 HCl HCl Cutinase Cutinase CALB 80 80 Hexane 80

60 60 60

ΔG‡/ kJ mol-1 ΔH‡/ kJ mol-1 −ΤΔS‡ / kJ mol-1 40 40 40

HCl 20 Cutinase 20 20 CALB

0 0 0 C4 C5 C6 C7 C8 C9 C10 C11 C12 C4 C5 C6 C7 C8 C9 C10 C11 C12 C4 C5 C6 C7 C8 C9 C10 C11 C12 Acyl chain length Acyl chain length Acyl chain length 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.

4 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 acid- catalysed 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 non- enzymatic 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 Forman-Kay JD: The 'dynamics' in the thermodynamics of binding. Nat Struct Biol 1999, 6(12): 1086- 1087. 16 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 O Solvent R1 O R1 CALB Hexane OH O + O 2 + O 1 R 6 Solvent R2 6 R =CH3 or C2H5 2 R =C2H5, C3HCHCH3 or C(CH3)3

‡ ‡ ‡ sec-alcohol E ∆∆G ∆∆H T∆∆S (298 K) ∆R-SV (298 K) (kJ/mol) (kJ/mol) kJ/mol) (Å3) 3-hexanol 340 -14.4 -9.0 +5.5 +19 2-butanol 8.3 -5.3 -10.7 -5.4 -21 3-methyl-2-butanol 810 -16.6 -24.3 -7.7 -46 3,3-dimethyl-2-butanol 460 -15.2 -20.4 -5.2 +27

For the three substrates 2-butanol, 3-methyl-2-butanol and 3,3-dimethyl-2- butanol 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-2- butanol 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 O O CALB + O O OH + n n OH Hexane n=2-10 n=2-10 a) b) 45 4 45 4 Activation enthalpy Activation entropy Rate constant Rate constant 40 40 3 3 35 35

30 2 30 2 ‡ −Τ ΔS ‡ ΔH k cat /K M k cat /K M -1 / kJ mol-1 relative C7 / kJ mol relative C7 25 25 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 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. 18 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 in- corporating 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 valinyl- tRNA 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 Linus Pauling, referenced by Nureki et al 23 20 Andrews PR, Craik DJ, Martin JL: Functional-group contributions to drug receptor interactions. J Med Chem 1984, 27(12): 1648-1657. 21 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. k −ΔG 22 Calculated as 1 = e RT k2 23 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. 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 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. 25 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. 26 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. 27 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 O O CALB + O O OH + n n OH n=2-10 Hexane n=2-10 a) Candida antarctica lipase B b) Humicola insolens cutinase 500 6

400

4 300

k -1 -1 k /K / M-1s-1 cat/KM / M s cat M 200 2

100

0 0 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 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 pro-

12 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 inter- ference. 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): 241- 246. 15 On solvent effects on enzymatic catalysis

Paper VI O O CALB + O O OH + n n OH Solvent n=2-10 n=2-10 a) Hexane b) Acetonitrile 4 4

3 3 k -1 -1 k /K / M-1s-1 cat/KM / M s cat M 2 2 k cat /K M k cat /K M relative C7 relative C7

1 1

0 0 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 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 C4 C5 C6 C7 C8 C9 C10 C11 C12 Δ G hexane-AcN / kJ mol-1 -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 O O CALB + O O OH + n n OH n=2-10 Solvent n=2-10 4

AcN corrected Hexane 3

k cat /K M relative C7

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-3- pentanol, 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 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. 31 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 O CALB O Effector OH + + 2-Pentanone OH 3-Pentanone O O 2-Methyl-2-pentanol 3-Methyl-3-pentanol 2-methylpentane 3-methylpentane a) b)

c) d)

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-2- pentanol in the active site of Candida antarctica lipase B. c) Superimposed structures of 2- pentanone. 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 2- pentanol 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 enzyme- substrate 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 Effector OH Water O CALB 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 non- competitively 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 app models show an apparent dissociation constant KS which deviates from the true constant KS , but only the model containing non-competitive inhibition has an effect app on the apparent maximum rate Vmax . The pure competitive model instead shows an 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 a) Pure competitive (dead-end) inhibition b) Competitive and non-competitive (mixed- type) 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 O N O N Solvent 2 O BSE2 O 2 H2O + + Water Water X HO XH X=O or NH a) B. subtilis esterase 2. Wild-type b) B. subtilis esterase 2. Glu188Phe mutant

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 O Solvent O Supercritical CO2 OH CALB + O + Decaline Hexane O Solvent O Cyclopentane 1,4-Dioxane 6 6 Tetrahydrofuran Acetone Dichloromethane Carbon disulfide

1000

cis-Decalin Cyclopentane 800 Hexane

Tetrahydrofurane Carbon Acetone 600 disulfide E 1,4-Dioxane Dichloro- methane

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 straight- forward: 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 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): 2335- 2341. 36 Krug RR, Hunter WG, Grieger RA: Enthalpy-entropy compensation .2. separation of chemical from statistical effect. J Phys Chem 1976, 80(21): 2341-2351. 37 Cornish-Bowden A: Enthalpy-entropy compensation: a phantom phenomenon. J Biosci 2002, 27(2): 121-126. 38 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. 39 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 ‡ ‡‡ ΔΔSH ‡ − TT12 k 21 T ‡ ΔH kTB kTB R RT Δ=HR ln Δ=SR +ln keei = yielding and where kB is the Bolzmann constant, h h TT21− kT 12 Thk1 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

‡ TT ΔΔHR >> 4 21 α 1 TT21− 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 TT 4R 21 α . The temperature interval used in the kinetics measurements varied TT21− 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 pro- perty 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

‡ ‡ TT(1+α ) k T ()Δ+Hkhδα (1) + TT Δ+=HRδ 12ln 21, and Δ+=SR‡ σ +ln 11When α <<1, δ = 2R 12 α . and TT−−(1α ) kT TkT TT− 21 12 11B 21

3TT21− ‡ ‡ σδ= . If the errors δ and σ dominate over the true variation in ΔS versus ΔH , a straight line 2TT12 3TT− with the slope 21 will be achieved in the compensation plot. An enthalpy-entropy compensation 2TT12 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. 40 Krug RR, Hunter WG, Grieger RA: Statistical interpretation of enthalpy-entropy compensation. Nature 1976, 261(5561): 566-567. 41 McBane GC: Chemistry from telephone numbers: The false isokinetic relationship. J Chem Educ 1998, 75(7): 919-922. 28 Enthalpy-entropy compensation

Paper II O Solvent O Supercritical CO2 OH CALB + O + Decaline Hexane O Solvent O Cyclopentane 1,4-Dioxane 6 6 Tetrahydrofuran Acetone Dichloromethane Carbon disulfide

O -2 O O

O -4 S C S

T ΔS ‡ / kJ mol-1 O CO Cl Cl -6

-8

-10 -26 -24 -22 -20 -18 -16 ΔH ‡ / kJ mol-1 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, 2 supercritical CO2, was removed, R 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 O Solvent O Supercritical CO2 OH CALB + O + Decaline Hexane O Solvent O Cyclopentane 1,4-Dioxane 6 6 Tetrahydrofuran Acetone Dichloromethane Carbon disulfide

O CO -13 O Cl Cl -14 S C S

O -15 ΔG ‡ / kJ mol-1 O O

-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 O CALB, O Solvent cutinase or + Hexane O HCl O OH + n n OH Toluene n=2-10 Solvent n=2-10 Acetonitrile a) b) C8 69 C12 C4 C9 C7 45 C11 67 C9 C10 65

‡ -1 C4 T ΔS / kJ mol ΔG ‡ / kJ mol-1 63 C6 35

C5 61

25 57 -30 -25 -20 -15 270 320 370 420 ΔH ‡ / kJ mol-1 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 C3 O

O n 2 T ΔS / kJ mol-1 n=2-10 C4 C5 ΔH / kJ mol-1 0 -6 -4 -2 0C6 2 4 6 8 10

C7 -2 C8 C9 C10 -4 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 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. 45 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 DEAD-

END 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. and are the dissociation constants for the inhibitor and substrate, respectively.

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 non- competitive 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 concentration. In the special case where , will equal . That happens 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!