Monophosphate and Thiamine Pyrophosphate : a Quantumchemical Description

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The coenzymes cyclic adenosine 3',5'-monophosphate and thiamine pyrophosphate : a quantumchemical description

Citation for published version (APA): Scheffers - Sap, M. M. E. (1979). The coenzymes cyclic adenosine 3',5'-monophosphate and thiamine pyrophosphate : a quantumchemical description. Technische Hogeschool Eindhoven. https://doi.org/10.6100/IR25489

DOI: 10.6100/IR25489

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Download date: 25. Sep. 2021 THE COENZYMES CYCLIC ADENOSINE 3', 5' -MONOPHOSPHATE AND THIAMINE PYROPHOSPHATE

A quantumchemical description

M. M. E. SCHEPPERS-SAP CO-ENZYMEN CYCLISCH ADENOSINE 3 1 ,5 1 -MONOFOSFAAT EN C:.'fiAMINE PYROFOSFAAT. EEN QUANTUMCHEMISCHE BESCHRIJVING.

Xaast water zijn proteinen (eiwitten) essentiële bestand delen van alle levende organismen, van de meest eenvoudige tot de meest complexe toe. In levende organismen hebben proteinen verschillende functies; ze treden op als: - e~zymen, dit zijn stoffen die scheikundige reacties kunnen versnellen of vertragen. Het zijn dus katalysatoren. - ~ntistoffen, die als wapen dienen in het arsenaal van verdedigingsmechanismen van organismen. - ~ou~stenen van lange eiwitketens. - :ransportmiddeZ, d.w.z. ze zijn verantwoordelijk voor het vervoer van belangrijke stoffen, o.a. zuurstof, in levende organismen. - scheikundige boodschappers. Een voorbeeld vormen de hor monen die chemische reacties laten plaatsvinden of op houden zodanig, dat levensprocessen mogelijk worden. :oals hierboven al is aangegeven, worden proteinen met katalytische activiteit enzymen genoemd. Vele enzymen hebben om werkzaam te kunnen zijn een, van proteinen ver schillend, deeltje nodig. Daar deze deeltjes mede verant Koordelijk zijn voor het totale reactieverloop noemt men ze co-enzymen. Het werk dat in dit proefschrift is beschre ven heeft betrekking op twee co-enzymen, namelijk cyclisch adenosine 3' ,5'-monofosfaat (afgekort: c-AMP) en thiamine pyrofosfaat (afgekort: TPP).

CycZisch adenosine 3',5'-monofosfaat In hogere organismen, zoals de mens, treedt c-AMP op als tweede boodschapper van veel hormonen. Hormonen (eerste boodschappers) die een celwand niet kunnen passeren, zijn toch in staat processen in de cel te beïnvloeden door er voor te zorgen, dat via de wand van de cel de boodschap doorgegeven wordt, waardoor dan het c-AMP i<~ordt gevormd in de cel. Het c-AMP activeert of inactiveert dan op zijn beurt enzymen in de cel en is zo in staat indirect vele processen te regelen. Na het bewerkstelligen van de ge wenste effecten in de cel dient c-AMP uitgeschakeld te worden. Dit gebeurt 6f doordat het door de cel onveranderd \vordt uitgescheiden 6f doordat het door enzymen omgezet wordt in adenosine 5'-monofosfaat (afgekort: 5'-ANP). Deze laatste reactie wordt als volgt weergegeven:

0 _::, 05'~~· 0--~p/ OH HO/ OH c-AMP water 5'-AMP R=adenine

Bij de vorming van 5'-AMP uit c-AMP komt veel warmte vrij. De hoeveelheid die vrij komt is groter dan bij reacties van soortgelijke verbindingen. Met behulp van computerberekeningen aan eenvoudige molecuulmodellen van c-M4P en 5'-AMP (R = H, waterstof) is geprobeerd een verklaring te vinden voor die grotere hoeveelheid warmte. De berekeningen zijn gedaan aan een voudigere moleculen omdat de rekentijd anders veel te groot wordt. De gegevens verkregen uit de berekeningen tonen aan dat het warmte-effect kan worden toegeschreven aan twee factoren: 1) het verschil in ruimtelijke vorm van de vijfring in c-AMP en 2) het verschil in aanhechting van watermole culen (de stoffen zijn opgelost in water) aan verschil lende kanten van de deeltjes 5 '-AMP en c-AMP. In 5'-AMP kan zich een watermolecule bevinden tussen de zuurstofatomen (0) op positie 1' en 5'. Dit is in c-AMP niet mogelijk, omdat de afstand tussen deze twee atomen te groot is. :~iamine pyrofosfaat TPP is een algemeen voorkomend co-enzym in levende orga nismen. Het is een voor de mens noodzakelijke voedings stof ter voorkoming van beriberi (verlammingsziekte). TPP treedt op als co-enzym bij reacties van ketocarbonzuren (bijvoorbeeld: pyruvaat deeltje CH 3COCOO-), waarbij kool zuurgas vrijkomt. De manier waarop TPP functioneert is ontdekt door R. Breslow, die vaststelde dat het reactieve centrum (hier vinden de reacties plaats met andere stof fen) zich bevindt op het koolstofatoom (positie 2) tussen stikstof (N) en zwavel (S). Uit proeven door R. Ereslow uitgevoerd aan de vijfring van TPP en erop lijkende vijf ringen is gebleken, dat de vorming van een reactief cen trum op positie 2 bij een vijfring waarin S vervangen is door een stikstofatoom (N, imidazolium systeem) moeilijker verloopt dan bij de thiazolium ring (dit is de naam van de vijfring in TPP). Deze bevindingen zijn echter tegen-

strijdig met spectrametrische gegevens van deze twee vijf ringen, waaruit men namelijk kan afleiden dat de vorming van het reactieve centrum in beide gevallen even snel zou moeten gaan. Aan eerder genoemde vijfringen en de te vormen vijfringen met een reactief centrum zijn computerberekeningen gedaan om te achterhalen welke factoren verantwoordelijk z n voor de, relatief gezien, grote snelheid waarmee bij het thiazolium systeem het reactieve centrum gevormd wordt. De gegevens tonen aan, dat het thiazolium systeem de electrenen (dit zijn de deeltjes die zorgen voor de bin- dingen tussen de atomen) die betrokken zijn bij de vorming van het reactieve centrum op een zodanige wijze heeft op geborgen, dat ze gemakkelijker te gebruiken zijn.

M.M.E. Scheffers-Sap Berlicum, 14 december 1979 THE COENZYMES CYCLIC ADENOSINE 3', 5' -MONOPHOSPHATE AND THIAMINE PYROPHOSPHATE

A quantumchemical description

PROEFSCHRIFT

ter verkrijging van de graad van doctor in de technische wetenschappen aan de Technische Hogeschool Eindhoven, op gezag van de rector magnificus, prof. ir. J. Erkelens, voor een commissie aangewezen door het college van dekanen in het openbaar te verdedigen op vrijdag 14 december 1979 te 16.00 uur

door

MARIA MARGARETHA ELISABETH SCHEFFERS-SAP

geboren te Tilburg

DRUK: WIBRD HELMONO DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOREN PROF. DR. H.M. BUCK EN PROF. DR. U.K. PANDIT

"Would you tell me, please, which way I ought to go from here?" "That depends a good deal on where you want to get to," said the Cat. "I don't much care where-" said Alice. "Then it doesn't matter which way you go," said the Cat. "-so long as I get somewhere," Alice added as an explanation. "Oh, you're sure to do that," said the Cat, "if you only walk long enough."

uit Alice's Adventures in Wonderland Contents

Chapter I General introduetion 1.1 Coenzymes 11 I.Z Cyelio adenosine 3',5'- monophosphate 12 I.3 Thiamine pyrophosphate 16

I.4 The va~idi of quantum- ohemioal ealoulations 17 Heferenoes 20

Chapl:er 11 Summary of the all-valenee methods used, the Extended-Hückel, CND0/2 and ab-initio method 11.1 Introduetion 21 II.Z The Extended-Hüekel method 1!.2.1 Theory 23 II.2.2 Parameters the ordinary and iterative EH calculations 25 II.3 The Complete NegZeet Differential Overlap method 11.3.1 Theory the CNDO method 26 II.3.2 Parametrization for the CND0/2 methad 29 II.3.3 The GEOMO program 30 11.4 Ab-initia calculations 31 11.5 Mulliken population ana is 32 II.6 Calculation of the solvation enthalpy 33 Heferences 36 Chapter 111 The solvent effect on the enthalpy of hydralysis of c-AMP 111.1 Introduetion 38 111.2 Geometriee of phoephate dieetere 41 111.3 The effeat of the solvent and the ribose ring puaker ing on the net enthalpies of hydralysis 111.3.1 Calaulation of net enthalpies of hydra lysis and net solvation enthalpies 46 111.3.2 Ribose ring puaker ing 51 111.4 Diecuesion 51 Referenaei and notes 55

Chapter IV , The influence of solvation and ribose ring puckering on the enthalpy of hydralysis of c-AMP IV.1 Hydragen bonding 58 1V.2 The water dimer 60 1V.3 Hydration sahemes of models of a-AMP • 5 1 -AMP and 3 '-AMP 62 1V.4 The aontribution of sol vation and ribose ring puakering to the net en thalpy of hydralysis of a-AMP 68 1V.S Hydragen bonding ae a model for the dynamias of enzyme aoenzyme aomplexes 69 Referenaes 72 Chapter V The acidity of thiamine pyro phosphate and related systems V.l IntPoduction V.1.1 Ristoriaal background 74 V.1.2 Relation structure of TPP to the oata- lytio aativity 77 V.2 CND0/2 calculations on 1,3- azolium systems V. 2. 1 d-Orbital aonjugation 80 V.2.2 Bonding and electron densities 85 V.3 Solvation enthalpies 91 V.4 The use of an MO desaription for the transition state and an estimation of the aati vation enthalpy V.4.1 The aharaater of the transition state 91 V.4.2 Estimation of the aativation enthalpy 92 V.4.3 H-D exchange reaations of arenes 95 Referenaes and notes 97

Chapter VI Thiamine pyrophosphate-catalyzed decarboxylation of pyruvate anion VI.l Introduetion 100 VI.2 The reaation saheme for the pyruvate deaarboxy lation reaation 101 VI.3 The net reaation enthal pies of pyruvate deoar

boxylations ~ith 1,3- azolium systems 103 VI.4 TPP as aocarboxylase 108 References 110 Appendix A 112

Appendix B 116

Summary 122

Samenvatting 124

Curriculum vitae 126

DankW"oord 127 The work described in this thesis has been financially supported by Unilever Research, Vlaardingen, The Netherlands CHAPTER I

General introduetion

I. 1 Coenzymes

Protein molecules serve several functions in living systems. Perhaps their most striking biochemical role is their ability to affect in a specific and efficient manner, the rates of the wide spectrum of reactions that constitute the dynamic aspect of the process of life. Proteins possess ing such catalytic activity are called enzymes 1 (for a classification, see Table I). They are distinguished from ordinary proteins by having active sites, which are res ponsible for the action of the enzymes. Some enzymes depend for activity only on their structures as proteins, while others also require one or more nonprotein compounds, called co;actors. Cofactors fall into two groups, the metal co factors and the organic cofactors. The latter group, which

Table 1.1 Classes of enzymes and types of reaction catalyzed

enzyme type of reaction catalyzed oxireductases oxidation-reduction transferases group transfer reactions hydrolases hydralysis lyases the addition of groups to double honds or vioe versa is omeras es isomerizations ligases condensation of two molecules coupled with cleavage of the pyrophosphate bond of ATP

11 are called ooenzymes 1 encompass a wide range of compounds which are related to vitamins. The catalytically active enzyme-cofactor complex is called the holoenzyme. When the cofactor is removed, the remaining protein, which is catalytically inactive by itself, is called apoenzyme. In case of a very tightly bound enzyme-coenzyme complex, the coenzyme is usually referred to as a prosthetio group. lfuereas coenzymes regulate chemica! reactivity, enzymes related to these coenzymes control the stereospecificity, 1 as is very impressively demonstrated for NADH • All enzymes exhibit various features that could conceivably be elements in the reguiatien of their activity in living cells. The rates of enzymatic reactions depend on: -the pH in the cell, -the substrate concentrations, -the cofactors. Some enzymes possess, in addition, properties that specifically endow them with regulatory roles in metabolism. Such more highly specialized forms are called regulatory enzymes. One class cernprises the allosterio enzymes, whose catalytic activity is modulated through the noneavalent binding of a specific compound (cofactor and termed an allosterio effector) at a site on the protein other than the catalytic site. The mechanism of action of an allasterie effector can be a direct or an indirect one. In this thesis attention has been given to two im portant coenzymes, namely cyclic adenosine 3' ,5'-monophos phate and thiamine pyrophosphate.

1.2 Cyolio adenosine 3',5'-monophosphate

Cyclic adenosine 3',5'-monophosphate 2 (c-~1P, Figure 1.1) is a universally occurring nucleotide of immense bio logica! importance. It has been first isolated in 1959 by Butherland and coworkers as part of their investigation on the mechanism of action of certain hormones, such as adrenaline, in regulating carbohydrate metabolism. On basis of their study they proposed that the immediate action of adrenaline and many other horrnanes lies in the activatien of the enzyme which is responsible for the production of

12 1.1 c-AMP

c-A~•P. In turn, c-AHP controls the activity of other enzymes, frequently by an allasterie activation. Since c-AMP trans mits and amplifies, within cells, the chemical signals delivered via the blood by horrnanes (first messengers), it is called a second messenger (Figure 1.2). In the breakdown of glycogen to blood glucose in the li ver ce 11, c-AMP acts as an all os teric effector (Figure 1.3). The enzyme protein kinase is inactive until c-AMP is present. The activated kinase perfarms the same function for a related enzyme, phosphorylase kinase. This enzyme activates in turn the phosphorylase. The result of this final activatien is the breakdown of glycogen. Whenever glycogen is degraded, it would be a waste of energy to continue the synthesis of additional glycogen. A specific enzyme, however, mediates the synthesis of glycogen, i.e. glycogen synthetase. At the time when some c-AMP molecules are initiating the reaction for the conversion of glycogen into glucose, others are generating the inactive form of glycogen synthetase. The concentratien level of c-AMP in the cell is re gulated by the action of two enzyrnes. c-AMP is formed from ATP by the action of adenyl cyclase, a rnernbrane-bound enzyrne, and it is converted into adenosine 5'-monophosphate (5'-AMP) by a specific phosphodiesterase (Figure 1 .4). The hydralysis of c-AMP into 5'-AMP is a highly exothermic

13 hormones ( first messenger l

adenyl cyclase I receptor} / ATP c-AMP I secend""" messenger l /!~ biochemica! responses (enzyme activation, gene expression l /l~ physiologicol respon,ses (glycogenolysis. membrone permeability l

Figure 1.2 The seaond messenger aonaept

c AMP 5'-AMP phosphodiesterase

odenyl -PP1 • 2P; pyrophosphatase ~;1 'Y'~+ IQSe ~ 92 adenylate kinase

ATP

Figure 1.4 Synthesis and aonversion of a-AMP

14 receptor cell membrane

ATP c-AMP +PPi L protein kinase _____,_ protein kinase + c-AMP-@ @:XID (inactive) © (active)

ATP + phosphorylase kinase ---- phosphorylase + ADP 2 ( inactive) Ca + kinase (active)

ATP + phosphohydrolase b phosphohydrolase a + ADP ( inactive) ( active)

glycogen + Pi glucose 1 - ph os phate ~ glucose 6- phosphate -glucose + Pi eelt membrane I blood glucose Figure 1.3 Conversion of glycogen into glucose 3 3 reaction • The large negative Gibbs free energy (-37.2 kJ/ mole) and enthalpy 3 (-46.4 kJ/mole) provides a thermadynamie harrier against the reversal through a phosphodiesterase.

I.3 Thiamine pyrophoaphate

When thiamine (vitamine B1) was isolated in 1911, the chief concern was its role in nutrition. Since then its structure has been elucidated, and its pyrophosphate ester was identified as cofactor for the enzyme pyruvate de carboxylase4. Thiamine pyrophosphate (TPP, Figure 1.5),

OH OH CH3 I I _ CH -CH -0 -P-O-P- 0 2 2 11 11 ~ 0 0 \_...5

Figure 1.5 TPP cocarboxylase, serves as a coenzyme for two classes of enzyrne-catalyzed reactions of the carbohydrate metabolism in which aldehyde groups are removed and/or transferred: (1) the decarboxylation of a-keto acids and (2) the for mation or degradation of a ketales (Figure 1.6). In these reactions the thiazole ring of TPP is a transient carrier 5 of a covalently bound "active" aldehyde group • The present view of the mechanisrn by which TPP functions as coenzyrne has arisen frorn the discovery that thiamine alone promotes nonenzyrnatic decarboxylation of pyruvate to yield acetaldehyde and carbondioxide. Studies of this model reaction disclosed that the hydragen at position 2 of the thiazole ring ionizes readily to yield a carbanion, which reacts with the carbonyl carbon atom of pyruvate at elevated temperatures to yield carbondi oxide and the hydroxyethyl derivative of the thiazole ring.

16 0 R, 11 / o- I R c H-C-OH 0 I c=o I ~ / R 0 11 co + R-C~ + R,-C-H + H+ 2 [ +TPP

11 :/ !-'' ~0C-H 0 0 0 OH 11 11 11 I R-C-H R- C- OH R-C-C-R I 2 H

1.6 Basic pathway for TPP-dependent reactions

The hydroxyethyl group may then undergo hydrolysis, to yield acetaldehyde, or react with an aldehyde to yield an acyloin. Thiamine must be supplied in the diet as precursor for TPP. TPP is formed by a transfer, catalyzed by a thiamine pyrophosphokinase, of the pyrophosphate group of ATP. When the supply of thiamine is restricted, then one or more enzymes requiring TPP will also be deficient. Thiamine is widespread among foods, but there is little synthesis by intestinal microorganisms, and symptons readily appear after dietary deprivation.

I.4 The validity of quantumchemiaal calculations Although molecular orbital (MO) calculations have been performed on a number of problems relevant to biochemical structure and the functions of biomolecules, it is well worth to consider the objections which can be raised to

17 such studies. Until quite recently, the principal problem in com bining experimental and theoretica! approaches to various subjects has been the gap between experimental data (solu tion of graatest interest) and theoretica! "free state" re sul ts. A fel~ attempts have been publisbed in li terature which explicitly incorporated solvent effects into the calculations. Yet it will be at least saveral more years before such efforts can provide data of accuracy equal to the experimental ones. Thus it is necessary to identify those theoretica! results which are subject to solvent effects. In this study theoretica! results of two types are presented: energies of reactions and electron densities. In a reaction, there are two basic quantities of interest: the relative energies of the compounds and the activatien energy of the reaction. While both of these quantities are subject to solvent effects without any doubt, the relativa total energies of the reaetauts and products will be difficult to predict in general. While thermodynamic properties (equilibrium constauts for, e.g. ionization, tautomerization and molecular asso ciation) may be very strongly solvent-dependent (as demon 6 strated by comparison of gas phase and solution basicities ) it appears unlikely that the intrinsic sleetronie structures of ions and molecules are dependent. It is well accepted that many functional groups undergo subtie electronic changes upon solvation, such as the spectroscopie changes accompanying hydrogen bonding. Yet there is no evidence from theory that attaching a hydrogen bonded water molecule, the electronic structure of a large molecule seriously changes. Furthermore, theoretica! "free state" calculations are capable of reproducing solution speetral characteris tics. For example, they accurately reflect changes as gross as covalent attachment of a proton to a nucleic 7 base in water , which is certainly a more significant change than adding a neutral non-covalently bound solvent molecule. It is then reasonable to assume that while the

18 solvent may cause subtle changes in the electrooie structure, it is highly unlikely and unprecedented that the polarity of a bond would be reversed on account of a change in sol vent alone. One should also note in this context the many successful correlations of experimental magnetic resonance parameters with simple charge or spin densities calculated 8 for the "free state" of a system • In Chapter II of this thesis a description is given of the quantumchemical methods which have been used. Especially the semiempirical CND0/2 metbod has been applied. Some results are supported by calculations using the ab- ~~tio method with the ST0-3G basis set. Furthermore, the metbod by which the solvation enthalpy has been calculated is discussed. Chapter III and IV present a study on the large exo thermic enthalpy of hydro is of c-AMP. It was found that a contribution to this large exothermic enthalpy is de li\·ered by a regio-specific hydratien in 5'-AHP and 3'-AMP a~~ via loss of strain in the ribose ring. In Chapter V the H-D exchange reactions of 1,3-azolium cations have been stuclied in order to explain the rate enhancement for the 1,3-thiazolium cations. It is clearly shown that the smaller amount of energy necessary for the 1,3-thiazolium cation to employ the appropriate a MO is responsible for the relatively small difference in exchange 9 rate between the 1,3-oxazolium and 1,3-thiazolium cation • In Chapter VI the reaction path for the decarboxylation of the pyruvate anion with 1,3-azolium cationsis described 9 •

19 Heferences 1. General information about enzymes and coenzymes: (a) H.R. Mahler and E.H. Cordes, "Biologica! Chemistry", Harper and Row, New York; 1971; (b) E. Buddecke, "Grundriss der Biochemie", W. de Gruyter, Berlin; 1974. 2. J.P. Jost and H.V. Rickenberg, Ann. Rev. of Biochemistry, 40, 741 (1971). 3. J.A. Gerlt, F.H. Westheimer and J.M. Sturtevant, J. Biol. Chem., 5059 (1975). 4. Reference la, pp 401-406. 5. J.J. Mieyal, R.G. Votaw, L.O. Krampitz and H.Z. Sable, Biochim. Biophys. Acta, lil• 205 (1967). 6. E.H. Ernett, Acc. Chem. Res., ~. 404 (1973). 7. W. Hug and I. Tinoco Jr., J. Am. Chem. Soc., 95, 2803 (1973); 96, 665 (1974). 8. J.B. Stothers, "Carbon-13 NMR Spectroscopy", Academie Press, New York; 1972; Chapter 4. 9. M.M.E. Scheffers-Sap and H.M. Buck, J. Am. Chem. Soc., lQ!, 4807 (1979).

20 CHAPTER 11

Su nunary o:f the all-valenee-elect rons methods used, the Extended-Hückel, CNDO /2 and ab-initio metbod

II.1 Introduetion The concept of molecular orbitals constructed from atomie orbitals is suggested as early as 1929 by Lennard-Jones 1 and subsequently referred to by Mulliken 2 as the ''linear combinat- tien atomie orbitals" (L.C.A.O.-MO) approach. The Hartree-Fock methad is a procedure for finding the best many electron wave function o/ (2.1) as an anti-symmetrized product of one electron orbitals ~-. In the case of molecules, l the functions (2.2) are molecular orbitals formed usually from a L.C.A.O.-MO approximation. p Z: ( -1 ) P [ 1); ( 1) a ( 1 )1); ( 2) 8 ( 2) .... ;f! Zn ( 2n) 8 ( 2n)] ( 2 . 1) \V 1 2 - \ /-:')".n. f p

l:c . Q ( 2. 2) i ]l ]ll ]l

The set of initial atomie functions $ is called the basis set. ]l Although the complete salution of the Hartree-Fock problom requires an infinite basis set, good approximations can be achieved with a limited number of atomie orbitals. The coeffi cients c . , which measure the contribution of each atomie or- ;n bital in the molecular orbitals, are parameters determined by a variational procedure, i.e. chosen so as to minimize the expression

E ( 2. 3)

21 where E represents the expectation value of the electronic energy associated with the Hamiltonian H of the given molecule. If only kinetic energy and Coulomb terms are taken into ac count and furthermore the Born-Oppenheimer approximation is assumed to be valid, the Hamiltonian operator is given by

2n 2n H L Hcore(~) + L 1/r ( 2. 4) ~ ~

Ec . (F -E.S ) = 0 v = 1 , ••••• , n (2.5) ~ ~1 ~\) 1 ~\)

in which n is the number of basis set functions used and

(2.6)

with S the overlap integral, <~ I~ >. ~V ~ V A non-trivial solution of the secular equation exists if

IF -E.S I = 0 (2.7) ~V 1 ~\) with the values Ei being the eigenvalues. Roothaan 3 has shown that for a closed shell system F~v is given by

F H~v +EL Pp [- !<~pJJvcr>] (2.8) ~\) pcr 0 where (2.9) and (2.10)

22 and P is the total electrooie popuiatien in the overlap 90 region between atomie orbitals p and o: ace 2 l: c .c . (2.11) i pl (jl The salution of the secular equation (2.7) requires the evaluation of the matrix terms F~v· The F~v's are functions of the coefficients c . and are evaluated by solving the ~1 secular equation. The Hartree-Feek procedure thus requires to make a preliminary guess of the values of the molecular popu lation distribution terms Ppa; these values are then used to calculate the matrix elements F and the next step is to )l\! solve the secular determinant. This, in turn, provides a better approximation to the wave function and an "improved" set of values P . The process is repeated until no difference is po found between successive improved wave functions. Finally, it may be shown that when such a calculation has been iterated to selfconsistency, the total electronic energy E of a closed shell molecule is given by

(2.12)

The main obstacles to the salution of this problem lie in the farmidabie number of multicentered integrals <)lv/ /pa> which arise even with the use of a minimal basis set, and the diffi culty involved in their evaluation. The CND0/2 approximation belongs to the SCF molecular orbital methods, whereas the Extended-Hückel methad is referred to as an approximate SCF-field theoryq. In the Extended-Hückel as weJl as the CND0/2 calculations the Slater 5 AO's of all valenee electrens are used as basis set.

II.2 The Extended-Hüokel method

II.2.1 Theory

The Extended-Hückel (EH) theory, developed by Hoffmann 6 ,

23 calculates a- and n-electron distributions simultaneously. In this method, the basis set for the linear combination of atomie orbitals is extended, with respect to the simple Hückel method, including all valenee shell atomie orbitals. The basis set used in the calculations consists of 1s orbital of hydrogen, 2s and 2p orbitals of carbon, oxygen and nitrogen, and 3s, 3p and 3d orbitals of sulphur and phos phorus. In the Hoffmann formulations H~~·s are chosen as the negative values of the valenee shell ionization poten tial (VSIP) and the Wolfsberg-Helmholtz approximation is used for estimating off-diagonal elements

(2.13)

The value of K, which is used as a sealing factor, is 7 chosen as 2.00 in accordance with earlier work 6 • • The over lap matrix is internally computed and the Hamiltonian matrix is constructed from it by equation (2.13). The complete set of (2.5) is solved with two matrix diagonali zations. The resultant wave functions are subjected to a Mulliken population analysis (see II.4.5), yielding overlap populations and gross atomie populations. The total energies 6 are calculated, according to Hoffmann , as

(2.14) i where €i and ni are the orbital energy and accupation number of the ith molecular orbital, respectively. Some objections against the use of semi-empirica! methods like the EH metbod have been discussed 8 • The correct symmetry and general shape of a molecule or ion might be correctly calculated, but good precise bond angles, lengtbs and force constants are not to be expected. In ordinary EH calculations excessive charges accumulate on more electro negative centers. This shortcoming is corrected by a metbod that assumes linear dependenee between the matrix elements and the calculated net charges. The most common variant of the EH metbod employs an iterative technique in which

24 the diagorral matrix elements are considered as a function of the net atomie charges. The calculation is iterated to charge consistency. Iterational treatment has led to im provement of the results for ionic species, but has given no significant difference for neutral systems 9 • The iterative 10 EH method, as proposed by Rein et a~. , calculates the total energies according to equation (2.15).

Etot = lJ:: n. (s.+h.) + E (2.15) ~. 1 1 1 core-core 1

~ Khere h. = <~ lhl~ > and the second term is the care re- l \1 \1 pulsive energy, calculated by:

Ecore-core (2.16)

- Aeff an d rAB b e1ng· e ff ect1ve· core c h arges o f atom A an d distance between atoms A and B, respectively. In equation (2.15), h represents the same one-electron operator of kinetic energy and core attraction as the one in the Hartree Fock method. The matrix elements H have been calculated \111 11 according to equation (2.17), as derived by Basch et al. :

2 H Xq + Yq + Z (2.17) \1\1 in which X, Y and Z are input parameters (Section II.2.2). At each iteration the H values are obtained from those of 11\1 the previous cycle by equation (2.18):

2 H H ( )(1-;\) + À(Xq +Yq+Z) (2.18) llll(n+1) J..lll n with À, the damping parameter, taken as 0.1. Iterations are continueduntil the atom charges remain constant to within 0.01 electrooie charge.

II.2.2 Parameters for the ordinary and iterative EH catauZations The orbital parameters (Table !1.1), except for sulphur,

25 entering the EH theory, namely, the valenee state ionization potentials (VSIP) and orbital exponents, are the same as those used by Boyd 12 in a molecular orbital study of ATP. For sulphur the data have been taken from a study by 13 BartelZet al. • The orbital exponents are just the Slater values, exeept for the H ls and P 3d orbitals, for whieh 14 the values are taken from SCF optimization ealculations • 6 The carbon and hydragen VSIP's are those in common usage , and the phosphorus and oxygen values are taken from SCF 13 eigenvalues of P0 • For the iterative EH ealeulations the constants for equation (2.17) are obtained from the atomie 11 speetral data as determined by Basehet al. •

Table 11.1 Parameters in ordinary and iterative EH cal culations

element orb i tal VSIP orbital x y z (eV) exponent (eV) (eV) (eV)

H 1 s 13.60 1. 200 13.62 27. 18 13.60 c 2s 21.40 1. 625 3.47 17.56 19.40 c 2p 11.40 1. 625 3.47 14.65 10.60 N 2s 26.00 1. 950 3.49 20. 11 25.56 N 2p 13.40 1. 950 3.44 12.70 8.28 0 2s 37.59 2.275 3.47 22.89 32.30 0 2p 14.62 2.275 3.46 18.57 15.80 p 3s 18.57 1. 600 1.77 13. 2 3 18.77 p 3p 13.98 1. 600 1. 51 15.25 20.51 p 3d 8.48 1. 400 1. 77 1. 18 1. 15 s 3s 23.06 1. 817 1. 51 15.25 20.51 s 3p 10.36 1. 817 1. 7 5 10.41 12. 31 s 3d 7.00 1. 200 1. 58 2.00 0.83

11.3 The fompZete EegZeet of QifferentiaZ QverZap methad

11.3.1 Theory of the CNDO methad 1f the full SCF equations are solved without any approximations, then the calculated energies and electron

26 distributions are dependent on the choice of the coordinate axis. The results must also be the same whether we choose to take a linear combination of atomie orbitals, ar a linear combination of hybridized orbitals. The results of an SCF calculation are invariant to an orthogonal trans formation of the atomie orbital basis. If one introduces approximations to the SCF equations then the conditions of rotational and hybridizational invariance must be conserved. 15 The approximations for the CNDO methad are : 1. Only valenee electrans are treated explicitly, the inner shells being treated as part of a rigid core.

2. c u 's are treated as if they farm an orthorrormal set; thus

s = éi (Kronecker delta) (2.19) ]JV ]JV 3. All two electron integrals which depend on the overlap of charge densities of different orbitals are neglected. This means that

éi éi y (2.20) ]JV pcr J.lP 4. The electron interaction integrals are assumed to depend on on the atoms to which the orbitals ~ and ~ belang. ]J ') Thus yJ.lP is set equal to yAB' measuring an average repulsion between an electron in a valenee atomie orbital on A and another in a valenee orbital on B. ~. The core matrix element H contains the interaction ]J]J energy of an electron in valenee orbital ~ on A with ]J the care of A and with the cores of all other atoms B

H (2.21) ]J]J

u (2.22) )J]J

6. Core matrix elements H , where ~ and ~ are different )JV ]J V but both belang to A, may in analogy to 4 be written:

H (2.23) )1\1

27 However, due to the mutual orthogonality of s, Px• Py and p , U is zero and the remaining terms are small, Z ]JV so H = 0 for lJ f v. ].JV 7. Core matrix elements H , where ~ is on atom A and ~P lJP lJ is on atom B, will be considered proportional to the overlap integral S ]Jf) :

H]Jf) (2.24)

Under these approximations, the matrix elements of the Fock Hamiltonian reduce to

FlJlJ UlJlJ + (PAA-!PlJlJ)yAA + B(~A) (PBBYAB-VAB) (2.25) 13~BS]JV - !PlJVYAB lJfV (2.26) (~lJ on A, $v on B)

The expression (2.26) applies even if 1J and v are on the same atom. Then S 0 and yAB is replaced by yAA. ]J\! The total energy is given by the sum of monoatomie and diatomic terros

Etot E SA + E e: (2.27) A A

For large intermolecular separations, the potential inte grals VAB' VBA and yAB all approximate rAB-l and with QA ZA-PAA (QA: net atomie charge on A), the last group of termsin (2.29) becomes QAQBrAB- 1. This shows that the theory takes proper account of the electrastatic interaction between charged atoms in a molecule.

28 II.3.2 Parametrization for the CND0/2 method 16 From the previous Section one obtains a penetratien integral term ZByAB-VAB in F~~· if one substitutes QB = ZB-PBB in equation (2.25). This term gives rise to calcul ated bonding energies even when the bond orders connecting two atoms are zero. In the CND0/2 method this deficiency is corrected in the simplest possible way by neglecting the penetratien integrals. Thus

(2.30)

The core matrix elements can be estimated from atomie data in tKo ways:

-I (2.31) )J and -A (2.32) ~

1\ith I the ionization potential, A the electron affinity and ZA the effective nuclear charge. U is in the CND0/2 ~~ method the average of both estimations:

- 1 (1 +A)- (Z - 1 )y (2.33) 2 ~ ~ AZ AA

The values used for the electronegativities -!(I +A) are 11 11 listed in Table 11.2. Initial estimates of the LCAO coefficients may be obtained by a HUckel-type theory using matrix elements (o) F -l(I +A) ( 2. 34) ~~ 2. 11 ~

(2.35) and the final solution is obtained as described in Sectien II.1. The bonding parameters S~B are approximated by

(2.36)

29 15 17 Table II.2 Values of parameters • -Bo !(Is+As) HIP +Ap) ~(Id+Ad) A co re element (eV) (eV) (eV) (eV) charge H 7. 176 - - 9 1 c 14.051 5. 572 - 21 4 N 19.316 7.275 - 25 5 0 25.390 9. 111 - 31 6 p 14.033 5.464 0.500 1 5 5 s 17.650 6.989 0.713 1 8 6

B~ and B~ are adjustable empirically determined parameters and chosen to give the best agreement between CND0/2 and ab-initio calculations. The sp and spd type calculations differ only by the omission of 3d functions from the basis set.

11.3.3 The GEOMO program 19 The GEOMO program perfarms LCAO calculations with any usual semi-empirical formalism (CNDO, INDO, MINDO). The algorithms in this program permit use of parametrization and allow direct minimization of energy with respect to any geometrie parameter. For our purposes the CND0/2 methad is used. A stable geometrie configuration of a molecule corresponds, in the Born-Oppenheimer approximation, to the minimum of the molecular energy, when the interatomie distanees vary. In the CND0/2 method the total energy (2.27) ean be decomposed into monoatomie terms, whieh do not depend on geometry, and diatomic ones. The other terms determining electron repulsing are negleeted. Therefore, the energy variations arise from diatomie terros (2.29) only, wherein the term rAB -1 is replaced by the nuclear repulsion term f(rAB). When the variatien of an internal eoordinate qz modifies the distance rAB' the variatien of EAB can be calculated from:

30 5EAB AB oB .. öf (r AB) l:L rzp ~ -1p2 + + • )lV 6qz 2 )1\.J ZAZB ;;: ij 6qz

6VAB oyAB - PAA-6-- (2.37) qz PAAPBB-6-qz whereas the quantities P, defined from c . 's, have zero )11 derivatives. The method for the minimization of the energy is the classical conjugate gradient metbod with the variable 20 metric, developed by Murtagh and Sargent • The SCF iterat ion procedure is performed until the energy converges with in 10-6 eV and the optimization is stopped when the minimum relative quadratic difference allowed for two consecutive 8 values of atomie coordinates is smaller than 10

11.4 Ab-initia aaZoulations 21 The CNDO and EH method use a minimal basis set of Slater-type atomie orbitals (STO's). Full Slater-type ca:culations are, however, time consuming, largely because of the evalustion of two-electron integrals. Replacing each STO by a linear combination of a small number of Gaussian type orbitals, is a possibility to reduce the computation time, since integrals invalving Gaussian functions can be evaluated analytically. The combination of K Gaussian-type orbitals (K 2-6) are obtained for STO with ç = 1 and then uniformly scaled. Thus

tjJ )1 r ( Ç' 1;3/2<1:)1' (1 ,1;.!:_) (2.38) where K tjJ 15 I ( 1 >!) E d1s,kg1s(a1k, k K

31 Here g 15 and g2p are the Gaussian-type orbitals:

~ 2 (2a/TI) 4 exp (-ar ) 2 (128a5/TI 3)l r exp(-ar )cose (2.40)

The constants d and a in (2.39) are chosen to minimize the integrals

(2.41)

Values for a and d along with the corresponding E values 21 are given by Hehre et aZ. • With the basis functions (2.39) the total energy can be obtained as described in Section II.1. In this study the Gaussian 70 program22 is used with an ST0-3G basis set.

II.S MuZZiken popuZation anaZysis 23

The density matrix is defined such that, if ~i l:c .cp (~. is the ith MO), f.l )..11 ).I 1 - the diagonal element of the density matrix is M 2 P l: n.c . (2.42) ).I )..I i= 1 1 )..11 where M is the number of occupied MO's ~i and ni is the accupation number of the ith MO - and the off-diagonal element of the density matrix is M P l: n.c .c . (2.43) fl\! i= 1 1 ]..11 \!1

The customary Mulliken definitions qf population analysis are:

- the net atomie QOpulation in atomie orbital ).I:

NAP(ll) pllll (since sllll 1) (2.44)

32 - the net atomie population on atom A: N m NAP(A) = E NAP(~) E P S (2.45) )l i::1 1111 1111 Khere Nm is the number of AO's on A - a measure for the interaction between ~ (on atom A) and Jl (on atom B):

p s (2.46) ].IV 11V

- the !Otal ~verlap EOpulation between atoms A and B:

TOP(AB) = E p s (2.47) 11V jlV Jl,V

II.6 CaZcuLation the solvation enthaLpy The first approximation which has been used for the solvation of monoatomie ions is the Born charging energy 24 25 term • The model for the solvent effect proposed by Jano considers the molecule to be enclosed in a sphere which is embedded in a polarizable solvent. The medium is character ized as a continuurn by its dielectric constant Ë and the solute molecule is represented by charge particles qA situated at fixed points !.A inside the sphere, which has radius a (Figure 2.1). Based on the electrastatic energy 26 of a charge dis tribution (2.48), Jano 25 derived a similar equation (2.49) for the solvation enthalpy as equation (2.50), which bas 27 been proposed by Boytink et aZ. •

U = l p(A)V(A)dv (2.48) with - U the electrastatic energy of a charge distribution p(A) - V(A) potential at point A.

(2.49)

(2.50)

33 2.1 IZZustration of the cZassiaaZ eZeatrostatia modeZ

with QA, QB: net charges on atoms A and B distance between atoms A and B effective radius, corresponding with the spherical cavity of the Ath ion which depends on the dielectric medium E dielectric constant of the solvent (EH = 80) 2 0 Comparison of (2.49) and (2.50) gives an approximation for the integral yAB ~ rAB-l' and for the monoatomie integral yAA ~rA-l' BortreZ and GueriZZot 28 worked out the algo 29 rithms for the EH program • Equation (2.50) expresses solely the electrastatic contribution from the total solvent-solute interaction. Moreover, it does riot involve any solvent effect upon the electronic structure of the solute molecule. This effect can be taken into account by incorporation of the solvent parameters into the Hamiltonian for solute molecules. V Comparison of both approaches by Miertu~ and KyseZ 30 shows that the major part of solvation stabilization is due to

34 the electrastatic contribution. Thus as an approximation of the solvation enthalpy, the electrastatic part, calculated according to equation (2.50), has been used.

The calculations have been performed on the Burroughs ï700 Computer at the Computing Centre, Eindhoven University of Technology.

35 References

1. J.E. Lennard-Jones, Trans Faraday Soc.,~. 668 (1929). 2. R.S. Mulliken, J. Chem. Phys., l• 375 (1935). 3. C.C.J. Roothaan, Rev. Mad. Phys., 23, 69 (1951). 4. J.A. Pople, Trans Faraday Soc., 49, 1375 (1953). 5. J.C. Slater, Phys. Rev., ~. 509 (1930); 34, 1293 (1959). 6. R. Hoffmann, J. Chem. Phys., ~. 1397 (1963). 7. G. Govil, J. Chem. Soc. A, 2464 (1970).

8. W.C. Herndon, Progr. Phys. Org. Chem., ~. 154 (1972). 9. B.J. Duke, Theoret. Chim. Acta (Berl.), ~. 260 (1968). 10. R. Rein, N. Fukuda, H. Win, G.A. Clarke and F.E. Harris, J. Chem. Phys., 45, 4743 (1966). 11. H. Basch, A. Visté and H.B. Gray, Theoret. Chim. Acta (Berl.), l• 458 (1965). 12. D.B. Boyd, Ph.D. Thesis, Harvard University, Cambridge, Mass., 1967. 13. L.S. Bartell, L.S. Su and H. Yow, Inorg. Chem., ~. 1903 (1970). 14. D.B. Boyd and W.N. Lipscomb, J. Chem. Phys., 46, 910 (1967). 15. J.A. Pople and D.L. Beveridge, "Approximate molecular orbital theory", McGraw-Hill Book Company, New York, N.Y., 1970. 16. See reference 15, pp 57-59. 17. J.N. Murrell and A.J. Harget, "Semi-empirica! self consistent field molecular orbital theory of molecules", Wiley Intersciences, London, 1972, pp 34-101. 18. H.H. Jaffé, Acc. Chem. Res., ~. 136 (1969). 19. D. Rinaldi, Comput. and Chem., 1, 109 (1976); Program 290, Quanturn Chemistry Program Exchange, Indiana University. 20. B.A. Murtagh and R.W.H. Sargent, Comput. J., ll• 185 (1970). 21. W.J. Hehre, R.F. Stewart and J.A. Pople, J. Chem. Phys., ~. 2657 (1969).

36 22. Gaussian 70, program 236, Quanturn Chemistry Program Exchange, Indiana Univers 23. R.S. Mulliken, J. Chem. Phys., Q, 1833, 1841, 2338, 2343 (1955). 24. W.M. Latimer, K.S. Pitzer and C.M. Klansky, J. Chem. Phys., l• 108 (1939). 25. I. Jano, C. R. Acad. Sc. Paris,! 261, 103 (1965). 26. J.G. Kirkwood, J. Chem. Phys., l· 351 (1934). 27. G.J. Hoytink, E. de Boer, P.H. v.d. Mey and W.P. Wey

land, Reel. Trav. Chim. Pays-Bas, ~. 487 (1956). 28. A. Bortrel and C.R. Guerillot, C. R. Acad. Sci. Ser. C, 27 ' 1663 (1973). 29. P. Dibout, EHT-SPD, program 256, Quanturn Chemistry Program Exchange, Indiana University. V V 30. S. Miertus and 0. Kysel, Chem. Phys., 21, 27 (1977).

37 CHAPTER 111

The solvent effect on the enthalpy of hydrolysis of c-AMP

III.l Int~oduation The coenzyme cyclic adenosine 3',5'-monophosphate (c-AMP), which acts as a "second messenger", has been re cognized in the past years 1 as a key substance in the regulation of many metabolic processes. lts level of con centration in the cell is controlled by the enzyme adenylate cyclase, which catalyzes the conversion of ATP into c-AMP. The conversion of c-AMP into adenosine 5'-monophosphate (5'-AMP) takes place via a phosphodiesterase. Most phospho diesterases degrade c-AMP solely into 5'-AMP. The isolation of a phosphohydrolase from Enterobaater aerogenes 2 has made hydralysis possible, which delivers a mixture of 5'-A}1P and adenosine 3'-monophosphate (3'-AMP), as stuclied by West 3 heimeP et aZ. • The hydralysis to either 3'-AMP or 5'-A,\1P involves a large exothermic Gibbs free energy 3 (-37.2 kJ/ mole) and enthalphy4 (-46.4 kJ/mole). Both values areabout 9 kJ/mole more negative than the values for the hydralysis of "energy rich" ATP into ADP and inorganic phosphate under the same conditions (Table III.1). The 3'-ester and 5'-ester bond of c-AMP have been concluded to be "high energy" bonds 3 • The discovery of phosphohydrolase from Enterobaater aerogenes affords the possibilities to measure the enthalpies of 4 hydrolysis of monocyclic and acyclic phosphatediesters • Joint consideration of hydralysis enthalpies and geometries of the alkyl phosphates and the nucleotides leads to some useful and general conclusions. The hydralysis data 4 (Table III.l) obtained for acyclic and monocyclic phosphates

38 are in agreement with their structures. The more negative

Table III.1 Enthalpies of hydralysis and OPO bond angles of phosphate diestersa

d. b a phosphate 1ester llHobsd OPO bond (kJ/mole) angle (degrees) ATP -37.2 - c-A~!Pd -46.4 - 1 cyclic guanosine 3 > 5 I- monophosphate (_~) -43.9e -

cyclic uridine 3 t '5 t- monophosphate CD -49.4 103 methyl S-D-ribofuranoside 3,5- cyclic phosphate (_1) 46.0

cyclic adenosine 2 t '3'- monophosphate -38.1 96 diethyl phosphate (_2) - 7.5 102 ethylene phosphate (IJ -26.8 98 trimethylene phosphate (~) 1 2. 5 104 tetramethylene phosphate (~) - 9.2 107g dimethyl phosphate C.!Q) - 7.3f 10 5

~The values refer to the hydralysis of singly charged di esters to form singly charged monoesters. bFor structures see Figure 3.1. 0 Hydrolysis enthalpy, measured at pH= 7.3, 25 °C by microcalorimetry 4 • dHydrolysis of c-AMP to 3'-AMP and 5'-AMP with similar enthalpies. eReference 4. tReferenee 5. gReference 6. entha of hydralysis of five-membered cyclic phosphates relative to acyclic phosphate esters have been attributed 7 8 4 to strain • , which is correlated with the OPO bond angles (Table III.1).The exothermicities of the hydralysis of cyclic 3',5'- and 2',3'-nucleotides suggest that these phosphodiesters may be strained with the farmer being more strained. In contrast to the enthalpies of hydrolysis, 9 13 several independent observations - show that cyclic 2' ,3'-

39 nucleotides are more strained than cyclic 3' ,5'-nucleotides with respect to their products of hydrolysis.

OH R 3' 0 0 -~ / ' :yP". 0 0 5' s'Y

1 R = adenine 5 R = adenine 2 R = guanine ~ R uridine .i R = methyl 11 R = H

§_ R = ethyl 7 n = 2 10 R =methyl 8 n = 3 9 n = 4

3.1 Struature of phosphate dieeters

So the large exothermic enthalpy of hydralysis of c-AMP is rather unexpected and can not be explained from the geo metries of cyclic 3' ,5'-nucleotides as well as strain 14 energy calculations • In order todetermine the cause of the pronounced exothermicity of the hydralysis of cyclic 3' ,5'-nucleotides, the methyl riboside cyclic phosphate (i) 4 has been examined by Westheiroer et aL. , since it would

40 eliminate any possible effect of the heterocyclic bases present in the nucleotides. The data for 2, ~ and ± clearly show that the base is nat responsible for the large exo thermic enthalpy of hydrolysis. As suggested by Westheimer e~ aZ. ~. a contribution to the enthalpy of hydralysis by so:vation may account for this phenomenon. In order to give a qualitative basis to this idea, the effect of the solvent on the enthalpies of hydra is of various phosphate diesters (~-~. lQ, ll) and of of c-AMP, with oxygen atoms replaced by methylene groups 3.2), has been examined by the semi-empirical Extended-Hückel methad (EH) and its iterative variant procedure (Chapter I I) .

III.2 Geometries of phosphate diesters The geometriesof ethylene phosphate 15 (2), trimethyl ene phosphate 16 (~), the 5'-methylene analogue of c-AMP 17 (12), their products of hydrolysis, 3'-AMP 18 13 and the 3'-methylene analogue of 3'-AMP 19 (~) arebasedon X-ray crystallographic data. Those for c-AMP 20 (l), 5'-AMP 21 diethy: (~) and dimethyl 22 phosphate (lQ) are based on quanturn chemical calculations. The geometries of the 3' methylene analogue of c-AMP (12_) and the 5'-methylene analogue of 5'-AMP C.U.) are estimated from c-AMP and 5' .-\~!P. The conformation of the ribose ring is taken to be the same in the cyclic and acyclic compound. The geometries of the 1' -methyl ene analogue of c-Al\1P, 5' -AMP and 3' -AMP 1~, 12• 18, respectively) are based on those of c-AMP and its products of hydrolysis, wherein the ribose ring is re 23 placed by a cyclopentane ring • is of X-ray crystallographic data, NMR studies and theoretical calculations offer an understanding of the and possible conformations of nucleotides. The possible conformations of c-AMP, 5'-AMP and 3'-AMP will be discussed here. The notations and conventions for the internal rotations as proposed by SundaraZingam 24 are adapted. From X-ray crystallographic and NMR data it is

41 OH R

0 3' -,-""' p / . o-'l' " os-Y 16

Figure 3.2 Methylene analogues of a-AMP, 5'-AMP and 3'-AMP

42 found that the torsional angle (for definition see Figure 3.3) about the glycosidic bond C(1')-~ (x), defining the relative orientation of the base with respect to the sugar,

A D \ s-s-ca /

(al (b)

re 3.3 Definition of rotatien angle a. Torsion angZe about the bond B-C in the sequenoe of atoms A-B-C-D is the angle through whioh the bond C-D is rotated with respect to the near bond A-B; a is oonsidered positive for a right handed rotation. (a) viewed perpendicula:r> to the bond;, (b) Newman projection

is in the anti region (-90°

24 24 in 5'-A~.IP and 3'-AMP , whereas that of c-AMP is the 20 25 26 C(~')-exo-C(3')-endo conformer • • (Figure 3.4). The conformation of the sugar ring in the 3'- and 5'-methylene analogue of c-AMP and their products of hydralysis is C(3')-endo C(Z')-exo and C(3')- ndo-C(4')-exo, respectively. 20 25 26 Literature data • • reveal that the phosphate ring in c-AMP and the 5-methylene analogue is fixed in a chair conformation. The Newman projections 1-III, IV-VI and VII IX, shown in Figure 3.5, illustrate the preferred con formations constrained along the C(4')-C(5'), C(5')-0(5') and C(3')-0(3') bands, respectively, in nucleotides. The conformational studies of nucleotides in recent years 27 show that 5'-AMP exists predominantly in the gauohe-gauche conformation about the C(4')-C(S') bond (I) and the C(5')- 0(5') bond (IV), with dihedral angles of about 60°. An

43 r------, r------, r-----, I I I I I I I I I I 1

0,- C • C • o,. C • /*Os· \3 0,· *Hs~ \3 /*Hsb \3

Hs· Hs· Os Hs. Hs. Os' b a b a H •• H.· H••

I 99 II gt III tg

IV g'g· y g't' VI t'g'

HJ' kPo 3 o3 P~

c.. · C - • • c,~c, 2 C4 C2 P03 VII t# VIII g" ( -) IX g" ( t)

F:gure 3.E Newman projectionsof the conformation of the ribose-phosphate backbone chain in 5'-AMP and 3'-AMP (g: gauche; t: trans)

44 c•. 3 ) C{l.') exo C{3') -endo( 4T

3 C(3')- endo- C(!,')- exo ( T4 )

?~g~re 3.4 Puckering of the ribose ring

important stereochemical consequence of a S-S'-nucleotide existing in the gg-g'g' conformation is that the atoms H(4'), C(4'), C(S'), O(S') and Pare in the same plane and that the four bond coupling path between H(4') and P is the 28 29 familiar "W" conformation (X). Hall et al-. • have shown

45 that the magnitude of the long-range coupling constant 4J(POCCH) exhibits a maximum of about 2.7 Hz fora planar "\1!" conformation and that this magnitude decreases with other conformations to zero coupling. For 5'-A.MP the ob 4 30 served values of J(PH(4')) are between 1.7-2.0 Hz • The mag_nitude of the 3J(HCOP) value 31 of 3'-A.MP indicates that the conformation about the C(3')-0(3') bond corresponds to that in which the phosphate group is gauche to H(3') (IX). From X-ray crystallographic data 18 it has been found that the orientation of the C(5')-0(5') bond in 3'-AMP with respect to the ring bonds C(4')-0(1') and C(4')-C(3') is gauche and trans, respectively, with dihedral angles 0(1')-C(4')-C(5')-0(5') of 57° and C(3')-C(4')-C(5')-0(5') of -172° (II). The lowest energy conformation 32 of 5'-Ai\IP and 3'-AMP is in good agreement with the structure deter 18 33 31 1 mined by X-ray crystallography • and by P- and H- 27 NMR studies of 3'- and 5'-nucleotides in solution • Because of the slight influence of the base on the hydro lysis4, ribofuranoside 3,5-cyclic monophosphate Cll) and the corresponding products of hydralysis are chosen as a simplified model for c-AMP, 5'-AMP and 3'-AMP, respectively. Por the methylene analogues the same simplification is adapted. The conventional numbering system24 for c-AMP is used.

III.3 The effect of the solventand the ribose ring puckering on the net enthalpies of hydralysis

III.3.1 Calculation of net enthalpies of hydralysis and net solvation enthalpies As suggested inSection III.1, solvation may contri bute4 to the large exothermic net enthalpy of hydralysis of c-AMP. Molecular orbital calculations have been performed on various phosphates (~-~. lQ-}l, 1±. ~) and their products of hydrolysis, using the semi-empirical EH methad and an iterative variant of this methad (Chapter II). The charge distribution (for the net charges of some important atoms in 11. 14 and 16 see Table III.2), determined by

46 both methods, tagether with the known atomie distances are used to calculate the solvation enthalpy according to equation (2.50).

Table III.2 Net charges (in electron units)a

charge d ens1ty . b on compound p 0 ( 1 ') 0(5') 0 ( 3') 0(6,7) 0.35 -0.83 0.42 -0.42 -0.67 0.40 -0.48 -0.37 -0.39 -0.35 14 0.22 -0.85 -0.41 -0.81 -0.66 0. 31 -0.48 -0.41 -0.40 -0.36 0. 18 -0.84 -0.80 -0.41 -0.67 0.33 -0.47 -0.39 -0.42 -0.38 aObtained by a Mulliken population analysis. bThe values in the first line are obtained by the EH method, those in the second line by the iterative variant.

In Table III.3 the calculated net enthalpies of hydralysis in the gas phase (~Hg ) and enthalpies of solvation ca 1 c (6Hs 0 1v) are given for the hydralysis reactions. From these ca 1 c values the net enthalpies of hydralysis in salution (LHsoln) are calculated according to oln = ~Hg + ca 1 c ~H~~Î~· Comparison of the results obtained with the EH method and the iterative variant reveals that the results of the latter metbod are in a better agreement with the experimental data. The correlation lines between 6Hsoln and the experimental data are shown in 3.6. Both methods give good correlation between the experimental and calculated values, the correlation coefficients being 0.995 and 0.998 for the normal and iterative EH method, respectively. The slope of the correlation lines is 2.95 and 2.30, respectively. This is the multiplicative factor by which the experimental and calculated values are inter related. This factor can be ascribed to the EH methad as 3 5 shown by Herndon •

47 Hsoln -t::. (kJ/motel

140 u-~. t 11-13" 120

100

4o s-2o.

10 20 30 40 50

- t::. H ex p ( kJ I mo!e )

Figure 3.6 Correlation between 6H 8 oln and AHexp for the hydralysis of phoaphate dieeters (· EH results, x results for iterative variant). For number ing of aompounda see Figure 3.2 and J.?

The calculated net enthalpies of solvation in Table III.3 indicate that solvation has an effect on the hydra lysis enthalpy. Moreover, this effeot is aonsiderably larger in the aase of the hydralysis of o-AMP with respect to the other phosphate diesters. This larger exothermicity is due, as is shown inSection III.4, to an extra stabi Zization of the hydralysis product with reapeet to the reactants by regio-specific hydragen bonding with water molecules.

48 Table III.3 Experimental and calculated net enthalpies of hydralysis aml net solvation enthalpiesa- with the Eli method with the iterative variant b .6.Hg c llHsolv d llHsoln e Mig c llHsolv d .6.Hsoln e .6.H exp calc calc calc calc hydralysis of kJ/mole kJ/mole kJ/mole kJ/mole kJ/mole kJ/mole kJ/mole model c-AMP f -46.4 -108.8 -21.8 -130.6 -79.4 -24.2 -103.6 (J -46.4 -112.1 -19.7 -131.8 -81. 3 -25.0 -106.3 ethylene phosphate -26.8 - 55.6 - 9.6 - 65.2 39.7 -11.9 - 51.6 trimethylene phosphate -1 2. 5 - 33.9 - 4.0 - 37.9 -19.8 - 9. 8 - 29.6 di ethyl phosphate - 7.5 - 3.8 - 9. 2 - 13.0 - 1.5 -11.0 - 12. 5 dimethyl phosphate - 7. 3 - 3. 1 - 9. 2 - 1 2. 3 - 1 . 8 -11.2 - 13. 0 1'-methylene analogue c-AJv!Ph - - 83.5 9.5 - 93.0 -48.3 -12.3 - 60.6 i - - 79.8 -10.8 - 90.6 -46. 1 -13.9 - 60.0 3 1 -methyl ene analogue c-AMP - - 9 4. 1 -17.7 -111.8 -40.3 -12.0 - 52.3 5 1 -methyl ene analogue c-AMP - - 6 8. 1 -11 . 6 - 79.7 -52.5 -18. 1 - 70.6 aAll values refer to the hydralysis of singly charged diesters to form singly charged mono esters (the lowest energy conformations of the compounds are given in Figure 3.7). bMeasured net enthalpy of hydralysis in solution~ cNet enûhalpy of hydralysis in gas phase. dCalculated 34 net enthalpy of solvation. eNet enthalpy of hydralysis in solution • fHydrolysis tomodelof 5 1 -AMP. gHydrolysis tomodelof 3 1 -AMP. hHydrolysis to 1 1 -methylene analogue of 5 1 -AMP. iHydrolysis to 1'-methylene analogue of 3'-AMP. ,-10 Dol)/ H 'I '/p""- 0 0

~~~c' ~o-e,; R 1 'c' ' '\Ic-c.- I Q' l\ : H H 11 R = H, model c- AMP 11. R = H, model 5'- AMP

H, 0 H-O I "- ;o, G P ., 'c/ ·'c/ ; f\1 . " A·~·l ' c- 1 R O '-'o I 0 "....c, I 0 I H

13 R = H, model 3'- AMP

• 0-H ,0 ...__.. / ,- •\ /C-C-,_ Oà.ö!.•P-O X / H-0 7 19 2- hydroxyethyl phosphote

• H \ '~-0/ _,9, '-è-c/ -,J\ / \'-, 0-P-0 ~ . H-0/ 8 20 3- hydroxypropyl phosphate

Q,, /0-R Q,,,, /0-R \ ' - l p - I p 0_"I 0 ót'l R;/ Hl' a mono-olkyl phosphate

.§_ R = ethyl 21 R = ethyl 10 R = methyl 22 R =methyl

Figure 3.7 Lowest energy structures of phosphate diesters and their products of hydralysis 50 III.3.2 Ribose ring puckering

Westheimer et al.~ have shown that the exothermic enthalpy of hydralysis can not be ascribed to strain in the phosphate diester ring. No attention has been given hitherto to the difference in conformation of the ribose ring of the nucleotides. The ribose ring has a C(3')-endo conformation for 5'-AMP and 3'-AMP, whereas that of c-AMP exists in a C(4')-exo-C(3')-endo conformation (F 3.4). Calculation of the difference in total enthalpy of a free tetrahydrofuran ring in the C(4')-exo C(3')-endo and C(3')-endo conformation shows that the difference in total enthalpy is 22.4 kJ/male and 18.8 kJ/mole for the EH and the iterative variant, respectively. The C(3')-endo conformer is the most stable one. This im p" aates that a part of the differenae in net enthalpies o; lysis can be explained by the of ribose pAakering in c-AMP, 5'-AMP and 3'-AMP. This conclusion is underlined by the data of the methylene analogues of c-AMP. The geometries of the ribose ring have been taken the same in the cyclic compound and the product of hydrolysis. In the next Chapter the contribution of both aspects, i.e. solvation and ribose ring puckering, in the net enthalpy of hydralysis will be considered.

III.4 Discussion In Figure 3.7 the lowest energy conformations of the various phosphate diesters and their products are drawn. Hydragen bonding with water molecules in the phosphate di esters occurs between the oxygen ligands of phosphorus. This is confirmed by ab-initia calculations on the dimethyl 36 phosphate anion (lQ), performed by Pullman et al. • Between the tetrahydrofuranyl oxygen and the phosphate ester oxygens in c-AMP no hydragen bonding is possible because of the large distance (4.0 R). A linear structure of the hydralysis products has the lewest energy. The hydragen bonding between the oxygen ligands remains. In

51 3-hydroxypropyl phosphate (lQ) and 2-hydroxyethyl phosphate (~) no effective hydragen bond interaction is possible between the hydroxyl oxygen and the phosphate ester oxygens. Hydragen bonding via one water molecule between 0(1') and 0(5') is possible in 3'-AMP as wellas in 5'-AMP, with a distance between these atoms of 3.0 ft and 2.9 ft, respective ly (Figure 3. 8). This stabilization does not exist in c-A~IP

14 R = H 11 R = H

Figure 3.8 5'-AMP and 3'-AMP with one moZeauZe of water between 0(1') and 0(5') and other phosphate diesters or their products of hydra lysis. The hydragen bonding via one water molecule in 3' AMP and 5'-AMP must be responsible for the larger net exothermic solvation enthalpy for the hydrolysis of c-M1P. The calculations of the enthalpy of solvation show that the difference in net solvation enthalpies (10-12 kJ/mole from the EH method and 12-15 kJ/mole from the iterative variant) arises mainly from the hydragen bonding via one molecule of water between 0{1') and 0(5'). This regio specific solvation contributes namely 10 kJ/mole and 12 kJ/mole for the EH method and the iterative variant, respectively. The net solvation enthalpies for the hydra lysis of the methylene analogues of c-AMP underline this

52 conclusion. When either 0(1') or 0(5') is replaced by a methylene group, the net solvation enthalpies diminish by about 12 kJ/mole. Upon replacing the 0(3') atom by a methylene group a difference of only 2 kJ/mole is observed. This smal! difference may be due to the different hydratien possibilities of 0(2') and 0(3'). Berthod and Pullman 37 have shown by ab-initio calculations on a free ribose ring that hydratien can occur on 0(2') and 0(3') separately, but that a bridge position is also possible. It seems that our proposed model is strongly supported 13 by C-NMR spin lattioe rela:r:ation times (T 1's), T1 data give an opportunity to analyze intermolecular effects, e.g. 38 hydragen bonding • Comparison of NT 1 values (:\: number of directly attached protons to the carbon atom) indicate the presence of anisotropy of segmental motion in a molecule. 39 As an example, Czarnieaki and Thornton compared the NT 1 values of the exocyclic carbon atom of galactose (24) and glucose (~) derivatives (Figure 3.9) of ganglioside head groups with each other and with the ring carbon atoms. They found that the exocyclic carbon atom of the glucose compound is isotropie with respect to the ring carbon atoms and explained this phenomenon by intermolecular

HO R, R, HO

:: a R1 H ; R2 = OCH3

b R, = OCH3 ; R2 = H

Figure 3.9 Gluaose and galactose derivatives hydragen bonding via one molecule of water between the exo cyclic CH 20H group and the pyranose ring oxygen atom. For

53 5'-AMP the NT 1 values of the ribose carbon atoms, as deter 40 mined by Norton and Allerhand , are between 0.18-0.22 s, whereas the value of the exocyclic C(5') atom is 0.20 s. This implicates that the degree of rotational freedom for C(5') is as large as that of the ring carbon atoms. This iso~ropy underlines our proposed model for the occurrence of regio-specific hydration between 0(1') and 0(5') in 5'-AMP via one molecule of water. X-ray arystaZZographia data 41 of the aminoglycosyl antibiotic puromycin dihydrochloride pentahydrate, which is a modification of 3'-AMP, wherein the phosphate moiety is replaced by p-methoxy-1-phenylalanyl amino group, demonstrate that hydragen bonding does occur between 0(1 ') and 0(5'). Although in this compound a phosphate group is replaced by a large amino acid group, the conformation of the 3'-amino-acyl nucleotide is in accordance with the 24 preferred conformations of acyclic nucleotides • It seems that puromycin provides a good conformational model for this compound. In eoncZusion, the large exothermia enthaZpy of hydralysis of c-AMP is primarily due to bath the differenae in aonformations of the ribose ring in c-AMP and its hydro Zytia produats as well as the relatively large net negative solvation enthalpy of the hydrolysis.

54 Beferences and Notes 1. J.P. Jost and H.V. Rickenberg, Annu. Rev. Biochem., 4 741 (1971). 2. J.A. Gerlt and G.J.R. Whitman, J. Biol. Chem., 250, 5053 (1975). 3. 0. Hayiaishi, P. Greengard and S.P. Colowick, J. Biol. Chem., 246, 5840 (1971). 4. J.A. Gerlt, F.H. Westheimer and J.M. Sturtevant, J. Biol. Chem., 250,5059 (1975). 5. J.P. Guthrie, J. Am. Chem. Soc., 99, 3991 (1977). 6. C.L. Coulter, J. Am. Chem. Soc., , 4048 (1975). ;, P.C. Haake and F.H. Westheimer, J. Am. Chem. Soc., ' 1102 (1961). 8. F.H. Westheimer, Acc. Chem. Res., l• 70 (1968). 9. S. Chang, D. McNally, S. Shary-Tehrany, M.J. Hickey and R.H. Boyd, J. Am. Chem. Soc., , 3109 (1970). 10. C.C. Browne and F.D. Rossini, J. Phys. Chem., ' 927 (1960). 11. J. Kumamoto, J.R. Cox, Jr. and F.H. Westheimer, J. Am. Chem. Soc., 2..!!• 4858 ( 1956). 12. H.G. Khorana, G.M. Teuer, R.S. Wright and J.G. Moffat, J. Am. Chem. Soc., .z.g,, 430 (1957). 13. P. Szabo and L. Szabo, J. Chem. Soc., 3758 (1960). 1+. J.A. Gerlt, Ph. D. thesis, Harvard University, Cam bridge, Mass. (1974). 15. T.A. Stertz and W.N. Lipscomb, J. Am. Chem. Soc.,~. 2488 (1965); in this paper the labelling of atoms in Table I and Figure 1 is contradictory. In Table I the set 0(2), 0(3), 0(4), 0(5), 0(6), C(7), C(8), should be replaced by 0(3), 0(6), 0(7), 0(2), C(4), C(5), 0(8). The correct value for y 0(5) = -0.2137. 16. Mazhar-ul-Hague, C.N. Caughlan and W.L. Moat, J. Org. Chem., ~. 1446 (1970). 17. S.M. Hecht and M. Sundaralingam, J. Am. Chem. Soc., ~. 4314 (1972). 18. (a) M. Sundaralingam and L.H. Jensen, J. Mol. Biol.,

55 .]1_, 914 (1965); (b) ~f. Sundaralingam, Acta Cryst., t.J., 495 (1966). 19. M. Sundaralingam and J. Abola, J. Am. Chem. Soc., 94, 5070 (1972). 20. J.N. Lespinasse and D. Vasilescu, Biopolymers, 1}, 63 (1974). 21. D. Vasilescu, J.N. Lespinasse, F. Camous and R. Cor nillon, FEBS Letters, lZ• 335 (1972). 22. D.G. Gorenstein, J.B. Findlay, B.A. Luxon and D. Kar, J. Am. Chem. Soc., 99, 3473 (1977). 23. Tables of interatomie distances and configuration in molecules and ions, A.D. Mitchell and L.C. Cross Ed., Special Publication no. 11, The Chemical Society, London, 1958; M 185. 24. M. Sundaralingam, Biopolymers, z, 821 (1969). 25. B.J. Blackburn, R.D. Lapper and I.C.P. Smith, J. Am. Chem. Soc., , 2873 (1973). 26. R.D. Lapper, H.H. Mantsch and I.C.P. Smith, J. Am. Chem. Soc., , 2878 (1973). 27. (a) C. Altona and M. Sundaralingam, J. Am. Chem. Soc., ~. 2333 (1973); (b) F.E. Hruska, D.J. Wood, T.N. McCaig, A. Smith and A. Holy, Ca~ J. Chem., ~. 497 (1974); (c) R.H. Sarmaand R.J. Mynott, J. Am. Chem. Soc., ~. 1641 (1973); (d) c. Altona, J.H. van Boom, J.R. de Jager, H.J. Koeners and G. van Binst, Nature, 247, 558 (1974). 28. L.D. Hall and R. B. Malcolm, Can. J. Chem., ~. 2092, 2102 (1972). 29. B. Donaldson and L.D. Hall, Can. J. Chem., ~. 2111 (1972). 30. R.H. Sarma, R.J. Mynott, D.J. Wood and F.E. Hruska, J. Am. Chem. Soc., 95, 6547 (1973). 31. O.B. Davies, Progr. in NMR Spectroscopy, }l. 135 (1978). 32. J.M. Thornton and P.M. Bayley, Biochem. J., 149, 585 (1975). 33. J. Kraut and L.H. Jensen, Acta Cryst., ~. 79 (1963). 34. P. George, R.J. Witonsky, M. Trachtman, C. Wu, W. Dor-

56 wart, L. Richman, W. Richman, F. Shurayh and B. Lentz, Biochim. Biophys. Acta, 223, 1 (1970).

35. W.C. Herndon, Prog. Phys. Org. Chem., ~. 154 (1972). 36. B. Pullman, A. Pullman, H. Berthod and N. Gresh, Theor. Chim. Acta (Berl.), , 93 (1975). 37. H. Eerthad and A. Pullman, Theor, Chim. Acta (Berl.), 47' 59 (1978). 38. J.R. Lyerla, Jr. and G.C. Levy, Top. Carbon-13 NMR Spectroscopy, l• 79 (1974). 39. ~t.F. Czarniecki and E.R. Thornton, J. Am. Chem. Soc., ~. 8279 (1977). ~0. R.S. Norton and A. Allerhand, J. Am. Chem. Soc., 8 1007 (1976). 41. ~1. Sundaralingam and S.K. Arora, J. Mol. Biol., .zl, 49 (1972).

57 CHAPTER IV

The inttuenee of solvation and ribose ring puckering on the enthalpy of hydrolysis of c-AMP

IV.1 Hydrogen bonding The elucidation of the possible interactions in solute-solvent systems is of fundamental importance for the understanding of the structural and functional proper ties of biomolecules. In fact, several studies 1 are direct ed in an effort to introduce explicitly the solvent effect, especially the influence of water into theoretica! com putations on biomolecules. Many studies employ the "tra ditional" approach to the problem through the use of a "continuum" model. This macroscopie representation, as is used in the previous Chapter, tries to account for the bulk effect of the surrounding medium. A second approach, which has been much less explored, consists of a "discrete" treatment in which one attempts to establish the individual sites of interaction of the solvent molecules with the system studied. The purpose of a macroscopie representation of the solvent is to interpret or predict the molecular behaviour in solution on a more direct basis. The essential problem consists of determining the most probable sites of binding of water molecules to biomolecules. Upon binding 2 3 of a water molecule with the system hydrogen bonds • are formed. The hydrogen bond has been of special interest to the chemists since Latimer and Rodebuah~ first pointed out the significanee of hydrogen bond mechanism to des cribe the structure of water. The interest greatly in creased when Watson and Crick 5 postulated hydrogen bonding to be a key feature of the structure of DNA. The term

58 hydragen bond has, however, no universally accepted defini tion. According to the simple valenee bond theory, a hydra gen atom should be capable of forming only one chemica! bond. In many cases hydragen is attached to two atoms. In such cases the additional bond is called a hydragen bond. Pimental and McCleZZan 2 define it as "an interaction between a group A-H and an atom or group of atoms B in the same or a different molecule when there is evidence of bond mation and that this new bond Zinking A-H and B, specificaZ- involves the hydragen atom already bonded to A". Of the tKo functional groups taking part in the interaction, A-H 6 6 serves as a proton donor and Bas a proton acceptor • ~!os t commonly known groups acting as proton donors are: the carboxyl, hydroxyl, amine and amide group. Moreover, the hydragen atom attached to phosphorus, sulphur and selenium, can take part in hydragen bonding. The disso ciation enthalpy of hydragen honds varies from a few kJ/ mole to about 170 kJ/mole, depending on the different functional groups which are involved. Of the semi-empirica! methods used to study hydragen bonding, the CND0/2 method (Chapter II) is far superior to the EH and MIND0/3 method. The latter methods are not suitable for the evaluation of hydragen bonding, as was found by Murthy and Rao 7 for the EH method, and by Zie ~inski et al. 8 and Klopman et al. 9 for the MIND0/3 method, since no stabilization is observed upon water dimer formation. Comparison of CND0/2 with ab-initia calculations on dimers reveals that the CND0/2 results turn out to be 10 11 very satisfactory. Comparison • of interaction enthalpies and intermolecular distances for dimers, calculated by ab-initio and CND0/2 procedures, show that CND0/2 calcula tions relatively good values. Hence the CND0/2 metbod represents a reliable and relatively cheap procedure and is as such very useful for the determination of interactions between the solvent and large molecules, where more accurate calculations are far outside the range accessible by present computational facilities. For the CND0/2 equi-

59 librium geometries, however, the calculated interaction enthalpies are too large and the intra- and intermolecular distauces too short. CND0/2 calculations at fixed ex perimental geometries reproduce the available experimental 12 enthalpies of association very satisfactorily • The hydratien schemes of the models of c-AMP and the products of hydralysis are stuclied with molecular orbital cal culations, using the GEOMO (CND0/2) program (Chapter II).

IV.2 The water dimer Interaction enthalpies which are more negative than those corresponding to water-water interaction, point to the existence of hydratien sites. In order to obtain in sight into the possible sites, dimerization of water molecules is first considered. Water dimers can exist in three basic conformations, i.e. linear, cyclic and bi furcated (Figure 4.1). The linear hydragen bond has been systematically studied, but less attention has been paid 13 to cyclic and bifurcated bonds • This is surprising since non-linear conformations occur frequently in the solid 14 15 state and very probably in biologica! systems • • There

linear

.Hi'\. . . s " H o · · o.....- 6 cyclic H;- I" . 4 H3

bifurcated

Figure 4.1 Water dimers

60 has been a long-standing discussion 16 as to whether the ground statesof simple dimers, e.g. (H 2o) 2 , are cyclic or linear. Calculations using the GEOMO-CND0/2 program, including geometry optimizations, are performed on the water dimer in the three conformations. The basic geometries, as found to be the most stable ones by Morokuma and Peterson 17 in ab-initia calculations, are used. In Table IV.1 the di merization enthalpies are given with the equilibrium oxygen-oxygen distance. The binding enthalpy of -26.0 kJ/mole fcr the linear conformer agrees favourably with the ex perimental value of -21.0 kJ/mole for the water diroer in

Table IV.l Water diroer results

dimer R(0-0) Mi dim ge ometry ~ kJ/mole

linear 2.53 -26.0 bifurcated 2.60 - 5. 5 cyclic 2.48 -12.6 the gas phase 13 and of -23.9 kJ/mole per hydragen bond in 13 ice • The enthalpy differences between the linear dimer and the other two conformers are in excellent agreement with the results of an ab-initia study by Morokuma and 17 Peterson • The net charges of the atoms of the water monoroer and dimers are listed in Table IV.2. Por the ie conformation the net charge transfer is zero, as is expect ed from the symmetry of the complex. The electron density of the hydrogen atom, which is participating in the hydrogen bond is reduced upon hydragen bond formation. This phenomenon can be explained by electron pair repulsion. The electrans of the H-0(4) bond are "pushed back" towards the 0(4) atom by the lone pair of 0(1).

61 Table IV.2 Net charges (in e.u.)a

HzO (H20lz (HzO)z CHz0)2 atom monomer linear bifurcated cyclic

0( 1) -0.266 -0.265 -0.268 -0.281 H(2) 0. 133 0. 151 0. 139 0. 128 H( 3) 0. 133 0. 151 0. 138 0.153 0(4) - -0.319 -0.291 -0.281 H(5) - 0. 175 0. 141 0.153 H(6) - 0.108 0. 141 0.128 {;.b - 0.037 0.009 o.ooo

aObtained by a Mulliken population analysis. bMagnitude of electron transfer.

IV.3 Hydration sahemes of models of a-AMP~ 5'-AMP and J'-AMP Primarily the geometries of the nucleotides are op timized and subsequently kept constant throughout the computations (for optimized geometries see Appendix A). Interaction with one molecule of water is considered for all possible hydratien sites. Whereas the probability that a water molecule will detach itself from the bulk water structure to bind directly to a hydragen atom of a me 18 thylene group is very small , only hydratien sites in volving the oxygen atoms and the hydroxyl hydragen atoms are studied. The geometry parameters, which determine the hydragen bonding of the water molecule with the nucleo tides, are optimized for each interaction in order to obtain the local minimum enthalpy. Interaction enthalpies are calculated by substracting the sum of the enthalpies of the isolated compounds from the enthalpy of the adduct. In Table IV.3 the interaction enthalpies (~Hhydr), inter molecular hydragen bond lengtbs and net charges of the water molecule are given for the models of c-AMP, 5'-AMP

62 and 3'-AMP, respectively. The optimized intermolecular hydrogen bond distances are between 1.38 Rand 1.63 R. These distauces are smaller than those obtained by ab initia calculations. The discrepancy can be ascribed to the CND0/2 method, which can underestimate bond lengths up to 10 • In general it is known that in hydrogen honds the 0 ... 0 distances range from 2.5 to 3.5 R. Less attention has been paid to the range of the O... H hydragen bond lengths. A~Zinger 19 has pointed out the difference between van der Waals contact radii and van der Waals potential minimum radii. The latter values rather than the former for the criterium of a hydrogen bonding interaction are used, the cut-off fora H... O bond is then (1.50 + 1.65)R. All distauces of less than 3.15 Rare classified as bonding interactions. This implies that, even when the 10% under estimation is taken into account, all hydrations considered are bonding interactions. The water molecule acts as a proton donor when it is linked to an anionic, hydroxyl or phosphate ester oxygen atom resulting in an overall transfer of electrans fróm the nucleotide to the water molecule. If interaction with the hydroxyl hydragen atom occurs, charge is transferred in the reverse direction, which is characteristic for water 6 acting as proton acceptor • A population analysis has been made for both the complexes and the isolated monomers (data, see Appendix B). Some interesting conclusions emerge from these results: - the hydrogen in the hydragen bond looses electron density upon hydragen bonding; the adjacent oxygen atoms gain electron density, the oxygen atom of the proton donor molecule displays the greatest change; - the largest loss of electrous occurs at the hydrogen, carbon or phosphorus atom, which is immediately attached to the proton acceptor atom; - all hydragen atoms, which are attached to the electro negative atom of the proton donor molecule and not in-

63 Table IV.3 Calculated interaction enthalpies, intermolecular hydrogen bond distances and net charges on the water molecule for hydrations of models of c-AMP, 5' -A~!P and 3' -AMP

b b a g numbera hHhydr t.Hhydr t>Hhydrb I t>Hhydr net charges (e.u.) on water o..... H distancesJ of water (kJ/mole) (kJ/mole) (kJ/mole) (kJ/mole) molecule for (.R) 1 ,molecule c-AMP 5 '-AMP 3'-AMP c-AMP 5'-MfP 3 '-AMP c-AMP 5'-AMP 3'-AMP 1 -121.8 -126.4 -126.8 -115. 1 -0.0818 -0.0846 -0.1073 1. 39 1.44 1. 38 2 -120.5 -118.9 118. 4 -11 5. 1 -0.0765 -0.0817 -0.0845 1. 38 (0(7')) 1.61 (0(7')) 1.64 (0(7') 3 -126.0 -124.7 -124.7 -113. 8 -0.0836 -0.0887 -0.1102 1. 39 1.47 1. 38 4 - 55.0 57. 1 - 34.4 - 23.9 -0.0688 -0.0437 -0.0641 1. 43 1. 58 1. 45 5 - 67.2 - 66.4 - 66.4 - 34.0 -0.0480 -0.0164 -0.0163 1. 59 (0(2')) 1. 59 (0(2')) 1. 54 (0(2') 6 - 68.0 - 66.8 - 66.8 - 34.0 0.0245 0.0300 0.0140 1. 54 1. 53 1.53 7 - 63.4 - 60.9 - 62.6 - 29.4 -0.0595 -0.0174 -0.0266 1.65 1.63 1.63 8 - 43.3 - 41.2 - 54.6 - 22.7 -0.0492 -0.0324 -0.0498 1. 49 1. 47 1. 53 9 - 39.9 - 44. 1 - 42.4 - 21.0 -0.0426 -0.0362 -0.0524 1. 53 1. 59 1.61 10 -- - 78.5 - 78.5 -- -- 0.0421 0.0379 -- 1.62 1.64 11 -- - 63.8 - 62.6 -- -- -0.0359 -0.0401 -- 1. 58 1. 56 12 -- - 68.0 - 70. 1 - 32.8d -- -0.0231 -0.0215 -- 1. 58 (0(1')) 1. 56 (0(1') 13 -- - 67.2 - 68.5 - 34.4d -- -0.0144 -0.0325 -- 1. ss (0(5')) 1. 58 (0( 1 t) 14 -- - 56.7 - 72.7 - 30.7/ -- 0.0341 0.0255 -- 1.49 1. 59 - 31.96 aFigure 4.2 presents the numbering of the hydration sites; bhHhydr = Hadduet- (Hnucl ~ Hwater)' with Hnucl' Hwater' Hadduet the total enthalpy of the nucleotide, the water molecule and adduct, respectively; 0 Results from other studies: for the phosphate moiety ref. 20, for the ribose ring ref. 21; dThis work; 6 ~Hhydr = -30.7 kJ/mole as reference for the H(0(3')) atom in 5'-AMP and hHhydr • -31.9 kJ/mole as reference for the H(O(S')) atom in 3'-AMP; fin parentheses the oxygen atom which is considered. model c-AMP R:H

model 5'- AMP R:: H

model 3'- AMP R = H

?igure 4.2 Hydration sehemes of modelsof e-AMP, 5'-AMP and 3'-AMP (numbers of water moleauZes coP:res pond to Table IV,3)

65 corporated in the hydrogen bond become more negative upon hydrogen bond formation. 13 These results are in line with those for simple dimers • The calculated interaction enthalpies point to the existence of a number of possible hydration sites with interaction enthalpies more negative than the corresponding water-water interaction (öHdim = -26.0 kJ/mole). However, the.fact that the CND0/2 metbod neglects three- and four center repulsions (Chapter II) favours conformations in which atoms can approach closer, which leads to a larger gain in binding enthalpy with respect to ab-initio results. The results for the phosphate moiety are in line with those obtained by ab-initio calculations for the dimethyl phos phate anion20 (Table IV.3). The values for the ribose unit are, however, more negative for the CND0/2 calculations with respect to ab-initio computations for the free ribose ring21 (Table IV.3). The latter show, in contrast with our results, that 0(1') and 0(5'), separately, do notact as hydration sites, because the interaction enthalpy is less negative than the dimerization enthalpy of water (öHdim = 21 -25.6 kJ/mole for ab-initia calculations ). The inter action enthalpies for the formation of a five- and seven membered ring between 0(1') and 0(5'), which are not studied by BePthod and Pu~~man 21 , are as large as those for the hydration of the H(0(2')) atom and the formation of a five-membered ring between 0(2') and 0(3'). Therefore it is assumed that the proposed hydrogen bonding between 0{1') and 0(5') exists. In addition ab-initio calculations with the program Gaussian 70 22 , using a minimal ST0-3G basis set, have been performed on a free ribose ring in the C(3')-endo conformation, which is present in 5'-AMP as well as in 3'-AMP. The geometry data of the ribose ring in 3'-AMP 23 are employed. Formation of a five- and saven merobered ring between 0(1') and 0(5') results in an inter action enthalpy of -34.4 kJ/mole and -33.2 kJ/mole, respectively (Figure 4.3). The hydrogen bond distance between 0(1') and H(H 20) was taken to be 1.74 Rand 1.83 R, respectively. CND0/2 calculations on the roodels of c-AMP

66 4.J Ribose ring in C(J')-endo conformation with three main hydration sites and the products of hydralysis have also been performed for these distances and give results which are in better agreement with the ab-initio results than the calculations which perfarm optimization to obtain an equilibrium distance. The interaction enthalpies are -43.3 and -41.6 kJ/mole for the five- and seven-membered ring between 0(1') and 0(5'). For the formation of a five-membered ring between 0(2') and 0(3') the interaction enthalpy, obtained with the Gaussian 70 program, equals -32.3 kJ/mole with the 0(2')-H(H20) distance 1.76 ~. The ab-initio results for the formation of a five- or seven-membered ring between 0(1') and 0(5') inthefree ribose ring show that this interaction enthalpy is 8-9 kcal/mole more negative than that of the water dimer. This value is in agreement with the value (10 kJ/mole) calculated according to equation (2.50) for the solvation enthalpy. The significanee in the interpretation of the physical and chemical properties of nucleotides has recently become increasingly evident. In an artiele publisbed by Bolton 24 and Kearna , a model has been proposed for intermolecular hydrogen bonding in c-AMP between the 2'-0H group of the ribose ring and the free phosphate oxygen atoms (with the 0(2')-0(7') distances assumed to be 3.6 ~). They conclude from 1H NMR spectra of cyclic nucleotides in aqueous and mixed solvents that the 2'-0H proton is protected against

67 exchange with bulk water. On the other hand, these authors 24 could not find any crystallographic evidence for the pro posed interaction. Our results and these obtained by Berthod and Pullman 21 demonstrate, however, that hydrogen bonding is possible via one molecule of water between the 0(2') and 0(3') atoms. Furthermore, crystallographic evidence 21 is available to support this model. The distance between the 2'-0H oxygen atom and the nearest phosphate oxygen atom in c-AMP is found to be 5.0 R25 and not 3.6 R (vide supra). As a corollary tothese data, an inter molecular hydrogen bonding, as proposed by Bolton and Kearns, is unlikely, instead a bond between the 2'-0H group and the 0(3') atom is indicated.

IV.4 The aontribution of solvation and ribose ring puokering to the net enthalpy of hydralysis of a-AMP The ab-initio results for the hydratien of 0(1') and 0(5') of the free ribose ring demonstrate that the con tinuurn approximation, as effered in the previous Chapter, gives a good estimation of the enthalpy of solvation for the position between 0(1') and 0(5'). Whereas ab-initio computations give a better approximation of the experi mental values, the difference in enthalpy between the two conformers as present in c-AMP, on the one hand, and 5 '-AMP and 3' -M1P, on the ether, is determined by ab-ini ti o

Table IV.4 Calculated and experimental values llHsolv llHribose puckering llHexp calc (kJ/mole) calc iterative (kJ/male) EH methad variant (kJ/mole) c-AMP a -46.4 -21.8° -24.2d -9.2 b -46.4 -19.7 -25.0 -9.2 trimethylene -12.5 - 4.0 - 9.8 - phosphate aHydrolysis to 5'-AMP; bHydrolysis to 3'-AMP· 0 11Hsolv ' calc (0(1')-0(5'))=-10 kJ/mole·' dllHsolvcalc (0(1')-0(5'))=-12 kJ/mole.

68 calculations with the program Gaussian 70. Tetrahydrofuran in these two conformations is used as a model. The enthalpy difference between the two conformers is 9.2 kJ/mole, with the C(3')-endo conformer being more stable with respect to the C(4')-exo-C(3')-endo conformer. In Table IV.4 the ex perimental and calculated data are listed for the hydralysis of c-M-lP and trimethylene phosphate, respect i vely. Al though one should be careful in camparing the calculated and ex perimental values, the data in Table IV.4 tagether with the net solvation enthalpy for the position between 0(1') and 0(5') (L'lHsolv -10 kJ/mole, obtained by the continuurn calc = model, Chapter III) reveal that for c-AMP the net solvation enthalpy and the difference in enthalpy obtained by pucker ing of the ribose ring are especially responsible for the large exothermic net enthalpy of hydrolysis.

IV.5 Hydragen bonding as a model for the dynamica of enzyme-coenzyme complexes In the previous Chapter a seven-membered ring model for the hydragen bonding between a water molecule and 5'-AMP has been proposed. The similarity of the data for the formation of a five- or seven-membered ring reveals that the formation of the farmer is also possible (Figure 4.4). The appearance of a five-membered ring makes a "through water" interaction possible via the "free" proton of the

Figure 4.4 Transformation of intermoZecuZar hydragen bonding

69 water molecule between 5'-A~W as well as 3'-AMP and other enzymic sites and therefore it opens the possibility of conformation change in the enzymes. The concentratien level of c-AMP in cells is controlled by i ts conversion, via the action of a phosphodiesterase, into 5'-AMP in a highly exothermic reaction. c-AMP serves as a messenger that regulates the enzymatic reactions in cells. It has also been shown to stimulate the activity of the genes via the synthesis of messenger RNA which in fact reproduces the information contained in the DNA of the genes. On the other hand, 5'-AMP acts as an inhibitor26 for these processes. An example is found in the enzymatic process, wherein the 3' to 5' exonuaZease activity associated with both mammelian and bacterial DNA polymerases is selectively inhibited 27 by nucleoside 5'-monophosphates, whereas the cyclic nucleo tides and the nucleoside 3'-monophosphates show no inhibition. It might be possible to explain these results with the proposed regio-specific hydrogen bonding between 0(1') and 0(5'). Por 5'-AMP the information for the inhibition can be given via the water molecule between 0(1') and 0(5'). This kind of information is absent in c-AMP for geometrical reasons. The fact that 3'-AMP differs considerably in its molecular behaviour with respect to 5'-AMP is probably due to the orientation of the binding sites for the enzyme in volving the phosphate moiety, the base and the "free" proton as characteristic for the enzyme interactions. It should be stressed that a cooperative effect, for geometrical reasens is probably only opera ti ve in 5' -AMP and absent in 3' -AMP. In 1941, Lipmann 28 suggested that phosphate compounds with large exothermic Gibbs free energies and enthalpies of hydralysis could act as energy sourees for biologica! systems. The data offered in the previous and this Chapter, together with the known data of ATP, and results obtained by Westheimer et al. 29 on cyclic 2',3'-nucleotides, indicate that there are at least three different methods for storing energy in phosphate compounds. These sourees are: (1) storage in pyrophosphate bonds, as exemplified30 by ATP and the many

70 kinase and phosphorylase enzyme systems with ATP as substrate or product; (2) phosphate ring strain, found in the cyclic 2' ,3'-nucleoside monophosphates 29 involved in the ribo nuclease-catalyzed hydralysis of RNA; (3) ribose ring en thalpy starage and solvation enthalpy, as for c-AMP. The thermodynamically favoured hydralysis may simply ensure that enzymatic hydralysis is an effective mechanism for lowering the concentration of c-AMP and increasing that of

5'-A~IP, when an inhibitive activity is required.

71 References 1. P. Claverie, J.P. Daudey, J. Langlet, B. Pullman, D. Piazzola and H.J. Huron, J. Phys. Chem., g, 405 (1978). 2." G.C. Pimenteland A.L. McClellan, "The hydragen bond", W.H. Freeman editor, San Francisco, California; 1960. 3. "The hydragen bond", vol. I, II and III, P. Schuster, G. Zundel and c. Sandorfy, eds., North-Holland Publushing Co., Amsterdam; 1976. 4. W.M. Latimer and W.H. Rodebush, J. Am. Chem. Soc., 4 , 1419 (1920). 5. J.D. Watson and F.H.C. Griek~ Nature, lil• 737 (1953). 6. M.D. Dolgushin and V.H. Pinchuck, Theoret. Chim. Acta (Berl.), ~. 157 (1977). 7. A.S.N. Muthy and C.N.R. Rao, Chem. Phys. Lett., ~~ 123 (1968). 8. T.J. Zielinski, D.L. Breen and R. Rein, J. Am. Chem. Soc., 100, 6266 (1978). 9. G. Klopman, P. Andreozzi, A.J. Hopfinger, 0. Kichuchi and M.J.S. Dewar, J. Am. Chem. Soc., 100, 6267 (1978). 10. P.A. Kollman and L.C. Allen, Chem. Rev., ~. 283 (1972). 11. P. Schuster, Z. Chem., ..:!.]_, 41 (1973). 12. P. Schuster, Int. J. Quanturn Chem., ~. 851 (1969). 13. Reference 3: Chapter 2. 14. Reference 3: Chapter 1. 15. R. Balasubramanian, R. Chidambaran and G. Ramachandian, Biochim. Biophys. Acta, 21 182, 196 (1970). 16. Reference 3: Chapter 22. 17. K. Morokuma and L. Pederson, J. Chem. Phys., ~. 2275 (1968). 18. A. Pullman, Bull. Soc. Chim. Belg.,~. 963 (1976). 19. W.L. Allinger, Adv. Phys. Org. Chem., ..:!.]_, 17 (1976). 20. B. Pullman, A. Pullman, H. Berthod and N. Gresh, Theoret. Chim. Acta (Berl.), 40, 93 (1975). 21. H. Berthod and A. Pullman, Theoret. Chim. Acta (Berl.), i2_, 59 (1978).

72 22. Gaussian 70, program 236, Quanturn Chemistry Program Exchange, Indiana University. 23. M. Sundaralingam, Acta Cryst., ~. 495 (1966). 24. P.H. Bolton and D.R. Kearns, J. Am. Chem. Soc., lQl, 479 (1979). 25. J.N. Lespinasse and D. Vasilescu, Biopolymers, ll• 63 (1974). 26. A.L. Lehninger, "Biochemistry" 2nd ed., Worth Publishers Inc., :--lew York; 1975, pp 630, 712, 734. 27. J.J. Byrnes, K.M. Downey, B.G. Que, M.Y.W. Lee, V.L.

Black and A.G. So, Biochemistry, ~. 3740 (1977). 28. F. Lipmann, Adv. Enzymol., 1, 99 (1941). ~9. J.A. Gerlt, F.H. Westheimer and J.M. Sturtevant, J. Biol. Chem., 250, 5059 (1975). 30. H.R. ~1ahler and E. H. Gordes, "Biological Chemistry", Harper and Row, New York; 1971.

73 CHAPTER V

Thè acidity of thiaDJ.ine py:rophosphate and :related systeDJ.s

V.1 Introduetion

V.1.1 Bistorical background Thiamine pyrophosphate (TPP) serves as coenzyme for various types of enzymatic reactions (Chapter I). The nature of the molecule itself, with its combination of an aromatic aminopyrimidine ring and a substituted aromatic 1,3-thiazolium ring, does not immediately suggest a unique mode of reactions with substrates. Nevertheless, various predictions have been made and tested until the currently accepted mechanism for catalysis by TPP evolved. Langenbeek and Hutschenreuter 1 have studied the ability of a variety of amines to catalyze both decarboxylation and acyloin condensation of a-keto acids, and they considered these reactions as.models for enzymatic decarboxylations. Many years later, Wiesner and VaZenta 2 proposed that the 4' amino group of TPP acted in an analogous manner in TPP catalyzed reactions. They postulated Schiff base (imine) formation, foliowed by formation of a carbanion on the bridge carbon atom with subsequent rearrangement to form a B-unsaturated acid, which could readily decarboxylate (Figure 5.1 (1)). Both key points (imine formation and an intermediate bridge methylene carbanion) in the suggested 3 mechanism have been shown to be highly unlikely • Catalysis of acyloin condensations by cyanide, such as the formation 4 of benzoin , was long known, as was the condensation of quaternary pyridinium compounds with aldehydes to yield

74 5 adducts at the position a to the quaternary nitrogen atom • The similarity between the thiazolium and the pyridinium 5 6 ring was recognized by Ugai et al. • • They found, however, that insteadof forming adducts, the 1,3-thiazolium deri vatives catalyzed acyloin condensations. These results made 7 8 ~izuhara and Handler , and Breslow suggest different

+/'-1., N ~§

(1)

F\ RCHO + N: S (2) Hx OH

R"'-c-...rOH l RCHO + --.R' (3)

5.1 Proposed meohanisms of oata is by TPF

75 mechanisms for the catalysis by TPP. Mizuhara and Handler proposed that the carbonyl carbon atom of the substrate is attacked by the tertiary nitrogen atom of the pseudo base (Figure 5.1 (2)), forming a zwitterionic adduct that can either cleave to give free aldehyde or condense with an other aldehyde molecule to form an acyloin. However, the acid chemistry of 1,3-thiazolium compounds has been des 9 10 cribed by Duolos and Haake , and Metzler , and they found no appreciable amount of pseudo base present in solution, at any pH. Hence this mechanism apparently did not explain TPP catalysis. Breslow 8 stuclied various 1,3-thiazolium compounds under the experimental conditions of Mizuhara and Handler, measuring the formation of acetoin from acetaldehyde and pyruvate. Ereslow concluded that the bridge methylene group must be activated by the adjacent quaternary nitrogen atom as well as by the adjacent aromatic ring, and he proposed a mechanism whereby the electron deficient carbonyl carbon atom of the substrate reacts with a carbanion formed by dissociation of one of the protons of the bridge methylene group (Figure 5.1 (3)). The adduct would be cleaved or condensed in an analogous way as de 7 11 picted by Mizuhara and Handler • Breslow established~ however, the laak of H-D exahange at the bridge methylene

CH3 R, CH3 R, CH3 R1 020 +M +'i=< R-N+H S R-N~ s R-NyS 25° y H D 1

p D 5 t , : 2 min 12 pD 7 t, : infinitesimal 12

Figure 5.2 H-D exchange on paaition C(2) of 1,3-thia zolium ring

76 group, but at the same time that the C(2) proton of the 1,3-thiazolium ring did exchange readily with deu:::erium 5.2). He proposed the H-D exchange reaction to occur via a particularly stable conjugate base (l)· The arguments in favour of this mechanism are supported by the lability of the proton at position Z of the thiazolium ring, which is demonstrated with the aid of infrared and 12 12 13 \MR data • Breslow • adapted the mechanism for catalysis of the benzoin condensation by the cyanide ion 4 to the cata is by TPP (Figure 5.3).

(1)

CH3 R, .H R-N S ~

(2)

5.3 Acyloin condensation (1) and decarboxylation of a-keto aaids (2)

V.1.2 Relation of struature of TPP to the aatalytic activity The generally accepted mechanisms for enzymatic reactions with TPP as coenzyme suggest that the structure of TPP has evolved so, as to stabilize carbanions on posi tien Z of the 1,3-thiazolium ring. In order to gain in sight into the features which determine the formation of 1 15 the carbanion, Haakeet al. "• studied the rate constants of deuterioxide-catalyzed generation of cations with

77 deuterium on position 2 (~) and the formation of carbanions on position 5 (i) via the decarboxylation of N-methylated- 1 ,3-azolium-5-carboxylates (~). The results of this study

CH3 CH3 C02 ·~ -co 2 CH3-NYX CH3 -~ D 4 l x = NCH3 2 .!! x =NCH3 !! x = s b x =s .Q. !:. x ::: 0 ~ x ::: 0

13 are shown in Table V.1. The similarity of both c-H(2) and 13 c-IJ(5) coupling constants 14 (Table V.1) in homologous 1,3-imidazolium and 1,3-thiazolium cations indicates that hydrogens at position 2 and 5, respectively. have similar potential acidity in the cations. On the other hand. the ohserved 11-D exchange and decarboxylation is much faster for the 1.3-thiazolium cation.

Table V. 1 Rates of H-D exchange and decarboxylation. and coupling constants

13 x kH-D J( C(2)-H) CH3 · rel 220 NCH 3 1 CH3-~ s 103.5 216 0 105.5 246

13 kdecarb J( C(5)-H) CH3 C02 x rel a NCH 1 201 CH -N@X 3 3 s 103.0 202 0 105.4 224

78 Until now, theoretica! contributions were only focussed on the thermadynamie acidity. It appeared that polarization of the a honds is principally responsible for stabilization of the 1,3-thiazolium ylid. An additional stabilization effect of sulphur on carbanions has usually been ascribed 16 18 18 to the possibility of (d-p)n - or (d-p)cr backbonding of the lone pair of the carbanion into the vacant d orbitals of sulphur. However, ab initio calculations 19 performed on simpler sulphur or oxygen containing anions (shown in Figure 5.4), show that stabilization of a carbanion by an

H y

H-J:)~y H..__xH--f--H H

X = O,S Y :: -, H,Li

?igure 5.4 adjacent sulphur atom is nat due to (d-p)n bonding, but to the greater polarizability of sulphur. In order to gain insight into the thermadynamie and kinetic acidity of 1,3-azolium cations, d-orbital partici pation, solvation, bonding and electron densities are con sidered in more detail. In the H-D exchange reaction the 14 15 formation of the conjugate base • is the rate-determining step, thus for the character of the transition state the HOHO and penultimate occupied MO of the conj bases are studied. For the kinetic acidity the HO's of the cations are taken into consideration. The systems investigated with the GEOMO program, using the CND0/2 metbod (Chapter Il) are shown in Figure 5.5. Although no H-D exchange rates are available for 1,3-phosphazolium systems, the cation and

79 HWH -H+ ... H-N~X .·- I 6 HWH H N~X H H B- .§. \ ... -H• H-N~X g_ x = NH H È. x = 0 7 .f. x = s d x = PH

FiguPe 5.5 Systems investigated related zwitterion are examined for the effect of d-orbital participation. The geometry of the 1,3-thiazolium, 1,3- imidazolium and 1,3-oxazolium system, determined by Sax e: 20 21 22 al. , Rerat and Albano et al. , respectively, is used. For the 1,3-phosphazolium cation and ylid the geometrical parameters are taken from phosphole 23 and the 1,3-imida zolium system. All internal parameters in the structures are optimized.

V.Z CND0/2 aalaulations on 1.3-azolium systems

V.2.1 d-Orbital aonjugation The enhanced acidity of protons adjacent to sulphur in its various oxidation states has been known for nearly 2 25 a century '. Most werkers, with some exceptions , have preferred an explanation for this phenomenon which implies a lowering of the energy of the transition state for proton abstraction (in case of kinetic acidity) or of a carbanion formation (in case of thermodynamic acidity) by (d-p)n

80 bonding, which is possible for atoms adjacent to second ro~ atoms. In recent years, the validity of the d-orbital model has been justified most frequently by reference to some experimental observations by Doering and Hoffmann 16 17 and by Oae et al. • Computations with and without ioclusion of 3d orbitals on the sulphur and phosphorus atom have been performed on compounds and ~. 6c and ~. and ]_s;_ and ~. in order to test the role of d orbitals in carbanion stabilization by sulphur as compared to nitrogen and oxygen. The results in Table V.2 show that dorbitals have no effect on the proton affinities of 6 and ]_, or conversely, on the C-H acidity of the cations 5. The introduetion of d orbitals just renders the basis set more flexible but lewers the enthalpy of the cation and conjugate base by the same amount. Optimized bond lengtbs of the 1,3-thiazolium and 1,3-phosphazolium cations and conjugate bases are shown in Table V.3. It is note worthy that the samebond lengths are obtained with the two basis sets. So this geometrical para meter is probably not sensitive to the presence or absence of d-type functions. The fact that the honds in the con jugate bases are langer than in the cations suggests the absence of (d-p)n conjugative effects, because such effects are expected to be manifested by a decrease in bond 2 6 length • The contribution of d-type functions to the MO's of

6c and ~. and 7c and d has been assessed by consideration of the coefficient matrix and charge distribution in these conjugate bases. In the coordinate system, shown in Figure 5.6, one (d-p)n and one (d-p)o interaction is possible on symmetry grounds, viz. (C2p y -X3d yz )n and (C X3d xz ) o. For the presence of (d-p)n and (d-p)o conjugation it is necessary that the coefficients of C2p , X3dyz and C2px, 1 X3dxz' respectively, are non-zero. Table V.4 lists the coefficients of the C2p and X3d functions in the two highest occupied MO's. The HOMO of the 1,3-thiazolium

81 Table V.2 Calculated enthalpy differences between ylids and cations

óH a,b .t;H a,a basis total enthalpy r r compound set (a. u.) (a. u.) (a. u.)

-Sa sp -48.11892 -6a sp -47.48897 0.6299S -7a sp -47.43444 0.67448 sp -S4.0S414 sp -S3.48088 O.S7326 0.63299 -7b sp -S3.4211S -Sc spd -46.52022 sp -46.24668 spd -4S.90095 0.61927 -45.62671 0.61997 -6c sp spd -45.86165 0.66857 -7c sp -45.57796 0.66872 -Sd spd -43.27787 -5d sp -42.88092 -6d spd -42.63474 0.64313 6d sp -42.23641 0.64451 -7d spd -42.59755 0.68032 -7d sp -42.20079 0.68013 al'll-lr Hylid-Hcation; bFormation of conjugate base on position 2; ePermation of conjugate base on position 5. conjugate base is essentially the carbon lone pair orbital and would have been expected to exhibit the greatest (d-p)o interaction. The (C2py-S3dyz)n interaction appears in the penultimate occupied MO. In case of the 1,3-phosphazolium conjugate base (C2py-P3dyz)n interaction occurs in the HOHO and (C2px-P3dxz)o interaction in the penultimate

82 Table V.3 Optimized bond 1 of 1,3-thiazolium and 1,3-phosphazolium cations and conjugate bases, computed bath with and without ioclusion of d orbitals in the basis set

bond length (ll.) c2-x cz x CçX CçX compound spda spa spda sp a

Sc 1. 680 1. 685 1. 689 1. 691

-6c 1.709 1 . 711 1. 698 1.695 -/C 1 • 6 8 0 1. 682 1. 713 1. 7 21 1 . 70 4 1.709 1.742 1.744 6d 1. 722 1 . 7 30 1 . 7 48 1.749 7d 1 • 71 2 1. 713 1 . 7 56 1 . 761

Basis set.

(a) coordinate system L:,y

(b) (d- p)Tt conjugation ( d- plcr conjugation CJ 0 Q y x----c a \:J o L, ----x

Figure 5.6 The nature of (d-p)n and Jo ugation in the aonjugate bases of 1,3-azoZium systems with X = S, PH and C C(2), C(S)

83 Table V.4 Coefficients of C2p and X3d orbitals which are appropriate for (d-p)rr and (d-p)cr interaction in the HOMO and penultimate occupied MOa

coefficientsb compound MO X3d 0 C2pd --6c HOMO 0.065 (xz) 0.532 (x) POMO 0.041 (yz) -0.278 ( )') -6d HOMO -0.069 (xz) -0.627 (x) POMO 0.081 (yz) -0.337 (y) -7c HOMO 0.071 (yz) -0.375 (y) POMO -0.091 (xz) -0.631 (x) -7d HOMO 0.081 (yz) -0.420 (y) POMO -0.079 (xz) -0.577 (x) aPOMO: penultimate occupied MO; bSymbols in parentheses refer to type of basis function; 0 X=S,P; dC2p refers to C(Z) in 6 and to C(S) in 2·

occupied ~10. The data of Table V.4 indicate that the HOMO has the greatest (d-p)cr interaction in case of 6c and 7c and the greatest (d-p)rr interaction for 6d and 7d. However, it is clear that the proper d-orbital coefficients are substantially smaller than those of the C2p orbitals in the MO, so that (d-p)rr and (d-p)cr conjugation can hardly be considered to constitute an essential basis for the explanation of the properties of the 1,3-thiazolium cation. The net orbital populations of X3dxy and X3dxz' 0.057 and 0.070 in 6c, 0.048 and 0.059 in 6d, 0.062 and 0.058 in 7.!::., and 0.067 and 0.051 in 7d. These values are too small to permit chemica! significanee to be attached to (d-p)rr and (d-p)cr conjugation. The total electronic population of the d orbitals is the same in the cations Sc and Sd as in the conjugate bases 6c and 7c, and 6d and 7d (0.34 e and 0.41 e, respectively). Thus the overall aonalusion is: 3d orbitals on sulphur and phosphorus in 1.3-azolium systems aat as

84 ?CZ~rization funetions rather than as i t valenee

Some analyses have stressed the potential importsnee of sulphur 3d orbitals in explaining the reactivity of the 14 18 27 28 1,3-thia:::olium cation and TPP ' ' • • For example, the greater stability of the 1,3-thiazolium transition state relative to the 1,3-imidazolium transition state, indicated kinetic exchange rates, has been attributed, at least in part, to ''(d-p)o overlap stabilization through interaction of a d orbital at sulphur with the a orbital directed away 28 :rom the ring at the 2 carbon" • The contention that (d-p)ê bonding might play a significant role has been taken as an explanation for the results of exchange rates studies 18 in 1,3-thiazolium ions and thiazoles • MO calculations on the potential importsnee of the sulphur 3d orbitals in acidity have yielded conflicting results. Ab-initia cal culations for an a-sulfinyl carbanion led to the conclusion that there were no d-orbital contributions to the higher 2 9 3 0 occupied riO' s • Streitwieser and Wi Zliams concluded from - i iti computations for the thiomethyl anion and its ugate acid that sulphur 3d orbitals stabilized the acid and the base to the same degree, and that sulphur stabilized arbanions by polarization rather than by d-orbital con jugation. A similar conclusion was drawn from ARCANA cal 31 culations on the structures of thione esters • On the other hand Extended Hückel studies of thiamine and TPP by Jordan 32 indicated a large 3d-orbital participation. The Extended Hückel methad is, however, known to overestimate net (Chapter II). The conclusions effered in this Section are therefore in accord with the conclusions of b-initio calculations performed on simpler, sulphur-con- 29 30 tain anions • • In the following Sections only the computations with d-type functions employed on sulphur and phosphorus will be considered.

V.2.2 Bonding and electron densities Table V.S and V.6 show the electron densities and the

85 Table V.S a- and TI-electron densitiesa 6b 7b -Sa -7a - At om a TI a TI a TI a 1f a 1f a 1f x, 3.527 1. 48 3.460 1 . 5 7 8 3.498 1.467 4. 411 1. 615 4.433 1. 67 4 4.464 1. 5 71 c2 2.862 0.92 3.492 0.65 2.84S 1. 024 2.84S 0.826 3.4S4 O.S86 2.803 0.971 N3 3.527 1. 48 3.460 1.578 3.S31 1 • 49 2 3.S51 1 . 461 3.477 1. 578 3.569 1. 430 c4 2.883 1. 06 2.889 1. 096 2.802 1 • 201 2.906 1. 042 2.919 1. 068 2.0899 1. 239 es 2.883 1. 06 2.889 1.096 3.S12 0.815 2.824 1. 0 ss 2.829 1.094 3.4S6 0.790 Hz 0.897 -- 0.991 0.885 -- 0.997 Hs 0.906 0.997 -- 0.900 1. 002 --

-6c -5d -6d -7d At om a 'IT a 1f (J 'IT a 'IT a TI a 1f x, 4.039 1.756 4. 19S 1. 907 4.316 1. 737 3.327 1. 482 3.429 1.6SS 3.S25 1. 467 cz 3.048 0.841 3.543 0.572 3.02S 0.900 2.949 1. 000 3.343 0.764 2.951 1. 033 N3 3. S41 1. 419 3.479 1 • s 18 3.S30 1. 444 3.4S4 1.528 3.412 1. ss 1 3.410 1. S87 c4 2.893 0.9S3 2.8S4 o. 972 2.809 1.068 2.897 0.902 2.862 0.9S7 2.832 0.986 es 3.014 1. 0 32 2.977 1. 033 3.436 0.849 2.979 1. 08S 3.07S 1. 073 3.369 0.926 Hz 0.892 -- 0.984 0.900 -- 0.993 Hs 0.870 1. 04 7 -- 0.871 0.9S7 -- ain electron units. Table V.6 Mulliken overlap populationa

Sa 7a Sb 6b 7b - - - - Bond (J rr û 7f û ;r û TI a TI û 7f c 2-X 0. 720 0. 144 0.693 0. 1 39 0.712 0. 136 0.629 0. 110 0.591 0. 104 0.613 0. 104 C2-N3 0. 720 0. 144 0.693 0. 139 0.683 0.143 0.722 0. 158 0.684 0. 153 0. 721 0. 160 N3-c4 0.673 0.091 0.670 0.077 0.642 0.083 0.663 0.078 0. 6 79 0.072 0.631 0.076 C4-C5 0.798 0. 211 0.801 0.223 0.845 0.232 0. 810 0.228 0.819 0.234 0.843 0.236 CçX 0.673 0.091 0.670 0.077 0.694 0. 108 0.560 0.060 0.570 0.056 0.599 0.074

0 -5c -6cb 7 -5db -6db Bond (J TI 0 7f 0 ;r 0 ;r 0 1T (J 1T c -X 0.266 0.875 0.275 2 0. 801 0. 196 0.744 0. 1 8 9 0.705 0.200 0.871 0.282 0.842 (0.175)(0.077)(0.182)(0.087)(0.178)(0.081) (0.193)(0.126)(0.213)(0.115)(0.131)(0.112) C2 N3 0.715 0. 145 0.697 0. 146 0. 714 0. 14 4 0. 71 5 0. 10 7 0.710 0. 119 0.718 0. 104 N3-c4 0.673 0.090 0.677 0.084 0.652 0.080 0.676 0. 104 0.664 0.095 0.659 0.098 C4-C5 0.793 0.203 0.830 0.215 0.861 0. 216 0.799 0. 19 5 0. 818 0.201 0.859 0. 214 c x 0.776 0. 136 0.708 0. 121 0.738 0. 1 3 2 0.815 0. 197 0.789 0. 1 7 5 0. 779 0. 18 7 (0.110) (0.076) (0.102) (0.077) (0.074) (0.074) (0.197)(0.080)(0.217){0.075)(0.213)(0.081) acr,n: Total overlap population in o and n bond, respectively; bln parentheses total (a-d) and d) overlap. overlap populations in the 1,3-azolium cations and conjugate bases. In the cations both the sulphur and phosphorus atom have positive character, whereas the nitrogen and oxygen atom are nearly neutral. The electropositive nature of 31 33 sulphur has been previously reported • • Upon deprotona tion sulphur gains the largest amount of electron density. None of the products formed has a classica! ylid structure 34 as was recently found by Aldrich et al. 35 in calculations with the ARCANA semi-empirica! MO method. GaZlo and 36 37 13 Sable • have pointed out that the c chemical shifts for the 1,3-thiazolium carbon atoms of thiamine do not correlate with the previously calculated rr-charge den sities38•39. The net atomie charges calculated by the CND0/2 methad provide a better correlation with the ex perimentally determined 13c chemical shifts. The 13c resonance for C(2) is at lower field than that for C(4), which is again at lower field than that for C(S). This is consistent with the net positive charges of C(2) relative to C(4) and C(S). To the extent that a correlation between the 13c chemica! shifts and the net atomie charges is to 40 be expected , the CND0/2 results seem to be more success ful at predicting the relative 13c chemica! shifts of the 1,3-thiazolium ring atoms than the ARCANA calculations 35 carried out by Aldrich et al. • In Table V.7 the calculated net charges of the proton like atoms at the carbon 2 (H(2)) and the nitrogen atom

Table V.7 Calculated net charges of H(2) and H(3) and corresponding pK's

net charge net charge compound pKa pKb Hz ' H3 Sa 0. 1034 17 0.1951 7.52 -Sb 0.1151 12 0.2054 1. 03 - 0.1077 14 0.2024 3.07 aAcidic pK as measured by Haake and Bausher 41 ; bBasic pK 1 5 as computed by Haake et al.

88 (H(3)) are given with the corresponding acidic and basic pK's. The calculated net charges correlate very well with the pK values. The correlation coefficient of the H(2) s vs the acidic pK and the H(3) charges vs the basic pK is -0.96 and -0.99, respectively. The TI bonding for the five-membered 1,3-azolium rings is extensively delocalized. The largest amount of TI lo cali:ation is in the C(4) C(S) bond, and with the N-CH-X fragment resembling a separate delocalized " netwerk. As is expected on symmetry considerations, the data in Table V.6 indicate that rr-bond density remains nearly the same upon generation of the conjugate base. The loss of electron density indicates that although the TI-bond density for the

X CH-X and X-C-X fragments does not change much, the ~ bcnds are shifted from C(2) to X and N in ~ and from C(S) toKards C(4) in l (Table V.6). Upon generation of the con jugate base the o framewerk displays the greatest change. The o honds (C(2)-X) and (C(2)-N(3)) of the 1,3-azolium systems show loss of electron charge density upon de protonation of C(2}. The electron density is transferred from the (N(3)-C(2)) o bond to C(2), whereas that of the (C(2}-X) o bond is shifted to X. It is found that the polarization of the (C(2)-X) o bond is stronger (for X = PH or S) relative to the (C(2)-N(3)) o bond. The (C(Z)-X) ~ bond is more polarized for X = S or PH than for X 0 or NH, respectively. Upon generation of a negative charge at C(S), the (C(4)-C(S)) o bond shows an increase of electron charge density, whereas the (C(S)-X) o bond shows a decrease when X is a second row atom and an increase when X is a first row atom. Upon deprotonation, a-electron density shifts from C(4) to C(S), C(S) to X (X= 0, S, PH) and from X to C(S) (X NH). The change in polarity in the (C(S}-X) a bond is greater for X = PH or S than X = 0 the (C(2)-X) o bond upon deprotonation at C(Z)). The above results can be ascribed to the much greater polari zability42 of both the sulphur (3.45 ~ 3 ) and phosphorus (4.42 ~ 3 ) atom with respect to the carbon (1.75 ~ 3 ), oxygen (0.73 ~ 3 ) and nitrogen (1.04 ~ 3 atom). The totaloverlap

89 population of the {C{2)-X) bond decreases upon generation of the conjugate base, whereas the (C(S)-X) bond follows the same line for X = S, PH, but increases for X = NH, 0. The difference in overlap population between cations and conjugate bases increases along the series of atoms X =S, PH, .0, NH. This is in line with the greater polarizability' 3 3 of the (C-S) bond (1.88 R ) with respect to the (C-0) bond (0.81 R3) and the (C-N) bond (0.57 R3). The larger decrease in overlap population of the (C(2)-S) bond indicates that this bond is more weakened with respect to the others. In the present systems a decrease in overlap population is accompanied by a lengthening of the bond (Table V.3 for X= s, PH; Table V.8 for X= NH, 0). These findings agree quite well with results of ab-initia calculations on a-oxa 19 30 and a-thia carbanions , and methanethiol and ethane •

Table V.8 Optimized bond lengths of 1,3-imidazolium and 1,3-oxazolium cations and conjugate bases

bond length CR) compound c2-X CçX

-Sa 1. 350 1. 39 2 6a 1. 36 2 1. 393 -7a 1. 352 1.400 1. 322 1. 3 71 -6b 1. 340 1.372 -7b 1. 324 1 • 38 3

The data in Table V.2 show that the relative therma dynamie acidity~ 4 (i.e. formation of a carbanion) has the same trend as the kinetic acidity (i.e. rate of H-D exchange of the cation), but the correlation is rather poor. Thus the greater polarizability of sulphur as well as the (C-S) bond which affords stabilization of the conjugate base of the 1,3-thiazolium cation with respect to the others, does ,,,,, ;'1''tc1y account for the relative small difference in Jl-D exchange between the 1,3-oxazolium and 1,3-thiazolium cation.

90 V.3 SoZvation enthalpies As is outlined in Chapter I, when discrepancies exist betKeen results of calculations in the gas phase and ex periments, it is worthwhile to consider the influence of solvation. The solvation enthalpies of the reactions in Figure 5.5, calculated according to equation (2.50), are shmm in Table V. 9. The data clearly show that the net solvation enthalpy does not account for the differences in reaction rates.

Table V.9 Net solvation enthalpies of deprotonation of 1,3-azolium cations

deprotonation net solvation enthalpy (kJ/mole) of position x NH 0 s PH c ( 2) -58.0 -58.4 -58.8 -59.6 c ( 5) 49.1 -48.6 -48.8 -49.7

V.~ The use of an MO desaription for the transition state and an estimation of the aativation entha

V.J.1 The aharaater of the transition state The H-D exchange reaction in 1,3-azolium systems is assumed to occur via an ylid. It is generally known 45 that in an endethermie reaction the transition state closely resembles the reaction product. Thus, it is fairly reason- le to assume that in the deprotonation of the 1,3-azoZium aations the transition state aZosely resembles the con 14 15 jugate base struature • • Therefore we describe the character of the transition state by using the HOMO and penultimate occupied MO of the conjugate base. The cal culations show that only the conjugate bases on position 2 and 5 of the 1,3-thiazolium cation have a HOMO with pre dominant a contribution, whereas the HOMO's of the other ugate bases mainly possess n contribution. The a HOMO

91 C1 HOMO n HOMO

y ~'

X = NH,O,PH

Figure 5.7 The HOMO's of the conjugate bases

(Figure 5.7) of the 1,3-thiazolium conjugate base is prin cipally the carbon lone pair orbital on the C(2) and C(5) atom. The n HOMO of the other conjugate bases is in the C(2) -zwitterion chiefly located on the C(2) atom and to a minor extent on X, whereas in the C(S)-zwitterion a similar situation is found for C(5) and C(4), respectively. The penultimate occupied MO is in the latter cases a a MO, i.e. the carbon lone pair orbital. The enthalpy difference between the TI HOMO and the penultimate a MO is small, namely 5.9 kJ/mole, 5.0 kJ/mole and 5.3 kJ/mole for 6a, 6b and 6d, and 4.8 kJ/mole, 4.1 kJ/mole and 4.3 kJ/mole for l!• 7b and 7d, respectively.

V.4.2 Estimation of the activation enthalpy As mentioned before, it hae been propoeed that de protonation of the aations and deuteration of the aonjugate

92 base take place in the plane of the 1,3-azolium systems 14 5.8). This invoZves that only a o MO is representa tive for the H-D exchange reaetion. All cations have, how ever, a HOMO with predominant TI character, whereas the penultimate occupied MO has o character, which is appropriate for the description of the H-D exchange on position 2. For the deprotonation of the C(S) atom a lm.,rer lying o MO is suitable, which is principally located on the atomie

_J(!:J\ y --- H

Pigure 5.8 Aetivated complex for proton abstraction of 1,3-azolium cations orbitals of C(S) and H(S). The enthalpy differences between the rr HOMO and the appropriate o MO are shown in Table V.10. Thus extra enthalpy will be necessary in order to use the appropriate lower lying occupied cr MO. The amount of activatien enthalpy in the H-D exchange reactions can be approximated by: the enthalpy difference between the conjugate base and the cation and an additional term for the enthalpy difference between the TI HOMO and the appropriate a MO of the cation. The calculated activatien enthalpies (Table V.10) are in excellent agreement with 44 the observed H-D exchange rates and decarboxylation rates • The correlation coefficient for the relative k exp vs the relative kcalc for the C(Z) and the C(S) position is 0.96 and 0.97, respectively. Comparison of the activatien en thalpies necessary for the generation of the C(Z) and C(S) zwitterion shows that they do not fit the relative exchange

93 Table V.10 Calculated activatien enthalpies and relative rates for the deprotonation of the C(2) and C(5) atom in 1,3-azolium systems

t.Ha Hb ka rel kd a rel calc exp (a. u.) (a. u.) <<1 1 ,3-imidazolium c 2 0. 1203 0.7503 1 5 10 5. 5 1, 3-oxazolium c 2 0. 11 39 0.6872 2.0 x 10 3 103.S 1,3-thiazolium c 2 0.0731 0. 6923 1. 0 x 10 1,3-phosphazolium c2 0.1010 0.7441 < 1 -

1,3-imidazolium Cs 0.2191 0.8936 <1 1 5 1,3-oxazolium CS 0.2316 0.8646 10 10S.4 2 10 3. 0 1,3-thiazolium c5 0.2022 0.8708 2.5 x 10 1,3-phosphazolium cs 0.2172 0.8975 <1 - aEnthalpy difference between 1r HOMO and appropriate cr NO in cation; bActivation enthalpy: Ha = t.H + t.Hr (t.Hr• see Table V.2); 0 Relative rates, calculated from the activatien enthalpies (T = 33 °C); dRelative rates as measured by 14 15 Haakeet aZ. • (pH 4-5, T = 33 °C).

4 1 15 rates (1:10 ) as observed by Haakeet aZ. q• • The difference in reaction enthalpy (Table V.2) is already too large to underline the difference in exchange rate and rate of decarboxylation. It should be kept in mind that rates of decarboxylation are compared with the generation of carban ions at position 5. For the reverse of the reaction, i.e. protonation, the transition state involves breaking the H-0 bond of the neutral sol vent with generation of a hydroxide or alkoxide ion. Data 46 for acetone and HCN give an estimation for the rate constant for protonation by 5 -1 water, namely kH 2o ~ 10 s From 13c-H coupling constants of 1,3-azolium cations it was expected that the 1,3-thiazolium cation would have a much lower exchange rate than the 1,3-oxazolium cation

94 and a similar rate as the 1,3-imidazolium cation. The ob served discrepancies were mainly ascribed 1 ~• 15 to d-orbital conjugation. In this Chapter it is, however, clearly demon strated that not d-orbital participation but the smaller amount of enthalpy necessary for the 1,3-thiazolium cation to employ the appropriate a MO, is responsible for the relatively small difference in exchange rate (factor 100) between the 1,3-oxazolium and 1,3-thiazolium cation.

V.4.3 H-D exchange reaations of arenes In the previous Section a hypothesis is offered for the estimation of the activatien enthalpy for H-D exchange reactions in aromatic 1,3-azolium cations. In ordertotest this hypothesis GEOHO-CND0/2 calculations with complete geometry optimization, have been performed for the gene ration of carbanions of various polycyclic aromatic hydro-

Table V.11 Calculated and experimental relative exchange rates of ArDa

liH b a d krel kre'e r liHMO calc exp Ar (T=49.9°) (T=49.9°) benzene 0.958066 0.0003 0.958366 1.0 1.0 2-biphenyl 0.916066 0.0419 0.957966 1. 4 7 1.2 3-biphenyl 0.864216 0.0927 0.956916 4.08 3.7 4-biphenyl 0.897166 0.0601 0.957266 2. 91 2.3 1- na ph thaiene 0.930206 0.0261 0.956306 7.40 6. s 2-naphthalene 0.909513 0.0476 0.957116 3.37 4. 1 9-phenanthrene 0.913492 0.0421 0.955592 14.80 1 7. 9 9-anthracene 0.924754 0.0603 0.955054 24.96 45. of 2-anthracene 0.913923 0.0717 0.955623 14.36 - 1-anthracene 0.864646 0.0912 0.955846 11.56 10.9 figures and numbering, Figure 5.9; (Ar-)-H(ArH); cllHMO=H~OMO(ArH)-H~ppropriate MO(ArH); dH!=liHr+liHMO; eRef. 47; fThe most serious error is that for anthracene-9-d which solubility problems produce a large error; gActivation enthalpy.

95 :00: 5 4 ·G-O·5 6 6' s'

:000: 5 10 4 3

Figure 5.9 Numbering of aromatie aompounds

carbons, e.g. benzene, biphenyl, naphthalene, anthracene, and phenanthrene. The relative rates of deuterium exchange with lithium cyclohexylamide, are determined by Streit wieser and Lawler~ 1 for various positions of the fore mentioned arenes. The experimental and calculated results are listed in Table V.ll. Comparison of ~Hr and the ex perimental values delivers a poor correlation, the correlation coefficient is -0.26. Taking into account the enthalpy difference of the rr HOMO and the appropriate a ~10, as is proposed in the previous Section, the experimental data and Ha are in good agreement. The correlation coeffi cient is 0.969 and the slope of the correlation line is 0.53. The fact that the data, obtained by the equation Ha = L'IHr + L'IHMO' are in good agreement with the experimental results points to direct polarization of electrous in the C-H bond to the carbon atom. The conclusion can be drawn that, taking into account the highest occupied MO's, it is possible to find fairly good relative H-D exchange rates for aromatic compounds with the CND0/2 method.

96 rences and notes 1. W. Langenbeek and Z. Hutschenreuter, z. Anorg. Allg. Chem., 188, 1 (1930). 2. K. Wiesner and z. Valenta, Experienta, , 190 (1956). 3. K.G. Stern and J.L. Melnick, J. Biol. Chem., 31 597 (1939). 4. A. Lapsworth, J. Chem. Soc.,~. 995 (1903); ~. 1209 (1904). 5. T. Ugai, S. Tanaka and S. Dokawa, J. Pharm. Soc. Jpn., 63, 269 (1943). 6. T. Ugai, S. Dokawa and S. Tsubokawa, J. Pharm. Soc. Jpn., &..±, 3 (1944}. 7 .. s .. ~1izuhara and P. Handler, J. Am. Chem. Soc.,~, 571 {1954). 8. R. Breslow, Chem. Ind. (London). R28 (1956). 9. J.M. Duclos and P. Haake, Biochemistry, , 5358 {1974). 10. D.E. Metzler, "The enzymes", Eds. P.D. Boyer, H. Lardy and K. Myrbäck, 2nd ed., p 295, Academie Press, New York; 1960. 11. R. Bres low, Chem. Ind. (London), 893 (1958). 12. R. Breslow, J. Am. Chem. Soc., !Q., 3719 (1958). 13. R. Ereslowand E. McNelis, J. Am. Chem. Soc.,~. 3080 (1959). 14. P. Haake, L.P. Eausher and W.B. Milier, J. Am. Chem. Soc., 2_l, 111 3 (1969). 15. P. Haake, L.P. Eausher and J.P. McNeal, J. Am. Chem. Soc., 2l_, 7045 (1971). 16. w. van E. Doering and A.K. Hoffman, J. Am. Chem. Soc., 2..1_, 521 (1955). 1 7. s. Oae, w. Tagaki and A. Ohno, Tetrahedron, ~. 417 (1964). 18. R.A. Olofson and J.M. Landesberg, J. Am. Chem. Soc., 8 ' 4263, 4265 (1966). 19. J.M. Lehn and G. Wipf, J. Am. Chem. Soc., 2§_, 7498 (1976).

97 20. M. Sax, P. Pulsinelli and J. Pletcher, J. Am. Chem. Soc. , ~. 1 5 5 ( 19 7 4) • 21. C. Rerat, "Molecular structures and dimensions", Yol. Al, N.V. Oosthoek, Utrecht (Netherlands), 1972, p 365. 22. V. Albana, P.L. Bellen, F. Pempa and V. Scatturin, "Molecular structures and dimensiens", vol. Al, :\.V. Oosthoek, Utrecht (Netherlands), 1972, p 230. 23. W. von Niessen, L.S. Cederbaum and G.H.F. Diercksen, J. Am. Chem. Soc., 98, 2066 (1976). 24. (a) D.J. Cram, "Fundamentals of carbanien chemistry", Academie Press, New York, 1965, pp 71-84; (b) H.A. Bend in "Organic Chemistry of sulphur compounds", vol. 3, N. Kharash and C.Y. Meyers, Eds., Pergamon Press, ~ew York. 25. H.H. Jaffé, J. Phys. Chem., ~. 185 (1954). 26. L.l\1. Tel, S. Welfe and l.G. Czismadia, Int. J. Quanturn Chem., J.., 475 (1973). 27. R. Coburn, J. Landerbur, 0. Kemp and R. Olefson, Tetrahedren, ~. 685 (1970). 28. R. Breslow, Ann. N.Y. Acad. Sci., 98, 445 (1962). 29. S. Wolfe, A. Rauk and I.G. Czismadia, J. Am. Chem. Soc., 89, 5710 (1967). 30. A. Streitwieser Jr. and J.E. Williams Jr., J. Am. Chem. Soc., 2.7.., 191 (1975). 31. H.S. Aldrich, Int. J. Quanturn Chem., QB 2 (1975). 32. F. Jerdan, J. Am. Chem. Soc.,~. 3623 (1974). 33. M. Gelus, P.M. Vay and G. Berthier, Theor. Chim. Acta (Berl.), 2_, 182 (1967). 34. A.W. Johnson, "Organic Chemistry Menegraphs Series", vol. 7, "Ylide Chemistry", Academie Press, New York, 1966, pp 1, 251, 304. 35. H.S. Aldrich, W.L. Alwerth and N.R. Clement, J. Am. Chem. Soc. , 100, 2362 (1978). 36. A. A. Gallo and H.Z. Sable, J. Biel. Chem., 249. 1382 (1974). 37. A.A. Gallo and H. Z. Sable, J. Biol. Chem. , 251, 2564 (1976).

98 38. B. Pullman and A. Pullman, "Quantum Chemistry", Inter science, New York, N.Y.; 1963, pp 636-656. 39. B. Pullman and C. Spanjaard, Biochem. Biophys. Acta, 46, 576 (1961). 40. A.J. Jones, D.M. Grant, M. Winkley and R.K. Robbins, J. Am. Chem. Soc., , 4071 (1970). 41. P. Haake and L.P. Bausher, J. Phys. Chem., ll, 2213 (1968). 42. J. Thorhallson, C. Fisk and S. Fraga, Theoret. Chim. Acta (Berl.), , 388 (1968). 43. H.A. Stuart, "Molekülstruktur", Springer Verlag, Berlin, 1967; pp 423-426. 44. As is shown in reference 14 and 15 the activation entha es and Gibbs free energies are almost the same while the activatien entropy is very small. Therefore, it is reasonable to campare relative activation en thalpies and experimental k values. 45. G.S. Hammond, J. Am. Chem. Soc., zz, 334 (1955). 46. M. Eigen, Angew. Chemie, Intern. Ed. Engl., ~. 1 (1964). 47. A. Streitwieser Jr. and R.G. Lawler, J. Am. Chem. Soc., .!U_, 5388 (1965).

99 CHAPTER VI

ThiaJD.ine pyrophosphate-catalyzed decarbox.y lation of pyruvate anion

VI.1 Introduation The decarboxylation of pyruvate to acetaldehyde by the enzyme pyruvate decarboxylase is a reaction which requires the coenzyme thiamine pyrophosphate 1 (TPP). On the basis of investigations of nonenzymatic model reactions, Breslow 2 has proposed that the enzymic reactions praeeed via 2-(1- carboxy-1-hydroxyethyl)thiamine pyrophosphate (.l!_), which is formed from TPP and pyruvic acid by reaction of the 1,3- thiazolium ring, ionized at C(Z), with the carbonyl group of pyruvic acid. Decarboxylation of this intermediate yields 2-(1-hydroxyethyl)thiamine pyrophosphate (~), which

C H OP 0 3- Q. R = CH 3 -<~"=è J CH 2- ; ~= 2 4 2 6 NH2

Q R= CH3 R1::: H

100 can loose acetaldehyde under formation of TPP. The proposed intermediate Za has been isolated from reaction mixtures Khich contained pyruvic acid and pyruvate decarboxylase 3 4 holoenzyme • • Moreover, it has been shown that pyruvate decarboxylase apoenzyme catalyzes the formation of acetal 3 5 from 2a • • Results similar tothese have also been obtained for pyruvate dehydrogenase, the enzyme which cat the TPP-dependent oxidative decarboxylation of 6 pyruvic acid to acetyl coenzyme A • Since most enzymic reactions in which TPP is a co factor are mechanistically similar to the pyruvate decar 7 boxylase reactions , the decarboxylation of the pyruvate anion by means of 1,3-azolium cationsis chosen as model reaction.

VI.2 The reaction scheme for the pyruvate decarboxylation re action In 6.1 the mechanistic path;vay is depicted for the entire reaction, which is consistent with the previous 8 9 modeland enzymic studies • Kinetic studies of the de carboxylation of 1b clearly show that the zwitterion is the species which decarboxylates. The most likely mechanism for the decarboxylation re action is the one that yields as the initial product the planar neutral enamine, which can be protonated in a sub sequant rapid reaction. The mechanism of decarboxylation closely resembles the one proposed for the decarboxylation 10 of 2-methyl 2-(2-pyridyl)butyric acid (1) • The fact that

101 0 0 11 11 .. CH - C-C- OH - 3

t==\ 0 0 + f \ 11 11 • I \ -N S + CH-C-C-OH -N S v.. ::______/'3 y -o-C-COOH I CH 3

0 I \ 11 NI S + CH -C-H )( 3 HO CH3

Figure 6.1 Meohanism for pyruvate deaarboxylation

this compound decarboxylates more rapidly in neutral aqueous salution than in a strong acid or base suggests that the zwitterion is the intermediate species. The inter mediacy of a planar enamine is clearly shown by the finding that decarboxylation of optically active 1 yielded racemie

X : 0, TTPP ; X : S, TTTPP

102 10 2-s-butylpyridine • The formation of enamines is also supported by the synthesis of activated analogues for TPP dependent enzymic reactions, e.g. thiamine thiazolone pyro phosphate (TTPP) and thiamine thiothiazolone pyrophosphate 1 1 (TTTPP) • The tautomerization of the enamine to the dipolar ion is presented as a proton transfer reaction from the adjacent hydroxyl group to carbon. This may occur directly or with the participation of another base. The final step in the mechanism is elimination of the conjugate base from the aleoholate anion. In order to understand the mechanistic aspects of the enzymic decarboxylation of the pyruvate anion in more detail, GEOMO-CND0/2 calculations, with geometry optimi zations have been performed for the reaction path as de picted in Figure 6.2. The geometry parameters of the 1,3-azolium ring of 6- 10 have been taken from the corresponding cations. Those for the 2-(1-carboxy-1-hydroxyethyl) group of 6 are obtained from lithium dihydrogen citrate 12 and for the 2-(1-hydroxy ethyl) group of ~ from X-ray crystallographic data of 2- 13 (1-hydroxyethyl)3,4-dimethyl-1,3-thiazolium cation • Por the enamine, carbondioxide and acetaldehyde, known dis 14 tances and bond angles are used • The structure of the enamine 2 has purposely been drawn with the hydroxyl group and nitrogen cis to one another, sirree examination of Dreiding models demonstrate that in the other geometrical isomer there is considerable steric interaction between a substituent of nitrogen and the vinylic methyl group. The geometrical data for the pyruvate anion are obtained from 15 X-ray crystallographic data • All internal parameters have been optimized.

VI.3 The net reaction enthalpies of pyruvate decarboxy lations with 1,3-azolium systems The net reaction enthalpies are listed in Table VI.1. Crosby et al. 9 have pointed out that the first step in the

103 decarboxylation has to be considered as a direct proton transfer between the carboxylate anion and C(2) of the 1,3- thiazolium cation (I, Figure 6.2). This reaction seems to be the most exothermic for the 1,3-oxazolium system. In the secend step (II) the ylid attacks the pyruvic acid rather than the pyruvate anion, because the greater electron withdrawing effect of the COOH group makes the keto carbon atom of the acid more reactive. For the 1,3-azolium com pounds with second row atoms as hetero-atom reaction II is more exothermic. Since it is assumed 11 that the enamine closely re sembles the transition state for decarboxylation of ~. the net reaction enthalpy of III is a measure for the relative rates of decarboxylation. It is obvious that decarboxy lation of 2-(1-carboxy-1-hydroxyethyl)-1,3-thiazolium (6d) will be the most rapid one. This is in agreement with our 16 recently publisbed results • In this study the lewest un occupied MO (LUMO) of 1,3-azolium cations has been examined in order to gain insight into the reactivity of the 1,3- thiazolium cation as electron acceptor in biochemica! de carboxylation reactions. As is shown in Table VI.2, the LUMO of the 1,3-thiazolium cation has the most negative enthalpy value with respect to the other 1,3-azolium cations. This means that the decarboxylation will occur most rapidly

Table VI.2 Enthalpy value of LUMO of 1,3-azolium cations

x NH 0 PH s E (a.u.) -0.1343 -0.1789 -0.1065 -0.2213 with TPP as catalyst. It should, however, be noticed that all these data refer to gas phase conditions. Starting from the enamine there are two possible ways to obtain the aleoholate anion (~), from which the ylid and the aldehyde can be formed, namely (1) tautomerization of the enamine to the dipolar ion ~ and (2) formation of 2-(1-hydroxyethyl)-1,3-azolium compounds (~) and subsequent ionization of the hydroxyl group. The data for reaction IV

104 IQ\ -- rl- NvX '-../ H-J8~ li fo III Ho-c-c""' I 'o- CH3 5 6

0 I \ 11 H-NI X ---- 2. + CH -CH -- H-J~~ y 3 HOXCH3 IJ[ -o-e H I CH3 7 8

I \ + H+ H-NI x H-N~ H-NfX0 -YI 1TI x HO-C- H -o-c-H HO CH3 I I CH3 CH 3 l ~

-H•t= x

NH .9. H-NYX0 .Q 0 HO-C- I PH f CH3 Q s 10

Figure 6.2 Reaction pathway

105 .... 0 en

Table VI.1 Net reaction enthalpiesa

l:\H 6Hr 6Hr t>Hr 6Hr 6Hr 6Hr r t.Hr a. u. a.u. a.u. a. u. a. u. a. u. a.u. a.u. x I II III IV V VI VII VIII NH -0.2166 -0.2606 0.2171 -0.2370 -0.2322 -0.4833 -0.2509 1.0599 0 -0.2673 -0.2397 0.1772 -0.2161 -0.2293 -0.4478 -0.2294 1.0205 PH -0.1974 -0.4823 0.3738 -0.1719 -0.1980 -0.4520 -0.1800 1.1094 s -0.2213 -0.4882 0. 1560 -0.2414 -0.1652 -0.4372 -0.2540 1 . 0 154

aNumbers of reactions are shown in Figure 6.2. and VII indicate that the latter is more exothermic. For the 1,3-thiazolium compounds this is in agreement with the pK values. The pK for the ionization of the hydroxyl a a group of 2-(1-hydroxyethyl)thiamine pyrophosphate in water 17 is probably about 12 •. The pK for the dissociation of 8 the a hydrogen atom of this compound has not been deter mined. A crude estimation 9 gives a value of pKa = 17 for this reaction. These pKa values show that in water the proton transfer from the hydroxyl group to the a carbon is favoured thermodynamically. The mechanism prediets that the a hydrogen of 2-(1- hydroxyethyl)thiamine pyrophosphate ought to exchange with solvent deuterium through interconversion as is shown in Figure 6.3. The net reaction enthalpies of VI and VIII

020 I \ .. I \ __,_ I \ .F\ ------=- -•N X -N~ X ....,--- -NI x ~ -N y X -=-- y ~ HO-C-D HO C~H HO)(CH c- I 3 / I HO ' CH3 CH CH 3 3

6.3 H-D exchange of 2-(1-hydroxyethy~Jthiamine pyrophosphate

show that most probably the 1,3-thiazolium compound will exchange most readily. In Table VI.3 the net charges on C(2) of~ are listed. The partial positive charge on C(2) of~ stahilizes the adjacent a carbanion and this helps to explain the ease of formation of the a carbanion bath 7 18 enzymatically and in model studies • These results stand in contrast to the results of X-ray crystallographic studies 13 of~. which place a partial negative charge on C(2). The discrepancy probably reflects the more indirect approach used in the X-ray crystallographic studies. The

107 Table VI.3 Net charges on C(2) of ~ --9a 9b --9c --9d net charge on C(2) (e.u.) 0.201 0.231 0.189 0.249 charge density at C(2) is an important factor in deter mining kinetic acidity of (Ca)-H. The order of net charges is the same as the order of net reaction enthalpies.

VI.4 TPP as aocarboxylaae Haake et al. 17 have shown that the relative rates for the formation of the ylids of 1,3-azolium cations are in the order 4b:4d:4a = 10 5· 5:10 3· 5:1. If the rate of ylid formation correlates with catalytic effectiveness, 1,3- oxazolium compounds should be better catalysts than 1,3- thiazolium compounds. There are, however, no data for in vivo catalysis by 1,3~oxazolium compounds. Breelow 19 has stuclied the benzoin condensation catalyzed by a number of 1,3-azolium species, including benzoxazolium compounds. In all cases, the benzoxazolium cations have shown no catalysis. This does, however, not implicate that 1,3- oxazolium compounds can not act as catalysts. Zottewies and Helmiek 20 have demonstrated that for benzothiazolium ions, the primary reason for the diminished reactivity of the 1-hydroxyethyl 0 chain is steric inhibition of resonance. Interaction between the hydroxyl group of this chain with the substituant bonded to nitrogen prevents maximum over lap, resulting in an effective delocalization of the electrans from the reactive C-H bond into the positively charged ring of the transition state. Codington and Wuerat 21 have synthesized an oxazolium analogue of thiamine. They have found that this compound does not function as a co carboxylase. Thus, the 1,3-oxazolium compounds seem to be ineffective in model and in vivo reactions where thiamine

108 CH R CH R 3 1 3 1 I \ - .H H -NI + H+ OH + -N x -NI x x v "eH x ~ H OH 0

?igv.re 6.4 Ring opening reaction of 1,3-azolium cations

is effective. Duclos and Haake 22 have considered the ring opening reaction of 1,3-azolium cations (Figure 6.4), since it has been assumed by Breslow 18 that there has to be a pH optimum, below which the concentratien of the ylid is too low for observable catalysis. Duclos and Haake have esta blished that at physiological pH (pH 7.4) the 1,3-oxazolium cations are kinetically and thermodynamically unstable. This explains why 1,3-oxazolium compounds are inactive in

{~vivo and in vitro: 1,3-oxazolium ions are unstable near neutrality, they hydrolyse to the ring-opened form. The 1,3-thiazolium and 1 ,3-imidazolium compounds are thermo dynamically stable at physiological pH, but as the pH in creases, a significant amount of ring-opened form of 1,3- thiazolium is present and above pH 9.5 this form predomi nates. The 1,3-imidazolium ions require very strongly basic solutions for ring opening. They form, however, ylids more than 10 3 times more slowly than the corresponding 1,3-thia zolium ions (vide supra). Therefore, of the 1,3-azolium compounds, the 1,3-thiazolium ion is suited for cocarboxy lase function. It is thermodynamically stable at pH 7.4, and the rate of formation of the 1,3-thiazolium ylid enables it to be an effective catalyst.

109 Referenoes

1. A.V. Morey and E. Juni, J. Biol. Chem., 243, 3009 (1968). 2. R. Breslow, Chem. Ind. (Londen), 893 (1957). 3. L.O. Krampitz, I. Suzuki and G. Gruell, Fed. Proc., 20, 971 (1961). 4. H. Holzer and K. Beaucamp, Biochim. Biophys. Acta, 46, 225 (1961). 5. H.W. Goedde, B. Ultich, C. Stahlmann and H. Holzer, Biochem. Z., 343, 204 ( 1965). 6. P. Scriba and H. Holzer, Biochem. z., l• 473 (1961); H.W. Goedde, H. Inouye and H. Holzer, Biochim. Biophys. Acta, 50, 41 (1961); L.P. Hager and L.O. Krampitz, Fed. Proc.,~. 536 (1963). 7. L.O. Krampitz, Ann. Rev. Biochim., ~. 213 (1969). 8. H.R. Mahler and E.H. Cordes, "Biologica! Chemistry", Harper and Row, New York, 1971, sec. edn.; pp 401-406. 9. J. Crosby, R. Stone and G.E. Lienhard, J. Am. Chem. Soc., 92, 2891 (1970). 10. W. van E. Doering and V.Z. Pasternak, J. Am. Chem. Soc., .zl, 143 (1950). 11. J.A. Gutowski and G.E. Lienhard, J. Biol. Chem., 251, 2863 (1976). 12. "f.1olecular structures and dimensions", vol. Al, N.V. Oosthoek (Netherlands), 1972. 13. fv!. Sax, P. Pulsinelli and J. Pletcher, J. Am. Chem. Soc., 96, 155 (1974). 14. "Tables of interatomie distances and configuration in molecules and ions", A.D. Mitchell and L.C. Cross Eds., Special Publication no 11, The Chemica! Society London, 1958. 15. S.S. Tavale, L.M. Paul and A.B. Biswas, Acta Cryst., 11· 1281 (1961). 16. M.M.E. Scheffers-Sap and H.M. Buck, J. Am. Chem. Soc., .!Q..!, 4807 (1979). 17. P. Haake, L. P. Bausher and J. P. ~icNeal, J. Am. Chem.

110 So c . , 9 3 , 7 0 4 5 ( 1 9 7 1 ) •

18. J.J. ~Iieyal, R.G. Votaw, L.O. Krampitz and H.Z. Sable, Biochim. Biophys. Acta, lil• 205 (1967). 19. R. Breslow, J. Am. Chem. Soc., 80, 3719 (1958). 20. J.A. Zoltewicz and L.S. Helmick, J. Org. Chem., 43, 1718 (1978). 21. J.F. Codington and H.H. Wuerst, Fed. Proc. Fed. Amer. S o c . E xp • Bi o 1. , 1§_, 1 6 5 ( 1 9 5 7) . 22. J.~1. Duclos and P. Haake, Biochemistry, .Jl., 5358 (1974).

111 APPENDIX A

CND0/2 optimized geometry of c-AMP

R ALP HA BETA at om N A B c R degrees degrees 0 ( 1' ) 1 0 0 0 o.ooo o.o 0.0 c ( 1') 2 1 0 0 1. 3 7 3 0.0 0.0 C(2') 3 2 1 0 1. 502 105.9 0.0 C(3') 4 3 2 1 1. 498 106.6 11.3 C(4') 5 4 3 2 1. 522 95.6 18.3 c (5') 6 5 1 2 1. 494 105.5 152.9 0(5') 7 6 5 1 1.373 110. 8 171.5 0(3') 8 4 5 1 1.396 115.3 -160.4 p 9 7 6 5 1. 610 109.0 53.3 0(6) 10 9 7 6 1. 664 108.6 -144.6 0(7) 11 9 7 6 1. 6 71 107.3 85.7 0(2') 12 3 2 1 1. 390 111 • 9 130.4 ll(1~) 13 2 3 4 1.104 110. 2 -130.2 H( 1t) 14 2 3 4 1.106 117. 2 105.3 H(2') 1 5 3 2 1 1 • 115 110. 2 -110.7 H(3') 16 4 3 2 1 . 130 110. 5 - 86.9 H(4') 17 5 4 3 1. 125 117. 4 81.8 5 1 1.099 114.6 - 68.7 H(S')a 18 6 H(5b) 19 6 5 1 1 • 1 0 1 114. 7 51.8 H(0(2')) 20 12 3 2 0.999 108. 1 105.7

N: number of atom; A: number of atom by which the bond length R for atom N is defined; B: number of atom by which, together with atom A, the bond angle ALPHA ( L NAB) is de fined; C: number of atom by which, tagether with atom A and B, the dihedral angle BETA (LL NABC) is defined.

112 c;.;D0/2 optimized geometry of 5'-AMP

R ALP HA BETA

a torn ~ A B c ~ degrees degrees

0 ( 1 ' ) 1 0 0 0 0.000 0.0 0.0 c ( 1 t) 2 1 0 0 1. 390 0.0 o.o C(2 t) 3 2 1 0 1. 496 107.1 0.0 C(3') 4 3 2 1 1. 495 102.3 - 30. 1 C(.f') 5 4 3 2 1. 383 99.9 42.2 c ( 5') 6 5 4 3 1. 379 119. 5 -133.9 0(5') 7 6 5 4 1 . 4 71 108. 3 - 78.1 p 8 7 6 5 1 • 794 115. 2 1 77. 2 0(2') 9 3 2 1 1 . 4 3 2 111. 3 - 88.7 ·o c3') 1 0 4 3 2 1. 390 108.3 170.0 0(6) 11 8 7 6 1. 6 7 3 106.3 17 7. 1 0 ( 7) 12 8 7 6 1. 6 71 108.9 50.3 0(8) 13 8 7 6 1.576 106.0 - 69.2 H( 1 ~) 14 2 3 4 1. 130 1 1 0 • 1 -121.9 H ( 1 b) 1 s 2 3 4 1.137 110. 4 12 4. 1 H(0(2')) 16 9 3 2 1 . 0 5 5 106.8 - 58.4 H(0(3')) 1 7 1 0 4 3 1. 051 108.8 56.6 H(2') 1 8 3 2 1 1.124 11 0. 9 99.4 H(3') 19 4 3 2 1. 111 11 7. 1 - 37.5 H(4') 20 5 4 3 1.133 118. 3 79.9 H(5~) 21 6 5 4 1 . 1 2 8 11 3. 8 78.8 H(5b) 22 6 5 4 1. 12 4 113. 8 - 78.8 H(0(8)) 23 13 8 7 0.929 119. 1 98.8

113 CND0/2 optimized geometry of 3'-AMP

R ALP HA BETA at om N A B c ~ degrees degrees 0(1') 1 0 0 0 0.000 0.0 o.o C ( 1 I) 2 1 0 0 1 . 391 0.0 o.o C(2') 3 2 1 0 1. 493 107.6 o.o C(3') 4 3 2 1 1. 497 102.8 - 21.6 C(4') 5 4 3 2 1. 502 99.5 36. 2 C(5') 6 5 4 3 1.480 114.7 -156.5 0(5') 7 6 5 1 1. 390 105.5 56.8 0(3') 8 4 5 1 1. 394 109.6 -158.5 p 9 8 4 5 1.770 94.9 -123.0 0(6) 10 9 8 4 1. 663 113. 5 51.3 0( 7) 11 9 8 4 1. 663 106.2 180.7 0(8) 12 9 8 4 1 • 7 50 101.9 - 65.4 0 (2 t) 13 3 2 1 1. 390 110.8 97.4 H( 1~) 14 2 1 5 0.991 111 • 6 117. 0 H( 11,) 15 2 1 5 1 . 1 00 106.9 -127.6 H(0(2')) 16 13 3 2 0.878 105.5 -148.5 H(3') 1 7 4 3 2 0.930 110.3 - 79. 1 H(4') 18 5 4 3 0.948 112.6 77.7 H(S~) 19 6 5 4 0.952 116.6 50.4 H(Si,) 20 6 5 4 1.012 107.4 - 68.8 H(0(5')) 21 7 6 5 1. 0 30 103.3 148.9 H(0(8)) 22 12 9 8 1. 032 109.8 - 78.0 H(2') 23 3 2 1 1. 081 111. 5 -143.9

114 115 APPENDIX B

Hydration scheme of c-MlP

numbera and water molecule characterb of net charge" on water molecule He 0 H"

1 A 0.2420 -0.3855 1L061- 2 A 0.2415 -0.4036 0.0756 3 A 0.2424 -0.3896 0.0626 4 A 0.2253 -0.3680 0.0"39 s A 0. 2107 -0.3473 0.0886 6 D 0.1674 -0.2906 0.14~6 7 A 0.2195 -0.3639 0.08H 8 A 0. 1962 -0.3372 0.0918 9 A 0.2004 -0.3395 0.0965

asee drawing; bA: proton acceptor, D: proton donor; eH involved in hydragen bond; dH nat involved in hydragen bond, except for formation of seven-membered ring (12); "in e.u.

116 c-A~!P continued

numbera atom and net chargese atoms and net chargese on of water on atom involved the atorns a dj a een t to molecule in hydrogen bond proton acceptor or donor

1 0(6) -0.4189 p 0.4308 2 0(6)/0(7) -0.4602/-0.5116 p 0.4363 3 0(7) -0.5299 p 0.4325 -1 0 (3') -0.2883 C (3' )/P 0.2112/0.4012 5 0(2')/0(3') -0.2499/-0.2386 C(2')/C(3') 0.1483/0.2018 6 H(0(2')) 0.2214 0(2') -0.3516 7 0(2') -0.2636 C(2' )/H(0(2')) 0.1475/0.1421 8 0(1 'l -0.2455 C ( 1 ')/C ( 4') 0.1391/0.1017 9 0(5') -0.2833 C(5' )/P 0.2156/0.3864

117 flydra ti on scheme of S '-M1P

...... " o,. o.. LJ

numbera and water molecule characterb of net charge (e. u.) on water molecule H" 0 Hd 1 A 0.2435 -0.3892 o. 0611 2 A 0.1588 -0.3951 0.1546 3 A 0. 2440 -0.3933 0.0606 4 A 0. 2411 -0.3604 0.0756 5 A 0.1594 -0.3258 0.1500 6 D 0.1548 -0.2756 0. 1508 7 A 0.1972 -0.3069 0.0923 8 A 0.1865 -0.3148 0.0959 9 A 0.2215 -0.3211 0.0634 10 D 0. 1102 -0.2644 0. 1121 11 A 0.2218 -0.3366 0.0789 12 A 0. 1569 -0.3501 0. 1701 13 A 0. 2311 -0.3269 0.0814 14 D o. 1 s 19 -0.2702 0.1524

Notes: see hydratien scheme of c-AMP

118 S '-A~lP, continued

numbera atom and net atoms and net chargese on of water on atom involved the atoms adjacent to molecule in hydrogen bond proton acceptor or donor

0(6) -0.441 p 0.4269 0(6)/ -0.4401/ p 0.4269 0(7) -0.4612 0(7) -0.4599 p 0.4364 4 0(3.) -0.2412 C(3')/!1(0(3') 0.0752/0.1302 5 0(2' )/ -0.2727/ C(Z' )/ 0.1508/ 0(3.) -0.2391 c (3.) 0.0645 H(O(Z')) 0. 146 7 0(2') -0.3144 0(2.) -0.2813 C(Z' )/fl(O(Z')) 0.1469/0.1099 8 0(1 ') -0.2509 C(l' )/C(4') 0.1278/0.2130 9 0(5') -0.3501 C(S' )/P 0.1621/0.4064 10 H(0(8)) 0.2347 0(8) -0.4652 11 0(8) -0.4936 11(0(8) )/P 0.1732/0.4113 0(1. )/ -0.2487/ C(1')/C(5')/ 0.1280/0.1366/ 0( ') -0 . .>601 C(4')/P 0.2131/0.3962 13 0(1' )/ -0.2412/ C(1')/C(5'l/ 0.1271/0.1298 0 5') -0.3556 C(4')/P 0.2132/0.3944

1 ~ H(0(3')) 0. 1680 0(3') -0.2818

119 llydration scheme of :i' -NIP

numbera and water molecule 'characterb of net chargee on water molecule H" 0 Hi

1 A 0.2412 -0.4149 0.0655 z A 0.1588 -0.3475 0.1542 3 A 0.2424 -0.4171 0.0645 4 A 0.2080 -0.3536 0.0905 5 A 0.1682 -0.2968 0.1123 6 D 0. 1397 -0.2840 0.1303 7 A 0.1554 -0.2747 0.1027 8 A 0.1991 -0.3558 0.1069 9 A 0.1944 -0.3539 0. 1071 10 D 0. 1248 -0. 2911 0. 1284 11 A 0.2054 -0.3339 0.0926 12 A 0.1476 -0.3281 0.1590 13 A 0.1831 -0.3119 0.0963 14 D 0.1992 -0.2805 0.1068

Notes: see hydration scheme of c-MIP

120 3'-AMP, continued

numbera atom and net atoms and net charges8 on i of \\ater on atom involved the atoms adjacent to molecule in hydragen bond proton acceptor ar donor

1 0(6) -0.4576 p 0.4342 2 0(6)/ -0.4536/ p 0. 4151 0(7) -0.4432 3 () ( 7) -0.4427 p 0.4349 4 0(3') -0.3378 C(3')/P 0.1453/0.4424 5 0(2' )/ -0.3071/ c (2' )/ 0.1455/ 0(3') -0.3357 c ( 3') o. 1426 6 H[O(Z')) 0.2053 0(2') -0.3400 7 0(2') -0.3091 C(Z')/H(O(Z')) 0.1398/0.1818 8 0(1') -0.2717 C(1')/C(4') 0.1429/0.1390 9 0(5') -0.2596 C(S')/H(O(S')) 0.1423/0.1142 10 H(0(8)) 0.1631 0(8) -0.3762 11 0(8) -0.3599 P/1!(0(8)) 0.4199/0.1093 12 0( 1 ')/ -0.2667/ C(1')/C(4')/ 0.1430/0.1378/ 0(5') -0.2696 C(5')/P 0.1426/0.4081 13 0(1 ')/ -0.2731/ C(1 ')/C(4' ]/ 0.1415/0.1301/ 0 (5') -0.2599 C(S')/P 0.1498/0.3987

14 H(O(S')) . 0. 1411 0(5') -0.2987

121 Sun1D1ary

In this thesis a quantumchemical study of the mole cular dynamics of the coenzymes cyclic adenosine 3' ,5' monophosphate (c-M·1P) and thiamine pyrophosphate (TPP) is presented. Molecular orbital calculations have been per formed using the Extended-Hückel and the CND0/2 method, and the ST0-3G ab-initia procedure. c-Ar.•P is a key substance in the regulation of en zymatic processes in the cell and it stimulates the activity of the genes via the synthesis of messenger ~~A. which in fact reproduces the information stored in the DNA of the gen. The level of concentratien of c-AMP in the cell is regulated via hydralysis with a phosphodi esterase, which yields adenosine 5'-monophosphate (5'-AMP). The hydro is to 5 '-M•P in vol ves a large exothermic enthalpy (-46.6 kJ/mole). In particular, attention has been focussed on the mechanistic aspects of this hydra lysis. The solvent effect on the enthalpy of hydralysis has been studied by the EH method for the hydrolysis of c-AMP and related cyclic phosphate diesters. The results show that the difference in enthalpy between c-AMP and related phosphate diesters can be explained, in part, by the difference in net solvation enthalpy. It has been calculated that the large exothermic net solvation enthalpy of the hydralysis of c-AMP can be ascribed to an extra stabilization of the hydralysis product with respect to the reactants and which is absent in the other cyclic phosphate diesters. The extra stabilization is due to

122 hydragen bonding with water between 0(1') and 0(5') in 5'-AMP. From CND0/2 calculations, with a water molecule situated between 0(1') and 0(5'), it is concluded that this position indeed is an important hydratien site and that formation of a five- as well as a seven-membered ring is possible. The occurrence of the former opens the potentia lity fora "through water" interaction of 5'-AMP with enzymic sites. In addition to the solvent effect the con formational difference of the ribose ring in c-AMP, on the one hand, and in 5'-A~1P, on theether hand, bas been taken into account. It is clearly demonstrated that this differ ence also contributes to the overall exothermic enthalpy of hydrolysis. Furthermore, attention bas been paid to the coenzymatic function of TPP. It serves as a coenzyme for enzymatic re actions: oxidative and nonoxidative decarboxylations of a-keto acids and formation of a ketols. The mechanism of the nonenzymatic reactions bas been observed with the discovery of Ereslow that the aromatic hydrogen at position 2 of the 1 ,3-thiazolium exchanges readily with solvent deuterium. The H-D exchange reactions of 1,3-azolium cations have been stuclied by the CND0/2 metbod with optimization of all geometrical parameters, in order to explain the rate enhancement for the 1,3-thiazolium cations. The following results are obtained: (a) stabilization of a carbanion by the adjacent sulphur atom is not due to (d-p) conjugation; (b) the 1 ,3-thiazolium conjugate base is stabilized with respect to the other conjugate bases by the greater pola rizability of sulphur; (c) the smaller amount of energy necessary for the 1,3-thiazolium cation, with respect to the ether cations, to use the penultimate cr MO, gives an explanation for the unique rate enhancement. Besides, the decarboxylation of the pyruvate anion by means of 1,3- azolium cations bas been examined with the CND0/2 method, since most enzymic reactions in which TPP is a cofactor are mechanistically similar to this reaction. The data suggest that the decarboxylation with the 1,3-thiazolium will be the most rapid one.

123 SaDtenva't'ting

In dit proefschrift wordt een quanturnchemisch onder zoek beschreven naar de moleculair-mechanistische aspecten van de coenzymen cyclisch adenosine 3',5'-monofosfaat (c-AMP) en thiamine pyrofosfaat (TPP). Molecular orbital berekeningen zijn uitgevoerd met Extended-HOckei (EH), CND0/2 en ST0-3G ab-initio procedures. c-AMP speelt een belangrijke rol in de regulatie van enzymatische reacties in de cel en het stimuleert de acti viteit van de genen door de synthese van messenger RNA, dat de informatie die opgeslagen ligt in het DNA van de genen reproduceert. De concentratie aan c-AMP in de cel wordt geregeld via een hydrolyse-evenwicht tussen c-AMP en ade nosine 5'-monofosfaat (5'-AMP). De vorming van 5'-At-lP blijkt sterk exotherm te zijn, de hydrolyse-enthalpie is -46.4 kJ/mol. Speciale aandacht is uitgegaan naar de me chanistische aspecten van deze hydrolyse. De invloed van het oplosmiddel op de hydrolyse-enthalpie is bestudeerd met de EH methode voor de hydrolyse van c-AMP en verwante cyclische fosfaat diesters. De resultaten tonen aan, dat het enthalpieverschil tussen c-AMP en de fosfaat diesters gedeeltelijk verklaard kan worden door het verschil in netto solvatatie-enthalpie. ~e exotherme netto solvatatie enthalpie voor de hydrolyse van c-AMP kan worden toege schreven aan een extra stabilisatie van het hydrolyse product ten opzichte van de uitgangsproducten. Deze stabilisatie wordt bepaald door een regio-specifieke hydratatie van de brugpositie tussen 0(1') en 0(5') in

124 5'-ANP. CND0/2 berekeningen, met een watermolecule geplaatst tussen 0(1') en 0(5') in 5'-AMP ondersteunen de veronder stelling, dat deze positie een belangr ke hydratatie site is. Het blijkt, dat zowel een vijf- als een zevenring ge vormd kan worden. Het voorkomen van een fring opent de mogelijkheid tot een interactie van 5'-AMP met enzymen. Verder is het verschil in conformatie van de ribose ring in c-A~1P en 5' -AMP bestudeerd. Er is duidel k aangetoond, dat dit verschil ook bijdraagt tot de exotherme hydrolyse enthalpie van c-AMP. Tevens is aandacht geschonken aan het werkingsmechanisme van TPP, dat optreedt als coenzym voor reacties in het carbohydraat metabolisme, waarin aldehyde-groepen worden geactiveerd. Moleculair-mechanistisch gezien speelt hierbij de C(2) positie van de 1,3-thiazolium ring een grote rol, wordt ondersteund door H-D uitwisselingsexperimen- ten Zow). De onverwacht grote H-D uitwisselingssnel- heid van het 1,3-thiazolium kation ten opzichte van andere 1,3-azolium kationen is bestudeerd met behulp van CND0/2 berekeningen. De volgende resultaten zijn verkregen: (a) stabilisatie van het carbanion door een naburig zwavel atoom kan niet worden toegeschreven aan (d-p) conjugatie; (b) de geconjugeerde base van het 1,3-thiazolium kation wordt ten opzichte van de andere geconjugeerde basen ge stabiliseerd door de grotere polariseerbaarbeid van het zwavelatoom en de zwavel-koolstof binding; (c) b de H-D uitwisselingsreactie kan slechts gebruik gemaakt worden van een er ~10. Bij de 1, 3-azolium kationen is dit de op één na hoogst bezette MO. De geringe hoeveelheid energie, die het 1,3-thiazolium kation nodig heeft om gebruik te maken van deze MO met betrekking tot de andere kationen, is ver antwoordel k voor de unieke snelheid van de H-D uitwisse ling in het 1,3-thiazolium kation. Bovendien is de decar boxylering van het pyruvaat anion met behulp van 1,3-azolium kationen bestudeerd. Het blijkt dat de laagst onbezette MO van het kation bepalend is voor de afsplitsing van kooldi oxide. Het unieke karakter van het 1,3-thiazolium kation wordt hiermee bevestigd.

125 Curriculum vitae

De schrijfster van dit proefschrift is geboren op 12 februari 1952 te Tilburg. Na het behalen van het diploma gymnasium B aan het St. Pauluslyceum te Tilburg begon zij in 1970 met de scheikunde-studie aan de Technische Hoge school te Eindhoven. Het afstudeerwerk verrichtte zij bij de vakgroep Organische Chemie van de afdeling Scheikundige Technologie met als afstudeerdocent p:of. dr. H.M. Buck. Op 29 oktober 1975 behaalde zij het ingenieursdiploma. Vanaf 1 november 1975 tot 1 augustus 1979 is zij verbonden geweest aan de Technische Hogeschool te Eindhoven als wetenschappelijk ambtenaar. In deze periode werd onder leiding van prof. dr. H.M. Buck het onderzoek, dat be schreven is in dit proefschrift, uitgevoerd. Sinds 1 augustus 1979 is zij als lerares scheikunde en natuurkunde werkzaam op het St. Pauluslyceum te Tilburg.

126 Dankwoord

Aan de totstandkoming van dit proefschrift hebben velen een bijdrage geleverd. In het bijzonder op het gebied van quanturnchemische berekeningen en de interpretatie van zoKel literatuurgegevens als resultaten. Voor al deze hulp en voor de prettige sfeer waarin ik heb kunnen werken wil ik een ieder bedanken. Verder ben ik diegenen zeer erkentel k, die een bij drage hebben geleverd aan de uiteindelijke vormgeving van dit proefschrift.

127 Stellingen

1. Bij de verklaring voor het niet uitwisselen van het 2'- 0H waterstofatoom van cyclisch adenosine 3' ,5'-mono fosfaat, wordt door Bolton en Kearns ten onrechte geen rekening gehouden met waterstofbrugvorming tussen 0(2') en 0(3').

P.H. Bolton en D.R. Kearns, J. Am. Chem. Soc., .lQJ_, 479 (1979).

2. Daar de nucleofiele aanval op een fosfaat-gesubstitueerd fosfoniumion voornamelijk plaatsvindt op de fosfaat groep, kan de alkyloverdracht in de door Ramirez et aZ. beschreven modelstof beter verklaard worden door een nucleofiele aanval op het vijfgecoördineerde inter mediair.

F. Ramirez, Y.F. Chaw, J.F. Mareeek en J. Ugi, J. Am. Chem. Soc., 96, 2429 (1974). -

3. De verwachting dat er optische activiteit aantoonbaar is na cyclodehydratatie van racemisch 4-hydroxycyclo hexanon met behulp van een optisch actief carbodiimide berust op een verkeerde interpretatie van de regels van asymmetrische inductie.

R.R. Hiatt, M.J. Shaio en F. George, J. Org. Chem., _ii, 3265 (1979). 4. Bij de in de literatuur veel voorkomende bewering dat fluorescentie werd gemeten bij "druk nul"-omstandig heden wordt vrijwel nooit rekening gehouden met long range energy transfer volgens het Förster-Dexter mechanisme.

R.G. Milier en E.K.C. Lee, Chem. Phys. Letters, 41, SZ (1976); K. Uchida, I. YamazaKI en H. Baba, Chem. Phys. Letters,~. 133 (1976).

S. Bij de bepaling van de bezettingsgraad van alkylchloor silanen die aan een silica-oppervlak gebonden zijn, worden koolstofatomen die geen deel uitmaken van de lineaire alkylketen ten onrechte verwaarloosd.

H. Hemetsberger, ~1. Kellermann en H. Rieken, Chromatographia, 10, 726 (1977). ---

6. De beschrijving van electreneninteracties in spira geconjugeerde modelsystemen met behulp van correlaties tussen berekende ladingsdichtheden en gemeten 13c chemical shifts kan gemakkelijk tot onjuiste conclusies leiden.

S.Q.A. Rizvi, J. Foos, F. Steel en G. Fraenkel, J. Am. Chem. Soc., 101, 4488 (1979); H. Dürr, K.H. Alberr-en M. Karisch, Tetrahedron, 35, 1285 (1979). --

7. In artikelen over quanturnchemische onderwerpen dient de algemene term energie gespecificeerd te worden naar de gebruikte rekenmethode.

8. Op het identificatieplaatje van de nederlandse militair wordt het land van herkomst ten onrechte met "Holland" aangeduid. 9. Niet bij ieder slot betekent linksom open en rechtsom dicht; niet bij iedere kraan betekent linksomdraaien meer en rechtsomdraaien minder vloeistof. Dergel ke situaties, die een potentiële bron van dagelijkse ergernis zijn, dienen door normalisatie te worden op geheven.

10. Het nederlandse handbal biedt te weinig mogelijkheden voor de niet-prestatie gerichte recreant die buiten competitieverband zijn sport wil beoefenen.

11. Doordat met name science-fiction schrijvers, futuro logen en schrijvers van populair-wetenschappelijk werk over een computer spreken als ware het een met rede begaafd individu dat zelfstandig informatie kan ver zamelen en beslissingen nemen, kan de mythevorming rond de computer alleen maar aanzienlijk versterkt worden. Het verdient dan ook aanbeveling te spreken over een rekenautomaat en te vermijden dat de indruk ontstaat dat het om een beslissingsmachine gaat.

12. In de promotiereglementen van Hogescholen en Universi teiten in Nederland dient duidelijker naar voren te komen, dat de promovendus zowel van het mannel k als het vrouwelijk geslacht kan zijn.

13. Om te trachten de afstand tot de wetenschap voor een ieder kleiner te maken, verdient het aanbeveling bij proefschriften een gepopulariseerde samenvatting te voegen.

M.M.E. Scheffers-Sap Berlicum, 14 december 1979