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

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

Document status and date: Published: 01/01/1979

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THE COENZYMES

CYCLIC ADENOSINE 3',

5' -MONOPHOSPHATE

AND

THIAMINE PYROPHOSPHATE

A quantumchemical

description

CO-ENZYMEN CYCLISCH ADENOSINE 31_,51_{-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

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:

c-AMP R=adenine water R 0 _::, 05'

~~·

0

--~p/

OH HO/ OH 5'-AMP

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 CH₃COCOO-), 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.

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.

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

DIT PROEFSCHRIFT IS GOEDGEKEURD DOOR DE PROMOTOREN

PROF. DR. H.M. BUCK EN

"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."

Chapter I

Chapl:er 11

Contents

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 Heferenoes

Summary of the all-valenee methods used, the Extended-Hückel, CND0/2 and ab-initio method

17 20

11.1 Introduetion 21

II.Z The Extended-Hüekel method

1!.2.1 Theory

II.2.2 Parameters the

ordinary and iterative

23

EH calculations 25

II.3 The Complete NegZeet

Differential Overlap method

11.3.1 Theory the CNDO method

II.3.2 Parametrization for the CND0/2 methad

II.3.3 The GEOMO program

11.4 Ab-initia calculations

11.5 Mulliken population ana is

II.6 Calculation of the solvation

26 29 30 31 32 enthalpy 33 Heferences 36

Chapter 111

_{The solvent effect on the}

enthalpy of hydralysis of c-AMP 111.1 Introduetion

111.2 Geometriee of phoephate dieetere

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

sol-38

41

vation enthalpies 46

111.3.2 Ribose ring puaker-ing

111.4 Diecuesion

Referenaei and notes

51

51

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

1V.S Hydragen bonding ae a model

for the dynamias of enzyme-aoenzyme aomplexes

Referenaes

68

69

Chapter V

Chapter VI

The acidity of thiamine pyro-phosphate and related systems

V.l IntPoduction V.1.1 Ristoriaal back-ground 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

Referenaes and notes

Thiamine pyrophosphate-catalyzed decarboxylation of pyruvate anion

VI.l Introduetion

VI.2 The reaation saheme for the pyruvate deaarboxy-lation reaation

VI.3 The net reaation enthal-pies of pyruvate deoar-boxylations ~ith 1,3-azolium systems VI.4 TPP as aocarboxylase References 95 97 100 101 103 108 110

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

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 enzymes1 _{(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 coco-factors. 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

vioe versa

is omeras es isomerizations

ligases condensation of two molecules coupled cleavage of the pyrophosphate bond of

or

with ATP

are called ooenzymes1 _{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,

as is very impressively demonstrated for NADH1

• 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 pyrophos,5'-monophos-phate.

1.2 Cyolio adenosine 3',5'-monophosphate

Cyclic adenosine 3',5'-monophosphate2 _{(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

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 l i 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

hormones ( first messenger l adenyl cyclase I receptor}

/

"""

ATP c-AMP I secend messenger l

/!~

biochemica! responses (enzyme gene activation, expression l

/l~

physiologicol respon,ses (glycogenolysis. membrone permeability l

Figure 1.2 The seaond messenger aonaept

c AMP phosphodiesterase odenyl

'Y'~

-PP1 • 2P;

~;1

₉₂

+

IQSe

~

ATP 5'-AMP pyrophosphatase adenylate kinase

receptor

ATP c-AMP +PPi

L

protein kinase _ _ ___,_

@:XID (

inactive) protein kinase

©

(active) + c-AMP-@

ATP + phosphorylase kinase - - - - phosphorylase

( inactive) Ca2 + kinase (active)

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

glycogen + Pi glucose 1 - ph os phate

~

glucose 6- phosphate -glucose + Pi

eelt membrane

I

blood glucose

reaction3

• The large negative Gibbs free energy3 (-37.2 kJ/

mole) and enthalpy3 _{(-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_{2 2}- 0 - P - O - P - 0 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 of a covalently bound "active" aldehyde group5

• 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.

0

o-11 / R

c

0

~

co

₂ +

:/

0 11 R-C-H R, I H-C-OH I

c=o

/

R I

[

~

_+TPP

0 11 R-C + R,-C-H

!-''

~0

11 C-H 0 11 R- C- OH 0 OH 11 I R-C-C-R I 2 H + 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

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 l i 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-strated by comparison of gas phase and solution basicities6₎

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 base in water7_{, 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

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 for the "free state" of a system8

•

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 rate between the 1,3-oxazolium and 1,3-thiazolium cation9

•

In Chapter VI the reaction path for the decarboxylation of the pyruvate anion with 1,3-azolium cationsis described9 •

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).

CHAPTER 11

Su nunary o:f the a l l - 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-Jones1 _and

subsequently referred to by Mulliken2 _{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.

\V i - /-:')" f \ .n. p Z: ( -1 ) P [ 1); _{1 (} 1) a ( 1 )1); _{2 ( 2) 8 ( 2) ....} ;f! Zn ( 2n) 8 ( 2n)] p l:c . Q ]l ] l l ]l ( 2 . 1) ( 2. 2) The set of initial atomie functions $ is called the basis set.

]l

Although the complete salution of the Hartree-Fock problom re-quires 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

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

L Hcore(~) + L 1/r

~ ~<v ~v

H ( 2. 4)

where Hcore(~) is a ene-electron operator, representing a sum of kinetic and potential energy of all electrans in the core and 1/r _11\) is a two-electron operator, which represents the mutual repulsion of the electrons in the atomie orbitals ~ and v. The variation theorem requires for each molecular orbital i, that the coefficients c . satisfy the following

~1

sets of simultaneous equations: Ec . (F -E.S )

=

0

~ ~1 ~\) 1 ~\) v

=

1 , ••••• , n (2.5)

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

~V 1 ~\) (2.7)

with the values Ei being the eigenvalues.

Roothaan3 _{has shown that for a closed shell system F~v}

is given by where and F ~\) H~v +EL Pp0 [<J.lvJJpcr>- !<~pJJvcr>] pcr (2.8) (2.9) (2.10)

and P

90 is the total electrooie popuiatien in the overlap

region between atomie orbitals p and o: ace

2 l: i

c .c .

pl (jl (2.11)

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 Slater5

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 Hoffmann6 ,

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 chosen as 2.00 in accordance with earlier work6_•7

• 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 are calculated, according to Hoffmann6_{, as}

i (2.14)

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 discussed8_{• 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

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 systems9_{• The iterative}

EH method, as proposed by Rein et a~. 10_{, calculates the}

total energies according to equation (2.15).

Etot

=

lJ:: _~. n. (s.+h.) _{1 1 1} + E _core-core (2.15)

1

~

Khere h.

=

<~ lhl~ > and the second term is the care

re-l \1 \1

pulsive energy, calculated by:

Ecore-core (2.16)

- eff _{A an} d _rAB b · _{e1ng e} ff _{ect1ve core c arges o} · h 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

according to equation (2.17), as derived by Basch et al. 11 _: H

\1\1 Xq 2 + Yq + Z (2.17)

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): H

llll(n+1) H ( )(1-;\) + À(Xq

2

+Yq+Z)

J..lll n (2.18)

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

entering the EH theory, namely, the valenee state ionization potentials (VSIP) and orbital exponents, are the same as those used by Boyd12 _{in a molecular orbital study of ATP.}

For sulphur the data have been taken from a study by

BartelZet al. 13

• The orbital exponents are just the Slater

values, exeept for the H ls and P 3d orbitals, for whieh the values are taken from SCF optimization ealculations14_•

The carbon and hydragen VSIP's are those in common usage6 ,

and the phosphorus and oxygen values are taken from SCF eigenvalues of P013

• For the iterative EH ealeulations the

constants for equation (2.17) are obtained from the atomie speetral data as determined by Basehet al. 11

•

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

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. The approximations for the CNDO methad are15

:

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

]JV ]JV (Kronecker delta) (2.19)

3. All two electron integrals which depend on the overlap of charge densities of different orbitals are neglected. This means that

éi éi y

]JV pcr J.lP (2.20)

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 repuls-ion 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 the care of A and with the cores

orbital ~ on A with

]J

of all other atoms B H

]J]J (2.21)

u

)J]J (2.22)

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

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)

same atom. Then S

applies even if 1J and v are on the 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: A A<B AB (2.27) A AB (P p -lp 2) with _EA E p

u

+ !EE jJ ]J]J ]J]J ]J\! ]J]J \)\) 2 ]J\! (2. 28) AB (2P 13 -1_{P 2+y} and _EAB

=

EE J.JV lJV 2 _{lJV AB} ) + jJ\) -1 (ZAZBrAB-PAAVAB-PBBVBA+PAAPBBYAB) (2.29) 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.

II.3.2 Parametrization for the CND0/2 method16

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: and -I )J -A ~ (2.31) (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 ~ ~ AZ AA (2.33)

The values used for the electronegativities -!(I +A) are

11 11

listed in Table 11.2. Initial estimates of the LCAO coeffi-cients may be obtained by a HUckel-type theory using matrix elements F ~~ (o) -l(I +A) 2. 11 ~ ( 2. 34) (2.35) and the final solution is obtained as described in Sectien II.1. The bonding parameters S~B are approximated by

Table II.2 Values of parameters15 •17

!(Is+As) HIP +Ap) ~(Id+Ad)

-Bo

_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 program19

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

-1

the term rAB 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:

5EAB AB oB .. _-1p2 öf (r AB) l:L rzp ~ + _ZAZB + ;;: _ij • )lV 6qz 2 )1\.J 6qz 6VAB oyAB (2.37)

-

PAA-6--_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 metric, developed by Murtagh and Sargent20• The SCF

iterat-ion procedure is performed until the energy converges with-in 10- 6 eV and the optimization is stopped when the mwith-inimum relative quadratic difference allowed for two consecutive values of atomie coordinates is smaller than 10 8

11.4 Ab-initia aaZoulations21

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 <ilzs'(l,.!:_) E _{dzs,kg1s(a2k'} k K <IJ 2 s ! ( 1 '.!:_) E d2p,kg2p(a2k' k (2.39)

Here g₁₅ and g₂p are the Gaussian-type orbitals:

~ 2 (2a/TI) 4_{exp (-ar )}

(128a5/TI3)l r exp(-ar2)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 are given by Hehre et aZ. 21

• 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 anaZysis23

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 .

).I )..I i= 1 1 )..11 (2.42)

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:

- the net atomie population NAP(A)

=

E NAP(~) )l on atom A: N m E P S i::1 1111 1111

Khere Nm is the number of AO's on A

(2.45)

- a measure for the interaction between ~ (on atom A) and Jl

(on atom B):

p

s

].IV 11V (2.46)

- the !Otal ~verlap EOpulation between atoms A and B: TOP(AB)

=

II.6 CaZcuLation E Jl,V p

s

11V jlV

the solvation enthaLpy

(2.47)

The first approximation which has been used for the solvation of monoatomie ions is the Born charging energy term24

• The model for the solvent effect proposed by Jano25

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 energy26 _{of a charge}

dis-tribution (2.48), Jano25 _{derived a similar equation (2.49)}

for the solvation enthalpy as equation (2.50), which bas been proposed by Boytink et aZ.27

•

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)

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 ₀

=

80) 2

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 GueriZZot28 _{worked out the}

algo-rithms for the EH program29 •

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 KyseZ30 _shows

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.

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.,

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

The

CHAPTER 111

solvent effect on

of hydrolysis of

the enthalpy

c-AMP

I I I . 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 years1 _{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 aerogenes2 _{has made}

hydralysis possible, which delivers a mixture of 5'-A}1P and adenosine 3'-monophosphate (3'-AMP), as stuclied by

West-heimeP et aZ. 3

• The hydralysis to either 3'-AMP or 5'-A,\1P

involves a large exothermic Gibbs free energy3 _{(-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" bonds3_•

The discovery of phosphohydrolase from Enterobaater aerogenes affords the possibilities to measure the enthalpies of

hydrolysis of monocyclic and acyclic phosphatediesters4 •

Joint consideration of hydralysis enthalpies and geometries of the alkyl phosphates and the nucleotides leads to some useful and general conclusions. The hydralysis data4

are in agreement with their structures. The more negative Table III.1 Enthalpies of hydralysis and OPO bond angles

of phosphate diestersa

phosphate d. 1ester b _llHobsd a OPO bond (kJ/mole) angle (degrees)

ATP -37.2

-c-A~!Pd -46.4

-cyclic guanosine 3 1 _{> 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 monodi-esters. bFor structures see Figure 3.1. 0Hydrolysis enthalpy, measured at pH= 7.3, 25 °C by microcalorimetry4_{• 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 to strain7

•8, which is correlated with the OPO bond angles4

(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, several independent observations9

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

OH 3'

Y

R 0 _-~ 0 / '

:yP".

0 0 5' s' 1 R = adenine

2

R = guanine ~ R uridine .i R ₌ methyl 11 R = H §_ R = ethyl 10 R =methyl 5 R

=

adenine 7 n

=

2 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 energy calculations14

• In order todetermine the cause of

the pronounced exothermicity of the hydralysis of cyclic 3' ,5'-nucleotides, the methyl riboside cyclic phosphate (i)

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 phosphate15 _{(2), trimethyl}

ene phosphate16 _{(~), the 5'-methylene analogue of c-AMP}17

(12), their products of hydrolysis, 3'-AMP18 _{13 and the}

3'-methylene analogue of 3'-AMP19 _{(~) arebasedon X-ray}

crystallographic data. Those for c-AMP20 _{(l), 5'-AMP}21

diethy: (~) and dimethyl22 _{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-placed by a cyclopentane ring23

•

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 SundaraZingam24 _are

OH

Y

R 0 3'

-""'

/

.

-, p -'l' "

o

os-16 17

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

\ a /

s-s-c

(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° < x < 90°), which corresponds to

x

=

3.8°, 25.7° and 50° for 3'-AMP, 5'-AMP and c-AMP, respectively. The ribose ring has a C(3')-endo conformation in 5'-A~.IP24 _{and 3'-AMP}24

, whereas that of c-AMP is the

C(~')-exo-C(3')-endo conformer20

•25•26 (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. Literature data20 _•25_•26 _{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 years27

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

r---,

I I I I

/*Os· \

0,- C3 • Hs· Hs· b a H •• I 99 IV g'g· HJ'

c,~c,

P03 VII t#

r---,

I I I I 1

*Hs~

\

0,·

C3 • Os Hs. b H.· II gt y g't'

kPo

3

c..

·

C2 -VIII g" ( -)

r---,

I I

/*Hsb \

o,.

C3• Hs. _a Os' H •• III tg VI t'g'

o

3

_P~

C4 • C2• 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)

c •.

C{l.') exo C{3') -endo(₄T3)

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

?~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 familiar "W" conformation (X). Hall et al-. 28

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-served values of 4J(PH(4')) are between 1.7-2.0 Hz30

• The

mag_nitude of the 3J(HCOP) value31 _{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 data18 _{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 conformation32 _{of 5'-Ai\IP}

and 3'-AMP is in good agreement with the structure deter-mined by X-ray crystallography18

•33 and by 31 P- and

1H-NMR studies of 3'- and 5'-nucleotides in solution27 •

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

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

1 ) and enthalpies of solvation

ca c (6Hs0

1 1

v) are given for the hydralysis reactions. From these ca c

values the net enthalpies of hydralysis in salution (LHsoln) are calculated according to oln

=

~Hg

1 +

ca 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 shown by Herndon 3 5•

-t::. Hsoln (kJ/motel

t

140 u-~

.

11-13" 120 100 80 60

4o

s-2o.

20 10 20 30 40 50 - t::. H ex p ( kJ I mo!e )

Figure 3.6 Correlation between 6H8oln 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.