Electrostatics in quantitative structure-activity relationship analysis

Journal of Molecular Structure (Theo&m), 256 (1992) 231-248 Elsevier Science Publishers B.V., Amsterdam

231

Electrostatics in quantitative structure-activity relationship analysis P.G. De Benedetti Dipartimento

di Chimica, Universit& di Modena, Via Campi 183,411OO Modena (Italy)

(Received 24 July 1991)

Abstract Simple ad hoc theoretical molecular descriptors were computed using three semiempirical methods (INDO, MNDO and AM1 ) for different prototropic forms of two conformationally optimized molecular series of 4aminodiphenylsulphones and 5-benzyl-2,4-diaminopyrimidines, which are inhibitors of the biosynthesis of folate. The molecular orbital descriptors derived show good linear correlations with the inhibitory potencies of both &phones (dihydropteroato synthase inhibitors) and benzylpyrimidines (dihydrofolate reductase inhibitors). The results obtained suggest that, in both cases, the electrostatic forces are dominant in the enzyme-inhibitor interaction. However, the role of the substituents in the sulphones considered is mainly connected with the modulation of the electronic structure of the electrostatic pharmacophore 4-NH*-C6Hl-SOz-, whereas in the case of benzylpyrimidines, once the Nl protonated pyrimidine ring recognizes and docks the enzyme active site, both potency and selectivity towards enzyme from different sources are controlled by the substituent pattern on the benzylic ring.

INTRODUCTION

The problem of correlating chemical features to biological activity is a quite complex one, and implies the reduction of a biological event in terms of chemical and/or physico-chemical concepts. The prime assumption made in this reductionistic approach rests on the fact that both xenobiotics and biological targets are molecules which are phenomenologically involved (via intermolecular interactions) in the production of the observed biological effects. The main aspects of this challenging problem have recently been illustrated within the framework of the well-known principles of quantitative structureactivity relationship (QSAR) analysis (i.e. the specific features of the interactions of drugs and biosystems which lead to a specific biological (pharmacological) response) [ 1,2]. The unifying principles of any QSAR analysis are strictly connected with the intra- and inter-molecular interactions which, in turn, are largely interpretable in terms of electrostatic models. In other words, dynamic concepts Correspondence to: P.G. De Benedetti, Dipartimento di Chimica, Universiti di Modena, Via Campi 183,411OO Modena, Italy. 0166-1280/92/$05.00

0 1992 Elsevier Science Publishers B.V. All rights reserved.

232

like molecular recognition, drug-receptor and ligand-biopolymer complementarity, and molecular similarity are approachable, from a static point of view, by making use of the appropriate congeneric molecular series and, above all, of the ad hoc molecular descriptors. It can be stated that the purpose of any quantitative structure-activity analysis is the molecular description, i.e. the elaboration of the most appropriate descriptors (for handling the problem), while mathematical methods only provide a tool for manipulating them in the descriptors space. Computer aided molecular modelling together with molecular orbital derived reactivity indices and electrostatic descriptors of the molecules have enormously expanded the possibilities in computing and modelling theoretical molecular descriptors ad hoc for the particular problem under study. According to the main aspects of the complementarity between ligand and the biopolymer [3], theoretical molecular descriptors can be classified into three main categories: geometric, hydrophobic and Coulombic. Geometric complementarity and derived descriptors are usually obtained by modelling and comparing the molecular shape of a congeneric molecular series. Molecular similarity can also be treated in shape-similarity terms with respect to one or more reference structures [ 41. Hydrophobicity is the well-known manifestation of the fact that apolar regions of interacting molecules tend to associate in order to minimize unfavorable hydration effects [ 3,5,6]. Apart from the entropic contribution to the hydrophobicity, which can be considered constant in some cases of strict congenericity [ 71, the enthalpic contribution to the free energy of association can be described in terms of electrostatic and dispersion intermolecular interactions. Ligand-biopolymer interactions are mainly based on electrostatic and dispersion forces. As a consequence the electronic charge distribution or potential revealed by the calculations are of great importance in any application of quantum mechanics to pharmacology and biology, especially as the theoretical methods can yield details of charge distribution within the molecule which cannot be obtained from the experiments. Coulombic similarity and complementarity can be studied in terms of molecular electrostatic potential (MEP) maps [ 31 which give a detailed description of the electrostatic shape of the molecule and are very useful for comparisons between molecules having very different geometries and low symmetry. However, in QSAR analysis we are dealing with congeneric molecular series which usually comprise molecules whose structural features are changed with respect to a lead compound (parent compound) and, consequently, we can identify a common structural moiety (the pharmacophore which recognizes the receptor) and a variable moiety (the optimization fragment) for the optimization of both biological activity and selectivity. In this context, the definition of Coulombic molecular descriptors which encode the electrostatic and disper-

233

sion forces that operate in the ligand-biopolymer interactions (in the lockand-key approximation) must take into account both the molecule as a whole, the different moieties and their mutual electronic influences observed or computed as differences along the molecular series considered. According to the principles of QSAR analysis, which are derived from the well-known linear free-energy relationship principles, differences are more meaningful than absolute values [2]. This important aspect renders the inherent approximations of the semiempirical methods for computing the wavefunction more acceptable and the derived theoretical descriptions useful and valuable in suggesting trends and correlations [ 21. In the present paper, we focus our attention on the electrostatic aspects of complementarity in ligand-biopolymer interactions as inferred from QSAR analysis of sulfones dihydropteroate synthase (DHPS ) inhibitors and benzyl pyrimidines dihydrofolate reductase (DHFR) inhibitors. METHODS

Conformational analysis and molecular orbital AM1 [ 81 calculations were performed using a VAX 6310 computer at the Computer Centre (CICAIA) of the University of Modena, using the AMPAC program (QCPE 506) [ 91. AM1 has recently been parametrized for sulphur [lo]. The computational details for the conformational analysis of sulphones have been reported elsewhere

[Ill.

Full geometry optimization was carried out at each step of the conformational analysis of 5-benzyL2,4diaminopyrimidine in its neutral and protonated form. The molecular modelling QUANTA system [ 121, implemented on the CYBER 910B-470 personal workstation, was used to make molecular comparisons and superpositions. ELECTROSTATIC

ASPECTS IN DIHYDROPTEROATE

SYNTHASE INHIBITION BY

SULPHONES

Studies on the synthesis of dihydropteroate and folate in several bacterial species have shown that sulphones, like sulphanilamides, owe their antibacterial activity to the inhibition (which is competitive with respect to the substrate 4-aminobenzoate (PAB ) ) of the DHPS [ 11. This enzyme catalyses the synthesis of dihydropteroate from PAB and hydroxymethyldihydropteridine pyrophosphate [ 11. A theoretical study on fourteen 4’ -substituted diphenylsulphones has suggested that sulphones and sulphanilamides can be considered as a congeneric chemical series on the basis of the electronic properties of the 4-NH,-C!,H,SO,- common moiety (as modulated by the substituents) and the bacteriostatic activity of these compounds [ 131. Thus, the classical theory of antime-

234

Fig. 1. Superposition of the absolute minimum conformation of the 4,4’-diaminodiphenylsulphone (DDS) and 4-aminobenzoate (PAB) in one of ita more stable conformations (the plane of the -COO- group is rotated 30” with respect to the phenyl ring).

tabolites, which is based on their competitive inhibitory effects, appears to have a sound rationale owing to the extent of the resemblance between the electrostatic features of the inhibitor and substrate and, hence, the complementarity with the electrostatic charactaristics of the enzyme active site (Fig. 1). A more accurate test of these conclusions has very recently been proposed. The test involves measuring the inhibitory effect of a large series of homo- and hetero-multisubstituted 4-aminodiphenylsulphones. On the basis of a QSAR analysis using both empirical and quantum chemical descriptors of the molecular structure it was concluded [ 14-161 that the electronic structure of the common moiety 4-NH2-CsH4-S02-, modulated by the substituents, is the determining factor connected with the inhibitory potency. In particular, the more electron rich the common moiety, the more active are the compounds. This situation is best realized by the design and synthesis of multisubstituted sulphones bearing electron-donor substituents, the most efficient one being the hydroxy group which can dissociate to give the hydroxylate anion. In fact, very recently [ 161, the inhibitory effect exerted by some newly synthesized 2’ ,4’ and 2’ ,4’ ,6’ -substituted diphenylsulphones on the enzymic activity has been studied and correlated with the theoretical electronic features of the SO, group. The 2’-CH3, 4’-OH; 2’,6’-(CH3)2, 4’-OH, and 2’-C1,4’-OH derivatives are about one order of magnitude more effective than the 4,4’ diaminodiphenylsulphone. This result, which is consistent with the previous ones, is (on interpretative grounds and recalling the electrostatic complementarity of the receptor) not usual. In fact, it is the electronic effect of the hydroxylate anion (transmitted through the SO, group) on the common biofunctional moiety which explains the enhanced inhibitory activity of these compounds and not the variable part of the molecules and/or the hydroxylate anion as such, i.e. postulating an additional peculiar electrostatic interaction [ 171. A molecular-modeling based QSAR analysis on a large set of multisubstituted sulphones has recently been reported [ 181 and the best equation proposed is logW,lJ =0.04( + O.O05)P, +0.47( + 0.05) @+5.18(

2 0.06)

235

m&$4, r=0.90, s=o.20

where C, is the concentrationof the inhibitor which halvesthe enxymicaotivity, PA is the sum of the thermodynamicprobabilities (i.e. PA= exp ( -Ei/RT) / Xexp(-Ei/RT) ) of the four postulated active conformations [ 19,201,and @ is the direction of the dipole moment of the substitutedphenyl ring relative to the cor~spo~~ng dipole moment of the most active analogue (2’ X1,4’ -NH2) [ 181. The main conclusion [ 181 was that both the dipole moment of the substitutedring and the existenceof the four postulatedactive conformations are important for the inhibitory potency. However, with the aim of clarifying the connection between the degree of conformations freedom and the electronic structure in this class of compounds, and of comparativelymodeflingtheir electrostaticpharmaeophore,we synthesizedone rigid analogue (see compound 13, Table 1) of 4,4’ diaminodiphenylsulphoneand tested its inhibitory potency on DHPS extracted from Escherichia coli (D. Iarossi and P.G. De Benedetti, unpublished results), Moreover,molecularorbitalcalculationson 18 multisubstitutedsulphoneswere performedusing the MNDO and the AM1 semiemp~ic~ methods and the results obtained were comparedwith resultsobtained recentlywithin the INDO method [ 161. Table 1 shows the electronic net charges on the SO, group (qso2), on the oxygen atom of the SO, group (o*) and on the NH, group (oNH2)computed with three different semiempiricalmethods (INDO, MNDO and AM1 ), and the DHPS inhibitory activities (APE) of the m~tisubstitu~d sulphonesconsidered. These derivatives show multiple conformational energy minima as was very recently assessed using a theoretical conformational analysis (MNDO) performed on compounds 1,&g and 11-13 of Tahle 1 [ll]. The multipleminima are due to the torsional freedom of the sulphur-carbonbond ( Bz)of the substitu~d phenyl ring. The other sulphur-carbontorsions angle considered (a,), lyingon the biofunctionalcommon moiety 4-NH2-CGH[4-S02is quite rigid, with the phenyl ring lying perpendicularto the Cl-S-Cl’ plane (8, = 90 ’ ). The most stable conformersof all the six derivativesconsideredare f?,=9W, S,=90° (butterfly conformation} and @,=90“, 8,=60”, The highly active derivativesare, in general,fess flexible. In the present work a theoreticalconformationalanalysiswas performedon the same derivatives(compounds 1,5,9 and 1 l-13) within the AM1 framework. The AM1 resultsare in full agreementwith the MNDO resultsobtained previously [ 111 and confirm that, in general,the most stable conformer corresponds to the butterfly conformation. Thus calculations on all the other compounds listed in Table 1 were done for the butterfly conformation. Comparisonof the data listed in Table 1 shows that the total net chargesare quite different in their absolute values, but not in their trends, as shown in Table 2 where the correlation coefficients, obtained from linear regression

-0.5663 -0.5668 -0.5472 -0.5567 -0.5356 - 0.5294 -0.5772 -0.5382 - 0.5356 - 0.5658

-0.6083 -0.5895 -0.5921 -0.5755 -0.5588

112'~CH3;4'-O122'~Ci;4'-o132'-OH;4'-o142',6'-(CH&;4'-OCHB 152',4'-(CH&;6'-OCHa 0.1768

0.1341

0.0989 0.1073 0.1213

0.1795 0.1524 0.1793 0.1532 0.2011 0.2030 0.1308 0.2045 0.2388 0.1555 - 0.5529 - 0.5540 -0.5512 -0.5510 - 0.5462 -0.5412 - 0.5566 - 0.5508 -0.5430 - 0.5542

0.2701-0.5671 0.3411-0.5632 0.3350-0.5646 0.4436-0.5567 0.4929-0.5538

0.4917 0.4665 0.5113 0.4764 0.5143 0.5414 0.4364 0.5404 0.6201 0.4751

INDO

AM1

INDO

MNRO

$0’

q em2f

14’-(NH,_.) 2 2’,4’-(CH,), 8 2’,4’-(OCH& 4 2’,4’-(NH& 6 2’,4’-(CH2 6 2’,4’-(NC& 7 2’,4’,6’-(CH& 8 2’,4’,6’-(OCH,), 9 2’,4’,6’-(Cl), 10 2’-CH,; 4’ -0CHs

No. X

-0.7106 -0.6967 -0.7046 -0.6668 -0.6559

- 0.6632 - 0.6636 - 0.6602 - 0.6692 -0.6502 - 0.6302 - 0.6656 -0.6524 -0.6497 - 0.6649

MNDO

0.0039 0.0049 0.0042 0.0045 0.6082 0.0696 0.6046 0.0031 0.0690 0.0050

INDO

-0.6882-0.0176 -0.6519-0.0166 -0.6578-0.0182 -0.5986 0.0048 -0.5861 0.0038

- 0.5877 -0.5903 -0.5830 -0.5924 - 0.5731 - 0.5565 -0.5978 -0.5764 -0.5515 -0.5911

AM1

p (NHn>

0.0241 0.0221 0.0216 0.0565 0.0527

0.0573 0.0570 0.0536 0.0560 0.0625 0.0687 0.0565 0.0497 0.0622 0.0567

MNDO

- 0.42 - 0.28 -0.51 -0.20 -0.35 -1.56 -0.23 - 1.11 -0.52 - 0.25

0.0066 0.66 0.0059 0.59 0.0073 0.29 0.0494-0.25 0.0464-0.48

0.0490 0.0508 0.0478 0.0483 0.0549 0.0688 0.0499 0.0437 0.0532 0.0506

AM1

APE

Selected molecular orbital descriptors computed by ‘hree different semiempirical methods and dihydropteroate synthase inhibitory activity of multisubstituted sulphones

TABLE1 ii

238 TABLE 2 Correlation matrix of the data given in Table 1 4

(Sod

q’o’

INDO MNDO AM1 INDO MNDO AM1 INDO 90 MNDO AM1 9 NH* INDO MNDO AM1

4

so2

APE

1.000

0.943 1.000

4

INDO MNDO

0.938 0.925 0.956 0.919 1.000 0.926 1.000

0.944 0.884 0.941 0.925 1.000

(NHn)

APE

AM1

INDO MNDO AM1

0.932 0.912 0.986 0.918 0.969 1.000

0.808 0.738 0.870 0.762 0.894 0.917 1.000

0.625 0.599 0.727 0.690 0.728 0.764 0.861 1.000

0.753 0.709 0.834 0.814 0.867 0.879 0.928 0.964 1.000

-0.845 -0.812 -0.827 - 0.892 -0.892 - 0.834 -0.685 -0.657 -0.786 1.000

analysis of the data values listed in Table 1, are reported. However, the effect of the substituent on the molecular orbital indices localized on the 4-NH, and SOz groups is, according to the variation A given at the bottom of each column in Table 1, in general; AM1 > MNDO > INDO. Hence the superiority of the AM1 method, at least for correlation purposes, is clear. Moreover, the correlation matrix (Table 2) shows, as expected, good linear trends between the total net charges on the SOz group and its oxygen atoms both in the different semiempirical methods and in the ApE. As for the NH2 group, which together with the SO2 group is essential for the biological activity [ 11,the trends obtained are in general less linear, apart from the AM1 electronic net charges. The best linear relationship obtained between the electronic net charges ) and the ApE of the multisubstituted sulphones considered is re(Q0h4BJrlo ported in Fig. 2 together with the linear equations including and excluding compound 18,which can be considered the rigid analogue of DDS (compound 1) (seeFig. 3). The improvement in the fit obtained by omitting compound 18 suggests that the loss of conformational freedom reduces the biological potency of this compound, with respect to the DDS, by about one order of magnitude. Similar considerations apply to the trimethoxy derivative (compound 8)) its biological potency being lower than predicted from its electronic features. At the same time, these results are consistent with [ 13-161 and extend [ 111 our previous conclusions supporting, on a simple basis, the findings of Hopfinger and coworkers [ 18-221 and their results for the anionic substituents. In fact: (a) the hypothesis of the existence of an “active sulphone conformation” is not necessary; (b) active compounds are more rigid, at the 13, torsional angle than are the less active analogues; and (c) the intramolecular

239 l,O APE .

a

0.5 W CO -

-0,5 -

-l,O-

n

n 18 -1,5 -

-2,01 -0,72

’

’

I -0,70

u

m

1

m

-0,68

*

I -0,66

.

m

I -0,64

s

I

I -0,62

q0 MNDO

APE= -24.02 ( f3.04)q0,,,,- 16.38( k2.04) (n= 18, k0.89, s=O.28, F=62.2) ApE= -23.30 ( f2.31)q”,mo-15.85( k1.55) (n=17, r=0.93,s=0.21, F=101.24) Fig. 2. The relationship between the enzymic inhibition activity parameters (APE ) and the MNDO electronic net charges on the oxygen atoms ( qoMmo) of the SO, group.

conformational entropy does not seem to be a key correlation property. Instead “some specific electrostatic interactions between the ligand and the receptor” seem to play the major role in the last QSAR model proposed by Lopez et al.

[181.

It seems that these postulated specific electrostatic interactions can be hypothesized to lie between the 4-NHz-CGH4-SO2 ligand moiety and the active site of the enzyme, as for the substrate 4-NHz-CGH4-COO- and as our previous results [ 11,13-161 and Fig. 1 clearly suggest. In fact, also in the case of the rigid analogue (compound 18 )the electrostatic model previously proposed [ 21 for the interaction between both sulphones and sulphanilamide inhibitors,

240

Fig. 3. Molecular superposition of the 4,4’-diamiuodiphenylsulphone (DDS) logue (compound 18,Table1 ) in their absolute minimum conformations.

and its rigid ana-

the substrate PAR and the active site of DHPS seems to be tenable. Moreover, this result is also consistent with the assumption that a generic substituent Y on sulphanilamides and sulphones (4-NH.&,H,-SO,-Y) is not directly involved in the interaction with the enzyme but its role is mainly connected with the electronic perturbation and, hence, electrostatic optimization of the biofunctional common moiety 4-NHz-C6H4-SO2 and, particularly, of the SOz group. These latter conclusions are the opposite of those that were drawn for the benzylpyrimidine inhibitors of DHFR where, once some peculiar electrostatic interactions of the 2,4diaminopyrimidine nucleus with the DHFR active site have been realized, both the selectivity towards DHFR from different sources and the potency depend strongly on the substituents on the benzylic ring. This topic is treated in the following section. ELECTROSTATIC

ASPECTS OF DIHYDROFOLATE

REDUCTASE

INHIBITION

BY

5-BENZYL-2.4-DIAMINOPYRIMIDINES

In a series of drugs interacting with the same receptor the reagent (the receptor) is a constant factor so the recognition of the drugs by the receptor will depend on their electron distribution and, hence, the electrostatic interactions are dominant in the recognition step. This leads to the concept of the recognition pharmacophore which may be defined as a certain electronic pattern which is necessary and sufficient for the recognition step to occur. Van der Waals forces show a sharper dependence on distance (proportional to r -6) than do Coulombic forces (proportional to

241

imidines which are highly selective inhibitors for bacterial dihydrofolate reductase (EC 1.5.1.3). This enzyme catalyses the nicotinamide adenine dinucleotide diphosphate (NADPH) -dependent reduction of dihydrofolic acid. The product (tetrahydrofolate) and other reduced folates are essential for the biosynthesis of purines, thymidylate, and several amino acids [ 231. Inhibitors of dihydrofolate reductase are effective in the treatment of the cancer (methotrexate ), malaria (pyrimethamine), and bacterial infections (trimethoprim). Trimethoprim (5 (3’ ,4’ ,B’-trimethoxybenzyl) -2,4diaminopyrimidine) is a potent bacterial’dihydrofolate reductase inhibitor and is widely used as a bacteriostatic agent in combination with sulphamethazole which, by inhibiting the dihydropteroate synthase involved in a previous step of the folate biosynthetic chain, exhibits strong synergism [ 241. Although conformational calculations have already been done [25-271 for some selected benzylpyrimidines, none of them have taken into account their Nl protonated form, which is the active form that binds the DHFR active site [ 281. It has recently been shown [2] that when different prototropic forms coexist in the biological test solution, the correct approach to QSAR analysis involves the search for the active prototropic form (like the active conformation) which interacts with the receptor. The molecular descriptors of this form should be defined and measured or computed. Different prototropic forms may have dramatically different electronic properties and, thereby, different electrostatic patterns. The computed energy differences relative to the global energy minimum for 5benzyl-2,4diaminopyrimidine in its neutral (AEN) and Nl protonated (AZZ’) forms are listed in Table 3. The molecular conformation of the benzylpyrimidine is determined by two principal torsional angles z1and r,. As for the neutral form, our results are essentially similar to those obtained in previous studies on trimethoprim [ 271. This suggests that methoxy substitution at the 3,4 and 5 positions of the benzylic ring does not change significantly the pattern of the potential energy surface for independent rotation of z1 and r,. Similar trends are obtained for the corresponding conformers of the Nl protonated form (Table 3). In fact, linear-regression analysis of the AE values for the neutral and protonated conformers gives the equation Up=0.97(

+0:07jAEN+0.12(

k1.02); n=24, r=0.94, s=13.99

Ghere the upper limit considered for AE is 40 kcal mol-‘. If we restrict the range of variation of AE to O-4 kcal mol-‘, the following equation is obtained Up=0.86(

+0.31)UN+0.05(

kO.89); n=13, r=0.61, ~~0.66

where a worse and more scattered trend is observed between the AE values of the different neutral and protonated conformers of the benzylpyrimidine in their energetically accessible conformational space.

TABLE 3 Computed energy differences relative to the global energy minimum of different conformers of 5-benzyl-2,4_diaminopyrimidine in ita neutral (AEN) and Nl protonated (AE’) forms

AEN

71

(deg.) zeg.1 (kcal mol-‘)

AEP

ALP (deg.) (kcal mol-‘)

Lwp

0 45 90 135

> 100 8.0 1.7 10.4

> 100

72

(kcal mol-‘)

>eg.) - 180

(kcal mol-‘)

0 45 90 135

> 100

> 100

86.4 21.5 > 100

>lOO 24.5 > 100

-45

0 45 90 135

40.2 96.9 20.0 2.6

29.3 > 100 24.6 1.0

-225

0 45 90 135

13.7 27.1 3.2 3.5

11.9 22.3 3.3 3.3

-90

0 45 90 135

2.0 3.1 2.5 1.3

2.9

-270

3.0 2.4 2.3

0 45 90 135

3.3 2.8 2.6 3.2

2.7 2.0 2.5 3.2

0 45 90 135

10.1 3.8 3.6 23.7

11.9 3.5 3.0 22.1

-315

0 45 90 135

27.2 2.7 20.1 > 100

37.3 1.4 25.7 >lOO

0

-135

Global minimum Neutral form Protonated form

7,

(deg.)

65.5 175.3

7,

(deg.

125.9 90.1

)

6.3 0.0 6.16

E(kca1 mol-‘) - 55363.02 - 55539.93

Caution should be used when trying to rationalize the biological activity by comparing the electron distribution and the electrostatic potential maps inside a congeneric set of molecules which show prototropic and conformational equilibria between neutral and charged species [ 2,7,11,29,30]. The most significant changes that occur on protonation in some selected molecular orbital indices computed on the absolute minimum energy conformers of benzylpyrimidine are reported in Fig. 4. These changes, mainly localized on the diaminopyrimidine ring, clearly suggest that Nl protonation, while producing a Coulombic interaction with one oxygen atom of the aspartic residue (Asp-27)) renders the adjacent 2-amino and 4-amino groups more efficient hydrogen bond donors

243

qN

q’W

sNL”MO

-0.2564 0.0250

Fig. 4. Absolute minimum-energy conformers of the neutral and pro&mated forms of trimethoprim. The most significant changes that occur in the molecular orbital indices upon protonation are reported as represented by the electronic net charges and the nucleophilic superdelocalizabilities of the nitrogen atoms of the diaminopyrimidine moiety.

towards the Thr-113 residue, in the case of the 2-amino group, and towards the hydroxyl oxygen of Tyr-100, in the case of the 4-amino one [27,31,32]. Finally, it is useful to stress that the computed absolute minimum energy conformer obtained for the protonated benzylpyrimidine is very close to that found for the crystal structure determination of the trimethoprim E. coli DHFR binary complex (q = - 177’) 72= 76’ ) and ternary (NADPH added) complex 7,=56”) [33]. (7,= -192”, From the above it is clear that the central role of the Nl protonated form of the diaminopyrimidine nucleus is in the recognition step and in the docking of this electrostatic pharmacophore to the DHFR active site. Recently, Baccanari et al. [ 28 ] have studied the selectivity of benzylpyrim-

244

idines for bacterial DHFR by using equilibrium and kinetic techniques. They showed that the in vitro antibacterial activities (E. coli) of trimethoprim and of a series of close structural analogues with different positions of methoxy group substitution on the benzylic ring varied according to their degree of substitution. Moreover, the relative antibacterial potencies of the compounds considered were directly proportional to the DHPS inhibition constant values (Ki ) , as determined by classical enzyme kinetics. Table 4 lists the most significant biological data determined by Baccanari et al. [ 281 together with some selected molecular orbital indices computed with the AM1 method and relative to the substituted benzylic ring. The molecular orbital indices listed in Table 4 are supposed to represent, in a simple way, the mutual electron perturbation between the substituents and the phenyl ring. The indices listed are: (a) the summation over the Kelectronic net charges on the carbon atoms of the phenyl ring (ZqzPh); (b) the summation over the absolute values of the total net charges on the phenyl ring (C 1qt 1Ph) and over the methoxy substituents (Z 1qt 1Sost), and (c) the summation over the absolute values of the total net charges on the substituted phenyl ring ( Eqtph + I2 1q” 1sost). The last part of Table 4 refers to the kinetic inhibition and equilibrium binary (DHFR-inhibitor complex) and ternary (DHFR-inhibitor-NADPH complex) constants, expressed as pK values, of E. coli and SR-1 rodent lymphoma dihydrofolate reductases. Correlation analysis of the data reported in Table 4 shows some interesting TABLE 4 Selected molecular orbital descriptors, kinetic (Ki) and equilibrium binary and ternary dissociation constants of E. coli and SR-1 dihydrofolate reductases No.

Benzyl substituent

Z~*r,,

zlqtlPb

CIPtlsd

(~l~tlPh+~l~tlsost~

1 2 3 4 5 6

Unsubstituted 3-(OCH,) 4-(OCHB) 3,4-(OCH,)z 3,5-(OCH& 3,4,5-(OCHA

- 0.0061 - 0.0837 - 0.0758 -0.1302 -0.1414 -0.1957

0.1331 0.4647 0.3813 0.4230 0.6295 0.8753

0.0329 0.6268 0.6180 1.2024 1.2524 1.7877

0.1660 1.0915 0.9993 1.6254 1.8819 2.6630

No.

Benzyl subatituent

pK (nM)

1 2 3 4 5 6

Unsubstituted 3-(OCH,) 4- ( 0CH3) 3,4-(OCH,)z 3,5-(OCH,), 3,4,5-(OCHA

pKdbi” (nM )

pK,t”’ bW

E. coli

SR-1

E. coli

SR-1

E. coli

SR-1

4.98 5.68 5.60 6.31 6.37 6.97

5.62 5.60 5.68 6.02 5.54 5.43

6.67 6.80 6.58 6.53 7.00 6.06

6.41 6.66 6.58 6.49 6.39 5.85

6.00 6.85 6.74 7.85 8.10 8.42

6.89 7.03 7.00 2.27 7.07 6.52

pKdmrSR-1

pK,fe’ E. coli

pKdbh E. coli pKdbi”SR-1

PKi E. coli PKi SR-1

~ltltls@at (~ls”lPh+cl~“lsost)

.X14tlPh

WPb

1.000

GxPh

- 0.949 1.000

zIQtlPh

Correlation matrix of the data given in Table 4

TAEILE 5

- 0.996 0.932 1.900

cle3wt

-0.997 0.965 0.994 1.000

(~l~tIn+~I~t180at)

bM)

- 0.996 0.993 0.999 0.994 1.000

E. coli

MC

0.175 -0.463 -0.146 - 0.241 -0.148 1.000

SR-1 0.639 - 0.696 -0.672 -0.686 -0.669 0.512 0.740 1.009

SR-1

WW

0.453 - 0.443 -0.481 - 0.476 -0.471 0.114 1.000

E. coli

P&~

0.891 0.983 0.970 0.965 -0.091 - 0.333 -0.599 1.000

0.292 0.499 0.296 0.359 0.292 0.793 0.676 0.819 - 0.168 1.000 -

SR-1

(nM)

- 0.977

E. coli

PIG*

246 trends as shown by the correlation matrix given in Table 5. In fact, the only significant correlation (r = 0.985 ) among the biological data for the inhibitors considered refers to the dissociation constant of the ternary E. coli DHFR complex (pKdti’ E. coli) and E. coli growth inhibition data values (pKi E. coli). This result, considered together with the lack of correlations for the biological data of the E. coli binary complex, and the poor and unselective correlations of the PKi SR-1 values for the corresponding binary (r=0.819)and ternary (r= 0.793) dissociation constants of DHFR (extracted from SR-1) complexes, clearly suggests that the involvement of NADPH is an important factor in the high affinity of trimethoprim for the DHFR extracted from E. coli, and that the lack of involvement with the mammalian enzyme determines the selectivity of trimethoprim as antibacterial [ 281. These findings are supported by the good correlations obtained between the molecular orbital indices and both the PKi E. coli and pKdwr E. coli data, whereas no correlations are observed with SR-1 derived biological data. Finally, it is useful to note that the best correlations obtained refer to molecular orbital indices localized on the substituents (C 1qt 1Sost) and that only a poor correlation with negative slope is obtained between the same molecular orbital indices and pKdbinE. coli. The latter observation suggests that the same electronic factors have the opposite effect for the compounds considered in the binary and ternary complexes with E. coli DHFR.

CONCLUSIONS

Electrostatic forces together with QSAR methods are of fundamental importance in predicting and explaining biological and pharmacological events in terms of intermolecular interactions. The examples considered in this work (sulphones and benzylpyrimidines which are inhibitors of folate biosynthesis) show that by making use of simple ad hoc electronic descriptors computed for the biologically active structural forms of the drugs, it is possible to rationalize their biological potencies in terms of electrostatic models. In fact, in the case of sulphones, the more electron rich the common moiety and, in particular, the SO, group, the higher their inhibitory potency. The role of the substituents is exhausted in modulating the electronic structure of the common moiety. As for benzylpyrimidine inhibitors, once the electrostatic requirements of the receptor site have been satisfied by the Nl protonated forms of the pyrimidine nucleus, both the potency and selectivity are modulated by the substituents on the benzylic ring.

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