An investigation of the opioid peptides by means of the graph-theoretical method

Journal of Molecular Structure (Theochem), 209 (1990) 211-222 Elsevier Science Publishers B.V., Amsterdam

211

AN INVESTIGATION OF THE OPIOID PEPTIDES BY MEANS OF THE GRAPH-THEORETICAL METHOD KRYSTYNA ROMANOWSKA Institute of Chemistry, Wroclaw University, ul. F. Joliot-Curie 14,50-383 Wroclaw (Poland) (Received 21 August 1989; in final form 2 March 1990)

ABSTRACT The set of opioid peptide molecules is examined by means of the QSAR method. A topological description is used to depict the features of the studied compounds and indices of graph-theoretical origin are used to investigate the correlations between structure and biological activity. The hypothetical hydrogen bonds causing the differences in conformations were implemented in the graph-theoretical representation of the examined molecules. Some suppositions concerning the opioid molecules’ conformation in the receptor-bound state as well as the nature of the opioid receptors are formulated.

INTRODUCTION

The endogenous peptides known as enkephalins are flexible linear pentapeptides Tyr-Xxx-Gly-Yyy-Zzz, e.g. Tyr-Gly-Gly-Phe-Met, Tyr-Gly-GlyPhe-Leu, which can act as natural analgesics [ 11.Some other peptides, “opioid peptides”, exhibit similar activity. The physiological mechanism of action of these compounds at the molecular level could be elucidated if the structure of the receptor and the conformation of the opioid peptide molecule were known. Investigations on the opiate receptors have enabled the characterization of some different subtypes of receptors [ 2,3] : ,u, 8, K and crreceptors are able to bind various opiate (or opioid peptide) molecules, but their detailed structure is not yet known. Enkephalins bind mainly to the 6 receptor, but some opioids can also bind to the p receptor [ 41. The important pharmacophores of the enkephalins have been found by modifying the opioid peptide molecules and monitoring their receptor-binding abilities, biological activity and receptor selectivity. For biological activity, residues 1, 3 and 4 (Tyr, Gly and Phe in Met-enkephalin) are found to be very important [ 51. During the past decade there have been numerous efforts to elucidate the conformation of opioid peptides and to correlate it with the biological activity of the considered compounds. In the conformational analysis of enkephalins 0166-1260/90/$03.50

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Elsevier Science Publishers B.V.

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theoretical energy calculations [ 6-101, crystal-structure determination [ ll131 and conformational studies in solution [ 14-181 were employed. Recognition of the conformation of the enkephalins is not an easy goal, as these molecules are quite flexible and instead of there being a single preferred conformation there may exist an equilibrium between some different conformational states. It is quite possible that this equilibrium depends on the molecular environment. Furthermore, the specific bioactive conformation may not be present in solution, but be adopted during the binding process with the receptor, as in a “zipper” -type model [ 191. Detailed geometric and electronic examination of flexible molecules is tedious and time consuming, so it would be of value if one could compare the properties in a series of molecules with minimal effort. Knowing the difficulties which one meets when applying conventional theoretical methods of structure elucidation (e.g. quantum chemistry and molecular mechanics) to flexible molecules and remembering that the connection between structure and biological activity is very important from the theoretical as well as the practical point of view, we will look for the simplest ways of correlating the structure-dependent molecular descriptors with biological properties. To this end we used a scheme which is basically the QSAR method [ 20,211. Our molecular descriptors are not connected to the physico-chemical properties of the molecules studied, but to their topology. A molecule can be considered as a graph, and a graph-theoretical description [22,23] is the basis of the present study. This approach has been successfully applied in the field of theoretical organic chemistry [ 24-271 as well as in biological and medicinal chemistry [ 28-331. The graph-theoretical indices concept has also been widely used in the QSAR scheme [28-441. In this work we will attempt to correlate the topological properties of the series of opioid peptides with their biological activities, measured by binding assays ( [ 3H ]DAGO and [ 3H] DSLET binding inhibition constants I&) as well as bioassays (IC,, for inhibition of electrically induced contraction of the GPI and the MVD ). The GPI is supposed to possess the ,u receptors and the MVD the 6 receptors [ 451, whereas [3H]DAG0 is a highly selective ,u receptor radioligand and [ 3H]DSLET a d-selective one. We have also tried to specify the probable differences between the receptor binding of the 6- and p-selective opioid peptides. METHOD OF CALCULATION

From the topological point of view, a molecule is a connected, undirected graph with atoms as vertices and bonds as edges. In the present analysis we used the adjacency matrix M for such graphs [ 221: the elements mij of M are equal to 1 if the i andi vertices are connected and 0 if not. In order to assess the use of M for compounds with heteroatoms we adopted a kind of weighting

213

scheme [46]: for non-zero values of mij, mii= (Z,,i+Z~~)/(2*2,,l), where 2,; is the number of o electrons in atom i in a given hybridization state and atom 1 is the sp3 carbon atom (Table 1). It should be noted that we do not follow the usual practice of hydrogen atom suppression in the graph-theoretical description of, for example, hydrocarbon molecules because hydrogen atoms in peptide molecules have different physice-chemical properties owing to differences in their bonding. One of the properties of graphs which can be easily derived from the matrix M is the number of paths of different length and this property is used throughout this paper. A path is defined as a sequence of vertices and edges which are adjacent and no vertex emerges more than once in a path. The collection of path numbers for a molecule is obtained by adding paths of the same length for all atoms in a molecule, pl, p2, .... pn, where the subscript indicates the length of the path andpi= C pi,+. Under these circumstances a molecule can atoms be represented by a sequence of path numbers which can be thought of as the components of the n-dimensional vector P : P = (p1,p2, .. ..p.). In order to minimize the role of molecular size, all path numbers are divided by the number of atoms in the molecule. Individual atoms and groups of atoms within a molecule can be characterized in a similar way; i.e. by looking for graph-theoretical indices defined by the multi-dimensional vectors representing molecules, or parts of them, which could be correlated with the biological activity of the studied compounds. Various kinds of topological indices have been widely used as parameters in the QSAR method (see e.g. refs. 38-44). Here we examine the following indices. (1) The sum of all path numbers: this is a kind of a “molecular identity (ID)” code [ 34,37,40,42]. (2) The lengths of vectors: P, representing the whole molecule; Pk, k = 1,2, 3,4, representing the amino acid residues of the studied peptides (we considTABLE 1 Parameters used for weighting of the matrix M elements Atom

&7

c spa c sp2 0 sp3 0 sp2 N sp3 N sp2 S H

4 3 2 1 3 2 2 1

214

ered the first four residues only, as the shortest peptides taken into account are tetrapeptides); P @*, , P,, , P,,, kl = 2,3,4, & = 1,2,3, describing the groups of four atoms which define the backbone torsional angles @, v/ and o; and PA, where A denotes the phenyl ring of the first residue (Tyr or Phe) present in all opioids taken into account. (3) The angles between all pairs of vectors mentioned in (2) above: L (P,

Pd; L (P, P,] k L (P, P,, 1; L (P, Pm, ); L (Pk, P,, 1; L (Pk, P,* ); L (Pk, ‘Cl&); ’ (‘&I, ‘@j); ’ (P&l9 p,l); L (pv/k19pm, ); ’ (pvk2, p,); ’ (pl#h9 Pm,1 and L (P,,,, P,); where k=l, 2,3,4, or A, kl=2, 3,4, &=l, 2,3,1=1,

2,3, j=l, 2,3,4, j#kl andj#k,. Hence, each molecule is described by a molecular ID value, 15 vector length values and 105 angle values. Some of these indices could, of course, be. interrelated. As our method is not suited for differentiation between D and L configurations, we limited our examinations to the peptides consisting of L-amino acids, except for residue 2 which is assumed to have D configuration (if it is not

glycine) . The molecules examined and their biological activities, A,,,,, are collected in Table 2. It has been established that, in some conformations of the enkephalin molecules, different intramolecular hydrogen bonds can occur [lo]. The existence of such a bond greatly influences the topology of a molecule, so we decided to imagine also some possible hydrogen bonds in the studied molecules and to test whether this supposition would change our results concerning the structure-activity relationships in any manner. The hydrogen bond can be implemented in the adjacency matrix as an ordinary additional bond. As a result, we can describe the considered molecules according to some different hydrogenbond patterns: (a) hydrogen bonds not taken into account; (b) l-+3 hydrogen bond; (c) 1+4 hydrogen bond; (d) 2-+4 hydrogen bond; (e) 4-+2 hydrogen bond; ( f) 4-+ 1 hydrogen bond and (g ) 3 -+ 1 hydrogen bond. Depending on the features of the molecular structure, the compounds here studied can be divided into classes according to their different features as follows. Scheme A: class I, linear compounds and class II, cyclic compounds. Scheme B: class I, compounds with aromatic residues 1 and 4; class II, compounds with aromatic residues 1 and 3 and class III, compounds with aromatic residues 1 and k, where k > 4 or there is no other residue of this type in the molecule. Scheme C: class I, linear compounds with aromatic residues 1 and 4; class II, linear compounds with aromatic residues 1 and 3; class III, cyclic compounds, connected residues 2 and 5, aromatic residues 1 and 4; class IV, cyclic compounds, connected residues 2 and 4, aromatic residues 1 and 3 and class V, cyclic compounds with aromatic residues 1 and k, where k> 4 or there is no other residue of this type.

215 TABLE 2 Biological activity of opioid peptides” Molecule

1 YGGFL 2 YAdGFL-NH2 3 Y (OdLD)-NH2 4 Y(OdGE)-NH, 5 Y (OdFD)-NH, 6 Y (DdFO)-NH, 7 Y (KdFE)-NH, 8 Y (EdFK)-NH, 9 Y (KdGFE)-NH2 10 Y (OdF(NM)D)-NH, 11 Y(OdGFD)-NH, 12 F(KdGFE)-NH, 13 Y(DdGFK)-NH2 14 Y (EdGFK)-NH, 15 Y(CdGFC)-NH2 16Y(OdGFL) 17 Y(KdGFL) 18 Y (KdGFM) 19 Y (KdGLF) 20 Y (A$GFL) 21 Y ($GFL) 22 Y (A;GFL)-NH, 23 F(KdGFL) 24 YAdFGYPS-NH2

log IC&l GPI

MVD

2.390935

1.056905 0.916980 4.606382 4.602060 3.588832 3.932981 0.716838 2.004321 -0.188425

0.883093 3.733197 3.942008 1.558709 2.717671 0.466867 0.902547 0.053078

1.382017 1.630428 0.178977 1.681241 0.681241 0.079182 0.526339 1.149219 1.369216 1.457882 2.021189 0.574031

Ref.

log Ki DAGO

DSLET

0.974512

0.403120

3.832509 3.245513 1.017033

3.911690 3.698101 3.346353

0.155336 -0.002614 0.117271 3.552668 -0.118045 0.671173

0.639486

1.692847 -0.161151 4.448706 0.432969 1.936514

2.408240 2.844477 -0.119186 2.676694 2.149219 1.535294 1.619093 1.910624 1.863917 1.6589965 3.609595

47 10 47 47 47 47 47 47 48 49 49 49 48 48 48 48 48 48 48 48 48 48 48 50

“Y, Tyr; G, Gly; F, Phe; L, Leu; A, Ala; 0, Orn; D, Asp; E, Glu; K, Lys; C, Cys; M, Met; P, Pro; S, Ser; A,, A,bu; Ab, Abu; A,, Aa; Xd, X residue in D configuration; (NM), (NMe ) .

For a detailed classification of the compounds considered in this work see Table 3. Within each topological scheme (A-C), different classes can eventually be described according to the different hydrogen-bond patterns described above. In the next step we looked for the correlations between biological activities, A ,,,_ of the considered opioid peptides and topological descriptors of these molecules using regression analysis. Four sets of dependent variables (A,,,, Table 2) were taken into account and for each set we investigated equations of the form A meas,,.=U(J +Ul Xj where xj are the topological descriptors of the compounds studied.

(1)

216 TABLE 3 Schemes of topologicaI classification of the opioid peptide molecules Scheme

Class

Molecules

A

I II

1,2,24 3-23

B

I II III

1,2,9,11-18,20-23 5-8,10,24 3,4,19

c

I II III Iv V

1,2,22 24 9,11-18,20,21,23 5-8,lO 3,4,19

RESULTS

In examining the possible correlations between structure and activity, we decided to adopt a significance level of P= 0,001 and to consider the correlation coefficient as the measure of correlation. First, we described all the compounds according to one hydrogen-bond pattern (see above) and tested whether it was possible to obtain a satisfactory correlation with any of the patterns a-g (Tables 4 and 5 ) . In the next step, we divided the set of molecules considered into subsets TABLE 4 Correlation between topoIogicaI descriptors and biological activity of opioid peptide@ Hydrogen-bond pattern

Dependent variable 1

2

3

4

;:

0.3846 0.3594 (45) (80)

0.3576 (111) 0.4570 ( 16 )

0.6160 (34) 0.6060 (73)

0.5898 (111) 0.7081 (16)

:

0.3599 (82) 0.6870 (44)

0.4588 (78) 0.6197 (45)

0.4882 (78) 0.7738 (53)

0.6631 (53) 0.7431 (111)

; g

0.5450 ((87) 0.5960 105 ) 0.3599 (44)

0.5259 (97) 0.4349 (44) 0.4588 (45)

0.5827 (19) 0.5696 (53) 0.4882 (53)

0.7219 (111) 0.6362 (19) 0.6631 (111)

“The maximum correlation coeffkients are presented. Codes of topological descriptors (independent variables) are given in parentheses (see Table 5 for code). Dependent variable 1: n=21, F,i,=O.6652. Dependent variable 2: n=20, r,,,i,=O.6’788. Dependent variables 3 and 4: n= 10, Fmi”=O.8721.

217 TABLE 5 Codes of some topologicaI descriptors (independent variables) Code 6 26 42

Descriptor

Code

50 54 60

IPdl 0i,p,) L (P3, P,) L (P3, P$Q) L (P4, p,, ) L (P,, Py13)

12 27 44 51 55 61

75 79 83 38 104 111

L (P,,P,) L (Pyl, I’, ) L (Pm,, P&) L(P,,P,) L (P,, P,) L (P, P4)

76 80 34 69 105 112

Descriptor IPUJZI L(Pl,P,) L (P3, p, ) L(P,,P,) L (P4, p,, ) L 0’4, P, ) L (P,,,P,) L(P,,,P$z) L (P,,, p, ) L(P,,P,) L (P,, p, 1 L (P, PA)

Code

Descriptor

IPCI

16 30 45 52 53 62

L L L L L

77 31 35 93 106 113

(Pz, P3) (P3, p,, ) (P3, p, ) (P,, p, ) (P4, p, )

L (P,,P,) L(PW1,PW) L (P,,,Po3) L(P,,P,) L (P,, P&) L (P, p, )

Code

Descriptor

19 34 49 53 59 73

L (PI, P4) L (Pz, p,, 1 L (P3, P,) L (P4, PA) L (P4, P,) L(P,,P,)

73 62 37 97 108

L(P,,P,) L (P,,,P,) L(P,,P,) L (P,, PC) L (P, P1)

TABLE 6 Correlation between topological descriptors and biological activity of opioid molecules’ Subsetb

Dependent variable

Hydrogen-bond pattern

1

a

c IV

0.9999(113)

b

c IV

0.9992(30)

C

A II

0.8091(78) 0.7625 (79)

d

B II c IV

e

B II c IV

g

B II c IV

2

3

4

0.9997(112) 0.9997(112)

0.9997(44) 0.9996(27) 0.9996(27)

0.9997 (44 )

0.9997(112) 0.9997(112)

“See text for definition of subsets. See Table 5 for definition of independent variables (given here in parentheses). bA II, dependent variable 1, n ~21; B II, dependent variables 3 and 4, n=4; C Iv, dependent variable 1, n=4; dependent variables 3 and 4, n=5; rmi, (n=4) =0.9990; rmh (n=5) =0.9911; r,i, (~~=21)=0.6652.

218 TABLE 7 Correiationbetweentopologicaldescriptorsand biologicalactivity of opioid molecules”Valuesof rz rms, (P=O.QOl) are presented Topological scheme

Classand hydrogenbond pattern

Dependentvariable 1

A

B

I c c

c C

c t b I

II

;:t b b bea bea e e a _ a u a-c a-c a w c NC cwc f-c aNa -d : .%. it: b -d b a _ e _ c * a N d-a c N

III f b b

I e

II e

II

III

C

C

f b f f e e e

c a a e d a g

IV d

v e f f e

: a c

a c c

c

e e a a e

i b f f f f f f a e e e e e e e e e f

e e a e : e a e : d : d b b c a 1

2

3

4

O&811(77) 0.6870(82)

0.6811(77) 0.6870(82) 0.7148(87) 0.7079(111) 0.7202(111) 0.7275(111) 0.8735(53) 0.9107(108) 0.9476(108) 0.~5(58) 0.6711(81) 0.6771(81) 0.7013(104) 0.6987(106) 0.7430(105) 0.7865(105) 0.6895(111) 0.6966(111) 0.6987(111) 0.7000(111) 0.7189(111) 0.7202(111) 0.7275(111) 0.7344(111) 0.8735(53) 0.8856(53) 0.9367(53) 0.9476(108) 0.9504(53 ) -O-9767(60) -0.9715(55) 0.8964(53) -0.9063(59) -0.9033(59) -0.9055(61)

“For furtherexplanationsee text. _, any pattern (as the dependentvariables2,3 and 4 are not given for the class C II compoundsf .

219 TABLE 8 Statistical characteristics of some relations between topological descriptors and biological activity of opioid peptides. Topological scheme of classification: C. Relations with maximum correlation coefficients are given Dependent Class and variable hydrogen-bond pattern

n

Independent variable

r

a,

a1

Standard error

I II III IV v 1

ee

a

c

e

21

L (P,,P,)

0.7865

-5.456278 + 0.000152

1.015201 + 0.00748

0.655110

2

f a

c

f

e

20

L(P,PJ

0.7344

f 1.153534 f 0.000018

0.414286 f 0.001275

0.919249

3

aae

e

b

10

L(P,,PW)

-0.9767

11.437093 k 0.000001

-0.402795 k 0.000298

0.320423

4

caa

e

c

10 L(P,,P,)

-0.9063

-8.573352 f 0.000003

-0.330521 f 0.001223

0.714198

according to each of the topological schemes of the classification A-C and tried to find a correlation between structure and activity within individual subsets, describing all compounds by one hydrogen-bond pattern (Table 6). Finally, we divided the considered opioid peptide molecules according to the topological schemes A-C. In each of the three schemes of classification, each class was allowed to be described by any of the hydrogen-bond patterns (a-g). The correlation coefficients obtained in this calculation are presented in Table 7. The statistical characteristics of the relations with maximum correlation coefficients for each dependent variable obtained within the C scheme of classification and allowing for different hydrogen-bond patterns in different topological classes are presented in Table 8. CONCLUSIONS

Considering all the opioid peptide molecules taken into account according to hydrogen-bond pattern (a) (hydrogen bonds not included in the adjacency matrix M), it was not possible to obtain a satisfactory correlation between any of the topological descriptors and any measure of the biological activity (see Table 4, hydrogen-bond pattern (a) ). Describing all the considered molecules according to one of the hydrogen-

bond patterns (a-g), we obtained only one significant correlation equation; i.e. that between the dependent variable log (IC,G,p) and the topological index L (P,, , Pm), assuming that the conformations of all compounds allow for the 1+4 hydrogen bond (see Table 4, hydrogen-bond pattern c ) . The partition of the considered molecules into subsets according to some topological features and assuming that compounds belonging to the same subset are described by the same hydrogen bond pattern led in some cases to satisfactory correlation between topological descriptors and biological activity, but the number of elements in the subsets is very small (Table 6). The assumption that the considered molecules should be classified according to some topological features and that different classes could be described using different hydrogen-bond patterns allowed us to obtain several significant correlations between biological activity and topological descriptors for the entire set of compounds examined simultaneously (Table 7). It can be seen that classification of the opioid peptide molecules according to topological features (linear vs. cyclic molecules and the position of aromatic residues) and with allowance for different hydrogen-bond patterns in different classes leads to significant correlations between topological descriptors and biological activity as measured for different types of receptors. The fact that for the same hydrogen-bond pattern no significant correlation for two (or more) dependent variables was obtained simultaneously could be considered as confirmation of the fact that different receptors have different steric demands. This result could also be regarded as evidence that the opioid peptide molecule can adopt different conformations as a result of interaction with different receptors. The fact that peptide molecules change their conformations upon interaction with, for example, metal ions is well established [ 51,521. ACKNOWLEDGEMENT

Partial support of this work by CPBP-01.12 is gratefully acknowledged.

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