Interim Report to the . “ National Acronautics and Space Administration Grant NsG 81-60 DENDRAL A SYSTEM FOR COMPUTER CONSTRUCTION, ENUMERATION ANI NOTATION OF ORGANIC MOLECULES AS TREE STRUCTURES AND CYULIC GRAPHS ; Part I, Notational Algorithm for Tree Structures II. Topology cf Cyclic Graphs III. Complete Chemical Graphs; Embedding rings in trees IV, Generator Algorithas VW, Directions for Further Analysis ; \ ’ Submitted by , Joshua Lederberg Professor of Genetics - . School of Medicine Stanford University Palo Alto, California Studics related to this report have been supported by research grants from the National Aeronautics and Space Administration (NsG 81-60), and from the Advanced Research Projects Agency of the Office of the Secretary of Defense (SD-183). Part III. Merch 13, 1968 . DRAFT VERSION Provisional version of DENDRAL. Part III Complete Chemical Graphs; Embedding Rings in Trees. This preliminary version is’ released at this time in order to facilitate the programming of DENDRAL for ringed structures, in particular the embedding of rings in trees. The external notation is subject to further revision. A more compact one can easily be devised that also provides for implictt data and merges some of the lists. For canonical ordering, it may be necessary to expand such a compact formula back to the explicity LISP lists of the generator programs, for example the edge crunt list, path modificr list, and vertex modifier list could be unified For the’ purposes of this report, we focus on the internal notation and the combinatorial and automorphism problems that have to be faced by the generator program. Formulas will be lists that can be read by a 4 LISP language processor. Note that comnas are redundant, "." is, however, in ‘no case the dot of a LISP dotted pair, and this character should be translated at input-output. ' This change of emphasis modifies some of the hierarchical choices, but none of the fundamental ideas developed in DENDRAL I (acyclic molecules) and DENDRAL Il (general survey of regular cyclic trivalent graphs). 2. - INDEX Section 3.1 is a glossary that should be consulted together with Table 3.1 as an authoritative definition of DENDRAL valuation, Section 3.2 elaborates the completion of ring definitions as mappings ‘on the nodes and edges of one of the VG's listed in Dendral Il. Section 3.3 specifies how rings are embedded in trees to complete the a . notation outlined in Dendral I. Section 3.4 deals with some problems of chirality Sections 3.5, ff, will be completed at a later date. ---- They will cover such topics as a _ abbreviated notations for human interaction ‘Petmanent labels and special mappings for frequently encountered rings Special treatment of aromaticity Efficient algorithism for dealing with symmetrics Optional hierarchies of DENDRAL classification ~ Heuristic questions of plausible structures Rings with tetravalent (spiro) vertices %,2OO CANONICAL FORMS . ~ In general, the canonical choice among automorphisms is the lowest valued vector description of the structure, evaluated cell by cel}, It is important to follow the standard hierarchy of choice, as given in Table 3.1. For example, the pendant radicals are listed ' first, in ascending DENDRAL order, before the lowest locant vector is selected, This convention is consistent with DEMDRAL I and facilitates interfacing the computer programs for linear and cyclic DENDRAL. _¢ R-COMPOSITION. A composition in which ring atoms are removed and RING. A molecule which is a pure cyclic structure, with no appended twigs. RINGED COMPOUND. A tree, possibily degenerate, in which a ring is embedded, R-TREE. A representation in which any ring is represented as a superatom, SUPERATOM. A node representing a previously defined complex of os atoms, treated as an stem by the gencrator VERTEX Grou, ve, CUBICAL GRAPH, An abstract, cubical (trivalent) graph, summarized in DENDRAL 2, on whose nodes and edges are mapped the vertex atoms and connecting Linear paths of the ring. | COMPOSITION. List of atoms comprising a molecule, e.g. (C3N102U2) or (C3H7N02). ot ' allocated to ring identifiers. In effect, the composition -. Of an R-tree, | LOCANT. An ordinal number specifying an atom or a bond in a molecule for the purpose of attaching a radical. ory substituting a hetgroatom CHIRALITY, Structural information not given by the topological connectivity. This usually concerns the orientation in space of tetrahedral carbon atoms with asymmetrically attached radicals, GENERATOR. A program to generate a complete buyirr edundant list of isomers of a given composition. ORTHOMESH. A particular ring system presented as if all heteroatoms are replaced by C atons. It is specified by a VG plus an FCL in canonical order. - GLOSSARY (continued) ? _EDGE COUNT LIST, ECL A mapping of path length; on to the edges -of a VG. 4. AL -RING_DEFINITION A ring will customarily be defined (as a superatom) at the head of a formula. That is to say, the gencrator will allocate progressively larger numbers of atoms to one or more rings, then build all possible R-trees compatible with that R-composition. This canonical sequence can, of course, be rearranged for heuristic ‘purposes. Each predefined ring will be given an arbitrary temporary label, x2, etc. Some rings may be permanently dcfined, since they occur so _frequently. The most prevalent example is the aromatic, benzene ring which is defined under the name Z5as ot co a OC O| a Zb bear ene . : . . 1} al le)" . : . e 26% = ((o) 6*()()) » Ne ator naphthalene ZN* = ((2A) (o*,. 4%, 4*)()()) As illustrated by this example, a ring definition will have the - form - orthomesh . . oe . . . ING ECL vi PA ' \ xn = ((vertex group) (edge count list) (vertex modifiers) (path modifiers))}, | where xn is the temporary label, or Zm for a permanent one. - s 12 ORTHOMESH ; The Orthonesh consists of the VERTEX GROUP, VC, and the EDGE COUNT LIST, FCL. Together these elements define a planar mesh whose shape has become conventionalized by chemical usage - it corresponds to a carbocyclic ring system on which changes from C to other atoms can be mapped by exception. Examples which anticipate later notation follow: FOND aati dentate WE se, 1 ae . 0 ee nes re GH OO ne Rete tee > sweet ete eeeees twee. /\ S 2 sas V G ECL V iM ( Cornmnrot wn ) f Z (c.vayo barry ere “ . ah (|) (ot) . N (4) Uf rer in VX bower AW ~ . oth ccL ety oN LS uy B (3 leona (2) savin Tes | i | | On N (.) : | (6,0,0,38) ~ vt De In 3.21, the VG is (0), i.e., the single ring, sans vertices, on which is mapped a single path. AN . Yo The inscribed O stands for the — | | aa *| |" aromatic character of the ring, = — i.e., a path with alternating YS Re single and double bonds; . C:C,C:C,C:C, — Chemical evidence shows that in such a case, each bond is equivalent and has a character intermediate between "." and ":",. We indicate this by the notation * which might be denoted in a radical as RCACACKC“C“C* or implicitly as 6%. More complex rings have 2(r-1) vertices, where r is the number of to included ring units (inscribed faces) as conventionally counted by \ chemists. Dendral II elaborates al] possible vertex groups. The majority of organic ringed molecules fall in the category VG=(0), and r & 4, v = 6 covers zs large a scope as the unpecialized generator is likely to be able to handle. These are reproduced here for convenience as Figure 3.21 and 3.22, The v vertices implied by the VG must now be specified, and then the 3v/2 edges whose lengths are given by the ECL. be ' 3.% % VERTEX MODIFIFRS, VM. -| The EDGE COUNT LIST, ECL, has a higher priority than the vertex 4 modifiers, VM, list an implicd list of the vertex atoms which " specifies (a) their’ composition and (b) their chirality. Since the most usual situation is all carbons _- Lg we Jocate exceptions to that standard. The VM list and its value is the 3-ple (vector) fo, 1) the non-carbon atoms in DENDRAL order, expressed as a ' : composition, e.g., N2, or NIL. , 2) A vertex locant list for these atons. 3) An explicit list of the chirality of successive vertex atoms ~ (".") "4", aos vA") referring to "unspecified", “dextro", tevall, "racemic"; see section 3.4 for details. At any place, the omission of a list or the value NIL, implies "unspecified". Cael “Tables of symmetries to elicit canonical forms will be provided or ean be deduced from the VG (see Figure 3.1). For the moment the simplest algorithm will be to try all the automorphisms exhaustively, and save only the canonical representations. ‘ > otf | PATH LIST. - {The ring definition is now completed by mapping linear paths onto the edges of the VG. In taking account of the symmetries, the sense of the path must be considered. Several representations are possible; in previous specifications, we displayed a vector of all paths in edge- number sequence: thus (.) (.C.C.N.) (.C.C.C.C.) for e <- on OU Each edge of a path list was mapped with a linear, two-ended radical, 123 4567 ‘ presented in previously defined notaticn] The ring atons are all enum erable; first the vertices, Vl, V2, etc., them the path atons in the order of their presentation in the formula. . . _ . - | Ve now find it more convenient and conformable to chemical | notation to map rings by exception. The path list will then consist © of 3 parts: | 2.22 ECL " (already in orthomesh) 1) A vector that assigns a count to each edge in sequence. Each node is implicitly numbered by its sequence in the formula 4 2,2(3 PATH MODIFIERS = PM 2) A composition indicating atoms replacing the implied C's. This includes double bonds as U's. (abbreviations are available for aromaticity) 23,90 F "3) A locant vector for these Feplacing atoms and bonds Example 3. 241 then becomes: Aid . yit [ beaut vector _ /~...... 7 ECL LAL ysl ‘| «Cop a ((ZA). ((0,3,4)-N. (1))) drthonesh is RA (0,3,4), So : | - (A) ((0,3,4)-NS (2,4))) DHS 2. [- | . —— ‘ : focondh vechar ° 7 EtL OO eee ((ZA) ((0,4,4)-NU (1, (V1,5)))) 2YUS3 LI - , Caution: in internal notation all bonds are - "numbered as nodejairs. When the pair is (n,nt1) only the lower node need be numbered in external, notation, Note: in man-machine~interaction displays, parentheses can be replaced by form atted labels and indentations to facilitate editing and commands. We can visualize a display { y , 9 in , G 2AA , WW k ws . “yr Dasy PY ECL (0,4,4) iL oN PLM NU N 1 Hs) wd “2 ot &. Vertex numbers can be replaced by arbitrary integers, e.g. numbered after all the path atoms. In this example, V1¢9, V2¢10. . By giving the edge count list ‘a higher priority than the Vit We facilitate the storing of common orthomeshes under a familiar ring label. This can then be edited there for specific compounds. Thus, 3, 2453can be input as orthomests JS So nee Pri a VG CL Nr | | | (DECALIN WG, 0,5) 5))) LA vi \. IN — DECALIN - re | q LN? The chemists name for this ds A(1), 8-aza-decalin, >. deeds BO since he follows a sonevhat different numbering system, e should not be difficult to construct algorithis for interconverting many DENDRAL | names with conventional chemical notation. ~ Ow | emd here bef, a ~ ragga diealt, | Dossinel’s ( Dyeohn v()) _ DENDRAL III 7 Oo a 4 Example of a complete definition with canonical numbering: t io . | | . \ ee h RY O61) (sux (1.0, v3 5.7)) ). 1 / 5 4 - | (Cras) (0,0,0, 2,4 47 (H1) GS 3 0, V3, 9, \, ; | VG ECL VN PiM a 2, os : 2¢ 3 3 SNE, 2 wit WHEN the aromatic ring 1s detected, this reduce | Qe \" . | 7 (Whar) (00,4, 24,48) V2) (8j210) ) -7O Embedding the ring in a tree. g The ring as now defined may be regarded as a superatom. However, it will, in general, have its own symmetries. Different locations have to be indicated for attaching further radicals. For example, the three ” . 4 + amino-phenols are all special cases of ON nthe 7 Nth of fer 2uNO | eon SO . oF ™ - , , . - We will, then first list all of the attached radicals in DENDRAL order without reference to position of attachment. Then we will write a vector of locants describing the successive positions of attachment. For example, - -{ Cty yo 7 ne, MN MN > (|,B) WR oh RCN). AHR mt NAD 2 (1,2), flo oW anse . aApndicol htc onmuhe ~o to, NH <> On | ~2 CF U B)..0 ON Cuan. \ There are, of course, any automorphisms for the locant vector. In this - lexample the locant vector is (2,43): 7 ‘Canonical . Automorphisms -2(1,4,3)..0C.N ' -2(1,3,4)..C:N O 0Z(4,1,2)..0C.N 02(3,6,5)..0C.N ete. The canonical form 1) lists the radicals in DENDRAL order, the efferent link being implied es first, end wna wee a od ° pea ary Ae 2) emong the automorphic permutations of the locants, selects the least vector. ll. Resolving the ambiguities of the locant vectors is again a messy prospect and the simpliest general solution is to test all the symmetry operations serjatim and compare the locant vectors. More efficient rules will soon emerge for the frequent cases. However, as one suggestion, the pendant radicals might be replaced, during computation, by ordinal numbers in order to simplify compari- sons. . When a - Ci, - appears in a ring, two substitutions are possible at the same path°atom. For the moment they are not distinguished. Chirality at vertices and path nodes is discussed later, 3.4. eee ended Det Sen eet au + na Seah Hie Ne SOOM eg CRIRALITY For many purposes we emphasize the topological and ean overlook the 3-dimensional spatial aspects of molecular structure. In real molecules, the lengths and. rotations of bonds are understocd to a widely varying precision, and may be greatly influenced by the history, energy-state, and immediate context of the molecule. In this sensc, the topological connectivity is only a formal representation of 7 genus of states which can sometimes be inferred from it. | However, one aspect of stereo-chemistry generates distinctions among chemically stable species of very great importance, especially for biologically interesting compounds. ‘This is chirality, which rests upon the alternating symmetry groups of the valence bonds of the C aton. The symmetries of the valences of carbon. The topological tetrahedron has the symactry S4, that is all 4l= 24 pemutations of its vertices (table 3.41). The carbon atom behaves, however, as a steric tetrahedron, _ $0 that two enanticmorphic, mirror images, must be distinguished for (C...abcd). These corresponding to odd and even alternating groups (table 3.410). . ~ We can now regard the chirality of asymmetric carbons as a special case , of the locant lists which specify substitutions on superatoms. The D- and L~ isomers of, say, glyceraldehyde would be described (with implicit H's given leading locants, Egntra locants) ‘ Cho eCiaae) ve, oo, Gon > | HON \ MoO CH.04 Chia — CHQOH CKO ° oo - Fe ee ee ee meee _ ee ee ee % ! | COME By pe glycerafdehyte RN, - eee r ! o In view of the bisection of 5, each locant list. has 12 automorphisms (table 3.401). Z.13 into the two A's, even and odd respectively, We can abbreviate €(1,2,3,4).as C(0) or "even", and C(1,2,4,3) as C(1) or "odd" respectively. We do not use the terms D-,L- or R-, S-, as these are based on a different set of rules for ordering the radicals (ef. Eliel, 1962; Prelog, 1966). However, the absolute configuration is fully dcfined in the \ which lists the radicals in DENDRAL-hierarchical order. It radical-gencration. ' asymmetric carbon, are: Yt 1) CLI 2) U3 3) 4) program a translation between these systems, but DENDRAL is present system, is casy to preferred for The rules, which are specially adapted for Radicals in DENDRAL sequence; however, The afferent link, if any, takes position 4 Implied hydrogens are assigned implicit, leading locants D-glyceraldehyde is taken as the prototype of the even group. ~< °m J 4 ‘ / / | ; A , \ Lo\ > | Yo dees a”? roe | “ ‘ te AY s 3 #; 4 a oat 3 2 > 2 EN J eA ‘ foun x1 / - Pe ~ . X / 7 fo NN * Tee =o ~ 3, oad . s\ 3 o. ee oY Y Gon a eee we ee 3 - TETRA HE EA ever! werd e606 B.Ua. x pf It is elementary that C(0):‘C(1) only when the C is asymmetric, i.e.,; the four substituents are all different. The generator program needs know only this. However, translation to D/L and R/S notation, . and conservation of chirality may be important in analytical manipula- tions and in programming stereospecific reactions. PATH ATOM ATTACHMENTS Each H~atom of the path atoms of the pure ring is a candidate for replacement by a radical. If the path atom is a saturated C, (-CH,-), the two H's are not necessarily equivalent in chirality Lees, when the image of the rest of ‘the ring differs, as seen from the C atom, via the afferent and efferdnt bonds. The image is obtained by cutting the bond, the attachment to the C is replaced by an H; the other cut edge then leads . oy to a radical which can be evaluated by DENDRAL rules. Thus in THYEXSH at (3), the image is (C,0.C.C.C.) afferent ly and C.C,.C.0.C, efferently. Hence, any difference in the further substituents at (3) will make that atom asymmetric. Customary notation fails to unify the several aspects of chirality: asymnetric C atoms in neu molecules, ring vertices and ring path atoms, DENDRAL furnishes a systematic evaluation of radicals and (2) a convention for absolute configurattions by the allocation of the sct 7 ee ee of radicals to the even or odd group, resnectively. | At a trivalent ring vertex, the weights at the C are ordered by the canonical numbering of the VG edges defined by the orthomesh and further substituents (Paragraph 3.22-3.24) in the ring. | The chirality of the vertices of a ring is designated by a chirality status vector displayed in the VM list. This will be a string of 0 and 1 bits, Other characters may be used to designate “unspecified” and racemic conditions (statistical mixtures). "e(0)." can be economically replaced . by "C+", "C(1), "by "C-", For a path atom, a the afferent and of ferent paths in the ring count “7. S as heaviest bond; Further substituents are then weighed as in Paragraph 4 JV 3.41. . x. a a CIS-TRANS ISOMERISY DENDRAL notation verti the distinctions of CIS- and trans- configurations of adjacent vertices in rings, which appears in customary 243 notation. In molecules of sufficient SYTACtLy , | decalin we will find an ambiguity: CIS will correspond to the chirality status 5 vector (10) as well as (01); trans to (11) or (00), as we shall see: ' (Revision of 1 . 72) perl? chirality at Vl: V1(1,2,3,4) .... H El E2 E3 in canonical order. These... V2 will be V2 (1,2,4,3) .... H El E2 E3. We thus have V1(0), V2(1) or the status vector (01). The symmetry, however, also permits the molecule to be inverted, i.e., G which gives the vector (10). The former is however canonical. By a corresponding argument, trans-decalin is a (00) or (11), the former canonical. f Note that the automorphisms of vertex chirality are resolved, and the path numbering fixcd, before locants are established for path modifiers and appended radicals. _ CIS/TRANS Isomerisn at double bonds. The same approach of producing an absolute valence assignnents can be used to describe geometrical isomerism at C= C, The double bond is taken to occupy two andjacent positions of the first C atom encountered, postulated as hoe chirality status C(0). The second is then matched to the first. It will be C(O) or C(1) in an absolute, canonical description, and only one of these if the conditions for geometric isomerism are met. e.g. . . ee 4 cs | mt ~ cm | | : WY Cc 2 / “\ an b K Cu, Cis— 2-Butene 3 ¢ (1,2,3,4).. Hct, C (1.2,4,3).. KCK, . Ce or” 7 b edd | OL . C ¢ KS c(1), C He AD An Amo Aryanrnts deserts aig . a AXIAL AND EQUATORIAL i Hexagonal rings often adopt a chain-like configuration in which one of the H's at a path -CH,- may be found to lie either close to the 2 plane of the ring (equatorial), the other above or below it (axial). _ These labels are part of! a steric rather than topological description, but can sometimes be referred from the absolute configuration. : | - . , a2 "Revision of edgernumbering canons for twin edges. : (Revision of 2.34) According to 2.34, the edges of a vertex group are nusibered by circuiting the polygon (Hamilton circuit), than the chords as first encountered. Wence the numbering and polarity of these examples. 2 3 x8 2A-1,2 EACG-lavd-7, eXe,, Edges &2 and-3, and £2 are twin edges, i.e., correspond to a span of l. The elaboration of symmetries is simplified if twin edges are not treated as chords, but are brought together in the sequence. Hence wed New fra a ay an ey WS (fs \ > Na ers : € aw \ Sk NA, aA 6A The revision of edge order may influence the edge count list, canonical orientation of the orthomesh, and node-numbering in certain situations. For’ \ example > now becomes | in place of A x dt s/\y | Nr 3 hy MAR 12 1963 Table 3.1 CANONS OF DENDRAL ORDER (inodified from DENDRAL {1}) Hierarchy of Vector Valuation in Decreasing Order of Significance -The DENDRAL-VALUE of a radical is a vector comprising: R-COUNT Rings Other atoms (except IH) COMPOSITION OF RADICAL Rings , Composition ..CNOPSU* = . . Orthomesh . . Vertex Croup VG Edge Count List ECL . Vertex Modifiers VM; chirality status Path modifiers PM Other atoms by atomic number C,N,0,P 8 U (unsaturation is counted as a lowest-valued atom) : 1 +’ APICAL, NODE . ~ Degree: Number of efferent radicals ; ~ Composition of node:ring (by value), SS CV OPS Afferent link: (3, :, .) ) ' : : APPENDANT RADICALS ~ attached to apical node vector of radicals in order of ascending* value . ' Jocant list (ring) or chirality (atom) on apical node The sequence might be reversed Kx to conform to chemists" notation which tends to assign hisher-valued ‘substituents to lower-nunbered atons, and orders atoms by valence as well as atonic number. , . a eRe “y . Tr ee} ae _ 4h % i AMAR “ Ca. Cres Tos Ve LtA4 cof, mh -haAm mam BSN | CBCn? ~ _ SymreXvics ote rm me aan on: 25 Ie bed el eee ee eet ete ae ee erm ee ee ee ee wa New en MO Oe ~ ow ! 4 *. a oo] fe io% rar) af La oo gts — = 2 maao= Looe ves YAN fy JI een - TABLE 3.410 The alternating groups A, (even) and (odd) even. 5 permutation 1234 1342 1423 2143 3214 2431 3124 3412 3241 | 4132 4213 4321 Together, these constitute the symmetric group, Sy (0) cycles (1) (2) (3) (4) (1) (234) (1) (243) — (2) (34) (123) (4) - (124) (3) (132) (4) (13) (24) * (134) (2) ~ (142) (3) . 43) (2) (14) (23) | Example: 1234 & 2143 - odd permutation 1243 1324 1432 2134 2341 2413 3142 3421 3214 4123 4231. 4312 C(1) . cycles (1) (2) (34) (1) (23) (4) (1) (24) (3) (12) (3) (4) (1234) (1243) (1342) (1324) (13) (2) (4) (1432) (14) (2) (3) (1423) a if Ring-symmetrics in DENDRAL. The input problem is to "produce all isomers of one benzene ring." The verbose output displays the permutation group and other characteristics the isomers, Chirality is disregarded for this CISOMERS CQUOTE C1GH14)) (MARCH-8-1968 VERSION) C4#PHENSH 1 4 . . COMPOSITION (CU « 40) €O ¢« 669) VAL CRING *#PHEN te) SYMMETRIES (€C€2+e 3e 4e Se Ge Jed CB 4e Se Ge e 36) CSe Ge Le Be Be Ae) Che le Se Be Ae Sed C6 & Be Be te Bed C4e Be Be 1e Ge Se) (Be Be Te be eo 36) Cle Ge Se Ae Be 269) UNIQUE-NODES (1-9) MOLECULES NO DOUBLE BOND EQUIVS 1. CH2e5e C2HS CH2.C*PHEN* 16)HS > 2- CH2.. CeHs C#PHEN% Jo 20 VH40CHS 5 Be CHE-ee CHS C#PHEN* 1. Be DH4eCH3 > Ae CH2ee C2HS C#PHEN# be 4. )H4eCH3 5 Se C#PHON:: 1.6 BeIH4tee C2HS CeHS be C#PHEN fe 3e9H4ee CEHS CéHSs >» Be CHeee CH3 CH3 CH2-e C2 PHEN% 1-29H5S » 9 CHeoe CH3 CH3 Cs PHEN xs 1» 2eHA.CH3 16. CHees CH3 CH3 C4PHEN le 3e JHALCHS 11. CH. ee CH3 CH3 C#PHEN: 1e Ae SHA. CHS le. CHe oe CH3 C*=PHEN 2.2)H5S C2H5 >» 13. C#PHEN*% J.6 26 3-6)H3-.e- CHB CH3 C2HS 14. C#PHEN% 126 Be 4c HSeee CHB CH3 CeHs 15. CSPHEN* Le Be 2eHBeee CHB CH3 C2H5 166 C2#PHEN® Le 3¢ 4¢)H3e06e CHE CH3 CeHs 17. C#PHEN* [fe 3 SedHSeee CHB CH3 C2HS 15.6 C*PHEN le 4e Be IHBoee CH3 CH3 C2H5 19. Coees CH3 CH3 -CH3 (PHEN* 1.9HS > 20-6 C&PHENS Jo Be Be AeHQeeee CHB CH3 21. C=PHEN = 1. Qe Be Se Heer CH3 CHS 226 C%#PHEN Je 2e 4e SeH2eeee CHB CH3 DONE sf CMMNIN14 containing at least the pregran's listing of of the ring, before listing exanple (e.g. at #12). ENCE Cle le le Le Le le Bed C4e Se Be Te 2 © Se de Be Qe 16) C56 Se 42) (2c fe Ge Se A u-, Lt” Lie" ie » oO a te a oie in s s i“ ? , é re CH3 CH3 » CH3 CH3 » +- CH3 CH3 » CL VG =GACA) The canonical numbering details then become: 10 wid . _ aul, % ECL= “( v3-42, 3 : . . (0, 3,0,2,0,4,0,2,0) IN 4 6 S VM: No heteroatom substitutions; the chirality vector is given by: vl....H1 82 (1) v4..=456 (3). v2....H12 3 (0) v5....H 567 (0) (100300) v3...eH 349 (0) v6....H 789 (0) (3) at v4 refers to the abrogation of chirality at a double-bonded vertex. PLM: No heteroatoms, but a double bond a’ (v4,5). The complete ring is then (xl = nor- (?-androstene) (x1 ( 6ACA (0,3,0,2,0,4,0,2,0)) (100300) (U ( (w4,5)) ) ------ orthomesh------------ --VM---- -----PLM------ VG ECL In the whole molecule, the canonical center is att and we have: cys | ° .C3H6.CH..CH3 CH3 CH..CH3 xl(1,vl,v5,7)...CH3 CH3 OH K 26 ack c Ve eed © & 7 @ 4 ro — C | | / SONS OH ( ce’ Nec ava C7 We have still to consider the chirality at x1(1) and x1(7)f These prove to be of Lg . , (2. Bf (es apare & giving the completed formula: ‘ ' . , . oi eLScH, .C3H6.CH..CH3 CH3 \y ; “effi ned: fecs) 0x) CH+.CH3 x1(1+,vl,v5,7-)...CH3 CH3 OH «tC4) iC) ; c7 = Q-- eyvenet even ~ + L(t) hla) cag ere k ; neo sc) 2(8) . He CH3< (yt) ete, < apcord 4\ ? rhe vl Ni [hus vG G SS s/™ ae |e vé { lo hv . > ‘ \o ee es WS VG ME ‘2 C18, ce eee pels OY 0 Of OX A [OKO VA = [SeRKZ Pre (UA U2 18,4, 4) a ~~" -c a ~ aw | C a | 1 : . : . S J / vi LN. | un Xe NN a f , ~C BQ | - XA EHS oes 2tS Cris cs . O \ (1), Cc \ - {Pir \> ~ Corrertions (see 3.246 - 3ee2el The vector for ECL of becomes (0,4,1,9,4,1) (5,9,9,4,3) 3.240 renumber to 3.3 The paragraph immediately preceding this should be numbered 3.2456 new ECL | (0,4.0,0,4.2) VN: (W,4) orn, (6u3 (19, %1,1,3)) or, aS an wAamAohe. (C448) (84 o0m2) (4) (3 (109) ) : new numbering Fi 3. uf Kh Mowad Be 7 yea v3 , corresponding change in - ye 8 permutation table. So : 3 (\ ‘\) ——amcoe & vt G&G wi Dobos Oni POs tpl , ¢/ 2 7,9 4 444) / : . pre STS peck OrrrTt i / poy i . % 8 f Y | f FL _ ORTOQOMLEAL SG. AY AALS $ VG- FEC. bee NS : . . , Vy © JG ake, CY, eS . | R, | 0,2,4 | ay 8 a | A me oun A eA a AS ‘i a Zh Ah? ya 3 oe | s” . rn as 2 A : 2 t 2. t “pn - i . / Ne ee ee eee ernns . C . women | We /™ o ef C ’ RA pots ey, _ = . ‘ 4 . : ve ’ f eta, DA l, r, 4 Bry G0 ™\ . a hae . LL yp?