An Intelligent Sketch Pad as Input to Molecular Structure Programs

14 An Intelligent Sketch Pad as Input to Molecular Structure Programs Carl Trindle Artificial Intelligence Applications in Chemistry Downloaded from pubs.acs.org by UNIV LAVAL on 09/23/15. For personal use only.

Chemistry Department, University of Virginia, Charlottesville, VA 22901

The programming and manipulation of chemical graphs i s awkward i n most f a m i l i a r programming languages. LISP, the Esperanto of artificial i n t e l l i g e n c e research, makes possible a representation of chemical s t r u c t u r a l formulas which i s much more nearly analogous to the chemist's view of such graphs. This i s a considerable computational advantage as well as a convenience for the user. We have designed a "functional fragment" representation of s t r u c t u r a l formulas, applicable to any molecule, which will resolve a crude sketch of a chemical structure into a list of fundamental fragments. Exploiting the PROPERTY feature of LISP and the distance geometry algorithms of Crippen we can recover Cartesian coordinates f o r each atom, suitable for input to molecular mechanics programs, or to ab i n i t i o electronic structure packages. Besides l o c a l geometries, the i n t e l l i g e n t sketchpad can contain any l o c a l properties, including bond types and strengths, chromophore o p t i c a l spectra, and nuclear magnetic resonance and infrared spectra c h a r a c t e r i s t i c of a l o c a l chemical environment.

Computational chemists have developed several remarkably powerful and r e l i a b l e computer codes, capable of describing the r e l a t i v e s t a b i l i t y of various conformations of macromolecules, and d e t a i l s of the e l e c t r o n i c structure of molecules of more modest s i z e (1). The properties of molecules which can be obtained by use of these programs c o r r e l a t e with important features of chemical r e a c t i v i t y and the properties of m a t e r i a l s . Molecular design, i n pharmac e u t i c a l s , photochemistry, and general materials science can be made much more e f f i c i e n t by the routine use of these computational systems. However, t h e i r use i s at present not widespread; i t i s l i m i t e d to a few large chemical companies. 0097-6156/86/0306-0159$06.00/0 © 1986 American Chemical Society

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One of the obstacles to wider use of the well-tested and powerf u l programs such as A l l i n g e r ' s molecular mechanics (2) and Pople's GAUSS80 (3) i s that the programs require such elaborate and awkward input. Users must o r d i n a r i l y prepare a l i s t of Cartesian coordinates of each atom. This i s cumbersome f o r molecules of even moderate s i z e . But more s i g n i f i c a n t l y , chemists powerful sense of three-dimensional molecular structure i s never expressed i n Cartesian coordinates. Instead chemists think more n a t u r a l l y of " i n t e r n a l coordinates," that i s bond lengths, primary valence angles, and l o c a l dihedral angles. Of course a f u l l set of i n t e r n a l coordinates defines i n p r i n c i p l e the set of Cartesian coordinates (4). Unfortunately, the usual algorithms f o r generating Cartesian coordinates from i n t e r n a l coordinates are s e n s i t i v e to small e r r o r s . These errors accumulate and can perpetrate enormities such as leaving rings unclosed, or forcing u n r e a l i s t i c a l l y short separations between nonbonded atoms. In the chemist's conceptual p i c t u r e , r e a l i s t i c bond distances f o r rings are maintained, even i f d i s t o r tions i n normal valence angles are required. The problem i s to transform the p i c t o r i a l view of molecules which i s the d a i l y companion of the chemist, to the numerical form required by programs, WITHOUT FORCING THE USER TO EFFECT THE TRANSLATION. We must not ask the chemist to do much more than i d e n t i f y the atoms, t h e i r c o n n e c t i v i t y , and some gross features of the stereochemistry. The s t r u c t u r a l formula i s the medium by which such simple yet r i c h l y evocative information i s conveyed. The s t r u c t u r a l formula does a f t e r a l l s u f f i c e f o r the chemist's work day to day. It should be adequate to convey the e s s e n t i a l information to useful computer programs. There w i l l be two major stages to the t r a n s l a t i o n of information from the chemist's p i c t o r i a l image to the r i g i d l y formatted input f i l e required by molecular mechanics or molecular o r b i t a l programs. F i r s t the sketch i s impressed on a d i g i t i z i n g tablet (perhaps as simple as a Koala Pad (R), or a more accurate d i g i t i z i n g t a b l e t ) . Then the graph must be interpreted and a t r i a l geometry generated.

Artificial Intelligence Applications in Chemistry Downloaded from pubs.acs.org by UNIV LAVAL on 09/23/15. For personal use only.

1

Accepting the Sketch. The (computationally) most convenient way to enter a s t r u c t u r a l diagram i s to use a d i g i t i z i n g tablet with a mouse or s t y l u s . Our experience has been with the Houston Instruments HIPAD (R). The software accompanying t h i s (and most ordinary) d i g i t i z i n g tablet accepts and stores l o c a l coordinates of p a r t i c u l a r points, and a set of pointers designating which v e r t i c e s are to be connected (5). In t h i s way the molecular topology can be s p e c i f i e d with no novel analysis or programming. I t would be more i n t e r e s t i n g from the point of view of A r t i f i c i a l I n t e l l i g e n c e research to i n t e r p r e t a sketch already on paper, by the analysis of dark and l i g h t elements (6). We have made only small progress i n t h i s task, but some preliminary remarks can make the d i f f i c u l t i e s c l e a r . The f i e l d of view i s resolved into p i c t u r e elements, and an o p t i c a l scanner would assign a numerical value corresponding to the darkness of the sketch at that l o c a t i o n . Heavy l i n e s would be easy to recognize, by the sequence of adjacent dark spots detected by the scanner. Intersections might be harder to recognize i f the g r i d i s coarse, but knowledge of the existence of l i n e s could guide the search, by estimates of the i n t e r s e c t i o n s by extrapolation. A planar graph (with no crossing l i n e s ) would

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seem t o p r e s e n t few d i f f i c u l t i e s . Vertices representing generalized atoms ( t h a t i s , "Me" i n p l a c e o f a f u l l y d e t a i l e d m e t h y l group) would have t o be more c a r e f u l l y s p e c i f i e d . The chemist would use B e r z e l i u s - n o t a t i o n c a p i t a l l e t t e r s f o r l a b e l s , w h i c h would have t o be i n t e r p r e t e d . T h i s i s a h a r d t a s k , as the p o s t o f f i c e has l e a r n e d . I t would be e s s e n t i a l f o r the system t o r e a l i z e when i d e n t i f i c a t i o n o f a v e r t e x i s i m p o s s i b l e o r ambiguous, and r e q u e s t guidance from the u s e r . F i g u r e 1 shows how v e r t i c e s a r e s p e c i f i e d . I t w i l l be n e c e s s a r y t o d i s t i n g u i s h the s t r o k e s which i d e n t i f y s i n g l e o r m u l t i p l e bonds from the s t r o k e s d e n o t i n g l o n e p a i r s , and i t w i l l be r e q u i r e d t o s u p p l y m i s s i n g hydrogens and l o n e p a i r s w h i c h a r e o f t e n o m i t t e d from c a s u a l s k e t c h e s . T h i s l a t t e r problem w i l l a l s o be e n c o u n t e r e d i f the s k e t c h i s i n p u t d i r e c t l y by the digitizing tablet. We r e t u r n t o t h a t l i n e of a p p r o a c h . P r e l i m i n a r y P r o c e s s i n g of the Sketch. Even a t t h i s e a r l y s t a g e , b e f o r e d i f f e r e n t atoms a r e d i s t i n g u i s h e d and hydrogens a r e f u l l y e x p r e s s e d , we have much o f the i n f o r m a t i o n needed f o r some k i n d s o f analysis. A l l o f the g r a p h - t h e o r e t i c a n a l y s i s o f p i systems (7), w h i c h may be c o n s i d e r e d t o be based on the H u c k e l model, uses no more than the c o n n e c t i v i t y between e q u i v a l e n t c e n t e r s . However p o w e r f u l the graph t h e o r y has been, i t cannot be d e n i e d t h a t i t s u p p r e s s e s much o f the d e t a i l e x p r e s s e d i n the s t r u c t u r a l d i a g r a m . T h e r e f o r e we w i l l n o t be c o n t e n t to s t o p a t t h i s s t a g e . I t w i l l be n e c e s s a r y a t minimum t o d e f i n e the t y p e o f atom p r e s e n t a t each v e r t e x . We r e d u c e the l a b o r n e c e s s a r y f o r t h i s s p e c i f i c a t i o n by (a) s u p p r e s s i n g hydrogens i n the p r e l i m i n a r y s k e t c h ; and (b) assuming as a d e f a u l t t h a t each v e r t e x r e p r e s e n t s a carbon atom, r e q u i r i n g an amendment o n l y f o r heavy atoms. Our software i s r e s p o n s i b l e f o r f i l l i n g i n hydrogens. This process i s f r e q u e n t l y ambiguous, g i v e n o n l y the s k e l e t o n o f heavy atoms. T h e r e f o r e the computer system w i l l sometimes i n t e r r o g a t e the u s e r f o r the number o f hydrogen atoms a t each v e r t e x . With t h i s i n f o r m a t i o n the t a s k o f c o m p l e t i n g a Lewis s t r u c t u r e i s l e f t t o the s o f t w a r e , w h i c h i s a t l e a s t as c a p a b l e o f t h i s t a s k as the a v e r a g e f i r s t - y e a r student. T h i s i s the f i r s t t a s k t h a t r e q u i r e s a n y t h i n g r e s e m b l i n g A r t i f i c i a l I n t e l l i g e n c e , so a few remarks on the d e s i g n may n o t be out o f p l a c e . A R o u t i n e t o A s s i g n Lewis S t r u c t u r e s . The p r o c e d u r e f o r a s s i g n i n g Lewis s t r u c t u r e s i s f a m i l i a r ( 8 ) . G i v e n t h e s e t o f atoms, one must sum the v a l e n c e e l e c t r o n s . In our LISP system, each ATOM can be a s s i g n e d PROPERTIES w h i c h may i n c l u d e the number o f v a l e n c e e l e c t r o n s i t c o n t r i b u t e s t o the m o l e c u l e , and e q u a l l y i m p o r t a n t , i t s s e t o f NEIGHBORS by w h i c h the s k e l e t o n o f the m o l e c u l e i s s p e c i f i e d . Each such l i n k i s a s s i g n e d a p a i r o f v a l e n c e e l e c t r o n s , and a census i s k e p t o f e l e c t r o n p a i r s i n the v i c i n i t y o f each atom. Among the PROPERTIES of each atom i s an e s t i m a t e o f i t s e l e c t r o n e g a t i v i t y , and the program a s s i g n s e l e c t r o n p a i r s t o f i l l o c t e t s u s i n g the e l e c t r o n e g a t i v i t y to s e t p r i o r i t y . The l a s t s t e p i s most " d i f f i cult." F o r each o f t h o s e atoms w h i c h l a c k a f u l l o c t e t , the system must l o o k among the NEIGHBORS f o r atom(s) p o s s e s s i n g a l o n e p a i r w h i c h i t might s h a r e . Of a l l those p o t e n t i a l d o n o r s , one chooses the atom w i t h the most n e g a t i v e f o r m a l charge. The m u l t i p l e bond

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of

A D i a l o g u e Accompanying t h e E n t r y a Molecule o f Moderate Complexity

SPECIFY

NON-CARBON

NUMBER : NUMBER: NUMBER: NUMBER: NUMBER:

1 8 10 12 0

SPECIFY

NET CHARGE: *1

HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS HYDROGENS

VERTICES: TYPE: TYPE: TYPE: TYPE:

AT AT AT AT AT AT AT AT AT AT AT

VERTEX VERTEX VERTEX VERTEX VERTEX VERTEX VERTEX VERTEX VERTEX VERTEX VERTEX

nitrogen oxygen oxygen oxygen

8 9 11 : 12 13

F i g u r e 1. A l l v e r t i c e s a r e f i r s t assumed t o be CARBON. The system r e q u e s t s t h a t t h e u s e r s p e c i f y non-CARBON v e r t i c e s ; i t w i l l b u i l d a set of u s e r ' s abbreviations.

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i s represented by the appearance of the donor several times i n the (revised) NEIGHBOR l i s t . When the Lewis structure routine finds an ambiguity which we would represent by a set of resonance structures, i t reports that f a c t and chooses the f i r s t l e g a l structure f o r further processing. Figure 2 shows the procedure i n p r a c t i c e . Representation of the Molecule i n LISP. We have used the chemist's sketch, or i t s Lewis structure equivalent, as the model of a data structure i n LISP (9). This language has the f l e x i b i l i t y needed to express an e s s e n t i a l l y non-numerical object, i n terms of l i s t s . LISP w i l l permit us to organize molecular structure information i n a way that mimics the human expert's knowledge. To accomplish t h i s representation, we must develop a clear idea how the chemist assimilates the information provided d i r e c t l y and e x p l i c i t l y by the sketch, and how the properties of the molecule are r e c a l l e d to the chemist's awareness. The s t r u c t u r a l formula at minimum i d e n t i f i e s the atoms and t h e i r connectivity. This hardly seems to be adequate i n complexity to express much molecular information. This apparent paradox i s resolved when we recognize that the chemist brings much of h i s experience to the task of i n t e r p r e t i n g the sketch, and much of the information i s evoked rather than transmitted by means of the s t r u c t u r a l formula. The atoms' names—carbon, n i t r o g e n — c a l l up a f l o o d of associations which (although they are almost never w r i t t e n exp l i c i t l y i n the chemist's sketch) are nonetheless part of the information i t can summon. Among t h i s data are the atomic mass, t y p i c a l valencies, l o c a l geometry, perhaps a van der Waals radius, and a guide to chemical behavior, i t s " e l e c t r o n e g a t i v i t y . " The connectivity can define some aspects of the geometry i n a useful semiquantitative way. The chemist has a very r e l i a b l e idea of the range of bond lengths; CC(single), 1.54 A; CC(double), 1.33 A, etc. By counting connections and recognizing the atoms being connected, one can assign good estimates of the distances between d i r e c t l y bonded atoms. The chemist's knowledge of molecular geometry extends beyond t y p i c a l values of bond distances. He w i l l also be able to predict many bond angles f a i r l y accurately. This i s equivalent to specifying a 1-3 nonbonded interatomic distance. The chemist's sketch portrays c i s and trans isomerization, syn and a n t i , and gauche conformations which specify either t o r s i o n angles, or i n d i r e c t l y , a 1-4 nonbonded distance. Besides primary bond distances and angles, and some s p e c i a l cases of t o r s i o n a l and dihedral angles, the chemist knows more global features of molecular geometry. However, such knowledge becomes more and more fragmentary; the longest distances i n a molecule are most poorly defined. A LISP S t r u c t u r a l Recognizer. A molecule i s represented i n our LISP program f i r s t as a l i s t of atoms. A numbering scheme assigns an unique l a b e l to each atom. Each atom has a c o l l e c t i o n of PROPERTIES; foremost among them i s i t s generic NAME. The name CARBON c a r r i e s with i t a van der Waals RADIUS and a VALENCE. Other properties can be added as desired. The major feature of a molecular sketch i s the topology or


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connectivity of the molecule. This i s expressed as the property NEIGHBOR f o r each atom. This i s j u s t the set of labels of other atoms connected to a p a r t i c u l a r atom. The NEIGHBOR property i s a compact way to store the adjacency matrix used i n graph theory. The chemist's sketch, processed into the l i s t representation j u s t described, i s not yet very valuable; the system at the moment i s very ignorant of the structure of the molecule i n question. But the chemist knows much of the molecule from l i t t l e more than the diagram. How does the chemist "see" a complex molecular diagram? In our judgement a chemist knows so much about a molecule because he recognizes recurrent fragments of moderate s i z e . Rings of varying atomic composition, structure, and s i z e ranging from carbonyl groups to s t e r o i d systems, are recognized at a glance. Many stereochemic a l l y well-defined fragments, such as spiro and norbornyl systems, are part of the chemist's conceptual t o o l k i t . Our programming task i s to assure that our system recognizes such fragments, with a l l the associated information on t h e i r structure and properties, with ease. Somehow we must discern the presence of meaningful, f a m i l i a r fragments i n the molecular l i s t . We mimic t h i s stock of informative portions of molecules i n our LISP system by l i s t s c a l l e d FRAGMENTS. The FRAGMENTS, permanent members of a growing data base, each cont a i n a set of ATOMS and a NEIGHBOR l i s t f o r each atom i d e n t i f y i n g the connectivity. Besides t h i s topological information, the fragments contain as PROPERTIES a stock of a t t r i b u t e s of the fragments. The f i r s t c o l l e c t i o n of PROPERTIES we gathered were interatomic d i s tances gleaned from c r y s t a l structures. A l l interatomic distances are defined w i t h i n a fragment. The system can now assign many (though not a l l ) interatomic distances i n an a r b i t r a r y molecule i f fragments could be discerned w i t h i n the sketch. We have developed a search technique which w i l l scan the MOLECULE and locate a l l fragments. Design of t h i s recognition algorithm i s d i f f i c u l t . The search routine shares some of the features of the "knapsack problem," a c l a s s i c d i f f i c u l t y i n computer science. We expect that we w i l l be able to speed t h i s step considerably. At present we scan a l l stored fragments, though that i s not the way an expert would proceed. We screen out many fragments by a s u p e r f i c i a l test that the atoms i n the fragment must be a subset of the atoms i n the molecule. The fragments are subjected to more and more thorough t e s t s , u n t i l recognition i s complete. These tests are e s s e n t i a l l y recursive applications of the requirement that i f a fragment i s to be i d e n t i f i e d i n a molecule, the environment of each atom i n the fragment must be found i n the molecule f o r the corresponding atom. More d e t a i l on the search condition may be found i n a previous a r t i c l e (10). Figure 3 shows a t y p i c a l fragment representation. In t h i s f i r s t formulation we have already established that i t i s most e f f e c t i v e to scan the largest candidate fragments f i r s t . I t i s desirable to recognize overlapping fragments; more distances are determined. However, i t i s i n e v i t a b l y the case that a substantial number of distances w i l l be l e f t undefined, p a r t i c u l a r l y the longest distances which would not be incorporated into a fragment. Distance Geometry Changes Distances to Cartesian Coordinates. Most esperimental measures of molecular geometry provide quantities which may be most d i r e c t l y interpreted as defining interatomic distances.

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An Intelligent Sketch Padfor Molecular Structure Programs

Assignment, FORMULA:

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An Intelligent Sketch Pad as Input to Molecular Structure Programs

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