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(1) The semiempirical linear free energy related (LFER) or .... sults from the pattern recognition analysis to make an educated guess as to their effe...
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9 A Computer System for Structure-Activity Studies Using Chemical Structure Information Handling and Pattern Recognition Techniques

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A. J. STUPER, W. E. BRUGGER, and P. C. JURS Department of Chemistry, The Pennsylvania State University, University Park, PA 16802

The study of relationships between chemical structures and their biological activity is currently receiving a great deal of attention. The term biological activity covers a range from pharmaceuticals and drugs to agricultural chemicals such as pest­ icides and herbicides to toxic reactions such as those of poisions, carcinogens, teratogens, and mutagens. A variety of methods have been exploited for structure-activity studies: (1) The semiempirical linear free energy related (LFER) or extrathermodynamic model developed by Hansch and co-workers. The LFER method is applied to homologous series of compounds that are related in that they are formed by placing substituents on a par­ ent compound. The method depends on defining quantitative corr­ elations between physicochemical parameters of a compound and the biological response observed. An equation of the form 2

log (1/C = aπ + bπ + ρσ + cE + d s

is fit to the set of data using linear regression. The variables are as follows: C is the concentration of the compound necessary to produce a standard biological response; π is the difference between the logarithm of the 1-octanol/water partition coefficient of the parent compound and the substituted compound; σ is the Hammett substituent constant that provides a measure of the elec­ tronic effect on the reaction rate; and E is a steric factor which compares sizes of substituents to that of methyl taken as a standard. (2) The de novo or additivity model proposed by Free and Wilson. In this approach the contributions to the parameter de­ fining biological response by each substituent group is assumed to be additive. The equation is s

Ai = y + Zj a

j # p

where μ is the overall average activity (the contribution of the constant part of the molecule, the parent structure), aj^ is the p

165 In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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c o n t r i b u t i o n t o the a c t i v i t y from the j t h s u b s t i t u e n t i n the p t h p o s i t i o n i n the parent s t r u c t u r e , and A i i s the standard b i o l o g i c a l response f o r drug compound i . Regression a n a l y s i s i s used t o obtain numerical values f o r the s u b s t i t u e n t c o n t r i b u t i o n s . (3) Quantum mechanical methods. These methods have been used t o c a l c u l a t e parameters t o be c o r r e l a t e d with a c t i v i t y and f o r the determination o f p r e f e r r e d conformations o f b i o l o g i c a l l y a c t i v e molecules. The purpose o f the present p r o j e c t was t o apply the ADAPT computer system t o s p e c i f i c s t r u c t u r e - a c t i v i t y problems. The ADAPT computer system combines techniques o f chemical s t r u c t u r e information handling and p a t t e r n r e c o g n i t i o n f o r the study o f chemical s t r u c t u r e - b i o l o g i c a l a c t i v i t y r e l a t i o n s . T h i s system can be used t o enter and s t o r e a s e t o f d i v e r s e chemical s t r u c t u r e s , generate s t r u c t u r a l d e s c r i p t o r s , and analyze them using p a t t e r n r e c o g n i t i o n methods. These three steps are i l l u s t r a t e d i n Figure 1. Several premises a r e i n v o l v e d i n t h i s approach t o the study of structure-activity relations: - S t r u c t u r e and b i o l o g i c a l a c t i v i t y are r e l a t e d . - S t r u c t u r e s o f compounds can be adequately represented as a set o f molecular d e s c r i p t o r s . -A r e l a t i o n can be discovered between the s t r u c t u r e and a c t i v i t y by a p p l y i n g p a t t e r n r e c o g n i t i o n methods t o a s e t o f t e s t e d compounds. -The r e l a t i o n can be e x t r a p o l a t e d t o untested compounds. Introduction to Pattern

Recognition

Chemical and b i o l o g i c a l data are being produced a t a p r o d i g ious r a t e . T h i s had l e d t o burgeoning i n t e r e s t i n computer a s s i s t ed methods f o r the accumulation, handling, and i n t e r p r e t a t i o n o f these data. Standard approaches t o the i n t e r p r e t a t i o n problem i n clude s t a t i s t i c a l i n t e r p r e t a t i o n , curve f i t t i n g and model f i t t i n g . The development o r v e r i f i c a t i o n o f mathematical expressions r e l a t ing independent v a r i a b l e s and observable dependent v a r i a b l e s i s the goal o f such s t u d i e s . The i n t e n t i s t o c r e a t e a model whose parameters represent q u a n t i t i e s with p h y s i c a l s i g n i f i c a n c e . Then best values f o r the parameters are developed from the data by model fitting. In the absence o f a mathematical model, curve f i t t i n g using general f u n c t i o n s , e_.£., polynomials, can be employed. Not a l l problems faced by the chemist, however, l e n d themselves t o such exacting s o l u t i o n : f r e q u e n t l y , equations d e s c r i b i n g processes o f i n t e r e s t are d i f f i c u l t o r impossible t o o b t a i n , and a host o f problems have not y i e l d e d t o a s a t i s f a c t o r y o r usable t h e o r e t i c a l exp l a n a t i o n . In the absence o f t h e o r e t i c a l l y - b a s e d s o l u t i o n s , empi r i c a l l y - d e r i v e d methods w i l l o f t e n s u f f i c e t o y i e l d u s e f u l and p r a c t i c a l s o l u t i o n s t o complex problems. Standard approaches t o the e x t r a c t i o n o f information from complex data forms have i n c l u d e d l i n e a r o p t i m i z a t i o n , information

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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Connection Tables

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DESCRIPTOR GENERATION

Data Matrix

PATTERN RECOGNITION ANALYSIS

Figure 1. Steps in experimental procedure

theory, and a p l e t h o r a o f s t a t i s t i c a l a n a l y s i s techniques. Since the e a r l y 1950's p a t t e r n r e c o g n i t i o n methods have a l s o been a p p l i ed to a v a r i e t y o f data i n t e r p r e t a t i o n problems and have p a r a l l e l ed the computer's growth i n speed and s o p h i s t i c a t i o n with a c o r r esponding expansion i n scope and c a p a c i t y . Pattern recognition techniques have found a p p l i c a t i o n i n such v a r i e d f i e l d s as compute r and information science, engineering, s t a t i s t i c s , b i o l o g y , p h y s i c s , medicine, and physiology. Each o f these d i s c i p l i n e s has adapted the b a s i c methods of p a t t e r n r e c o g n i t i o n to i t s own s p e c i f i c requirements. Pattern recogniton comprises the d e t e c t i o n , p e r c e p t i o n , and r e c o g n i t i o n o f i n v a r i a n t p r o p e r t i e s among sets o f measurements o f o b j e c t s or events. The purpose of p a t t e r n r e c o g n i t i o n i s generall y to c a t e g o r i z e a sample o f observed data as a member o f the c l a s s t o which i t belongs. T h i s general approach has been a p p l i e d to problems from a number o f d i v e r s e f i e l d s . Several e x c e l l e n t r e views o f the p a t t e r n r e c o g n i t i o n l i t e r a t u r e have appeared which dramatize the enormous breadth o f p a t t e r n r e c o g n i t i o n a p p l i c a t i o n s (1-5). There i s a growing l i t e r a t u r e addressed to the a p p l i c a t i o n s o f p a t t e r n r e c o g n i t i o n t o chemical data i n t e r p r e t a t i o n . Pattern r e c o g n i t i o n methods are uniquely s u i t e d to a v a r i e t y o f s t u d i e s because of s e v e r a l novel a t t r i b u t e s . No mathematical model i s used, but r a t h e r r e l a t i o n s h i p s are sought which provide d e f i n i t i o n s o f s i m i l a r i t y between d i v e r s e groups o f data. Pattern r e c o g n i t i o n techniques are able to d e a l with high dimensional data (data f o r which more than three measurements are used to represent each o b j e c t ) . Such high dimensional data can not be d i r e c t l y v i s u a l i z e d or d i s p l a y e d . In a d d i t i o n p a t t e r n r e c o g n i t i o n t e c h n i ques can d e a l with multisource data or data i n which the r e l a t i o n ships are discontinuous. In multisource data each measurement can

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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be the r e s u l t o f an independent generating algorithm or experiment, and each can have a d i f f e r e n t s c a l e , o r i g i n , d i s t r i b u t i o n , e t c . from a l l the other measurements. Therefore, there w i l l be no d i r e c t f u n c t i o n a l r e l a t i o n s h i p between the measurements i n multisource data as there must be, f o r example, i n an absorbance vs. concentrat i o n p l o t . In a p p l i c a t i o n s o f p a t t e r n r e c o g n i t i o n to s t r u c t u r e a c t i v i t y r e l a t i o n s , the data i s always multisource data. For problems p r o v i d i n g multisource data, i t i s d i f f i c u l t to know i n advance whether an appropriate s e t of measurements has been generated to e f f e c t a s a t i s f a c t o r y s o l u t i o n . The generation o f s u f f i c i e n t l y i n formative multisource measurements can become i n i t s e l f a major p a r t o f the o v e r a l l p a t t e r n r e c o g n i t i o n experiment. When a number o f measurements are a v a i l a b l e , p a t t e r n r e c o g n i t i o n can be used to judge t h e i r r e l a t i v e q u a l i t y o r u t i l i t y with regard to s p e c i f i c questions. I t i s t h i s a b i l i t y to d e f i n e r e l a t i o n s through use of a d i v e r s e s e t o f measurements which a f f o r d s p a t t e r n r e c o g n i t i o n t e c h niques t h e i r u t i l i t y i n such a wide v a r i e t y o f f i e l d s . When p r o p e r l y used, p a t t e r n r e c o g n i t i o n techniques a l l o w the chemist to develop c r i t e r i a which r e l a t e the presence o f p r o p e r t i e s to a p a r t i c u l a r sub-set o f the t o t a l number o f measurements. Once the important measurements are i d e n t i f i e d , they can be used to guide the development o f subsequent experiments. For example, i f a chemist were to f i n d t h a t ten s t r u c t u r a l parameters were important i n d i c a t o r s o f a p a r t i c u l a r b i o l o g i c a l e f f e c t , then he might hypothesize s e v e r a l as y e t unstudied s t r u c t u r e s , and use the r e s u l t s from the p a t t e r n r e c o g n i t i o n a n a l y s i s to make an educated guess as to t h e i r e f f e c t s . A l t e r n a t i v e l y , the f a c t t h a t the p a r t i c u l a r ten parameters were shown t o be important may l e a d to added i n s i g h t s i n t o the problem. T h i s a b i l i t y to p i c k a subset o f the o r i g i n a l measurements which contains the bulk o f the t o t a l i n f o r mation content i s extremely d e s i r a b l e . As r e l a t i o n s between seve r a l v a r i a b l e s are not e a s i l y deduced through o b s e r v a t i o n , t h i s i s an extremely u s e f u l c a p a b i l i t y of p a t t e r n r e c o g n i t i o n . B a s i c P a t t e r n Recognition System. A general p a t t e r n r e c o g n i t i o n system f o r s t r u c t u r e - a c t i v i t y s t u d i e s must be capable o f acce p t i n g numerical d e s c r i p t o r s from the d e s c r i p t o r development rout i n e s performing p r i o r f e a t u r e s e l e c t i o n p r e p r o c e s s i n g the data, and c l a s s i f y i n g the compound. A schematic r e p r e s e n t a t i o n o f t h i s b a s i c system i s shown i n F i g u r e 2. I t c o n s i s t s o f four i n t e r r e l a t e d subunits: p r i o r f e a t u r e s e l e c t i o n , p r e p r o c e s s i n g , c l a s s i f i c a t i o n , and feedback feature s e l e c t i o n . The p r i o r f e a t u r e s e l e c t i o n r o u t i n e accepts the data to be c l a s s i f i e d and transforms them to make the c l a s s i f i c a t i o n task e a s i e r . Then, the preprocessor attempts to pursue the f o l l o w i n g two goals simultaneously: (a) to reduce o r e l i m i n a t e the f r a c t i o n o f information contained i n the raw data t h a t i s i r r e l e v a n t or even confusing; and (b) to preserve s u f f i c i e n t information to allow d i s c r i m i n a t i o n among the p a t t e r n c l a s s e s . The c l a s s i f i e r operates on the transformed p a t t e r n vect o r to produce a c l a s s i f i c a t i o n d e c i s i o n . The feedback loop i n -

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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Studies

d i c a t e s t h a t the p a t t e r n r e c o g n i t i o n system may use the r e s u l t s o f i t s c l a s s i f i c a t i o n t o develop a s u p e r i o r f e a t u r e e x t r a c t i o n app­ roach. The e n t i r e p a t t e r n r e c o g n i t i o n system i s g e n e r a l l y imple­ mented w i t h computer software.

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Classifiers. Methods o f c l a s s i f i c a t i o n f a l l n a t u r a l l y i n t o two c a t e g o r i e s : parametric and nonparametric methods. Parametric t r a i n i n g methods c o n s i s t o f e s t i m a t i n g the s t a t i s t i c a l parameters o f the samples forming t h e t r a i n i n g s e t and then u s i n g these s t a t ­ i s t i c a l parameters f o r the s p e c i f i c a t i o n o f the d i s c r i m i n a n t f u n c t i o n . Nonparametric d i s c r i m i n a n t f u n c t i o n s a r e developed d i r e c t l y from a sample o f data themselves. Learning Machines. Data t o be used i n p a t t e r n r e c o g n i t i o n s t u d i e s are represented as v e c t o r s , X = (x^, x # ···/ n ) ' where XJ represents one o b s e r v a t i o n . S t r u c t u r e s o f molecules can be coded i n t h i s format u s i n g numerical d e s c r i p t o r s f o r the Xj e n t r i ­ es. F o r example, e n t r i e s c o u l d i n c l u d e the molecular weight, num­ bers o f oxygen atoms, length, volume, l i p o p h i l i c i t y , d i p o l e moment, number o f times a p a r t i c u l a r substructure i s imbedded i n the s t r u c t u r e , e t c . F o r computational convenience an e x t r a d e s c r i p ­ t o r , whose value i s s e t equal t o a constant, i s added t o each pattern vector. Data represented as v e c t o r s can be thought o f e i t h e r as p o i n t s i n an η-dimensional E u c l i d e a n space o r as v e c t o r s p o i n t i n g from the o r i g i n t o those p o i n t s , hence p a t t e r n v e c t o r s . Thus, a set o f data such as a c o l l e c t i o n o f mass s p e c t r a o r a s e t o f s u i t ­ ably encoded chemical s t r u c t u r e s can be represented as a s e t o f η-dimensional p a t t e r n v e c t o r s . Experience shows t h a t p o i n t s r e ­ p r e s e n t i n g p a t t e r n s with common c h a r a c t e r i s t i c s c l u s t e r i n l i m i t ­ ed regions o f the p a t t e r n space. F o r example, a s e t o f p o i n t s r e ­ p r e s e n t i n g the molecular s t r u c t u r e s o f compounds a c t i v e as t r a n ­ q u i l i z e r s may c l u s t e r i n a d i f f e r e n t r e g i o n . There i s an important r e l a t i o n s h i p connecting the number o f p o i n t s i n a data s e t , m, and the number o f d e s c r i p t o r s p e r p o i n t , n, the d i m e n s i o n a l i t y o f the space. As shown by N i l s s o n (6) and by Tou and Gonzalez {!) t h e a b i l i t y o f a b i n a r y p a t t e r n c l a s s i f i e r to separate p o i n t s i s high, even f o r random p o i n t s , i f m i s l e s s than twice as l a r g e as n. The p r o b a b i l i t y o f f i n d i n g a l i n e a r d e c i s i o n s u r f a c e capable o f s e p a r a t i n g any randomly p l a c e d 50 p o i n t s i n a 25-dimensional space i s n e a r l y u n i t y . D i r e c t t e s t s i n our l a b o r a t o r y a r e i n agreement w i t h the theory o f BPC's and show t h a t one has not e l i m i n a t e d the p o s s i b i l i t y o f meaningless t r a i n i n g u n t i l m i s two p o i n t f i v e o r three times as l a r g e as n. Thus, i f one f i n d s a s e p a r a t i n g l i n e a r d e c i s i o n s u r f a c e f o r 75 p o i n t s i n a 25-space, then the p r o b a b i l i t y i s overwhelming t h a t the s e p a r a t i o n i s meaningful, and i t i s not a mathematical a r t i ­ fact. I f the c l u s t e r s a r e dense and a r e f a r apart from each other, and i f the d i m e n s i o n a l i t y o f the space i s s u f f i c i e n t l y low, then x

2

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d i s p l a y o r mapping techniques can be used. T h i s i s done by p e r ­ forming a one-to-one mapping o f p a t t e r n p o i n t s from the o r i g i n a l η-dimensional space t o a 2- o r 3-dimensional space with as l i t t l e d i s t o r t i o n as p o s s i b l e . I f these techniques can be s u c c e s s f u l l y employed, then one can observe the c l u s t e r s d i r e c t l y on a 2- o r 3-dimensional p l o t . An a l t e r n a t i v e way t o i n v e s t i g a t e the s t r u c t u r e o f the s e t o f p o i n t s i s t o separate the c l u s t e r s from one another by d e c i s i o n s u r f a c e s . The simplest d e c i s i o n s u r f a c e i s a hyperplane. Two c l u s t e r s o f p o i n t s which can be completely separated by a hyper­ plane a r e s a i d t o be l i n e a r l y separable. Any hyperplane has a s s o c i a t e d with i t a normal v e c t o r , c a l l e d here the weight v e c t o r . The weight v e c t o r c o n s i s t s o f an ordered sequence o f components, W = (w^, w # w ) , which stands i n one t o one correspondence with the components o f the p a t t e r n s t o be c l a s s i f i e d . Specifi­ c a t i o n o f the components o f the weight v e c t o r i s completely e q u i ­ v a l e n t t o s p e c i f i c a t i o n o f t h e p o s i t i o n o f a hyperplane d e c i s i o n surface. Any p a t t e r n p o i n t i n a hyperspace can be c l a s s i f i e d with r e s p e c t t o a hyperplane d e c i s i o n s u r f a c e by t a k i n g the dot product between t h a t p a t t e r n v e c t o r and the normal v e c t o r , o r weight v e c t ­ or: 2

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THEORY AND APPLICATION

n

s = W.X = w^x^ + W2X2 + ... + w x n

n

= Iw|

|x| cos θ

i n which θ i s the angle between the two v e c t o r s . Since |w| and |x| are always p o s i t i v e , then the value o f θ determines the s i g n o f the dot product. For p a t t e r n s on one s i d e o f the plane the dot prod­ u c t i s always p o s i t i v e , and f o r p a t t e r n s on the opposite s i d e the dot product i s always negative. The dot product i s normally com­ puted from the summation o f p a i r w i s e products o f the components o f the two v e c t o r s f o r convenience. The correspondence between c a t e ­ gory 1 and category 2 and the two s i d e s o f the hyperplane i s a r b itary. The l o g i c a l o p e r a t i o n d e s c r i b e d above i s performed by a t h r e s ­ h o l d l o g i c u n i t o r TLU. The TLU accepts the p a t t e r n v e c t o r t o be c l a s s i f i e d , c a l c u l a t e s t h e dot product between the p a t t e r n v e c t o r and the weight v e c t o r , compares the dot product a g a i n s t zero, and c l a s s i f i e s the p a t t e r n according t o the s i g n o f the dot product. D i s c r i m i n a n t Function Development. Given the system d i s c u s s e d above f o r performing c l a s s i f i c a t i o n s , the outstanding problem i n the development o f u s e f u l p a t t e r n c l a s s i f i e r s becomes t h a t o f f i n d ­ i n g u s e f u l d e c i s i o n s u r f a c e s . T h i s can be done, f o r the nonpara­ m e t r i c systems o f i n t e r e s t , by a method c a l l e d t r a i n i n g . A t r a i n ­ i n g s e t o f p a t t e r n s whose c o r r e c t c l a s s i f i c a t i o n s a r e known i s used t o develop an e f f e c t i v e d e c i s i o n s u r f a c e . The members o f the t r a i n i n g s e t o f o b j e c t s a r e presented t o the TLU being t r a i n e d one a t a time. The weight v e c t o r being trained i s i n i t i a l i z e d a r b i t r a r i l y . When an i n c o r r e c t c l a s s i f i -

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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Studies

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c a t i o n i s made, the weight v e c t o r i s a l t e r e d . The a l t e r a t i o n i s performed i n such a way as to i n s u r e t h a t the new weight v e c t o r w i l l c o r r e c t l y c l a s s i f y the p a t t e r n . T h i s process continues u n t i l a l l the p a t t e r n s o f the t r a i n i n g s e t are c o r r e c t l y c l a s s i f i e d . If the procedure does not f i n d a weight v e c t o r capable o f c o r r e c t l y c l a s s i f y i n g a l l the members o f the t r a i n i n g s e t , then the r o u t i n e i s terminated i n order t o conserve computer time. Learning Machine A t t r i b u t e s . The c a p a b i l i t i e s and performance o f l e a r n i n g machines can be d e s c r i b e d i n terms o f three p r i n cipal attributes: r e c o g n i t i o n , convergence r a t e , and p r e d i c t i o n . Recognition i s the a b i l i t y o f the t r a i n e d b i n a r y p a t t e r n c l a s s i f i e r to c o r r e c t l y c l a s s i f y the members o f i t s t r a i n i n g s e t . Recognition i s 100% f o r a b i n a r y p a t t e r n c l a s s i f i e r whose d e c i s i o n s u r f a c e i s i n the r e g i o n between two separated c l u s t e r s . That i s , a f t e r t r a i n i n g i s complete f o r such a case, the TLU can c o r r e c t l y c a t e g o r i z e any of the members o f the t r a i n i n g s e t . Convergence r a t e r e f e r s t o the r a t e a t which a TLU approaches 100% r e c o g n i t i o n . Since computer time i s an expensive commodity, i t i s o f i n t e r e s t t o minimize t r a i n i n g time. The t r a i n i n g procedures used to f i n d u s e f u l TLU*s are commonly a l t e r e d so as t o force rapid learning. P r e d i c t i o n r e f e r s t o the a b i l i t y o f the TLU to c o r r e c t l y c l a s s i f y unknowns which were not members o f the t r a i n i n g s e t . P r e d i c t i o n i s the most i n t e r e s t i n g and p o t e n t i a l l y u s e f u l o f the a t t r i b u t e s because high p r e d i c t i v e a b i l i t y demonstrates t h a t the TLU has been able to l e a r n something about how to d i s c r i m i n a t e between the two c l a s s e s being t r a i n e d f o r , and the a b i l i t y to c o r r e c t l y c l a s s i f y unknown s p e c t r a i n t o u s e f u l chemical c a t e g o r i e s i s one d r i v e behind a l l automation o f chemical data i n t e r p r e t a t i o n . P r e d i c t i v e a b i l i t y i s normally t e s t e d by s p l i t t i n g the a v a i l a b l e data s e t i n t o two p a r t s - a t r a i n i n g s e t and a p r e d i c t i o n s e t . A f t e r t r a i n i n g i s complete, and without f u r t h e r adjustment o f the weight v e c t o r , the members o f the p r e d i c t i v e s e t are c l a s s i f i e d and the percentage c o r r e c t i s taken as the p r e d i c t i v e a b i l i t y . Another approach, known as the leave-one-out procedure, i n v o l v e s t r a i n i n g a BPC using a t r a i n i n g set c o n t a i n i n g a l l the data on hand except one member, and then p r e d i c t i n g the c l a s s o f the one unknown a f t e r t r a i n i n g i s complète. When averaged over a number of independent t r i a l s , the percentage o f unknowns c o r r e c t l y c l a s s i f i e d i s a measure o f the p r e d i c t i v e a b i l i t y . Feedback Feature S e l e c t i o n . A f t e r a s e r i e s o f weight v e c t o r s have been t r a i n e d f o r the same q u e s t i o n , then they can be used to perform feedback feature s e l e c t i o n . One method t h a t has been used f o r a number o f problems i s weight-sign feature s e l e c t i o n . Implementation o f t h i s method takes advantage o f the f a c t t h a t the exact o r i e n t a t i o n of a t r a i n e d weight v e c t o r (that i s , the r e l a t i v e magnitudes of i t s components) depends on the i n i t i a l i z a t i o n used p r i o r to t r a i n i n g , the magnitude o f the nth component o f the p a t t e r n

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v e c t o r s , x ^ the feedback t r a i n i n g methods employed, the sequence i n which the members o f the t r a i n i n g s e t a r e presented t o the c l a s s i f i e r during t r a i n i n g , and s e v e r a l other f a c t o r s . In other words, the exact o r i e n t a t i o n o f a t r a i n e d weight vector depends on the d e t a i l s o f how i t was found. In weight-sign feature s e l e c t ion a p a i r o f weight v e c t o r s i s developed f o r the same question but u s i n g s l i g h t l y d i f f e r e n t approaches, £.CJ.. , d i f f e r e n t i n i t i a l i z a t i o n s . Then the a l g e b r a i c s i g n s o f t h e i r components are compared pairwise. When the components o f the two weight v e c t o r s t h a t both correspond t o a p a r t i c u l a r d e s c r i p t o r disagree i n s i g n , t h a t desc r i p t o r i s discarded; when the signs agree, the d e s c r i p t o r i s r e tained. The procedure i s repeated i t e r a t i v e l y u n t i l two weight v e c t o r s are t r a i n e d t h a t a r e i n complete agreement f o r a l l d e s c r i p t o r s t h a t a r e most u s e f u l f o r a p a r t i c u l a r c l a s s i f i c a t i o n . More r e c e n t l y , a new feedback f e a t u r e s e l e c t i o n procedure much s u p e r i o r t o the weight-sign method has been developed. The v a r i ance f e a t u r e s e l e c t i o n method a l s o takes advantage o f the f a c t t h a t the o r i e n t a t i o n o f a t r a i n e d weight v e c t o r i s dependent on how i t was developed. Here, a group o f weight v e c t o r s a r e t r a i n e d f o r a c l a s s i f i c a t i o n problem i n a manner designed t o e x p l o i t these dependencies. The s e r i e s o f weight v e c t o r s i s then used t o rank the d e s c r i p t o r s t h a t were most u s e f u l i n s e p a r a t i n g the two c l a s s e s under i n v e s t i g a t i o n . The ranking i s done by developing an ordered l i s t o f the d e s c r i p t o r s based on the r e l a t i v e v a r i a t i o n o f the corresponding weight vector components among the s e r i e s o f t r a i n e d weight v e c t o r s . Then the i n t r i n s i c d e s c r i p t o r s (those forming the minimal s e t o f d e s c r i p t o r s s u f f i c i e n t t o e f f e c t separation) can be discarded. The variance f e a t u r e s e l e c t i o n method has been a p p l i e d to a wide v a r i e t y o f problems i n our l a b o r a t o r y . Chemical A p p l i c a t i o n s o f P a t t e r n Recognition. Application s t u d i e s o f chemical problems using p a t t e r n r e c o g n i t i o n techniques have been reported i n a number o f areas (8-14). These a r e l i s t e d i n subsets because each general area r e q u i r e s some d i f f e r e n t approaches and techniques. (1) S p e c t r a l Data A n a l y s i s . E l u c i d a t i o n o f chemical s t r u c ture information from s p e c t r o s c o p i c data i s the area that has r e c e i v e d the most a t t e n t i o n from those p r a c t i c i n g p a t t e r n recognition. Studies have been done with mass s p e c t r a , i n f r a r e d s p e c t r a , s t a t i o n a r y e l e c t r o d e polarograms, gamma-ray s p e c t r a , proton and C n u c l e a r magnetic resonance s p e c t r a . (2) M a t e r i a l s Science. The c l a s s i f i c a t i o n o f m a t e r i a l s as t o o r i g i n o r s u i t a b i l i t y w i t h respect t o production s p e c i f i c a t i o n s has been reported. The data used are g e n e r a l l y multi-source data coming from a v a r i e t y o f a n a l y t i c a l techniques. (3) C l a s s i f i c a t i o n o f Complex Mixtures. The i d e n t i f i c a t i o n o f petroleum samples by a n a l y z i n g a n a l y t i c a l data by p a t t e r n r e c o g n i t i o n techniques has been reported. Data used f o r c l a s s i f i c a t i o n i n d i f f e r e n t s t u d i e s has i n c l u d e d gas chromatograms, i n f r a r e d s p e c t r a , fluorescence s p e c t r a , t r a c e metals c o n c e n t r a t i o n s . A 1 3

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second example o f data a n a l y s i s o f complex mixtures i s from the b i o l o g i c a l mixtures, e_.£., serum, are f e a s i b l e and have been reported, (4) Modeling o f Chemical Experiments. Pattern r e c o g n i t i o n techniques have been used t o model complex chemical systems where the d e t a i l s o f the chemical and/or p h y s i c a l i n t e r a c t i o n s were not completely understood, e_.£.,. r e l a t i v e r e t e n t i o n o f compounds on d i f f e r e n t chromatographic l i q u i d phases. (5) P r e d i c t i o n o f P r o p e r t i e s from Molecular S t r u c t u r e . A number o f s t u d i e s o f the a p p l i c a t i o n o f p a t t e r n r e c o g n i t i o n to the problem o f searching f o r c o r r e l a t i o n s between molecular s t r u c t u r e and b i o l o g i c a l a c t i v i t y have been reported.

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A p p l i c a t i o n s o f P a t t e r n Recognition t o S t r u c t u r e - A c t i v i t y R e l a t i o n s A p p l i c a t i o n s t o S t r u c t u r e - A c t i v i t y R e l a t i o n s . W i t h i n the l a s t few years r e p o r t s have begun to appear o f work d e a l i n g with c l u s t e r a n a l y s i s and p a t t e r n r e c o g n i t i o n a p p l i c a t i o n s to drug s t r u c t u r e a c t i v i t y r e l a t i o n s t u d i e s . A paper by Hansch, Unger, and Forsythe (15) d i s c u s s e d the a p p l i c a t i o n o f h i e r a c h i c a l c l u s t e r a n a l y s i s techniques to the problem o f s e l e c t i o n o f s u b s t i t u e n t s . The data used to represent each drug were the l i p o p h i l i c π constant, e l e c t ­ r o n i c parameters, the approximate s t e r i c molar r e f r a c t i v i t y and molecular weight constants — physicochemical parameters. A paper by H i l l e t aJU (16) d i s c u s s e d the problem o f drug design as app­ roached by using a t h r e e - l a y e r perceptron network. Forty-six 1,3-dioxane molecules were used as the data s e t f o r t r a i n i n g and p r e d i c t i o n o f perceptrons t o determine a n t i c o n v u l s a n t a c t i v i t y . P r e d i c t i v e a b i l i t i e s i n the range o f 68 t o 76 percent were r e p o r t ­ ed. A paper by T i n g e t a l . (17) reported c o r r e l a t i o n s between the low r e s o l u t i o n mass s p e c t r a o f s i x t y - s i x drugs and t h e i r pharma­ c o l o g i c a l a c t i v i t y as sedatives o r t r a n q u i l i z e r s . T h i s paper was c r i t i c i z e d with regard t o the s e t o f drugs used i n the a n a l y s i s (18) and with regard to the number o f drugs used and t h e i r r e l a t i v e s i m i l a r i t i e s (19). Several papers (20-22) have r e c e n t l y appeared r e p o r t i n g s t u d i e s i n which molecules were represented by a l i s t o f s t r u c t u r a l f e a t u r e s o f the molecules. Adamson and Bush (20) used l i b r a r y searching programs t o generate a l l s t r u c t u r a l fragments i n t h e i r data s e t and represented the drugs by l i s t s o f the number of occurences o f each substructure i n the molecules. Chu (21) used a number o f p a t t e r n r e c o g n i t i o n and c l u s t e r a n a l y s i s programs to analyze a s e t o f s i x t y - s i x drugs represented by f o r t y - s i x fragments. Kowalski and Bender (22) used three p a t t e r n r e c o g n i t i o n c l a s s ­ i f i e r s t o attempt t o c l a s s i f y 200 drugs w i t h respect to a c t i v i t y f o r the Adenocarcinoma 755 B i o l o g i c a l A c t i v i t y T e s t . T h e i r paper has been c r i t i c i z e d f o r the choice o f the twenty d e s c r i p t o r s used (23). Chu e t a l . (24) reported on the a p p l i c a t i o n o f p a t t e r n r e c o g n i t i o n and s u b s t r u c t u r a l a n a l y s i s t o the problem o f i n v e s t i ­ g a t i n g the a n t i n e o p l i a s t i c a c t i v i t y o f a s e t o f drugs i n the

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experimental mouse b r a i n tumor system. The s e t o f molecules were represented by augmented atom fragments, "heteropath" fragments, and r i n g fragments. Nearest neighbor and l e a r n i n g machine methods of c l a s s i f i c a t i o n were employed, and i t was concluded t h a t these methods could be s u c c e s s f u l l y a p p l i e d t o the problem. C r a i g and Waite (25) have reported the use of p a t t e r n r e c o g n i t i o n techniques to the p r e d i c t i o n o f t o x i c i t y o f o r g a n i c compounds.

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S t r u c t u r e - A c t i v i t y Studies Using P a t t e r n

Recognition

In order to apply p a t t e r n r e c o g n i t i o n techniques t o s t u d i e s o f molecular s t r u c t u r e - b i o l o g i c a l a c t i v i t y c o r r e l a t i o n s the data must be taken through a number o f i n d i v i d u a l steps. These are l i s t e d i n order t o show how i n t e r r e l a t e d the steps become. (a) I d e n t i f y data s e t . (b) E n t e r molecular s t r u c t u r e s . A complete d e s c r i p t i o n o f the s t r u c t u r e o f each molecule must be entered i n t o a file. (c) Generate usable f i l e . A subset o f compounds must be s e l e c t e d from the master s t r u c t u r e f i l e . T h i s may i n volve searching o f keys f o r the s t r u c t u r e s , and w i l l r e q u i r e c a r r y i n g along an i d e n t i f y i n g l a b e l f o r each s t r u c ture. (d) D e s c r i p t o r development. The molecular s t r u c t u r e s s t o r e d i n a general purpose form (£.2/ 9 connection t a b l e s ) must be decomposed i n t o sets o f d e s c r i p t o r s . The three gene r a l c l a s s e s are t o p o l o g i c a l , geometrical, and e x t e r n a l l y generated d e s c r i p t o r s . (e) Form data matrix. The subset o f the a v a i l a b l e d e s c r i p t o r s t o be used i s i d e n t i f i e d , and a matrix o f data i s generated. I t may be p a r t i t i o n e d i n t o a t r a i n i n g s e t and a prediction set. (f) P r i o r feature s e l e c t i o n . Techniques can be a p p l i e d to determine which d e s c r i p t o r s are expected to be most important. (g) Discriminant development. The data s e t i s used t o develop a d i s c r i m i n a n t f u n c t i o n . A f t e r development, the d i s criminant f u n c t i o n can be t e s t e d on unknowns to assess predictive a b i l i t y . (h) Feedback feature s e l e c t i o n . The r e s u l t s o f c l a s s i f i c a t i o n can be used to i d e n t i f y the most u s e f u l d e s c r i p t o r s . One o f the primary p r e r e q u i s i t e s f o r a u s e f u l general purpose p a t t e r n r e c o g n i t i o n system i s a general, data-independent, f i l e management system. A general purpose system has been developed (26) t h a t c o n s i s t s o f a s e t o f i n t e r a c t i v e computer r o u t i n e s known c o l l e c t i v e l y as ADAPT (Automated Data A n a l y s i s using Pattern recogn i t i o n Techniques). T h i s system p r o v i d e s a g e n e r a l i z e d framework t h a t takes i n t o account the p r a c t i c a l c o n s i d e r a t i o n s inherent i n the implementation o f the p a t t e r n r e c o g n i t i o n framework shown i n F i g u r e 1.

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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ADAPT A r c h i t e c t u r e . F i g u r e 1 does not make c l e a r the i n h e r e n t d i v e r s i t y o f the data h a n d l i n g problem. Not only must measurements from the transducer(s) be i n p u t , but they must be s t o r e d and l a b e l l ed. Each data p o i n t must be given a c l a s s d e s i g n a t i o n and i n d e n t i f i c a t i o n number. C l a s s d e s i g n a t i o n s must be e a s i l y assigned o r m o d i f i e d . T h i s ease o f d e f i n i t i o n and r e d e f i n i t i o n i s o f utmost importance i n the o v e r a l l data a n a l y s i s . The source o f the data i s a l s o important. Sources such as d i g i t i z e d s p e c t r a o r complex molecular s t r u c t u r e s would have widely d i f f e r e n t storage r e q u i r e ments. Since the o p e r a t i o n s performed on one type o f data may bear l i t t l e s i m i l a r i t y t o the o p e r a t i o n s performed on o t h e r types o f data, a system designed with a high degree o f modularity i s r e q u i r e d . To accomodate these requirements, the ADAPT system i s implemented i n independent segments. Each segment can execute independently, o b t a i n i n g a l l necessary i n f o r m a t i o n e i t h e r from a s e t o f d i s c s t o r age f i l e s o r by i n t e r a c t i o n with the user. T h i s mode o f o p e r a t i o n o f f e r s s e v e r a l advantages, t h e most obvious o f which i s a savings i n core storage. The modularity decreases the complexity o f the system and p r o v i d e s a means t o i n c o r p o r a t e a d d i t i o n a l algorithms i n t o the system a t any time. Thus the e n t i r e system i s adapted t o any user's i n d i v i d u a l requirements s i n c e o n l y those o v e r l a y s which are r e l e vant t o the p a r t i c u l a r problem a t hand need be executed. In addi t i o n , these r o u t i n e s a r e r e l a t i v e l y inexpensive t o use because they do not r e q u i r e l a r g e s c a l e f a c i l i t i e s f o r e x e c u t i o n . Finally, the system i s i n t e r a c t i v e i n the sense t h a t the user d i r e c t s which manipulations are t o be performed upon the data. ADAPT thus c o n s i s t s o f a framework w i t h i n which an u n l i m i t e d number o f independent segments can be supported. Each segment performs a s p e c i f i c , independent o p e r a t i o n ranging from i n i t i a l input o f data t o f i n a l output o f r e s u l t s . The g e n e r a l u t i l i t y o f the system a r i s e s from the f a c t t h a t the user has a l a r g e number of o p t i o n s t o choose from, and he can c o n v e n i e n t l y i n t e r a c t with h i s data s e t . I n t e r a c t i o n with ADAPT i s p r o v i d e d v i a a T e k t r o n i x 4010 CRT t e r m i n a l . Data i s s t o r e d i n a s e r i e s o f d e f i n e d f i l e s on c a r t ridge d i s c s . T h i s allows f a s t access and ease o f manipulation. C u r r e n t l y , ADAPT c o n s i s t s o f approximately 70 d e f i n e d f i l e s which use 2.4 m i l l i o n bytes o f storage (one c a r t r i d g e d i s c ) . The ADAPT r o u t i n e uses approximately 90,000 bytes o f core storage f o r i t s l a r g e s t o v e r l a y and i s c u r r e n t l y implemented using a s i x t e e n - b i t M0DC0MP 11/25 computer l o c a t e d i n the Department o f Chemistry a t The Pennsylvania State U n i v e r s i t y . The segments o f the ADAPT system can be broken down i n t o the following l i s t : (1) F i l e generator, i n c l u d i n g g r a p h i c a l i n p u t o f s t r u c t u r e s (2) C l a s s maker (3) Three-dimensional model b u i l d e r (4) D e s c r i p t o r developer

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(5) (6) (7) (8) (9)

Collator Preprocessor P r i o r feature s e l e c t o r D i s c r i m i n a n t developer Feedback feature s e l e c t o r

(1) F i l e Generator. The l i b r a r y o f drugs t o be s t u d i e d i s e n t e r ed through the f i l e generator r o u t i n e . S t r u c t u r e s are input by drawing them i n two dimensions on the screen o f an i n t e r a c t i v e graphics t e r m i n a l under the c o n t r o l o f a general s t r u c t u r a l input r o u t i n e , UDRAW, which has been f u l l y d e s c r i b e d elsewhere (27). A molecule's s t r u c t u r e , along with corresponding pharmacological data, i s entered i n t o a d i s c r e s i d e n t permanent f i l e . Information saved f o r f u t u r e use i n c l u d e s a compressed connection t a b l e , r i n g information, a l i s t o f reported a c t i v i t i e s , the two-dimensional coordinates o f the atoms when entered ( f o r p o s s i b l e redrawing o f the s t r u c t u r e s l a t e r ) , an i d e n t i f i c a t i o n number, and the chemical name o f the compound. In a d d i t i o n t o generation, the f i l e can be a l t e r e d by making changes t o information s t o r e d f o r a drug, a drug can be e n t i r e l y d e l e t e d from the f i l e , o r any f i l e member can be d i s p l a y e d . A s e l e c t i o n o f r e c a l l a b l e molecular backbones can be s t o r e d f o r more convenient entry o f s e r i e s o f s t r u c t u r a l l y r e l a t e d compounds. These s t r u c t u r e s can then be made t o appear upon the i n i t i a l UDRAW sketch pad and a complete molecule can be b u i l t up s t a r t i n g from t h i s backbone. This allows the user t o input a s e r i e s o f s t r u c t u r a l l y s i m i l a r compounds without redrawing the base s t r u c t u r e each time. The r o u t i n e t h a t oversees s t r u c t u r e input and f i l e generation can maintain a f i l e o f 1000 s t r u c t u r e s and a s s o c i a ted a u x i l i a r y information. The f i r s t s t r u c t u r e f i l e now s t o r e d i n the system c o n s i s t s o f approximately one thousand c e n t r a l nervous system agents taken from the l i t e r a t u r e (28). Among the b i o l o g i c a l a c t i v i t y c l a s s e s reported there are a n a l g e s i c s , a n t i c o n v u l s a n t s , depressants, hypnotics, r e l a x a n t s , s e d a t i v e s , s t i m u l a n t s , and t r a n q u i l i z e r s ? there are approximately f o r t y c l a s s e s a l t o g e t h e r , many o f which overlap. The second f i l e o f molecular s t r u c t u r e s c u r r e n t l y r e s i d e n t on the ADAPT d i s c f i l e c o n s i s t s o f 184 5 , 5 - d i s u b s t i t u t e d b a r b i t u r a t e s taken from a reference volume (29). A study using t h i s data s e t w i l l be discussed i n a l a t e r s e c t i o n . The t h i r d f i l e contains approximately 500 compounds comprising an o l f a c t i o n data s e t taken from Amoore (30). Molecules reported to have musk, camphor, mint, ether, f l o r a l , pungent, and p u t r i d odors are present. T h i s data s e t i s being used i n s t u d i e s o f the r e l a t i o n between molecular s t r u c t u r e and odor q u a l i t y . The f o u r t h f i l e c o n s i s t s o f a s e t o f molecules comprising an o l f a c t i o n data s e t taken i n a study o f t r i g e m i n a l d e t e c t i o n o f compounds. These compounds are being employed i n a study o f the s i m i l a r i t i e s and d i f f e r e n c e s observed i n t r i g e m i n a l as opposed t o

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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o l f a c t o r y d e t e c t i o n o f chemicals by humans.

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(2) C l a s s Maker. The c l a s s maker r o u t i n e i s used t o access the l i b r a r y f i l e and t o create s e t s o f l i b r a r y members t h a t s a t i s f y q u e r i e s entered by the user. Thus, t h e s e t o f a l l f i l e members which have been reported t o be sedatives can be formed i n t o an a c t i v e data s e t . T h i s r o u t i n e i s used t o generate c l a s s e s o f s t r u c t u r e s t o be used as data s e t s f o r the development o f d i s c r i m inants by another s e c t i o n o f ADAPT. When the property being sought i s known q u a n t i a t i v e l y , the data s e t i s assembled i n i n c r e a s i n g sequence. Then a s e r i e s o f d i s c r i m i n a n t s can be t r a i n e d f o r d i f f e r e n t t h r e s h o l d c u t o f f s between the a c t i v e and i n a c t i v e c l a s s e s without moving any data but only by r e a l l o c a t i n g c l a s s memberships. (3) Three-Dimensional Model B u i l d e r . The three-dimensional mole c u l a r model b u i l d e r routine i s used t o d e r i v e information on the s p a c i a l conformation o f molecules. A molecule can be viewed as a c o l l e c t i o n o f p a r t i c l e s h e l d together by simple harmonic o r e l a s t i c f o r c e s . These f o r c e s can be d e f i n e d by p o t e n t i a l energy f u n c t i o n s whose terms are the atom coordinates o f the molecule. T h i s f u n c t i o n can then be minimized t o o b t a i n a s t r a i n - f r e e t h r e e dimensional model o f the molecule. Geometric parameters can then be e x t r a c t e d . A wealth o f information already e x i s t s d e s c r i b i n g the procedures and r e s u l t s o f s e v e r a l d i f f e r e n t molecular mechani c s algorithms (31,32). Therefore, f i n d i n g and implementing an a l g o r i t h m t o model sets o f molecules i s a r e l a t i v e l y s t r a i g h t forward procedure. A modified v e r s i o n o f the molecular mechanics routine described by Wipke, e t a l (33-35) has been developed and i n t e r f a c e d t o the ADAPT system so t h a t geometric d e s c r i p t o r s can be d e r i v e d from the r e s u l t i n g molecular s t r u c t u r e . The molecular mechanics r o u t i n e , MOLMEC, used i n conjunction with the ADAPT system i s h i g h l y i n t e r a c t i v e and r e l i e s on g r a p h i c a l input and output. A graphics u n i t i s a l s o supported and i s u t i l i z ed by MOLMEC f o r d i s p l a y i n g the molecule being modelled. The s t r u c t u r e input s e c t i o n o f MOLMEC has been designed t o allow the user t o e i t h e r read the molecule's connection t a b l e from ADAPT*s d i s c f i l e s o r e l s e accept the s t r u c t u r e from the CRT v i a UDRAW (27). Thus, MOLMEC can be used independently o f the ADAPT system. Once the molecule has been entered, c o n t r o l branches t o the i n t e r a c t i v e s e c t i o n where the user can d i r e c t the d i f f e r e n t phases o f modelling as w e l l as monitor the r e s u l t s . In the s t r a i n minimization s e c t i o n , the atom coordinates are s y s t e m a t i c a l l y a l t e r e d u n t i l a minimum i s found i n the s t r a i n o r p o t e n t i a l energy f u n c t i o n . The a c t u a l s t r a i n f u n c t i o n used i n MOLMEC i s : w

E

strain

s

The

Ebond first

+

E ngle a

+

Etorsion

+

E on-bond n

+

E s

tereo

four terms o f the f u n c t i o n are commonly found i n a l l

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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molecular mechanics s t r a i n f u n c t i o n s and are m o d i f i e d Hooke's Law f u n c t i o n s . The l a s t term o f the f u n c t i o n has been added t o assure the proper stereochemistry about an asymmetric atom. The a c t u a l minimization o f the f u n c t i o n i s b e s t accomplished by some type o f n o n l i n e a r programming method (£.£., steepest descent) · In MOLMEC, an adaptive p a t t e r n search r o u t i n e (36) i s used because i t does n o t r e q u i r e a n a l y t i c a l d e r i v a t i v e s . The amount o f time necessary t o o b t a i n good molecular models depends upon the number o f atoms i n the molecule, the i n i t i a l s t r a i n o f the molecule, and the degrees o f freedom i n the s t r u c t u r e . I f a s m a l l molecule i s being modelled, only one pass through the minimization s e c t i o n may be s u f f i c i e n t t o o b t a i n a good s t r u c t u r e . However, t h i s i s seldom the case. U s u a l l y , t h e molecules are r a t h e r l a r g e and r e q u i r e s e v e r a l passes. The a c t u a l amount o f time p e r pass i s l i m i t e d by a c u t o f f parameter so t h a t the user may analyze the progress o f t h e modelling a t d i f f e r e n t i n t e r v a l s . The graphics i n t e r a c t i o n s e c t i o n o f MOLMEC c o n t a i n s r o u t i n e s capable o f r o t a t i n g and a l i g n i n g the molecule i n t o any d e s i r e d p o s i t i o n . Since the graphics u n i t i s o n l y a two-dimensional screen, r o t a t i o n i s e s s e n t i a l t o o b t a i n a good view o f the s t r u c t u r e . Furthermore, these r o u t i n e s are u s e f u l i n l o c a t i n g atoms trapped i n l o c a l minima. I f such an atom i s found, the user can move the trapped atom t o a new p o s i t i o n by a MOVE r o u t i n e found i n the graphics s e c t i o n . N a t u r a l l y , i f the s t r u c t u r e i s a l t e r e d the molecule should be passed through the minimization r o u t i n e a t l e a s t once more. When the molecule i s f i n a l l y i n a low s t r a i n energy conformat i o n , the molecular parameters can be e i t h e r l i s t e d on an output device, o r e l s e the s t r u c t u r e ' s coordinate matrix can be s t o r e d on a d i s c f i l e f o r .further p r o c e s s i n g . An automatic v e r s i o n o f MOLMEC has a l s o been developed so t h a t l a r g e molecular data s e t s can be modelled without continuous superv i s i o n . The program c o n s i s t s on an i n p u t s e c t i o n , which reads the molecule's connection t a b l e and present coordinate matrix from the ADAPT f i l e s , a m i n i m i z a t i o n s e c t i o n w i t h a l l output suppressed, and a s e c t i o n which s t o r e s the f i n a l coordinate matrix. Good models can e a s i l y be obtained i n t h i s manner. However, before the coordinate matrices can be used f o r c a l c u l a t i n g d e s c r i p t o r s , the s t r u c t u r e s a r e reviewed t o make sure t h a t the molecules are i n acceptable conformations. Once modelling i s complete, geometric d e s c r i p t o r s can be d e r i v e d . D e s c r i p t o r s c u r r e n t l y being used i n c l u d e the absolute o r r e l a t i v e magnitudes o f t h e p r i n c i p a l moments o f i n e r t i a o f t h e molecule, the presence o r absence o f p a r t i c u l a r s p a c i a l arrangements o f atoms which have been c a l l e d pharmacophores, and the molecular volume. (4) D e s c r i p t o r Developer. The next step i n s t u d i e s o f s t r u c t u r e a c t i v i t y r e l a t i o n s i s t h e development o f d e s c r i p t o r s f o r the molec u l e s contained i n the a c t i v e data s e t . T h i s s u b j e c t has been

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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d i s c u s s e d i n a recent p u b l i c a t i o n (37). D e s c r i p t o r s belong t o two general c l a s s e s : t o p o l o g i c a l and geometrical. T o p o l o g i c a l desc r i p t o r s are d e r i v e d from the t o p o l o g i c a l r e p r e s e n t a t i o n o f a compound — the connection t a b l e . Geometrical d e s c r i p t o r s are d e r i v ed from the three-dimensional model o f the molecule. The i n d i v i d ual d e s c r i p t o r s that have been used i n reported s t u d i e s are desc r i b e d i n the f o l l o w i n g paragraphs. (a) Atom and bond d e s c r i p t o r s — Fragment d e s c r i p t o r s . Atom d e s c r i p t o r s i n c l u d e the number o f C., N, 0, S, P, F, C l , Br, I atoms i n the s t r u c t u r e . Numbers o f bonds o f each type are a l s o generated. Both atom and bond d e s c r i p t o r s are developed d i r e c t l y from the s t o r e d connection t a b l e . (b) Substructure D e s c r i p t o r s . Searching the molecule f o r the presence o f l a r g e r fragments provides an a l t e r n a t i v e method f o r generating d e s c r i p t o r s . I f the substructure i s found i n the mole c u l e , the d e s c r i p t o r can be given a value o f one. Otherwise, i t has a value o f zero. Therefore, to generate substructure d e s c r i p t o r s f o r a given molecular data s e t , two things are needed: a substructure searching a l g o r i t h m and a l i b r a r y of appropriate substructures. Algorithms f o r substructure searching f a l l i n t o two general c a t e g o r i e s . The f i r s t , atom-by-atom searching, i s the e a s i e s t to implement on a d i g i t a l computer because i t simply matches the s t r u c t u r e and substructure atoms and a s s o c i a t e d bonds one a t a time using a l l p o s s i b l e combinations. However, f o r l a r g e s t r u c t u r e s and substructures the time r e q u i r e d f o r a s i n g l e search becomes p r o h i b i t i v e because o f the number o f p o s s i b l e combinations i n c r e a s e s f a c tor i a l l y . The second category u t i l i z e s s e t r e d u c t i o n techniques t o accomplish the substructure search, and f a c t o r i a l c a l c u l a t i o n s are not i n v o l v e d . Although they are more complex than atom-by-atom searching techniques, algorithms implementing s e t r e d u c t i o n are very a t t r a c t i v e because o f t h e i r searching speed. Several d i f f e r ent algorithms have been d e s c r i b e d which use s e t r e d u c t i o n (38-40). In the ADAPT system, a v a r i a t i o n o f the techniques d e s c r i b e d by Sussenguth (38) i s used f o r generating substructure d e s c r i p t o r s . The m o d i f i c a t i o n s allow f o r g r e a t e r substructure s p e c i f i c i t y , a wider v a r i e t y of substructure types, and numeric i n s t e a d of b i n a r y searches. A d i s c u s s i o n o f the changes made i n the Sussenguth's a l g o r i t h m has been reported (41_) and w i l l not be d e t a i l e d here. The problem of c r e a t i n g a substructure l i b r a r y i s not as easy to s o l v e as o b t a i n i n g a good substructure searching algorithm. One approach t o t h i s problem i n v o l v e s the systematic combing o f the b a s i c atom and bond fragments i n t o s u b s t r u c t u r e s . However, the f i n a l number o f substructures generated i n t h i s manner would be t o t a l l y unmanageable. The d i s c r i m i n a t i o n between usable and usel e s s substructures would r e q u i r e some type o f p a t t e r n r e c o g n i t i o n system, and t h i s approach i s not f e a s i b l e . A more workable approach to the problem i s to study the data s e t o f molecules under i n v e s t i g a t i o n and allow the chemist to decide on a c o l l e c t i o n o f

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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substructures to be a p p l i e d t o the data s e t . The ADAPT system u t ­ i l i z e s t h i s second method to generate a substructure l i b r a r y . A set o f substructure d e s c r i p t o r s can now be generated. Two types of searches are p o s s i b l e . For a general search, a match i s made i f the i n d i c a t e d substructure i s l o c a t e d anywhere i n the molecule; a l l r i n g information i s ignored. However, during a s p e c i f i c search, r i n g information i s taken i n t o c o n s i d e r a t i o n . Therefore, i f the substructure i s not s p e c i f i e d to be i n a r i n g , i t cannot p o s s i b l y be matched to a molecular fragment t h a t i s con­ t a i n e d i n a r i n g system. The a c t u a l information contained i n any one s u b s t r u c t u r a l des­ c r i p t o r depends h i g h l y upon the judgement o f the person s e l e c t i n g the substructure l i b r a r y , i n some a p p l i c a t i o n s , good d e s c r i p t o r s can be obtained immediately because s u f f i c i e n t a p r i o r i knowledge e x i s t s . However, i n other cases, a t r i a l - a n d - e r r o r procedure may be warranted where a l a r g e number o f p o s s i b l e substructures are generated and poor d e s c r i p t o r s are e l i m i n a t e d by some prescreening criterion. In g e n e r a l , substructure d e s c r i p t o r s serve a very im­ p o r t a n t purpose i n t h a t they r e s t o r e a p o r t i o n o f the s t r u c t u r a l information l o s t i n the atom and bond fragmentation. Nevertheless, considerable s t r u c t u r a l information i s s t i l l missing. (c) Environment D e s c r i p t o r s . The d e s c r i p t i o n of s t r u c t u r e s using fragment and substructure d e s c r i p t o r s i n d i c a t e the components o f a molecule. However, the manner i n which these i n d i v i d u a l p a r t s are connected i s not d e s c r i b e d . Environment d e s c r i p t o r s take i n t o account how d i f f e r e n t areas o f a molecule f i t together and provide a measure o f the "environment" i n which a s i n g l e atom fragment finds i t s e l f . The environment d e s c r i p t o r describes the fragment's surround­ ings by i n c l u d i n g i t s f i r s t and second nearest neighbors and t h e i r bonds i n t o a s i n g l e parameter which r e f l e c t s the atom and bond types connected t o i t . There may be more than one i d e n t i c a l f r a g ­ ment i n a molecule but they do not n e c e s s a r i l y belong to the same f u n c t i o n a l group. For example, the fragment, -C-, i s found once i n both s t r u c t u r e s A and Β below, but twice i n s t r u c t u r e C: Ο

OU

t\ CH -C-0-CH 3

C = CH - CH

3

CH (A)

0 II

l 3

CH ~ 3

CH. ,

C - CH ~ 2

3

CH = C CH

3

(B)

3

(C)

Obviously, the environment seen by t h i s fragment would be d i f f e r ­ ent i n each o f the three cases. Of course, t h i s d i f f e r e n c e i s de­ pendent upon the d e f i n i t i o n incorporated t o c a l c u l a t e the e n v i r o n ­ ment d e s c r i p t o r . In the ADAPT system, the three forms most o f t e n used are: bond environment d e s c r i p t o r s (BED), weighted e n v i r o n ­ ment d e s c r i p t o r s (WED), and augmented environment d e s c r i p t o r s (AED).

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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The procedure used t o c a l c u l a t e these three parameters f o r a p a r t i c u l a r environment fragment i s as f o l l o w s : (1) A s s i g n a r b i t r a r y values t o each type o f atom and bond. The v a l u e s already employed i n the connection t a b l e w i l l suffice. (2) For "BED", sum the number o f bonds connected t o the f r a g ­ ment's f i r s t and second nearest neighbor. (3) For "WED", sum the values assigned t o each bond type i n ­ stead o f merely counting the bonds. (4) For "AED", sum the product o f the bond's assigned value and the assigned values f o r the two atoms which form the bond. The BED, WED, and AED v a l u e s f o r the fragment and s t r u c t u r e s g i v e n above are as f o l l o w s : f o r s t r u c t u r e A, BED = 5, WED = 6, AED = 11; f o r s t r u c t u r e B, BED = 5, WED = 6, AED = 6; f o r s t r u c t u r e C., BED = 12, WED = 15, AED = 17. Since there may be more than one fragment p r e s e n t , the en­ vironment d e s c r i p t o r i n d i c a t e s the sum o f a l l the environments f o r a given fragment. T h i s f e a t u r e makes them u s e f u l when used i n con­ j u n c t i o n with s u b s t r u c t u r e d e s c r i p t o r s . The s u b s t r u c t u r e d e s c r i p ­ t o r s i n d i c a t e the number o f times a p a r t i c u l a r fragment i s found i n the molecule and the environment d e s c r i p t o r s i n d i c a t e the con­ t e x t i n which the fragment i s found. The r o u t i n e t h a t generates the environment d e s c r i p t o r s must have access t o the f i l e o f molecular s t r u c t u r e s and t o the atom centered fragment l i b r a r y which i s c o n s t r u c t e d by the user. The a c t u a l c a l c u l a t i o n o f the environment d e s c r i p t o r s proceeds extrem­ e l y r a p i d l y s i n c e both the fragment l o c a t i o n and necessary c a l c u ­ l a t i o n s are e a s i l y done by a computer. The concept o f the environment i s not l i m i t e d t o c o n n e c t i v i t ­ i e s , but c o u l d take i n t o account e l e c t r o n d e n s i t i e s , bond d i s t a n c e s , e l e c t r o n e g a t i v i t i e s , o r other p h y s i c a l parameters. T h i s can be done by r e p l a c i n g the v a l u e s assigned i n step one by the d e s i r e d parameters. In t h i s manner, more i n f o r m a t i v e d e s c r i p t o r s may be obtained. Use o f the environment d e s c r i p t o r s may r e v e a l r e l a t i o n s which are not p a r t i c u l a r l y obvious. Note t h a t both s t r u c t u r e s A and Β have the same BED and WED v a l u e s . These s t r u c t u r e s , which a t f i r s t glance appear q u i t e d i f f e r e n t , do indeed have these parameters i n common. However, when one takes i n t o account the type o f atoms connected t o these bonds the d i f f e r e n c e becomes apparent. Such r e l a t i o n s h i p s may o r may not prove s i g n i f i c a n t . Their ultimate u t i l i t y depends on the type o f environment measure, the molecule being coded, and the problem being attacked. (d) Geometric D e s c r i p t o r s . Geometric d e s c r i p t o r s are d e r i v ­ ed from the three-dimensional c o n f i g u r a t i o n as generated by MOLMEC. P r e s e n t l y , two b a s i c types o f geometric d e s c r i p t o r s are c a l c u l a t e d from the molecular s t r u c t u r e s . The three p r i n c i p a l axes o f the molecule form the b a s i s f o r the f i r s t type o f geometric d e s c r i p t o r . Since the o r i e n t a t i o n o f the o r i g i n a l molecule i n space i s

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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e s s e n t i a l l y random, the r a d i i must be s o r t e d i n some manner. T h i s i s done by a r b i t r a r i l y a s s i g n i n g X t o the longest r a d i u s , Y t o the second longest r a d i u s , and Ζ t o the s h o r t e s t r a d i u s . Once s o r t e d , the three r a t i o s , X/Y; X/Z and Y/Z, are a l s o c a l c u l a t e d . Due t o t h e i r small values, a l l o f the r a d i i are m u l t i p l i e d by some con­ s t a n t s c a l i n g f a c t o r t o prevent l o s s o f information during t r u n ­ c a t i o n . These s i x geometric parameters are then used as new des­ c r i p t o r s and c o n s t i t u t e t h e f i r s t s e t o f geometric d e s c r i p t o r s . The van der Waals volume o f a molecule i s the other type o f geometric d e s c r i p t o r generated i n the ADAPT system. Before t h i s c a l c u l a t i o n can be done, the bond d i s t a n c e s and the van der Waals r a d i i o f the atoms must be known. The bond d i s t a n c e s are e a s i l y obtained from the molecular modelling r e s u l t s . For the van d e r Waals r a d i i , an a r t i c l e p u b l i s h e d by A. Bondi (42) was consulted. The volume occupied by an atom i s taken as t h a t o f a sphere with r a d i u s equal t o the van der Waals r a d i u s o f the atom minus the volume o f o v e r l a p with adjacent atoms. The o v e r l a p volumes a r e c a l c u l a t e d from standard s p h e r i c a l geometry formulas. The a c t u a l volume i s not found f o r two reasons: the assumption o f sphere and s p h e r i c a l segments i s not t o t a l l y c o r r e c t , and the r a d i i used were s e l e c t e d as being the "best" values from a l a r g e c o l l e c t i o n o f data using an e m p i r i c a l s e l e c t i o n method. The t o t a l molecular v o l ­ ume f o r the molecule i s taken as the sum o f the c o n t r i b u t i o n s f o r each atom found as d e s c r i b e d above. The volume c o n t r i b u t i o n s o f attached hydrogens are a l s o i n c l u d e d i n the c a l c u l a t i o n o f the t o t a l volume. In order t o make the r o u t i n e more v e r s a t i l e , the o p t i o n o f e i t h e r using standard bond d i s t a n c e s o r modelled bond d i s t a n c e s i s i n c l u d e d . Since MOLMEC uses the standard bond d i s t a n c e s t o d e t e r ­ mine a low s t r a i n geometry, i t i s not s u r p r i s i n g t h a t f o r a w e l l modelled data s e t , the molecular volumes c a l c u l a t e d using the two d i f f e r e n t bond d i s t a n c e s are very s i m i l a r . However, d i s c r e p a n c i e s can a r i s e when the molecule contains r i n g s o f f i v e o r fewer atoms which cause a l a r g e amount o f bond s t r a i n . The volumes are i n i t i ­ a l l y c a l c u l a t e d i n u n i t s o f c u b i c Angstroms per atom but are then converted t o u n i t s o f c c per mole. The molecular volume can then be used as another geometric d e s c r i p t o r . Each geometric d e s c r i p t o r contains some information about the molecule. The r a d i i and r a t i o s d e s c r i b e the general shape o f the molecule which may be very important i n systems where receptor s i t e s are i n v o l v e d . However, t h i s i s only a r e l a t i v e shape s i n c e the model obtained i s f o r the molecule i n a vacuum: i n some environments, the molecule's shape w i l l change, e s p e c i a l l y i f long chains are present. On the other hand, the molecular volume i s e s s e n t i a l l y constant r e g a r d l e s s o f how the molecule i s bent. How­ ever, l i k e any other d e s c r i p t o r , the a c t u a l value o f any geometric d e s c r i p t o r depends upon the s p e c i f i c a p p l i c a t i o n i n which i t i s used. (5)

Collator.

The c o l l a t o r r o u t i n e i s used t o s e l e c t which o f the

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9. STUPER ET AL.

Structure-Activity

Studies

183

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a v a i l a b l e d e s c r i p t o r s w i l l be i n c l u d e d i n the data s e t t o be passed t o other p a r t s o f ADAPT, The experimenter has complete f l e x i b i l i t y i n d e c i d i n g which data s e t o r subset t o use and how t o s t r u c t u r e problems when they are t o be passed t o the p r i o r f e a t u r e s e l e c t i o n algorithms o f the d i s c r i m i n a n t development algorithms. T h i s r o u t i n e i s used t o s e l e c t f i r s t one subset o f the a v a i l a b l e d e s c r i p t o r s t o be used f o r d i s c r i m i n a n t development, and then on subsequent t r i a l s other subsets o f d e s c r i p t o r s . Thus, o v e r a l l performance o f the system can be evaluated with respect t o which d e s c r i p t o r s a r e being i n c l u d e d i n the a n a l y s i s . (6) Preprocessor. The preprocessor r o u t i n e accepts the raw desc r i p t o r s developed by the d e s c r i p t o r development r o u t i n e s and p e r forms the d e s i r e d preprocessing necessary f o r f u r t h e r p r o c e s s i n g . One example o f such p r e p r o c e s s i n g i s a u t o s c a l i n g , where each desc r i p t o r over a data s e t i s a l t e r e d so t h a t the mean i s zero and the standard d e v i a t i o n i s u n i t y . The s t a t i s t i c s l i t e r a t u r e c a l l s t h i s procedure s t a n d a r d i z i n g t h e v a r i a b l e s . (7) P r i o r Feature S e l e c t i o n . A f t e r a s e t o f drugs have been formed i n t o a l a b e l l e d data s e t ready f o r p r e s e n t a t i o n t o the d i s criminant developer, i t i s d e s i r a b l e t o submit i t t o feature s e l e c t i o n i f p o s s i b l e . One method f o r s e l e c t i n g the d e s c r i p t o r s expected t o be most u s e f u l has been the use o f the well-known F i s h e r r a t i o (e_.£., 21). A number o f other s t a t i s t i c a l l y based methods suggest themselves, but they mostly r e q u i r e making the assumption t h a t the b e s t , i..e_., most s e p a r a t i n g , d e s c r i p t o r s i d e n t i f i e d one a t a time w i l l a l s o be the best s e t o f d e s c r i p t o r s . T h i s assumption i s r a r e l y v a l i d . In the s t u d i e s performed t o date, we have u s u a l l y t r i e d t o s e l e c t subsets o f d e s c r i p t o r s i n as wise a manner as we c o u l d devise; we have r e l i e d on being able t o i n v e s t i g a t e a l a r g e enough number o f subsets o f d e s c r i p t o r s t o f e e l reasonably c o n f i d e n t t h a t we have found good d e s c r i p t o r s e t s . Feature s e l e c t i o n i s performed as an i n t e g r a l p a r t o f s t e p wise descriminant a n a l y s i s such as t h a t implemented i n the BMD (43) package as BMD07M. T h i s w i l l be d i s c u s s e d l a t e r i n the s e c t i o n on d i s c r i m i n a n t development and feedback feature s e l e c t i o n . (8) D i s c r i m i n a n t Developer. The d i s c r i m i n a n t developer accepts the s e t o f data generated by the previous s e c t i o n s o f ADAPT and attempts t o develop d i s c r i m i n a n t f u n c t i o n s capable o f c o r r e c t l y c l a s s i f y i n g t h e data. The development o f such d i s c r i m i n a n t s can proceed through the use o f (a) e r r o r c o r r e c t i o n feedback l e a r n i n g machines, (b) i n t e r a c t i v e l e a s t squares development o f l i n e a r d i s criminant f u n c t i o n , (c) other parametric and nonparametric r o u t i n e s . The e r r o r c o r r e c t i o n feedback t r a i n i n g method has been used i n the s t u d i e s on b a r b i t u r a t e s t o be d e s c r i b e d i n the f o l l o w i n g s e c t i o n o f this article. The i t e r a t i v e l e a s t squares development method was developed s e v e r a l years ago i n t h i s l a b o r a t o r y (44) and has been

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i n t e r f a c e d i n t o ADAPT, (9) Feedback Feature S e l e c t i o n . In many chemical a p p l i c a t i o n s o f p a t t e r n r e c o g n i t i o n a s e t of data i s coded using more d e s c r i p t o r s than are necessary t o c o r r e c t l y c l a s s i f y the members. However, the necessary and unnecessary d e s c r i p t o r s cannot u s u a l l y be i d e n t ified a priori. (When they can, t h i s i s o b v i o u s l y the method o f choice.) Therefore, feature s e l e c t i o n must o f t e n be approached from a systems viewpoint, whereby the r e s u l t s o f c l a s s i f i c a t i o n are used to t r y to i d e n t i f y the minimal s e t o f necessary d e s c r i p t o r s . T h i s approach i s shown by the feedback loop i n Figure 2. An e a r l y approach to feedback feature s e l e c t i o n was weights i g n feature s e l e c t i o n . Here, two weight v e c t o r s , i n i t i a l i z e d with each component equal to +1 or -1, r e s p e c t i v e l y , were developed using e r r o r c o r r e c t i o n feedback t r a i n i n g with i d e n t i c a l t r a i n i n g s e t s . A component by component comparison was made between the two t r a i n e d weight v e c t o r s , and those d e s c r i p t o r s correspondi n g t o weight v e c t o r components with s i g n disagreements were d i s carded. T h i s method was shown to be e f f e c t i v e f o r some c l a s s e s of data i n s e v e r a l s t u d i e s . The variance feature s e l e c t i o n method, d e s c r i b e d e a r l i e r , has been incorporated i n t o ADAPT and has been used e f f e c t i v e l y on s e v e r a l types of data. The variance method allows r a p i d e x t r a c t i o n o f f e a t u r e s r e s p o n s i b l e f o r l i n e a r seperability. I t i s much s u p e r i o r t o the weight-sign method i n terms of speed and r e l i a b i l i t y . B a r b i t u r a t e Study The s e t o f compounds used i n the present study c o n s i s t s o f 160 5,5·-substituted b a r b i t u r a t e s s e l e c t e d from a standard r e f e r ence (290 . These compounds range i n molecular weight from 172 t o 276 and have d u r a t i o n times ranging from 10 minutes to 600 minutes. The method of a d m i n i s t r a t i o n was e i t h e r i n t r a p e r i t o n e a l o r subcutaneous, using mice, r a t s , o r r a b b i t s as t e s t animals. The compounds were grouped i n t o c l a s s e s according to the dura t i o n o f depressant e f f e c t . These c l a s s e s were formed by d i v i d i n g the d u r a t i o n time expressed i n minutes by ten. The r e s u l t i n g c l a s s d e s i g n a t i o n was rounded up i f the remainder was f i v e o r g r e a t e r , and down otherwise. Thus a compound whose duration time was 227 minutes would be p l a c e d i n c l a s s 23, whereas a compound having a d u r a t i o n time o f 223 minutes would be p l a c e d i n t o c l a s s 22. Compounds with a d u r a t i o n greater than 650 minutes were p l a c e d i n t o c l a s s 65. T h i s r e s u l t e d i n a t o t a l o f 65 d i f f e r e n t c l a s s e s which are d i s t r i b u t e d as shown i n F i g . 3. Three types o f d e s c r i p t o r s were employed f o r these s t u d i e s ; numeric fragment d e s c r i p t o r s , s u b s t r u c t u r a l d e s c r i p t o r s , and environmental d e s c r i p t o r s . The d e s c r i p t o r s were generated using the automated d e s c r i p t o r packages d e s c r i b e d p r e v i o u s l y . A l i s t o f the i n i t i a l s e t of d e s c r i p t o r s used i s given i n Table 1. Each d e s c r i p t o r i s contained i n a minimum o f 20% o f the s t r u c t u r e s . In no case

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

9.

STUPER ET

AL.

Structure-Activity Studies

Numerical Prior Descriptors — F e a t u r e —Preprocessing Selection

Di scrimi nant Resu1ts Function —». of ^Development -, Analysis



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Figure 2.

185

Feedback Feature Selection

Basic pattern recognition system for studies of structure-activity relationships

I2H

ΙΟ

ω

3

2\

200

1

400

600

DURATION TIME (MIN.)

Figure 3.

Histogram of barbiturate duration times for the drugs in the data set

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

186

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TABLE I·

Molecular S t r u c t u r e D e s c r i p t o r s f o r the B a r b i t u r a t e Data Set

ATOM AND BOND DESCRIPTORS

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1 3 5 7

Number Number Number Number

of of of of

atoms Carbon atoms Oxygen atoms double bonds

2 4 6 8

Number o f bonds Number o f Nitrogen atoms Number o f s i n g l e bonds Length a

ENVIRONMENT DESCRIPTORS 15

Atom Centered Fragment

General

9 - 11

CH -

1, 2, 3

12 - 14

-CH -

1, 2, 3

15 - 17

-CH-

1, 2, 3

3

2

24 - 26

I -C I 0 =

1, 2, 3

27 - 29

-HC =

1, 2, 3

30 - 35

>C -

1, 2, 3

18 - 23

Cyclic

1, 2, 3

1, 2, 3

1, 2, 3

SUBSTRUCTURAL DESCRIPTORS 36

C H

3

C H

39 42

a

b

-CH-

2"

37

-CH (CH )CH -

38

CH -

40

-CH CH -

41

CH CH CH -

43

-HC =

2

3

2

2

3

3

2

2

L e n g t h * 4*(Number o f s i n g l e bonds) + 2*(Number o f double bonds) l

» BED, 2 » WED, 3 » AED

In Chemometrics: Theory and Application; Kowalski, B.; ACS Symposium Series; American Chemical Society: Washington, DC, 1977.

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STUPER ET AL.

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does any one d e s c r i p t o r , o r any b i n a r y combination o f d e s c r i p t o r s , c o n t a i n s u f f i c i e n t information to s u c c e s s f u l l y c l a s s i f y the data. Thus the a c t i v e data s e t c o n s i s t s o f 160 compounds each coded with 43 d e s c r i p t o r s . Preprocessing o f the raw data p r i o r t o c l a s s ­ i f i c a t i o n c o n s i s t e d o f a u t o s c a l i n g so t h a t each d e s c r i p t o r had an average o f zero and a standard d e v i a t i o n o f 127. T h i s allowed the data t o be truncated to i n t e g e r values with a n e g l i g i b l e l o s s o f precision. (Loss of p r e c i s i o n i s known t o be n e g l i g i b l e as r e c a l ­ c u l a t i o n a f t e r t r u n c a t i o n y i e l d e d a standard d e v i a t i o n o f 127 and a mean o f 0 +0.17.) Net r e t e n t i o n o f information was assured by t e s t i n g the p r e d i c t i v e a b i l i t y f o r each d e s c r i p t o r before and a f t e r preprocessing. A value o f 250 was used f o r X + i because i t p r o v i d ­ ed f a s t t r a i n i n g and high p r e d i c t i v e a b i l i t y . Since the data were c o l l e c t e d from a s e r i e s o f s t u d i e s on d i f f e r e n t animals, a t d i f f e r e n t l a b o r a t o r i e s , i t i s not unreason­ able to expect the c l a s s i f i c a t i o n s to d i f f e r . I t was t h e r e f o r e f e l t t h a t an e r r o r range would take i n t o account the v a r i a t i o n s due t o d i f f e r e n t c l a s s i f i c a t i o n methods. Thus, any one c l a s s i f i e r w i l l develop a r u l e which answers the question, "Is the d u r a t i o n time l e s s than χ minutes?", where there i s a deadzone o f s e v e r a l minutes around t h i s l e v e l . Thus, t o t e s t f o r d i s c r i m i n a t i o n a b i l ­ i t y a t a t h r e s h o l d l e v e l o f 100 minutes using a t h i r t y minute deadzone, a l l members from c l a s s e s 1 through 10 would c o n s t i t u t e one category, and a l l members from 14 through 65 would c o n s t i t u t e the other category. The l i n e a r l e a r n i n g machine was used to develop d i s c r i m i n a n t f u n c t i o n s which b i s e c t the data with as many d i f f e r e n t thresholds as p o s s i b l e , o b t a i n i n g 100% r e c o g n i t i o n a b i l i t y f o r each range. Attempts a t such d i s c r i m i n a t i o n were accomplished using f i r s t a f i f t y , and l a t e r a t h i r t y , minute e r r o r range. To generate a p r e l i m i n a r y estimate o f the c l u s t e r i n g and s e l f consistency of the data the f o l l o w i n g experiment was done. F i v e t r a i n i n g s e t / p r e d i c t i o n s e t s were chosen with seven compounds i n each p r e d i c t i o n s e t and the remaining compounds i n each t r a i n i n g set. The o v e r a l l data s e t i s d i v i s i b l e i n t o halves by 59 t h r e s ­ holds using 50 minute e r r o r ranges. A l l f i v e t r a i n i n g s e t s were used to develop independent d i s c r i m i n a n t s a t each o f the 59 t h r e s ­ holds. These d i s c r i m i n a n t s were then used to p r e d i c t the seven unknowns i n the r e s p e c t i v e p r e d i c t i o n s e t . The c l a s s assignments were made by examining the sequence o f responses produced by the 59 p r e d i c t i o n s ; i f only one change from answers o f "greater than" t o " l e s s than" occurred, t h i s p o i n t was taken as the p r e d i c t e d d u r a t i o n time. I f there were s e v e r a l changes i n p r e d i c t e d r e s ­ ponse, then the p r e d i c t e d duration time was taken as 30 minutes greater than the s h o r t e s t d u r a t i o n time i n d i c a t e d by the f i r s t change i n response. When t h i s procedure was used, 19 o f the 35 unknowns were c l a s s i f i e d as having duration times w i t h i n 20 min­ utes o f the a c t u a l value and 31 were c l a s s i f i e d as having d u r a t i o n times w i t h i n 50 minutes o f the a c t u a l value. The d u r a t i o n times

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n

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TABLE I I .

F i n a l Sets o f Molecular S t r u c t u r e D e s c r i p t o r s Supporting L i n e a r D i s c r i m i n a n t Functions a t Thresholds I and I I .

THRESHOLD I

THRESHOLD I I

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ATOM AND BOND DESCRIPTORS Number o f Oxygen atoms

Number o f Oxygen atoms

Number o f double bonds

Number o f s i n g l e bonds

SUBSTRUCTURAL DESCRIPTORS

ENVIRONMENT DESCRIPTORS

CHo-

CH -(G,2) 3

ι -CH-(G,1)

-CH 2

-CH CH -

-HO(G,2)

CH CH -

>C=(G 3) (C,l)

2

3

2

f

2

Average Predictive Ability b

a

ATOM AND BOND DESCRIPTORS

G = General

93.8%

0

SUBSTRUCTURAL DESCRIPTORS

ENVIRONMENT DESCRIPTORS

CHo

-HC-(G,1) -HC=(G,1)

—CH CH ~ 2

2

i >C=(G,3) -C(C,3) i -CH CH (CH )2

3

Average Predictive Ability

94.9%

1 3

search, C = C y c l i c search, 1 = BED, 2 = WED, 3 = AED

^ P r e d i c t i v e a b i l i t y measured using leave one out procedure

o f only four compounds were i n e r r o r by more than 50 minute e r r o r range used f o r each t h r e s h o l d . Thus t h i s p r e l i m i n a r y experiment showed t h a t a s e t o f l i n e a r c l a s s i f i e r s working i n concert c o u l d p r e d i c t the d u r a t i o n times o f the compounds i n the data s e t reas­ onably a c c u r a t e l y . S i m i l a r r e s u l t s were obtained f o r the 61 poss­ i b l e thresholds developed using a 30 minute e r r o r range. In order t o g a i n a b e t t e r i n s i g h t i n t o these r e l a t i o n s h i p s two thresholds were s u b j e c t t o exhaustive f e a t u r e s e l e c t i o n . The t h r e s h o l d I data i n c l u d e s c l a s s e s 1 through 10 and 14 through 65. The t h r e s h o l d I I data i n c l u d e s c l a s s e s 1 through 24 and 28 through

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65. The r e s u l t s o f the s e l e c t i o n process and a p r e d i c t i v e a b i l i t y e s t i m a t i o n i s reported i n Table I I , Through a p p l i c a t i o n o f the variance feature s e l e c t i o n method, a s e t o f features r e s p o n s i b l e f o r t h e s e p a r a b i l i t y o f the data were found. Removing any o f these d e s c r i p t o r s r e s u l t s i n the l o s s of l i n e a r s e p a r a b i l i t y . Therefore, the d e s c r i p t o r s s e l e c t e d cons t i t u t e a minimum set capable o f supporting the r e l a t i o n s h i p w i t h i n the data. The p r e d i c t i v e a b i l i t y , estimated by the leave one out procedure (45), i n d i c a t e d that these f e a t u r e s were capable o f p r o v i d i n g accurate information concerning the d u r a t i o n o f b a r b i t urate a c t i v i t y . Thus, i t i s c l e a r t h a t a r e l a t i o n s h i p i s present which i s r e a d i l y i d e n t i f i e d using the ADAPT system. Further i n v e s t i g a t i o n s using t h i s data set have uncovered several interesting correlations. D e t a i l s o f the experimental r e s u l t s a r e reported elsewhere (46). What has been sought f o r here i s a c l e a r demonstration o f the u t i l i t y o f ADAPT i n e l l u c i d a t i n g r e l a t i o n s w i t h i n a l a r g e body o f data. Note t h a t feature s e l e c t i o n o f the two s p e c i f i c thresholds was e a s i l y accomplished as was i n i t i a l development o f d i s c r i m i n a n t s f o r 61 d i f f e r e n t classes. C l e a r l y such s t u d i e s would be inconvenient without the degree o f o r g a n i z a t i o n provided by automation o f the d e s c r i p t i v e , storage, and p a t t e r n r e c o g n i t i o n techniques. The ADAPT system has c o n s i s t e n t l y shown high u t i l i t y i n s e v e r a l areas and promises t o continue t o a i d i n the a p p l i c a t i o n o f p a t t e r n r e c o g n i t i o n t o problems i n chemistry.

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