Computers in Flavor and Fragrance Research - American Chemical

4 Mathematical Approaches for Quantitative Design of Odorants and Tastants SUSAN S. SCHIFFMAN

Downloaded by UNIV LAVAL on May 5, 2016 | http://pubs.acs.org Publication Date: August 22, 1984 | doi: 10.1021/bk-1984-0261.ch004

Duke Medical Center, Department of Psychiatry, Durham, N C 27710

Odor and taste q u a l i t y can be mapped by multidimensional scaling (MDS) techniques. Physicochemical parameters can be related to these maps by a variety o f mathematical methods including multiple regression, canonical correlation, and partial l e a s t squares. These approaches t o s t u d y i n g QSAR ( q u a n t i t a t i v e structure-activity relationships) in the c h e m i c a l senses, along w i t h procedures developed by the p h a r m a c e u t i c a l i n d u s t r y , may ultimately be u s e f u l in d e s i g n i n g f l a v o r compounds by computer.

I t i s n o t y e t p o s s i b l e t o design a m o l e c u l e w i t h s p e c i f i c odor (or t a s t e ) c h a r a c t e r i s t i c s because t h e r e l a t i o n s between sensory p r o p e r t i e s o f f l a v o r compounds and t h e i r m o l e c u l a r p r o p e r t i e s a r e not w e l l understood. As a consequence, t h e development o f compounds w i t h d e s i r e d f l a v o r q u a l i t i e s h a s h a d t o r e l y o n r e l a t i v e l y t e d i o u s s y n t h e t i c approaches. Recent advances, however, i n computer-based methods developed by t h e p h a r m a c e u t i c a l i n d u s t r y t o s t u d y QSAR ( q u a n t i t a t i v e 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 h i p s ) may u l t i m a t e l y be h e l p f u l i n t h e r a t i o n a l d e s i g n o f new f l a v o r - s t r u c t u r e s w i t h p r e d i c t a b l e s e n s o r y a t t r i b u t e s . R e s u l t s f r o m QSAR s t u d i e s may a l s o p r o v i d e i n s i g h t i n t o t h e mechanism o f t h e m o l e c u l e - r e c e p t o r i n t e r a c t i o n . QSAR s t u d i e s o f f l a v o r m o l e c u l e s r e q u i r e t w o t y p e s o f d a t a as i n p u t : 1. Q u a n t i t a t i v e measures obtained i n psychophysical experiments that describe the sensory p r o p e r t i e s o f the molecules. 2. Physicochemical parameters that provide a d e s c r i p t i o n of t h e m o l e c u l a r p r o p e r t i e s r e l e v a n t t o t h e f l a v o r properties. U n d e r s t a n d i n g t h e r e l a t i o n s b e t w e e n t h e p s y c h o p h y s i c a l and p h y s i c o c h e m i c a l p r o p e r t i e s c a n be a c h i e v e d b y a v a r i e t y o f m a t h e m a t i c a l methods d e s c r i b e d i n t h i s paper. 0097-6156/ 84/ 0261 -0033506.00/0 © 1984 American Chemical Society

Warren and Walradt; Computers in Flavor and Fragrance Research ACS Symposium Series; American Chemical Society: Washington, DC, 1984.

34

COMPUTERS IN FLAVOR AND

Obtaining q u a n t i t a t i v e sensory data. In the past, the q u a n t i f i c a t i o n o f o d o r (and t a s t e ) q u a l i t y has r e l i e d upon r a t i n g s on v e r b a l d e s c r i p t o r s . T h i s a p p r o a c h has s e v e r a l d r a w b a c k s i n t h a t : (a) i t i s h i g h i n e x p e r i m e n t e r c o n t a m i n a t i o n b e c a u s e a p r i o r i a s s u m p t i o n s m u s t be made a b o u t t h e r e l e v a n t a t t r i b u t e s and (b) t h e r e i s c o n s i d e r a b l e v a r i a b i l i t y among s u b j e c t s because of i n d i v i d u a l d i f f e r e n c e s i n i n t e r p r e t a t i o n of t h e m e a n i n g s and r e l a t i v e i m p o r t a n c e o f t h e w o r d s . The r e c e n t l y d e v e l o p e d m e t h o d o l o g y o f m u l t i d i m e n s i o n a l s c a l i n g (MDS) o v e r c o m e s t h e s e d r a w b a c k s by u s i n g d i r e c t m e a s u r e s o f s i m i l a r i t y as i n p u t (1). i s i m p l y a m a t h e m a t i c a l t o o l t h a t uses e x p e r i m e n t a l j u d g m e n t s o f p e r c e i v e d f l a v o r s i m i l a r i t y t o d e r i v e a map that r e p r e s e n t s t h e t a s t e o r s m e l l q u a l i t i e s o f s p e c i f i c m o l e c u l e s as p o i n t s i n a space. Compounds j u d g e d s i m i l a r i n t a s t e ( o r o d o r ) s e n s a t i o n a r e a r r a n g e d by MDS p r o c e d u r e s c l o s e t o one a n o t h e r i n a r e s u l t a n t s p a t i a l map; t h o s e d i s s i m i l a r a r e l o c a t e d f a r f r o m one a n o t h e r . An e x a m p l e f r o m g e o g r a p h y i l l u s t r a t e s how MDS p r o c e d u r e s work. Maps o f t h e U n i t e d S t a t e s f r e q u e n t l y g i v e t a b l e s o f i n t e r c i t y d i s t a n c e s among m a j o r c i t i e s . I f MDS w e r e a p p l i e d t o a l l c o m b i n a t i o n s of d i s t a n c e s between these c i t i e s , the a n a l y s i s w o u l d a c c u r a t e l y r e c o v e r t h e u n d e r l y i n g s t r u c t u r e , t h a t i s , a map o f t h e c i t i e s i n p r o p e r r e l a t i o n s h i p t o one a n o t h e r . The d i f f e r e n c e b e t w e e n g e o g r a p h i c a l and f l a v o r s p a c e s i s s i m p l y t h a t we don't know a p r i o r i w h a t f l a v o r s p a c e s l o o k l i k e . T h e r e a r e many ways t o o b t a i n d i s t a n c e - l i k e m e a s u r e s among f l a v o r compounds. F i r s t , s t i m u l i a r e g e n e r a l l y e q u a t e d i n s u b j e c t i v e i n t e n s i t y so t h a t j u d g m e n t s a r e b a s e d on q u a l i t y r a t h e r t h a n i n t e n s i t y . O d o r a n t s a r e d i l u t e d i n an o d o r l e s s g r a d e o f d i e t h y l p h t h a l a t e and t a s t a n t s , i n d e i o n i z e d w a t e r . Then s u b j e c t s r a t e a l l the n ( n - l ) / 2 p o s s i b l e p a i r s f o r a set of η s t i m u l i a l o n g an u n d i f f e r e n t i a t e d 5" l i n e : M D S


FRAGRANCE RESEARCH

exact same

8

most different

S i m i l a r i t y m e a s u r e s c a n a l s o be o b t a i n e d u s i n g a 10 p o i n t s c a l e (e.g., f r o m 1 t o 10) o r by o b t a i n i n g c o n f u s a b i l i t i e s among triads. Odorants (or t a s t a n t s ) confused most f r e q u e n t l y are c o n s i d e r e d more s i m i l a r . M i s s i n g d a t a d e s i g n s c a n be u s e d t o r e d u c e t h e number o f a c t u a l s t i m u l u s p r e s e n t a t i o n s . The s i m i l a r i t y j u d g m e n t s a r e t h e n a n a l y z e d by one o f a number o f s p e c i a l l y d e s i g n e d c o m p u t e r p r o g r a m s t h a t have b e e n d e t a i l e d by S c h i f f m a n , R e y n o l d s and Young (1). Some p r o g r a m s , s u c h as INDSCAL, ALSCAL, and MULT IS CALE, n o t o n l y p r o v i d e m u l t i d i m e n s i o n a l a r r a n g e m e n t s o f m o l e c u l e s b a s e d on t h e i r f l a v o r s i m i l a r i t y but p r o v i d e q u a n t i t a t i v e measures t h a t d e l i n e a t e the i n d i v i d u a l d i f f e r e n c e s i n r e s p o n s e f o r e a c h s u b j e c t as w e l l . The


4.

SCHIFFMAN

35

Design of Odorants and Tastants

maps o b t a i n e d by MDS c a n be i n t e r p r e t e d by a v a r i e t y o f s t a t i s t i c a l techniques, including m u l t i p l e regression, canonical c o r r e l a t i o n , p a r t i a l l e a s t s q u a r e s , and a v a r i e t y o f o t h e r methods t o d e t e r m i n e those p r o p e r t i e s o f m o l e c u l e s r e s p o n s i b l e f o r t h e i r f l a v o r p r o p e r t i e s ; these approaches a r e d e s c r i b e d below. O b t a i n i n g r e l e v a n t p h y s i c o c h e m i c a l parameters. The c h o i c e o f p h y s i c o c h e m i c a l p a r a m e t e r s t o r e l a t e t o MDS s p a c e s i s c r u c i a l i f t h e p r o p e r t i e s f o u n d t o be m a t h e m a t i c a l l y i m p o r t a n t a r e i n d e e d appropriate chemical p r e d i c t o r s f o r future design of molecules w i t h d e s i r e d f l a v o r p r o p e r t i e s . U n f o r t u n a t e l y , we o f t e n have no i d e a what p h y s i c o c h e m i c a l p r o p e r t i e s a r e i n d e e d i m p o r t a n t , a l t h o u g h many o f t h e p a r a m e t e r s d e s c r i b e d i n t h e e x a m p l e s b e l o w as w e l l a s t h o s e g i v e n i n T a b l e I ( s e e 2* 2) probably relevant. H y d r o p h o b i c b o n d i n g , c h a r a c t e r i z e d by t h e o i l - w a t e r p a r t i t i o n c o e f f i c i e n t , has been i m p l i c a t e d i n i n t e n s e sweetness, p e r c e p t i o n o f b i t t e r n e s s , as w e l l a s o d o r i n t e n s i t y . H o w e v e r , i t w i l l be shown i n S t u d y 2 b e l o w t h a t when t h e c o n c e n t r a t i o n s o f p y r i d y l ketones a r e a d j u s t e d t o equal s u b j e c t i v e i n t e n s i t i e s , the p a r t i t i o n c o e f f i c i e n t i s not p a r t i c u l a r l y important i n discriminating qualitative differences. Short range e l e c t r i c a l p r o p e r t i e s such as d i s p e r s i o n bonding a r e probably an i m p o r t a n t s o u r c e o f s p e c i f i c i t y and may e x p l a i n why d i f f e r e n t o d o r q u a l i t i e s a r e produced by i d e n t i c a l s u b s t i t u e n t s a t d i f f e r e n t p o s i t i o n s of a molecule. D i s p e r s i o n bonding i s r e l a t e d t o t h e p o l a r i z a b i l i t y o f m o l e c u l e s and i n v e r s e l y t o t h e s i x t h p o w e r o f t h e i r s e p a r a t i o n . Longer range e l e c t r i c a l f o r c e s , whether i o n i o n , i o n - d i p o l e , o r d i p o l e - d i p o l e a r e a l s o l i k e l y t o be s i g n i f i c a n t . Hydrogen bonding has been i m p l i c a t e d i n sweet perception. C h a r g e t r a n s f e r e f f e c t s s u c h a s e l e c t r o n d o n a t i o n by e t h e r s and many a r o m a t i c compounds a s w e l l a s e l e c t r o n a c c e p t a n c e of m e r c a p t a n s i s p r o b a b l y i m p o r t a n t . S t e r i c r e p u l s i o n , though n o t b o n d i n g b u t n e v e r t h e l e s s a n o n - c o v a l e n t i n t e r a c t i o n , may a l s o contribute to specificity.


a

r

e

Examples Four s t u d i e s a r e d e s c r i b e d here t h a t r e l a t e p h y s i c o c h e m i c a l p r o p e r t i e s t o o d o r q u a l i t y as d e f i n e d by maps d e r i v e d by m u l t i d i m e n s i o n a l s c a l i n g procedures. The m a t h e m a t i c a l procedures u s e d t o r e l a t e t h e p h y s i c o c h e m i c a l p r o p e r t i e s t o t h e maps a r e d i s c u s s e d as w e l l . S t u d y 1: Broad range o f odorants. A group o f odorants t h a t v a r i e d w i d e l y i n q u a l i t y and s t r u c t u r e w e r e a r r a n g e d o n t h e b a s i s o f o d o r s i m i l a r i t y i n a t w o d i m e n s i o n a l s p a c e shown i n F i g u r e 1 (4). The s p a c e d e r i v e d i s t w o - d i m e n s i o n a l w i t h a n a f f e c t i v e l y r a t h e r p l e a s a n t subset f a l l i n g t o t h e l e f t and a r a t h e r


Warren and Walradt; Computers in Flavor and Fragrance Research ACS Symposium Series; American Chemical Society: Washington, DC, 1984. ]

S octanol )

Signa values or charge from molecular o r b i t a l calculations

λ

E l e c t r o s t a t i c bonding Interactions between charges : ion-ion, ion-dipole, and dipole-dipole (There i s more s p e c i f i c i t y f o r dipole-dipole interactions than those involving ions.)

[drug]water

[ d r u

Molar r e f r a c t i v i t y χ i o n i z a t i o n potential or molar r e f r a c t i v i t y alone, Hildebrand's molar a t t r a c t i o n constant, or parachor

(where Ρ *=

Log Ρ

Physical properties correlated with strength

Dispersion bonding London forces, induced dipole-induced dipole bond (Although a molecule may not have a permanent dipole, an instantaneous dipole can r e s u l t from v i b r a t i o n of electrons r e l a t i v e to the nucleus and ultimately induce a dipole i n a neighbouring molecule. Ehergy of interaction f a l l s o f f at 1/R .)

Hydrophobic bonding (A bond formed because water molecules tend to associate with one another rather than with non-polar molecules. The energy involved i n 'Squeezing out" water i s equivalent to a bond.)

Interaction

Table I. Relation o f parameters t o nonroovalent bonding (adapted from (2), see (3))


Warren and Walradt; Computers in Flavor and Fragrance Research ACS Symposium Series; American Chemical Society: Washington, DC, 1984. Signa values or E(lemo) and E(homo) from molecular o r b i t a l calculations

van der Waals' r a d i i o r Taft Es values

S t e r i c repulsion (Intermolecular forces can be repulsive as w e l l as a t t r a c t i v e i n nature. Two molecules ultimately reach a minimi m distance between then as they approach one another, and t h i s distance i s the sum of the van der Waale' r a d i i of the interacting groups. Hence, the van der Waals' radius i s considered a measure of the e f f e c t i v e s i z e of an atom i n noncovalent interactions. Van der Waals' radius i s correlated w i t h another measure o f s t e r i c repulsion, Es.)

Sane as f o r e l e c t r o s t a t i c bonding; only f o r the atom involved i n the hydrogen bond

Charge transfer bonding (When a molecule w i t h a good electron donor comes i n contact w i t h a molecule which i s a good electron acceptor, the donor may transfer sane of i t s charge t o the acceptor.)

Hydrogen bonding (As a very small hydrogen atom i s the bridge between two electrogegative atoms, the interacting molecules can approach s u f f i c i e n t l y close t o each other t o produce an a t t r a c t i o n strong enough t o be considered a bond, rather than j u s t another dipole-dipole interaction. )



n-Hexyl acetate

Benzothiazole

• n-Caproic acid

J

Hydrogen sulfide

• Skatole

Cyclohexene · •Pyridine

Cyclopentene

•Propionic acid • n- Butyric acid ^Acetic acid Thiophene

•Allyl disulfide

F i g u r e 1. Two-dimensional space f o r a broad range o f odorants. Compounds l o c a t e d c l o s e t o one another have s i m i l a r odor q u a l i t y (from Réf. U).

Citronellol-*

T

alpha erpineol ornyl acetate Butyl alcohol Cyclohexane Acetone Benzene Cyclopentone Butyl alcohol , 'Carbon tetrachloride W

η-Propyl alcohol 'éapnc acid /

•Limonene Guajocol •Turpentine

•Phenol

Menthol •Hydroxycitronellal • Vanillin n-Decyl alcohol i^Geraniol Ethyl alcohol; • •n-Undecyl alcohol •Aldehyde C-14 * f n-Nonyl alcohol Nitrobenzene · φ ^ Dlphenyl methane Citral

Methyl salicylate é · θ η η ο Γ η ι ς aldehyde |6enz aldehyde

•S-8001

• Eugenol

II


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unpleasant group t o the r i g h t . B e c a u s e no s i n g l e f a c t o r ( s u c h as m o l e c u l a r w e i g h t , number o f d o u b l e bonds, o r d i p o l e moment) c o u l d i n d i v i d u a l l y a c c o u n t f o r q u a l i t y , S c h i f f m a n (4) w e i g h t e d a s e r i e s o f v a r i a b l e s shown i n F i g u r e 2 and was a b l e t o r e c a p t u r e 84% o f t h e i n t e r s t i m u l u s d i s t a n c e s i n a two d i m e n s i o n a l space. The m a t h e m a t i c a l p r o c e d u r e u s e d t o m a x i m i z e t h e c o n f i g u r a t i o n a l s i m i l a r i t y i n F i g u r e 1 w i t h a s p a c e g e n e r a t e d by t h e w e i g h t e d p h y s i c o c h e m i c a l p a r a m e t e r s i s b a s e d on a l e a s t squares method i n w h i c h the b a s i c m a t r i x e q u a t i o n s a r e :

« p + κ

f Ρ - DQ Ρ DQ + Downloaded by UNIV LAVAL on May 5, 2016 | http://pubs.acs.org Publication Date: August 22, 1984 | doi: 10.1021/bk-1984-0261.ch004

β

Β

w h e r e : η i s t h e t o t a l number o f s t i m u l i , and Ρ i s a n n ( n - l ) / 2 c o l u m n v e c t o r whose e l e m e n t s p — r e p r e s e n t a l l t h e i n t e r s t i m u l u s d i s t a n c e s b e t w e e n s t i m u l u s i and s t i m u l u s j . The p r o x i m i t y m e a s u r e s b a s e d on w e i g h t e d p h y s i c o c h e m i c a l p a r a m e t e r s a r e g i v e n by P, an n ( n - l ) / 2 c o l u m n v e c t o r . D i s an [ n ( n - l ) / 2 ] by k s c a l a r d i s t a n c e m a t r i x whose e l e m e n t s d r e the squared d i f f e r e n c e s b e t w e e n s t i m u l u s i and J f o r e a c h k p h y s i c o c h e m i c a l p a r a m e t e r . The w e i g h t s f o r k p h y s i c o c h e m i c a l p a r a m e t e r s a r e r e p r e s e n t e d by Q, a k e l e m e n t c o l u m n v e c t o r o f w e i g h t s . Ε i s an n ( n - l ) / 2 column v e c t o r r e p r e s e n t i n g the e r r o r between the s u b j e c t i v e p r o x i m i t i e s and t h e p r o x i m i t i e s b a s e d on p h y s i c o c h e m i c a l measures. The e r r o r t o be m i n i m i z e d i s : a

l e a d i n g t o the l e a s t squares

solution

Q «= ( D ' D ) "

1

D'P

T h i s m e t h o d o l o g y c a n be h e l p f u l i n r e l a t i n g s t r i c t q u a n t i t a t i v e measures of o l f a c t o r y q u a l i t y w i t h q u a n t i t a t i v e p h y s i c o c h e m i c a l m e a s u r e s . However, t h e r e s u l t s f o r t h i s s p e c i f i c s t u d y s u g g e s t t h a t t h e r a n g e of m o l e c u l a r s t r u c t u r e s and o l f a c t o r y q u a l i t y are too broad t o d e r i v e p r a c t i c a l i n f o r m a t i o n for the r a t i o n a l design of molecules w i t h s p e c i f i c f l a v o r qualities. S t u d y 2: P y r i d y l ketones. A n a r r o w e r r a n g e o f compounds, a g r o u p o f p y r i d y l k e t o n e s , was e x a m i n e d by S o u t h w i c k and S c h i f f m a n (5). Two-dimensional c r o s s - s e c t i o n s through the t h r e e d i m e n s i o n a l s p a c e a c h i e v e d by t h e MDS a r e shown i n F i g u r e s 3a and 3b. The f i r e t d i m e n s i o n s e p a r a t e s t h e t h r e e 2 - p y r i d y l k e t o n e s t h a t h a v e p o p c o r n - n u t t y aromas f r o m t h e s i x o t h e r compounds t h a t are green-vegetable i n character.


C O M P U T E R S IN F L A V O R A N D F R A G R A N C E R E S E A R C H


40

MEAN RAMAN INTENSITY

(cm-')

Figure 2. A s e r i e s o f v a r i a b l e s and t h e i r weights that were used t o account f o r the MDS space i n F i g u r e 1.


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é

-0933 -1.200 -1.200

^ ^ ^ - ^ ^ ^C-CH CH CH

\ 3

1

1

-0.800

1

1

-0400

1

1

1

0.400

1

1

0.800

1

1

1.200

Figure 3. Two-dimensional c r o s s - s e c t i o n s through a t h r e e dimensional space achieved from odor s i m i l a r i t y data among p y r i d y l ketones (from Ref. 5 ) .


42

COMPUTERS IN FLAVOR A N D F R A G R A N C E RESEARCH

Two m e t h o d s w e r e u s e d t o r e l a t e a s e r i e s o f p h y s i c o c h e m i c a l d e s c r i p t o r s t o t h e s p a c e i n F i g u r e 3, a v e c t o r m o d e l a n d a n i d e a l p o i n t m o d e l ( s e e i , 6 ) . The v e c t o r m o d e l assumes t h a t t h e r e i s a d i r e c t i o n through t h e space that corresponds t o i n c r e a s i n g amounts o f a c h e m i c a l d e s c r i p t o r . The d i r e c t i o n o f t h e v e c t o r c a n be f o u n d b y l i n e a r r e g r e s s i o n t e c h n i q u e s i n w h i c h a physicochemical v a r i a b l e i s regressed over the coordinates o f the c o n f i g u r a t i o n . Weighted combinations o f t h e c o n f i g u r a t i o n c o o r d i n a t e s a r e sought t h a t best e x p l a i n the v a r i a b l e . When y^ i s t h e v a l u e o f t h e p h y s i c o c h e m i c a l p a r a m e t e r f o r stimulus i , then


h

b

- o

+

b

(

l *il>

+ · · · • b (x r

i r

) - b

Q

• Σ

b a=l

a

(x

i a

)

w h e r e y^ i s t h e v a l u e o f t h e v a r i a b l e y ^ i f t h e l i n e a r r e l a t i o n s h i p w e r e p e r f e c t ; b^, b2» e t c . a r e t h e r e g r e s s i o n weights; b i s t h e i n t e r c e p t ; x^ i s t h e coordinate f o r the i s t i m u l u s on the r d i m e n s i o n . The m o s t common m e t h o d t o s o l v e f o r the values o f b i s c a l l e d l e a s t squares r e g r e s s i o n i n which the c o e f f i c i e n t s a r e chosen t o m a x i m i z e G where: Q

G « Σ i-1

(y. -

The i d e a l p o i n t m o d e l i s u s e f u l when a p o i n t i n t h e s p a c e c a n be f o u n d t h a t i s m o s t l i k e t h e p h y s i c o c h e m i c a l p a r a m e t e r . Thus, t h e i d e a l p o i n t i s t h e h y p o t h e t i c a l s t i m u l u s , i f i t e x i s t e d , t h a t w o u l d c o n t a i n t h e maximum amount o f t h e p h y s i c o c h e m i c a l a t t r i b u t e . The a t t r i b u t e r e a c h e s i t s maximum a t the i d e a l p o i n t and f a l l s o f f i n a l l d i r e c t i o n s as t h e square o f t h e d i s t a n c e f r o m t h e i d e a l p o i n t . The i d e a l p o i n t i s l o c a t e d i n an MDS s p a c e by a s p e c i a l k i n d o f r e g r e s s i o n p r o p o s e d by C a r r o l l (6) t h a t c o r r e l a t e s t h e p h y s i c o c h e m i c a l a t t r i b u t e v a l u e s w i t h t h e s t i m u l u s c o o r d i n a t e s a n d a dummy v a r i a b l e c o n s t r u c t e d f r o m t h e sums o f s q u a r e s o f t h e c o o r d i n a t e s f o r e a c h p o i n t :

*i -

b

o

+

ί a a«l b

+

b

r l +

a»l

The r e s u l t s o f v e c t o r a n d i d e a l p o i n t a n a l y s e s a r e g i v e n i n T a b l e s I I a n d I I I r e s p e c t i v e l y a s a n a l y z e d b y t h e p r o g r a m PREFMAP ( 6 , 1 ) . Two kindβ o f i d e a l p o i n t s w e r e f o u n d , a p o s i t i v e i d e a l point f o r which the relevance o f a d e s c r i p t o r decreases w i t h i n c r e a s i n g d i s t a n c e o f t h e s t i m u l i f r o m t h e i d e a l p o i n t and a negative i d e a l point, f o r which therelevance increases w i t h i n c r e a s i n g d i s t a n c e f r o m t h e i d e a l p o i n t . The c o r r e l a t i o n s f o r t h e v e c t o r a n d i d e a l p o i n t a n a l y s e s a r e g i v e n i n T a b l e IV. I t


4.

SCHIFFMAN


43


can be s e e n t h a t o d o r q u a l i t y i s h i g h l y c o r r e l a t e d f o r b o t h v e c t o r and i d e a l p o i n t m o d e l s w i t h t h e r a t i o o f t h e r e l a t i v e i n t e n s i t i e s o f t h e i o n s a t m/e 106 and 107 o b t a i n e d i n mass spectroscopic fragmentation. I n t e r a c t i o n of the r i n g nitrogen w i t h the substituent i n the 2-poeition i s responsible f o r the f r a g m e n t a t i o n pathway as w e l l as odor q u a l i t y . The Q - n.m.r. chemical s h i f t s were a l s o h i g h l y c o r r e l a t e d w i t h odor i n the v e c t o r m o d e l w i t h t h e f i r s t and s e c o n d d i m e n s i o n s o f t h e o d o r q u a l i t y space. I n f r a r e d s t r e t c h i n g f r e q u e n c i e s , l o g k' ( a measure o f column r e t e n t i o n used i n h i g h p r e s s u r e l i q u i d c h r o m a t o g r a p h y ) , and l o g Ρ ( o c t a n o l - w a t e r p a r t i t i o n c o e f f i c i e n t ) were o n l y weakly c o r r e l a t e d w i t h q u a l i t y . The h i g h c o r r e l a t i o n s f o r n e g a t i v e i d e a l p o i n t s ( u n l i k e p o s i t i v e i d e a l p o i n t s ) do n o t provide strong support f o r a physicochemical parameter.

Table I I D i r e c t i o n Cosines o f F i t t e d Physicochemical

Vectors

1

Dimension 2

3

1

-0.9966

-0.0101

-0.0815

l o g k'

2

-0.9294

-0.3662

0.0468

carbonyl s h i f t

3

-0.6541

0.7561

0.0216

carbonyl

4

-0.7974

0.5873

-0.1384

concentration

5

0.6900

-0.7227

0.0399

mass spectrum r a t i o

6

0.9133

-0.4054

-0.0387

l o

*

P

oct

frequency

S t u d y 3: P y r a z i n e s . A n o t h e r m e t h o d o f r e l a t i n g p h y s i c o c h e m i c a l p a r a m e t e r s t o a n MDS s p a c e , c a n o n i c a l c o r r e l a t i o n , was e m p l o y e d by S c h i f f m a n and L e f f i n g w e l l ( 7 ) . I n t h i s c a s e p y r a z i n e s w e r e arranged i n a 3-dimensional space on the b a s i s o f odor q u a l i t y ( F i g u r e 4 a and 4b). Then a s e t o f d e s c r i p t o r s g i v e n i n T a b l e V w e r e g e n e r a t e d by ADAPT, a c o m p u t e r s y s t e m f o r a u t o m a t e d d a t a a n a l y s e s by p a t t e r n r e c o g n i t i o n t e c h n i q u e s ( S t u p e r and J u r s , 8 ) . The s u b s t r u c t u r e s t h a t w e r e u s e d t o g e n e r a t e t h e e n v i r o n m e n t d e s c r i p t o r s a r e g i v e n i n F i g u r e 5. C a n o n i c a l r e g r e s s i o n ( s e e 1) was u s e d t o f i n d l i n e a r r e l a t i o n s h i p s b e t w e e n t h e two s e t s o f v a r i a b l e s , t h a t i s , t h e s t i m u l u s c o o r d i n a t e s o f t h e MDS s p a c e and t h e p h y s i c o c h e m i c a l attributes. The e q u a t i o n s f o r c a n o n i c a l c o r r e l a t i o n a r e : h i

'

a

k o

+

a

k i

+

· · ·

+

a

kr

^iP


44

COMPUTERS IN FLAVOR AND FRAGRANCE RESEARCH

Table Π Ι

Coordinates of Ideal Points

1

3

^ o c t

1

negative i d e a l point

-0.11853

0.05568 -0.02633

log k'

2


-0.11396

0.06849 -0.03036

carbonyl s h i f t

3


-O.05810

-0.04761 -0.03163

carbonyl frequency

4

positive i d e a l point

-0.32895

0.18924 -0.06022

concentration

5

positive i d e a l point

-0.08281

-0.01206 -0.02496

mass spectrum r a t i o

6

positive ideal point

0.12824

-0.06688 -0.04036

P


Dimension 2

Table I ? C o r r e l a t i o n s

(a)

(b)

(c)

I d e a l P o i n t Model

V e c t o r Model

1

0.9584

0.3933

2

0.9489

0.3995

3

0.9725

0.9058

c a r b o n y l frequency

4

0.4861

0.4730

concentration

5

0.9499

0.8250

masβ spectrum r a t i o

6

0.9715

0.9555

l Q

g

P

oct

l o g k' carbonyl

shift


SCHIFFMAN


Η Ο^ΝΛνΗ 3

H

3

C

V

N CH V

3

7

3

C H

3

II

Η

Computers in Flavor and Fragrance Research - American Chemical

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