Computer Modeling of Carbohydrate Molecules - American Chemical

Chapter 6

Ab Initio Molecular Orbital Calculations on Carbohydrates Conformational Properties of Deoxygenated Furanose Sugars 1

Eugenia C. Garrett and Anthony S. Serianni Downloaded by MONASH UNIV on May 21, 2013 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch006

Department of Chemistry and Biochemistry, University of Notre Dame, Notre Dame, IN 46556

Ab initio molecular orbital calculations have been conducted on the four deoxytetrofuranoses, 2-deoxy-α- and β-D-glycero-tetrofuranoses and 3-deoxy-α- and β-D-glycerotetrofuranoses, to assess the effect of furanose ring conformation on structural parameters (e.g., bond lengths, angles and torsions) and on total energies. Geometric optimizations of the planar and ten non-planar (envelope) forms of each compound were performed using the STO-3G and 3-21G basis sets, allowing a full comparison of results and a general assessment of the potential errors and limitations associated with calculations of intact carbohydrates using these basis sets. A limited inspection of more extended basis sets (e.g., 6-31G*) was also conducted. Proposed models for the conformational dynamics of the four deoxytetrofuranoses are evaluated in light of calculations conducted previously on the structurally-related D-aldotetrofuranoses, yielding important information on the effect of ring deoxygenation on furanose conformational behavior. The c o n f o r m a t i o n a l p r o p e r t i e s o f f u r a n o s e r i n g s h a v e r e c e i v e d c o n s i d e r a b l e a t t e n t i o n i n recent years because o f t h e i m p a c t t h e s e p r o p e r t i e s may h a v e i n m e d i a t i n g biological processes " . Most n o t a b l e i n t h i s r e s p e c t a r e the β-D-ribofuranose 1 and 2-deoxy-P~D-erythro-pentose 2 ( S c h e m e 1) c o m p o n e n t s o f r i b o - (RNA) a n d d e o x y r i b o n u c l e i c (DNA) a c i d s . I t i s w e l l known t h a t t h e f u r a n o s e r i n g adopts s p e c i f i c shapes depending on i t s l o c a l s t r u c t u r a l environment i n a biopolymer. F o r e x a m p l e , i n tRNA, t h e 1

8

1

To whom correspondence should be addressed. 0097-6156/90/0430-0091$08.25A) © 1990 American Chemical Society

In Computer Modeling of Carbohydrate Molecules; French, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

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r i b o f u r a n o s e r i n g p r e f e r s a C3'-endo c o n f o r m a t i o n i n h e l i c a l segments, whereas t h e C2'-endo c o n f o r m e r i s commonly o b s e r v e d i n l o o p r e g i o n s . I n DNA, t h e d e o x y r i b o s e r i n g assumes a C3'-endo c o n f o r m a t i o n i n t h e Α - f o r m , w h e r e a s i n B-DNA, t h e C 2 ' - e n d o o r C 3 ' - e x o c o n f o r m e r s a r e p r e f e r r e d . Thus, t h e d e o x y r i b o s e ring e x p e r i e n c e s s i g n i f i c a n t c o n f o r m a t i o n a l change i n t h e i n t e r c o n v e r s i o n o f A-DNA a n d B-DNA, a p r o c e s s t h a t presumably occurs i n v i v o . An a p p r e c i a t i o n o f t h e f a c t o r s that determine furanose r i n g conformational dynamics i s a p r e r e q u i s i t e t o understanding t h e e n e r g e t i c s o f DNA a n d RNA c o n f o r m a t i o n a l i n t e r c o n v e r s i o n in solution. Furanose r i n g s a r e a l s o found as components of biologically-important polysaccharides, although t h e i r role i n determining the overall conformational properties o f t h e s e b i o p o l y m e r s has n o t been s t u d i e d v e r y extensively. T h e c o n f o r m a t i o n a l d y n a m i c s o f f u r a n o s e r i n g s may b e d e s c r i b e d by t h e mechanisms o f p s e u d o r o t a t i o n " and inversion. The f o r m e r mechanism d e s c r i b e s a c o n t i n u o u s pathway o f i n t e r c o n v e r s i o n between twenty i d e a l i z e d nonp l a n a r ( e n v e l o p e , t w i s t ) c o n f o r m e r s ( F i g u r e s 1 a n d 2) t h a t d o e s n o t i n v o l v e t h e p l a n a r f o r m ( e . g . , E —· E —» °E). I n v e r s i o n d e s c r i b e s i n t e r c o n v e r s i o n between nonp l a n a r f o r m s v i a t h e p l a n a r f o r m ( e . g . , E —• p l a n a r —> °E). I t i s n o t c l e a r whether one o r b o t h o f t h e s e m e c h a n i s m s p l a y a r o l e i n DNA a n d RNA c o n f o r m a t i o n a l dynamics i n v i v o , although i t i s g e n e r a l l y h e l d that b a r r i e r s t o conformer i n t e r c o n v e r s i o n a r e low . Although f r e q u e n t l y employed t o assess furanose c o n f o r m a t i o n i n s o l u t i o n , e x p e r i m e n t a l NMR p a r a m e t e r s such as chemical s h i f t s and s p i n - c o u p l i n g constants a r e not unequivocal i n e s t a b l i s h i n g p r e f e r r e d furanose geometries because o f t h e e f f e c t o f conformational a v e r a g i n g on t h e s e v a l u e s . F u r t h e r m o r e , NMR c a n n o t address t h e issue o f conformer e n e r g e t i c s . At present, t h e r e f o r e , i t appears that t h e best approach t o evaluate f u r a n o s e c o n f o r m a t i o n a l dynamics i s one t h a t employs c a l c u l a t i o n a l and e x p e r i m e n t a l components. Several e m p i r i c a l and s e m i - e m p i r i c a l c a l c u l a t i o n a l s t u d i e s have been r e p o r t e d on t h e r e l a t i v e f l e x i b i l i t i e s o ft h e f u r a n o s e r i n g i n DNA a n d R N A ' " , y i e l d i n g c o n f l i c t i n g conclusions. F o r example, L e v i t t and W a r s h e l have p r o p o s e d a f l e x i b l e model f o r deoxyribose dynamics i n DNA, w h e r e a s a m o r e r i g i d m o d e l i s p r e f e r r e d b y O l s o n a n d Sussman . I t i s evident t h a t t h e c o n f o r m a t i o n a l dynamics of furanose rings i s not completely understood a t present, and that t h e vast m a j o r i t y o f t h e reported s t u d i e s have been c o n f i n e d t o 1 and 2 because o f t h e i r obvious b i o l o g i c a l roles. I t i sour contention that e x p e r i m e n t a l ( e . g . , NMR) a n d c o m p u t a t i o n a l s t u d i e s o f o t h e r r i n g c o n f i g u r a t i o n s ( e . g . , arabino, lyxo, xylo ) are e s s e n t i a l t o a t t a i n i n g a g l o b a l understanding o ft h e s t r u c t u r a l behavior o f these rings. 9

Downloaded by MONASH UNIV on May 21, 2013 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch006

1 0

1 1

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1 6

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1 7

1 9

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6.

GARRETT AND SERIANNI

Ab Initio Molecular Orbital Calculations 93

5

HO

OH

β-D-ribofiiranose 1

OH

2-deoxy-p-D-erythropentose 2


Scheme 1

north

south F i g u r e 1. The p s e u d o r o t a t i o n a l itinerary " describing the interconversion of non-planar furanose conformers. Regions o f t h e i t i n e r a r y a r e denoted as n o r t h , s o u t h , e a s t and west as i n d i c a t e d . E n v e l o p e and t w i s t c o n f o r m e r s a r e d e n o t e d b y Ε a n d T, r e s p e c t i v e l y . 1 2

1 4


94

COMPUTER MODELING OF CARBOHYDRATE MOLECULES We h a v e b e e n i n t e r e s t e d i n a p p l y i n g ab initio m o l e c u l a r o r b i t a l c a l c u l a t i o n s t o f u r a n o s e r i n g s i n an a t t e m p t t o b e t t e r d e f i n e t h e i r s t r u c t u r e s and conformational properties. I n a r e c e n t s t u d y , we e x a m i n e d t h e t e t r o f u r a n o s e s , a - a n d β-D-erythrofuranose (3, 4) a n d a - a n d β-D-threofuranose ( 5 , 6) ( S c h e m e 2) u s i n g t h e G a u s s i a n 80 p r o g r a m d e v e l o p e d b y P o p l e a n d coworkers . Complete geometric o p t i m i z a t i o n s of the p l a n a r a n d t e n e n v e l o p e f o r m s w e r e p e r f o r m e d on e a c h i s o m e r w i t h t h e STO-3G b a s i s s e t , a n d r e f i n e d w i t h s i n g l e - p o i n t 3-21G c a l c u l a t i o n s . W h i l e t h i s work revealed several i n t e r e s t i n g findings, i t s obvious s h o r t c o m i n g was t h e c h o i c e o f b a s i s s e t . A s a c o n s e q u e n c e , t h e p r e s e n t s t u d y was i n i t i a t e d t o a d d r e s s two p r o b l e m s : (1) t o e x a m i n e t h e e f f e c t o f b a s i s s e t o n c a l c u l a t e d f u r a n o s e g e o m e t r i e s and t o t a l e n e r g i e s , and (2) t o e x a m i n e t h e e f f e c t o f r i n g d e o x y g e n a t i o n o n f u r a n o s e c o n f o r m a t i o n and dynamics. We h a v e c h o s e n t w o d e o x y f u r a n o s e s a s m o d e l s y s t e m s , 2-deoxy-oc- and 2 - d e o x y β-D-gIycero-tetrofuranose (7, 8) a n d 3 - d e o x y - a - a n d 3d e o x y ^ - D - g l y c e r o - t e t r o f u r a n o s e (9, 10) (Scheme 3 ) , w h i c h a r e t h e monodeoxy a n a l o g u e s o f t h e t e t r o f u r a n o s e s 3-6. C o m p l e t e g e o m e t r i c o p t i m i z a t i o n s h a v e b e e n p e r f o r m e d on e l e v e n c o n f o r m e r s o f e a c h c o m p o u n d (10 e n v e l o p e , 1 p l a n a r ) u s i n g t h e STO-3G a n d 3-21G b a s i s s e t s f o r c o m p a r a t i v e p u r p o s e s , and o p t i m i z e d g e o m e t r i c p a r a m e t e r s (bond l e n g t h s , a n g l e s and t o r s i o n s ) and t o t a l e n e r g i e s a r e t a b u l a t e d and d i s c u s s e d i n t h e c o n t e x t o f t h e p s e u d o r o t a t i o n and i n v e r s i o n models. 2 0


2 1

Experimental 2 1

T h e G a u s s i a n 80 p r o g r a m , a s i m p l e m e n t e d o n a n IBM 3 7 0 / 3 0 3 3 m a i n f r a m e c o m p u t e r a t t h e N o t r e Dame C o m p u t i n g C e n t e r , was u s e d f o r m o s t o f t h e c a l c u l a t i o n s . C a l c u l a t i o n s were a l s o c o n d u c t e d w i t h t h e G a u s s i a n 8 6 program as i m p l e m e n t e d on a D i g i t a l V a x S t a t i o n 3200 computer. G e o m e t r i c o p t i m i z a t i o n s were p e r f o r m e d w i t h t h e m i n i m a l STO-3G b a s i s s e t ' and t h e s p l i t - v a l e n c e 3-21G b a s i s s e t . C o m p u t a t i o n s were p e r f o r m e d on t e n e n v e l o p e (E) f o r m s ( F i g u r e 2 ) , e a c h w i t h o n e a p p r o p r i a t e e n d o c y c l i c t o r s i o n a n g l e f i x e d a t 0° ( t o m a i n t a i n a g i v e n envelope form), while a l l remaining molecular parameters were o p t i m i z e d by a n a l y t i c g r a d i e n t methods; f o r p l a n a r f o r m s , t w o e n d o c y c l i c t o r s i o n a n g l e s w e r e f i x e d a t 0°. I n i t i a l e s t i m a t e s o f s t r u c t u r a l p a r a m e t e r s (bond l e n g t h s , a n g l e s a n d t o r s i o n s ) w e r e made b y i n s p e c t i o n o f crystallographic data ' . Geometry o p t i m i z a t i o n s r e q u i r e d a b o u t 6 h a n d 12 h o f c p u t i m e p e r c o n f o r m e r f o r t h e STO-3G a n d 3-21G b a s i s s e t s , r e s p e c t i v e l y , o n t h e IBM computer. Several c a l c u l a t i o n s using Gaussian 8 6 and Gaussian 8 8 w e r e p e r f o r m e d a t t h e 4-31G, 4-31G*, 6-31G a n d 6-31G* l e v e l s o n t h e p l a n a r f o r m o f 2 - d e o x y - a - D 2 2 3

2 3

2 4

2 5

2 6

2 7

2 2 a

2 2 b


6. GARRETT AND SERIANNI


OH

2


*E (envelope) conformation

T i (twist) conformation

F i g u r e 2. T h e t w o c l a s s e s o f n o n - p l a n a r f u r a n o s e conformers o f 3-deoxy-P-D-glycero-tetrofuranose 10. T h e *E ( e n v e l o p e ) c o n f o r m e r h a s C 2 , C 3 , C4 a n d 0 4 c o p l a n a r a n d C I o u t - o f - p l a n e . The Ί (twist) conformer h a s C 3 , C4 a n d 0 4 c o p l a n a r a n d C I a n d C2 o u t - o f - p l a n e . 2

λ

a-D-erythrofuranose 3

β-D-erythrofuranose 4

a-D-threofuranose 5

β-D-thrcofuranose 6

Scheme 2

2-deoxy-a-D-glycero-tetrofuranose 7

2-deoxy-P-D-glycero-tetroftiranose 8

Ο

Ο

Q-

OH

Q

OH

OH

3-deoxy-a-D-glycero-tetrofuranose 9

3-deoxy-P-D-glycero-tetrofuranose 10 Scheme 3


96


glycero-tetrose 7 to estimate the e f f e c t of extended b a s i s s e t s on o p t i m i z e d m o l e c u l a r parameters. T h e o r e t i c a l c a l c u l a t i o n s of sugars are complicated b y t h e c h o i c e o f C-0 b o n d r o t a m e r s f o r t h e h y d r o x y g r o u p s i n the molecule. I t was i m p r a c t i c a l t o i n v e s t i g a t e a l l r o t a m e r c o m b i n a t i o n s f o r e a c h c o n f o r m e r o f 7-10, as t h i s would r e q u i r e n i n e o p t i m i z a t i o n s (3 ) per conformer. The c h o i c e o f C-0 r o t a m e r s , t h e r e f o r e , was made b y m o d e l i n s p e c t i o n w i t h the aim of m i n i m i z i n g intramolecular h y d r o g e n b o n d i n g and o p t i m i z i n g s t e r e o e l e c t r o n i c e f f e c t s a t CI ( F i g u r e 3 ) . In the l a t t e r regard, our p r e v i o u s ab i n i t i o c a l c u l a t i o n s have shown t h a t t h e most s t a b l e C l 0 1 r o t a m e r i s t h a t h a v i n g OH-1 gauche t o HI a n d t h e r i n g o x y g e n , as e x p e c t e d f r o m t h e " e x o a n o m e r i c e f f e c t " ' ; t h e s e o b s e r v a t i o n s were v e r i f i e d i n the d e o x y f u r a n o s e s . The i m p l i c a t i o n s o f t h i s a p p r o a c h a r e d i s c u s s e d i n m o r e d e t a i l i n the Results s e c t i o n . The n o m e n c l a t u r e u s e d i n t h i s p a p e r t o d e s c r i b e furanose r i n g conformation d e r i v e s from t h e work of S u n d a r a l i n g a m and c o w o r k e r s ' i n which a pseudorot a t i o n a l pathway d e s c r i b e s the i n t e r c o n v e r s i o n of nonplanar conformers (Figure 1). Two p a r a m e t e r s , Ρ ( p h a s e a n g l e ) and T ( p u c k e r i n g a m p l i t u d e ) , a r e r e q u i r e d t o define the complete r i n g s t r u c t u r e of a conformer. The r e l a t i o n s h i p between furanose r i n g conformation and Ρ i s i l l u s t r a t e d i n F i g u r e 1, w h e r e , f o r e x a m p l e , t h e E conformation c o r r e s p o n d s t o Ρ=0.1π. To s i m p l i f y t h e p r e s e n t a t i o n o f d a t a , c o n f o r m e r s a r e i d e n t i f i e d by Ρ/π, where E c o r r e s p o n d s t o a v a l u e o f Ρ/π=0.1, E to a value o f 0.3, a n d s o f o r t h . 2

2 0


2 8

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m

3

3

4

Results A. B o n d L e n g t h s . P r e v i o u s ab i n i t i o c a l c u l a t i o n s w i t h t h e ST0-3G b a s i s s e t on t h e t e t r o f u r a n o s e s 3-6 showed t h a t e n d o c y c l i c C-C a n d C-0 b o n d l e n g t h s v a r y systematically with ring conformation . The three e n d o c y c l i c C-C b o n d s i n t h e d e o x y t e t r o f u r a n o s e s 7-10 show s i m i l a r c y c l i c behavior ( F i g u r e 4A, 4 C ) ; f o r e x a m p l e , t h e C1-C2 b o n d l e n g t h i s m a x i m a l a t 0.3 a n d 1.3 Ρ / π (i.e., in c o n f o r m a t i o n s w h e r e s u b s t i t u e n t s on C I a n d C2 are e c l i p s e d ) a n d m i n i m a l a t 0.9 a n d 1.9 Ρ / π ( i . e . , i n c o n f o r m a t i o n s w h e r e s u b s t i t u e n t s on C I a n d C2 are maximally staggered). C u r v e s o b s e r v e d f o r C2-C3 and C3C4 b o n d l e n g t h s a r e s i m i l a r i n s h a p e b u t a r e p h a s e s h i f t e d r e l a t i v e t o t h a t f o r C1-C2 b y 0.2 Ρ / π a n d 0.4 Ρ/π, r e s p e c t i v e l y . S i m i l a r curves are obtained with the 3-21G b a s i s s e t ( F i g u r e 4B, 4 D ) , a l t h o u g h b o n d l e n g t h s a r e s h o r t e r and c u r v e a m p l i t u d e s g r e a t e r w i t h t h i s b a s i s set. In g e n e r a l , anomeric c o n f i g u r a t i o n does not a f f e c t t h e r e s p o n s e o f e n d o c y c l i c C-C b o n d l e n g t h t o r i n g conformation ( F i g u r e 4B, 4D). I n c o n t r a s t t o C-C b o n d l e n g t h s , t h e r e s p o n s e o f e n d o c y c l i c C-0 b o n d s i n 7 - 1 0 d e p e n d s on r i n g conformation 2 0


GARRETT A N D SERIANNI


0 4 ^ ^ 0 2

Ab Initio Molecular Orbital Calculations

C2

HI

04

H2

C2

C I ^ - ^ C 3

HI

Α"

C4

H2

Η

ά

D

F i g u r e 3. T h e i n i t i a l e x o c y c l i c C-0 r o t a m e r s u s e d f o r c o n f o r m a t i o n a l energy c a l c u l a t i o n s on t h e d e o x y t e t r o f u r a n o s e s 7 ( A ) , 8 ( Β ) , 9 (C) a n d 10 ( D ) . T h e C l - 0 1 rotamers were chosen t o o p t i m i z e t h e "exoanomeric effect"28,29.



3

I ι

Β.

•Ό

f

ι ύ

Α.

D.

2

2

1.580

Ρ/π (radians)

1.560 -ι 1.555 H 1.550 1.545 1.5401 1.535 1.530 1.525 1.5201 1.515 1.510 • I ' I ' I ' I » I ' I ' I ' I ' I 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

Ρ/π (radians)

1.540 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1.545

1.550

1.555

1.560

1.565

1.5701

1.575

F i g u r e 4. T h e e f f e c t o f r i n g c o n f o r m a t i o n o n f u r a n o s e r i n g e n d o c y c l i c C-C b o n d l e n g t h s i n 7 (A a n d B) a n d 8 (C a n d D) u s i n g t h e STO-3G (A a n d C) a n d 3 - 2 1 G (B a n d D) b a s i s s e t s . C 1 - C 2 (•) , C 2 - C 3 (•) , C3-C4 ( A ) .

Ρ/π (radians)

1.520 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1.525

1.5301

1.535

1.5401

1.545 Η

I.550

1.5551

Ρ/π (radians)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0

1.560

Ι.540

1.5451

1.550

1.555-1

1.560

1.5651

1.570


00


6.



and a n o m e r i c c o n f i g u r a t i o n . Computations at the 3-21G l e v e l show t h a t , f o r (X-anomers, t h e C l - 0 1 b o n d i s s h o r t e s t a t a b o u t 1.7 Ρ / π a n d l o n g e s t a t a b o u t 0.5 Ρ/π ( F i g u r e 5B), whereas the o p p o s i t e i s found f o r β-anomers ( F i g u r e 5D). A s i m i l a r p a t t e r n i s o b s e r v e d f o r t h e C4-04 bond. In c o n t r a s t , the Cl-04 bond i n α-anomers i s s h o r t e s t a t 0.7 Ρ / π a n d l o n g e s t a t 0.1 Ρ / π , w i t h a l o c a l m i n i m u m a t 1.5 Ρ / π ; f o r β - a n o m e r s , t h e c u r v e s a r e s i m i l a r e x c e p t t h a t t h e g l o b a l m i n i m u m o c c u r s a t a b o u t 1.5 Ρ/π a n d t h e l o c a l m i n i m u m a t 0.7 Ρ / π ( F i g u r e 5B, 5D). C o m p a r i s o n o f STO-3G a n d 3-21G basis sets (Figure 5A-D) s h o w s t h a t c u r v e s h a p e s a r e c o n s e r v e d , b u t C-0 bonds d e c r e a s e o v e r a l l i n l e n g t h and t h e magnitude o f bond l e n g t h c h a n g e i s e n h a n c e d i n t h e 3-21G calculations. R e l a t i v e b o n d l e n g t h s a l s o c h a n g e w i t h b a s i s s e t as shown i n F i g u r e 5A-D; t h e m o r e r e l i a b l e 3-21G b a s i s s e t shows t h a t C4-04 > C l - 0 4 > C l - 0 1 f o r a l l f u r a n o s e conformations. STO-3G c a l c u l a t i o n s o n t h e t e t r o f u r a n o s e s 3-6 s h o w e d t h a t C-H b o n d s i n t h e v i c i n i t y o f t h e r i n g o x y g e n ( e . g . , C l - H l , C4-H4R, C 4 - H 4 S ) d e p e n d o n r i n g conformation . The o b s e r v e d d e p e n d e n c e on c o n f o r m a t i o n was e x p l a i n e d b y p o s t u l a t i n g t h a t t h e s e C-H bonds i n c r e a s e i n l e n g t h as t h e y become more a n t i p e r i p l a n a r t o a l o n e - p a i r o r b i t a l of the r i n g oxygen . Similar behavior i s observed i n the deoxytetrofuranoses 7-10 with t h e STO-3G a n d 3-21G b a s i s s e t s ( F i g u r e s 6 and 7 ) . Curves obtained with computations using the s p l i t - v a l e n c e b a s i s s e t , however, are s h i f t e d t o s h o r t e r bond lengths and g e n e r a l l y have g r e a t e r a m p l i t u d e s . It i s also i n t e r e s t i n g t o note t h a t the c a l c u l a t e d C l - H l bond l e n g t h i s s i g n i f i c a n t l y l o n g e r t h a n t h e C4-H4K a n d C4-H4S b o n d s u s i n g t h e STO-3G b a s i s s e t , w h e r e a s a l l t h r e e b o n d s a r e c o m p a r a b l e i n l e n g t h w i t h t h e 3-21G basis set. 2 0

2 0

B. C o o r d i n a t e d B o n d L e n g t h s I n t h e V i c i n i t y o f t h e Anomeric Center. In D-aldofuranoses, the Cl-01 bond i s q u a s i - a x i a l i n °E-Ei c o n f o r m e r s (0.7 Ρ / π ) o f oc-anomers, and E - E c o n f o r m e r s (1.7 Ρ / π ) o f β - a n o m e r s ( F i g u r e 1 ) . In c o n t r a s t , the C l - 0 1 bond assumes a q u a s i - e q u a t o r i a l o r i e n t a t i o n i n E Q ^ E a n d °E-E c o n f o r m e r s o f a- and βanomers, r e s p e c t i v e l y . The o r i e n t a t i o n o f t h e C l - 0 1 b o n d i s e x p e c t e d t o h a v e a p r o f o u n d e f f e c t on r i n g e l e c t r o n i c s t r u c t u r e i n the v i c i n i t y of the anomeric center. An i n s p e c t i o n o f C-0 a n d C-H b o n d l e n g t h s i n t h e v i c i n i t y o f t h e a n o m e r i c c a r b o n (e.g., C4-04, 04-C1, C l - 0 1 , Cl-Hl) f o r q u a s i - a x i a l and q u a s i - e q u a t o r i a l o r i e n t a t i o n s o f t h e C l - 0 1 b o n d ( F i g u r e s 5-7) reveals several interesting relationships. When t h e C l - 0 1 b o n d i s q u a s i - a x i a l , t h e C l - 0 1 and C4-04 b o n d s a r e m a x i m a l o r n e a r m a x i m a l i n l e n g t h , w h e r e a s t h e 04-C1 and C l - H l bond l e n g t h s a r e a t o r n e a r t h e i r minimum v a l u e s (Scheme 4 A ) . In c o n t r a s t , when t h e C l - 0 1 b o n d i s q u a s i - e q u a t o r i a l , C l - 0 1 and C4-04 b o n d l e n g t h s a r e a t o r n e a r minima, and C l - 0 4 and C l - H l b o n d s a r e m a x i m a l o r n e a r m a x i m a l i n l e n g t h (Scheme 4 B ) . 0

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F i g u r e 5. T h e e f f e c t o f r i n g c o n f o r m a t i o n o n C-0 b o n d l e n g t h s i n 7 (A a n d B) a n d 8 (C a n d D) u s i n g t h e STO-3G (A a n d C) a n d 3 - 2 1 G (B a n d D) b a s i s s e t s . C 4 - 0 4 (•) , Cl-04 (•), C l - O l ( A ) .

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In Computer Modeling of Carbohydrate Molecules; French, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990. Ρ/π (radians)

F i g u r e β. T h e e f f e c t o f r i n g c o n f o r m a t i o n o n t h e C l - H l b o n d l e n g t h i n 7 (A a n d B) a n d 8 (C a n d D) u s i n g t h e S T 0 - 3 G (A a n d C) a n d 3 - 2 1 G (B a n d D) b a s i s s e t s .

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Ρ/π (radians) F i g u r e 7. The e f f e c t o f r i n g c o n f o r m a t i o n o f t h e C4H4i* ( o p e n s y m b o l s ) a n d C 4 - H 4 S ( s o l i d s y m b o l s ) i n 7 (A) a n d 8 ( B ) . STO-3G d a t a a r e s h o w n i n s q u a r e s ; 3-21G d a t a a r e shown i n t r i a n g l e s .

Cl-Ol axial

Cl-Ol equatorial Scheme 4


6. GARRETT AND SERIANNI


T h e s e e f f e c t s s u g g e s t η-σ* d o n a t i o n t o t h e 0 4 - C 1 b o n d f r o m t h e r i n g o x y g e n when C l - 0 1 i s q u a s i - a x i a l , a s expected from t h e "anomeric e f f e c t " " . This donation w o u l d be e x p e c t e d t o d e c r e a s e t h e 04-C1 b o n d l e n g t h a n d i n c r e a s e t h e C4-04 a n d C l - 0 1 b o n d l e n g t h s ; t h e e x p l a n a t i o n o f t h e e f f e c t o f C l - 0 1 bond o r i e n t a t i o n on the C l - H l bond l e n g t h i s l e s s obvious. I t i s also p o s s i b l e t h a t t h e s e o b s e r v e d t r e n d s may b e a f f e c t e d b y t h e C l - 0 1 t o r s i o n a n g l e ; i n t h i s s t u d y o n l y one C l - 0 1 t o r s i o n was s t u d i e d ( F i g u r e 3) w h i c h was c h o s e n t o o p t i m i z e t h e "exoanomeric e f f e c t " ' . T h e i m p l i c a t i o n s o f t h e a b o v e o b s e r v a t i o n s may b e important, e s p e c i a l l y i f s i m i l a r trends are observed i n pyranose anomers. F o r example, w i t h r e s p e c t t o the mechanism o f a c i d - c a t a l y z e d h y d r o l y s i s o f p y r a n o s i d e s , e n d o c y c l i c C-0 b o n d c l e a v a g e ( p r e c e e d e d b y 0 5 p r o t o n a t i o n ) may b e a s s i s t e d i n β - a n o m e r s i n w h i c h t h e C l - 0 1 b o n d i s e q u a t o r i a l , s i n c e t h e 0 4 - C 1 b o n d may a l r e a d y b e extended i n t h e s e anomers. By a s i m i l a r a r g u m e n t , e x o c y c l i c C-0 s c i s s i o n ( p r e c e e d e d b y 0 1 p r o t o n a t i o n ) may be a s s i s t e d i n t h e h y d r o l y s i s o f α - p y r a n o s i d e s i n w h i c h the C l - 0 1 i s a x i a l and extended, thus r e s e m b l i n g t h e transition state. Post and K a r p l u s have r e c e n t l y suggested that enzyme-catalyzed g l y c o s i d e h y d r o l y s i s of β - p y r a n o s i d e s may i n d e e d t a k e p l a c e b y r i n g o x y g e n p r o t o n a t i o n , f o l l o w e d b y e n d o c y c l i c C-0 b o n d s c i s s i o n . 3


2 8

2 9

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3 2

C. Bond A n g l e s . Force-field calculations h a v e shown t h a t e n d o c y c l i c bond angles i n furanoses v a r y systematically with ring conformation. P r e v i o u s ab 2 0 i n i t i o c a l c u l a t i o n s on t h e t e t r o f u r a n o s e s 3 - 6 revealed a s i m i l a r d e p e n d e n c y on c o n f o r m a t i o n t h a t i s e s s e n t i a l l y u n a f f e c t e d by anomeric c o n f i g u r a t i o n . The C1-C2-C3 b o n d a n g l e s h o w e d m a x i m a a t 0.4 a n d 1.4 Ρ/π a n d m i n i m a a t 0.9 a n d 1.9 Ρ/π. The r e m a i n i n g f o u r c u r v e s were p h a s e s h i f t e d b y 0.2 Ρ/π i n o r d e r a r o u n d t h e r i n g . CCO a n d COC a n g l e s were f o u n d t o be c o m p a r a b l e i n m a g n i t u d e , and l a r g e r t h a n CCC b o n d a n g l e s . Similar results are o b t a i n e d f r o m S T 0 - 3 G c a l c u l a t i o n s o n 7-10 (Figure 8A). T h e o b s e r v e d s i m i l a r i t y i n CCO a n d COC a n g l e s , h o w e v e r , i s not c o n s i s t e n t with angle bending f o r c e s that predict COC t o b e g r e a t e r t h a n CCO. C a l c u l a t i o n s w i t h t h e 3-21G b a s i s s e t p r o d u c e t h e same o v e r a l l p a t t e r n o f e n d o c y c l i c b o n d a n g l e r e s p o n s e t o c o n f o r m a t i o n ( F i g u r e 8B, 8 C ) , b u t a p p e a r t o more a c c u r a t e l y p r e d i c t t h e e x p e c t e d t r e n d i n t h e i r r e l a t i v e m a g n i t u d e s , t h a t i s , COC > CCO > CCC. I n t e r e s t i n g l y , 3-21G d a t a s u g g e s t s t h a t t h e COC b o n d angle i s minimal at conformations i n which the r i n g o x y g e n i s o u t - o f - p l a n e (°E , E ) , b u t t h e s e m i n i m a a r e n o t equivalent. T h e g l o b a l m i n i m u m o c c u r s a t °E i n ccanomers, and a t E i n β-anomers, t h a t i s , i n c o n f o r m a t i o n s where C l - 0 1 assumes a q u a s i - a x i a l o r i e n t a t i o n ( F i g u r e 9 ) . 3 3

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F i g u r e 8. T h e e f f e c t o f r i n g c o n f o r m a t i o n o n e n d o c y c l i c b o n d a n g l e s i n 7: C1-C2-C3 ( A ) , C2-C3-C4 ( Δ ) , C 3 - C 4 - 0 4 (•) , C 4 - 0 4 - C 1 ( • ) , 0 4 - C 1 - C 2 (0) . (A) STO-3G d a t a . (B a n d C) 3 - 2 1 G d a t a s h o w i n g d i f f e r e n c e s b e t w e e n CCC, CCO a n d COC b o n d a n g l e s .



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D. Bond T o r s i o n s . The e f f e c t o f f u r a n o s e r i n g s t r u c t u r e a n d c o n f i g u r a t i o n on p u c k e r i n g a m p l i t u d e i s n o t c u r r e n t l y understood q u a n t i t a t i v e l y . R e c e n t ab i n i t i o s t u d i e s o f t h e t e t r o f u r a n o s e s 3-6 indicate that puckering amplitude d e p e n d s o n c o n f o r m a t i o n , a n d r a n g e s f r o m 16°-24°. The p u c k e r i n g a m p l i t u d e s o f 7-10, d e t e r m i n e d f r o m ST0-3G and 3-21G c a l c u l a t i o n s , a r e shown i n F i g u r e 10. The 3-21G c a l c u l a t i o n s p r e d i c t larger puckering amplitudes than STO-3G c a l c u l a t i o n s , w h i c h i s c o n s i s t e n t w i t h s i m i l a r c o m p a r i s o n s made o n n o n - c a r b o h y d r a t e f u r a n o i d r i n g systems . F u r t h e r m o r e , t h e e f f e c t o f c o n f o r m a t i o n on p u c k e r i n g amplitude i s not c o m p l e t e l y conserved between t h e two b a s i s s e t s . C u r v e s f o r 9 a n d 10 a p p e a r s o m e w h a t f l a t t e r t h a n t h o s e f o r 7 a n d 8, w i t h 8 s h o w i n g t h e l a r g e s t v a r i a t i o n of puckering with conformation. The p s e u d o r o t a t i o n a l i t i n e r a r y (Figure 1), t h e r e f o r e , appears t o be more c i r c u l a r f o r 9 and 10 t h a n f o r 7 and 8. P u c k e r i n g m i n i m a n e a r 0.0 a n d 1.0 Ρ/π w e r e c o m m o n l y o b s e r v e d i n STO-3G c a l c u l a t i o n s o f t h e t e t r o f u r a n o s e s 3 6, a n d i n s p e c t i o n o f t h e STO-3G d a t a i n F i g u r e 10 r e v e a l s a similar result. I n c o n t r a s t , l o c a l m i n i m a a r e more c o m m o n l y o b s e r v e d a t 0.5 a n d / o r 1.5 Ρ/π i n 3-21G c a l c u l a t i o n s (Figure 10), t h a t i s , i n conformations h a v i n g the r i n g oxygen o u t - o f - p l a n e . Presumably the p u c k e r i n g i s r e d u c e d i n °E a n d E conformers i n order t o m a i n t a i n a m a x i m a l COC b o n d a n g l e . T h e i s s u e o f e x o c y c l i c C-0 c o n f o r m a t i o n i n t h e o r e t i c a l c a l c u l a t i o n s o f s u g a r s i s c o m p l i c a t e d by a l a c k o f knowledge o f t h e i n t r i n s i c and e x t r i n s i c ( e . g . , s o l v e n t - m e d i a t e d ) f a c t o r s c o n t r o l l i n g C-0 t o r s i o n s i n t h e s e m o l e c u l e s , e s p e c i a l l y f o r C-0 b o n d s i n v o l v i n g n o n anomeric carbons. The i n i t i a l C l - 0 1 b o n d t o r s i o n s u s e d f o r c a l c u l a t i o n s on 7 - 1 0 ( F i g u r e 3) w e r e s e l e c t e d t o o p t i m i z e t h e " e x o a n o m e r i c e f f e c t " ' , a s p r e v i o u s ab i n i t i o c a l c u l a t i o n s a t t h e STO-3G l e v e l o n t h e t e t r o f u r a n o s e s 3 - 6 , and e x p e r i m e n t a l e v i d e n c e ' , indi cates t h a t the Cl-01 rotamer having the anomeric h y d r o x y l p r o t o n gauche to 04 a n d H I i s m o s t s t a b l e . The e x o a n o m e r i c d i h e d r a l a n g l e ( H l - C l - O l - H ) , however, does appear t o d e p e n d somewhat on r i n g c o n f o r m a t i o n ( F i g u r e 1 1 ) . O f t h e r e m a i n i n g C-0 t o r s i o n s i n 7 - 1 0 , C3-03 and C 2 - 0 2 r o t a m e r s w e r e c h o s e n i n 7 a n d 9, r e s p e c t i v e l y , t o minimize or prevent p o t e n t i a l i n t r a m o l e c u l a r bonding. In 9, g e o m e t r i c o p t i m i z a t i o n o f a l l t e n e n v e l o p e f o r m s d i d n o t i n d u c e a c h a n g e i n t h e i n i t i a l C2-02 r o t a m e r , a l t h o u g h t h e t o r s i o n a n g l e was r e f i n e d b y t h e o p t i m i z a t i o n (Figure 12). I n c o n t r a s t , f o r 7, geometric o p t i m i z a t i o n i n d u c e d a s i g n i f i c a n t change i n t h e C3-03 rotamer (from the i n i t i a l rotamer i n F i g u r e 3 t o t h a t h a v i n g t h e h y d r o x y p r o t o n a n t i t o H3) ( F i g u r e 13) d u r i n g o p t i m i z a t i o n of the E conformer. Presumably this r o t a t i o n a l c h a n g e was d r i v e n b y h y d r o g e n b o n d i n g b e t w e e n 0 1 a n d 03 i n E w h e r e b o t h C-0 b o n d s a r e q u a s i - a x i a l a n d t h u s p r o p e r l y o r i e n t e d f o r Η-bonding. To p r e v e n t t h i s


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F i g u r e 10. The e f f e c t o f r i n g c o n f o r m a t i o n on f u r a n o s e r i n g p u c k e r i n g a m p l i t u d e i n 7 ( A ) , 8 ( Β ) , 9 (C) a n d 1 0 (D) u s i n g t h e STO-3G ( o p e n s y m b o l s ) a n d 3 - 2 1 G ( s o l i d symbols) b a s i s s e t s .

Ρ/π (radians)

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Ρ/π (radians)

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108

COMPUTER MODELING OF CARBOHYDRATE MOLECULES 80η


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B.

S 60 0.0 0.2 0.4 0.6 0.8

1.0

1.2

1.4

1.6

1.8

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Ρ/π (radians) F i g u r e 11. The e f f e c t o f r i n g c o n f o r m a t i o n on t h e H l C l - O l - H e x o c y c l i c t o r s i o n a n g l e i n 8 (A) a n d 9 ( B ) . STO-3G d a t a a r e s h o w n i n f i l l e d s y m b o l s , a n d 3-21G d a t a a r e shown i n open s y m b o l s .

60-1

40 I ' ι • ι • ι • ι • ι 0.0

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• ι • ι • ι • ι • ι 1.2

1.4

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Ρ/π (radians)

F i g u r e 12. The e f f e c t o f r i n g c o n f o r m a t i o n on t h e H2C 2 - 0 2 - H t o r s i o n a n g l e i n 9 u s i n g t h e STO-3G (filled s y m b o l s ) a n d 3-21G ( o p e n s y m b o l s ) b a s i s s e t s .


6.



i n t e r a c t i o n , whose p r e s e n c e w o u l d p r e s u m a b l y add greater s t a b i l i t y t o t h e E c o n f o r m e r and t h u s i n v a l i d a t e our a t t e m p t t o s t u d y i n t r i n s i c e n e r g i e s , t h e C3-03 t o r s i o n was h e l d c o n s t a n t (-60 °) ( F i g u r e 3) f o r 3-21G o p t i m i z a t i o n s of the E conformer. Due t o s i m i l a r r o t a t i o n s during o p t i m i z a t i o n , the Cl-01 (-70°) a n d C 3 - 0 3 (-60°) w e r e h e l d c o n s t a n t d u r i n g E o p t i m i z a t i o n , whereas t h e C l - 0 1 t o r s i o n (-70°) was h e l d c o n s t a n t d u r i n g E optimization. I n 10, t h e C l - 0 1 t o r s i o n was h e l d c o n s t a n t a t 70° ( F i g u r e 3) d u r i n g 3-21G o p t i m i z a t i o n s of the E , E E and E 3 c o n f o r m e r s . C l e a r l y t h e p r o b l e m o f C-0 r o t a m e r s i s c o m p l e x a n d adds u n c e r t a i n t y t o the r e s u l t s of these c a l c u l a t i o n s . D i f f e r e n t i a l i n t r a m o l e c u l a r hydrogen bonding i n puckered conformers, i f present, would notably a f f e c t the c a l c u l a t e d d e p e n d e n c e o f r i n g c o n f o r m a t i o n on t o t a l energy. I n t h i s s t u d y we s o u g h t t o r e d u c e t h i s c o n t r i b u t i o n t o t o t a l e n e r g y and t h e r e b y s t u d y t h e i n t r i n s i c behavior of the molecule. In aqueous s o l u t i o n , p o t e n t i a l i n t r a m o l e c u l a r hydrogen b o n d i n g w i l l compete w i t h i n t e r m o l e c u l a r hydrogen bonding, with the latter p o s s i b l y d o m i n a t i n g due t o t h e l a r g e e x c e s s o f s o l v e n t . This being the case, i n t r a m o l e c u l a r hydrogen bonding may n o t , i n g e n e r a l , be a m a j o r d e t e r m i n a n t o f p r e f e r r e d f u r a n o s e c o n f o r m a t i o n i n aqueous s o l u t i o n . However, the p r e s e n c e of a water s o l v e n t cage around the sugar w i t h i t s own h y d r o g e n b o n d i n g n e t w o r k may i n d u c e o t h e r p r e s e n t l y unknown f o r c e s t h a t p r e f e r e n t i a l l y a c t t o s t a b i l i z e or d e s t a b i l i z e s p e c i f i c furanose conformers. E v e n i n s t r u c t u r e s i n w h i c h t h e r e i s no o p p o r t u n i t y for i n t r a m o l e c u l a r h y d r o g e n b o n d i n g ( e . g . , 8), the e f f e c t of C-0 o r i e n t a t i o n on c a l c u l a t e d r i n g s t r u c t u r e a n d e n e r g e t i c s r e m a i n s t o be e s t a b l i s h e d . R e c e n t ab initio c a l c u l a t i o n s on 2 - d e o x y - p - D - e r y t h r o f u r a n o s y l a m i n e using t h e 3-21G b a s i s s e t showed t h a t t h e c o n f o r m a t i o n o f t h e C3-03 bond d i d not s i g i f i c a n t l y a f f e c t t h e e n e r g y p r o f i l e o f the m o l e c u l e ; i n c o n t r a s t , however, the energy p r o f i l e o f t h e c o r r e s p o n d i n g 2 - f l u o r o d e r i v a t i v e was notably a f f e c t e d by C3-03 b o n d c o n f o r m a t i o n b e c a u s e o f intramolecular OH—F interactions. 2

2

3

4

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4

l f

3 7

EL. Conformational Energy C a l c u l a t i o n s . Ab initio c a l c u l a t i o n s o n t h e t e t r o f u r a n o s e s 3-6 u s i n g t h e ST0-3G basis set showed t h a t r i n g c o n f i g u r a t i o n s i g n i f i c a n t l y affects preferred conformation. Total energyc o n f o r m a t i o n c u r v e s f o r α - D - e r y t h r o f u r a n o s e 3, OC-Dthreofuranose 5 and β - D - t h r e o f u r a n o s e 6 r e v e a l e d a s i n g l e ( g l o b a l ) m i n i m u m a t 0.4 Ρ / π , 0.4 Ρ / π a n d 1.6 Ρ/π, respectively. S i n g l e - p o i n t r e f i n e m e n t o f t h e STO-3G e n e r g i e s a t t h e 3-21G l e v e l gave s l i g h t l y phase-shifted c u r v e s and l a r g e r e n e r g y d i f f e r e n c e s , but t h e p r e s e n c e o f a s i n g l e ( g l o b a l ) e n e r g y m i n i m u m was c o n s e r v e d . In c o n t r a s t , β - D - e r y t h r o f u r a n o s e 4 showed r a d i c a l l y 2 0


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d i f f e r e n t b e h a v i o r , w i t h t h e ST0-3G d a t a p r o d u c i n g a r e l a t i v e l y f l a t energy-conformation curve w i t h a g l o b a l m i n i m u m a t 1.2 Ρ/π. S i n g l e - p o i n t 3-21G r e f i n e m e n t o f t h e s e d a t a , however, produced a curve w i t h two w e l l d e f i n e d m i n i m a o f c o m p a r a b l e e n e r g i e s a t 0.0 a n d 1.0 Ρ/π, a r e s u l t w h i c h a p p e a r s t o be more c o n s i s t e n t w i t h experimental data*. This d i s p a r i t y between b a s i s s e t s i n d i c a t e s t h a t S T 0 - 3 G c a l c u l a t i o n s may n o t b e r e l i a b l e i n p r e d i c t i n g accurate conformational energy p r o f i l e s i n some f u r a n o s e s . I n t h i s s t u d y , we e x a m i n e d t h e e f f e c t o f b a s i s s e t more t h o r o u g h l y b y c o n d u c t i n g c o m p l e t e g e o m e t r i c o p t i m i z a t i o n s w i t h t h e STO-3G a n d 3-21G b a s i s s e t s t o o b t a i n and compare c o n f o r m a t i o n a l e n e r g y p r o f i l e s on 7-10 (Figure 14). In a l l four cases, t h e energy d i f f e r e n c e between t h e l e a s t and most s t a b l e c o n f o r m e r s i s g r e a t e r i n 3-21G d a t a t h a n i n STO-3G d a t a . I n 7, 8 a n d 10, t h e g e n e r a l shape o f t h e p r o f i l e i s m a i n t a i n e d , although a d d i t i o n a l " f i n e s t r u c t u r e " a p p e a r s t o a r i s e a t t h e 3-21G level. In contrast, there i s a notable difference between b a s i s s e t s f o r 9. Of t h e f o u r s t r u c t u r e s s t u d i e d , 9 i s t h e o n l y isomer having c i s - 1 , 2 h y d r o x y l g r o u p s , a n d c a r e was t a k e n t o c h o o s e a C 2 - 0 2 t o r s i o n t o prevent p o t e n t i a l i n t r a m o l e c u l a r hydrogen bonding between t h e a d j a c e n t h y d r o x y g r o u p s a t 01 a n d 0 2 . The c a u s e o f t h e d i s p a r i t y i s p r e s e n t l y u n c l e a r , b u t more c o n f i d e n c e i s p l a c e d o n t h e r e s u l t o b t a i n e d f r o m t h e 3-21G a n a l y s i s . B a s e d o n t h e m o r e r e l i a b l e 3-21G d a t a , t h e c o n f o r m a t i o n a l b e h a v i o r o f 7 - 1 0 i s s u m m a r i z e d i n Scheme 5. I n 7 , n o r t h - s o u t h i n t e r c o n v e r s i o n ( F i g u r e 1) b e t w e e n t h e two most s t a b l e c o n f o r m e r s , E and E , o c c u r s p r e d o m i n a n t l y v i a e a s t c o n f o r m e r s (Εχ a n d °E) t h r o u g h a comparatively low a c t i v a t i o n b a r r i e r . In contrast, the t w o m o s t s t a b l e n o r t h a n d s o u t h c o n f o r m e r s o f 8, E a n d E2, i n t e r c o n v e r t p r e d o m i n a n t l y v i a w e s t c o n f o r m e r s , E a n d E, and t h e a c t i v a t i o n b a r r i e r i s higher. Iti s i n t e r e s t i n g t o note t h a t t h e i n t e r c o n v e r s i o n o f n o r t h and s o u t h c o n f o r m e r s o f t h e s t r u c t u r a l l y - r e l a t e d 2-deoxy~P-De r y t h r o - p e n t o s e 2, appears t o occur predominantly through e a s t c o n f o r m e r s ; t h e p r e s e n c e o f a d e s t a b i l i z i n g 1,3i n t e r a c t i o n b e t w e e n 0 1 a n d C5 ( n o t p r e s e n t i n e a s t conformers) d e s t a b i l i z e s west conformers o f 2. This d e s t a b i l i z i n g i n t e r a c t i o n i s absent i n west conformers o f 8, t h e r e b y p e r m i t t i n g a w e s t i n t e r c o n v e r s i o n p a t h w a y . I n 9, a s o u t h c o n f o r m e r ( E) i s h i g h l y p r e f e r r e d , a l t h o u g h a l o c a l minimum i s o b s e r v e d a t c o n f o r m e r s n e a r E (north conformer). The p a t h w a y o f i n t e r c o n v e r s i o n i s c h a r a c t e r i z e d by a high energy b a r r i e r through east conformers ( E °E, E ) . Two m i n i m a a r e o b s e r v e d f o r 1 0 , a g l o b a l minimum a t west c o n f o r m e r s , E a n d E , a n d a l o c a l m i n i m u m a t °E. I n t e r c o n v e r s i o n between these conformers i s c h a r a c t e r i z e d by high energy b a r r i e r s which are comparable f o r t h e n o r t h and south pathways. 2

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Ο F i g u r e 13. The E conformer o f 7 showing t h e p o t e n t i a l f o r i n t r a m o l e c u l a r hydrogen bonding between t h e hydroxyl substituents a t C I a n d C3. The C3-03 bond t o r s i o n c h a n g e i n d u c e d d u r i n g 3-21G g e o m e t r y o p t i m i z a t i o n o f t h i s s t r u c t u r e was p r e s u m a b l y d r i v e n b y this interaction. 2

2-dcoxy-a-D-glycero-tctrofuranose 2E(0.0) * E,(0.33) oE(0.55) * Ea(0.17) interconversion via east conformers. low energy barrier

2-dcoxy-P-D-glycero-tetrofuranose * E ( 0 . 0 ) * Eo(1.65) · * 1Ε (1.70) E (0.90) interconversion via west conformers. high energy barrier 2

3-deoxy-a-D-glycero-tetrofuranose 2E(0.0)

E!(2.00) ^ oE(3.03) ^ E (2.97) interconversion via east conformers, high energy barrier 4

*E(2.93)

3-deoxy-P-D-glyœro-tetrofuranose *E(0.0) Eo(0.05) oE(3.00) interconversion via north or south conformers, high energy barrier Scheme 5


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F i g u r e 14. The e f f e c t o f r i n g c o n f o r m a t i o n on r e l a t i v e e n e r g y o f 7 ( A ) , 8 ( Β ) , 9 (C) a n d 10 ( D ) . STO-3G d a t a a r e s h o w n i n f i l l e d s y m b o l s , a n d 3-21G d a t a a r e s h o w n i n open symbols. E n e r g i e s o f t h e p l a n a r forms a r e i n d i c a t e d on t h e y - a x e s .


S 2 ^ S Ε


6.


Ab Initio Molecular Orbital Calculations113

The a b o v e e n e r g y p r o f i l e s s u g g e s t s i g n i f i c a n t l y different conformational b e h a v i o r i n 7-10 both i n terms o f p r e f e r r e d g e o m e t r i e s a n d modes o f c o n f o r m a t i o n a l i n t e r c o n v e r s i o n i n t h e gas phase. Inherent i n t h e above a n a l y s i s i s t h e a s s u m p t i o n t h a t t h e 3-21G c a l c u l a t i o n s p r o v i d e a r e l i a b l e p i c t u r e o f gas phase b e h a v i o r . Of course, t h i s assumption w i l l require v a l i d a t i o n through c a l c u l a t i o n s w i t h more s o p h i s t i c a t e d b a s i s s e t s , e s p e c i a l l y those employing d - o r b i t a l s (e.g., 6-31G*). In a d d i t i o n , while i t i s d i f f i c u l t t o extrapolate the d a t a i n F i g u r e 14 t o c o n d i t i o n s i n a q u e o u s s o l u t i o n , i t i s nevertheless clear that the nature of conformational a v e r a g i n g , w h i c h a f f e c t s t h e i n t e r p r e t a t i o n o f NMR p a r a m e t e r s , depends on r i n g c o n f i g u r a t i o n , and t h a t a s i n g u l a r a p p r o a c h t o NMR p a r a m e t e r i n t e r p r e t a t i o n c a n n o t be a p p l i e d t o a l l f u r a n o s e s t r u c t u r e s . E n e r g y p r o f i l e s i n F i g u r e 14 a l s o r e v e a l t h a t p l a n a r furanose forms a r e o f t e n o f lower energy than puckered conformers. F o r example, r e l a t i v e conformational e n e r g i e s d e t e r m i n e d f o r 7 w i t h t h e 3-21G b a s i s s e t i n d i c a t e t h a t t h e p l a n a r c o n f o r m e r i s more s t a b l e t h a n t h e E c o n f o r m e r ; i n 8, t h e p l a n a r c o n f o r m e r i s c a l c u l a t e d t o b e m o r e s t a b l e t h a n °E. T h e s e observations suggest that the conformational d y n a m i c s o f some f u r a n o s e r i n g s may n o t b e c o m p l e t e l y d e s c r i b e d b y pseudorotation; i n t h e s e c a s e s , c o n f o r m e r i n t e r c o n v e r s i o n may o c c u r b y b o t h i n v e r s i o n and p s e u d o r o t a t i o n a l pathways, w i t h t h e l a t t e r b e i n g t h e more p r e f e r r e d r o u t e . 0

E_ E f f e c t o f B a s i s S e t on O p t i m i z e d M o l e c u l a r Parameters in Furanoses. T h e a b o v e r e s u l t s i n d i c a t e t h a t t h e 3-21G b a s i s s e t i s , i n g e n e r a l , m o r e r e l i a b l e t h a n t h e STO-3G basis set i n molecular o r b i t a l c a l c u l a t i o n s of furanoses. H o w e v e r , t h e 3-21G b a s i s s e t l a c k s p o l a r i z a t i o n f u n c t i o n s w h i c h may b e i m p o r t a n t i n s t u d i e s o f f u r a n o s e s t h a t c o n t a i n b o t h e n d o c y c l i c and e x o c y c l i c oxygen atoms. We conducted a l i m i t e d study t o assess the e f f e c t of e x t e n d e d b a s i s s e t s on c a l c u l a t e d g e o m e t r i e s by o p t i m i z i n g the planar conformer of 2-deoxy-a-D-glycerot e t r o s e 7 u s i n g t h e STO-3G, 3-21G, 4-31G, 4-31G*, 6-31G a n d 6-31G* b a s i s s e t s . T h e s e d a t a a r e s h o w n i n T a b l e 1. R e s u l t s o b t a i n e d w i t h t h e 4-31G a n d 6-31G b a s i s s e t s w e r e very s i m i l a r and a r e d i s c u s s e d below as a s i n g l e group (4-31G/6-31G). R e s u l t s o b t a i n e d w i t h t h e 4-31G* a n d 631G* b a s i s s e t s a r e d i s c u s s e d b e l o w a s a s i n g l e g r o u p ( 4 3 1 G * / 6 - 3 1 G * ) f o r t h e same r e a s o n . Implicit i n the f o l l o w i n g d i s c u s s i o n i s the assumption that the observed t r e n d s b e t w e e n b a s i s s e t s w i l l be i n d e p e n d e n t o f f u r a n o s e r i n g c o n f i g u r a t i o n and conformation. Bond l e n g t h s g e n e r a l l y decrease w i t h b a s i s s e t i n t h e o r d e r STO-3G, 3-21G, 4 - 3 1 G / 6 - 3 1 G a n d 4 - 3 1 G * / 6 - 3 1 G * . F o r e x a m p l e , t h e C 2 - C 3 b o n d l e n g t h i s 1.557 Â ( S T O - 3 G ) , 1.546 A ( 3 - 2 1 G ) , 1.539 Â ( 4 - 3 1 G / 6 - 3 1 G ) a n d 1.536 Â (4.31GV6-31G*) , f o r an o v e r a l l d e c r e a s e i n l e n g t h o f



114


1.3% ( 0 . 0 2 1 Â ) . T h e C-0 b o n d l e n g t h s d e t e r m i n e d f r o m STO-3G a n d 4 - 3 1 G V 6 - 3 1 G * d e c r e a s e b y 2.2 - 3 . 2 % . T h e C-H b o n d s d e c r e a s e i n t h e o r d e r STO-3G 3-21G 4-31G/631G, b u t a r e s l i g h t l y l e n g t h e n e d r e l a t i v e t o 4 - 3 1 G / 6 - 3 1 G i n t h e 4-31G*/6-31G* d a t a . Bond a n g l e s a r e a l s o n o t a b l y a f f e c t e d by b a s i s s e t ( T a b l e 1 ) . I t i s i n t e r e s t i n g t o n o t e t h a t t h e 3-21G b a s i s s e t p r e d i c t s a s i m i l a r COC b o n d a n g l e (113.0°) a s t h e 4 - 3 1 G * a n d 6-31G* b a s i s s e t s (113.8°); t h e s e v a l u e s a r e s u b s t a n t i a l l y l a r g e r t h a n t h a t p r e d i c t e d b y t h e STO3G b a s i s s e t (110.4°). The l a r g e s t d i f f e r e n c e s b e t w e e n b a s i s s e t s o c c u r s f o r t h e COH b o n d a n g l e s ( e . g . , f o r C 3 0 3 - H , 104.2° w i t h STO-3G a n d 113.7° w i t h 6-31G); t h e s e d e v i a t i o n s c o u l d be s i g n i f i c a n t , as t h e s e a n g l e s a f f e c t the p o s i t i o n o f hydroxyl protons and thus t h e i r a b i l i t y t o p a r t i c i p a t e i n i n t r a - and i n t e r m o l e c u l a r hydrogen bonds. Bond t o r s i o n s a r e n o t g r e a t l y a f f e c t e d by b a s i s s e t . The l a r g e s t d i f f e r e n c e o c c u r s f o r t h e C l - 0 1 b o n d t o r s i o n w h i c h v a r i e s f r o m 66.5° ( 6-31G*) t o 75.4° ( 3 - 2 1 G ) , w i t h t h e STO-3G a n g l e (68.3°) i n c l o s e r a g r e e m e n t w i t h t h e 6-31G* result. I n c o n t r a s t t h e C3-03 bond t o r s i o n i s o n l y s l i g h t l y a f f e c t e d by b a s i s s e t . This o b s e r v a t i o n points to the s i g n i f i c a n t l y d i f f e r e n t factors governing the e x o a n o m e r i c C-0 t o r s i o n s i n s u g a r s w h i c h may n o t b e p r o p e r l y t r e a t e d b y some b a s i s s e t s . Since two oxygen a t o m s a r e i n v o l v e d i n r e g u l a t i n g t h e e x o a n o m e r i c C-0 t o r s i o n , use o f basis sets with p o l a r i z a t i o n functions may b e r e q u i r e d t o moire a c c u r a t e l y e v a l u a t e i t s b e h a v i o r .

Discussion P r e v i o u s ab i n i t i o m o l e c u l a r o r b i t a l s t u d i e s o f t h e aldotetrofuranoses u s i n g t h e m i n i m a l STO-3G b a s i s s e t showed t h a t bond l e n g t h s , bond a n g l e s and bond t o r s i o n s are a f f e c t e d by furanose r i n g c o n f i g u r a t i o n and conformation. Of p a r t i c u l a r i n t e r e s t were t h e changes i n bond l e n g t h s , e s p e c i a l l y t h o s e bonds i n t h e v i c i n i t y o f the anomeric center. Such changes i n bond l e n g t h might be i m p o r t a n t i n d e t e r m i n i n g t h e s t r u c t u r e a n d r e a c t i v i t y of f u r a n o s e anomers. Furthermore, s u b t l e changes i n o v e r a l l m o l e c u l a r dimensions as a f u n c t i o n o f r i n g c o n f o r m a t i o n may b e i m p o r t a n t i n m e d i a t i n g m o l e c u l a r r e c o g n i t i o n and c a t a l y s i s between enzymes and f u r a n o s e substrates. However, bond l e n g t h changes o b s e r v e d w i t h t h e s i m p l e STO-3G b a s i s s e t r e m a i n e d t o b e v a l i d a t e d b y c a l c u l a t i o n s w i t h more e x t e n d e d b a s i s s e t s . T h i s s t u d y h a s c o m p a r e d STO-3G a n d 3-21G o p t i m i z e d g e o m e t r i e s o f f u r a n o s e c o n f o r m e r s a n d h a s shown t h a t , i n g e n e r a l , t h e o v e r a l l p a t t e r n s o f bond l e n g t h changes p r e d i c t e d b y t h e STO-3G a n d 3-21G b a s i s s e t s a r e s i m i l a r , a l t h o u g h t h e absolute changes d i f f e r w i t h b a s i s s e t . In p a r t i c u l a r , t h e s y s t e m a t i c c h a n g e s o f C-H a n d C-0 b o n d lengths near t h e anomeric center suggest a r o l e i n 2 0


6.



determining chemical r e a c t i v i t y (i.e., glycoside h y d r o l y s i s , anomerization) and p r e f e r r e d conformation. P r e v i o u s s t u d i e s c o n d u c t e d w i t h t h e ST0-3G b a s i s s e t on a l d o t e t r o f u r a n o s e s s u g g e s t e d t h a t t h e ST0-3G b a s i s s e t may n o t b e r e l i a b l e i n p r e d i c t i n g t o t a l e n e r g y p r o f i l e s f o r furanose conformers. F o r example, t h e e n e r g y p r o f i l e f o r β-D-erythrofuranose 4 d e t e r m i n e d f r o m S T 0 - 3 G o p t i m i z a t i o n was s i g n i f i c a n t l y d i f f e r e n t t h a n t h a t d e t e r m i n e d f r o m s i n g l e - p o i n t 3-21G c a l c u l a t i o n s u s i n g t h e same S T 0 - 3 G o p t i m i z e d m o l e c u l a r p a r a m e t e r s ; t h e l a t t e r r e s u l t s a p p e a r e d more c o n s i s t e n t w i t h e x p e r i m e n t a l data. The p r e s e n t s t u d y p r o v i d e s f u r t h e r e v i d e n c e t h a t e n e r g y p r o f i l e s a r e n o t r e l i a b l e when o b t a i n e d w i t h t h e m i n i m a l b a s i s s e t . T h e g r e a t e r r e l i a b i l i t y o f 3-21G e n e r g y c a l c u l a t i o n s d e r i v e s f r o m i t s a b i l i t y - a s shown i n t h i s study - t o p r e d i c t bond l e n g t h s and bond angles i n c l o s e r agreement t o those observed e x p e r i m e n t a l l y . T h u s , we conclude that carbohydrate c a l c u l a t i o n s u s i n g ab i n i t i o m e t h o d s s h o u l d be c o n d u c t e d w i t h b a s i s s e t s no l e s s s o p h i s t i c a t e d t h a n t h e 3-21G b a s i s s e t i f r e a s o n a b l e s t r u c t u r e s a n d e n e r g e t i c s a r e t o be o b t a i n e d . The c a l c u l a t e d t o t a l e n e r g y p r o f i l e s f o r t h e a l d o t e t r o f u r a n o s e s 3, 5 a n d 6 c o n t a i n a well-defined g l o b a l m i n i m u m , s u g g e s t i n g t h a t t h e s e compounds, a t l e a s t i n t h e gas phase, p r e f e r conformations found i n a limited region of the pseudorotational itinerary. This behavior i s notably d i f f e r e n t than that o f the a l d o t e t r o f u r a n o s e 4 and t h e deoxytetrofuranoses 7, 8 a n d 10. C a l c u l a t e d t o t a l energy p r o f i l e s o f the l a t t e r compounds c o n t a i n g l o b a l and l o c a l minima o f r e l a t i v e l y similar energies. T h u s , 4, 7, 8 a n d 10 a p p e a r t o b e m o r e c o n f o r m a t i o n a l l y mobile i n t h e gas phase. I n some c a s e s , these p r e f e r r e d conformations are s i m i l a r ( i . e . , they are contiguous along t h e p s e u d o r o t a t i o n a l i t i n e r a r y ) , whereas i n others these conformations may b e n o t a b l y d i f f e r e n t ( i . e . , n o r t h and south geometries). Furthermore, the d y n a m i c s o f c o n f o r m e r i n t e r c o n v e r s i o n d i f f e r s b e t w e e n 4, 7, 8 a n d 10, s i n c e energy b a r r i e r s between p r e f e r r e d conformers d i f f e r f o r each s t r u c t u r e . These c a l c u l a t i o n s show t h a t s t r u c t u r e a n d c o n f i g u r a t i o n h a v e a p r o f o u n d e f f e c t on t h e c o n f o r m a t i o n a l dynamics o f f u r a n o s e r i n g s , at l e a s t i n t h e gas phase. Solution studies of 4 appear t o s u p p o r t t h e c o n f o r m a t i o n a l b e h a v i o r p r e d i c t e d b y ab i n i t i o m e t h o d s ; t h e s o l u t i o n b e h a v i o r o f 7-10 i s c u r r e n t l y under i n v e s t i g a t i o n . The a b s o l u t e changes i n t o t a l e n e r g y w i t h furanose r i n g c o n f o r m a t i o n a p p e a r t o b e g r e a t e r w i t h t h e 3-21G b a s i s s e t t h a n w i t h STO-3G c a l c u l a t i o n s . I t i s l i k e l y t h a t t h e s e b a s i s s e t s r e p r e s e n t t h e two extreme l i m i t s , a n d t h a t c a l c u l a t i o n s c u r r e n t l y u n d e r w a y w i t h t h e 6-31G* b a s i s s e t w i l l y i e l d t o t a l energy p r o f i l e s with absolute energy changes i n t e r m e d i a t e i n magnitude. Hydroxyl group o r i e n t a t i o n i n computational studies of carbohydrates s t i l l remains a problem. T h i s study has


2 0

2 0

7


115

116


T a b l e 1. Comparison o f Optimized M o l e c u l a r Parameters For t h e P l a n a r Conformer of 2-Deoxy-a-D-glycero-tetrose Obtained With D i f f e r e n t Basis Sets Basis Set


Parameter

1

ST0-3G

3-21G

4-31G

4-31G*

6-31G

6-31G*

Rl-2 R2-3 R3-4 R4-5 R5-6 R5-7 R7-8 Rl-9 Rl-10 R2-11 R2-12 R12-13 R3-14 R3-15

1.557 1.559 1.437 1.437 1.106 1.431 0.991 1.086 1.087 1.097 1.434 0.991 1.095 1.096

1.546 1.544 1.445 1.424 1.079 1.420 0.967 1.081 1.079 1.082 1.442 0.966 1.079 1.077

1.539 1.531 1.439 1.418 1.079 1.411 0.953 1.081 1.078 1.082 1.433 0.952 1.078 1.076

1.536 1.533 1.404 1.391 1.085 1.386 0.949 1.083 1.081 1.085 1.402 0.948 1.083 1.081

1.540 1.532 1.441 1.420 1.080 1.412 0.952 1.082 1.080 1.083 1.434 0.951 1.079 1.077

1.537 1.534 1.405 1.392 1.085 1.387 0.948 1.084 1.082 1.086 1.404 0.947 1.084 1.082

Al-2-3 A2-3-4 A3-4-5 A4-5-6 A4-5-7 A5-7-8 A2-1-9 A2-1-10 A3-2-11 A3-2-12 A2-12-13 A2-3-14 A2-3-15

104 .4 110. 1 110. 4 107 . 7 109. 6 103. 7 111. 6 110. 6 110. 0 108. 2 104 .2 111. 0 109. 1

105 107 113 107 110 109 112 109 110 106 110 112 108

.3 .5 .0 .8 .2 .8 .0 .3 .7 .3 .8 .3 .2

105. 7 106. 9 113. 6 107. 5 110. 2 112. 2 111. 6 110. 1 111. 0 106. 8 113 . 5 112. 9 109. 5

104 .5 108. 0 113. 8 107. 6 110. 6 108. 5 111. 8 110. 3 110. 4 108. 1 109. 6 112. 1 109. 5

105 106 113 107 110 112 111 110 111 106 113 112 109

.8 .9 .6 .5 .3 .5 .6 .3 .0 .9 .7 .9 .7

104.5 108.0 113.8 107.5 110.7 108. 6 111. 9 110.4 110.5 108.0 109.7 112 . 1 109.5

T3-4-5- 6 T3-4-5- 7 T6-5-7- 8 T3-2-1- 9 T 3 - 2 - 1 - 10 T 4 - 3 - 2 - 11 T 4 - 3 - 2 - 12 Tll-2-12-13 T l - 2 - 3 - 14 T l - 2 - 3 - 15

121. 2 119. 0 68.3 120. 8 117 . 9 118. 0 121. 4 57.8 120. 7 120. 4

122 117 75. 122 115 120 120 58. 119 118

.2 .2 4 .1 .4 .1 .3 9 .1 .8

122. 117. 72.7 121. 117. 120. 120. 57.8 118. 118.

121. 7 118. 8 66.7 121. 1 117. 9 119. 1 121. 4 57 .1 119. 6 119. 5

122 .7 117 .9 71.:5 121 .5 117 .5 120 .7 120 .9 57 . 9 118 .5 118 .4

121.7 118.8 66.5 121.2 117 . 9 119.3 121.4 57.3 119. 6 119. 6

7 8 6 2 7 7 5 4

L

R, A and Τ r e f e r t o bond l e n g t h s ( i nÂ ) , bond a n g l e s ( i n °) , a n d b o n d t o r s i o n s ( i n °) u s e d t o s e t t h e Z - m a t r i x input f i l e . A t o m n u m b e r i n g s i n 7 a r e s h o w n i n S c h e m e 6.


7

6.


Ab Initio Molecular Orbital Calculations117 4

14 15

Ο Η 8 Η

Ο

Η 13

10

12


Scheme 6 c o n f i r m e d t h a t t h e C l - 0 1 bond i n a l d o f u r a n o s e s p r e f e r s t o b e gauche t o t h e r i n g o x y g e n a n d anti t o C2, as p r e d i c t e d by t h e exoanomeric e f f e c t ' . Thus, f o r t h e C l - 0 1 bond, a r a t i o n a l argument e x i s t s t o l i m i t i t s c o n f o r m a t i o n . However, t h e r e a r e no r u l e s a t p r e s e n t t o d e d u c e p r e f e r r e d C-0 t o r s i o n s f o r n o n - a n o m e r i c r i n g h y d r o x y l groups. I t i s not i n c o n c e i v a b l e t h a t hydroxyl group o r i e n t a t i o n may a f f e c t t h e o v e r a l l e n e r g e t i c s o f conformer i n t e r c o n v e r s i o n , e s p e c i a l l y i n condensed phases. I n t r a m o l e c u l a r and i n t e r m o l e c u l a r hydrogen bonding are l i k e l y to s t a b i l i z e / d e s t a b i l i z e s p e c i f i c conformers and thereby a f f e c t t h e o v e r a l l energy p r o f i l e . We h a v e a s s e s s e d t h i s p o s s i b i l i t y b y o p t i m i z i n g t h e p l a n a r a n d e n v e l o p e c o n f o r m e r s o f 8 w i t h 0 3 - H a n t i t o H3 ( C a s e I ) a n d w i t h 0 3 - H a n t i t o C4 ( C a s e I I ) . These r e s u l t s a r e shown i n F i g u r e 15. The o v e r a l l s h a p e o f t h e two p r o f i l e s i s c o n s e r v e d , w i t h e a c h p r o f i l e s h o w i n g one g l o b a l minimum a n d one l o c a l minimum. However the g l o b a l minimum i n Case I i s t h e l o c a l minimum : Case I I . 2 8

0.0

0.5

1.0

2 9

1.5

2.0

2.5

3.0

3.5

4.0

Ρ/π (radians) F i g u r e 15. The e f f e c t o f C3-03 b o n d c o n f o r m a t i o n on t h e e n e r g y p r o f i l e o f 8. G e o m e t r i e s were o p t i m i z e d w i t h t h e 3-21G b a s i s s e t . C a s e I , 0 3 - H b o n d a n t i t o H3, c l o s e d s y m b o l s ; C a s e I I , 0 3 - H b o n d a n t i t o C4, o p e n symbols. In Computer Modeling of Carbohydrate Molecules; French, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1990.

118


Thus, f o l l o w i n g t h e lowest energy pathway between minima m i g h t r e q u i r e C3-03 b o n d r o t a t i o n i n 8. This cursory examination indicates that, while t h e l o c a t i o n o f energy m i n i m a may n o t b e a f f e c t e d b y n o n - a n o m e r i c h y d r o x y l c o n f o r m a t i o n s , t h e r e l a t i v e e n e r g i e s o f t h e s e m i n i m a may i n d e e d depend on t h e s e c o n f o r m a t i o n s . Acknowledgments The g r a n t s u p p o r t o f t h e N a t i o n a l I n s t i t u t e s o f H e a l t h (GM 3 3 7 9 1 ) a n d t h e R e s e a r c h C o r p o r a t i o n ( 1 0 0 2 8 ) i s g r a t e f u l l y acknowledged.


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6. GARRETT AND SERIANNI Ab Initio Molecular Orbital Calculations 119

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