Modeling of Glucopyranose - American Chemical Society

Chapter 7

Modeling of Glucopyranose The Flexible Monomer of Amylose 1

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Alfred D. French , R. S.Rowland ,and Norman L. Allinger 1

Southern Regional Research Center, U.S. Department of Agriculture, P.O. Box 19687, New Orleans, LA 70179 Department of Biochemistry, University of Alabama, Birmingham, AL 35294 Department of Chemistry, University of Georgia, Athens, GA 30602

Downloaded by MONASH UNIV on May 21, 2013 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch007

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The variability of the distance between O1 and O4 (D) in glucopyranose rings was modeled with the computer program CHARMM, three versions of MM2, and MM3. D is of interest because models of amylosic oligomers have dramatically different shapes when they are built with glucose residues that have large or small D. In the Cambridge Structural Database (excepting cycloamyloses), D ranges between 4.05 and 4.67 Å, with a mean of 4.411 Å. Models with lowest energy from the five programs had D values of 4.55 ± 0.02 Å when the dielectric constant was set for isolated molecules (1.5). Higher dielectric constants had no effect on D of MM2 models, but D in an MM3 model was 4.47 Å when the dielectric constant was set to 4, appropriate for crystals. The residue geometry was optimized at 13 different values of D, giving different bond and torsion angles. Amounts of change in these angles were similar to those in the database, as were their values at a given D. The most severe differences were about 3° for O5-C1-O1 and C3-C4-O4. Predicting correct amounts of change shows that a modeling force field is suitably partitioned among the various terms for bond length stretching, torsional rotation, van der Waals interaction, etc., and validates it for other modeling studies. The energy needed to deform the residue over the observed range of D is less than 2 kcal/mol. Goebel and Brant (1.) showed t h a t t h e l i k e l y shapes o f computer models o f amylose, a polymer o f l->4 l i n k e d a-D-glucose, depend on t h e e x a c t geometry o f t h e monomeric u n i t as w e l l as on t h e v a l e n c e bond and t o r s i o n a n g l e s a t t h e g l y c o s i d i c l i n k a g e . Subsequently, t h e d i s t a n c e between 01 and 04 (D) o f t h e monomer ( F i g u r e 1) was found t o be an i n d i c a t o r o f r e s i d u e geometry t h a t c o r r e l a t e s w i t h t h e shapes o f models o f v a r i o u s s i n g l e - and d o u b l e - h e l i c e s o f amylose (2,3). The c o r r e l a t i o n o f t h i s i n d i c a t o r w i t h t h e number of residues i n macrocycles o f c r y s t a l l i n e cycloamyloses (3.) was c o n f i r m e d by Saenger (4) and t h i s v a r i a b l e v i r t u a l - b o n d l e n g t h i s

0O97-6156/90/043O-O120$06.25/0 © 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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e x p l i c i t l y i n c o r p o r a t e d i n t h e f i b e r d i f f r a c t i o n and m o d e l i n g s o f t w a r e o f Zugenmaier and Sarko (5.) . V a r i a t i o n i n D a f f e c t s t h e shape o f amylose models t h r o u g h changes i n t h e s p a t i a l r e l a t i o n s h i p between t h e 01-CI bond v e c t o r and t h e 04-C4 v e c t o r (3) . W h i l e D o f ct-D-glucose r e s i d u e s has a wide range and works f a i r l y w e l l f o r d e s c r i b i n g t h e f l e x i b i l t y i n amylose h e l i c e s , D i s n e a r l y c o n s t a n t i n β-D-glucose r e s i d u e s d e s p i t e s i m i l a r v a r i a b i l i t y i n r i n g shape. The d i f f e r e n c e i n t h e e x t e n t o f v a r i a t i o n o f D f o r t h e two anomeric forms a r i s e s because t h e bond v e c t o r s a r e r o u g h l y p e r p e n d i c u l a r i n t h e α r i n g b u t p a r a l l e l i n the β ring. Therefore, t h e study o f other p o l y s a c c h a r i d e s may r e q u i r e i n d i c a t o r s o f r e s i d u e geometry o t h e r t h a n t h e v i r t u a l bond l e n g t h , which so n i c e l y s i m p l i f i e s t h e m o d e l i n g o f amylose. V a r i a t i o n i n o l i g o m e r i c , and hence, p o l y m e r i c shape a r i s i n g from g l u c o s e r e s i d u e s w i t h d i f f e r e n t D i s shown i n F i g u r e 2 by two m a l t o t e t r a o s e models. Both models a r e b u i l t from r e s i d u e s h a v i n g c o n f o r m a t i o n s , and t h e i r v a l e n c e - b o n d and t o r s i o n a n g l e s a t t h e glycosidic linkage are identical. However, t h e d i s t a n c e between t h e t e r m i n a l 01 and 04 atoms i s 13.7 Â i n t h e upper t e t r a m e r and 5.8 Â i n t h e lower model. The upper model i s composed o f t h e α-residues w i t h i n t r a - r e s i d u e D o f 4.570 Â from t h e c r y s t a l s t r u c t u r e r e p o r t on m e t h y l - p - m a l t o s i d e (6.) · The lower model i s composed o f n o n - r e d u c i n g r e s i d u e s from α-maltose (2) w i t h D o f 4.052 Â . The c o v a l e n t c h e m i c a l environments o f t h e two r e s i d u e s a r e s i m i l a r so t h e g e o m e t r i c d i f f e r e n c e s must be due m o s t l y t o d i f f e r e n t c r y s t a l packings. The 0.518 Â d i f f e r e n c e i n D i t s e l f a f f e c t s t h e t e t r a m e r shape. However, t h e major d i f f e r e n c e r e s u l t s from c u m u l a t i v e v a r i a t i o n s i n t h e l o c a t i o n o f a d j a c e n t r e s i d u e s , which a r i s e from d i f f e r e n c e s o f about 30° i n t h e a n g l e s between t h e C l - 0 1 and C4-04 bond v e c t o r s . R e s i d u e s w i t h i n t e r m e d i a t e v a l u e s o f D l e a d t o c u r v a t u r e s i n t e r m e d i a t e t o t h e above t e t r a m e r s . By s u p e r i m p o s i n g t h e C2, C3, C5 and 05 atoms o f t h e s e two r e s i d u e s , t h e i r s t r u c t u r a l d i f f e r e n c e s c a n be seen ( F i g u r e 3 ) . The r e s i d u e p a i r s were f i t t e d by an a l g o r i t h m (j8) f u r n i s h e d as p a r t o f t h e CHEM-X m o d e l i n g system (CHEM-X i s d e v e l o p e d and d i s t r i b u t e d b y C h e m i c a l D e s i g n L t d , Oxford, E n g l a n d ) . The C3-C4-C5 p l a n e i n t h e l o n g r e s i d u e i s more p e r p e n d i c u l a r t o t h e s e a t o f t h e c h a i r , w h i l e i t s 05-C1-C2 p l a n e i s r o t a t e d more towards c o p l a n a r i t y w i t h t h e seat o f the c h a i r . Motions o f these three-atom planes, p l u s s m a l l e r v a r i a t i o n s i n t h e bond a n g l e s such as 0 5 - C l - O l , a r e a m p l i f i e d (by t h e l e n g t h s o f t h e C l - 0 1 and C4-04 bonds) t o g i v e t h e o b s e r v e d range o f D. However, s t a n d a r d m o d e l i n g programs a r e b a s e d on bond and t o r s i o n a n g l e s , n o t motions o f p l a n e s , so o u r m o d e l i n g s t u d y f o c u s e s on changes i n t h e o r d i n a r y i n t e r n a l c o o r d i n a t e s . About a decade ago, Pensak and F r e n c h i n v e s t i g a t e d t h i s f l e x i b i l i t y w i t h t h e program MM1 and a l i m i t e d s e t o f c r y s t a l l o g r a p h i c r e s u l t s (.9) . S i n c e then, t h e number o f c r y s t a l s t u d i e s has i n c r e a s e d , and new m o d e l i n g s o f t w a r e was d e v e l o p e d i n attempts t o improve a c c u r a c y . T h e r e f o r e , we have r e i n v e s t i g a t e d t h i s problem. W h i l e we f o c u s on c h a n g i n g D, we b e l i e v e t h a t t h e a b i l i t i e s and d e f i c i e n c i e s d i s c l o s e d i n o u r study w i l l a p p l y t o o t h e r m o d e l i n g s t u d i e s such as c o n f o r m a t i o n a l a n a l y s e s o f d i s a c c h a r i d e s w i t h f l e x i b l e residues. I n t h i s study, we assume t h a t c r y s t a l s t r u c t u r e s w i l l have t h e l o w e s t p o s s i b l e t o t a l o f i n t r a - and i n t e r - m o l e c u l a r p o t e n t i a l energy. However, t h e p a r t i t i o n i n g o f t h e p o t e n t i a l energy between i n t r a - and i n t e r - m o l e c u l a r terms w i l l v a r y among c r y s t a l s t r u c t u r e s , d i s t o r t i n g t h e g l u c o s e r e s i d u e s away from t h e shape o f l o w e s t energy i n a way t h a t w i l l r e f l e c t m o r e - o r - l e s s random



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F i g u r e 1. d-D-Glucose i n t h e s t a r t i n g c o n f o r m a t i o n u s e d h e r e i n . H y d r o x y l groups a r e p o i n t e d c l o c k w i s e , and 06 i s gauche t o 05 and gauche t o C4 (the gg p o s i t i o n ) .

F i g u r e 2. Two m a l t o t e t r a o s e g l u c o s e h a v i n g d i f f e r e n t D. and t o r s i o n a n g l e s .

models c o n s t r u c t e d from r e s i d u e s o f They have i d e n t i c a l l i n k a g e bond

F i g u r e 3. Comparison o f t h e r e s i d u e g e o m e t r i e s used t o make t h e t e t r a m e r s i n F i g u r e 2.


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d i f f e r e n c e s i n t h e p a r t i t i o n i n g o f t o t a l energy. In a large p o p u l a t i o n o f d i f f e r e n t c r y s t a l s t r u c t u r e s t h a t c o n t a i n one o r more g l u c o s e r e s i d u e s , t h e D o b s e r v e d most f r e q u e n t l y s h o u l d c o r r e s p o n d c l o s e l y t o a model o f l o w e s t energy. D values observed l e s s f r e q u e n t l y would c o r r e s p o n d t o models o f h i g h e r energy, and s t r u c t u r a l d e t a i l s such as bond- and t o r s i o n - a n g l e s s h o u l d agree when D v a l u e s o f t h e models and r e a l r e s i d u e s a g r e e . Even though i t i s h a r d t o d e t e r m i n e t h e l e a s t e n e r g e t i c shape o f t h e g l u c o s e r i n g by experiment, comparisons o f changes i n t h e v a r i o u s m o l e c u l a r p a r a m e t e r s w h i l e D changes c a n i n d i c a t e how w e l l t h e f o r c e f i e l d works. A n o t h e r use f o r a s t u d y o f t h i s t y p e i s e s t a b l i s h i n g t h e range o f monomeric v a r i a t i o n as a p r e l u d e t o study o f o t h e r polymers.


Modeling

Software

F o r o u r work, t h r e e v e r s i o n s o f t h e program MM2 (1977, 85 and 87) (10,11) were used as w e l l as a p r e - r e l e a s e v e r s i o n o f MM3, t h e s u c c e s s o r t o MM2 (12). (MM2(77) i s a v a i l a b l e from t h e Quantum C h e m i s t r y Program Exchange, Department o f C h e m i s t r y , I n d i a n a U n i v e r s i t y , Bloomington, I n d i a n a 47901, as a r e t h e two r e c e n t v e r s i o n s t o academic u s e r s . Commercial u s e r s c a n g e t MMP2(85), MM2(87) and MM3 from M o l e c u l a r D e s i g n L t d , 2132 F a r a l l o n D r i v e , San Leandro, C a l i f o r n i a . MM3 i s a l s o a v a i l a b l e , t o f o r - p r o f i t and n o t f o r - p r o f i t u s e r s , from T e c h n i c a l u t i l i z a t i o n Corp., Inc., 235 G l e n V i l l a g e C o u r t , P o w e l l , Ohio 43065). MM2 and MM3 a r e i n t e n d e d t o model a wide v a r i e t y o f m o l e c u l e s . T h i s wide a p p l i c a b i l i t y i s attempted t h r o u g h use o f c o m p l i c a t e d p o t e n t i a l energy terms. The CHARMM program (13) ( a v a i l a b l e from P o l y g e n C o r p o r a t i o n , 200 F i f t h Avenue, Waltham, M a s s a c h u s e t t s 02154) was a l s o t e s t e d . T h i s g e n e r a l - p u r p o s e ( m o l e c u l a r mechanics, dynamics, e t c . ) program has a s i m p l e r p o t e n t i a l t h a t i s o f t e n used f o r p r o t e i n s , b u t i t c a n a p p l y t o c a r b o h y d r a t e s t h r o u g h t h e use o f p a r a m e t e r s d e v e l o p e d e s p e c i a l l y f o r c a r b o h y d r a t e s (14,) . To i l l u s t r a t e t h e d i f f e r e n t c o m p l e x i t i e s , CHARMM's e n e r g i e s a r i s i n g from t o r s i o n a l terms depend o n l y on t h e two c e n t r a l atoms, and t h e r e i s o n l y one c o s i n e term. F o r MM2 and MM3, t h e r e a r e t h r e e c o s i n e terms f o r each four-atom sequence t h a t d e f i n e s a t o r s i o n angle. MM2 t r e a t s l o n e p a i r s o f e l e c t r o n s on h y d r o x y l and e t h e r oxygen atoms as s e p a r a t e "atoms" t h a t a l s o must be parameterized. T h e r e f o r e , many more p a r a m e t e r s must be used w i t h t h e MM2 and MM3 programs t h a n t h e CHARMM program. (The parameters f o r a l l t h e atomic sequences i n g l u c o s e , and many o t h e r m o l e c u l e s , a r e f u r n i s h e d w i t h MM2 and MM3.) In a n o t h e r example o f d i f f e r e n c e s i n c o m p l e x i t y , t h e bonds t r e t c h i n g energy i n CHARMM i s c a l c u l a t e d w i t h a harmonic o s c i l l a t o r function. MM3 s o l v e s t h e p r o b l e m d e s c r i b e d by F r e n c h , T r a n and Perez i n t h i s book f o r MM2's c u b i c s t r e t c h i n g f u n c t i o n by u s i n g a q u a r t i c f u n c t i o n f o r bond s t r e t c h i n g . Additional c o m p l e x i t y i n MM3 i s d e s c r i b e d i n Ref. 12. C a r b o h y d r a t e s have been i n c l u d e d i n t h e wide range o f m o l e c u l e s used i n t h e p a r a m e t e r i z a t i o n o f MM2 and o f MM3. A l c o h o l and e t h e r parameters have u s u a l l y been d e t e r m i n e d from s i m p l e a l c o h o l s and e t h e r s t h e m s e l v e s . However, c a r b o h y d r a t e s c o n t a i n some u n u s u a l f e a t u r e s i n t h e a c e t a l l i n k a g e s , and i n t h e many v i c i n a l hydrogen-bonded h y d r o x y l groups. The "anomeric e f f e c t " , f i r s t d i s c o v e r e d by Edward (15) and p o p u l a r i z e d by Lemieux (16), i s b e s t known i n c a r b o h y d r a t e s , a l t h o u g h , o f c o u r s e , i t o c c u r s i n o t h e r c l a s s e s o f compounds as w e l l . One apparent r e s u l t o f t h i s e f f e c t i s t h a t an a x i a l a l k o x y s u b s t i t u e n t i s o f t e n more s t a b l e t h a n t h e c o r r e s p o n d i n g e q u a t o r i a l s u b s t i t u e n t when a t t a c h e d a t t h e CI p o s i t i o n o f a t e t r a h y d r o p y r a n y l r i n g . T h i s e f f e c t c a n be



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mimicked i n m o l e c u l a r mechanics by a s u i t a b l e t o r s i o n a l p o t e n t i a l t h a t i s i n c l u d e d i n MM1 and a l l v e r s i o n s o f MM2. A n o t h e r anomeric e f f e c t i s t h a t a c e t a l C-0 bonds, and t o a l e s s e r e x t e n t , t h e bonds between a c e t a l carbons and e t h e r oxygens, a r e s h o r t e n e d o r e l o n g a t e d as a f u n c t i o n o f t h e i r a s s o c i a t e d t o r s i o n a l angles. J e f f r e y and T a y l o r m o d i f i e d MM1 t o account f o r t h e s e anomeric e f f e c t s (IT) and s i m i l a r a d d i t i o n s were put i n t h e s t a n d a r d 1985 v e r s i o n o f MM2 (11). The p a r a m e t e r i z a t i o n o f MM3 f o r anomeric e f f e c t s i s p r e l i m i n a r y , w i t h r e c e n t (18-20) r e s u l t s b e i n g monitored. V e r s i o n s o f MM2 b e f o r e 1987 c a l c u l a t e e n e r g i e s f o r hydrogen bonds t h a t are t o o h i g h , compared t o experiment. W i t h t h e 1987 r e l e a s e , m o l e c u l a r e n e r g i e s a r e lowered by a v a r i a b l e amount when an atomic sequence t h a t c o u l d c o r r e s p o n d t o an hydrogen bond i s detected. The amount depends on t h e geometry o f t h e atoms i n v o l v e d i n t h e sequence. MM3 was p a r a m e t e r i z e d t o account f o r hydrogen b o n d i n g from t h e b e g i n n i n g . S i n c e t h e MM3 p o t e n t i a l f u n c t i o n does not use l o n e p a i r s , i t has a p r a c t i c a l advantage o v e r MM2, e s p e c i a l l y f o r carbohydrates. The l o n e p a i r s , r e q u i r e d f o r c o r r e c t use w i t h MM2, i n c r e a s e t h e number o f "atoms" i n a c a r b o h y d r a t e m o l e c u l e , o f t e n by 50%, c a u s i n g c a l c u l a t i o n s w i t h MM2 t o t a k e t w i c e as l o n g as w i t h MM3. Modeling

Details

The s t a r t i n g c o o r d i n a t e s were from a model r e s i d u e ( F i g u r e 1) w i t h 06 i n t h e gg p o s i t i o n (the t o r s i o n a n g l e 05-C5-C6-06 i s - 6 0 ° ) . The secondary h y d r o x y l s were a r r a n g e d c l o c k w i s e . T h i s d e s c r i p t i o n a p p l i e s when t h e r i n g i s viewed from above (H4 i s c l o s e r t o t h e v i e w e r t h a n C4). The t o r s i o n a n g l e s between t h e h y d r o x y l hydrogens and t h e hydrogen atoms on t h e carbons a r e r o u g h l y + 6 0 ° a t C l , C2 and C4 and -60° a t C3. P r e l i m i n a r y s t u d i e s showed t h a t t h i s arrangement has l o w e s t energy when u s i n g t h e MM2(85) f o r c e f i e l d . I n i t i a l l y , t h e d e f a u l t d i e l e c t r i c c o n s t a n t s o f 1.5 were used (1.0 f o r CHARMM), s u i t e d t o i s o l a t e d m o l e c u l e s . T h i r t e e n models w i t h v a l u e s o f D i n t h e range from 3.9 t o 5.1 Â were o p t i m i z e d w i t h each program. D was kept a t t h e s t a r t i n g v a l u e s by u s i n g p r o v i s i o n s w i t h i n t h e programs t o f i x some atoms a t s p e c i f i e d c o o r d i n a t e s w h i l e o p t i m i z i n g a l l o t h e r atomic p o s i t i o n s . The MM2(77), MMP2(85) and MM2(87) programs were v e r s i o n s f o r Vax computers d i s t r i b u t e d by t h e QCPE; MM3 was a p r e - r e l e a s e Vax v e r s i o n . CHARMM r e s u l t s were k i n d l y p r o v i d e d by P r o f e s s o r Brady. S e l e c t i o n from t h e Cambridge

Crystallographic

Database

The b o n d - l e n g t h s , bond-angles and t o r s i o n a n g l e s o f each model were compared w i t h i n f o r m a t i o n from 46 g l u c o s e r e s i d u e s i n c r y s t a l s t r u c t u r e s i n t h e 1989 Cambridge S t r u c t u r a l Database (CSD) (21) (Table 1 ) . R e s i d u e s from c y c l o a m y l o s e s were not i n c l u d e d s i n c e t h e i r m a c r o c y c l e s o f 6-8 g l u c o s e r e s i d u e s impose a d d i t i o n a l , s y s t e m a t i c l i m i t s on t h e r i n g geometry ( 3 ) . M o l e c u l e s t h a t c o n t a i n e d d i s o r d e r e d oxygen atoms, such as 1-kestose, were a l s o not included. No s t r u c t u r e s w i t h c r y s t a l l o g r a p h i c R f a c t o r s g r e a t e r t h a n 0.10 were used. Only one R exceeded 0.07 and t h e mean i s 0.044. D ranges o v e r more t h a n 0.6 Â, w h i l e t h e C l — C 4 d i s t a n c e v a r i e s o n l y one e i g h t h as much, as shown i n T a b l e 2.


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Table 1: Refcode, Journal Codon, Volume, Year, Page, [D] and Compound Name

BAGZEO CRBRAT 93 135 1981 [4.367] 1-Ο-α-D-Glucopyranosyl-D-mannitol dihydrate BAVCAC JLACBF * 2372 1981 [4.567] 6-0- (GC-D-Glucopyranosyl) -D-glucitol BAXSEY01 ZKKKAJ 161 69 1982 [4.326, 4.510] 4-Nitrophenyl-α-D-glucopyranoside BIZHIB CRBRAT 108 163 1982 [4.5160] 4-O-a-D-Glucopyranosyl-D-glucitol BOPXEJ ZKKKAJ 160 259 1982 [4.666, 4.442] Phenyl-cc-D-glucopyranoside CEKLUZ ACSCEE 40 389 1984 [4.639] Disodium uridine diphophoglucose dihydrate CELGIJ ACSCEE 40 531 1984 [4.130] 0- a-D-Glucopyranosyl-(1-2)-Ο-β-D-fructofuranosyl-(6-2)-βD-fructofuranoside monohydrate (6-kestose) CIMDUX ACSCEE 40 1338 1984 [4.495] Disodium glucose-1-phosphate hydrate DECGPY10 JACSAT 98 6628 1976 [4.360] 1- Decyl cc-D-glucopyranoside DEKYEX CRBRAT 137 21 1985 [4.414, 4.526] a-D-Glucopyranosyl-a-D-glucopyranoside DUDXOP IJBMDR 7 363 1985 [4.480, 4.483, 4.237] Methyl-a-maltrotrioside tetrahydrate FONYUC ACSCEE 43 1809 1987 [4.218] 4-O-a-D-Glucopyranosyl-N-methylmoranoline dihydrate GAFVIS CRBRAT 169 1 1987 [4.483] Octyl α-D-glucopyranoside monohydrate GAFVOY CRBRAT 169 1 1987 [4.291] Octyl α-D-glucopyranoside hemihydrate GLUCMH11 ACBCAR 29 365 1973 [4.513] α-D-Glucose monohydrate GLUCSA01 ACBCAR 35 656 1979 [4.486] a-D-Glucose GLUCUR20 ACBCAR 27 1969 1971 [4.476] a-D-Glucose-urea complex IMATUL ACBCAR 29 514 1973 [4.370] Isomaltulose monohydrate KGLUCP02 ACSCEE 40 389 1984 [4.401] Dipotassium glucose-l-phosphate dihydrate LACTOS10 ACBCAR 27 994 1971 [4.455] α-Lactose monohydrate MALTOS11 ACBCAR 33 2490 1977 [4.410] β-Maltose monohydrate MALTOT ACBCAR 34 213 1978 [4.052, 4.224] α-Maltose MELEZT01 ACBCAR 32 2598 1976 [4.324, 4.422] Melezitose monohydrate MELIBM10 ACBCAR 34 508 1978 [4.574] 6-O-Galactopyranosyl-(α,β)-glucopyranose monohydrate (melibiose H 0) MGLUCP ACBCAR 24 897 1968 [4.375] Methyl α-D-glucopyranoside 2

Continued on next page



126


Table 1. Refcode, Journal Codon, Volume, Year, Page, [β] and Compound Name (Continued) MMALTS ACCRA9 23 1038 1967 [4.570] Methyl β - m a l t o s i d e monohydrate MOGLPR CRBRAT 80 15 1980 [4.356] Methyl-3-O-a-D-glucopyranosyl-a-D-glucopyranoside PHMALT ACBCAR 32 155 1976 [4.555, 4.338, 4.478, 4.221] Phenyl-Ct-maltoside PLANTE10 ACBCAR 28 425 1972 [4.368] Planteose dihydrate RAFINO ACBCAR 26 290 1970 [4.427] Raffinose pentahydrate STACHY10 ACSCEE 43 806 1987 [4.322] O-Ot-D-Galactopyranosyl- (1-6) -O-OC-D-galactopyranosyl(1-6) -O-oc-D-glucopyranosyl- (1-2) - α - D - f ructofuranoside pentahydrate (stachyose) SUCROS11 ACBCAR 29 797 1973 [4.534] Sucrose TRECAB CRBRAT 31 265 1973 [4.402] a , α - D - T r e h a l o s e - c a l c i u m bromide monohydrate TREHAL01 ACBCAR 28 3145 1972 [4.210, 4.340] a, α - T r e h a l o s e dihydrate TURANS01 ACBCAR 34 1873 1978 [4.545] O-a-D-Glucopyranosyl-(1-3)-β-D-fructopyranose (turanose)


7.

FRENCH ET AL.

T a b l e 2.

1—4

Distances

(Â) f o r G l u c o s e

01—04 Mean D i s t a n c e S t d . D e v i a t i o n o f Sample S t d . D e v i a t i o n o f Mean Minimum Maximum


127


4.411 0.130 0.019 4.052 4.666

Residues

C1--C4 2.881 0.020 0.003 2.845 2.919

S y s t e m a t i c changes i n bond a n g l e s and t o r s i o n a n g l e s were i n d i c a t e d by p l o t t i n g t h e p a r a m e t e r s a g a i n s t D w i t h t h e program GRAPHER, a v a i l a b l e from Golden Software, P.O. Box 281, Golden, C o l o r a d o 80402. The e x p e r i m e n t a l bond and t o r s i o n a n g l e v a l u e s were f i t t e d to f i r s t order l i n e s . The c u r v e s f o r t h e models were c o n n e c t i o n s o f t h e p o i n t s by s t r a i g h t l i n e segments. O v e r a l l Modeling

Results

The energy v s . D c u r v e s a r e shown i n F i g u r e 4 f o r t h e f i v e f o r c e f i e l d s with d e f a u l t d i e l e c t r i c constants. (The e n e r g i e s from e a c h program were n o r m a l i z e d by s u b t r a c t i n g t h e l o w e s t energy o b t a i n e d . ) A l l f o r c e f i e l d s p r e d i c t a minimum near 4.55 Â, w h i l e t h e o l d work w i t h MM1 gave a minimum a t 4.27 Â, c l o s e t o t h e m i d d l e o f t h e range o b s e r v e d a t t h a t time (4.30 Â ) . The mean C l — C 4 d i s t a n c e f o r t h e f i v e models w i t h D o f 4.5 Â i s 2.869 Â w h i l e t h e MM1 model had a s h o r t v a l u e , 2.795 Â, t h a t was o u t s i d e o f t h e o b s e r v e d range. Although the normalized curves i n F i g u r e 4 are n e a r l y i d e n t i c a l , t h e raw v a l u e s o f t h e minimal e n e r g i e s a r e d i f f e r e n t . MM2(77) and MMP2(85) v a l u e s a r e 13.0 and 13.3 k c a l / m o l , w h i l e MM2(87) gave 9.3 k c a l and MM3 gave 4.0 k c a l . The d e c r e a s e f o r MM2(87) i s caused by t h e c l o c k w i s e hydrogen b o n d i n g . MM3 i s a new force f i e l d . T o t a l s t e r i c e n e r g i e s from MM1, MM2 and MM3 c a n be used t o c a l c u l a t e e n t h a l p i e s o f f o r m a t i o n by a d d i n g t h e s t e r i c energy t o t h e sum o f s t r a i n - f r e e e n t h a l p i e s . T h i s i s n o t t h e c a s e f o r CHARMM, which gave a minimum o f 70.2 k c a l / m o l . MMP2(85) and MM2(87) models w i t h t h e hydrogen on 01 gauche t o t h e r i n g oxygen (as i n c r y s t a l l i n e g l u c o s e ) gave n o r m a l i z e d c u r v e s t h a t were n e a r l y i d e n t i c a l t o t h o s e i n F i g u r e 4. D i e l e c t r i c c o n s t a n t s o f 4 ( s o l i d phase) and 80 (aqueous s o l u t i o n ) f o r MMP2(85) models a l s o gave t h e same c o r r e c t e d c u r v e s . Changes o f t h e p o s i t i o n o f t h e hydrogen on 01 and d i e l e c t r i c c o n s t a n t were n o t i n v e s t i g a t e d w i t h CHARMM o r MM2(77). W i t h MM3, a d i e l e c t r i c c o n s t a n t o f 4.0 s h i f t e d t h e minimum i n t h e energy v s . D c u r v e t o 4.472 Â, w i t h a C l — C 4 d i s t a n c e o f 2.882. (These v a l u e s were t a k e n from a model t h a t was o p t i m i z e d w i t h o u t any c o n s t r a i n t on t h e 0 1 — 0 4 d i s t a n c e . ) While about 3.2 s t a n d a r d d e v i a t i o n s l a r g e r t h a n t h e mean D i n t h e CSD, t h e model v a l u e i s s l i g h t l y s m a l l e r t h a n i n c r y s t a l s o f g l u c o s e - u r e a complex (4.476 Â) (22), g l u c o s e (4.486 Â) (23) and g l u c o s e monohydrate (4.513 À) (24), t h e o n l y u n s u b s t i t u t e d g l u c o s e s t r u c t u r e s i n t h e CSD. Based on t h e study w i t h MM3 and t h e d i e l e c t r i c c o n s t a n t o f 4, p r e d i c t e d and o b s e r v e d d i s t r i b u t i o n s o f D a r e shown i n F i g u r e 5. The p r e d i c t e d d i s t r i b u t i o n c o r r e s p o n d s t o an unskewed G a u s s i a n curve. D i s t r i b u t i o n s f o r t h e o t h e r programs and MM3 w i t h t h e vacuum d i e l e c t r i c c o n s t a n t were s i m i l a r , b u t t h e i r maxima were l o c a t e d a t about 4.55 Â . We judged t h a t d i s t a n c e t o be t o o l o n g , i n p a r t because t h e mean o b s e r v e d v a l u e i s about 0.14 Â (7.4 standard deviations) smaller. Also, those p r e d i c t e d d i s t r i b u t i o n s based on vacuum d i e l e c t r i c c o n s t a n t s c a l l e d f o r a l a r g e f r a c t i o n o f



128


- ' i — 7 1

1

1

1

1

1

1

1

1

1

1

1

1

1

3.8 3.9 4.0 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5.0 5.1 5.2

01—04 DISTANCE (A)

F i g u r e 4. Energy v s . D as c a l c u l a t e d by f i v e d i f f e r e n t m o d e l i n g programs. D e f a u l t d i e l e c t r i c c o n s t a n t s were used. The v a l u e s graphed were n o r m a l i z e d by s u b t r a c t i n g t h e l o w e s t v a l u e found w i t h each program from a l l t h e o t h e r energy v a l u e s .

0.40 η 0.35 0.30

Η

Ο 0.25 -J

01—04 DISTANCE (A) F i g u r e 5. Frequency o f D, as o b s e r v e d (bar graph) and as p r e d i c t e d by MM3, u s i n g a d i e l e c t r i c c o n s t a n t o f 4.0. The s q u a r e s a r e t h e f r a c t i o n s c a l c u l a t e d a t each 0.1 A, and t h e c u r v e i s a normal g a u s s i a n c u r v e t h a t was f i t t e d t o t h r e e o f t h e p r e d i c t e d p o i n t s .


7.

FRENCH ET A L


129

t h e o b s e r v e d p o p u l a t i o n t o have D l a r g e r t h a n 4.7 Â, and t h e r e a r e no o b s e r v a t i o n s o f D as l a r g e as 4.7 Â.


D e t a i l e d Comparisons o f t h e Model and E x p e r i m e n t a l

Residues

A l l f i v e modeling programs gave s i m i l a r l y a c c u r a t e m o l e c u l a r parameters. One program would f i t one parameter b e t t e r than a n o t h e r program, b u t o v e r a l l t h e q u a l i t i e s o f f i t were s i m i l a r . However, t h e MM3 work w i t h a d i e l e c t r i c c o n s t a n t o f 4 gave s l i g h t l y b e t t e r o v e r a l l agreement and p r e d i c t e d a b e t t e r d i s t r i b u t i o n o f D and so t h a t i s t h e o n l y work d i s c u s s e d i n d e t a i l below. The v a r i o u s o b s e r v e d p a r a m e t e r s were examined f o r bi-modal d i s t r i b u t i o n t h a t might have r e s u l t e d , f o r example, from one f a m i l y w i t h 06 i n g t p o s i t i o n s , and a n o t h e r f a m i l y w i t h 06 i n gg p o s t i o n s in crystals. A l l p a r a m e t e r s seemed t o be randomly d i s t r i b u t e d , c o n s i s t e n t w i t h s l i g h t d e f o r m a t i o n s due t o v a r i o u s c r y s t a l - p a c k i n g arrangements. Parameters l i k e l y t o be c o r r e l a t e d w i t h changes i n D a r e shown i n T a b l e 3 f o r t h e t h r e e u n s u b s t i t u t e d c r y s t a l l i n e r e s i d u e s , t h e A r n o t t - S c o t t (25) and CSD averaged r e s i d u e s and t h e MM3 models f r e e l y o p t i m i z e d and h e l d a t 4.40 Â. CSD and A r n o t t S c o t t v a l u e s a r e based m o s t l y on x - r a y d i f f r a c t i o n s t u d i e s done a t room temperature, w i t h o u t subsequent c o r r e c t i o n s f o r t h e r m a l motion. These c o r r e c t i o n s c a n l e n g t h e n t h e bond l e n g t h s by about 0.005 Â and i n c r e a s e bond a n g l e s by about 0.2°. Such e r r o r s a r e probably not important i n understanding t h e f l e x i b i l i t y of glucose, but c a n e x p l a i n some d i s c r e p a n c i e s . Bond Lengths. S i n c e t h e p a r a m e t e r i z a t i o n f o r anomeric e f f e c t s i n MM3 i s p r e l i m i n a r y , i t i s n o t s u r p r i s i n g t h a t t h e g r e a t e s t bondl e n g t h d i s c r e p a n c y i s f o r t h e Cl-01 d i s t a n c e . F u r t h e r i n d i c a t i o n s o f problems r e l a t e d t o anomeric e f f e c t s a r e t h a t C5-05 and 05-C1 d i s t a n c e s a r e l o n g e r i n c r y s t a l s than i n MM3 models w h i l e t h e o t h e r , e x o c y c l i c C-0 bonds (not shown) a r e modeled v e r y w e l l . One e x p l a n a t i o n i s t h a t t h e f o c u s i n p a r a m e t e r i z a t i o n has been f o r compounds w i t h a c a r b o n atom a t t a c h e d a t 01, as i n a m e t h y l g l y c o s i d e , i n s t e a d o f t h e hydrogen i n t h i s work. A l s o , t h e C l - 0 1 and C l - 0 5 l e n g t h s v a r y w i t h t o r s i o n a n g l e about C l - 0 1 , a f a c t o r n o t m o n i t o r e d i n t h i s s t u d y o f t h e CSD. The mean l e n g t h o f t h e c r y s t a l l o g r a p h i c C5-C6 bond (1.512 Â ) i s s h o r t e r t h a n f o r t h e models by 0.015 Â (not shown). T h i s s l i g h t s h o r t e n i n g (compared t o average C-C d i s t a n c e s ) has been o b s e r v e d b e f o r e (26) b u t has been g i v e n no a t t e n t i o n i n m o d e l i n g s t u d i e s as f a r as we know. The e n d o c y c l i c C-C d i s t a n c e s agree w e l l . Bond A n g l e s . Many o f t h e bond a n g l e s show changes w i t h D. The e n d o c y c l i c a n g l e s a r e p l o t t e d i n F i g u r e 6. The s c a t t e r i n t h e s e e x p e r i m e n t a l l y d e t e r m i n e d bond a n g l e s i s h i g h b u t t h e t r e n d s a r e c l o s e t o t h o s e p r e d i c t e d by t h e models. The e x o c y c l i c a n g l e s t o 01 and 04 a r e i n F i g u r e 7. The d i s c r e p a n c i e s between models and experiment f o r t h e s e a n g l e s a r e t h e most s e v e r e . The model a n g l e s bend a t a r a t e t h a t i s c o n s i s t e n t w i t h t h e e x p e r i m e n t a l r e s u l t s , but a r e o f f s e t by as much as 3 degrees. T o r s i o n Angles. E n d o c y c l i c t o r s i o n a n g l e s change s y s t e m a t i c a l l y w i t h D by as much as 29°/A ( F i g u r e 8 ) . The s i x d i f f e r e n t r i n g t o r s i o n a n g l e s have e x p e r i m e n t a l ranges o f 10.7 t o 1 8 . 0 ° . Despite t h e s c a t t e r i n t h e e x p e r i m e n t a l p o i n t s , t h e agreements between t h e o b s e r v e d and p r e d i c t e d s l o p e s a r e e n c o u r a g i n g . Mean D e v i a t i o n o f F i t . A l s o shown i n T a b l e 3 a r e t h e mean d i s t a n c e s between t h e i n d i v i d u a l atoms o f v a r i o u s p a i r s o f r i n g s


130


T a b l e 3:

Parameters f o r C r y s t a l l i n e and Model G l u c o s e R e s i d u e s ( D i s t a n c e s a r e i n Â and a n g l e s a r e i n degrees)

Study

Urea Glue. Complx.

Glue. Hydrate

A-S AVG

CSD AVG

MM3 ε=4

MM3 ε=4 Fixed at 4.40 A


Parameter Ol—04 C1--C4 C1-C2 C2-C3 C3-C4 C4-C5 C5-05 05-C1 Cl-01 C4-04

4.476 2.889 1.517 1.526 1.520 1.524 1.444 1.414 1.384 1.422

4.486 2.874 1.534 1.525 1.520 1.529 1.428 1.427 1.391 1.426

4.513 2.867 1.510 1.522 1.521 1.513 1.451 1.427 1.412 1.435

4.400 2.887 1.523 1.521 1.523 1.525 1.436 1.414 1.415 1.426

4.411 2.881 1.523 1.521 1.522 1.527 1.441 1.417 1.407 1.428

4.472 2.882 1.524 1.524 1.526 1.530 1.425 1.407 1.436 1.438

4.400 2.871 1.523 1.524 1.526 1.530 1.425 1.407 1.435 1.436

05-C1-C2 C1-C2-C3 C2-C3-C4 C3-C4-C5 C4-C5-05 C5-05-C1 05-C1-01 C2-Cl-01 C3-C4-04 C5-C4-04

110..0 110..9 109..7 109..2 109..8 113..9 112..0 109..1 111..8 106..2

110..1 111..1 109..9 111..2 108..8 113..8 111..5 109..3 108..2 110..9

110..9 112..7 109..0 111..4 108..9 113..1 110..2 110..1 108..6 109..2

109.2 110.5 110.4 110.2 119.9 113.9 109.2 108.4 110.4 109.9

110..0 110..6 109..9 110..8 110..1 114..0 110..7 108..1 110..2 108..2

110.2 111.4 108.6 109.7 109.9 114.8 108.6 111.0 107.2 109.2

110.2 111.1 108.7 110.0 109.7 114.1 107.9 110.9 107.0 108.8

05--C1-C2-C3 CI- -C2-C3-C4 C2--C3-C4-C5 C3--C4-C5-05 C4--C5-05-C1 Co--05-C1-C2

55..4 -54..5 55..2 -57..4 61..1 -59..5

54..1 -51..3 53..3 -57..5 62..2 -60..9

53..0 -50..5 53..5 -58..5 61..4 -58..7

56.9 -53.5 52.5 -54.8 61.4 -62.0

56..4 -53..6 52..8 -54.,4 59..2 -60..1

54.8 -54.5 55.4 -57.3 60.0 -58.3

55.8 -54.0 54.7 -57.2 60.8 -59.8

0.561

0.568

0.571

Puckering Q

(Â)

#

0.574

0.567

0.560

0.568

θ

1.9

3.5

4.9

2.4

1.2

2.7

1.5

Φ**

267

323

303

24

45

233

258

Average D e v i a t i o n o f 6 R i n g Atoms F i t t e d by L e a s t Squares (A) Urea Complex Glucose Hydrate Arnott-Scott Cambridge* MM3 8=4 4.47 MM3 ε=4 4.40

.019 .020 .016 .014 .010 .010

.013 .019 .019 .020 .016

.026 .025 .021 .020

.008 .021 .016

.017 .013

.007

*

T h i s r i n g was c o n s t r u c t e d from t h e average v a l u e s o f t h e above p a r a m e t e r s . The r i n g came w i t h i n 0.0096 A o f closing. I t s 0 1 — 0 4 d i s t a n c e was 4.416 A. T h i s number r e f l e c t s t h e s l i g h t g e o m e t r i c a l changes r e s u l t i n g from c l o s i n g t h e r i n g b a s e d on average parameters i n s t e a d o f u s i n g t h e average v a l u e o f t h e o b s e r v e d r i n g s (0.564 Â ) . ** V a l u e s o f φ do n o t i m p l y s i g n i f i c a n t l y d i f f e r e n t s t r u c t u r e s when θ i s c l o s e t o z e r o .



F i g u r e 6. E n d o c y c l i c bond a n g l e s f o r g l u c o p y r a n o s e p l o t t e d a g a i n s t D. The r e g r e s s i o n l i n e b a s e d on t h e o b s e r v e d v a l u e s i s dashed, and t h e model v a l u e s a r e shown by t h e s o l i d l i n e .



F i g u r e 7. F i g u r e 6.

E x o c y c l i c bond a n g l e s t h a t c o u l d a f f e c t D as i n


FRENCH ET A L



7.


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a f t e r t h e r i n g s were superimposed, b a s e d on a l l s i x r i n g atoms. I n o r d e r t o i n c l u d e a comparison w i t h a summary o f t h e c r y s t a l l o g r a p h i c d a t a , a r i n g was p r o d u c e d from t h e average bond l e n g t h s and a n g l e s and t o r s i o n a n g l e s i n t h e CSD. A f t e r g e n e r a t i n g a l l t h e r i n g atoms, s t a r t i n g w i t h CI and p r o g r e s s i n g by i n c r e a s i n g c a r b o n number, t h e d i s t a n c e between 05 and CI was 0.0096 Â s h o r t e r t h a n t h e average v a l u e , b u t t h e r i n g was used w i t h o u t f u r t h e r ado. I t f i t t h e A r n o t t - S c o t t a v e r a g e d r e s i d u e (25) v e r y c l o s e l y , and was s i m i l a r t o t h e MM3 models. On a h i g h - r e s o l u t i o n v i d e o d i s p l a y , r i n g s appear t o be i d e n t i c a l i f t h e i r mean d e v i a t i o n o f f i t f o r s i x atoms i s l e s s t h a n 0.020 Â, w h i l e s l i g h t d i f f e r e n c e s c a n be seen i n t h e p o s i t i o n s o f pendant atoms. Cremer-Pople P u c k e r i n g . P y r a n o s e r i n g geometry i s f o r m a l l y d e s c r i b e d by t h e Cremer-Pople p u c k e r i n g parameters Q, Θ, and φ (27). These p a r a m e t e r s were c a l c u l a t e d f o r t h e atomic c o o r d i n a t e s i n t h e CSD and f o r t h e models w i t h a program w r i t t e n by L a r r y Madsen. Q i s t h e d e v i a t i o n o f t h e r i n g atoms from a mean p l a n e , φ i n d i c a t e s t h e p o s i t i o n o f p u c k e r i n g (which atoms d e v i a t e most from t h e mean p l a n e ) , and θ i n d i c a t e s t h e e x t e n t o f d i s t o r t i o n from t h e p e r f e c t C - c o n f o r m a t i o n . F i g u r e 9a i l l u s t r a t e s t h e s e c o n c e p t s (see a l s o F i g u r e 3 i n t h e i n t r o d u c t o r y c h a p t e r o f t h i s book). T a b l e 3 i n c l u d e s t h e p u c k e r i n g p a r a m e t e r s f o r t h e seven e x p e r i m e n t a l and model r i n g s . There i s a v e r y s m a l l o b s e r v e d range o f a m p l i t u d e (Q), and Q i s e s s e n t i a l l y i n v a r i a n t w i t h D i n b o t h models and t h e CSD. The CSD mean i s 0.564 Â w h i l e t h e b e s t MM3 model has a Q o f 0.570 A, agreeing well. F i g u r e 9b d i s p l a y s t h e o b s e r v e d Q v a l u e s and t h e l i n e from t h e MM3 models. F i g u r e 9c p l o t s θ v s . D f o r t h e models and o b s e r v e d c r y s t a l structures. F o r t h i s graph, t h e s i g n o f θ was changed f o r p o i n t s with φ > 180° t o preserve a s t r a i g h t l i n e . The CSD r e g r e s s i o n l i n e i s c l o s e t o t h e model l i n e . P e r f e c t c h a i r s (Θ - 0.0°) a r e found f o r a model w i t h D o f 4.35 A and f o r t h e CSD l i n e a t 4.43 A. The l e a s t e n e r g e t i c model has a θ o f 2.7°; t h e r e i s no r e a s o n why t h e e n e r g e t i c a l l y o p t i m a l r e s i d u e s h o u l d be a p e r f e c t c h a i r . 4

F i g u r e 9d shows t h e φ v s . D r e l a t i o n s h i p , and t h e view i n F i g u r e 9e i s down toward t h e t o p o f t h e Cremer-Pople sphere which has been p r o j e c t e d onto a p l a n e . The 0,0 p o i n t c o r r e s p o n d s t o t h e p e r f e c t C- shape. I n t h i s p l o t , t h e dashed l i n e c o r r e s p o n d s t o t h e φ = 60/240 m e r i d i a n and i s n o t a r e g r e s s i o n l i n e . F i g u r e 9e shows t h a t θ v a r i e s away from a p e r f e c t c h a i r i n a l l d i r e c t i o n s . T h e r e f o r e , g l u c o s e r e s i d u e s would be f l e x i b l e when m o d e l i n g g l u c a n s w i t h o t h e r l i n k a g e s as w e l l . These s t u d i e s o f p u c k e r i n g s u p p o r t t h e d e s c r i p t i o n o f t h e p r i m a r y changes i n t h e r i n g as t h e 01-04 d i s t a n c e changes t h a t was given i n the introduction. When θ i s 9 0 ° , a ώ o f 6 0 ° i n d i c a t e s a conformer and a φ o f 2 4 0 ° i n d i c a t e s a B. Above t h e s e e q u a t o r i a l p o i n t s on t h e φ=60/240 m e r i d i a n , a t θ » 54.7°, a r e t h e and E h a l f b o a t s . T h e r e f o r e , models w i t h s h o r t D (with φ n e a r 60°) t e n d toward t h e E ^ conformers and t h e models w i t h l o n g e r D and φ n e a r 2 4 0 ° t e n d towards t h e E h a l f - b o a t s . Q s t a y s almost c o n s t a n t d u r i n g changes i n D because l e n g t h e n i n g o f D moves CI towards t h e mean p l a n e w i t h C4 moving s i m u l t a n e o u s l y f u r t h e r away from t h e mean p l a n e . 4

l f

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Figure 9a. Spherical polar depiction of pyranose puckering. The equatorial belt is the path of facile pseudorotation through all the Boats and Skew-boats (φ rotation). Perfect chairs are at the North and South poles, and the Half-boat (Envelope) forms are at θ of 54.7 °. This diagram has a reversed direction of positive pseudorotation from that shown in figure 3, Chapter 1.

0.60

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01—04 DISTANCE (A) Figure 9b. Observed and predicted Q puckering parameters vs. D. The range of observed values is quite small.



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360.00 π

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4.7

Figure 9d. The φ puckering parameter, plotted against D. At 4.35 A, the length for a perfect chair, φ changesfrom60* to 240*.



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Figure 9e. A projection of the Cremer-Pople sphere (see Fig. 9A) onto a plane perpendicular to the polar axis. Θ and φ values for experiment and models were converted to cartesian coordinates, with the model points connected by solid lines. The central (0,0) point corresponds to a perfect chair, and the dashed line follows the 60 * -240 * meridian.


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D i s c u s s i o n and C o n c l u s i o n s The m o d e l i n g work shows t h a t t h e energy t o deform t h e pyranose r i n g o v e r t h e o b s e r v e d range o f D o f 4.05 t o 4.67 A ( l e s s t h a n 2 k c a l / m o l ) can come r e a d i l y from e n v i r o n m e n t a l l y v a r i a b l e f a c t o r s such as hydrogen bonding and van d e r Waals f o r c e s . Further, e x a m i n a t i o n o f T a b l e 1 s u p p o r t s our a s s e r t i o n t h a t such f o r c e s a r e t h e main cause o f t h e s e d e f o r m a t i o n s . B e s i d e s t h e example o f nonr e d u c i n g r e s i d u e s from m a l t o s e s w i t h D o f 4.052 and 4.570 A c i t e d i n t h e i n t r o d u c t i o n , one may compare t h e g l u c o s e r e s i d u e i n s u c r o s e (4.534 A) w i t h t h e analogous g l u c o s e r e s i d u e s i n t h e s u c r o s e m o i e t y i n 6-kestose (4.130 A) and 1-kestose (28) (4.575 A). Five residues i n T a b l e 1 come from a,α-trehalose. (A s i x t h r e s i d u e i s r e l a t e d by symmetry t o t h e r e s i d u e from TRECAB.) While t h e a f o r e m e n t i o n e d g l u c o s e r e s i d u e s i n s u c r o s e and m a l t o s e m o i e t i e s a r e merely i s o l a t e d from t h e l o c a t i o n s o f c h e m i c a l d i f f e r e n c e s , t h e t r e h a l o s e r e s i d u e s are a l l c h e m i c a l l y i d e n t i c a l . T h e i r D v a l u e s range f r o m 4.210 A t o 4.526 A. On t h e o t h e r hand, t h e A r n o t t - S c o t t averaged r i n g , which was d e r i v e d from a v a r i e t y o f pyranose s u g a r s , i s n e a r l y i d e n t i c a l t o t h e average r i n g p r o d u c e d i n t h i s paper from o n l y g l u c o s e r e s i d u e s . The a l t e r a t i o n s i n r i n g geometry a r i s i n g from t h e a l t e r n a t e h y d r o x y l group p o s i t i o n s must be v e r y s m a l l f o r t h e two r i n g s t o have a mean d e v i a t i o n o f o n l y 0.008 A. When d e t e r m i n i n g t h e range o f l i k e l y h e l i c a l shapes from i n t r i n s i c p r o p e r t i e s o f amylose, t h i s v a r i a b i l i t y i n monomer shape i s almost as i m p o r t a n t as h i n d e r e d r o t a t i o n about t h e bonds l i n k i n g t h e monomers. T h i s c o n c l u s i o n i s s u p p o r t e d by c o n f o r m a t i o n a l a n a l y s e s o f m a l t o s e such as shown i n F i g u r e 5 o f t h e i n t r o d u c t o r y c h a p t e r o f t h i s book. There a r e r e l a t i v e l y s m a l l ranges (about 40°) o f a l l o w e d t o r s i o n a l r o t a t i o n w i t h i n one k c a l / m o l o f t h e minimum (one must c o r r e c t f o r t h e f a c t t h a t t h e r e a r e two g l u c o s e r e s i d u e s i n m a l t o s e when making such a c o m p a r i s o n ) . As soon as c r y s t a l s t r u c t u r e d e t e r m i n a t i o n s o f g l u c o s e became a v a i l a b l e , t h e q u e s t i o n a r o s e as t o which o f t h e s l i g h t l y d i f f e r e n t g e o m e t r i e s would be most a p p r o p r i a t e f o r m o d e l i n g amylose. This q u e s t i o n i m p l i e s t h a t t h e r e s i d u e geometry would remain f i x e d i n a r i g i d - r e s i d u e t y p e o f m o d e l i n g s t u d y . W h i l e not i d e a l , t h i s a p p r o x i m a t i o n s t i l l has some u t i l i t y , a r i s i n g from t h e s h e e r s i z e of p o l y m e r i c m o l e c u l e s . I f environmental e f f e c t s are ignored, i t seems t h a t t h e A r n o t t - S c o t t average r e s i d u e remains a good c h o i c e . B e t t e r s t i l l , a s e r i e s o f s t u d i e s s h o u l d be done w i t h r e s i d u e s w i t h d i f f e r e n t g e o m e t r i e s , and t h e o v e r a l l c o n c l u s i o n s s h o u l d i n c l u d e r e s u l t s from each r e s i d u e geometry. The s e l e c t i o n o f t h e r e s i d u e s i s s i m p l i f i e d f o r amylose by u s i n g D as a c r i t e r i o n . A l t e r n a t i v e l y , t h e θ and φ p u c k e r i n g parameters c o u l d be used. The MM3 r i n g w i t h l o w e s t energy l e a d s t o c o l l a p s e d (V-type) amylose h e l i c e s w i t h about e i g h t r e s i d u e s p e r t u r n and would a l s o be s u i t e d f o r m o d e l i n g t h e more extended n a t i v e s t a r c h double h e l i c e s w i t h s i x r e s i d u e s p e r t u r n (See F i g u r e 6 and t h e m a t e r i a l on n-h maps i n t h e i n t r o d u c t o r y c h a p t e r o f t h i s book. The c h a p t e r by P e r e z , Imberty and S c a r i n g e a l s o d i s c u s s e s n a t i v e s t a r c h helices). The b e s t MM3 model i s a l s o r e a s o n a b l y c l o s e i n s t r u c t u r e to b o t h o f t h e average r e s i d u e s which l e a d t o c o l l a p s e d amylose h e l i c e s w i t h seven r e s i d u e s p e r t u r n (2). A model w i t h D o f 4.25 A, s u i t e d f o r c o l l a p s e d , s i x - r e s i d u e p e r t u r n h e l i c e s , has an i n t e r n a l energy about 0.4 k c a l / m o l h i g h e r t h a n t h e minimum. The e x t e n s i v e d a t a on g l u c o s e p e r m i t study o f t h e r a t e s o f s y s t e m a t i c changes o f m o l e c u l a r parameters t h a t c o r r e l a t e w i t h D i n models and c r y s t a l s t r u c t u r e s . A l l f i v e m o d e l i n g programs b a l a n c e d bond s t r e t c h i n g , a n g l e b e n d i n g and t o r s i o n a l motion w e l l enough t h a t t h e r a t e s o f most changes were c o n s i s t e n t w i t h experiment.



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Since these f a c t o r s are w e l l balanced, f lex:.ble-residue c o n f o r m a t i o n a l a n a l y s e s u s i n g any o f t h e s e f o r c e f i e l d s s h o u l d be r e a s o n a b l y c o r r e c t , w i t h i n l i m i t a t i o n s such as n e g l e c t o f environment. Comparing t h e mean d e v i a t i o n s o f f i t i n T a b l e 3, i t seems t h a t the q u a l i t y of the modeling software enables p r e d i c t i o n of the s t r u c t u r e of t h e g l u c o s e r i n g by modeling t o be comparable t o p r e d i c t i o n by c r y s t a l s t r u c t u r e d e t e r m i n a t i o n . The s t r u c t u r e o f t h e l e a s t e n e r g e t i c MM3 r i n g i s e s p e c i a l l y c l o s e t o t h e c r y s t a l s t r u c t u r e of t h e g l u c o s e - u r e a complex and v e r y c l o s e t o c r y s t a l l i n e g l u c o s e i t s e l f and t o g l u c o s e monohydrate. There a r e some d e f e c t s i n t h e model t h a t we hope can be r e s o l v e d i n a f u t u r e r e l e a s e o f MM3. The bond l e n g t h s and bond a n g l e s around t h e anomeric c e n t e r a r e t h e most p r e s s i n g . A l t h o u g h t h e r e was l i t t l e e f f e c t o f d i f f e r e n t anomeric s u b s t i t u e n t s on bond l e n g t h s w i t h t h e MM2 f o r c e f i e l d , t h i s w i l l have t o be s t u d i e d a t l e n g t h w i t h MM3, as w e l l as f o l l o w i n g t h e t o r s i o n a n g l e s t h a t can a f f e c t t h e s e bond l e n g t h s . On t h e o t h e r hand, t h e magnitude o f t h e s e e r r o r s i s p r o b a b l y not v e r y i m p o r t a n t when a t t e m p t i n g t o determine the p r o p e r t i e s o f a polymer. Of t h e e r r o r s i n v o l v i n g bond l e n g t h s and bond a n g l e s , t h o s e i n v o l v i n g bond a n g l e s a r e p r o b a b l y more i m p o r t a n t i n modeling t h e polymer. S i n c e t h e s t u d i e s w i t h MM1 a decade ago (9.), t h e p r e d i c t e d b e s t D i n c r e a s e d 0.2 Â and t h e mean e x p e r i m e n t a l D grew 0.11 Â. Improvement o f t h e s o f t w a r e i s perhaps most e a s i l y shown by t h e b e t t e r C l — C 4 d i s t a n c e which was p r e v i o u s l y p r e d i c t e d t o be o u t s i d e t h e o b s e r v e d range. The c u r r e n t model p r e d i c t s t h a t a few s t r u c t u r e s s h o u l d be o b s e r v e d w i t h D between 4.7 and 4.9 Â, and perhaps some w i l l e v e n t u a l l y be found. More low-temperature d i f f r a c t i o n r e s u l t s would be welcome. However, t h i s modeling s t u d y o f i s o l a t e d models has not accommodated two f a c t o r s t h a t might s h o r t e n t h e upper l i m i t on D and skew t h e d i s t r i b u t i o n . Residues w i t h D l o n g e r t h a n 4.6 Â may not f i t t o g e t h e r i n c r y s t a l s as compactly as s h o r t e r r e s i d u e s . Such a d e c r e a s e i n t h e d e n s i t y would i n c r e a s e t h e p a c k i n g energy. A n o t h e r p o t e n t i a l cause o f a skewed d i s t r i b u t i o n i s t h e i n f l u e n c e o f p u c k e r i n g s o t h e r than t h o s e w i t h φ = 60 and 2 4 0 ° . F i g u r e 9e shows t h a t t h e models m o s t l y p u c k e r e d a l o n g t h a t l i n e , w h i l e t h e c r y s t a l s t r u c t u r e s have much more random p u c k e r i n g s . F o r a g i v e n i n c r e a s e i n p o t e n t i a l energy, t h e random p u c k e r i n g s c o u l d r e s u l t i n s h o r t e r D t h a n t h o s e from models t h a t were p u r e l y p u c k e r e d on t h e E — E p a t h . 4

1

D i s t r i b u t i o n V e r s i o n of

MM3

A f t e r c o m p l e t i o n o f t h i s work, t h e parameters f o r MM3 f o r a l c o h o l s and e t h e r s were f i n a l i z e d , and papers d e s c r i b i n g t h e s e parameters were s u b m i t t e d t o J . Am. Chem. Soc. Most o f t h e r e s u l t s f o r g l u c o s e do not change s i g n i f i c a n t l y , a l t h o u g h t h e r e a r e some s m a l l differences. F o r example, D i s 4.469 Â compared t o 4.471 Â. A n o t a b l e change r e g a r d s t h e O l - C l - 0 5 bond a n g l e , which i n c r e a s e d 1.8°, w h i l e t h e C-C4-04 a n g l e s d e c r e a s e d by 0.5°.

Acknowledgments Much o f t h e d a t a m a n i p u l a t i o n and some o f t h e g r a p h i c s were t h e work o f Mrs. L i n d a Lew. Dr. B r i a n V i n y a r d a s s i s t e d w i t h some o f t h e s t a t i s t i c a l a n a l y s e s , and James Wadsworth p r o v i d e d a program f o r f i t t i n g a gaussian curve. P r o f e s s o r s D a v i d B r a n t and George J e f f r e y p r o v i d e d h e l p f u l comments on t h e m a n u s c r i p t . Mention o f commercial p r o d u c t s and t h e i r vendors i s not an endorsement by t h e


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U.S. Department o f A g r i c u l t u r e , r e p r o d u c t i o n o f t h e work.

but f o r t h e purposes o f

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Modeling of Glucopyranose - American Chemical Society

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