Conformation and Packing Analysis of Polysaccharides and Derivatives

9 Conformation and Packing Analysis of Polysaccharides and Derivatives Detailed Refinement of Trimethylamylose Downloaded via TUFTS UNIV on July 9, 2018 at 19:59:59 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

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P. ZUGENMAIER, A. KUPPEL, and E. HUSEMANN Institut fur Makromolekulare Chemie der Universität Freiburg, D7800 Freiburg i.Br., Germany (BRD) Trimethylamylose (TMA) i s a n a-(l-*4) l i n k e d m e t h y l a t e d D - g l u c a n t h a t c a n be p r e p a r e d b y homogeneous m e t h y l a t i o n o f c o m m e r c i a l l y a v a i l a b l e amy l o s e (_1) . I t i s known t h a t t h e a-(1*4) l i n k a g e i n the p o l y s a c c h a r i d e backbone r e s u l t s i n a f l e x i b l e c h a i n c o n f o r mation t h a t gives r i s e t o d i f f e r e n t c r y s t a l l i n e polymorphs. F o r example,amylose, the u n s u b s t i t u t e d p o l y s a c c h a r i d e , c r y s t a l l i z e s i n a t l e a s t t h r e e p o l y m o r p h s , known a s A-, B-, V - a m y l o s e s . O f t h e s e , o n l y t h e s t r u c t u r e o f V - a m y l o s e (2^) i s c h a r a c t e r i z e d i n d e t a i l a t t h e p r e s e n t t i m e . I t was o r i g i n a l l y t h o u g h t t h a t V-amyl o s e c r y s t a l l i z e s a s a s i x f o l d h e l i x w i t h t h e same symmetry. N o t u n t i l r e c e n t l y , h o w e v e r , was a t w o f o l d s c r e w a x i s a l o n g i t s c h a i n e s t a b l i s h e d , thus i n d i c a t i n g that three chemically i d e n t i c a l r e s i d u e s c o m p r i s e d one c r y s t a l l o g r a p h i c a s y m m e t r i c u n i t , b u t w i t h n o n i d e n t i c a l conformations. Nonetheless, the conformation o f t h e V - a m y l o s e b a c k b o n e c a n be d e s c r i b e d a s a n a p p r o x i m a t e s i x f o l d h e l i x . A n o t h e r p o l y m e r o f t h e a-(1-^4) l i n k a g e t y p e w h i c h h a s b e e n c h a r a c t e r i z e d i n moderate d e t a i l , i s amylose t r i a c e t a t e (ATA)(3). I t s c h a i n c o n f o r m a t i o n c a n b e s t be d e s c r i b e d b y a 1 4 ^ h e l i x , t h a t i s , a l e f t h a n d e d h e l i x w i t h 14 r e s i d u e s i n 3 t u r n s . The r i s e p e r r e s i d u e f o r V - a m y l o s e a n d f o r ATA a r e q u i t e d i f f e r e n t , as a r e t h e c o n f o r m a t i o n a n g l e s r e s p o n s i b l e f o r t h e i r h e l i c a l s t r u c t u r e s . T h e r e f o r e , i t was o f i n t e r e s t t o u s t o d e t e r m i n e t h e c h a i n c o n f o r m a t i o n o f TMA, a n d e s p e c i a l l y t h e i n f l u e n c e o f t h e methyl s u b s t i t u e n t s on the conformation o f i t s backbone. A l t h o u g h e x c e l l e n t f i b e r X - r a y d i a g r a m s o f TMA h a v e b e e n obtained i n t h i s laboratory (4) , i t was n o t u n t i l r e c e n t l y t h a t an a t t e m p t c o u l d b e made t o s o l v e t h e c r y s t a l s t r u c t u r e . F i r s t , d i f f i c u l t i e s were e n c o u n t e r e d i n e s t a b l i s h i n g a unique u n i t c e l l and i t s symmetry. T h e s e d i f f i c u l t i e s were overcome o n l y when e l e c t r o n d i f f r a c t i o n p a t t e r n s became a v a i l a b l e f r o m TMA s i n g l e c r y s t a l s . S e c o n d l y , i t i s o n l y r e c e n t l y t h a t a s o p h i s t i c a t e d mod e l i n g method became a v a i l a b l e t o d e a l s i m u l t a n e o u s l y w i t h c o n f o r m a t i o n and p a c k i n g o f p o l y s a c c h a r i d e d e r i v a t i v e s i n w h i c h 1

D e c e a s e d N o v e m b e r 9,1975.

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simultaneous r o t a t i o n o f a l l s u b s t i t u t e n t groups could be handled. T h i s was necessary i n order to o b t a i n a phasing model f o r r e f i n e ment a g a i n s t X-ray data. Experimental Trimethylamylose was prepared by homogeneous methylation o f commercial AVEBE amylose. S u i t a b l e f i b e r s f o r X-ray measurements were obtained by s t r e t c h i n g TMA f i l m s , c a s t from methylene c h l o r i d e , about 300 % i n a stream o f hot a i r a t 60 C. Such f i b e r s showed p e r f e c t o r i e n t a t i o n but low c r y s t a l l i n i t y . Annealing a t 220 C f o r about 10 minutes improved c r y s t a l l i n i t y d r a m a t i c a l l y but d i d not a f f e c t the o r i e n t a t i o n o f the c r y s t a l l i t e s . A t y p i c a l X-ray f i b e r diagram o f an annealed sample taken with a c y l i n d r i c a l camera o f 5.73 cm r a d i u s i s shown i n F i g . 1. In t h i s d i f f r a c t i o n photograph the m e r i d i o n a l r e f l e c t i o n s are s c a r c e l y d e t e c t a b l e due to the n e a r l y p e r f e c t o r i e n t a t i o n o f the c r y s t a l l i t e s . When the f i b e r was t i l t e d i n t o the c o r r e c t p o s i t i o n s , a l l even numbered m e r i d i o n a l r e f l e c t i o n s up t o 1 = 10 were observed while a l l odd numbered were absent. The f i b e r repeat d i s t a n c e c_was de termined from t h i s p a t t e r n but no unique s o l u t i o n f o r the other u n i t c e l l parameters was found. T h e r e f o r e , attempts were made to s o l v e t h i s problem by e l e c t r o n d i f f r a c t i o n o f polymer s i n g l e c r y s t a l s . The l a t t e r were obtained by two methods. F i r s t , TMA was d i s s o l v e d i n d i e t h y l e n e g l y c o l ( 5 g ^ l ) , heated t o 24θ C and then slowly c r y s t a l l i z e d a t 180 - 150 C. In the second method, TMA was d i s s o l v e d i n a solvent-nonsolvent mixture o f dioxane (2g/l) and 60 % octane and then c r y s t a l l i z e d a t room temperature. The s i n g l e c r y s t a l s obtained by these two methods showed d i f f e r e n t morpholo g i e s ( c f . F i g . 2a, b ) . C r y s t a l l i z a t i o n a t room temperature r e s u l t e d i n s p h e r u l i t i c c r y s t a l s . The outer p a r t s o f the s p h e r u l i t e s showed s i n g l e c r y s t a l s represented i n F i g . 2a. C r y s t a l l i z a t i o n a t e l e v a t e d temperatures r e s u l t e d i n l a m e l l a r type c r y s t a l s which are shown i n F i g . 2b. The corresponding X-ray powder d i a grams are shown i n F i g . 2c and d, r e s p e c t i v e l y . Only the s i n g l e c r y s t a l s grown a t e l e v a t e d temperatures showed a d i f f r a c t i o n i n tensity d i s t r i b u t i o n which corresponded to the f i b e r X-ray p a t t e r n o f F i g . 1. TMA s i n g l e c r y s t a l s grown a t room temperature gave a q u i t e d i f f e r e n t p a t t e r n and i t has been shown (_4) t h a t t h i s r e s u l t s from dioxane having been i n c o r p o r a t e d i n the c r y s t a l l a t tice. E l e c t r o n d i f f r a c t i o n p a t t e r n s obtained from TMA s i n g l e c r y s t a l s grown a t e l e v a t e d temperatures are s c h e m a t i c a l l y represented i n F i g . 2e. The u n i t c e l l parameters a_, b and f = 90 c o u l d now be absolu t e l y determined with the help o f an i n t e r n a l standard. The l i m i t i n g planes o f the lamellae o f F i g . 2b c o u l d now a l s o be determined and indexed w i t h (100) r e p r e s e n t i n g the width o f the c r y s t a l s while the two planes r e p r e s e n t i n g the f r o n t edges i n some o f the lammelae (e.g. lower l e f t corner) are (110) and (110). With a_ and b l y i n g i n the d e p i c t e d plane i t became c l e a r t h a t the chains o f 0


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Fiber diffraction pattern of TMA taken with a cylindrical camera of 5.73-cm radius

Figure 2a. Electron micrograph of single crystals of TMA grown at room temperature in a solvent-nonsolvent mixture of dioxane and 60% octane

Figure 2b. Electron micrograph of single crystals of TMA grown at 180°-150°C in diethyleneglycol



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Figure 2c. Powder x-ray pattern of single crystals of Figure 2a on a fiat film

Figure 2d. Powder x-ray pattern of single crystals of Figure 2b on afiatfilm

Figure 2e. Schematic representation of the electron diffraction pattern obtained from a single crystal shown in Figure 2b


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TMA are p e r p e n d i c u l a r to t h a t plane. The e l e c t r o n d i f f r a c t i o n patterns a l s o suggested t h a t twofold screw axes were p r e s e n t along both a_ and b. With values o f a_ and b from e l e c t r o n d i f f r a c t i o n and £ from X-ray f i b e r diagrams, the r e f l e c t i o n s of the f i b e r p a t t e r n of F i g . 1 c o u l d now be indexed with an orthorhombic u n i t c e l l . I t s parameters were r e f i n e d by a l e a s t squares procedure and are a = 17.24 ± 0.01 2, b = 8.704 ± 0.009 A, c ( f i b e r repeat) = 15.637 ± 0.Ç08 8 a t room temperature. The measured d e n s i t y i s ρ = 1.20 g/cm . With twofold screw axes i n a l l three d i r e c t i o n s a_, b and c_ the most probable space group i s P 2 ^ 2 ^ 2 ^ . T h e r e f o r e , the u n i t c e l l contains segments of two chains running through i t i n an a n t i p a r a l l e l f a s h i o n , as demanded by space group symmetry, with f o u r t r i m e t h y l g l u c o s e monomer u n i t s per f i b e r repeat. The r e l a t i v e X-ray r e f l e c t i o n i n t e n s i t i e s were obtained from c y l i n d r i c a l f i l m diagrams taken i n an evacuated camera. The i n t e n s i t y was recorded along each l a y e r l i n e with a Joyce-Loebl r e c o r d i n g densitometer. Areas o f i n d i v i d u a l peaks were measured by p l a n i m e t r y and used as a measure o f uncorrected r e l a t i v e i n t e n s i t y . I n t e n s i t i e s thus obtained were c o r r e c t e d f o r Lorentz (_5) and p o l a r i s a t i o n f a c t o r s , a r c i n g of r e f l e c t i o n s , unequal film-to-sam p l e d i s t a n c e s o f d i f f r a c t e d rays and were then converted to r e l a t i v e s t r u c t u r e amplitudes. In those i n s t a n c e s where observed i n t e n s i t i e s were a c t u a l l y a composite o f c o n t r i b u t i o n s from two or more unique d i f f r a c t i o n p l a n e s , the value o f the c a l c u l a t e d s t r u c ture amplitude was taken as IF

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' cl ι ι CI with m. the m u l t i p l i c i t y and the summation being over a l l planes contrièuting to the composite. The s t r u c t u r e amplitudes o f unobserved r e f l e c t i o n s were assigned one h a l f o f the minimum observab l e i n t e n s i t y i n the corresponding r e g i o n o f d i f f r a c t i o n angle. R e s u l t s and D i s c u s s i o n Stereochemical Model A n a l y s i s . The method of generating models of h e l i c a l s t r u c t u r e s has been d e s c r i b e d i n p r e v i o u s papers (_5,6) . A f l e x i b l e r i n g conformation was i n t r o d u c e d which allowed v a r i a t i o n , when necessary, i n bond lengths , bond and conformation angles, u s i n g as the refinement c r i t e r i o n the o p t i m i z a t i o n of the f u n c t i o n (2) : N

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j=l The f i r s t term i n t h i s f u n c t i o n r e p r e s e n t s the bonded and the se cond term the nonbonded i n t e r a c t i o n s , with: A. any c a l c u l a t e d bond l e n g t h , bond o r conformation angle o l the molecule;


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Figure 3. Bond lengths fa), bond angles (θι), and conformation angles ( ) required for the description of the α-Ό-glucose residue. Hydrogen atoms are not shown. The angle φ measures rotation of the entire helix about its axis, and the distance r is constant for a given helix and virtual bond length.

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A . a v e r a g e o r s t a n d a r d v a l u e o f A.; S?fc . w e i g h t o r s t a n d a r d d e v i a t i o n f o r t h e a v e r a g e v a l u e Ν number o f o p t i m i z a t i o n p a r a m e t e r s s e l e c t e d ; d _ ^ n o n b o n d e d e q u i l i b r i u m d i s t a n c e b e t w e e n atoms i _ and j _ ; 1

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d. . nonbonded d i s t a n c e b e t w e e n atoms i _ and j_ ( o n l y r e p u l s i v e i n t e r a c t i o n s are used, t h a t i s , the second term i s s e t t o z e r o i f d.. >d .. ) ; w. . t h e welght°lactor f o r t h e a t o m p a i r i ^ , j _ ; W ^ v e r a l l w e i g h t f a c t o r o f nonbonded i n t e r a c t i o n s ; η number o f nonbonded c o n t a c t s c o n s i d e r e d . The a c t u a l c o n s t a n t s u s e d f o r t h i s c a l c u l a t i o n a r e s u m m a r i z e d i n r e f e r e n c e 2_. The s t r a t e g y u s e d was t o e s t a b l i s h f i r s t a s u i t a b l e c h a i n c o n f o r m a t i o n t o be r e f i n e d l a t e r f o r o p t i m a l p a c k i n g . F o r t h e d e s c r i p t i o n o f t h e c h a i n two s e q u e n c e s o f a t o m s , a s shown s c h e m a t i c a l l y i n F i g . 3, a r e n e e d e d . The o p e n b o n d s a n d a n g l e s , i . e. t h e b o n d C ( l ) - C ( 2 ) and t h e a n g l e s C ( 3 ) - C ( 2 ) - C ( 1 ) and C ( 2 ) - C ( 1 ) - 0 ( 5 ) a r e c o n s t r a i n e d t o s t a y w i t h i n g i v e n l i m i t s . As a t r i a l model f o r t h e a-(l-»4) l i n k e d g l u c a n any α-D-glucose r e s i d u e i n t h e C I c h a i r c o n f o r m a t i o n may s e r v e , a s t h e l a t t e r i s t h u s f a r t h e o n l y c o n f o r m a t i o n f o u n d i n a m y l o s e and i t s d e r i v a t i v e s . P e n d a n t atoms a n d b r a n c h e s a r e a d d e d t o t h e monomer r e s i d u e t o c o m p l e t e t h e c h a i n d e s c r i p t i o n . The m o d e l i s t h e n r e f i n e d b y m i n i m i z i n g t h e f u n c t i o n Y. M o d e l s w i t h h i g h v a l u e s o f Y_ and w i t h many s h o r t c o n t a c t s b e l o w the e s t a b l i s h e d l i m i t s are disregarded. F o r TMA w i t h f o u r r e s i d u e s p e r f i b e r r e p e a t d i f f e r e n t f o u r f o l d h e l i c e s w e r e c o n s i d e r e d ; h o w e v e r , a l l b u t a 4^ h e l i x h a d t o be d i s r e g a r d e d . The 0 ( 6 ) s u b s t i t u e n t c o u l d be p l a c e d e i t h e r i n t h e v i c i n i t y o f g t o r t g r o t a t i o n a l p o s i t i o n b u t n o t n e a r gg. ( F o r 0 ( 6 ) r o t a t i o n n o m e n c l a t u r e s e e R e f . 8). As t h e g l y c o s i d i c a n g l e b e t w e e n a d j a c e n t r e s i d u e s i s v a r i e d by t u r n i n g t h e c o m p l e t e r e s i d u e a r o u n d t h e v i r t u a l b o n d ( c f . F i g . 3 ) , more t h a n one s o l u t i o n f o r a c e r t a i n range o f t h e g l y c o s i d i c a n g l e can e x i s t f o r e v e r y t y p e o f t h e he l i x , a s shown i n F i g . 4. Two r o t a t i o n a l p o s i t i o n s f o r t h e v e c t o r r ^ (see F i g . 3^, c a n be f o u n d w h i c h r e s u l t i n a g l y c o s i d i c a n g l e θ o f a b o u t 120 for 4 h e l i x o f TMA. One s o l u t i o n o f t h e two c a n be r u l e d o u t b e c a u s e o r s h o r t n o n b o n d e d c o n t a c t s b e t w e e n a d j a c e n t r e s i d u e s . Of a l l t h e f o u r f o l d h e l i c e s w h i c h w e r e t e s t e d i n t h i s manner o n l y one s o l u t i o n was f o u n d f o r t h e b a c k b o n e c o n f o r m a t i o n . E v e n when t h e f o u r f o l d symmetry was removed l e a v i n g o n l y a two f o l d s c r e w a x i s a s i n d i c a t e d b y t h e X - r a y d a t a , t h e minimum e n e r g y c o n f o r m a t i o n s t a y e d v e r y c l o s e t o a 4^ h e l i x (9). In the second refinement s t e p , the a l l o w e d c h a i n conformation w i t h t h e s u b s t i t u e n t s i n a l l p o s s i b l e r o t a t i o n a l p o s i t i o n s were p a c k e d w i t h i n t h e u n i t c e l l , i n a g r e e m e n t w i t h s p a c e g r o u p P2^2 2^. T h i s symmetry l i m i t e d t h e p o s s i b l e c h a i n a r r a n g e m e n t s c o n s i d e r a b l y , b y i m p o s i n g a n t i p a r a l l e l p a c k i n g o f c h a i n s and t w o f o l d s c r e w a x e s i n a l l t h r e e d i r e c t i o n s o f t h e u n i t c e l l . The b e s t p a c k i n g o f t h e c h a i n s was s o u g h t b y f i r s t r o t a t i n g and t r a n s l a t i n g a f i x e d


122


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Figure 4. Glycosidic angle θ (C(l) — 0(4)2 — C(4)2) as a function of rotation of the complete residue (φ^) around the virtual bond vector of a 4 helix of TMA 3

c h a i n backbone w i t h r o t a t i o n a l r e f i n e m e n t o f t h e s u b s t i t u e n t s , but o m i t t i n g methyl hydrogens a t t h i s stage. Very l i t t l e f u r t h e r c h a n g e was o b s e r v e d i n t h e c h a i n b a c k b o n e when t h e c o n f o r m a t i o n was s u b s e q u e n t l y s i m u l t a n e o u s l y r e f i n e d w i t h p a c k i n g . I n t h e f i n a l s t a g e o f p a c k i n g a n a l y s i s , t h e TMA s t r u c t u r e was r e f i n e d by o p t i m i z i n g t h e v i r t u a l bond l e n g t h ( i . e . , t h e d i s t a n c e b e t w e e n two a d j a c e n t g l y c o s i d i c o x y g e n s 0 ( 4 ) . . . 0 ( 4 ) 2 ) a n d b y i n t r o d u c i n g t h e m e t h y l h y d r o g e n s . The e t h e r b r i d g e a n g l e a n d o x y g e n c a r b o n d i s t a n c e s o f t h e s u b s t i t u e n t s were k e p t a t c o n s t a n t v a l u e s . The o p t i m a l v i r t u a l b o n d l e n g t h was f o u n d t o b e 4.45 £. The c o m p l e t e d a n a l y s i s o f TMA r e v e a l e d a l m o s t i d e n t i c a l r o t a t i o n a l p o s i t i o n s f o r t h e C(2M) a n d C(3M) m e t h y l s o f two a d j a c e n t r e s i d u e s , b u t d i f f e r e n c e s appeared i n t h e r o t a t i o n a l p o s i t i o n s o f t h e 0 ( 6 ) g r o u p s . The 0 ( 6 ) o f one r e s i d u e was n e a r t h e t g p o s i t i o n whereas t h e 0 ( 6 ) o f t h e second r e s i d u e appeared near g t . The p a c k i n g a n a l y s i s f a v o r e d o n l y t h i s one u n i q u e s o l u t i o n . X - r a y I n t e n s i t y A n a l y s i s . The s t a r t i n g m o d e l f o r t h e s t r u c t u r e r e f i n e m e n t a g a i n s t X - r a y d a t a was t h e m o d e l o b t a i n e d f r o m t h e a b o v e c o n f o r m a t i o n a n d p a c k i n g a n a l y s i s . The same v a r i a b l e p a r a m e t e r s were used a s i n s t e r e o c h e m i c a l r e f i n e m e n t , b u t t h e f u n c t i o n t o b e m i n i m i z e d was now t h e c r y s t a l l o g r a p h i c d i s a g r e e m e n t i n d e x

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(3)

F

w h e r e | F I and I F | a r e t h e o b s e r v e d a n d c a l c u l a t e d s t r u c t u r e a m p l i tudes, r e s p e c t i v e l y . I n a d d i t i o n , an a n i s o t r o p i c temperature f a c q


9.

ZUGENMAIER ET AL.

Conformation

and Packing

Analysis

123

t o r was i n t r o d u c e d i n t h i s s t a g e o f r e f i n e m e n t . The s t r a t e g y o f r e f i n e m e n t was t h e same a s p r e v i o s l y d e s c r i b e d (2^) . O n l y m i n o r d i f f e r e n c e s between t h e s t a r t i n g model and t h e r e f i n e d model r e s u l t e d , b u t a stereochemically unacceptable r o t a t i o n a l p o s i t i o n o f t h e m e t h y l c a r b o n s , w h i c h w e r e r o t a t e d w i t h i n a 10 r a n g e away f r o m t h e b e s t p a c k i n g m o d e l , was o n e o f t h e d i f f e r e n c e s . Therefore, i n order t o maintain the stereochemical c r i t e r i a f o r a l l r o t a t a b l e s u b s t i t u e n t s , t h e f i n a l p a c k i n g m o d e l was k e p t f i x e d a n d o n l y t h e h e l i x was a l l o w e d t o s h i f t a l o n g t h e £ a x i s and t o r o t a t e a r o u n d i t d u r i n g t h e f i n a l R - i n d e x r e f i n e m e n t . The c o o r d i n a t e s o f one a s y m m e t r i c u n i t (two r e s i d u e s ) o f t h e r e s u l t i n g b e s t m o d e l a r e l i s t e d i n T a b l e I a n d t h e m o d e l i s shown i n F i g . 5. B e c a u s e a 4^ h e l i x b u t w i t h d i f f e r e n t p o s i t i o n s o f s u b s t i t u e n t atoms h a d b e e n assumed a s a m o d e l i n o r d e r t h a t i t c o u l d b e handled i n t h e present stage o f c a l c u l a t i o n , t h e coordinates o f the backbone have t o be c o n s i d e r e d as a v e r a g e d v a l u e s w i t h r e s p e c t t o two c o n s e c u t i v e r e s i d u e s . The p o l a r c o o r d i n a t e s a r e a l s o l i s t e d i n T a b l e I , a c c o r d i n g t o t h e r e s i d u e d e f i n i t i o n o f F i g . 3. S i g n i f i c a n t d i f f e r e n c e s i n t h e r o t a t i o n a l p o s i t i o n s o f t h e two r e s i d u e s a r e o n l y observed f o r t h e 0(6) s u b s t i t u e n t s and f o r t h e r o t a t i o n o f t h e m e t h y l h y d r o g e n s . The c o r r e s p o n d i n g bond l e n g t h s , b o n d a n g l e s a n d c o n f o r m a t i o n a n g l e s a r e shown i n T a b l e I I . The d e v i a t i o n from t h e average v a l u e s as a r e s u l t o f t h e refinement a r e shown i n p a r e n t h e s i s . None o f t h e b o n d l e n g t h s e x c e e d e d one s t a n d a r d d e v i a t i o n a n d o n l y t h r e e bond a n g l e s exceeded t h e s t a n d a r d d e v i a t i o n o f 1.5 , w h i c h i n c l u d e d t h e g l y c o s i d i c b o n d a n g l e o f 121.5 . M a j o r c h a n g e s f o r c o n f o r m a t i o n a n g l e s o c c u r r e d w i t h r e s p e c t t o t h e p o s i t i o n o f two a d j a c e n t r e s i d u e s a s c o m p a r e d w i t h V - a m y l o s e (_2) . The s h o r t e s t i n t e r - a n d i n t r a m o l e c u l a r c o n t a c t s are l i s t e d i n Table I I I and a l l a r e l a r g e r than t h e e s t a b l i s h e d l i m i t s ( Π ). The o b s e r v e d a n d c a l c u l a t e d s t r u c t u r e a m p l i t u d e s f o r TMA a r e l i s t e d i n T a b l e I V . The R - i n d e x o b t a i n e d w i t h t h e c o o r d i n a t e s o f T a b l e I was 0.32 w i t h a l l r e f l e c t i o n s i n c l u d e d a n d 0.31 w i t h o n l y t h e o b s e r v e d r e f l e c t i o n s . The e s t i m a t e d i n t e n s i t i e s o f t h e o b s e r v e d e v e n numbered m e r i d i o n a l r e f l e c t i o n s a g r e e d w i t h t h e c a l c u l a t e d ones. Conclusion I t became c l e a r d u r i n g t h e r e f i n e m e n t p r o c e d u r e t h a t e v e n t h o u g h t h e TMA b a c k b o n e s t r u c t u r e c a n b e a p p r o x i m a t e d b y a 4 h e l i x , p a c k i n g o f t h e c h a i n s u p e r i m p o s e s a t w o f o l d a x i s o n l y . The e f f e c t o f t h i s i s a r o t a t i o n o f c o n s e c u t i v e 0(6) s u b s t i t u e n t s i n t o two d i f f e r e n t p o s i t i o n s . The same was f o u n d t o b e t h e c a s e i n t h e s t r u c t u r e o f V - a m y l o s e (2) , i n w h i c h t h e b a c k b o n e c o u l d b e a p p r o x i m a t e d b y a 6^ h e l i x b u t t h e t h r e e 0 ( 6 ) g r o u p s o f c o n s e c u tive r e s i d u e s were a l l found t o be i n d i f f e r e n t r o t a t i o n a l p o s i t i o n s . Here a g a i n a t w o f o l d a x i s i s superimposed b u t t h r e e r e s i d u e s form t h e asymmetric u n i t . T h i s r e s u l t e d i n both t h e b e t t e r


124


Table I : Coordinates o f the asymmetric u n i t f o r t r i m e t h y l a m y l o s e (VB=4.45 8). T h e v i r t u a l b o n d v e c t o r s a r e a p p r o x i m a t e d b y a 4^ h e l i x . The p o l a r c o o r d i n a t e s o f t h e p e n d a n t atoms a r e d i f f e r e n t f o r t h e two r e s i d u e s , B e s t R v a l u e i s o b t a i n e d f o r a r o t a t i o n b y 2° a n d a s h i f t o f 1.73 8 a l o n g t h e c - a x i s . The a s y m m e t r i c u n i t has t o b e s h i f t e d b y 1/4 a_ f o r s p a c e g r o u p P 2 2 2 . 1

X

Y

Ζ

(h

r.

1

1

Θ. 1 (deg r.)

A)

0(4) C(l) C(2) C(3) C(4) C(5) C(6) 0(2) 0(3) 0(5) 0(6)tg

O.OOO -2.540 -2.672 -1.476 -1.277 -1.190 -1.075 -2.717 -1.683 -2.348 0.278

-1.503 -Ο.138 -1.612 -2.055 -1.151 0.289 1.267 -2.359 -3.395 0.649 1.474

O.OOO 2.949 2.585 1.752 0.542 1.030 -0.125 3.796 1.300 1.788 -0.552

1.420 1.524 1.523 1.431 1.430 1.518 1.423 1.429 1.416 1.434

-1.7 169.1 -58.9 0 63.7 -176.7 -172.1 -70.2 -59.8 151.0

C(2M) C(3M) C(6M)

-4.000 -1.093 0.372

-2.311 -4.376 2.212

4.437 2.165 -1.779

1.435 1.435 1.435

78 144 170

H(l) H(2) H(3) H(4) H(5) H(6A) H(6B)

-3.408 -3.555 -0.610 -2.095 -0.332 -1.500 -1.649

0.179 -1.760 -2.041 -1.252 0.406 2.186 0.922

3.448 2.037 2.346 -0.109 1.623 0.151 -0.934

H(2M1) H(2M2) H(2M3) H(3M1) H(3M2) H(3M3) H(6M1) H(6M2) H(6M3)

-4.716 -3.950 -4.271 -0.803 -0.252 -1.793 -0.024 -0.168 1.379

-1.948 -1.675 -3.275 -3.920 -4.796 -5.133 3.174 1.715 2.286

3.761 5.271 4.751 3.066 1.698 2.365 -1.640 -2.530 -2.067

0(4)2 C(l)2 C(2)2 C(3)2 C(4)2 C(5)2 C(6)2

-1.503 -0.138 -1.612 -2.055 -1.151 0.289 1.309

O.OOO 2.540 2.672 1.476 1.277 1.190 1.052

3.909 6.858 6.495 5.661 4.451 4.939 3.823

67.7 111.4 105.8 44.2 113.9 107.6 109.7 108.9 113.7 113.0

15

109.5

1.05

12

109.5

1.05

63

109.5

-174.3

1 6 5 4 3 9 7 8 2 10

113 113 113

1.05

1.519

i

107.1


9

9.

ZUGENMAIER ET AL.

Conformation

and Packing

Analysis

(Table I continued) - 2 . 356 0(2)2 0(3)2 - 3 . 394 0(5)2 0. 649 2. 611 0(6)2gt

2.747 1.700 2.348 0.737

7.710 5.224 5.697 4.313

1.427 1.426

-172.6 -70.9

107.8 109.5

1.426

67.0

112.4

C(2M)2 C(3M)2 C(6M)2

- 2 . 299 -4. 372 3.048

4.043 1.075 -0.578

8.324 6.067 3.940

1.435 1.435 1.435

78 142 112.8

H(l)2 H(2)2 H(3)2 H(4)2 H(5)2 H(6A)2 H(6B)2 H(2M1)2 H(2M2)2 H(2M3)2 H(3M1)2 H(3M2)2 H(3M3)2 H(6M1)2 H(6M2)2 H(6M3)2

0. 179 - 1 . 760 -2.041 - 1 . 252 0. 406 1. 349 0. 997 - 2 . 897 - 1 . 304 - 2 . 650 -4. 442 -4.086 - 5 . 305 3. 463 2. 229 3. 771

3.408 3.555 0.610 2.095 0.332 1.945 0.306 4.714 4.384 3.979 1.601 0.083 1.080 -0.549 -1.235 -0.914

7.357 5.946 6.255 3.800 5.533 3.271 3.153 7.782 8.329 9.311 6.973 6.259 5.586 2.976 3.949 4.623

1.05

74

109.5

1.05

73

109.5

1.05

84

109.5

113 113 113

P o l a r c o o r d i n a t e s m i s s i n g i n t h e second r e s i d u e a r e t h e same a s i n t h e f i r s t o n e .


125

126


Table I I Bond lengths, bond angles and conformation angles f o r the asymmetric u n i t o f Table I . D i f f e r e n c e s from the average residue values (10) are shown i n b r a c k e t s .

Parameter

F i r s t residue

Second r e s i d u e

1.431 1.523 1.523 1.524 1.416 1.420 1.524 1.430 1.423 1.429 1.518 1.434

1 .427 1 .426 1 .519 1 .426

Bond Lengths 0 ( 4 ) -C(4) C ( 4 ) -C(3) C(4) -C(5) C ( l ) -C(2) C ( l ) -0(5) C(l) -0(4)2 C ( 3 ) -C(2) C(5) -0(5) C(2) - 0 ( 2 ) C(3) -0(3) C ( 5 ) -C(6) C(6) -0(6)

Bond Angles

( 0.005) ( O.OOO) (-0.002) ( 0.001) ( 0.002) ( 0.005) ( 0.003) (-0.006) ( O.OOO) ( O.OOO) ( 0.004) ( 0.007)

( 0.004) (•-0.003) ( 0.005) (•-0.001)

(deg.)

0(4) -C(4)-C(3) 0(4) -C(4)-C(5) C(3) - C ( 4 ) - C ( 5 ) C(4) -C(3)-C(2) C ( 4 ) -C

Conformation and Packing Analysis of Polysaccharides and Derivatives

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