- Email: [email protected]
The hydrogen bonding in native cellulose
232
Biochimica et Biophysica A cta, 343 (1974) 232--237
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA 27371 T H E H Y D R O G E N BONDING IN NATIVE C E L L U L O S E
K.H. GARDNER and J. BLACKWELL Department o f Macromolecular Science, Case Western Reserve University Cleveland, Ohio 44106 (U.S.A.)
(Received October 12th, 1973)
Summary The crystal structure of native cellulose has been investigated by X-ray methods, using the diffraction data f r om oriented specimens of V a l o n i a cellulose, and rigid-body least-squares r e f i n e m e n t procedures. Models containing chains with the same and with opposite sense have been refined against the observed intensity data. Both refined models contain the same h y d r o g e n bonding n e t w o r k with one intermolecular and two intramolecular bonds per glucose residue, The r e f i n e m e n t also indicates a small but significant preference for the model containing chains with the same sense.
We have investigated the crystal structure of native cellulose, using X-ray diffraction data from the highly crystalline cellulose of the cell walls of the alga V a l o n i a v e n t r i c o s a . Crystallographic study of cellulose dates from work of Meyer and Misch [ 1 ] , who determined the unit cell dimensions from ramie cellulose to be a = 8.35 i\, b = 7.9 X, c = 10.3 A (fiber axis), and 7 -- 96 ° (in keeping with the n o m e n c l a t u r e presently in use in p o l y m e r crystallography, c is designated the fiber axis and the monoclinic angle (~/) is obtuse). This unit cell contains two cellulose chains and has space group P2~. T he cellulose chains each possess 2-fold screw-axes and the space group s y m m e t r y is satisfied whether the chains have the same or opposite sense, i.e. w h e t h e r they are "parallel" or "anti-parallel". Solution of the question of chain polarity in cellulose is essential for an understanding of the biosynthesis and p o l y m o r p h i c transformations. However, num er ous later attempts to determine the structure [2--4] have been unsuccessful, and it has been considered that the relatively small q u a n t i t y of diffraction data was insufficient to distinguish between parallal and anti-parallel chains. In the present work, we have applied rigid-body least-squares refi nem ent methods to the diffraction data from V a l o n i a cellulose. Specimens were prepared by pulling oriented fibers from the purified, intact cell wall, which were then bundled and placed perpendicular to the X-ray beam. The X-ray fiber
233
Fig. 1. X - r a y d i f f r a c t i o n p a t t e r n of a b u n d l e o f o r i e n t e d f i b e r s o f V a l o n i a c e l l u l o s e . T h e f i b e r b u n d l e h a s been tilted to observe the w e a k 002 reflection. On further tilting the a p p a r e n t fifth layer meridional r e f l e c t i o n s p l i t s a n d is o b s e r v e d as t h e 1 0 5 r e f l e c t i o n .
d i a g r a m f o r such a s p e c i m e n is s h o w n in Fig. 1. As was first s h o w n in t h e low t e m p e r a t u r e e l e c t r o n d i f f r a c t i o n w o r k b y H o n j o a n d W a t a n a b e [ 5 ] , the measu r e d d-spacings can be i n d e x e d b y a (H--W) u n i t cell c o n t a i n i n g eight cellulose chains w i t h a d o u b l i n g o f a a n d b d i m e n s i o n s , i.e. f o u r t i m e s t h e size o f t h e M e y e r and Misch (M--M) u n i t cell. O u r u n i t cell is m o n o c l i n i c w i t h space g r o u p P2~, a n d has d i m e n s i o n s a = 1 6 . 3 4 £ , b = 1 5 . 7 2 h , c {fiber axis) = 1 0 . 3 8 A, a n d 7 = 97.0 ° . T h e o b s e r v e d intensities w e r e m e a s u r e d f r o m d e n s i t o m e t e r traces o f t h e X - r a y p h o t o g r a p h , a n d c o r r e c t e d as d e s c r i b e d b y Cella et al. [ 6 ] . A t first glance t h e p r o b l e m s in refining an 8-chain m o d e l a p p e a r insurm o u n t a b l e in view of t h e p r e v i o u s difficulties f o r t h e 2-chain u n i t cell. H o w ever, the d a t a w h i c h n e c e s s i t a t e s t h e d o u b l i n g of t h e a a n d b axes consists of o n l y t h r e e w e a k r e f l e c t i o n s ( f r o m a t o t a l o f 41 o b s e r v e d r e f l e c t i o n s ) w h i c h can be i n d e x e d w i t h o d d h a n d / o r o d d k indices o n l y . T h e r e m a i n i n g r e f l e c t i o n s w i t h o d d h or k are t o o w e a k t o be o b s e r v e d or, if p r e s e n t , are in p o s i t i o n s w h e r e t h e y are o v e r l a p p e d b y o b s e r v e d r e f l e c t i o n s w i t h even h a n d ]z. T h e w e a k n e s s o f t h e s e r e f l e c t i o n s indicates t h a t t h e d i f f e r e n c e b e t w e e n the f o u r M--M u n i t cells w h i c h m a k e u p t h e 8-chain H - - W u n i t cell m u s t be v e r y small. T h u s we have used t h e 2-chain M--M u n i t cell as an a d e q u a t e a p p r o x i m a t i o n to t h e Valonia cellulose s t r u c t u r e , a n d h a v e r e f i n e d t h e s t r u c t u r e b a s e d o n t h e intensities for the r e f l e c t i o n s w i t h even h a n d even k.
234
\
O
05"
02"
\ Fig. 2. P r o j e c t i o n of ( 0 2 0 ) p l a n e s h o w i n g t h e h y d r o g e n b o n d i n g n e t w o r k a n d the n u m b e r i n g of the a t o m s . E a c h glucose r e s i d u e f o r m s t w o i n t r a m o l e c u l a r b o n d s ( O 3 - - H . . . O 5 ' a n d O 6 . . . H - - O 2 ' ) a n d one i n t e r m o lecular b o n d (O6--H...O3).
Unit cell structures containing both parallel and anti-parallel chains were refined to give the "best f i t " between observed and calculated structure factors, using the linked-atom least-squares m e t h o d of Arnott and Wonacott [7]. Atomic coordinates for the cellulose chains were computed from standard bond lengths and angles for pyranose ring structures [8]. The resulting chain had two glucose residues related by a 21 screw axis repeating in 10.38 A with an intramolecular O3--H...O5' hydrogen bond of length 2.75 A (see Fig. 2 for numbering of atoms). Constrained in this manner the chain was completely rigid except for possible rotation of the --CH2OH side chain (torsion angle ×. has a value of zero when the C6--O6 bond is cis to the C4--C5 bond; counterclockwise rotation of the group when looking down the C5--C6 bond represents positive rotation). Two such chains were packed in the 2-chain unit cell; parallel and anti-parallel chain models were set up and refined separately. The refinement considered six possible variables: (1) the translation of one chain (along the helix axis) with respect to the other; (2) the rotation of the chains about their respective helix axes (both chains rotated to the same extent); (3) the rotation of the second chain about its helix axis with respect to the position of the first chain; (4) the torsion angle ~( for rotation of the --CH2 OH group about the C5--C6 bond; (5) a scale factor; (6) the overall isotropic temperature factor. Refinement of these six variables for both parallel and anti-parallel chain models was performed to produce the best (least squares) fit for the intensity data. The preliminary analysis resulted in unweighted crystallographic R values of Rp = 0.179 and R A = 0.207 for parallel and anti-parallel structures, respec-
235 tively*. In addition to the 36 observed non-meridional reflections, some 40 predicted reflections in the range covered by the X-ray phot ograph have intensities too low to be det ect ed. The full r e f i n e m e n t then considered the observed reflections, and those unobserved reflections which had calculated intensities higher than the estimated threshold value for detection; the latter reflections were assigned Fo values of two-thirds the m i n i m u m observable figure. The final models for the parallel and anti-parallel chain alternatives gave weighted R r ! values of Rp = 0.233 and R A = 0.299, using a weighting scheme of w = 1 and w = 1/2 for the F o values for the observed and unobserved reflections, respectively. Th e refined isotropic t e m p e r a t u r e factors for the final parallel and antiparallel models are 2.5 and 2.2, respectively. One result of the refinements is t ha t the orientation of the --CH2 OH side chains is similar for bot h parallel and anti-parallel chain models: ×p = 80.3 ° , ×A = 70.2°- The groups are positioned within approx. 20 ° of the so-called tg c o n f o r m a t i o n [9] (×tg = 60°). The h y d r o g e n bonding n e t w o r k is contained in the (020) plane and is compatible with either parallel or anti-parallel chains. The n e t w o r k is shown in Fig. 2; all of the - O H groups can form hydrogen bonds with acceptable bond distances and angles. The parallel chain structure contains intrachain bonds: O3--H...O5' and O 6 . . . H - O 2 ' with bond lengths 2.75 A and 2.87 A, respectively, along bot h sides of each cellulose chain, and an interchain b o nd from 0 6 to 0 3 of the neighboring chain along the a axis, with length 2.79 )~. No h y d r o g e n bonding is possible along the unit cell diagonals or along the b axis. This hydr ogen bonding n e t w o r k is similar to t hat first proposed by Jones [2,3] based on infrared dichroism and equatorial and meridional intensities for ramie cellulose. The relative shift bet w e e n O1 in the chains is 0.27 c a n d - - 0 . 3 1 c in the parallel and anti-parallel structures, respectively, and the structures contain no bad contacts. With the except i on of the relative sense of the second chain in the unit cell, the structures are the same. Indeed, the sensitivity of the R values t o the value of ~( underlines the fact that the experimental data is more sensitive to the --CH2 OH orientation than the relative chain sense. However, statistical tests [ 1 0 ] , based on the n u m b e r of observations, the n u m b e r of refined parameters, and the ratio of the R values for the alternative models, indicate that the parallel chain system is in significantly bet t er agreement with the X-ray diffraction data than the anti-parallel model. The hypothesis that the proposed anti-parallel model is as good a model as the parallel model can be rejected at a significance level of less than 0.5%. Thus a parallel chain model is proposed for cellulose. The ab and ac projections of the refined structure are shown in Figs 3a and 3b. In the 2-chain unit cell, the (x,y) positions of the chain axes in adjacent h y d r o g e n - b o n d e d sheets are defined by the P21 s y m m e t r y of the unit cell, *
A survey of R values for possible models indicates that four basic structures need to be eonsidered. With the glycosidic oxygen, O1, of the origin chains placed with its Z component equal to 0.0 ( Z 0 1 = 0 . 0 ) : ( a ) p a r a l l e l c h a i n s o r i e n t e d " u p " in t h e u n i t cell w i t h a s h i f t o f O 1 t o a p p r o x . + 1 / 4 c (a c h a i n is d e f i n e d as " u p " w h e n Z 0 5 ~ Z C 5 ); ( b ) p a r a l l e l c h a i n s o r i e n t e d " d o w n " w i t h a s h i f t o f O 1 t o a p p r o x . + 1 / 4 c ; ( c ) a n t i - p a r a l l e l c h a i n s w i t h a n " u p " c h a i n a t t h a t o r i g i n a n d a s h i f t o f O 1 in the "down" chain to approx. --1/4c; and (d) anti-parallel chains with an "up" chain at the origin a n d a s h i f t o f O 1 i n t h e " d o w n " c h a i n t o a p p r o x . + 1 / 4 c . S u b s e q u e n t l y , i t w a s f o u n d t h a t (a) a n d (c) w e r e t h e b e s t p a r a l l e l a n d a n t i - p a r a l l e l m o d e l s , r e s p e c t i v e l y .
236
(a)
\ \ (b) Fig. 3. P r o j e c t i o n s of t h e p r o p o s e d parallel 2-chain m o d e l for cellulose. T h e u n i t cell is v i e w e d (a) p e r p e n d i c u l a r to the a b p l a n e (along the fiber axis), a n d (b) p e r p e n d i c u l a r to the a c plane.
while in the 8-chain unit cell the s y m m e t r y defines only the relation of alternate h y d r o g e n - b o n d e d sheets. It seems possible that the larger 8-chain unit cell could be due in part to small shifts of h y d r o g e n - b o n d e d sheets past each other in the a direction. The structure refined by least squares for the 2-chain unit cell would thus represent an "average" structure.
Acknowledgements We th an k Dr S. A r n o t t of Purdue University for allowing one of us (K.H.G.) to spend two m ont hs in his laboratory during 1972 and for making available his linked-atom least-squares r e f i n e m e n t programs, on which our programs are based. This work was s uppor t ed by N.S.F. grant No. G H 34227, N.I.H. grant No. AM14777 and N.I.H. Research Career D e v e l o p m e n t Award No. AM70642 (to J.B.).
237
References 1 2 3 4 5 6 7 8 9 10
M e y e r , K . H . a n d Misch, L. ( 1 9 3 7 ) Helv. China. A c t a 2 0 , 2 3 2 J o n e s , D.W. ( 1 9 5 8 ) J. P o l y m . Sci. 3 2 , 3 7 1 J o n e s , D.W. ( 1 9 6 0 ) J. P o l y m . Sci. 4 2 , 1 7 3 N i e d u s z y n s k i , I.A. a n d A t k i n s , E . D . T . ( 1 9 7 0 ) B i o c h i m . B i o p h y s . A c t a 2 2 2 , 1 0 9 H o n j o , G. a n d W a t a n a b e , M. ( 1 9 5 8 ) N a t u r e 1 8 1 , 3 2 6 Celia, R . J . , Lee, B. a n d H u g h e s , R . E . ( 1 9 7 0 ) A c t a C r y s t . A 2 6 , l l S A r n o t t , S. a n d W o n a c o t t , A. ( 1 9 6 6 ) P o l y m e r 7, 1 5 7 A r n o t t , S. a n d S c o t t , W.E. ( 1 9 7 2 ) J. C h e m . Soc. P e r k i n T r a n s . II, 3 2 4 S u n d a r a l i n g a m , M. ( 1 9 6 8 ) B i o p o l y m e r s 6, 1 8 9 H a m i l t o n , W.C. ( 1 9 6 5 ) A c t a C r y s t . 1 8 , 5 0 2
Biochimica et Biophysica A cta, 343 (1974) 232--237
© Elsevier Scientific Publishing Company, Amsterdam -- Printed in The Netherlands
BBA 27371 T H E H Y D R O G E N BONDING IN NATIVE C E L L U L O S E
K.H. GARDNER and J. BLACKWELL Department o f Macromolecular Science, Case Western Reserve University Cleveland, Ohio 44106 (U.S.A.)
(Received October 12th, 1973)
Summary The crystal structure of native cellulose has been investigated by X-ray methods, using the diffraction data f r om oriented specimens of V a l o n i a cellulose, and rigid-body least-squares r e f i n e m e n t procedures. Models containing chains with the same and with opposite sense have been refined against the observed intensity data. Both refined models contain the same h y d r o g e n bonding n e t w o r k with one intermolecular and two intramolecular bonds per glucose residue, The r e f i n e m e n t also indicates a small but significant preference for the model containing chains with the same sense.
We have investigated the crystal structure of native cellulose, using X-ray diffraction data from the highly crystalline cellulose of the cell walls of the alga V a l o n i a v e n t r i c o s a . Crystallographic study of cellulose dates from work of Meyer and Misch [ 1 ] , who determined the unit cell dimensions from ramie cellulose to be a = 8.35 i\, b = 7.9 X, c = 10.3 A (fiber axis), and 7 -- 96 ° (in keeping with the n o m e n c l a t u r e presently in use in p o l y m e r crystallography, c is designated the fiber axis and the monoclinic angle (~/) is obtuse). This unit cell contains two cellulose chains and has space group P2~. T he cellulose chains each possess 2-fold screw-axes and the space group s y m m e t r y is satisfied whether the chains have the same or opposite sense, i.e. w h e t h e r they are "parallel" or "anti-parallel". Solution of the question of chain polarity in cellulose is essential for an understanding of the biosynthesis and p o l y m o r p h i c transformations. However, num er ous later attempts to determine the structure [2--4] have been unsuccessful, and it has been considered that the relatively small q u a n t i t y of diffraction data was insufficient to distinguish between parallal and anti-parallel chains. In the present work, we have applied rigid-body least-squares refi nem ent methods to the diffraction data from V a l o n i a cellulose. Specimens were prepared by pulling oriented fibers from the purified, intact cell wall, which were then bundled and placed perpendicular to the X-ray beam. The X-ray fiber
233
Fig. 1. X - r a y d i f f r a c t i o n p a t t e r n of a b u n d l e o f o r i e n t e d f i b e r s o f V a l o n i a c e l l u l o s e . T h e f i b e r b u n d l e h a s been tilted to observe the w e a k 002 reflection. On further tilting the a p p a r e n t fifth layer meridional r e f l e c t i o n s p l i t s a n d is o b s e r v e d as t h e 1 0 5 r e f l e c t i o n .
d i a g r a m f o r such a s p e c i m e n is s h o w n in Fig. 1. As was first s h o w n in t h e low t e m p e r a t u r e e l e c t r o n d i f f r a c t i o n w o r k b y H o n j o a n d W a t a n a b e [ 5 ] , the measu r e d d-spacings can be i n d e x e d b y a (H--W) u n i t cell c o n t a i n i n g eight cellulose chains w i t h a d o u b l i n g o f a a n d b d i m e n s i o n s , i.e. f o u r t i m e s t h e size o f t h e M e y e r and Misch (M--M) u n i t cell. O u r u n i t cell is m o n o c l i n i c w i t h space g r o u p P2~, a n d has d i m e n s i o n s a = 1 6 . 3 4 £ , b = 1 5 . 7 2 h , c {fiber axis) = 1 0 . 3 8 A, a n d 7 = 97.0 ° . T h e o b s e r v e d intensities w e r e m e a s u r e d f r o m d e n s i t o m e t e r traces o f t h e X - r a y p h o t o g r a p h , a n d c o r r e c t e d as d e s c r i b e d b y Cella et al. [ 6 ] . A t first glance t h e p r o b l e m s in refining an 8-chain m o d e l a p p e a r insurm o u n t a b l e in view of t h e p r e v i o u s difficulties f o r t h e 2-chain u n i t cell. H o w ever, the d a t a w h i c h n e c e s s i t a t e s t h e d o u b l i n g of t h e a a n d b axes consists of o n l y t h r e e w e a k r e f l e c t i o n s ( f r o m a t o t a l o f 41 o b s e r v e d r e f l e c t i o n s ) w h i c h can be i n d e x e d w i t h o d d h a n d / o r o d d k indices o n l y . T h e r e m a i n i n g r e f l e c t i o n s w i t h o d d h or k are t o o w e a k t o be o b s e r v e d or, if p r e s e n t , are in p o s i t i o n s w h e r e t h e y are o v e r l a p p e d b y o b s e r v e d r e f l e c t i o n s w i t h even h a n d ]z. T h e w e a k n e s s o f t h e s e r e f l e c t i o n s indicates t h a t t h e d i f f e r e n c e b e t w e e n the f o u r M--M u n i t cells w h i c h m a k e u p t h e 8-chain H - - W u n i t cell m u s t be v e r y small. T h u s we have used t h e 2-chain M--M u n i t cell as an a d e q u a t e a p p r o x i m a t i o n to t h e Valonia cellulose s t r u c t u r e , a n d h a v e r e f i n e d t h e s t r u c t u r e b a s e d o n t h e intensities for the r e f l e c t i o n s w i t h even h a n d even k.
234
\
O
05"
02"
\ Fig. 2. P r o j e c t i o n of ( 0 2 0 ) p l a n e s h o w i n g t h e h y d r o g e n b o n d i n g n e t w o r k a n d the n u m b e r i n g of the a t o m s . E a c h glucose r e s i d u e f o r m s t w o i n t r a m o l e c u l a r b o n d s ( O 3 - - H . . . O 5 ' a n d O 6 . . . H - - O 2 ' ) a n d one i n t e r m o lecular b o n d (O6--H...O3).
Unit cell structures containing both parallel and anti-parallel chains were refined to give the "best f i t " between observed and calculated structure factors, using the linked-atom least-squares m e t h o d of Arnott and Wonacott [7]. Atomic coordinates for the cellulose chains were computed from standard bond lengths and angles for pyranose ring structures [8]. The resulting chain had two glucose residues related by a 21 screw axis repeating in 10.38 A with an intramolecular O3--H...O5' hydrogen bond of length 2.75 A (see Fig. 2 for numbering of atoms). Constrained in this manner the chain was completely rigid except for possible rotation of the --CH2OH side chain (torsion angle ×. has a value of zero when the C6--O6 bond is cis to the C4--C5 bond; counterclockwise rotation of the group when looking down the C5--C6 bond represents positive rotation). Two such chains were packed in the 2-chain unit cell; parallel and anti-parallel chain models were set up and refined separately. The refinement considered six possible variables: (1) the translation of one chain (along the helix axis) with respect to the other; (2) the rotation of the chains about their respective helix axes (both chains rotated to the same extent); (3) the rotation of the second chain about its helix axis with respect to the position of the first chain; (4) the torsion angle ~( for rotation of the --CH2 OH group about the C5--C6 bond; (5) a scale factor; (6) the overall isotropic temperature factor. Refinement of these six variables for both parallel and anti-parallel chain models was performed to produce the best (least squares) fit for the intensity data. The preliminary analysis resulted in unweighted crystallographic R values of Rp = 0.179 and R A = 0.207 for parallel and anti-parallel structures, respec-
235 tively*. In addition to the 36 observed non-meridional reflections, some 40 predicted reflections in the range covered by the X-ray phot ograph have intensities too low to be det ect ed. The full r e f i n e m e n t then considered the observed reflections, and those unobserved reflections which had calculated intensities higher than the estimated threshold value for detection; the latter reflections were assigned Fo values of two-thirds the m i n i m u m observable figure. The final models for the parallel and anti-parallel chain alternatives gave weighted R r ! values of Rp = 0.233 and R A = 0.299, using a weighting scheme of w = 1 and w = 1/2 for the F o values for the observed and unobserved reflections, respectively. Th e refined isotropic t e m p e r a t u r e factors for the final parallel and antiparallel models are 2.5 and 2.2, respectively. One result of the refinements is t ha t the orientation of the --CH2 OH side chains is similar for bot h parallel and anti-parallel chain models: ×p = 80.3 ° , ×A = 70.2°- The groups are positioned within approx. 20 ° of the so-called tg c o n f o r m a t i o n [9] (×tg = 60°). The h y d r o g e n bonding n e t w o r k is contained in the (020) plane and is compatible with either parallel or anti-parallel chains. The n e t w o r k is shown in Fig. 2; all of the - O H groups can form hydrogen bonds with acceptable bond distances and angles. The parallel chain structure contains intrachain bonds: O3--H...O5' and O 6 . . . H - O 2 ' with bond lengths 2.75 A and 2.87 A, respectively, along bot h sides of each cellulose chain, and an interchain b o nd from 0 6 to 0 3 of the neighboring chain along the a axis, with length 2.79 )~. No h y d r o g e n bonding is possible along the unit cell diagonals or along the b axis. This hydr ogen bonding n e t w o r k is similar to t hat first proposed by Jones [2,3] based on infrared dichroism and equatorial and meridional intensities for ramie cellulose. The relative shift bet w e e n O1 in the chains is 0.27 c a n d - - 0 . 3 1 c in the parallel and anti-parallel structures, respectively, and the structures contain no bad contacts. With the except i on of the relative sense of the second chain in the unit cell, the structures are the same. Indeed, the sensitivity of the R values t o the value of ~( underlines the fact that the experimental data is more sensitive to the --CH2 OH orientation than the relative chain sense. However, statistical tests [ 1 0 ] , based on the n u m b e r of observations, the n u m b e r of refined parameters, and the ratio of the R values for the alternative models, indicate that the parallel chain system is in significantly bet t er agreement with the X-ray diffraction data than the anti-parallel model. The hypothesis that the proposed anti-parallel model is as good a model as the parallel model can be rejected at a significance level of less than 0.5%. Thus a parallel chain model is proposed for cellulose. The ab and ac projections of the refined structure are shown in Figs 3a and 3b. In the 2-chain unit cell, the (x,y) positions of the chain axes in adjacent h y d r o g e n - b o n d e d sheets are defined by the P21 s y m m e t r y of the unit cell, *
A survey of R values for possible models indicates that four basic structures need to be eonsidered. With the glycosidic oxygen, O1, of the origin chains placed with its Z component equal to 0.0 ( Z 0 1 = 0 . 0 ) : ( a ) p a r a l l e l c h a i n s o r i e n t e d " u p " in t h e u n i t cell w i t h a s h i f t o f O 1 t o a p p r o x . + 1 / 4 c (a c h a i n is d e f i n e d as " u p " w h e n Z 0 5 ~ Z C 5 ); ( b ) p a r a l l e l c h a i n s o r i e n t e d " d o w n " w i t h a s h i f t o f O 1 t o a p p r o x . + 1 / 4 c ; ( c ) a n t i - p a r a l l e l c h a i n s w i t h a n " u p " c h a i n a t t h a t o r i g i n a n d a s h i f t o f O 1 in the "down" chain to approx. --1/4c; and (d) anti-parallel chains with an "up" chain at the origin a n d a s h i f t o f O 1 i n t h e " d o w n " c h a i n t o a p p r o x . + 1 / 4 c . S u b s e q u e n t l y , i t w a s f o u n d t h a t (a) a n d (c) w e r e t h e b e s t p a r a l l e l a n d a n t i - p a r a l l e l m o d e l s , r e s p e c t i v e l y .
236
(a)
\ \ (b) Fig. 3. P r o j e c t i o n s of t h e p r o p o s e d parallel 2-chain m o d e l for cellulose. T h e u n i t cell is v i e w e d (a) p e r p e n d i c u l a r to the a b p l a n e (along the fiber axis), a n d (b) p e r p e n d i c u l a r to the a c plane.
while in the 8-chain unit cell the s y m m e t r y defines only the relation of alternate h y d r o g e n - b o n d e d sheets. It seems possible that the larger 8-chain unit cell could be due in part to small shifts of h y d r o g e n - b o n d e d sheets past each other in the a direction. The structure refined by least squares for the 2-chain unit cell would thus represent an "average" structure.
Acknowledgements We th an k Dr S. A r n o t t of Purdue University for allowing one of us (K.H.G.) to spend two m ont hs in his laboratory during 1972 and for making available his linked-atom least-squares r e f i n e m e n t programs, on which our programs are based. This work was s uppor t ed by N.S.F. grant No. G H 34227, N.I.H. grant No. AM14777 and N.I.H. Research Career D e v e l o p m e n t Award No. AM70642 (to J.B.).
237
References 1 2 3 4 5 6 7 8 9 10
M e y e r , K . H . a n d Misch, L. ( 1 9 3 7 ) Helv. China. A c t a 2 0 , 2 3 2 J o n e s , D.W. ( 1 9 5 8 ) J. P o l y m . Sci. 3 2 , 3 7 1 J o n e s , D.W. ( 1 9 6 0 ) J. P o l y m . Sci. 4 2 , 1 7 3 N i e d u s z y n s k i , I.A. a n d A t k i n s , E . D . T . ( 1 9 7 0 ) B i o c h i m . B i o p h y s . A c t a 2 2 2 , 1 0 9 H o n j o , G. a n d W a t a n a b e , M. ( 1 9 5 8 ) N a t u r e 1 8 1 , 3 2 6 Celia, R . J . , Lee, B. a n d H u g h e s , R . E . ( 1 9 7 0 ) A c t a C r y s t . A 2 6 , l l S A r n o t t , S. a n d W o n a c o t t , A. ( 1 9 6 6 ) P o l y m e r 7, 1 5 7 A r n o t t , S. a n d S c o t t , W.E. ( 1 9 7 2 ) J. C h e m . Soc. P e r k i n T r a n s . II, 3 2 4 S u n d a r a l i n g a m , M. ( 1 9 6 8 ) B i o p o l y m e r s 6, 1 8 9 H a m i l t o n , W.C. ( 1 9 6 5 ) A c t a C r y s t . 1 8 , 5 0 2