The Configurational Statistics of Pullulan and Some Related Glucans

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Downloaded by UNIV OF CALIFORNIA SAN DIEGO on January 27, 2017 | http://pubs.acs.org Publication Date: April 21, 1981 | doi: 10.1021/bk-1981-0150.ch007

The Configurational Statistics of Pullulan and Some Related Glucans DAVID A. BRANT and BRUCE A. BURTON Department of Chemistry, University of California, Irvine, C A 92717

The work reported here has been c a r r i e d out i n the context o f a program to develop r e l i a b l e conformational energy functions f o r polysaccharides i n s o l u t i o n (1, 2 ) . A q u i t e s a t i s f a c t o r y model for aqueous amylosic chains has been developed; details are reported at length elsewhere (3, £ , 5, 6 ) . Here procedures applied successfully to amylose are extended to the closely r e l a t e d g l u c a n p u l l u l a n as p a r t o f an e f f o r t to t e s t the g e n e r a l i t y of the method. Information of p o t e n t i a l a p p l i c a b i l i t y to the dextran family o f polysaccharides i s d e r i v e d i n the process. Ori.ng to the c u r r e n t absence o f appropriate experimental measurements o f the c o n f i g u r a t i o n dependent p r o p e r t i e s (7) o f p u l l u l a n , o n l y an u n r e f i n e d t h e o r y o f the c o n f i g u r a t i o n a l s t a t i s t i c s o f p u l l u l a n can be developed at the present time U , 2) . I t i s nevertheless i n s t r u c t i v e to i n v e s t i g a t e the s e n s i t i v i t y of the c a l c u l a t e d r e s u l t s to v a r i o u s parameters o f the theory, and to c o n t r a s t the behavior p r e d i c t e d for p u l l u l a n on the b a s i s o f an unrefined model with that o f some other g l u c a n s . The r e s u l t s o f these i n v e s t i g a t i o n s are presented here p r i m a r i l y i n the form o f p r o j e c t i o n drawings o f r e p r e s e n t a t i v e polymer c h a i n conformations (2 5) . f

S t r u c t u r e and P r o p e r t i e s o f P u l l u l a n P u l l u l a n i s an e x t r a c e l l u l a r a - D - g l u c a n p r o d u c e d by t h e o r g a n i s m A u r e o b a s i d i u m p u l l u l a n s {8) . Whereas t h e linear component o f s t a r c h , amylose, i s a homo polymer o f a-1,4-1 inked D-glucose (Figure la) , p u l l u l a n has the same s t r u c t u r e with approximately every third a-l 4-1inkage replaced by an a-1,6-linkage (Figure lb) (£, 10_, _ U ) . For present purposes p u l l u l a n has been taken to be a r e g u l a r l y repeating polymer o f m a l t o t r i o s e u n i t s l i n k e d by a - l 6 - l i n k a g e s . The term dextran r e f e r s to a widely studied family o f m i c r o b i a l p o l y s a c c h a r i d e s comprising homopolymeric a-1,6-D-glucan chains possessing v a r i a b l e d e g r e e s o f c h a i n b r a n c h i n g (8) . P u l l u l a n and d e x t r a n a r e f

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0097-6156/81/0150-0081$05.00/ 0 © 1981 American Chemical Society Brant; Solution Properties of Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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amorphous polymers r e a d i l y s o l u b l e i n water whereas amylose is p a r t i a l l y c r y s t a l l i n e and d i s p l a y s only l i m i t e d s o l u b i l i t y i n t h i s medium. These d i f f e r e n c e s are presumably r e l a t e d i n p a r t to the greater conformational freedom inherent i n the a - 1 , 6 - l i n k a g e s . Because p u l l u l a n i s s i m i l a r i n chemical s t r u c t u r e to amylose and i s a v a i l a b l e i n l a r g e amounts i n pure form for experimental studies, i t provides an i d e a l system i n which to t e s t the g e n e r a l i t y o f methods d e v e l o p e d to t r e a t t h e c o n f o r m a t i o n a l s t a t i s t i c s o f amylose. It r e p r e s e n t s , moreover, a l o g i c a l step i n the d i r e c t i o n of a t h e o r e t i c a l treatment o f d e x t r a n . S t r u c t u r a l Parameters As s p e c i f i e d below, the s t r u c t u r a l geometry o f the glucose residues (Figure 1) was taken to be that o f e i t h e r the mean a-D-glucose residue described by Arnott and Scott (12) or the mean a-D-glucose residue i n c r y s t a l l i n e cyclohexaamylose (13). The valence angle at the oxygen o f the g l y c o s i d i c l i n k a g e was chosen to be 1 1 1 . 5 ° f o r a - 1 , 6 - l i n k a g e s (14) and e i t h e r 1 1 4 . 5 ° or 1 1 7 . 0 ° for a - l , 4 - l i n k a g e s .4) , as s p e c i f i e d below. Methods of C a l c u l a t i o n Conformational energies were estimated using methods described p r e v i o u s l y (_1, 3) • present c a l c u l a t i o n s , however, terms were also introduced as i n d i c a t e d below to account for inherent b a r r i e r s to bond r o t a t i o n and for the ancmeric e f f e c t , following methods proposed by Abe and Mark (15) > Thus, t h r e e f o l d t o r s i o n a l I

n

t

n

e

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b a r r i e r s of 1.8 and 2.8 k c a l m o l were included i n seme cases f o r the C-0 and C-C bonds, r e s p e c t i v e l y ; the energy maxima i n these terms occurred for t o r s i o n angles 0, 120, and 2 4 0 ° . (See reference 1 f o r conventions p e r t i n e n t to t o r s i o n angles and other geometric parameters.) A maximum ancmeric s t a b i l i z a t i o n energy o f 1

1.1 k c a l m o l " was associated with the j r o t a t i o n (Figure 1 ) , which resembles the C - 0 bond r o t a t i o n i n poly(oxymethylene) (15) . Rotation ca (Figure lb) i s s i m i l a r to the C-C r o t a t i o n i n p o l y (oxyethylene) and, hence, r e a l i z e s a maximum s t a b i l i z a t i o n energy - 1

of 1.0 k c a l m o l (15) . No s i g n i f i c a n t anomeric e f f e c t attends the r o t a t i o n ^ . Where i n c l u d e d , the ancmeric term operates i n the t o r s i o n angle range 120 to 3 6 0 ° and provides maximal s t a b i l i z a t i o n at about 180 and 3 0 0 ° . Polyner chain dimensions, reported here as the dimensionless c h a r a c t e r i s t i c r a t i o C^ (1, 2, 4) , were c a l c u l a t e d from the s t r u c t u r a l geometry and conformational energy estimates using methods described e a r l i e r (16); approximations inherent i n the c a l c u l a t i o n s have been discussed i n d e t a i l (1, 2, 4, _5, 16). The

Brant; Solution Properties of Polysaccharides ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

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c h a r a c t e r i s t i c r a t i o i s defined to be p r o p o r t i o n a l to the mean square end-to-end d i s t a n c e o f the polymer c h a i n , unperturbed by the long range excluded volume e f f e c t (1, 2); i t s observed value i s c l o s e to 5 for aqueous amylosic chains (4). Projection drawings o f r e p r e s e n t a t i v e conformations o f the s e v e r a l glucans treated were generated by an e l a b o r a t i o n of Monte Carlo methods described e a r l i e r (5). D e t a i l s o f the c a l c u l a t i o n s w i l l be presented l a t e r i n the context o f e f f o r t s to f i t theoretical c a l c u l a t i o n s o f the c h a r a c t e r i s t i c r a t i o to experimental r e s u l t s .


R e s u l t s and D i s c u s s i o n Amylose. A conformational energy contour map f o r a d i m e r i c segment o f an amylosic c h a i n i s shown i n Figure 2 (1-6). The Hybl e t a l . r e s i d u e geometry (13_) and p o t e n t i a l f u n c t i o n s w i t h o u t inherent t o r s i o n a l or ancmeric terms (3) were used. The angle at the g l y c o s i d i c oxygen was 1 1 4 . 5 ° . Energy contours are drawn at l f

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5, and 25 k c a l m o l " r e l a t i v e to the g l o b a l energy minimum; dashed contours imply negative absolute e n e r g i e s . Only one s i g n i f i c a n t low energy domain appears i n the conformation space o f the amylose dimer near the p o s i t i o n \> | = 0, 0 ° . T h i s conformer i s depicted in Figure l a . Throughout most o f the conformation space o f the dimeric segment i n t o l e r a b l e s t e r i c c o n f l i c t s occur as s i g n i f i e d by the l a r g e domain o f high energy where contour l i n e s have been omitted. The energy surface i n Figure 2 i s r e f i n e d i n the sense that the c h a r a c t e r i s t i c r a t i o p r e d i c t e d from i t (1, 2, A, 5) a g r e e s w e l l w i t h e x p e r i m e n t a l measurements o f and its f

temperature c o e f f i c i e n t for amylosic chains i n aqueous media (17) . Figures 3 and 4 show p r o j e c t i o n s into mutually orthogonal (xy and yz ) planes o f one conformation o f a 100-residue amylosic chain. C i r c l e s represent the g l y c o s i d i c oxygens. These oxygens are connected i n the drawings by v i r t u a l bonds spanning the glucose r e s i d u e s , which, f o r c l a r i t y , are not shown. The o r d i n a t e and a b s c i s s a o f the p r o j e c t i o n drawings are measured in Sngstrom u n i t s and r e f e r to axes o f an a r b i t r a r y C a r t e s i a n coordinate system. D e t a i l s o f the computation are presented elsewhere (5). The conformation depicted in F i g u r e s 3 and 4 was chosen to be r e p r e s e n t a t i v e o f chains i n a l a r g e Monte Carlo sample o f such c h a i n s , a l l o f which possess conformations c o n s i s t e n t with the energy surface in Figure 2; i t s end-to-end extension i s c l o s e to the mean value for chains i n the sample. I t i s best to regard these p r o j e c t i o n drawings, and those which f o l l o w , as snapshots o f a polymer c h a i n , taken simultaneously from mutually orthogonal d i r e c t i o n s , which have served to capture the chain i n one o f the countless conformations a v a i l a b l e to i t ( 2 ) . In f a c t the shapes of a l l o f the chains shown here are extremely l a b i l e , and the



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Figure 1. Projection drawings of dimeric a-D-glucan chain segments linked 1,4 (a) and 1,6 (b): (O) oxygens or hydroxyls; (o) hydrogens; (%)carbons; and (®) hydroxymethyl groups. Conventions relating to torsion angles , if/, and w and other structural features are given elsewhere (I).

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Figure 2. Conformational energy contour diagram for the dimeric segment in Figure la. Energy contours are drawn at 1, 5, and 25 kcal mol above the energy minimum; dashed contours correspond to negative absolute energies. References to details of the calculation are provided in the text. 1



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Figure 3. Projection into the xy plane of an arbitrary coordinate system of one particular amylose chain conformation consistent with the energy surface of Figure 2. Circles represent the glycosidic oxygens. These are connected by virtual bonds spanning the sugar residues; for clarity the residues are not shown.

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Figure 4.

i 1

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Projection into the yz plane of the same amylose chain conformation shown in Figure 3



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p r o j e c t i o n drawings represent j u s t a s i n g l e f l e e t i n g conformation which w i l l have changed s u b s t a n t i a l l y an i n s t a n t l a t e r (2, 5 ) . Examination o f the amylosic chain conformation i n F i g u r e s 3 and 4 as w e l l as numerous others i n the Monte Carlo sample (5) d i s c l o s e s the s t a t i s t i c a l or random c o i l nature o f the c h a i n . At the same time the p s e u d o h e l i c a l c h a r a c t e r o f the c h a i n ' s backbone t r a j e c t o r y i s r e a d i l y a s c e r t a i n e d (2_, 5). This l a t t e r feature p l a y s an important r o l e i n the behavior o f the c h a i n , as d i s c u s s e d elsewhere in t h i s volume (6, 18, 19, 20, 21, 22). Among the s e v e r a l c h a r a c t e r i s t i c s o f the amylosic c h a i n , i t i s of p a r t i c u l a r i n t e r e s t to c h a r a c t e r i z e i t s s t i f f n e s s as w e l l as i t s extension. These questions have already been addressed at some length C5, 16) . Here we would simply l i k e to p o i n t out t h a t , in a d d i t i o n to the c h a r a c t e r i s t i c r a t i o , the c o n f i g u r a t i o n a l entropy, and the p e r s i s t e n c e l e n g t h , a l l commonly used as measures of s t i f f n e s s and extension, i t may be useful to consider a kind o f c o r r e l a t i o n f u n c t i o n defined by the mean p r o j e c t i o n o f a u n i t vector along the f i n a l v i r t u a l bond o f the c h a i n onto a u n i t v e c t o r aligned with the i n i t i a l v i r t u a l bond. This function is shown in F i g u r e 5 for the conformational energy map of Figure 2; d e t a i l s o f the c a l c u l a t i o n w i l l be presented i n another p l a c e . The o s c i l l a t o r y c h a r a c t e r o f the c o r r e l a t i o n f u n c t i o n i s a c l e a r r e f l e c t i o n o f the p s e u d o h e l i c a l nature o f the c h a i n t r a j e c t o r y . We see in F i g u r e 5 that c o r r e l a t i o n o f the d i r e c t i o n s o f the i n i t i a l and f i n a l bonds o f the c h a i n p e r s i s t s even for chains (or chain segnents) with degrees o f p o l y m e r i z a t i o n o f 100 or more. The c o r r e l a t i o n f u n c t i o n has decayed to 1/e a f t e r 20 r e s i d u e s . T h i s measure o f the c o r r e l a t i o n l e n g t h , expressed i n numbers o f glucose r e s i d u e s , may i n some cases be more meaningful than the p e r s i s t e n c e l e n g t h , which i s a c o r r e l a t i o n length expressed i n distance units (5). C e r t a i n l y i t i s improper, as i s sometimes done, to t r y to express the c o r r e l a t i o n length i n residue u n i t s by taking the r a t i o o f the p e r s i s t e n c e length to the ( v i r t u a l bond) length o f a s i n g l e r e s i d u e . I f t h i s i s done for the amylosic chains o f Figures 2-5, which possess a p e r s i s t e n c e length o f about

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and a v i r t u a l bond length of 4.258, the c o r r e l a t i o n length i n residue u n i t s i s g r o s s l y underestimated. (The term "persistence length" in t h i s paper r e f e r s to the magnitude o f the mean end-to-end v e c t o r . ) Other s k e l e t a l geometries and p o t e n t i a l functions can be j u s t i f i e d for amylose i n a d d i t i o n to those chosen to generate F i g u r e s 2-5. If, f o r example, the A r n o t t and Scott residue geometry (12) i s used i n conjunction with p o t e n t i a l functions which include terms for inherent t o r s i o n a l b a r r i e r s and the ancmeric e f f e c t , the contour diagram o f F i g u r e 6 i s obtained. Here the g l y c o s i d i c b r i d g e angle was taken to be 117.0 °. T h i s energy surface y i e l d s a c h a r a c t e r i s t i c r a t i o almost f i v e times the



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Figure 5. The ordinate displays the mean projection of a unit vector along the final virtual bond of an amylosic chain consistent with Figure 2 onto a vector aligned with the initial virtual bond. The abscissa is chain length, measured in glucose units. The horizontal line through the figure is the inverse of the base of natural logarithms.

Figure 6. An energy surface as in Figure 2, but based on alternative assumptions about skeletal geometry and conformational energy functions as described in the text


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experimental v a l u e , and, t h e r e f o r e , presumably represents a l e s s r e a l i s t i c c h a i n model. A t y p i c a l c h a i n conformation c o n s i s t e n t with t h i s surface i s drawn i n F i g u r e 7, where the tendency toward pseudohelical t r a j e c t o r i e s seen in Figures 3 and 4 p e r s i s t s . Now, however, the chain i s c l e a r l y more extended with greater mean p i t c h and fewer residues per turn i n the pseudohel i c a l segments. The associated c o r r e l a t i o n f u n c t i o n shown i n Figure 8 o s c i l l a t e s l e s s d r a m a t i c a l l y because o f the l a r g e r pseudohelical p i t c h , i . e . , each v i r t u a l bond i s , on the average, more n e a r l y c o l i n e a r with i t s predecessor. The p e r s i s t e n c e length c a l c u l a t e d for t h i s c h a i n model i s 66 X, but the c o r r e l a t i o n length measured i n glucose residues (defined by the decay o f the c o r r e l a t i o n function) is apparently smaller than i n the case o f the p r e c e d i n g , more r e a l i s t i c , c h a i n model, which has a p e r s i s t e n c e length l e s s than h a l f as l a r g e . Dextran. We w i l l use the term "dextran" in the present context to denote the l i n e a r

The Configurational Statistics of Pullulan and Some Related Glucans

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