A Model for Amylose-Iodine Binding - ACS Symposium Series (ACS

32 A Model for Amylose-Iodine Binding ATTILIO CESÀRO and WALTER KONIC Laboratory of Macromolecular Chemistry, University of Trieste, 34127 Trieste, Italy

Downloaded by UNIV QUEENSLAND on September 20, 2013 | http://pubs.acs.org Publication Date: April 21, 1981 | doi: 10.1021/bk-1981-0150.ch032

DAVID A . BRANT Department of Chemistry, University of California, Irvine, CA 92717

Perhaps the best known property o f amylose in aqueous s o l u t i o n i s i t s r e a c t i o n with iodine in the presence of iodide to give a dark blue complex. Notwithstanding considerable study over a p e r iod of many y e a r s , a complete d e s c r i p t i o n of the conformation and stoichiometry of the d i s s o l v e d complex has yet to emerge, in part because of the l a r g e number of independent v a r i a b l e s that must be c o n t r o l l e d and separately studied in order to carry out a complete investigation ( 1 ) . It i s furthermore evident that a f u l l understanding of the aqueous complex has been e l u s i v e because i t may e x i s t in various states of aggregation, which depend upon k i n e t i c as well as e q u i l i b r i u m f a c t o r s (1, 2, 3, 4 ) . C o n f l i c t i n g models continue to appear as an outgrowth of e f f o r t s to i n t e r p r e t hydrodynamic data (1, 3, 4, 5) and recent r e s u l t s from resonance Raman (6, 7, 8, 9 ) , Moessbauer (8), and c i r c u l a r dichroism (9) s p e c t r o s copy. In what follows we review b r i e f l y some o f these r e s u l t s i n order to describe c e r t a i n features of the complex on which general agreement seems to have been achieved. Subsequently we present a simple model, based on some widely accepted c h a r a c t e r i s t i c s o f the complex, which i s capable of c o r r e l a t i n g a number o f these f e a tures . Structure and Stoichiometry o f the Complex There seems l i t t l e doubt that the d i s s o l v e d complex i s an i n c l u s i o n compound in which iodine r e s i d e s within the annular c a v i t y of a more or l e s s regular h e l i c a l amylose c h a i n . This p i c t u r e emerged e a r l y from the work of Rundle and coworkers on the c r y s t a l l i n e (10) and d i s s o l v e d (V1_) complex and has not been s e r i o u s l y challenged by any more recent s t u d i e s . Despite the acknowledged h e l i c a l character of the d i s s o l v e d complex, i t i s very c l e a r from hydrodynamic evidence that the complexed polymer does not adopt a r i g i d , r o d - l i k e conformation; indeed, the hydrodynamic volume o f the polymer decreases upon complexation with iodine (J_ 3, 5) · The spectroscopic p r o p e r t i e s o f the d i s s o l v e d complex imply that the bound iodine i s arrayed in l i n e a r sequences, but neither the f

0097-6156/81/0150-0477$05.00/0 © 1981 American Chemical Society In Solution Properties of Polysaccharides; Brant, D.; ACS Symposium Series; American Chemical Society: Washington, DC, 1981.

478

SOLUTION PROPERTIES OF POLYSACCHARIDES

d i s t r i b u t i o n o f i o d i n e c h a i n l e n g t h s n o r even t h e mean c h a i n l e n g t h has been e s t a b l i s h e d . The complex a b s o r b s s t r o n g l y n e a r 600 nm, where t h e unbound i o d i n e s p e c i e s have no s i g n i f i c a n t ab sorption. E x t e n s i v e i n v e s t i g a t i o n s ( 1 2 , 13, 14) have e s t a b l i s h e d t h a t t h e w a v e l e n g t h o f maximum a b s o r p t i o n i n t h i s b a n d , max, i s a s t r o n g f u n c t i o n o f t h e mean d e g r e e o f p o l y m e r i z a t i o n χ o f the amy lose chains. T h i s e f f e c t s a t u r a t e s above χ * 100, where λ a c h i e v e s an a s y m p t o t i c upper l i m i t n e a r 640 nm. A n a l o g y w i t h the Kuhn model f o r t h e p o l y e n e s (15) has been r e c o g n i z e d ( 1 6 ) and e x p l o i t e d C3). The λ a l s o depends somewhat on t h e d e g r e e o f s a t u r a t i o n o f t h e complex and moreso on t h e c o n c e n t r a t i o n o f i o d i d e i o n (1). Even t h e s t o i c h i o m e t r y o f t h e complex c o n t i n u e s t o be d e b a t e d . I f we d e n o t e t h e m o l a r c o n c e n t r a t i o n s o f I - , I 2 , and I " a s [ I - ] i , [ Ι ] , and [ I - ] i , where i c a n be r e p l a c e d , r e s p e c t i v e l y , b y t , D , o r f t o r e f e r t o t h e t o t a l , bound, and f r e e (unbound) c o n c e n t r a t i o n s o f t h e s e s p e c i e s , t h e n we c a n e x p r e s s t h e s t o i c h i o m e t r y o f t h e complex i n t e r m s o f t h e r a t i o R o f bound t r i i o d i d e t o t o t a l


χ

2

3

i

bound i o d i n e as R = [ I [Ig]b + [I -] ). It has now been rep e a t e d l y c o n f i r m e d (J_) t h a t R c a n n o t be z e r o ; t h a t i s , i o d i d e ( o r other negative) i o n s a r e mandatory f o r development o f t h e blue color. A l t h o u g h some t r e a t m e n t s ( 1 7 , 18) o f t h e complex assume t h a t t h e bound s p e c i e s i s I - (R = 1 ) , a c a r e f u l a n a l y s i s o f t h e e x i s t i n g d a t a r e v e a l s no e v i d e n c e f o r a s t r u c t u r e o f s u c h h i g h c h a r g e d e n s i t y , a t l e a s t i n s o l u t i o n ( 1 , 19, 20). The most r e c e n t work on t h e s u b j e c t , u s i n g a v a r i e t y o f t e c h n i q u e s , f a v o r s R * 0.3 (20) o r R = 0.5 (8, 21). The l a t t e r v a l u e a r i s e s from X - r a y c r y s t a l l o g r a p h i c s t u d i e s o f t h e α-cyclodextrin-I - complex (21) and r e s o n a n c e Raman and Moessbauer s p e c t r o s c o p y o f t h e a m y l o s e - i o d i n e complex and c e r t a i n model compounds ( 8 ) . S p e c t r o s c o p i c d e t e r m i n a t i o n s o f t h e f r e e and bound i o d i n e - c o n t a i n i n g s p e c i e s i n d i l u t e aqueous i o d i d e s o l u t i o n (20) have s u g g e s t e d t h e s t o i c h i o m e t r y o f s m a l l e r c h a r g e d e n s i t y R = 0.3 ± 0.1. These and o t h e r r e s u l t s t h u s s u p p o r t a s t o i c h i o m e t r y w i t h R i n t h e r a n g e 0.2-0.5 and s u g g e s t t h a t R may depend somewhat on s u c h v a r i a b l e s a s mean p o l y m e r c h a i n l e n g t h , i o d i d e and/or s a l t c o n c e n t r a t i o n , and p h y s i c a l s t a t e o f t h e complex ( i . e . , c r y s t a l l i n e o r d i s s o l v e d ) . Some i n f o r m a t i o n a l s o e x i s t s c o n c e r n i n g t h e e n e r g e t i c s o f t h e complexation r e a c t i o n . In p a r t i c u l a r , the c o o p e r a t i v i t y o f the i o d i n e b i n d i n g p r o c e s s has been a c c e p t e d f o r many y e a r s ( 2 2 , 23). D i r e c t c h a r g e t r a n s f e r i n t e r a c t i o n between i o d i n e and t h e o x y g e n atoms o f t h e p o l y s a c c h a r i d e a n n u l u s has been p r o p o s e d ( 9 , 24, 25), but i n t h e s o l i d s t a t e no s u c h i n t e r a c t i o n h a s been found f o r t h e α-cyclodextrin-pentaiodide s t r u c t u r e ( 2 1 ) . Even more i n t e r e s t i n g i s t h e f i n d i n g t h a t α-cyclodextrin c r y s t a l l i z e d w i t h I2 i n t h e ab sence o f I- does n o t have I2 m o l e c u l e s i n l i n e a r a r r a y b u t r a t h e r as i s o l a t e d m o l e c u l e s w i t h i n t h e d e x t r i n c a v i t y (2(3). The e n t h a l py o f c o m p l e x a t i o n i s found t o be c o n s t a n t f o r t h o s e c h a n g e s i n r e a c t i o n c o n d i t i o n s w h i c h l e a v e max unchanged (20), and i t v a r i e s w i t h amylose c h a i n l e n g t h i n a way t h a t m i m i c s t h e dependence o f 3

b

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

32.

CESARO E T A L .

A mylose-lodine

Binding

479

λ on the degree of polymerization (V\). We therefore b e l i e v e t h a t the rather large enthalpy change Oca. -17 kcal/mole o f bound I ) must sustain i t s l a r g e s t c o n t r i b u t i o n from the cooperative i n t e r a c t i o n s between the atoms o f the l i n e a r bound iodine chains and a much smaller c o n t r i b u t i o n from i n t e r a c t i o n s o f the bound species with the polymer c h a i n . These ideas are i m p l i c i t in the amylose-iodine binding model of Schneider and coworkers (27) who treated the system using a cooperative one dimensional I s i n g model with v a r i a b l e R. They were able to f i t t h e i r iodine binding data assuming a p o l y i o d i n e chain o f about 35 iodine atoms, a length c o n s i d e r a b l y greater than the optimal iodine chain length suggest ed by most other workers (J_, 9.). It i s c l e a r from the accumulated evidence that the s t a b i l i z a t i o n energy o f the complex can be r e a l i z e d only i f the t r i i o d i d e ion i s present. Moreover, I ~ has a c o n s i d e r a b l y higher a f f i n i t y for the polysaccharide matrix^ than does Ip in the absence o f coop e r a t i v e i n t e r a c t i o n s along the p o l y i o d i n e chain (3^, 28^. These circumstances suggested to us that the complexation process is i n i t a t e d by the binding of I " to the polysaccharide with subse quent propagation of the p o l y i o d i n e chain p r i n c i p a l l y by molecules of I^ (3) . In what follows we pursue the consequences o f t h i s idea using the matrix method o r i g i n a l l y developed by Zimm and Bragg (29) to t r e a t the polypeptide h e l i x c o i l t r a n s i t i o n and adapted by Schneider (27) and others (30) to t r e a t the case o f cooperative binding of l i g a n d s to a macromolecule. Given the pseudo-helical trajectory characterizing significant sequences aqueous amylosic chain (3Y) , the present model allows the uncom plexed polymer to occur in both h e l i c a l and random c o i l sequences (32). To be c o n s i s t e n t with the known c r y s t a l l i n e s t r u c t u r e o f the complex (10) and the observed changes in amylose chain dimen sions which accompany iodine binding (3,) , the model permits b i n d ing only to h e l i c a l sequences.


2

T h e o r e t i c a l Model Let the polymer chain be capable o f assuming two d i f f e r e n t conformational s t a t e s , c o i l and h e l i x , the l a t t e r capable o f b i n d ing iodine as I^ or I Thus an amylose molecule may be d e s c r i b ed as a sequence of c o i l and h e l i x s i t e s , which for present pur poses can each be taken to comprise approximately six glucose residues. C o i l states can be denoted by c , unbound h e l i x s t a t e s by h , and h e l i x states bound e i t h e r to I^ or I " by b . We define "complex" as any uninterrupted sequence o f b s t a t e s , regardless o f length. Then in the usual fashion (300 we define the s t a t i s t i c a l weight matrix LI indexed for s i t e s i-1 and i as a.


SOLUTION

480

A

1


h b c

PROPERTIES

h

b

c

Ί 1

π η

1

7Γ

ωρ ωρ Ρ

OF

POLYSACCHARIDES

where each e l e m e n t g i v e s t h e r e l a t i v e p r o b a b i l i t y ( s t a t i s t i c a l weight) f o r f i n d i n g s i t e i i n a p a r t i c u l a r state h , b, o r c s p e c i f i e d b y t h e column i n d e x , g i v e n t h a t s i t e i - 1 i s i n t h e p a r t i c u l a r s t a t e i n d i c a t e d b y t h e row i n d e x . A l l s t a t i s t i c a l weights are de f i n e d r e l a t i v e t o t h a t f o r t h e unbound h e l i c a l s t a t e w h i c h i s c o n sequently assigned u n i t weight regardless o f the state o f the preceding s i t e . The p a r a m e t e r i s then the s t a t i s t i c a l weight f o r i n i t i a t i o n o f any new sequence o f complex t h r o u g h b i n d i n g o f I ~ a t a s i t e w h i c h f o l l o w s a n y unbound s i t e , h o r c . P r o p a g a t i o n o r any sequence o f c o m p l e x , assumed f o r s i m p l i c i t y t o o c c u r o n l y through a d d i t i o n o f t o the growing i o d i n e c h a i n , r e c e i v e s a w e i g h t η. P a r a m e t e r s and a r e a n a l o g o u s , r e s p e c t i v e l y , t o t h e Zimm-Bragg ( 2 9 ) p a r a m e t e r s s and . T h u s , d e s c r i b e s t h e s t a t i s t i c a l w e i g h t o f a c o i l s t a t e r e l a t i v e t o unbound h e l i x , and i s a j u n c t i o n o r i n i t i a t i o n parameter t o account f o r the p o s s i b l e coope r a t i v i t y o f t h e p u t a t i v e c o n f o r m a t i o n a l t r a n s i t i o n i n amylose i n the absence o f i o d i n e . The p a r t i t i o n f u n c t i o n Ζ f o r a c h a i n o f m s i t e s i s g i v e n ( 3 0 ) π

p

ω

σ

p

ω

by Ζ = Ρ U

m

Q

(2)

Q =

(3)

where

Ρ = [1 0 0 ] ,

The a v e r a g e number o f s e q u e n c e s o f c o m p l e x , n ( i . e . , t h e a v e r a g e number o f s e q u e n c e - i n i t i a t i n g I " i o n s ) , and t h e a v e r a g e number o f p r o p a g a t i n g I m o l e c u l e s , n , may be o b t a i n e d b y d i f f e r e n t i a t i o n o f Ζ (30) t ana t h e s e d e r i v a t i v e s may a l s o be computed a s m a t r i x p r o d u c t s (33)

„

s

llSZ

s

n

=

3lnZ

=

η

3 ΐηη

z-1 s G™ Τ

ζ

-1 s

τ

\Ρ */*η « /»

where


(4)

( 5 )

32.

CESÀRO

ET

AL.

S =


and,

A mylose-lodine

[ 1 0

0 0 0 0]

481

Binding

(6)

,T=

l e t t i n g α = π o r η,

(7)

**

[8 il J

1

w i t h £ b e i n g t h e n u l l m a t r i x o f o r d e r t h r e e and U = 3 U / 3 l n a . C o n n e c t i o n o f t h e o r y w i t h e x p e r i m e n t i s made t h r o u g h t h e o b s e r v a b l e p a r a m e t e r s θ, d e f i n e d a s t h e f r a c t i o n o f s i t e s b o u n d , and R. d e f i n e d above. These a r e g i v e n b y n + n n θ = JL

R=

(8)

-1

n

+ n

= L

(9)

where L i s t h e a v e r a g e l e n g t h o f t h e complex s e q u e n c e s measured i n numbers o f b i n d i n g s i t e s . The number o f o b s e r v a b l e s d e s c r i b e d h e r e i s n o t s u f f i c i e n t t o determine u n i q u e l y t h e s e v e r a l parameters o f the t h e o r y . We c a n , however, a s s i g n ρ and ω on t h e b a s i s o f i n d e p e n d e n t i n f o r m a t i o n c o n c e r n i n g t h e c o n f o r m a t i o n o f aqueous a m y l o s i c c h a i n s i n t h e a b sence o f i o d i n e . A r e a l i s t i c model o f aqueous a m y l o s e ( 3 1 ) d i s c l o s e s t h a t p e r h a p s 25% o f an a m y l o s e c h a i n i n w a t e r m i g h t be c l a s s i f i e d as n e a r l y r e g u l a r h e l i x a t any i n s t a n t , b u t t h e c h a i n c o n f o r m a t i o n i s e x t r e m e l y l a b i l e , and t h e r e i s no e v i d e n c e f o r a n y c o n f o r m a t i o n a l c o o p e r a t i v i t y i n t h e a b s e n c e o f i o d i n e . Hence, t h e c o o p e r a t i v i t y p a r a m e t e r ω may be s e t e q u a l t o u n i t y , and f o r c o n v e n i e n c e we a l s o t a k e ρ = 1, w h i c h i m p l i e s e q u a l p r o p o r t i o n s o f h e l i x and c o i l i n t h e a b s e n c e o f i o d i n e . C a l c u l a t i o n s n o t r e p o r t ed i n d e t a i l h e r e r e v e a l t h a t t h e r e s u l t s d e s c r i b e d b e l o w a r e quite i n s e n s i t i v e t o t h e exact numerical value o f ρ , provided ω = 1 and ρ i s o f o r d e r u n i t y .


482

SOLUTION

PROPERTIES

OF

POLYSACCHARIDES

Parameters π and η c l e a r l y must depend on the r e s p e c t i v e con centrations of I and I present i n the system. I t i s conven t i o n a l to express the equations for l i g a n d binding t o macromole c u l e s i n terms o f the concentrations o f the free s p e c i e s , and i t i s r e a d i l y shown (30) that π and η are a p p r o p r i a t e l y expressed by π = KJI ~ ]

(10)

f

and


η =K [ j v n c. ι

(11)

where Κ i s the i n t r i n s i c a s s o c i a t i o n constant for binding o f I " to the polymer and Κ i s the constant for adding I ^ t o the a l r e a d y - i n i t i a t e d complex sequence. The parameter m, which counts the binding s i t e s per c h a i n , might i n i t i a l l y be thought t o equal approximately o n e - s i x t h o f the degree o f polymerization x, but, as we s h a l l see, t h i s i d e n t i t y proves i n c o r r e c t w i t h i n the confines of the present simple model, and m must be l e f t as an adjustable parameter o f the data f i t t i n g procedure. Hence, the t h e o r e t i c a l parameters ι (or Κ ) , η (or Κ ) , and m exceed by one the number o f experimental q u a n t i t i e s a v a i l a b l e i n the present work. Let i t be noted f i n a l l y that the concentrations [ I and [ I ] are not independent, but, r a t h e r , r e l a t e d through trie reac t i o n stoichiometry 2

f

I

2

+ I" = I ~

(12)

3

The e q u i l i b r i u m constant f o r t r i i o d i d e formation i s about 10 (34) , but since measured values o f Κ are normally one o r two orders o f magnitude l a r g e r than t h i s , the above r e a c t i o n i s an e f f e c t i v e b u f f e r f o r I ^ . Thus propagation o f the p o l y i o d i n e chain of the complex sequence depends, i n e f f e c t , on t o t a l free i o d i n e [I " ] + [Ip^f» the e q u i l i b r i u m i n Equation 12 has been taken i n i o account i n generating binding isotherms with the theory. 11

a n d

f

Experimental In order to produce a continuous binding isotherm (25°C) under r i g o r o u s l y c o n t r o l l e d c o n d i t i o n s the method o f gradient d i l u t i o n (35) was used. A s o l u t i o n c o n t a i n i n g polymer and I " a t known concentrations was used t o d i l u t e continuously a second s o l u t i o n , i d e n t i c a l except f o r the presence o f I ^ a t a known c o n c e n t r a t i o n high enough to saturate the amylose binding s i t e s . The m i x t u r e , i n c r e a s i n g l y d i l u t e i n i o d i n e , i s pumped through a flow c e l l i n the spectrophotometer and monitored a t λ = 640 nm. The polymer sample was s l i g h t l y s u b s t i t u t e d (DS = 0.3) carboxymethylamylose ( CMA). Use o f the i o n i c d e r i v a t i v e as a model for amylose o b v i ates problems with the s o l u b i l i t y o f unsubstituted amylose i n the presence o f i o d i n e (_3, 32). A l l m a t e r i a l s and the gradient d i l u -


CESARO

32.

ET

AL.

Amylose-lodine

483

Binding

t i o n s p e c t r o p h o t o m e t e r i c method have been d e s c r i b e d e l s e w h e r e ( 3 ^ 20). Instrument parameters c h a r a c t e r i s t i c o f the g r a d i e n t m i x i n g system were d e t e r m i n e d b y d i l u t i n g w i t h water an aqueous s o l u t i o n o f t r i s ( e t h y l e n e d i a m i n e ) c o b a l t ( I I I ) p e r c h l o r a t e , aqueous s o l u t i o n s o f w h i c h c o n f o r m t o t h e L a m b e r t - B e e r Law o v e r a wide r a n g e o f c o n centration. Hence, t h e a b s o r b a n c e A a t t i m e t ( c o r r e c t e d f o r t h e t i m e l a g between m i x i n g chamber and s p e c t r o p h o t o m e t e r cell) i s g i v e n f o r t h e e x p o n e n t i a l g r a d i e n t used b y A = A exp(-at)

(13)


Q

where a = f / v i s t h e r a t i o o f t h e f l o w r a t e f t o t h e volume o f t h e m i x i n g chamber v . I n a t y p i c a l e x p e r i m e n t t h e measured f = 1.503 ml/min and a = 0.0628 m i n " t o y i e l d ν = 23.93 m l . D i r e c t mea surement o f ν y i e l d e d 24.0 m l t o c o n f i r m t h e r e l i a b i l i t y o f Equa t i o n 13. S l i g h t c h a n g e s i n f l o w r a t e from d a y t o d a y made i t n e c e s s a r y t o determine t h i s parameter f o r each e x p e r i m e n t . Results Experimental Binding Isotherms. Experimental binding iso t h e r m s , p l o t t e d as A v s . [ I ] . Ξ [ I + [I2]t, a r e shown i n F i g u r e 1 f o r CMA a t pH 6 f o r t h r e e d i f f e r e n t p o t a s s i u m i o d i d e c o n centrations, Under t h e c o n d i t i o n s o f t h e s e e x p e r i m e n t s no c o r r e c t i o n o f [ I ] t f o r d i s p r o p o r t i o n a t i o n o f I2 was r e q u i r e d . For p u r p o s e s o f c o m p a r i s o n w i t h t h e o r y we c o n v e r t A t o 0 u s i n g t h e d e f i n i t i o n θ Ξ (A - A )/(A - A ) , where A i s t h e v a l u e o f A a t i n f i n i t e d i l u t i o n o f I (t°= . I ti s also possible t o convert [I] to [ I ] Ξ + [I2]f using c o n s e r v a t i o n o f t o t a l i o d i n e and s p e c t r o p h o t o m e x r i c a n a l y s i s o f [ I " ] , + Clp-'b' and a s a c o n t r o l , d i r e c t s p e c t r o p h o t o m e t r y measurement o f [ I ~ ] and [ I 3 f possible. T h e o r e t i c a l Binding Isotherms. F i g u r e 2 shows a t y p i c a l p l o t o f 0 v s . [ 1 ] f . The p o i n t s r e p r e s e n t e x p e r i m e n t a l d a t a t a k e n from c u r v e a o f F i g u r e 1, and t h e c u r v e s a r e t h e o r e t i c a l i s o t h e r m s c a l c u l a t e d u s i n g E q u a t i o n 8 and c o r r e s p o n d i n g t o t h e v a l u e s f o r t h e p a r a m e t e r s Κ , Κ , and m g i v e n i n t h e f i g u r e l e g e n d . The p o s i t i o n o f the t h e o r e t i c a l c u r v e s a l o n g the [ I ] a x i s i s governed p r i m a r i l y b y t h e v a l u e o f Κ , w h i l e Κ and m c o n t r o l t h e s l o p e and sym m e t r y o f t h e isotherm*. The s e a r c h f o r t h e o r e t i c a l p a r a m e t e r s g i v i n g t h e b e s t f i t t o t h e m i d p o i n t , ( I n [1]f.) / · °P m i d p o i n t , (3θ/8lη [ I ] f ) i / o f t h e e x p e r i m e n t a l i s o t h e r m s was c a r r i e d out by a g r a p h i c a l procedure ( 3 6 ) . I n t h i s way a s e r i e s o f b i n d i n g i s o t h e r m s f o r CMA a t pH = 6, 25°C, and w i t h i n the range 1 0 - 1 0 M has been f i t w i t h Κ = (4.85 ± 0.35) x 10 , Κ = (1.30 ± 0.08) χ 10 , and m = 3-4. f i g u r e 2 exemplifies the q u a l i t y o f f i t achieved. We t a k e t h e d i s c r e p a n c y between t h e v a l u e s o f m r e q u i r e d t o f i t t h e e x p e r i m e n t a l d a t a and t h e p o t e n t i a l number o f b i n d i n g s i t e s i n t h e p o l y m e r c h a i n , i . e . , x/6 = 300, t o be a c l e a r r e f l e c t

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Figure 1. Experimental binding isotherms for CMA (0.1 g/L, pH 6) plotted as A (pathlength—0.2 cm) vs. the natural logarithm of [I] for various [I'] : (a) 1.0 χ 10~ M; (b) 2.0 χ W M; and (c) 8.0 χ 10 M. t

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Figure 2. The experimental isotherm of Curve a in Figure 1 (O) plotted as the degree of saturation θ vs. the natural logarithm of [I] . Curves are theoretical iso therms corresponding to [T ] = 1.0 X 10~ and the choices of parameters: (α) Κ = 1.22 χ 10 , K, = 5.25 χ 10 , m = 3; (b) Κ 1.37 Χ 10 , K = 4.50 χ 10 , m = 4. f

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t i o n o f t h e i n a d e q u a c y o f E q u a t i o n 11, w h i c h i m p l i e s t h a t t h e p r o p a g a t i o n c o n s t a n t Κ f o r e x t e n d i n g t h e complex sequence i s i n d e p e n d e n t o f sequence l e n g t h . Whatever t h e o r i g i n o f t h e c o o p e r a t i v e i n t e r a c t i o n along the l i n e a r i o d i n e c h a i n , i t c l e a r l y d e pends f o r i t s r e a l i z a t i o n on t h e p r e s e n c e o f I ~. I t i s t h e r e f o r e c o n s i s t e n t w i t h the fundamental assumptions o r the p r e s e n t model, i . e . , i n i t i a t i o n o f complex b y I ~ and p r o p a g a t i o n ( p r e d o m i n a n t l y ) by I 2 , t h a t t h e r a n g e o f t h e c o o p e r a t i v e i n t e r a c t i o n s h o u l d be c o n f i n e d t o 3-4 b i n d i n g s i t e s . This evidence that long p o l y i o d i n e s e q u e n c e s do n o t d e v e l o p i n t h e complex a t any d e g r e e o f s a t u r a t i o n i s moreover c o n s i s t e n t w i t h t h e h y d r o d y n a m i c r e s u l t s ( 1 , 3. 4, 5) w h i c h show no i n d i c a t i o n o f s t i f f e n i n g o r e x t e n s i o n o f t h e d i s s o l v e d a m y l o s i c random c o i l when t h e i o d i n e complex i s f o r m e d , even a t h i g h Θ. I n a d e q u a c i e s d i s c l o s e d i n t h e model b y t h e d i s c r e p a n c y between m and x/6 c o u l d p r e s u m a b l y be a d d r e s s e d b y a r e v i s i o n o f E q u a t i o n 11 w h i c h would a l l o w Κ t o v a r y w i t h p o l y i o d i n e chain length. We w i l l n o t a d d r e s s t h a t q u e s t i o n h e r e b u t w i l l i n s t e a d pursue o t h e r a t t r i b u t e s o f the present model, which i s not v i t i a t e d b y t h e d e f i c i e n c i e s o f E q u a t i o n 11 p r o v i d e d a t t e n t i o n i s r e s t r i c t e d t o modest v a l u e s o f Θ f o r w h i c h t h e p r o b l e m s e n g e n d e r e d by E q u a t i o n 11 a r e a v o i d e d ( c f . s e q . ) . n

C o m p a r i s o n o f T h e o r e t i c a l and E x p e r i m e n t a l Complex S t o i c h i o m etries. W i t h t h e v a l u e s o f Κ and Κ e s t a b l i s h e d i n f i t t i n g t h e CMA b i n d i n g i s o t h e r m s we have n e x t used E q u a t i o n 9 t o compute L , t h e a v e r a g e l e n g t h o f t h e complex s e q u e n c e s , a s a f u n c t i o n o f t h e number o f b i n d i n g s i t e s m f o r o l i g o m e r i c a m y l o s e s a t θ = 1/2. R e s t r i c t i n g a t t e n t i o n t o θ = 1/2 a v o i d s t h e u n r e a l i s t i c a l l y l o n g p o l y i o d i n e c h a i n s p r e d i c t e d by t h e m o d e l f o r l a r g e m a t h i g h θ. The r e s u l t s f o r C l ~ ] = 10 M a r e p r e s e n t e d i n F i g u r e 3a a s a p l o t o f L j/2 v s . χ = 6m. Because t h e p r e s e n t model p e r m i t s o n l y one I ~ per complex s e q u e n c e , t h e s t o i c h i o m e t r y R o f t h e complex i s r e l a t e d s i m p l y t o L a s g i v e n i n E q u a t i o n 9. T h u s , t h e asymp t o t i c v a l u e o f L

A Model for Amylose-Iodine Binding - ACS Symposium Series (ACS

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