Computer Modeling of Carbohydrate Molecules - American Chemical

Chapter 1

Computer Modeling of Carbohydrates An Introduction 1

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Alfred D. French and J. W. Brady

Downloaded by 80.82.77.83 on April 18, 2017 | http://pubs.acs.org Publication Date: July 6, 1990 | doi: 10.1021/bk-1990-0430.ch001

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Southern Regional Research Center, U.S. Department of Agriculture, P.O. Box 19687, New Orleans, LA 70179 Department of Food Science, Cornell University, Ithaca, NY 14853-7201

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Carbohydrates comprise a larger portion of the organic world than all other types of biomolecules combined. Cellulose, the primary structural polysaccharide of plant cell walls, is possibly the most abundant of all biopolymers, and monomers, oligomers and polymers of glucose and fructose serve as the energy reserves and primary foods of the biosphere. Carbohydrates are also the bases for large industries and even of entire national economies. Traditional interest in these mainstays of carbohydrate chemistry has recently been supplemented by a growing appreciation of the importance of the carbohydrate fractions of glycopeptides and glycoproteins in many diverse biological roles, such as recognition processes (1). In both their industrial and biological functions, the 3-dimensional characteristics of carbohydrates are important. Many of these stereochemical features are described for carbohydrates in the classic text by Stoddart (2). The importance of stereochemistry is underscored by the unique chemical and physical properties of the individual sugars, many of which are configurational isomers. Stereochemistry also plays a role in determining the p r o p e r t i e s of polysaccharides. M o l e c u l a r shape i s as s i g n i f i c a n t f o r t h e p r o p e r t i e s o f an i n d u s t r i a l l y m o d i f i e d s t a r c h as i t i s f o r t h e r e c o g n i t i o n o f one p a r t i c u l a r b l o o d t y p e and t h e r e j e c t i o n o f o t h e r s . Coincident with t h i s i n c r e a s e d i n t e r e s t i n carbohydrates, t e c h n i q u e s f o r s t u d y i n g m o l e c u l a r shape have improved. Single c r y s t a l d i f f r a c t i o n e x p e r i m e n t s can (and o f t e n do) g i v e a f a s t and p r e c i s e d e s c r i p t i o n o f molecules i n the s o l i d s t a t e . Recent advances i n nmr p r o v i d e i n c r e a s i n g l y d e t a i l e d c o n f o r m a t i o n a l i n f o r m a t i o n about t h e s o l i d s t a t e as w e l l as on s o l u t i o n s . However, t h e s t r u c t u r a l c h a r a c t e r i s t i c s o f many c a r b o h y d r a t e m o l e c u l e s remain unknown. I t i s o f t e n d i f f i c u l t t o o b t a i n t h e s i n g l e c r y s t a l s needed f o r c r y s t a l l o g r a p h y , even i f t h e r e q u i r e d amount (100 o r so m i l l i g r a m s ) o f pure m a t e r i a l i s a v a i l a b l e t o attempt c r y s t a l growth. Some c a r b o h y d r a t e s p e r s i s t as s y r u p s , and o l i g o m e r s and polymers o f t e n form o n l y m i c r o c r y s t a l l i n e p a r t i c l e s o r f i b e r s t h a t y i e l d i n a d e q u a t e d a t a f o r a complete s t r u c t u r a l d e t e r m i n a t i o n by d i f f r a c t i o n methods alone. I n 1960, D.W. Jones supplemented f i b e r d i f f r a c t i o n d a t a from c e l l u l o s e w i t h a computer model, a l i s t o f p r o p o s e d atomic c o o r d i n a t e s t h a t was s t o r e d i n a d i g i t a l computer (3.) . He t h e n

0097-6156/90/0430-0001$06.00/0 © 1990 American Chemical Society

French and Brady; Computer Modeling of Carbohydrate Molecules ACS Symposium Series; American Chemical Society: Washington, DC, 1990.


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COMPUTER MODELING OF CARBOHYDRATE MOLECULES

c a l c u l a t e d t h e d i f f r a c t i o n i n t e n s i t i e s t h a t would a r i s e from t h e model and compared them w i t h t h e o b s e r v e d i n t e n s i t i e s . The model was r e p e a t e d l y r e a d j u s t e d , w i t h i n t e n s i t i e s c a l c u l a t e d and compared a t e a c h adjustment, i n a t r i a l and e r r o r s t u d y . W h i l e i n c o n c l u s i v e , t h i s was one o f t h e f i r s t r e p o r t s o f computer m o d e l i n g o f a carbohydrate. More r e c e n t l y , t h e i n t e r p r e t a t i o n o f c o u p l i n g c o n s t a n t s and n u c l e a r O v e r h a u s e r e f f e c t s from nmr s p e c t r a has been e x p e d i t e d by computer models t h a t p r o v i d e a ready s o u r c e o f d i s t a n c e s and a n g l e s . S i n c e t h e s e e a r l y e f f o r t s , computer m o d e l i n g has become an i n t e g r a l p a r t o f some p r o c e d u r e s f o r s t r u c t u r a l d e t e r m i n a t i o n . S e v e r a l p a p e r s i n t h i s volume d i s c u s s t h e c o m b i n a t i o n o f f i b e r d i f f r a c t i o n w i t h m o d e l i n g t h r o u g h m i n i m i z a t i o n o f t h e sum o f d i f f r a c t i o n i n t e n s i t y e r r o r p l u s t h e i n t r a - and i n t e r - m o l e c u l a r energies. S e v e r a l o t h e r p a p e r s c o v e r augmentation o f nmr d a t a w i t h t h e o r e t i c a l s i m u l a t i o n s i n v a r i o u s ways. In 1963, V.S.R. Rao u n d e r t o o k a more a m b i t i o u s t a s k : the p r e d i c t i o n of the l i k e l y conformations of p o l y s a c c h a r i d e s from a c o m p u t e r i z e d s u r v e y o f model s t r u c t u r e s (£). As a r e s u l t o f a t o m i c o v e r l a p , some model c o n f o r m e r s had h i g h e r e n e r g i e s t h a n o t h e r s , a c r i t e r i o n by which most models c o u l d be r e j e c t e d . These p r e d i c t i o n s were not accompanied by e x p e r i m e n t a l d a t a f o r t h e s u b j e c t m o l e c u l e s , l e a v i n g to experimentalists the task of corroboration or r e f u t a t i o n . A l t h o u g h many advances i n computers and methods have o c c u r r e d i n t h e i n t e r v e n i n g decades, p r e d i c t i n g p o l y s a c c h a r i d e c o n f o r m a t i o n s b a s e d upon r e l a t i v e c o n f o r m a t i o n a l e n e r g i e s c o n t i n u e s t o be o f s u b s t a n t i a l interest. Theory i s b e s t combined w i t h experiment, so t h a t each can support the other. However, some problems a r e not amenable t o e x p e r i m e n t . A c y c l i c g l u c o s e , f o r example, o c c u r s i n such s m a l l c o n c e n t r a t i o n s t h a t e x p e r i m e n t a l d a t a i s overwhelmed by d a t a f r o m t h e p y r a n o s e forms. I n c o n t r a s t , a model i s e a s i l y b u i l t and s t u d i e d . Tasks t h a t a r e even more h y p o t h e t i c a l a r e a l s o w i t h i n t h e c a p a b i l i t i e s o f m o d e l i n g , such as a comparison o f m o l e c u l a r p r o p e r t i e s w i t h and w i t h o u t a hydrogen bond. A good m o d e l i n g s t u d y p r o v i d e s a framework f o r i n t e g r a t i n g t h e e x p e r i m e n t a l r e s u l t s f r o m various techniques to provide a greater o v e r a l l understanding. T h e o r e t i c a l Background

f o r Computer M o d e l i n g

M o l e c u l a r m o d e l i n g c a l c u l a t i o n s attempt t o p r e d i c t p h y s i c a l p r o p e r t i e s f o r m o l e c u l a r systems based on t h e n u m e r i c a l s o l u t i o n o f the e q u a t i o n s t h a t embody t h e p h y s i c a l laws t h a t g o v e r n t h e i r b e h a v i o r (5,6). A t t h e most fundamental l e v e l , t h i s approach i n v o l v e s t h e d i r e c t s o l u t i o n o f Schrôdinger's e q u a t i o n f o r t h e n u c l e a r and e l e c t r o n i c d e g r e e s o f freedom. Since these studies determine e n e r g i e s d i r e c t l y from f i r s t p r i n c i p l e s , they are r e f e r r e d t o as ab i n i t i o c a l c u l a t i o n s . Such c a l c u l a t i o n s r a p i d l y become i m p o s s i b l e i n t h e p r a c t i c a l sense f o r systems c o n t a i n i n g more t h a n a few atoms h e a v i e r t h a n hydrogen, and i t becomes n e c e s s a r y t o i n v o k e v a r i o u s a d d i t i o n a l approximations t o extend these c a l c u l a t i o n s t o systems c o n t a i n i n g more t h a n about two dozen atoms. S m a l l monosaccharides have m o l e c u l a r s i z e s a t t h e upper l i m i t o f the range t h a t i s c u r r e n t l y t r e a t a b l e w i t h ab i n i t i o methods. An example o f t h e a p p l i c a t i o n o f ab i n i t i o c a l c u l a t i o n s t o c a r b o h y d r a t e s i s g i v e n i n t h e p a p e r by G a r r e t t and S e r i a n n i i n t h i s volume. S e m i e m p i r i c a l quantum m e c h a n i c a l c a l c u l a t i o n s , which use s i m p l i f i e d m o l e c u l a r H a m i l t o n i a n s w i t h parameters t a k e n from experiment, e x t e n d quantum m e c h a n i c a l c a l c u l a t i o n s t o l a r g e r m o l e c u l e s . However, t h e r e l i a b i l i t y i s r e d u c e d compared t o t h e b e s t ab i n i t i o r e s u l t s . Recent advances i n s e m i e m p i r i c a l quantum methods (see t h e c h a p t e r


1.

FRENCH AND BRADY

Introduction

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h e r e i n by D i e t e r and Stewart) make them q u i t e v i a b l e f o r m o l e c u l e s the s i z e o f a d i s a c c h a r i d e , f o r example, which can be e s p e c i a l l y u s e f u l i f s t e p s a l o n g t h e pathway o f some c h e m i c a l change a r e t o be modeled. However, a l t e r n a t e approaches a r e needed t o e x t e n d t h e o r e t i c a l d e s c r i p t i o n s t o l a r g e r m o l e c u l e s and condensed-phase systems.


Molecular

Mechanics

One such approach i s t o t r e a t t h e motions o f atomic n u c l e i as c l a s s i c a l p a r t i c l e s , s i n c e most o f t h e q u a n t a l c h a r a c t e r o f m o l e c u l e s r e s i d e s i n t h e i r e l e c t r o n i c motions. I t i s t h e n p o s s i b l e t o use t h e Born-Oppenheimer a p p r o x i m a t i o n t o s o l v e f o r t h e e l e c t r o n i c e n e r g i e s at f i x e d n u c l e a r p o s i t i o n s , and t o t r e a t t h e s e e l e c t r o n i c e n e r g i e s as the p o t e n t i a l energy f i e l d f o r t h e n u c l e a r m o t i o n s . After this s e p a r a t i o n , a n a l y t i c , e m p i r i c a l energy f u n c t i o n s may be used t o approximate t h e way i n which t h e m o l e c u l a r energy changes w i t h t h e c o o r d i n a t e s o f t h e c o n s t i t u e n t atoms. We w i l l c a l l any t e c h n i q u e a " m o l e c u l a r mechanics" (mm) c a l c u l a t i o n i f i t uses such a n a l y t i c energy f u n c t i o n s t o p r e d i c t changes i n a system's energy a r i s i n g f r o m v a r i a t i o n s i n i t s atomic c o o r d i n a t e s (5/6). Of t h e p a p e r s i n t h i s volume, t h e m a j o r i t y r e p o r t s mm s t u d i e s o f one t y p e o r a n o t h e r . The e m p i r i c a l energy f u n c t i o n s used i n mm c a l c u l a t i o n s u s u a l l y c o n s i s t o f sums o f terms r e p r e s e n t i n g v a r i o u s , e a s i l y - c o n c e p t u a l i z e d c o n t r i b u t i o n s t o t h e t o t a l e n e r g y o f a m o l e c u l e . F o r example, such e n e r g y f u n c t i o n s g e n e r a l l y c o n t a i n terms t o r e p r e s e n t t h e e n e r g y o f s t r e t c h i n g o r c o m p r e s s i n g c h e m i c a l bonds, b e n d i n g bond a n g l e s , and c h a n g i n g t o r s i o n a n g l e s . These f u n c t i o n s a l s o g e n e r a l l y c o n t a i n terms t o r e p r e s e n t v a n d e r Waals (non-bonded) i n t e r a c t i o n s and e l e c t r o s t a t i c i n t e r a c t i o n s between t h e v a r i o u s p a r t i a l l y c h a r g e d atoms and/or d i p o l e s i n a m o l e c u l e . An example o f such an energy f u n c t i o n i s g i v e n by e q u a t i o n (1) i n t h e p a p e r by Madsen, e t a l . i n t h i s volume. I f t h e energy components have been c a r e f u l l y s e l e c t e d , t h e n t h e s e s e m i e m p i r i c a l e x p r e s s i o n s may g i v e a u s e f u l a p p r o x i m a t i o n t o t h e f u n c t i o n a l dependence o f t h e m o l e c u l a r e n e r g y . The a d j u s t a b l e parameters t h a t appear i n t h e s e f u n c t i o n s c a n t h e n be s e l e c t e d by e x h a u s t i v e comparison o f c a l c u l a t e d m o l e c u l a r p r o p e r t i e s w i t h e x p e r i m e n t a l measurements, i n o r d e r t o g i v e t h e most p h y s i c a l l y r e a l i s t i c r e p r e s e n t a t i o n p o s s i b l e w i t h t h e chosen f u n c t i o n a l form. Two c h a r a c t e r i s t i c s o f c a r b o h y h d r a t e s t r u c t u r e a r e o f t e n g i v e n s p e c i a l a t t e n t i o n when c o n s t r u c t i n g p o t e n t i a l f u n c t i o n s . Although hydrogen b o n d i n g and "anomeric e f f e c t s " a r e c e r t a i n l y i m p o r t a n t i n o t h e r compounds, t h e y a r e t h o u g h t t o be e s p e c i a l l y i m p o r t a n t f o r carbohydrates. Hydrogen Bonding. Because o f g r e a t s t r e n g t h ( f o r a t t r a c t i o n s n o t b a s e d on c o v a l e n t i n t e r a c t i o n s ) , s h o r t range, and s t r o n g a n g u l a r dependence, hydrogen b o n d i n g i s o f t e n a p o w e r f u l s t r u c t u r i n g f o r c e . T h i s i s c e r t a i n l y t r u e f o r c a r b o h y d r a t e s , which have h y d r o x y l groups t h a t c a n s i m u l t a n e o u s l y donate and a c c e p t p r o t o n s o f hydrogen bonds. R o t a t a b i l i t y o f t h e h y d r o x y l groups and p o s s i b l e b i f u r c a t i o n make p r e d i c t i o n o f hydrogen b o n d i n g s t r u c t u r e s d i f f i c u l t , b u t t h e e n e r g y of hydrogen b o n d i n g i s a major f o r c e i n d e t e r m i n i n g c a r b o h y d r a t e structures. Some p u b l i s h e d p o t e n t i a l f u n c t i o n s t r e a t hydrogen bonds i n t h e same way as a l l o t h e r e l e c t r o s t a t i c i n t e r a c t i o n s . Other programs use s e p a r a t e terms f o r hydrogen b o n d i n g energy o r , i n c a p i t u l a t i o n t o t h e c o m p l e x i t y , s i m p l y i g n o r e hydrogen b o n d i n g altogether. To i n d i c a t e t h e impact o f hydrogen b o n d i n g on s t u d i e s o f m o l e c u l a r shape, one c a n l o o k ahead t o F i g u r e 5, a c a l c u l a t i o n o f t h e



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COMPUTER MODELING OF CARBOHYDRATE MOLECULES i n t r a m o l e c u l a r energy f o r v a r i o u s c o n f o r m a t i o n s o f m a l t o s e . Imagine t h e e f f e c t o f a new, a d d i t i o n a l , i n t e r m o l e c u l a r , hydrogen bond w i t h a h e a t o f f o r m a t i o n o f -5 k c a l / m o l . T h i s h y p o t h e t i c a l new hydrogen bond might be p o s s i b l e o n l y n e a r a c o n f o r m a t i o n o f φ - 0 ° , ψ •• 1 8 0 ° , a p o i n t t h a t i s more t h a n 3 k c a l / m o l above t h e c e n t r a l minimum t h a t had been based s o l e l y on i n t r i n s i c f o r c e s . When t h e new, inter m o l e c u l a r bond i s c o n s i d e r e d , t h e minimum a t φ - 0 ° , ψ * 180° would be f a v o r e d compared t o t h e c e n t r a l minimum, c o m p l e t e l y c h a n g i n g t h e r e s u l t s from t h e m o d e l i n g s t u d y . The p a p e r by T r a n and Brady h e r e i n shows changes i n t h e p r e f e r r e d c o n f o r m a t i o n t h a t depend on t h e p r e s e n c e o r absence o f an i n t r a m o l e c u l a r hydrogen bond. Because o f t h e e f f e c t s o f i n t e r m o l e c u l a r hydrogen bonds (and o t h e r i n t e r m o l e c u l a r f o r c e s - see t h e c h a p t e r by R a g a z z i e t a l . ) , t h e s t u d y o f i s o l a t e d m o l e c u l e s may n o t be as h e l p f u l as d e s i r e d f o r t h e p r e d i c t i o n o f c o n f o r m a t i o n s i n condensed phases. While i t w i l l always be i n t e r e s t i n g t o know t h e vacuum c o n f o r m a t i o n s , i t may be n e c e s s a r y t o e x p l i c i t l y i n c l u d e hydrogen b o n d i n g p a r t n e r s f o r t h e p r e d i c t i o n of conformations i n s o l i d s or s o l u t i o n s . S i n c e t h e energy o f hydrogen bond f o r m a t i o n i s l a r g e r e l a t i v e t o t h e Boltzmann c o n s t a n t t i m e s room t e m p e r a t u r e , e r r o r s i n t h e t r e a t m e n t o f hydrogen bonds i n m o d e l i n g s t u d i e s can r e s u l t i n t h e p r e d i c t i o n o f s t r u c t u r e s t h a t would be q u i t e i m p r o b a b l e f o r a g i v e n s e t o f e x p e r i m e n t a l conditions. U n c e r t a i n t y r e g a r d i n g hydrogen bonds overshadows many other types of e r r o r s i n modeling s t u d i e s . Anomeric E f f e c t s . Several characteristics discovered f i r s t f o r c a r b o h y d r a t e s a r e a s s o c i a t e d w i t h anomeric c a r b o n atoms. For example, d e s p i t e t h e lower energy i n c y c l o h e x a n e o r c y c l o p e n t a n e f o r e q u a t o r i a l s u b s t i t u e n t s , a x i a l (a) forms a r e o f t e n p r e f e r r e d f o r s u b s t i t u e n t s a t t h e anomeric c e n t e r i n s o l u t i o n s o f s u b s t i t u t e d s u g a r s such as m e t h y l g l y c o s i d e s . The a x i a l anomers o f t h e s e g l y c o s i d e s a l s o t e n d t o be more s t a b l e toward a c i d h y d r o l y s i s . S e c o n d l y , t h e C-0 bond l e n g t h s a r e a l t e r e d i n t h e v i c i n i t y o f t h e anomeric carbon, depending on t h e anomeric form and t h e r o t a t i o n a l o r i e n t a t i o n o f t h e s u b s t i t u e n t a t t a c h e d t o t h e g l y c o s i d i c oxygen atom. These a g l y c o n groups o f g l y c o s i d e s a l s o e x h i b i t a marked o r i e n t a t i o n a l p r e f e r e n c e f o r gauche c o n f o r m a t i o n s , a phenomenon known as t h e exo-anomeric e f f e c t . These e f f e c t s , t h e s u b j e c t s o f a r e c e n t , comprehensive r e v i e w (2)/ a r e now r e c o g n i z e d as g e n e r a l c h a r a c t e r i s t i c s o f m o l e c u l e s t h a t have two e l e c t r o n e g a t i v e heteroatoms l i n k e d t o a t e t r a h e d r a l carbon c e n t e r . Except f o r the r e a d i l y observed d i f f e r e n c e s o f C-0 bond l e n g t h s i n c a r b o h y d r a t e c r y s t a l s , t h e r e i s s u b s t a n t i a l c o n t r o v e r s y r e g a r d i n g t h e magnitude and t h e o r e t i c a l b a s i s f o r t h e s e e f f e c t s (JB) . F o r example, t h e apparent p r e f e r e n c e f o r a x i a l s u b s t i t u e n t s may not be so much an i n t r i n s i c p r o p e r t y o f t h e molecule. I n s t e a d , t h e p r e f e r e n c e may depend more on t h e r e l a t i v e energies of s o l v a t i o n , s i n c e these preferences r e f e r t o d i s s o l v e d molecules. S e v e r a l m o l e c u l a r mechanics p o t e n t i a l f u n c t i o n s have attempted t o i n c o r p o r a t e s u i t a b l e t r e a t m e n t s o f t h e s e e f f e c t s (9-12). Energy M i n i m i z a t i o n . The p h r a s e " m o l e c u l a r mechanics c a l c u l a t i o n " i s perhaps a s s o c i a t e d most o f t e n w i t h t h e d e t e r m i n a t i o n o f an " i d e a l " s t r u c t u r e t h r o u g h automated o p t i m i z a t i o n o f atomic p o s i t i o n s , where t h e t e r m " i d e a l s t r u c t u r e " u s u a l l y i s t a k e n t o mean t h e l o w e s t - e n e r g y structure. T h i s energy m i n i m i z a t i o n approach i s b a s e d on t h e assumption (which a l s o u n d e r l i e s many quantum m e c h a n i c a l s t u d i e s ) t h a t p h y s i c a l l y o b s e r v e d p r o p e r t i e s w i l l be t h o s e o f t h e s i n g l e s t r u c t u r e w i t h t h e l o w e s t m e c h a n i c a l energy, i m p l i c i t l y e q u a t i n g t h e



1.

FRENCH AND BRADY

Introduction

5

f r e e energy o f t h e system w i t h t h i s m e c h a n i c a l p o t e n t i a l energy (or enthalpy). The s t r u c t u r e o f l o w e s t energy can be sought i n v a r i o u s ways, f r o m e l a b o r a t e e n e r g y m i n i m i z a t i o n c a l c u l a t i o n s t o s i m p l y s e a r c h i n g f o r c o n f o r m a t i o n s t h a t a v o i d s t e r i c o v e r l a p s , as Ramachandran f i r s t d i d w i t h h i s s t u d i e s o f a l l o w e d d i p e p t i d e c o n f o r m a t i o n s (13). Even m o d e l i n g s t u d i e s t h a t use i n t e r a c t i v e computer g r a p h i c s t o v i s u a l l y "dock" one m o l e c u l e on t h e s u r f a c e o f a n o t h e r on a v i d e o s c r e e n c o u l d be c o n s i d e r e d as mm e n e r g y minimizations. I n t h i s s i t u a t i o n , an i n t u i t i v e " f e e l " f o r t h e r e p u l s i v e energy r e s u l t i n g from atomic o v e r l a p s g u i d e s t h e modeler i n moving t h e two m o l e c u l e s . O t h e r t y p e s o f mm c a l c u l a t i o n s , such as m o l e c u l a r dynamics (see t h e c h a p t e r by Madsen e t a l . , t h i s volume) and Monte C a r l o s i m u l a t i o n s (14), attempt t o s i m u l a t e t h e ensemblea v e r a g e d b e h a v i o r o f m o l e c u l a r systems. These l a s t two methods d i r e c t l y i n c l u d e e n t r o p i e e f f e c t s so t h a t r e l a t i v e f r e e e n e r g i e s can be c a l c u l a t e d . A l s o , m o l e c u l a r p r o p e r t i e s d e t e r m i n e d by t h e s e s t u d i e s a r e b a s e d on w e i g h t e d averages o v e r t h e many d i f f e r e n t possible states. L i m i t a t i o n s o f M o l e c u l a r Mechanics Philosophical Limitations. I t must be remembered t h a t i n any o f t h e s e c a l c u l a t i o n s u s i n g an a n a l y t i c s e m i e m p i r i c a l energy f u n c t i o n , the d i v i s i o n o f t h e m o l e c u l a r energy i n t o a r b i t r a r y c a t e g o r i e s i s a s i m p l i s t i c c a r i c a t u r e of the actual p h y s i c a l s i t u a t i o n . Therefore, mm has i n e v i t a b l e l i m i t a t i o n s on how a c c u r a t e l y i t can model t h e b e h a v i o r o f r e a l m o l e c u l e s . As an example o f t h e s e l i m i t a t i o n s , t h e f o r c e c o n s t a n t f o r b e n d i n g a g i v e n bond a n g l e i n a model w i l l depend t o some e x t e n t on whether t h e two bonds t h a t d e f i n e t h e a n g l e a r e a l l o w e d t o s t r e t c h o r compress, and, i f so, by how much (as i n a s o c a l l e d " v a l e n c e f o r c e f i e l d " i n m o l e c u l a r s p e c t r o s c o p y ) . Because o f t h e s e i n t e r r e l a t i o n s h i p s , o b s e r v e a b l e s t r u c t u r a l parameters and e n e r g i e s cannot, i n g e n e r a l , be used d i r e c t l y i n p a r a m e t e r i z a t i o n . R o t a t i o n s about t o r s i o n a n g l e s w i l l a l s o i n v o l v e d e f o r m a t i o n s o f t h e bond l e n g t h s and a n g l e s , as w e l l as van d e r Waals i n t e r a c t i o n s . Furthermore, many e m p i r i c a l energy f u n c t i o n s t r e a t bond l e n g t h s and a n g l e s as harmonic o s c i l l a t o r s , w h i l e i n r e a l i t y , t h e r e may be s i g n i f i c a n t a n h a r m o n i c i t y i n t h e s e motions even f o r t h e r m a l l y a c c e s s i b l e d e f o r m a t i o n s . Harmonic f u n c t i o n s do not p r o v i d e f o r bond breakage a t l a r g e e x t e n s i o n s , o r f o r bond exchange, which means t h a t commonly used mm energy f u n c t i o n s cannot t r e a t c h e m i c a l r e a c t i o n s . A l l o f t h e s e problems can t o some e x t e n t be a d d r e s s e d by making the e n e r g y f u n c t i o n s more complex o r by i n t r o d u c i n g more a d j u s t a b l e parameters. F o r example, Morse f u n c t i o n s c o u l d be u s e d i n s t e a d o f harmonic o s c i l l a t o r s f o r bond d e f o r m a t i o n s . A l s o , bond s t r e t c h e s and bends c o u l d be c o u p l e d . However, t h e b a s i c p h i l o s o p h i c a l l i m i t a t i o n of mm methods remains. That b e i n g s a i d , i t i s a l s o t r u e t h a t mm methods can p r o v i d e s t r u c t u r e s and e n e r g i e s t h a t a r e as good as, o r b e t t e r , t h a n t h o s e r e s u l t i n g f r o m more e l e g a n t and time-consuming methods, i f ram i s u s e d w i t h i n i t s l i m i t a t i o n s . Strategic Limitations. W h i l e t h e a c t u a l a p p l i c a t i o n o f mm c a l c u l a t i o n s t o c a r b o h y d r a t e m o l e c u l e s i s i n most c a s e s s t r a i g h t f o r w a r d , t h e r e a r e a number o f p i t f a l l s t h a t may t r a p t h e unwary. The f i r s t c o n c e r n s t h e c h o i c e o f an a p p r o p r i a t e p o t e n t i a l energy f u n c t i o n t o be used f o r a p a r t i c u l a r problem. The a d j u s t a b l e parameters t h a t appear i n t h e energy f u n c t i o n must be c a r e f u l l y chosen t o g i v e t h e c l o s e s t match p o s s i b l e t o r e l e v a n t e x p e r i m e n t a l data. U n f o r t u n a t e l y , because o b s e r v a b l e atomic c h a r a c t e r i s t i c s v a r y as a f u n c t i o n o f environment, atomic p a r a m e t e r s d e v e l o p e d f o r t h e



6


v a p o r phase may not be t r a n s f e r a b l e t o t h e same atom o r group i n a s o l u t i o n or a c r y s t a l . F o r t h e same reason, d i f f e r e n t p o t e n t i a l energy f u n c t i o n s , c o n t a i n i n g d i f f e r e n t a p p r o x i m a t i o n s and w i t h d i f f e r e n t c h a r a c t e r i s t i c s , may be needed f o r t y p e s o f m o l e c u l e s t h a t a r e as d i f f e r e n t as p r o t e i n s and c a r b o h y d r a t e s . Simply m i x i n g parameters t a k e n from d i s p a r a t e s o u r c e s can l e a d t o a v e r y poor a p p r o x i m a t i o n , r e g a r d l e s s o f how u s e f u l t h e i n d i v i d u a l parameters were i n t h e i n t e g r a l u n i t from which t h e y came. A wide v a r i e t y o f f o r c e f i e l d s f o r c a r b o h y d r a t e s has been d e v e l o p e d (9-12, 15-22), as w e l l as g e n e r a l - p u r p o s e f o r c e f i e l d s such as MM3 (23). S e v e r a l a s p e c t s o f f o r c e f i e l d development a r e d i s c u s s e d i n t h e c h a p t e r by Rasmussen and F a b r i c i u s , and a paper h e r e i n by S c a r s d a l e e t a l . d i s c u s s e s m o d i f i c a t i o n s t o a f o r c e f i e l d used f o r p r o t e i n s t o accommodate t h e c a r b o h y d r a t e f r a c t i o n o f a g l y c o p e p t i d e . Some c a r e s h o u l d be t a k e n t o s e l e c t a c o m b i n a t i o n o f energy f u n c t i o n and parameter s e t t h a t i s a p p r o p r i a t e f o r t h e p r o b l e m a t hand. In c a s e s of nonstandard s t r u c t u r e s , users should t e s t the a p p l i c a b i l i t y of the f o r c e f i e l d t o t h e most analogous system p o s s i b l e f o r which experimental data are a v a i l a b l e . ( T h i s i s a good i d e a f o r s t a n d a r d s t r u c t u r e s , too!) Energy m i n i m i z a t i o n c a l c u l a t i o n s a r e f r e q u e n t l y f r a u g h t w i t h operational d i f f i c u l t i e s . Most a r i s e from t h e complex n a t u r e o f t h e p o t e n t i a l energy f u n c t i o n f o r a l a r g e m o l e c u l e w i t h many i n t e r n a l d e g r e e s o f freedom ( 5 , 6 ) . T y p i c a l mm programs c o n t a i n one o r more energy m i n i m i z a t i o n a l g o r i t h m s t h a t can be used t o a u t o m a t i c a l l y a d j u s t t h e atomic p o s i t i o n s t o reduce t h e m o l e c u l a r energy. Usually, t h i s p r o c e d u r e i s a p p l i e d r e p e a t e d l y u n t i l a l o c a l minimum i n energy i s approached c l o s e l y enough t h a t f u r t h e r e f f o r t would r e s u l t i n i n s i g n i f i c a n t improvement. New u s e r s a r e sometimes tempted t o t e r m i n a t e t h e s e o p t i m i z a t i o n s p r e m a t u r e l y because o f t h e t i m e r e q u i r e d t o produce what a r e o f t e n s m a l l improvements i n energy. However, because o f t h e c o m p l e x i t y o f t h e t o t a l energy f u n c t i o n f o r a l a r g e m o l e c u l e , l a r g e s t r u c t u r a l t r a n s i t i o n s can o c c u r s u r p r i s i n g l y l a t e i n an o p t i m i z a t i o n . E a r l y t e r m i n a t i o n o f t h e m i n i m i z a t i o n can m i s s t r a n s i t i o n s t h a t would lower t h e energy s u b s t a n t i a l l y a f t e r a l o n g p e r i o d o f minor change. The M u l t i p l e Minimum Problem. Attempts t o f i n d t h e m o l e c u l a r s t r u c t u r e w i t h t h e l o w e s t energy a r e d i f f i c u l t f o r m o l e c u l e s as c o m p l i c a t e d as c a r b o h y d r a t e s . The b i g g e s t o b s t a c l e i s t h e " m u l t i p l e minimum problem" which a r i s e s because energy s u r f a c e s f o r complex m o l e c u l e s have more t h a n one l o c a l minimum, and because a l g o r i t h m s t h a t m i n i m i z e t h e energy i n mm (or quantum mechanics) programs w i l l p r o c e e d from t h e s t a r t i n g c o n f o r m a t i o n t o t h e c l o s e s t l o c a l minimum on t h e energy s u r f a c e and s t o p . T h i s i s shown i n F i g u r e 1, where a t y p i c a l energy m i n i m i z a t i o n s t a r t s from a s t r u c t u r e w i t h a h i g h energy on t h e f a r l e f t p a r t o f t h e c u r v e , and t e r m i n a t e s i n t h e l o c a l minimum a t A, s i n c e t h e r e i s no g e n e r a l s o l u t i o n t o t h e p r o b l e m o f the g l o b a l minimization of a multidimensional f u n c t i o n . In g e n e r a l t h e r e i s no way t o know t h a t A i s not t h e g l o b a l minimum u n l e s s a d d i t i o n a l energy m i n i m i z a t i o n s a r e s t a r t e d from a s t r u c t u r e h a v i n g a c o n f o r m a t i o n beyond b a r r i e r B. F i g u r e 1 a l s o i l l u s t r a t e s one o f t h e problems t h a t comes from a s s o c i a t i n g t h e l o w e s t energy s t r u c t u r e w i t h t h e p h y s i c a l l y o b s e r v e d structure. P o i n t C has t h e l o w e s t p o t e n t i a l energy (the g l o b a l minimum), but beyond b a r r i e r D t h e r e i s a n o t h e r minimum a t Ε t h a t i s not q u i t e as deep b u t much b r o a d e r t h a n t h e minimum a t C. As a r e s u l t , t h e Boltzmann-weighted i n t e g r a l o v e r t h i s c o n f o r m a t i o n i s l a r g e r t h a n t h a t f o r t h e C w e l l , meaning t h a t t h e w e l l a t Ε w i t h s l i g h t l y h i g h e r p o t e n t i a l energy i s a c t u a l l y t h e f a v o r e d form due t o



1.

FRENCH AND BRADY

7

Introduction

i t s lower f r e e energy. However, i t s h o u l d a l s o be c l e a r t h a t , e x c e p t f o r the c r y s t a l l i n e s t a t e , the observed e q u i l i b r i u m p r o p e r t i e s of such systems would be Boltzmann-weighted averages o f t h e c h a r a c t e r i s t i c s o f a l l t h r e e w e l l s (indeed, o f a l l p o s s i b l e s t a t e s ) . S e v e r a l papers i n t h i s book have c o n v e r t e d t h e c a l c u l a t e d e n e r g i e s f o r t h e many c o n f o r m a t i o n s s t u d i e d i n t o p o p u l a t i o n s f o r t h e c a l c u l a t i o n o f average p r o p e r t i e s . The motions o f t h e system, such as can be s i m u l a t e d by m o l e c u l a r dynamics s t u d i e s (see t h e c h a p t e r by Madsen e t a l . ) , can a l l o w an e q u i l i b r i u m p a r t i t i o n i n g between a l l o f t h e p o s s i b l e forms. I f t h e dynamics s i m u l a t i o n i s run l o n g enough, t h e m o l e c u l e w i l l spend enough time i n each c o n f o r m a t i o n t o be r e p r e s e n t a t i v e o f t h e r e a l system and t h e f r e e energy can be determined. T a k i n g a s p e c i f i c example o f t h e m u l t i p l e minimum p r o b l e m from c a r b o h y d r a t e c h e m i s t r y , suppose t h a t g l u c o s e was o p t i m i z e d f r o m a s t a r t i n g shape w i t h 06 o f t h e p r i m a r y a l c o h o l group n e a r one o f t h e t h r e e s t a g g e r e d p o s i t i o n s t h a t r e s u l t from r o t a t i o n about t h e C5-C6 bond. T y p i c a l l y , t h e m o d e l i n g s o f t w a r e would produce a model w i t h 06 i n t h e " b e s t " p o s i t i o n c l o s e t o t h e p o s i t i o n i n t h e s t a r t i n g model, but would not t e s t t h e o t h e r two l i k e l y 06 p o s i t i o n s . To l e a r n which o f t h e t h r e e p o s i t i o n s i s " b e s t " , s t a r t i n g models w i t h 06 i n t h e o t h e r two s t a g g e r e d p o s i t i o n s might a l s o be o p t i m i z e d and t h e e n e r g i e s o f a l l t h r e e models compared. (We note t h a t t h i s s i m p l e t r e a t m e n t has not y e t p r o d u c e d agreement w i t h experiment.) Monosaccharides have many s t r u c t u r a l v a r i a t i o n s t h a t c o r r e s p o n d t o l o c a l minima t h a t must be c o n s i d e r e d . A c y c l i c c a r b o h y d r a t e s can r o t a t e a t each carbon, and each o f t h e t h r e e s t a g g e r e d conformers i s l i k e l y t o c o r r e s p o n d t o a l o c a l minimum. The shapes o f s u g a r r i n g s also often vary. Furanose r i n g s u s u a l l y have two major l o c a l minima and a p a t h o f i n t e r c o n v e r s i o n . E x p e r i m e n t a l e v i d e n c e shows a c l e a r p r e f e r e n c e f o r o n l y one c h a i r form f o r some p y r a n o s e r i n g s , but others c o u l d e x i s t i n s e v e r a l conformers. F o r example, t h e C ^ C and S conformers must a l l be c o n s i d e r e d as p o s s i b l e s t r u c t u r e s f o r L - i d u r o n a t e , as d i s c u s s e d by R a g a z z i e t a l . i n t h i s book. Each secondary h y d r o x y l group c o u l d a l s o have one o f t h r e e staggered conformations. The number o f l o c a l minima a r i s i n g from each t y p e o f v a r i a t i o n must be m u l t i p l i e d by t h e number o f each o t h e r t y p e t o g i v e t h e t o t a l number o f l o c a l minima t h a t s h o u l d be anticipated. Any a n a l y s i s o f o l i g o m e r s o r polymers must acknowledge t h e h o p e l e s s l y l a r g e numbers o f l o c a l minima i n t h e s e m o l e c u l e s . F o r t u n a t e l y , some s i m p l i f y i n g assumptions can be made (see t h e p a p e r s h e r e i n by T r a n and Brady and by F r e n c h , T r a n and P e r e z ) . The paper h e r e i n by Tvaroâka, Kozâr and H r i c o v i n i d e s c r i b e s a random walk method t o sample a l t e r n a t e arrangements o f pendant g r o u p s . 4

1

4

2

Q

Comparison w i t h Experiment. F o r c a r b o h y d r a t e s , m o d e l i n g work has o f t e n sought t o produce a t h e o r e t i c a l s t r u c t u r e t h a t matches t h e r e s u l t s from a h i g h l y a c c u r a t e d i f f r a c t i o n e x p e r i m e n t . T h i s approach i s p r o b l e m a t i c , however, because c r y s t a l p a c k i n g can d i s t o r t a m o l e c u l e from t h e shape t h a t i t would have as an i s o l a t e d m o l e c u l e . As shown i n t h e c h a p t e r by F r e n c h , Rowland and A l l i n g e r , when t h e same, r e l a t i v e l y r i g i d g l u c o s e r e s i d u e appears i n numerous c r y s t a l l i n e environments, t h e r e a r e s u b s t a n t i a l d i f f e r e n c e s i n t h e conformation. Of c o u r s e , t h e e r r o r s i n t h e e x p e r i m e n t a l d e t e r m i n a t i o n must a l s o be c o n s i d e r e d . These problems a s i d e , d i f f r a c t i o n s t u d i e s s t i l l may not p r o v i d e r e s u l t s t h a t d e s c r i b e m o l e c u l a r s t r u c t u r e s i n one o f t h e most interesting states: aqueous s o l u t i o n . For s o l u t i o n s , d i f f r a c t i o n experiments a r e l e s s r e l e v a n t , and nmr and c i r c u l a r d i c h r o i s m a r e t h e b e s t s o u r c e s o f e x p e r i m e n t a l i n f o r m a t i o n (see t h e c h a p t e r by


8


TvaroSka, Kozâr and H r i c o v i n i i n t h i s b o o k ) . One way t o account f o r t h e e f f e c t o f s o l v e n t on c o n f o r m a t i o n might be t o r e p r e s e n t t h e m o l e c u l e w i t h o u t e n v i r o n m e n t a l i n f l u e n c e s , and t h e n e x p l i c i t l y i n c l u d e the solvent o r other environmental molecules i n the calculation. W h i l e a v o i d i n g b u i l t - i n i n f l u e n c e s o f environment i s a s a t i s f y i n g c o n c e p t , i t i s d i f f i c u l t t o o b t a i n by experiment parameters t h a t l a c k t h o s e i n f l u e n c e s . S e v e r a l methods have been u s e d t o s t u d y s o l v a t i o n e f f e c t s , i n c l u d i n g continuum d e s c r i p t i o n s (24) and t h e e x p l i c i t t r e a t m e n t o f s o l v e n t m o l e c u l e s i n Monte C a r l o and m o l e c u l a r dynamics s i m u l a t i o n .


Conformational Analysis R a t h e r t h a n c o l l e c t i n g and comparing s t r u c t u r e s t h a t c o r r e s p o n d t o t h e m u l t i p l e minima, i t i s o f t e n more u s e f u l t o d e p i c t how t h e energy changes d u r i n g v a r i a t i o n s o f one o r more o f t h e most i m p o r t a n t s t r u c t u r a l f e a t u r e s , g e n e r a t i n g a s u r f a c e s i m i l a r t o F i g u r e 1. Such a comprehensive s t u d y o f t h e energy s u r f a c e i s c a l l e d c o n f o r m a t i o n a l a n a l y s i s (CA). I n CA, t h e energy i s c a l c u l a t e d a t s u i t a b l e i n c r e m e n t s o f i m p o r t a n t c o n f o r m a t i o n a l c o o r d i n a t e s , and p l o t t e d , a t l e a s t c o n c e p t u a l l y , on a one-, two- o r m u l t i - d i m e n s i o n a l g r i d . Such energy maps d e p i c t t h e h e i g h t s o f t h e b a r r i e r s and t h e w i d t h s o f t h e minima, as w e l l as showing t h e p o s i t i o n s o f t h e minima. CA o f M o n o s a c c h a r i d e s . The s i m p l e s t t y p e o f c o n f o r m a t i o n a l a n a l y s i s f o r g l u c o p y r a n o s e might be a s y s t e m a t i c r o t a t i o n o f i t s p r i m a r y a l c o h o l group. The hydroxymethyl group c o u l d be r o t a t e d i n i n c r e m e n t s o f 2 0 ° , w i t h t h e s t r u c t u r e o p t i m i z e d a t each i n c r e m e n t i n a l l respects except f o r t h e primary a l c o h o l p o s i t i o n . Even t h i s " s i m p l e " a n a l y s i s i s c o m p l i c a t e d because a t some p o i n t s a l t e r n a t e h y d r o x y l hydrogen o r i e n t a t i o n s on t h e r o t a t i n g oxygen atom may r e s u l t i n l o w e r energy t h a n t h a t g i v e n by t h e s t a r t i n g o r i e n t a t i o n . U s u a l l y , however, t h e s e a l t e r n a t e h y d r o x y l group o r i e n t a t i o n s w i l l n o t o c c u r a u t o m a t i c a l l y a s a r e s u l t o f t h e energy m i n i m i z a t i o n process. I t w i l l be n e c e s s a r y t o t r y each p o s s i b l e s t a g g e r e d r o t a t i o n o f t h e h y d r o x y l group a t each r o t a t i o n o f t h e hydroxymethyl group. That change may i n t u r n r e q u i r e changes i n t h e r o t a t i o n o f t h e h y d r o x y l group on C4, and so f o r t h . V a r i a t i o n s i n r i n g conformation are often the primary i n t e r e s t , even when t h e g e n e r a l t y p e o f r i n g shape i s known. R i n g shapes a r e d e s c r i b e d s e m i - q u a n t i t a t i v e l y by t h e i r p u c k e r i n g , a measure o f t h e d e p a r t u r e from an a l l - p l a n a r shape. The Cremer-Pople (C-P) system (25,26) p e r m i t s t h e d e s c r i p t i o n o f N-membered r i n g s w i t h N-3 parameters, a v e r y u s e f u l s h o r t h a n d . A l t h o u g h t h e C-P p u c k e r i n g n o t a t i o n a p p l i e s t o r i n g s o f any s i z e , 5- and 6-membered r i n g s a r e d e s c r i b e d here because t h e y a r e e s p e c i a l l y common i n c a r b o h y d r a t e s . Furanose C o n f o r m a t i o n s . F i g u r e 2 shows t h e d i f f e r e n t e n v e l o p e (E) and t w i s t (T) forms f o r t h e 5-membered r i n g s . This "conformational wheel" i s f o r k e t o f u r a n o s e s , i n which t h e r i n g c a r b o n atoms a r e numbered 2-5; t h e carbons o f a l d o f u r a n o s e s a r e numbered 1-4. (The c o n f o r m a t i o n s o f some a l d o f u r a n o s e s a r e d e s c r i b e d i n t h e c h a p t e r by G a r r e t t and S e r i a n n i . ) The h y d r o c a r b o n analogue, c y c l o p e n t a n e , r e a d i l y i n t e r c o n v e r t s between a l l a d j a c e n t Ε and Τ forms, a phenomenon known as p s e u d o r o t a t i o n . I n c a r b o h y d r a t e s , w i t h a r i n g oxygen atom and v a r i e d s u b s t i t u e n t s , some forms have lower energy than others. Therefore, there are b a r r i e r s s e v e r a l kcal/mol high t o f a c i l e pseudorotation.


1.

FRENCH AND BRADY


15.00

Introduction

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- i

0.00 -I

1

1

1

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CONFORMATIONAL CHANGE ->

F i g u r e 1. P o t e n t i a l energy v a l u e s as some ( u n s p e c i f i e d ) c o n f o r m a t i o n a l v a r i a b l e i s changed. A r e p r e s e n t s a l o c a l ( f a l s e ) minimum and C r e p r e s e n t s t h e g l o b a l minimum (assuming t h a t a l l o t h e r v a r i a b l e parameters a r e a l s o i n t h e l e a s t e n e r g e t i c c o n f o r m a t i o n s ) . Β and D a r e b a r r i e r s t h a t a r e n o t overcome d u r i n g m i n i m i z a t i o n , and Ε i s a b r o a d minimum t h a t c o n t a i n s a range o f s t r u c t u r e s . I n s o l u t i o n , b o t h C and Ε s t r u c t u r e s would be p r e s e n t i n s u b s t a n t i a l amounts. Because o f t h e s m a l l e n t h a l p y d i f f e r e n c e between C and E, and t h e g r e a t e r number o f s t r u c t u r e s b e l o n g i n g t o t h e Ε c l a s s i f i c a t i o n , Ε s t r u c t u r e s would dominate.

F i g u r e 2. P u c k e r i n g a n g l e s (φ) f o r p e r f e c t e n v e l o p e (E) and symmetrical t w i s t (T) forms o f f r u c t o f u r a n o s e . The n o n - p l a n a r r i n g atoms i n symmetrical t w i s t s a r e d i s p l a c e d e q u a l l y above and below t h e ring. The a m p l i t u d e o f p u c k e r i n g (Q) i s t h e r a d i u s o f t h e c i r c l e .


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F o r five-membered r i n g s , t h e r e a r e two major C-P p u c k e r i n g parameters, φ and Q. The phase a n g l e o f p u c k e r i n g , φ, d e s c r i b e s t h e p o s i t i o n on t h e c o n f o r m a t i o n a l wheel a t which t h e p u c k e r i n g o c c u r s ( F i g u r e 2). The p u c k e r i n g amplitude, Q, d e s c r i b e s t h e e x t e n t o f d e v i a t i o n o f t h e r i n g atoms from a mean p l a n e . These two parameters a r e c o n v e n i e n t l y d e p i c t e d i n a p l a n a r p o l a r c o o r d i n a t e system. A c o n f o r m a t i o n a l a n a l y s i s o f t h e f u r a n o s e r i n g e n t a i l s a 3 6 0 ° range o f φ; Q v a l u e s w i l l range from 0 t o 0.6 o r 0.8 Â.


The e n e r g i e s o f t h e d i f f e r e n t r i n g c o n f o r m a t i o n s a r e a f f e c t e d by t h e r o t a t i o n a l o r i e n t a t i o n s o f t h e two p r i m a r y a l c o h o l groups o f fructofuranose. T h e r e f o r e , a l l 9 combinations o f l i k e l y o r i e n t a t i o n s o f t h e s e groups must be c o n s i d e r e d b e f o r e t h e energy d i f f e r e n c e s i n h e r e n t i n d i f f e r e n t r i n g c o n f o r m a t i o n s c a n be u n d e r s t o o d (French, A.D.; Tran, V.H. B i o p o l y m e r s , I n P r e s s ) . Pyranose C o n f o r m a t i o n s . F i g u r e 3 shows t h e d i f f e r e n t c o n f o r m a t i o n s f o r 6-membered r i n g s (adapted from a drawing by J e f f r e y and Y a t e s (27)). There i s a θ parameter b e s i d e s Q and φ because s e v e r a l t y p e s o f p u c k e r i n g a r e p o s s i b l e f o r a g i v e n Q and φ. In a d d i t i o n t o t h e Ε (envelope) n o t a t i o n used i n F i g u r e 3, six-membered r i n g s w i t h o n l y one o u t - o f - p l a n e atom a r e a l s o c a l l e d s o f a s o r h a l f - b o a t s . The Ε d e s c r i p t o r was s e l e c t e d h e r e because S i s a l r e a d y used t o denote skewed pyranose c o n f o r m a t i o n s (which have two atoms on o p p o s i t e s i d e s o f t h e p l a n e , s e p a r a t e d by one atom) . The H l a b e l i s a l r e a d y used f o r h a l f - c h a i r s , which have two a d j a c e n t atoms on o p p o s i t e s i d e s o f t h e mean p l a n e . T y p i c a l l y , t h e Ε and Η forms a r e n o t important u n l e s s a double bond i s p r e s e n t . S p h e r i c a l p o l a r c o o r d i n a t e s a r e used f o r c o n f o r m a t i o n a l r e p r e s e n t a t i o n o f p y r a n o s e r i n g s i n t h e C-P system. U n l i k e t h e f r e e pseudorotation of cyclopentane, the s t a b l e conformations o f c y c l o h e x a n e conformers a r e i n deeper energy w e l l s . Even among t h e ( l e s s s t a b l e ) e q u a t o r i a l (Θ - 90°) forms, p s e u d o r o t a t i o n i s somewhat hindered. S u b s t i t u t i o n s o f heteroatoms i n t h e r i n g and a d d i t i o n s o f hydroxylic or other e x o c y c l i c substituents further s t a b i l i z e or d e s t a b i l i z e o t h e r conformers compared t o c y c l o h e x a n e . A c o n f o r m a t i o n a l a n a l y s i s o f an i d u r o n a t e r i n g has been r e p o r t e d b a s e d on v a r i a t i o n o f φ and θ (28), and a s t u d y o f t h e g l u c o p y r a n o s e r i n g (29) b a s e d on t h e c o n f o r m a t i o n a l d e s c r i p t o r s o f P i c k e t t and S t r a u s s (30) i s a l s o a v a i l a b l e . Most modeling s o f t w a r e packages do n o t v a r y p u c k e r i n g i n i n c r e m e n t s o f t h e C-P p a r a m e t e r s (REFINE (28.) i s an e x c e p t i o n ) b u t a u t i l i t y f o r producing r i n g s with s p e c i f i c puckerings i s a v a i l a b l e (31) ) . I n s t e a d , most programs have " d i h e d r a l d r i v e r s " t h a t a l l o w f o r t h e s p e c i f i c a t i o n o f s t a r t i n g and e n d i n g v a l u e s o f t o r s i o n a n g l e s as w e l l as increment s i z e . A n o t h e r mechanism f o r changing c o n f o r m a t i o n i s a v a i l a b l e i n some programs. T h i s a l l o w s t h e p o s i t i o n s o f s e l e c t e d atoms t o be f i x e d i n space w h i l e a l l o w i n g a l l o t h e r atoms t o r e l a x t o p o s i t i o n s of lowest l o c a l energy. Some programs a l l o w v a r i a t i o n o f one o r two o f t h e c o o r d i n a t e s o f s e l e c t e d atoms w h i l e h o l d i n g t h e other coordinate(s) fixed. T h i s can be used t o r e s t r a i n r i n g atoms to a s p e c i f i c puckering. Optimized pyranose r i n g s with v a r i o u s r e s t r a i n e d c o n f o r m a t i o n s have p u c k e r i n g a m p l i t u d e s t h a t v a r y s u b s t a n t i a l l y (Haasnoot, C.A.G., p e r s o n a l communication). A l t e r n a t e Conformational Representations. I n some i n s t a n c e s , t h e C-P f o r m a l i s m does n o t p r o v i d e t h e most e c o n o m i c a l d e s c r i p t i o n , as e x e m p l i f i e d by t h e s i x - a t o m r i n g o f d i h y d r o p y r a n . L i k e cyclohexene, d i h y d r o p y r a n has a double bond t h a t e n f o r c e s e s s e n t i a l c o p l a n a r i t y on f o u r c o n t i g u o u s r i n g atoms. W h i l e t h e C-P p u c k e r i n g d e s c r i p t i o n f o r



1.

FRENCH AND BRADY

Introduction

11

F i g u r e 3. The c o n f o r m a t i o n a l sphere f o r p y r a n o i d r i n g s . The p e r f e c t c h a i r s a r e a t t h e n o r t h and s o u t h p o l e s (θ = 0 and 180°, respectively). The boat and skew (B and S d e s i g n a t i o n s ) a t t h e equator permit p s e u d o r o t a t i o n t h a t i s s l i g h t l y hindered, at l e a s t f o r cyclohexane. The e n v e l o p e s , Ε ( a l s o c a l l e d s o f a s and h a l f - b o a t s ) , and h a l f - c h a i r s , H, a r e n o t o b s e r v e d f o r r i n g s composed o f s a t u r a t e d c a r b o n and oxygen atoms, b u t a r e i m p o r t a n t forms f o r r i n g s w i t h u n s a t u r a t e d c a r b o n atoms. The a m p l i t u d e o f p u c k e r i n g c o r r e s p o n d s t o t h e r a d i u s of t h e s p h e r e .



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d i h y d r o p y r a n i n v o l v e s a l l f i v e o f t h e d i s k s i n F i g u r e 3, most c o n f o r m a t i o n s cannot be a c c e s s e d w i t h o u t g r e a t energy p e n a l t y because o f t h e d o u b l e bond. T h e r e f o r e , t h e c o n f o r m a t i o n a l s u r f a c e can be simplified. The two r i n g atoms t h a t a r e o p p o s i t e t h e ends o f t h e d o u b l e bond i n d i h y d r o p y r a n a r e a l l o w e d t o d e v i a t e from t h e p l a n e e n f o r c e d by t h e d o u b l e bond. The r i n g c o n f o r m a t i o n s can be a d e q u a t e l y summarized by p l o t t i n g t h e energy a g a i n s t t h e d i s p l a c e m e n t s o f t h e s e two atoms ( F i g u r e 4 ) . T h i s p r o v i d e s a q u i c k i n d i c a t i o n o f t h e p o s i t i o n and a m p l i t u d e o f p u c k e r i n g . A n o t h e r example o f e c o n o m i c a l r e p r e s e n t a t i o n i s d i s c u s s e d i n a c h a p t e r by F r e n c h , Rowland and A l l i n g e r . Therein, t h e f l e x i n g of t h e g l u c o p y r a n o s e r i n g w i t h i n t h e C c o n f o r m a t i o n was s t u d i e d by p l o t t i n g t h e energy v s . t h e d i s t a n c e between 01 and 04. I n t h a t paper, t h e C-P n o t a t i o n i s a l s o used t o advantage. 4


1

CA o f D i s a c c h a r i d e s . Because o f t h e m u l t i p l e minima problem, d i s a c c h a r i d e s a r e i n h e r e n t l y more c o m p l i c a t e d t o model t h a n monosaccharides. More computer time i s r e q u i r e d t o o p t i m i z e d i s a c c h a r i d e s t r u c t u r e s because t h e cpu t i m e depends r o u g h l y on t h e number o f atoms s q u a r e d . A t y p i c a l CA o f a d i s a c c h a r i d e d e t e r m i n e s t h e v a r i a t i o n i n energy f o r a l l mutual o r i e n t a t i o n s o f t h e two monosaccharide r e s i d u e s . These o r i e n t a t i o n s a r e e x p r e s s e d by t h e g l y c o s i d i c l i n k a g e t o r s i o n a n g l e s , φ and ψ, shown i n F i g u r e 5. The o r i e n t a t i o n s o f t h e secondary h y d r o x y l groups a r e i m p o r t a n t because t h e i r p o s i t i o n s o f t e n a f f e c t t h e c a l c u l a t e d energy i n pyranose r i n g s by s e v e r a l k c a l / m o l . The p r e f e r r e d s i d e group o r i e n t a t i o n s w i l l change when φ and ψ change, so s e v e r a l p o s s i b l e arrangements must be considered. In s i m p l e work, t h e h y d r o x y l hydrogen atoms a r e sometimes i g n o r e d w i t h t h e j u s t i f i c a t i o n t h a t t h e y c o u l d u s u a l l y rotate to avoid a c o n f l i c t . CA's o f d i s a c c h a r i d e s g i v e d i f f e r e n t r e s u l t s depending on whether o r not t h e r e s i d u e s a r e a l l o w e d t o a d j u s t i n t e r n a l l y a t each increment. I f t h e i n t e r n a l bond a n g l e s and t o r s i o n a n g l e s f o r each r e s i d u e i n a d i s a c c h a r i d e a r e a l l o w e d t o change i n r e s p o n s e t o i n f l u e n c e s from t h e o t h e r r e s i d u e d u r i n g CA, t h e s t u d y i s c a l l e d a flexible-residue analysis. I f not, t h e n t h e s t u d y i s c a l l e d a r i g i d residue analysis. The CA o f m a l t o s e , shown i n F i g u r e 5, i s a f l e x i b l e - r e s i d u e map. Some d i s a d v a n t a g e s o f t h e r i g i d - r e s i d u e method are: 1. 2.

3.

R i g i d maps depend on t h e e x a c t c h o i c e o f s t a r t i n g model (8.) . Important minima on t h e energy s u r f a c e a r e l i k e l y t o be i g n o r e d s i n c e e n e r g i e s a r e h i g h on most o f t h e s u r f a c e e x c e p t n e a r t h e s t a r t i n g shape. B a r r i e r s between minima a r e l i k e l y t o be g r o s s l y overestimated.

Disadvantages 1. 2.

o f f l e x i b l e - r e s i d u e models i n c l u d e :

Much more computer t i m e i s needed. The i n p u t and r e s u l t s a r e more c o m p l i c a t e d .

S e v e r a l r e c e n t p a p e r s compare t h e two t y p e s o f a n a l y s i s (32-34) (see a l s o t h e paper h e r e i n by T r a n and B r a d y ) . B r a n t and C h r i s t compare t h e a b i l i t i e s o f t h e two approaches t o p r e d i c t e x p e r i m e n t a l b e h a v i o r i n t h e i r chapter herein. Two s t r a t e g i e s f o r c o n s t r u c t i n g r e l a x e d maps a r e d i s c u s s e d i n t h e c h a p t e r s by T r a n and Brady and by F r e n c h , T r a n and P e r e z .



1.

FRENCH AND BRADY

Introduction

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F i g u r e 4. C o n f o r m a t i o n a l map f o r d i h y d r o p y r a n . Because o f t h e d o u b l e bond, 4 atoms a r e always almost c o p l a n a r and a l i m i t e d number of conformations i s probable. The energy c o n t o u r s a r e a t 2 k c a l / m o l i n t e r v a l s , s t a r t i n g 1 k c a l / m o l above t h e minima. The f a v o r e d c o n f o r m a t i o n s a r e h a l f - c h a i r s , and t h e e a s i e s t p a t h s o f t r a n s i t i o n between t h e two a r e t h r o u g h t h e boat forms. The symmetry o f t h i s energy map a p p l i e s o n l y t o d i h y d r o p y r a n , and not t o d e r i v a t i v e s which cause i n c r e a s e s and d e c r e a s e s i n t h e s i z e s o f t h e a l l o w e d (lowenergy) a r e a s . T h i s map was c a l c u l a t e d w i t h MMP2(85) a t i n c r e m e n t s o f 0.1 A s h i f t o f t h e two n o n - p l a n a r atoms. Three o f t h e c a r b o n atoms were h e l d i n a p l a n e w h i l e C6 and 01 were h e l d a t s p e c i f i c d i s t a n c e s above and below t h e p l a n e . O t h e r w i s e , t h e s t r u c t u r e was f u l l y r e l a x e d a t each i n c r e m e n t . The r e a d e r may e n j o y p l o t t i n g t h e i n d i c a t e d p a t h o f c o n f o r m a t i o n a l i n t e r c h a n g e ( p s e u d o r o t a t i o n ) on a copy o f F i g u r e 3.




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Φ F i g u r e 5. C o n f o r m a t i o n a l map f o r m a l t o s e , c a l c u l a t e d w i t h MMP2(85), u s i n g t h e methods t h a t a r e d e s c r i b e d i n t h e c h a p t e r h e r e i n by F r e n c h , T r a n and Perez w i t h f o u r s t a r t i n g models, φ and ψ were v a r i e d i n s t e p s o f 2 0 ° . C o n t o u r s a r e a t i n t e r v a l s o f one k c a l / m o l .


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W h i l e most CA's o f d i s a c c h a r i d e s have depended o n l y on i n t r i n s i c c h a r a c t e r i s t i c s o f t h e m o l e c u l e , e x p e r i m e n t a l r e s u l t s depend s t r o n g l y on t h e environment. By experiment, Kamide and S a i t o (35) have shown t h a t t h e degree o f f l e x i b i l i t y o f c e l l u l o s e and i t s d e r i v a t i v e s i s s t r o n g l y dependent on t h e d i e l e c t r i c c o n s t a n t o f t h e s o l v e n t as w e l l as t h e e x a c t t y p e and degree o f s u b s t i t u t i o n . S i n c e a s u b s t a n t i a l p o r t i o n o f the polymer f l e x i b i l i t y depends on t h e e x t e n t o f v a r i a b i l i t y o f t h e t o r s i o n a n g l e s a t t h e intermonomer l i n k a g e , t h e dependence o f polymer f l e x i b i l i t y on t y p e o f s o l v e n t and s u b s t i t u t i o n means t h a t the d i s a c c h a r i d e f l e x i b i l i t y a l s o s h o u l d depend on t h o s e factors. N o n - p o l a r s o l v e n t s a l l o w e d t h e m o l e c u l e s t o have g r e a t e r f l e x i b i l i t y than d i d p o l a r s o l v e n t s (35). CA o f P o l y s a c c h a r i d e s . P o l y s a c c h a r i d e s adopt a wide v a r i e t y o f shapes t h a t depend on t h e i r c o m p o s i t i o n and t h e i r environment. In s o l u t i o n , polymers a r e almost always random c o i l s t h a t have l o c a l r e g i o n s t h a t might be s i m i l a r t o c o n f o r m a t i o n s t h a t a r e found i n t h e s o l i d s t a t e . The c h a p t e r by B r a n t and C h r i s t d i s c u s s e s c o n f o r m a t i o n s o f p o l y s a c c h a r i d e s i n s o l u t i o n s b o t h i n terms o f t h e s e l o c a l r e g i o n s and by t h e o v e r a l l shape o f t h e random c o i l i n terms o f end-to-end distance, etc. The f o l l o w i n g d i s c u s s i o n c o n c e r n s o n l y l i n e a r (unbranched) m o l e c u l e s , and r e f e r s o n l y t o r e g u l a r polymers, i . e . , t h o s e t h a t have r e p e a t e d sequences o f monomeric r e s i d u e s l o c a t e d by s c r e w - a x i s ( h e l i c a l ) symmetry. The parameters η and h a r e s i m p l e d e s c r i p t o r s o f t h e conformations of r e g u l a r h e l i c e s , η i s t h e number o f r e s i d u e s (or r e p e a t e d r e s i d u e sequences) p e r h e l i x t u r n , and h i s t h e r i s e p e r r e s i d u e a l o n g t h e h e l i x a x i s ( F i g u r e 6). By d e f i n i t i o n , i f a l l r e s i d u e s and l i n k a g e s a r e i d e n t i c a l t o t h e i r p r e d e c e s s o r s and s u c c e s s o r s , t h e polymer i s a h e l i x . A h e l i x can be l e f t - h a n d e d o r r i g h t handed ( F i g u r e 6); a h e l i x w i t h η = 2 has b o t h c h i r a l i t i e s s i n c e t h e second r e s i d u e can be g e n e r a t e d from t h e f i r s t e q u a l l y w e l l by r o t a t i o n about t h e h e l i x - a x i s i n e i t h e r d i r e c t i o n . Some workers d e s i g n a t e l e f t - h a n d e d h e l i c e s by n e g a t i v e v a l u e s o f n, w h i l e o t h e r workers have used n e g a t i v e v a l u e s o f h f o r l e f t - h a n d e d s t r u c t u r e s . H e l i c e s can be n o n - i n t e g r a l ; a h e l i x w i t h η = 3.5 would have seven r e s i d u e s c o m p l e t i n g two h e l i x t u r n s . An a l t e r n a t e n o m e n c l a t u r e (see t h e p a p e r by M i l l a n e h e r e i n ) d e s c r i b e s o n l y t h e symmetry o f t h e h e l i x and c o n f l i c t s somewhat w i t h e s t a b l i s h e d c r y s t a l l o g r a p h i c nomenclature. I n t h i s system, t h e number o f r e s i d u e s p e r c r y s t a l l o g r a p h i c r e p e a t i s g i v e n , w i t h a s u b s c r i p t o f t h e number o f h e l i x t u r n s per r e p e a t . Thus, a p o l y s a c c h a r i d e might be d e s c r i b e d as an 8~ h e l i x . I n n-h nomenclature, η would be 2.666, and h would be o n e - t h i r d of the l e n g t h of the f i b e r repeat d i s t a n c e . A third a l t e r n a t i v e (see t h e paper by R a g a z z i e t a l . h e r e i n ) d e s c r i b e s h e l i c e s i n terms o f t h e r o t a t i o n p e r r e s i d u e about t h e h e l i x a x i s . Thus, a φ^ o f 180° i n d i c a t e s a h e l i x w i t h two r e s i d u e s p e r t u r n , and 90° i n d i c a t e s a f o u r - f o l d h e l i x . To a n a l y z e c o n f o r m a t i o n s o f p o l y s a c c h a r i d e s , workers have m o d i f i e d the φ-ψ programs u s e d f o r CA o f d i s a c c h a r i d e s t o i n c l u d e m o n i t o r i n g d i s t a n c e s t o atoms f a r t h e r t h a n t h e next r e s i d u e along the chain. When a m o d e l i n g program has been s u i t a b l y m o d i f i e d f o r polymers, i t g i v e s an e x t r e m e l y h i g h energy r e g i o n a t h = 0. T h i s i s because, f o r η > 1, h = 0 r e q u i r e s s u c c e s s i v e h e l i x t u r n s t o occupy t h e same space, a p h y s i c a l i m p o s s i b i l i t y . The r e s u l t s o f such s t u d i e s a r e o b t a i n e d i n φ, ψ space and a r o u t i n e c a l c u l a t e s t h e η and h v a l u e s as f u n c t i o n s o f φ and ψ . This c o n v e r s i o n depends on t h e e x a c t c o o r d i n a t e s o f t h e r e s i d u e and a p r e c i s e g l y c o s i d i c bond a n g l e . However, most m o n o s a c c h a r i d e s a r e



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N-H MAP FOR 1,4 UNKED GLUCAN, MM3 BEST RESIDUE 4.25 , ,

(Left)

RESIDUES PER TURN

(Right)

F i g u r e 6. An n-h map f o r amylose (a-l->4 glucan) a l o n g w i t h d e f i n i t i o n s o f l e f t - and r i g h t - h a n d e d h e l i c e s and η and h. With t h e thumb a l i g n e d a l o n g t h e h e l i x a x i s , t h e hand w i t h t h e f o r e f i n g e r t h a t f o l l o w s t h e h e l i x backbone i n d i c a t e s t h e c h i r a l i t y . (An i n v e r t e d l e f t - h a n d h e l i x i s s t i l l left-handed!) The number o f r e s i d u e s , n, p e r h e l i x r e p e a t , r , ( o r p i t c h , p) shown i s s i x , and t h e r i s e p e r r e s i d u e , h, i s i n d i c a t e d . There a r e two a l l o w e d zones (shaded) on t h i s n-h map, f o r r i g h t - and l e f t - h a n d e d h e l i c e s . The g l y c o s i d i c a n g l e was a l l o w e d t o have v a l u e s o f 110 - 122°. The r e s i d u e geometry was t h e o p t i m i z e d MM3 model, t a k e n from t h e c h a p t e r i n t h e s e p r o c e e d i n g s by F r e n c h , Rowland and A l l i n g e r , and g i v e s r i s e t o c o l l a p s e d h e l i c e s (low h v a l u e s ) w i t h 7 and 8 r e s i d u e s p e r t u r n and extended ( l e f t - h a n d e d ) h e l i c e s w i t h 4 r e s i d u e s p e r t u r n . H e l i c e s w i t h η = -6 and h = 3.5 A, c o r r e s p o n d i n g t o n a t i v e s t a r c h (see t h e c h a p t e r by Imberty, P e r e z and S c a r i n g e ) a r e a l s o a l l o w e d . Other r e s i d u e g e o m e t r i e s expand t h e ranges o f t h e a l l o w e d h e l i c a l shapes considerably.


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somewhat f l e x i b l e (29) ( a l s o see t h e c h a p t e r h e r e i n by F r e n c h , Rowland and A l l i n g e r ) , and p o l y s a c c h a r i d e s o f t e n c r y s t a l l i z e i n v a r i o u s shapes t h a t r e q u i r e v a r i a t i o n s i n t h e geometry o f t h e c o n s t i t u e n t monosaccharides. Therefore, a thorough c o n f o r m a t i o n a l a n a l y s i s f o r a p o l y s a c c h a r i d e r e q u i r e s e i t h e r t h e use o f f l e x i b l e r e s i d u e s o r p a r a l l e l s t u d i e s w i t h s e v e r a l r i g i d r e s i d u e s t h a t span t h e i m p o r t a n t range o f r e s i d u e v a r i a t i o n . When f l e x i b i l i t y o f t h e r e s i d u e s and l i n k a g e s i s i n c o r p o r a t e d , t h e v a l u e s o f φ and ψ cannot s p e c i f y η and h. Thus, an a l t e r n a t e r e p r e s e n t a t i o n (3j>) o f conformation-space ( F i g u r e 6) i s u s e f u l . I t p l o t s the r e s u l t s of the a n a l y s i s ( i n t h i s example, f o r i n t e r - r e s i d u e , h a r d - s p h e r e c o n t a c t s ) o f each n-h c o m b i n a t i o n on a g r i d o f η and h.


Practical Perspectives Simple w i r e , b a l l and s t i c k , and s p a c e - f i l l i n g models have been u s e f u l i n t h e p r a c t i c e o f c h e m i s t r y f o r many y e a r s . We do not p r e d i c t t h a t computer m o d e l i n g w i l l e l i m i n a t e p h y s i c a l models. There w i l l always be advantages t o c o n c r e t e r e p r e s e n t a t i o n s o f attempts t o describe molecules. I n s t e a d , computer m o d e l i n g o f f e r s an unprecedented degree o f q u a n t i f i c a t i o n and an avenue t o a n a l y s i s o f dynamic b e h a v i o r not p o s s i b l e w i t h p h y s i c a l models. A l s o , computer models can be b u i l t v e r y q u i c k l y . Many o f t h e t e c h n i q u e s f o r computer modeling were d e v e l o p e d some time ago but t h e slow speed and h i g h c o s t o f computers p r e v e n t e d t h e i r wide a p p l i c a t i o n . Now, compared t o l a b o r a t o r y i n s t r u m e n t s , a computer s u i t e d f o r many t y p e s o f modeling s t u d i e s may seem q u i t e inexpensive. ( I t even may seem i n e x p e n s i v e compared t o a good c o l l e c t i o n of r e a l models!) I n t h e p a s t decade, t h e p r i c e / p e r f o r m a n c e r a t i o o f computers has improved by two o r d e r s o f magnitude and i t appears t h a t improvements w i l l c o n t i n u e . The p r o s p e c t o f w i d e s p r e a d and l u c r a t i v e markets f o r e a s y - t o - u s e m o d e l i n g s o f t w a r e has s p u r r e d development o f s o f t w a r e packages t h a t can be used by t h o s e who a r e not f u l l - t i m e computer s p e c i a l i s t s . The keys t o use by n o n - s p e c i a l i s t s a r e t h e g r a p h i c a l u s e r i n t e r f a c e and t h e a v a i l a b i l i t y o f "canned" s o f t w a r e . (The c h a p t e r by J e f f r e y adds p e r s p e c t i v e on t h e use o f "canned" software.) A number o f programs f o r modeling a r e a v a i l a b l e from t h e Quantum C h e m i s t r y Program Exchange (QCPE), Department o f Chemistry, I n d i a n a U n i v e r s i t y , Bloomington, I n d i a n a 47901, f o r a s l i t t l e a s $100, and f a i r l y comprehensive packages such a s TRIBBLE c o s t $400. Commercially d e v e l o p e d packages sometimes i n c o r p o r a t e r o u t i n e s o r even e n t i r e programs from t h e QCPE (with p r o p e r c r e d i t ) but can c o s t as much a s $100,000 o r even more. However, academic and o t h e r n o t - f o r - p r o f i t u s e r s can o f t e n buy t h e same s o f t w a r e a t d i s c o u n t s up t o 97%. The computing time r e q u i r e d f o r t h e o r e t i c a l s t u d i e s v a r i e s w i d e l y depending on t h e t y p e o f modeling b e i n g done. F o r example, t h e m i n i m i z a t i o n o f p o t e n t i a l e n e r g i e s f o r 13 g l u c o s e r e s i d u e s w i t h d i f f e r e n t 01—04 d i s t a n c e s b y f i v e d i f f e r e n t programs r e q u i r e d about two cpu hours on a DEC M i c r o v a x 3100. A f a i r l y thorough (relaxed) c o n f o r m a t i o n a l a n a l y s i s o f a d i s a c c h a r i d e might t a k e a week o f cpu time on t h e same computer. S o l u t i o n dynamics s i m u l a t i o n s o f a d i s a c c h a r i d e might r e q u i r e s e v e r a l cpu months b e f o r e r e l i a b l e r e s u l t s c o u l d be o b t a i n e d on t h e same machine. The l a t t e r p r o b l e m i s c l e a r l y a c a n d i d a t e f o r a super-computer. Computers c o s t i n g i n t h e range o f $10,000 t o $20,000 can e x e c u t e most o f t h e w i d e l y a v a i l a b l e modeling s o f t w a r e packages. This i s q u i t e i n e x p e n s i v e compared t o t h e c o s t o f d e v e l o p i n g major s o f t w a r e , o r even o f c o n t i n u o u s l y c o n v e r t i n g new r e l e a s e s o f programs w r i t t e n f o r a n o t h e r computer. T h e r e f o r e , i t may be q u i t e r e a s o n a b l e t o buy a



18


s p e c i f i c computer j u s t because i t w i l l r u n a p a r t i c u l a r program without f u r t h e r e f f o r t . The a d v i c e t h a t u s e r s s h o u l d s e l e c t s o f t w a r e f i r s t and t h e n hardware has p r o v e n s o l i d o v e r t h e y e a r s . Another view i s t h a t no s i n g l e s o f t w a r e system i s l i k e l y t o p r o v i d e a l l t h e answers and t h a t major hardware e x p e n d i t u r e s s h o u l d s u p p o r t as many c a n d i d a t e programs as p o s s i b l e . One a s p e c t o f computer m o d e l i n g i s easy t o i g n o r e u n t i l work commences. Running even a r e l a t i v e l y slow computer f o r hours, weeks o r months produces a tremendous amount o f i n f o r m a t i o n . Hundreds o f megabytes o f d i s k space a r e needed t o c o n t a i n a l a r g e m o d e l i n g package and t h e o u t p u t from two o r t h r e e p r o d u c t i v e p e o p l e . F o r l a r g e s i m u l a t i o n s , t h e a n a l y s i s o f t h e s e d a t a s e t s becomes t h e r a t e l i m i t i n g s t e p f o r p r o d u c t i v i t y o f t h e modeler. Some o f t h i s d a t a w i l l be managed by a l a r g e m o d e l i n g system, b u t as t h e u s e r r e q u e s t s more s o p h i s t i c a t e d i n f o r m a t i o n from m o d e l i n g , development o f u n i q u e programs may be n e c e s s a r y . F o r example, major m o d e l i n g packages u s u a l l y do n o t p r o v i d e o u t p u t o f t h e C-P p u c k e r i n g p a r a m e t e r s . C o o r d i n a t e s o f s t r u c t u r e s o u t p u t from a m o d e l i n g s t u d y must be p u t i n t o t h e c o r r e c t form f o r i n p u t t o a program f o r p u c k e r i n g parameters i f that information i s desired. F o r such r e a s o n s , some computer s k i l l s a r e needed. Conclusions Can a c a r b o h y d r a t e c h e m i s t become a computer modeler? Having s t a r t e d s e v e r a l p e o p l e w i t h d i v e r s e backgrounds on m o d e l i n g s t u d i e s , b o t h o f us t h i n k t h a t i s more l i k e l y t h a n a modeler becoming a bench c h e m i s t . A d m i t t e d l y , t h e r e a r e many p i t f a l l s f o r t h e b e g i n n e r and v e x i n g problems f o r t h e e x p e r i e n c e d worker. The a b i l i t i e s o f m o d e l i n g a r e often oversold. However, t h e promise and honest s u c c e s s i n d i c a t e d by t h e c o l l e c t e d p a p e r s i n t h i s book show t h a t computer m o d e l i n g o f c a r b o h y d r a t e s has a l r e a d y produced a wide v a r i e t y o f u s e f u l r e s u l t s .

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Albersheim, P.Α.; Darvill, A.G. Scientific American 1985, September, 58-64. Stoddart, J.F. Stereochemistry of Carbohydrates; WileyInterscience, New York, 1971. Jones, D.W. J. Polym. Sci., 1960, 42, 173-188. Rao, V.S.R.; Sundararajan, P.R.; Ramakrishnan, C.; Ramachandran, G.N. In Conformation in Biopolymers, Vol. 2, Academic Press: London, 1963. Brooks, C.L.; Karplus, M.; Pettitt, B.M. Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, Advances in Chemical Physics Series, Vol. LXXI. Wiley, New York, 1988. McCammon, J.Α.; Harvey, S.C. Dynamics of Proteins and Nucleic Acids, Cambridge University Press, Cambridge, 1987. Tvaroska, I.; Bleha, T. in Advances in Carbohydrate Chemistry and Biochemistry; Tipson, R.S.; Horton, D. Eds.; Academic: San Diego, 1989, Vol. 47, pp 45-123. Tvaroska, I.; Pérez, S. Carbohydr. Res. 1986, 149, 389-410. Lemieux, R.U.; Bock, K.; Delbaere, L.T.J.; Koto, S.; Rao, Can. J. Chem. 1980, 58, 631-653. Tvaroška, I. Carbohydr. Res. 1984, 125, 155-160. Nørskov-Lauritsen, L.; Allinger, N.L. J. Comput. Chem. 1984, 5, 326-335. Marsden, Α.; Robson, B.; Thompson, J.S. J. Chem. Soc. Faraday Trans. I, 1988, 84, 2519-2536.


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19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36.

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