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Multiprocessor Molecular Mechanics KENT R. WILSON Department of Chemistry, University of California, San Diego, La Jolla, Calif. 92037 "Chemical phenomena must be treated as if they were problems in mechanics." Lothar Meyer, co-discoverer, with Mendeleev, of the periodic table, 1868. (1) Life is based on marvelous biomolecular machinery, and a central theme in molecular biology has been the role of this machinery's precise molecular architecture. Such molecular architecture, however, is only a static snapshot of a moving, ever changing microscopic world. We are building a macroscopic machine, NEWTON, an internal network of several computer processors, to help the human chemist or molecular biologist investigate and understand the molecular dynamics, the detailed time evolution, as well as the structure of biomolecular systems, for example of enzymes, of membranes, of biomolecular self-assembly. Chemists have long known that such biomolecular behavior is in theory derivable from mechanics, but computational barriers to such a molecular mechanical approach to atomic motions have seemed insurmountable. We have now designed an instrument which will closely interface a human chemist through three-dimensional visual and touch interaction to an extraordinarily powerful networked computer system capable of integrating the classical mechanical coupled differential equations describing the motions of several hundred atoms under their mutual interatomic force fields in such rapid fashion that the chemist can watch the interacting bio- and solvent molecules evolve and reach into a volume of space to actually manipulate simulated atoms, feeling the changing forces upon them, in order to set up and guide the molecular system into the desired chemical pathway. Potential applications span all molecules; their structures, properties and reactions, but particular biomolecular applications include protein conformation, the dynamics of enzyme-substrate interaction, allosteric effects, membrane transport, drug-receptor dynamics and drug design (enzyme blocking agents, antibiotics, specific 17
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c o m p l e x i n g agents), antigen-antibody i n t e r a c t i o n and b i o m o l e c ular self-assembly. L
Introduction and B a c k g r o u n d
S i n c e N e w t o n i n the 17th c e n t u r y , i t has b e e n c l e a r that the s t r u c t u r e ( s t a t i c s ) as w e l l as the m o t i o n s ( d y n a m i c s ) of a set of p a r t i c l e s a r e b a s e d o n the f o r c e s b e t w e e n t h e m . Thus, e v e r s i n c e the a t o m i c t h e o r y c r y s t a l l i z e d i n the 19th c e n t u r y , c h e m i s t s h a v e d r e a m e d that the p r o p e r t i e s of m o l e c u l e s w o u l d s o m e d a y be d e r i v a b l e f r o m the f o r c e s between a t o m s . We now k n o w that the p r o b l e m d i v i d e s into two p a r t s : that a q u a n t u m m e c h a n i c a l t r e a t m e n t i s r e q u i r e d f o r the e l e c t r o n s i n o r d e r to d e r i v e the p o t e n t i a l (or f o r c e ) f i e l d w i t h i n w h i c h the n u c l e i m o v e ; but that f o r p u r p o s e s of u n d e r s t a n d i n g m o l e c u l a r s t r u c t u r e o r the m e c h a n i s m of c h e m i c a l r e a c t i o n , o n c e the f o r c e s a r e k n o w n the m o t i o n s of the n u c l e i m a y u s u a l l y be t r e a t e d b y classical mechanics with reasonable accuracy. It i s t h e c l a s s i c a l p a r t of t h e p r o b l e m , the n u c l e a r m o t i o n s , w h i c h w e w i l l discuss here. W h i l e c h e m i s t s h a v e s u c c e s s f u l l y l e a r n e d h o w to u n d e r stand c h e m i c a l reactions by calculating atomic motions i n a f o r c e f i e l d f o r s i m p l e r e a c t i o n s i n v o l v i n g a h a n d f u l of a t o m s , s u c h c a l c u l a t i o n s f o r r e a c t i o n s of o r g a n i c m o l e c u l e s of o r d i n a r y c o m p l e x i t y , l e t a l o n e t h e l a r g e r m o l e c u l e s of b i o c h e m i s t r y , h a v e b e e n too l e n g t h y to h a n d l e w i t h p r e s e n t day c o m p u t e r t e c h nology. A typical organic reaction including solvent effects m i g h t i n v o l v e 100 a t o m s , e a c h s p e c i f i e d i n x , y a n d z , a n d t h u s t h e s o l u t i o n ( i n N e w t o n i a n o r L a g r a n g i a n f o r m ) of 300 c o u p l e d s e c o n d o r d e r d i f f e r e n t i a l e q u a t i o n s , e a c h w i t h u p t o 300 v a r i a b l e s . B i o l o g i c a l p o l y m e r s , e. g . p r o t e i n s a n d n u c l e i c a c i d s , m a y r e q u i r e t h o u s a n d s of a t o m s to r e p r e s e n t t h e i r p r o p e r t i e s a n d reactions. W h i l e the a m o u n t of c o m p u t e r t i m e n e c e s s a r y to i n t e g r a t e s u c h a s e t of c o u p l e d d i f f e r e n t i a l e q u a t i o n s i s i t s e l f a c o n s i d e r a b l e o b s t a c l e , the g r e a t e s t c a l c u l a t i o n a l p r o b l e m w h i c h has p r e v e n t e d a " m e c h a n i c a l m o l e c u l e " a p p r o a c h to o r g a n i c a n d b i o c h e m i c a l r e a c t i o n s is a m o r e subtle one: the e n o r m o u s phase s p a c e of i n i t i a l a t o m i c p o s i t i o n s a n d m o m e n t a w h i c h m u s t b e s e a r c h e d to f i n d the r e g i o n l e a d i n g to c h e m i c a l l y i n t e r e s t i n g results. Most molecular conformations, relative orientations a n d r e l a t i v e a p p r o a c h v e l o c i t i e s do not l e a d to the d e s i r e d chemical reaction. If o n e w e r e t o t a k e a b r u t e f o r c e a p p r o a c h
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and s y s t e m a t i c a l l y s e a r c h t h r o u g h j u s t f i v e d i f f e r e n t i n i t i a l position vectors and five different initial v e l o c i t y vectors for a t y p i c a l 100 a t o m o r g a n i c r e a c t i o n , l o o k i n g f o r t h o s e w h i c h l e a d t o t h e r e a c t i o n i n q u e s t i o n , t h e s e t o f 300 c o u p l e d d i f f e r e n t i a l equations w o u l d h a v e to be i n t e g r a t e d ~ 25*^0 t i m e s J S u c h a b r u t e f o r c e a p p r o a c h is not m e r e l y d i f f i c u l t w i t h p r e s e n t c o m p u t e r s ; it i s i m p o s s i b l e and w i l l r e m a i n so. On the other h a n d , the w e l l t r a i n e d h u m a n c h e m i s t h a s , o r t h i n k s h e h a s , a r e a s o n a b l y g o o d c o n c e p t i o n of w h a t t h e a t o m s m u s t be d o i n g if c h e m i c a l r e a c t i o n i s to o c c u r . If h e c o u l d s o m e h o w w a t c h the atoms i n t h r e e d i m e n s i o n s and r e a c h i n and a d j u s t o r s t e e r the m o l e c u l e s into c h e m i c a l l y r e a s o n a b l e p r o x i m i t y , orientation, conformation and velocity, readjusting the c a l c u l a t i o n i n p r o c e s s , he c o u l d c o l l a p s e an i m p o s s i b l y l a r g e s e a r c h space into a manageable s i z e . We have developed a t e c h n i q u e of m a n - m a c h i n e t o u c h c o m m u n i c a t i o n to do j u s t t h i s , a l l o w i n g us to r e a c h into t h r e e d i m e n s i o n a l s p a c e a n d a d j u s t s i m u l a t e d a t o m s w h i l e f e e l i n g the f o r c e s i n v o l v e d a n d s i m u l t a n e o u s l y w a t c h i n g c o m p u t e r g e n e r a t e d 3D i m a g e s of the i n t e r acting molecules. A c h e m i s t s t e e r i n g the c a l c u l a t i o n and w a t c h i n g the r e s u l t s w i l l q u i c k l y l e a r n , w e b e l i e v e , to c o n v e r g e on the s m a l l e r r e g i o n of c h e m i c a l l y m e a n i n g f u l i n i t i a l c o n d i t i o n s . T h u s a tight m a n - m a c h i n e s y m b i o s i s c a n d e v e l o p , the h u m a n b e i n g p r o v i d i n g h i s s t r o n g p o i n t s of r e c o g n i t i o n of m e a n i n g f u l c h e m i c a l p a t t e r n s , of p u r p o s e , of d i r e c t i o n , of i n t u i t i o n , a n d t h e c o m p u t e r p r o v i d i n g s t o r a g e of p a r a m e t e r s a n d r a p i d a n d e x a c t c a l c u l a t i o n of t h e i r i m p l i c a t i o n s i n t e r m s of m o l e c u l a r d y n a m i c s , i n o t h e r w o r d s , c o m p u t i n g t h e m o t i o n s of t h e a t o m s i n a m o l e c u l a r s y s t e m u n d e r a g i v e n set of i n t e r a t o m i c f o r c e s and s t e e r e d i n i t i a l c o n d i t i o n s . If a h u m a n i s to g u i d e s u c h c h a n g i n g a n d r e a c t i n g m e c h a n i c a l m o l e c u l e s , the c a l c u l a t i o n m u s t be f a s t enough to m a t c h the t i m e s c a l e of h u m a n i n t e r a c t i o n . Even for a molecular system of 100 a t o m s , o n l y a l a r g e , d e d i c a t e d p r o c e s s o r c o u l d k e e p u p with a human partner for such a task. To handle several h u n d r e d a t o m s w o u l d r e q u i r e a c o n v e n t i o n a l p r o c e s s o r of the c o m b i n e d c a l c u l a t i o n a l s p e e d of s e v e r a l d o z e n I B M 3 6 0 / 6 5 ' s . F o r l a r g e r b i o l o g i c a l p o l y m e r s , s i n c e t h e n u m b e r of i n s t r u c t i o n s s c a l e s as N ^ , w h e r e Ν i s the n u m b e r of a t o m s , no p r e s e n t p r o c e s s o r appears adequate. H o w e v e r , as w i l l be d i s c u s s e d b e l o w , the n e e d e d c o m p u t a t i o n a l speeds c a n be obtained w i t h p r e s e n t l y a c h i e v a b l e l o g i c , m e m o r y and b u s s p e e d s b y d i s t r i b u t i n g the c o m p u t a t i o n a l l o a d
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among several fast specialized processors, running in parallel and p i p e l i n e d m o d e s . P r o c e s s o r costs in instructions/dollar s e c o n d h a v e n o w d r o p p e d to the r a n g e w h e r e b i o m o l e c u l a r d y n a m i c s c a n be i n v e s t i g a t e d f o r m o l e c u l a r s y s t e m s w i t h a l a r g e e n o u g h n u m b e r of a t o m s to b e i n t e r e s t i n g a n d i m p o r t a n t . We have designed such a system, have run a much scaled down test, a n d a r e n o w c o n s t r u c t i n g a f i r s t p r o t o t y p e of a f u l l s y s t e m . A. Chemistry. T h e s t u d y of the p r o p e r t i e s of m o l e c u l e s as d e r i v e d f r o m i n t e r a t o m i c f o r c e s has d e v e l o p e d m a i n l y i n two d i v e r s e a r e a s : the m o l e c u l a r d y n a m i c s of v e r y s m a l l m o l e c u l e s i n c h e m i c a l p h y s i c s a n d t h e m o l e c u l a r s t a t i c s , i . e. t h e c o n f i g u r a t i o n , of l a r g e r m o l e c u l e s , p a r t i c u l a r l y t h e s t r u c t u r e of o r g a n i c m o l e c u l e s a n d the c o n f o r m a t i o n of p r o t e i n s . I n c h e m i c a l p h y s i c s , o n e of t h e m a j o r t h e m e s o f t h e p a s t d e c a d e h a s b e e n the u n d e r s t a n d i n g of c h e m i c a l p r o c e s s e s , i n c l u d i n g c h e m i c a l r e a c t i o n s , i n t e r m s of t h e s c a t t e r i n g of a t o m s a n d s m a l l m o l e c u l e s ( 2 , 3). O n e of the m a i n r e a s o n s f o r t h e b l o s s o m i n g of t h i s a p p r o a c h to c h e m i s t r y h a s b e e n t h e d e v e l o p m e n t of e x p e r i m e n t a l t e c h n i q u e s , o f t e n i n v o l v i n g m o l e c u l a r b e a m s a n d m o r e r e c e n t l y l a s e r s , c a p a b l e of s t u d y i n g i n d i v i d u a l m o l e c u l a r events w i t h s u f f i c i e n t d e t a i l and p r e c i s i o n that c o n c l u s i v e t e s t s of t h e o r e t i c a l s c a t t e r i n g p r e d i c t i o n s a r e possible. It i s c l e a r t h a t t h e f u n d a m e n t a l t h e o r e t i c a l b a s i s o f i n t e r a t o m i c and i n t e r m o l e c u l a r f o r c e s m u s t be a n a l y z e d f r o m a q u a n t u m m e c h a n i c a l v i e w p o i n t (4), a s t h e e l e c t r o n s h a v e s m a l l enough m a s s and m o m e n t u m that t h e i r w a v e n a t u r e cannot be i g n o r e d on the m o l e c u l a r s c a l e . It h a s , h o w e v e r , a l s o b e c o m e c l e a r i n the p a s t d e c a d e that i f one h a s i n h a n d a n i n t e r a t o m i c f o r c e f u n c t i o n , u s u a l l y e x p r e s s e d i n t e r m s of a m u l t i d i m e n s i o n a l p o t e n t i a l e n e r g y s u r f a c e u p o n w h i c h the m o r e m a s s i v e n u c l e i m o v e , a surface w h i c h has either been calculated quantum m e c h a n i c a l l y o r a r r i v e d at b y a n a l y s i s of e x p e r i m e n t a l m e a s u r e m e n t s , t h e n the c a l c u l a t i o n of s t a t i c m o l e c u l a r s t r u c t u r e o r dynamic m o l e c u l a r evolution and c h e m i c a l reaction can usually b e h a n d l e d w i t h r e a s o n a b l e a c c u r a c y b y the a p p r o x i m a t i o n of classical mechanics. T h i s type of m o l e c u l a r d y n a m i c s a p p r o a c h (5) h a s b e e n l i m i t e d t o s m a l l m o l e c u l e s o f o n l y a f e w a t o m s b e c a u s e of c o m p u t a t i o n a l d i f f i c u l t y . While in chemical physics, m o l e c u l a r dynamics has been d e r i v e d f r o m i n t e r a t o m i c p o t e n t i a l (or f o r c e ) f u n c t i o n s , i n organic and p o l y m e r c h e m i s t r y m o l e c u l a r structure has been
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studied on this b a s i s . O n the organic m o l e c u l a r scale, researchers have included H i l l , Westheimer, Dashevsky, Kitaigorodsky, Allinger, Lifson, Hendrickson, Wibert, Boyd, S c h l e y e r , M i s l o w a n d m a n y o t h e r s (6, 7, 8 ) . This technique h a s a l s o b e e n e x t e n d e d p a r t of the w a y i n t o d y n a m i c s , to a n a l y s i s of p a t h w a y s b e t w e e n s t r u c t u r e s b y c a l c u l a t i o n of e n e r g i e s at v a r i o u s i n t e r m e d i a t e c o n f i g u r a t i o n s i n o r d e r to s t u d y , f o r e x a m p l e , i s o m e r i z a t i o n (9, 1 0 ) . In p o l y m e r c h e m i s t r y , p a r t i c u l a r l y p r o t e i n c o n f o r m a t i o n , a l a r g e body of r e s e a r c h h a s b e e n c a r r i e d o u t b y m a n y g r o u p s i n c l u d i n g t h o s e of R a m a c h a n d r a n , S c h e r a g a , L i f s o n , F l o r y , L i q u o r i , and H o p f i n g e r (11, 12). P r o t e i n c o n f o r m a t i o n i s u s u a l l y t r e a t e d as a n e n e r g y m i n i m i zation p r o b l e m with constraints. M o s t bonded interactions between atoms are f i x e d as c o n s t r a i n t s i n bond length and bond a n g l e , and a l l o w a b l e d e g r e e s of f r e e d o m a r e u s u a l l y r o t a t i o n s about c e r t a i n bonds. Nonbonded interactions are specified in t e r m s of a s s u m e d p o t e n t i a l f u n c t i o n s . A s e a r c h is then c a r r i e d out to t r y to f i n d the g l o b a l p o t e n t i a l e n e r g y m i n i m u m , s u b j e c t to the c o n s t r a i n t s . T h i s m i n i m u m i s t h e n a s s u m e d to c o r r e s p o n d to the m o s t p r o b a b l e c o n f o r m a t i o n f o r the p r o t e i n , although m o r e r e c e n t l y the l o c a l l y a v a i l a b l e phase s p a c e has b e e n e s t i m a t e d as w e l l i n o r d e r to b e t t e r t a k e n into a c c o u n t the e n t r o p y c o n t r i b u t i o n to the f r e e e n e r g y w h i c h s h o u l d m o r e c o r r e c t l y be m i n i m i z e d . We plan a somewhat different approach, related in c o o r d i n a t e s t o w o r k b y L e v i t t (13) a n d b y H e r m a n s a n d M c Q u e e n (14), w h i c h i s e a s i e r t o g e n e r a l i z e t o n o n p o l y m e r s a n d m u c h s i m p l e r to p r o g r a m a n d to s p l i t i n t o t a s k s f o r m u l t i p l e p r o cessors. Bonded and nonbonded i n t e r a t o m i c interactions w i l l a l l be t r e a t e d b y the s a m e f o r m a l i s m , not as c o n s t r a i n t s , but e x p l i c i t l y as f o r c e f u n c t i o n s , w h i c h m a y h o w e v e r be f u n c t i o n s of the v e c t o r p o s i t i o n s of s e v e r a l n e i g h b o r i n g a t o m s a n d n e e d n o t be r e s t r i c t e d to t w o b o d y i n t e r a c t i o n s . A s f r e q u e n t l y as w e c a n , i n s t e a d of e x p r e s s i n g f o r c e s e x p l i c i t l y i n t e r m s of a n g l e s , t h e y w i l l be e x p r e s s e d i n t e r m s of v e c t o r o p e r a t i o n s s u c h as d i s t a n c e and the i n n e r p r o d u c t , w h i c h c a n be c a l c u l a t e d m u c h f a s t e r than the c o r r e s p o n d i n g t r i g o n o m e t r i c f u n c t i o n s . W e w i l l u s e f o r c e f u n c t i o n s i n s t e a d of the e q u i v a l e n t p o t e n t i a l f u n c t i o n s and w i l l not m i n i m i z e f o r c e o r p o t e n t i a l e n e r g y , but r a t h e r a s s i g n the c o r r e c t m a s s e s to the a t o m s a n d l e t e a c h one m o v e u n d e r the s u m of the f o r c e s u p o n i t . It i s i n t e r e s t i n g t o f u r t h e r c o m p a r e e n e r g y m i n i m i z a t i o n for molecular statics with molecular dynamics. For large
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m o l e c u l e s , e a c h t y p e o f c a l c u l a t i o n m u s t s p e n d m u c h of i t s t i m e i n e v a l u a t i n g the p o t e n t i a l o r f o r c e . T h u s the a d d i t i o n a l c o m p u t e r t i m e i s n o t a s l a r g e a s o n e m i g h t t h i n k t o go f r o m a c a l c u l a t i o n w h i c h s e a r c h e s f o r a static s t r u c t u r e i n w h i c h the a t o m s a r e m o v e d i n o r d e r to f i n d a n e n e r g y m i n i m u m to a calculation involving a molecular dynamic approach in which a c t u a l a t o m i c t r a j e c t o r i e s a r e c a l c u l a t e d f r o m the a c c e l e r a t i o n s of a t o m s of d e f i n e d m a s s u n d e r t h e f o r c e s i m p a r t e d b y o t h e r atoms. Given a machine which will calculate molecular dynamics, one c a n a l s o c a l c u l a t e s t r u c t u r e , b y r e m o v i n g e n e r g y u n t i l a t o m i c m o t i o n s t o p s , t h r o u g h the a d d i t i o n of a v i s c o u s f o r c e p r o p o r t i o n a l to the n e g a t i v e of e a c h a t o m s v e l o c i t y v e c t o r . T h i s r e l a x a t i o n t e c h n i q u e i s e q u i v a l e n t c o n c e p t u a l l y to d u n k i n g an i n i t i a l l y v i b r a t i n g m o l e c u l e into a f l u i d . A s an energy m i n i m u m is a p p r o a c h e d a n d a t o m i c m o t i o n s l o w s d o w n , the v i s c o s i t y c a n be d e c r e a s e d to s p e e d a p p r o a c h to e q u i l i b r i u m . There are two c e n t r a l difficulties w e l l known i n energy m i n i m i z a t i o n p r o t e i n c o n f o r m a t i o n studies w h i c h m u s t be dealt with also i n using our approach. The f i r s t is being trapped i n a l o c a l (but n o t g l o b a l ) e n e r g y m i n i m u m . This is probably less likely than with s i m p l e energy m i n i m i z a t i o n schemes, as o u r a t o m s w i l l h a v e m o m e n t u m a n d a r e l i k e l y to b o u n c e o n t h r o u g h m a n y l o c a l m i n i m a on t h e i r w a y to a d e e p e r m i n i m u m . W e s u s p e c t i n a d d i t i o n that the h u m a n o p e r a t o r w a t c h i n g the 3 D v i s u a l d i s p l a y (8, 9) w i l l b e a b l e t o r e c o g n i z e l o c a l t r a p p i n g a s c l u s t e r s of a t o m s " c a t c h " o n e a c h o t h e r , a n d r e a c h i n w i t h the t o u c h i n t e r f a c e to n u d g e t h e m a p a r t . A further serious d i f f i c u l t y i s o u r l a c k of p r e c i s e k n o w l e d g e of the a p p r o p r i a t e f o r c e f u n c t i o n s t o u s e (7, 1 5 , 1 6 ) . W e expect a long and d i f f i c u l t c o u r s e of r e s e a r c h b e f o r e t h i s i m p r e c i s i o n i s r e s o l v e d for organic and b i o c h e m i c a l molecules i n general and we d i s c u s s s o m e d i r e c t i o n s of a p p r o a c h i n a l a t e r s e c t i o n . Our m a c h i n e s h o u l d b e one m e a n s of s p e e d i n g t h i s r e s e a r c h . C l a s s i c a l c a l c u l a t i o n s of the d y n a m i c s of l a r g e n u m b e r s of p a r t i c l e s h a v e a l s o b e e n m a d e i n at l e a s t t h r e e o t h e r a r e a s : a s t r o p h y s i c s ( 1 7 ) , p l a s m a p h y s i c s (18) a n d t h e s t a t i s t i c a l m e c h a n i c s of a s s e m b l i e s of a t o m s a n d m o l e c u l e s . The stellar and p l a s m a m e c h a n i c s f i e l d s s h a r e m a n y s i m i l a r i t i e s as w e l l as m u t u a l a s p e c t s w h i c h d i f f e r e n t i a t e t h e m f r o m the m o l e c u l a r m e c h a n i c s w e a r e d i s c u s s i n g , s o m e of w h i c h a r e s u m m a r i z e d i n the f o l l o w i n g table. 1
3.
WILSON
Molecular
Mechanics
23
Feature
P l a s m a & Stellar
Molecular
i)
Often m a c r o s c a l e , gross effects, many particles needed, less detail.
Microscale, local effects u s u a l l y dominate, .". l e s s p a r t i c l e s n e e d e d , more precision.
S c a l e of Effects
-1
ii)
S c a l e of Interaction
Long range; potentials.
iii)
Interaction Complexity
2-body usually sufficient; somet i m e s m a g n e t i c as w e l l as e l e c t r o s t a t i c for plasmas.
2-body sufficient for m a n y i n t e r a c t i o n s , but multibody essential in many cases.
iv)
Particle Complexity
A n y t e s t p a r t i c l e at given location would feel same force with e x c e p t i o n of m a g n i tude and s i g n (plasma).
Different test particles (elements) would feel quite different force fields.
v)
ShortRange Collisions
For many purposes c o l l i s i o n s c a n be ignored.
Collisions
vi)
Calculational Techniques
Fourier Transform methods between configuration and field useful.
Fourier Transform m e t h o d s at l e a s t initially appear less useful.
r
Usually short range; r' potentials or shielded Coulomb.
essential.
M o r e c l o s e l y r e l a t e d to o u r a p p r o a c h a r e s t a t i s t i c a l m e c h a n i c a l c a l c u l a t i o n s o n l a r g e a s s e m b l i e s of a t o m s o r m o l e c u l e s u s i n g c l a s s i c a l m e c h a n i c s to f o l l o w the t r a j e c t o r i e s . W h i l e m o s t w o r k has u s e d v e r y s i m p l i f i e d p o t e n t i a l s , s u c h as h a r d spheres, m o r e recently r e s e a r c h has begun with potentials w h i c h a r e q u i t e i n the s p i r i t of t h o s e n e e d e d to c o n s i d e r m o r e c o m p l e x m o l e c u l a r p r o c e s s e s , f o r e x a m p l e the c e n t r a l f o r c e m o d e l f o r w a t e r b y L e m b e r g a n d S t i l l i n g e r (19) w h i c h a l l o w s f o r the p o s s i b i l i t y of d i s s o c i a t i o n . B. Computer. Our design for a h i e r a r c h i c a l , d i s t r i b uted, s e m i - p a r a i l el, pipelined computer network follows n a t u r a l l y a l o n g t h e h i s t o r i c a l p a t h of c o m p u t e r e v o l u t i o n . A s
24
COMPUTER
L o r i n (20) p o i n t s
NETWORKING
AND
CHEMISTRY
out,
" I t i s t h i s p r o c e s s of p e r c e i v i n g the e x i s t e n c e of s m a l l e r a n d s m a l l e r f u n c t i o n s a n d t h e n i m p l e m e n t i n g t h e m i n f u n c t i o n a l l y s p e c i a l i z e d u n i t s that i s the p r o c e s s of ' m a t u r a t i o n ' i n c o m p u t e r d e v e l o p ment. T h e r e d u c t i o n of a v i e w of a s y s t e m f r o m a n u n d i f f e r e n t i a t e d m a s s i n t o a c o l l e c t i o n of d i s c r e t e f u n c t i o n s i s the p r o c e s s b y w h i c h the c o m p u t e r s have matured. M u c h of t h i s h a s b e e n m a d e p o s s i b l e b y t e c h n o l o g y b u t m u c h of i t i s i n d e p e n d e n t . It i s i n t e r e s t i n g to note t h e r e i s a l w a y s a t h r e e - s t a g e c y c l e i n d e s i g n a d v a n c e : (1) R e c o g n i z e t h e f u n c t i o n . (2) I d e n t i f y t h e s t r u c t u r e t h a t c o u l d p e r f o r m i t . (3) B u i l d m o r e r e s o u r c e s i n t o t h i s s t r u c t u r e , i . e . elaborate it, until it evolves into a h i g h l y i n t e l l i gent a s y n c h r o n o u s s u b s y s t e m c a p a b l e of r e l i e v i n g the ' m a i n p a t h ' of c o n s i d e r a b l e b u r d e n . " T h i s is the d i r e c t i o n we have f o l l o w e d . A s s e v e r a l a u t h o r s h a v e i n d i c a t e d (21), h i e r a r c h i c a l s t r u c t u r e s , h i g h e r l e v e l s b e i n g c o m p o s e d of s i m i l a r s u b u n i t s t h e m s e l v e s c o m p o s e d of s m a l l e r s u b u n i t s , e t c . , a r e a n a t u r a l r e s u l t of the e v o l u t i o n of c o m p u t e r h a r d w a r e a n d s o f t w a r e , as w e l l as of the e v o l u t i o n of l i f e a n d of s o c i a l a n d e c o n o m i c organizations (including universities). M a n himself is a d i s t r i b u t e d p a r a l l e l p r o c e s s o r of i n f o r m a t i o n (22), " a c o l l e c t i o n of a s y n c h r o n o u s s u b p r o c e s s o r s w i t h h i g h l y d i s t r i b u t e d i n t e l l i gence t h r o u g h o u t the s u b s y s t e m " (20). M a n y p a r a l l e l p r o c e s s o r s have been proposed and a cons i d e r a b l e v a r i e t y b u i l t (23) f o r u s e i n p a t t e r n r e c o g n i t i o n , associative processing, optical processing, m a x i m u m likelih o o d c a l c u l a t i o n , s i g n a l p r o c e s s i n g a n d the s o l u t i o n of c o u p l e d d i f f e r e n t i a l e q u a t i o n s (24). O u r m a c h i n e , w h i c h w i l l be e m p l o y e d f o r the s o l u t i o n of the c o u p l e d d i f f e r e n t i a l e q u a t i o n s c o r r e s p o n d i n g to N e w t o n ' s S e c o n d L a w (and t h u s the n a m e N E W T O N ) f o r a s e t of i n t e r a c t i n g a t o m s , h a s s e v e r a l a n t e cedents. T h e y i n c l u d e the L o c k h e e d D i f f e r e n t i a l E q u a t i o n P r o c e s s o r ( 2 4 ) , I l l i a c I V a n d i t s S o l o m o n p r e d e c e s s o r s ( 2 3 , 24), a l t h o u g h I l l i a c I V s e e m s b e t t e r s u i t e d due to i t s l o c a l d a t a p a t h s t r u c t u r e to the s o l u t i o n of d i f f e r e n t i a l e q u a t i o n s i n v o l v i n g f i x e d n e i g h b o r s (or i n t e r c o m m u n i c a t i n g c e l l s ) r a t h e r t h a n to o u r p r o b l e m i n w h i c h the s p e c i f i c n e i g h b o r s w i t h w h i c h each a t o m m u s t c o m m u n i c a t e can be continually shifting. A c l o s e r
3.
WILSON
Molecular
25
Mechanics
r e s e m b l a n c e i s to the P a r a l l e l E l e m e n t P r o c e s s i n g E n s e m b l e ( P E P E ) b e i n g c o n s t r u c t e d f o r the A r m y A d v a n c e d B a l l i s t i c M i s s i l e Defense Agency in a project w h i c h has involved B e l l L a b s , Systems Development C o r p . , H o n e y w e l l and B u r r o u g h s (23). It i s a h i g h l y p a r a l l e l m a c h i n e c o n s i s t i n g o f a g e n e r a l p u r p o s e h o s t c o m p u t e r ( C D C 7600) a n d m a n y P r o c e s s i n g E l e m e n t s , e a c h of w h i c h c a n t r a c k a n i n c o m i n g m i s s i l e . It r e s e m b l e s N E W T O N i n that it r e q u i r e s v e r y fast floating point s p e e d s (~ 1 m i l l i o n i n s t r u c t i o n s p e r s e c o n d , M I P S ) i n e a c h P r o c e s s i n g E l e m e n t and that an i m p o r t a n t a s p e c t is s p a t i a l d i s c r i m i n a t i o n , the d i s t i n g u i s h i n g of w h i c h o b j e c t s a r e n e a r b y . It d i f f e r s i n t h a t t h e o b j e c t s a r e p r e s u m e d n o n - i n t e r a c t i n g . T h u s , the s t r u c t u r e i s s i n g l e i n s t r u c t i o n s t r e a m , m u l t i p l e data s t r e a m (true p a r a l l e l ) w i t h o u t n e e d f o r d i r e c t e l e m e n t to element c o m m u n i c a t i o n , w h i l e our atoms are interacting and e a c h a t o m i h a s i t s o w n s p e c i f i c f o r c e f u n c t i o n , ^F- ( r . . . J*]\j)W e m u s t t h e r e f o r e u s e a m u l t i p l e (but s i m i l a r ) i n s t r u c t i o n s t r e a m , m u l t i p l e data s t r e a m (semiparallel) distributed s t r u c t u r e and p r o v i d e f o r i n t e r c o m m u n i c a t i o n a m o n g the p r o cessing elements. In a d d i t i o n , P E P E u s e s a s s o c i a t i v e m e m o r y t e c h n i q u e s to d i s t i n g u i s h w h i c h o t h e r o b j e c t s a r e the n e a r n e i g h b o r s of e a c h o b j e c t , w h i l e , f o r r e a s o n s o f c o s t / p e r f o r m a n c e , w e p l a n to u s e a n a c t i v e d i s c r i m i n a t o r . O t h e r p a r a l l e l o r d i s t r i b u t e d s y s t e m s of i n t e r e s t a r e t h e Carnegie-Mellon Multi-Mini Processor (C.mmp), Korn s proposal for a multiple m i n i c o m p u t e r differential equation s o l v e r , and N e i l s e n ' s i m p l e m e n t a t i o n of s u c h a s y s t e m . C.mmp i s a s y m m e t r i c s e t o f u p t o 16 m i n i c o m p u t e r s ( D E C P D P - 1 1 ' s ) w i t h a n e q u i v a l e n t n u m b e r of m e m o r y u n i t s , a l l i n t e r c o n n e c t e d t h r o u g h a c r o s s - b a r s w i t c h so that any p r o c e s s o r c a n a c c e s s a n y m e m o r y a n d u p t o 16 s e p a r a t e a n d s i m u l t a n e o u s p r o c e s s o r m e m o r y connections are possible. It i s d e s i g n e d t o b e m u c h m o r e of a g e n e r a l p u r p o s e c o m p u t e r t h a n N E W T O N , a n d thus requires h a r d w a r e and software flexibility beyond our needs. O n the o t h e r h a n d , it i s not d e s i g n e d f o r l a r g e f l o a t i n g p o i n t number crunching, w h i c h is our need. K o r n (25) i n 1 9 7 2 p r o p o s e d a s y s t e m of s e v e r a l P D P 1 1 / 4 5 ' s w i t h f l o a t i n g p o i n t p r o c e s s o r s a n d s h a r e d m e m o r i e s f o r the o n - l i n e s o l u t i o n of coupled differential equations d e s c r i b i n g d y n a m i c a l s y s t e m s . It w a s d e s i g n e d a s a r e p l a c e m e n t f o r h y b r i d d i g i t a l - a n a l o g differential a n a l y z e r s , and would have been a worthy p r e c u r s o r t o the c o m p u t i n g e n g i n e p a r t of N E W T O N i f h e h a d b e e n a b l e to b u i l d i t . W h i l e w e c a n r u n m u c h f a s t e r , as w i l l be s e e n , 1
26
COMPUTER
NETWORKING
AND
CHEMISTRY
b e c a u s e of o u r s p e c i a l i z e d b a r r e l - r o l l d i s c r i m i n a t o r a n d f l o a t i n g p o i n t a r r a y p r o c e s s o r s , K o r n f o r e s a w m a n y of t h e a s p e c t s o f p a r a l l e l c o m p u t a t i o n a p p l i e d to c o u p l e d d i f f e r e n t i a l e q u a t i o n s o l v i n g w h i c h w e p l a n to i m p l e m e n t . A s y s t e m r e l a t e d te K o r n s w i l l be i m p l e m e n t e d at L o m a L i n d a U n i v e r s i t y b y N e i l s en i n the n e a r f u t u r e and a p p l i e d to c o u p l e d d i f f e r e n t i a l e q u a t i o n s y s t e m s (26). 1
C. Visual Interface. A l r e a d y i n the 1950's, i n r e a l time m i l i t a r y c o m m a n d and control systems, C R T display c o n s o l e s a n d a l i g h t g u n w e r e d e v e l o p e d (27). In the I960 s m o r e sophisticated v i s u a l d i s p l a y and i n t e r a c t i o n s y s t e m s w e r e d e s i g n e d , f o r e x a m p l e S u t h e r l a n d ' s " S k e t c h p a d " (28). Several groups have developed software and hardware for three d i m e n sional computer v i s u a l d i s p l a y , i n c l u d i n g d i g i t a l and h y b r i d graphics systems, a head mounted stereoscopic display which m o v e s w i t h t h e v i e w e r (29) a n d s e v e r a l v i s i b l e s u r f a c e a l g o r i t h m s a n d h a r d w a r e p r o c e s s o r s (30, 31). 1
T h e s e 3D v i s u a l output s y s t e m s s t i m u l a t e d the d e v e l o p m e n t of i n p u t s y s t e m s f o r c o m m u n i c a t i n g 3D p o s i t i o n to c o m p u t e r s , i n c l u d i n g the L i n c o l n W a n d s y s t e m u s i n g a n u l t r a s o n i c s i g n a l a n d 4 p o i n t m i c r o p h o n e s (32), the 3D s o n i c p e n a n d s t r i p m i c r o phone s y s t e m u s e d b y W i p k e at P r i n c e t o n to i n t e r a c t w i t h m o l e c u l a r i m a g e r y (33), s y s t e m s e m p l o y i n g r o t a t i o n a l a n d translational stages with r a d i a l or linear potentiometers (34), and a " V i c k e r s W a n d " s y s t e m u s i n g t h r e e r e t r a c t a b l e c o r d s (35) , s i m i l a r i n c o n c e p t t o t h e f o u r c o r d s y s t e m w e u s e f o r t h e " T o u c h y F e e l y " , our f i r s t touch interface. B u r t o n and Sutherland developed a s y s t e m ( " T w i n k l e Box") w h i c h a l l o w s the r e a l - t i m e m e a s u r e m e n t of m u l t i p l e 3 D p o s i t i o n s (36) . S m a l l l i g h t s a t t a c h e d t o a n o b j e c t ( w h i c h c a n f o r e x a m p l e be a d a n c i n g m a n ) f l a s h i n s e q u e n c e , and m u l t i p l e one d i m e n s i o n a l s c a n n e r s p i c k u p the p o s i t i o n s . We plan a related s y s t e m to p i c k u p b o t h p o s i t i o n a n d o r i e n t a t i o n w i t h o u r n e x t t o u c h i n t e r f a c e , " T o u c h y T w i s t y " , d e s i g n e d to a l l o w the u s e r to a s s e m b l e objects ( m o l e c u l e s ) w h i l e f e e l i n g t h e i r a n g u l a r and positional interactions. D. T o u c h I n t e r f a c e . In 1965 S u t h e r l a n d s u g g e s t e d t h a t a c o m p u t e r d i s p l a y s y s t e m should s e r v e as m a n y senses as p o s s i b l e if i t i s to p r o v i d e a " w i n d o w into the m a t h e m a t i c a l wonderland constructed i n computer m e m o r y " , and p r e d i c t e d t h e u s e f u l n e s s of a u g m e n t i n g s i g h t a n d s o u n d w i t h f o r c e d i s p l a y
3.
WILSON
Molecular
Mechanics
27
(37). H e s u g g e s t e d i m p l e m e n t a t i o n of c o m p u t e r c o n t r o l l e d kinesthetic presentation through joysticks and mechanical a r m s . T w o g r o u p s , B a t t e r a n d B r o o k s at the U n i v e r s i t y of N o r t h C a r o l i n a a n d N o l l at B e l l L a b s , f i r s t i m p l e m e n t e d t o u c h c o m munication with computers. B a t t e r a n d B r o o k s (38) b u i l t a n d p r o g r a m m e d G R O P E - 1 , an on-line interactive computer display s y s t e m i n v o l v i n g two d i m e n s i o n a l input to the c o m p u t e r and b o t h v i s u a l and f o r c e f e e d b a c k to the u s e r . G R O P E - 1 was a p i l o t s y s t e m h a v i n g o n l y t w o d e g r e e s of f r e e d o m , χ a n d y , a n d w a s d e s i g n e d to t e s t the c o n c e p t of k i n e s t h e t i c o u t p u t b y e x e r t i n g p r o g r a m m a b l e f o r c e s on the f i n g e r s as one m o v e d a k n o b i n a p l a n e , thus e n a b l i n g the u s e r to e x a m i n e e l e m e n t a r y force fields by e x p e r i e n c i n g p o s i t i o n dependent f o r c e s p r o p o r t i o n a l to f o r c e s that w o u l d be e x e r t e d on a p a r t i c l e i n a f i e l d . T h e u s e r c o u l d b o t h c h a n g e the p o s i t i o n of a p a r t i c l e i n c o n c e p t u a l s p a c e a n d f e e l the f o r c e n e e d e d to m o v e the p a r t i c l e i n the f i e l d . In a d d i t i o n to G R O P E - 1 , B a t t e r a n d B r o o k s d i s c u s s the i m p l e m e n t a t i o n of k i n e s t h e t i c d i s p l a y t h r o u g h a m e c h a n i c a l a r m , w h i c h they h a v e c o n t i n u e d to d e v e l o p . N o l l (34) d u r i n g t h e s a m e p e r i o d b u i l t a n d t e s t e d a 3 D touch c o m m u n i c a t i o n s y s t e m , r e p o r t i n g on it i n his thesis i n 1971. Orthogonally m o v i n g stages are used, culminating i n a knob g r a s p e d b y the h a n d . P o s i t i o n is p i c k e d off b y t h r e e l i n e a r potentiometers and force exerted by three torque m o t o r s linking the s t a g e s . S o f t w a r e w a s w r i t t e n i n o r d e r to s i m u l a t e o b j e c t s and s u r f a c e s ( s p h e r e , c u b e , s p h e r e w i t h i n a cube). N o l l d i s c u s s e s m a n y a s p e c t s of t o u c h c o m m u n i c a t i o n , f r o m p r a c t i c a l to p h i l o s o p h i c a l , a n d s u g g e s t s a v a r i e t y of a p p l i c a t i o n s i n c l u d i n g s t u d i e s i n p e r c e p t u a l p s y c h o l o g y of c l a s h b e t w e e n v i s i o n and touch, investigations b y m o t o r - s k i l l p s y c h o l o g i s t s , l a t c h i n g onto o b j e c t s b y t o u c h as a m e a n s of i m p r o v i n g v i s u a l d i s p l a y s , t e s t i n g of m a n u a l d e x t e r i t y , e d u c a t i o n , d e s i g n of o b j e c t s s u c h as t e l e p h o n e s w i t h p r o p e r " f e e l " to the h a n d s , a i d to the b l i n d , a n d m a n - t o - m a n t o u c h c o m m u n i c a t i o n (for e x a m p l e , a cloth purchaser in New Y o r k remotely feeling a manufacturer's cloth in Tokyo). II.
System
Design
O u r t a s k i s to f i n d the set of f o r c e f u n c t i o n s · · · -£n^' i = 1 to Ν w h i c h d e s c r i b e the i n t e r a t o m i c f o r c e s as f u n c t i o n s o f a t o m i c p o s i t i o n s jc\ o f Ν a t o m s i n a b i o m o l e c u l a r s y s t e m a n d then integrate Newton' s Second L a w ,
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=
m. ι
-1
^(Εχ···
* >. N
NETWORKING
i=
AND
CHEMISTRY
1 to Ν
t o g i v e t h e t r a j e c t o r i e s of t h e a t o m s w i t h a d d i t i o n a l i n i t i a l s t e e r i n g f o r c e s a d d e d b y the u s e r t h r o u g h the t o u c h i n t e r f a c e . C a r r y i n g out the t a s k c a n b e d i v i d e d i n t o t w o p a r t s : f i n d i n g the f o r c e functions and i n t e g r a t i n g the equations, c h e m i s t r y and computation. A. Chemistry. T h e m o s t d i f f i c u l t q u e s t i o n , one w i t h m a n y c l u e s a n d a d e a r t h of a c c u r a t e a n s w e r s , i s , " w h a t a r e reasonable interatomic force functions which describe inter atomic interactions?" T h e i r nature is w e l l described by L i f s o n a n d W a r s h e l l (39). " I t i s c o m m o n l y a s s u m e d that the u s e of e m p i r i c a l and s e m i - e m p i r i c a l energy functions i n c o n f o r m a t i o n a l a n a l y s i s is ' c l a s s i c a l , i n c o n t r a d i s t i n c t i o n to q u a n t u m mechanical calculations. W e suggest that the b a s i c d i f f e r e n c e is that the l a t t e r i s a d e d u c t i v e m e t h o d , s e e k i n g to p r e d i c t o b s e r v a b l e p h e n o m e n a f r o m a f u n d a m e n t a l l a w (the S c h r o d i n g e r e q u a t i o n ) , w h i l e t h e f o r m e r is an inductive method, seeking a c o m m o n analytical r e p r e s e n t a t i o n to a l a r g e s e t of o b s e r v a b l e p h e n o m e n a . In fact, t h e r e is nothing ' c l a s s i c a l ' i n these functions, as they a r e not d e d u c e d f r o m c l a s s i c a l p h y s i c s . They m a y j u s t as w e l l be c o n s i d e r e d as a n e m p i r i c a l r e p r e s e n t a t i o n of t h e B o r n - O p p e n h e i m e r a p p r o x i m a t i o n , a c c o r d i n g to w h i c h the g r o u n d s t a t e of m o l e c u l e s i s a c o n t i n u o u s f u n c t i o n of the a t o m i c c o o r d i n a t e s . " 1
T h e b a s i c a s s u m p t i o n w h i c h w e m a k e , one w h i c h i n d e e d i s t h e b a s i s of o u r g e n e r a l u n d e r s t a n d i n g of l a r g e r m o l e c u l e s , i s t h a t m o l e c u l e s to a r e a s o n a b l e d e g r e e of a c c u r a c y c a n be d e s c r i b e d h i e r a r c h i c a l l y , as a s s e m b l e d f r o m s u b u n i t s w h i c h at least approximately preserve their properties (including force f u n c t i o n d e s c r i p t i o n ) f r o m m o l e c u l e to m o l e c u l e . These subunits are usually functional groups or m o n o m e r s . (This division of m o l e c u l e s i n t o f u n c t i o n a l g r o u p s a n d m o n o m e r s i s so i n g r a i n e d i n u s as c h e m i s t s that i t f o r m s t h e b a s i s of o u r m o l e c u l a r n o m e n c l a t u r e . ) T h e c o r o l l a r y to t h i s a s s u m p t i o n i s that the
3.
WILSON
Molecular
Mechanics
29
f o r c e s w h i c h affect an a t o m are l o c a l , i n that t h e r e is s o m e s p h e r e w h i c h one c a n d r a w a r o u n d an a t o m , s u c h that the p o s i t i o n s of a t o m s o u t s i d e the s p h e r e h a v e a n e g l i g i b l e d i r e c t effect on the c e n t r a l a t o m . ( T h i s i s not to s a y t h e y d o n ' t i n d i r e c t l y affect i t b y a f f e c t i n g a t o m s i n s i d e the s p h e r e w h i c h i n t u r n a f f e c t the c e n t r a l a t o m . ) T h i s l o c a l i z a t i o n of i n t e r a t o m i c e f f e c t i s a t l e a s t i m p l i c i t i n o u r u s u a l a n a l y s e s of m o l e c u l a r s t r u c t u r e a n d o n l y f o r the c a s e of e x t e n d e d c o n j u gated s y s t e m s o r u n s h i e l d e d c h a r g e s i s the s p h e r e l i k e l y to be very large. T h e i m p l i c a t i o n i s that one c a n f i n d the f o r c e o n a p a r t i c u l a r a t o m i f one k n o w s the p o s i t i o n s a n d n a t u r e s of t h e o t h e r a t o m s w i t h i n i t s s p h e r e , i n d e p e n d e n t of t h e p o s i t i o n s of a l l the o t h e r a t o m s o u t s i d e the s p h e r e . T h u s one c a n h o p e to d e v e l o p l i b r a r i e s of s u b u n i t f o r c e f u n c t i o n s w h i c h c a n p r o v i d e at l e a s t s t a r t i n g p o i n t s f o r f o r c e f u n c t i o n d e s c r i p t i o n s of l a r g e r m o l e c u l e s . T h e r e a r e two m a j o r paths one c a n take to t r y to f i n d these force functions: calculate t h e m or deduce t h e m f r o m experimental measurements. 1. Forces - Theoretical. S i n c e the q u a n t u m r e v o l u t i o n i n the late 1920's and e a r l y 1930's, w e h a v e k n o w n h o w i n t h e o r y to c a l c u l a t e the n e e d e d i n t e r a t o m i c p o t e n t i a l (or f o r c e ) f u n c t i o n s (4). Despite the i m m e n s e growth i n c o m p u t e r power i n the p a s t two d e c a d e s , w e s t i l l cannot p r a c t i c a l l y h a n d l e the f u l l ab i n i t i o f o r c e f u n c t i o n c a l c u l a t i o n s f o r l a r g e r m o l e c u l e s even on the l a r g e s t c o m p u t e r s . We can, however, handle subu n i t s l i k e the f u n c t i o n a l g r o u p s and s i m p l e r m o n o m e r s to reasonable a c c u r a c y , and this approach has been and c e r t a i n l y w i l l c o n t i n u e to be a s i g n i f i c a n t s o u r c e of f o r c e d a t a . In a d d i t i o n , it h a s m o r e r e c e n t l y b e c o m e c l e a r that the f o r c e s b e t w e e n n o n - c h e m i c a l l y i n t e r a c t i n g a t o m s and g r o u p s of atoms can quite reasonably be d e r i v e d f r o m l o c a l i z e d c a l c u l a t i o n s w h i c h r e q u i r e o n l y the w a v e f u n c t i o n s of the s e p a r a t e a t o m s o r g r o u p s as i n p u t (40, 41). This is an i m p o r t a n t step f o r w a r d , b e c a u s e it r e d u c e s a p r o b l e m w h i c h s c a l e d as N ^ , i n w h i c h Ν i s the n u m b e r of i n t e r a c t i n g a t o m s o r g r o u p s , to one s c a l i n g as N . In a d d i t i o n to the ab i n i t i o a p p r o a c h e s , t h e r e a r e v a r i o u s s e m i - e m p i r i c a l theoretical approaches w h i c h can be useful. F i r s t , t h e r e a r e s e m i - e m p i r i c a l m e t h o d s f o r s o l v i n g the q u a n t u m m e c h a n i c a l equations t h e m s e l v e s . S e c o n d , the l o n g r a n g e r e g i o n of i n t e r a t o m i c f o r c e s i s f a i r l y w e l l u n d e r s t o o d , f o r
30
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e x a m p l e C o u l o m b r~ f o r charge interaction and V a n der W a a l s r " ^ for L o n d o n d i s p e r s i o n f o r c e s , and we can calculate such l o n g r a n g e f o r c e s at l e a s t a p p r o x i m a t e l y f r o m c h a r g e d i s t r i butions and p o l a r i z a b i l i t i e s . 2. F o r c e s - E x p e r i m e n t a l . M o s t of o u r f o r c e i n f o r m a t i o n , h o w e v e r , w i l l h a v e to c o m e at t h i s s t a g e f r o m p o s t u lating reasonable adjustable force functions and then tuning t h e m to m a t c h e x p e r i m e n t a l o b s e r v a t i o n s of p a r a m e t e r s w h i c h depend upon these forces. S u c h methodology has been the b a s i s of m u c h of the c o n f o r m a t i o n a l c a l c u l a t i o n w o r k i n o r g a n i c c h e m i s t r y a n d p o l y m e r c h e m i s t r y (6, T, > ο S
i)
t h o s e too f a r a w a y to d i r e c t l y a f f e c t i t (most other atoms i n l a r g e r molecules),
ϋ)
those w h o s e effect c a n be t r e a t e d b y a two b o d y i n t e r a c t i o n w h i c h d e p e n d s o n l y on the c l a s s to w h i c h e a c h of the t w o a t o m s b e l o n g s (for e x a m p l e nonbonded i n t e r a c t i o n b e t w e e n an H a t o m on aliphatic C and a ketone Ο atom),
iii)
t h o s e w h i c h a r e s p e c i f i c a l l y b o n d e d to the a t o m i n question by bonds w h i c h don't change t h e i r f o r c e f u n c t i o n c h a r a c t e r d u r i n g the c h e m i c a l p r o c e s s , and
iv)
t h o s e a t o m s w h o s e i n t e r a c t i o n w i t h the a t o m in question changes i n force function nature a s a f u n c t i o n of t h e p o s i t i o n s of o t h e r a t o m s , in other words full multibody interactions, f o r e x a m p l e bond w e a k e n i n g and f o r m a t i o n due to the a p p r o a c h of o t h e r a t o m s at a c t i v e s i t e s in chemical reactions.
eu
3· eu u m &D
•Η
CO eu
u υ
S o m e of the a b o v e c l a s s i f i c a t i o n s c h e m e c a n b e r e f l e c t e d i n the c o m p u t e r h a r d w a r e and s o f t w a r e i n s u c h a w a y as to vastly increase its calculational speed B. Computational System. We are now i n an era i n w h i c h i f one c a n u n d e r s t a n d the s t r u c t u r e of a c o m p u t a t i o n a l p r o b l e m , one c a n often d e s i g n a s p e c i a l i z e d c o m p u t a t i o n a l s y s t e m w h i c h d i s t r i b u t e s the v a r i o u s p a r t s of the c a l c u l a t i o n a m o n g v e r y e f f i c i e n t s u b u n i t s , s u c h that the c o m p u t a t i o n c a n be h a n d l e d m u c h f a s t e r and m u c h l e s s e x p e n s i v e l y than w i t h a general purpose computer. F o r example, our molecular dynamics computation has t h r e e l e v e l s w h i c h s c a l e q u i t e d i f f e r e n t l y w i t h N , the n u m b e r of atoms. T h e f i r s t i s the e x p l o r a t i o n a n d c h o i c e of i n i t i a l c o n d i t i o n s ( c o o r d i n a t e s a n d v e l o c i t i e s o r m o m e n t a ) of the a t o m s , w h i c h s c a l e s as V ^ , i n w h i c h V i s the v o l u m e of p h a s e s p a c e to be e x p l o r e d f o r e a c h a t o m . T h i s s e a r c h s p a c e of i n i t i a l
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a t o m i c c o n d i t i o n s i n c r e a s e s as the N t h p o w e r , and a b r u t e f o r c e approach quickly becomes unmanageable for any computer. The c h o i c e of i n i t i a l c o n d i t i o n s i s t h u s m u c h b e t t e r h a n d l e d b y c l o s e l y i n v o l v i n g a h u m a n c h e m i s t and r e l y i n g on h i s c a l i b r a t e d i n t u i t i o n , h i s s p a t i a l , g e o m e t r i c a l s e n s e of w h a t i s c h e m i c a l l y appropriate. T h i s i s the r e a s o n f o r the c l o s e a t t e n t i o n to v i s u a l and touch interfaces: to i n v o l v e the h u m a n c h e m i s t i n a c o n venient, comfortable symbiotic relationship with a computer s y s t e m i n s u c h a w a y as to g r e a t l y m a g n i f y h i s a b i l i t y to s o l v e problems in molecular mechanics. S e c o n d i s the d i s c o v e r y of w h i c h a m o n g the o t h e r N - l a t o m s a r e n e a r enough to the a t o m u n d e r c o n s i d e r a t i o n to d i r e c t l y c o n t r i b u t e to the f o r c e o n i t . T h i s p a r t of t h e p r o b l e m s c a l e s as N ^ , a n d f o r l a r g e r m o l e c u l e s q u i c k l y d o m i n a t e s the computational load. A s shown below, we have designed a s p e c i a l b a r r e l - r o l l d i s c r i m i n a t o r w h i c h c a n s o l v e t h i s p a r t of the c o m p u t a t i o n so r a p i d l y that it no l o n g e r r e p r e s e n t s a m a j o r d i f f i c u l t y , at l e a s t f o r the r a n g e of Ν u p to a t h o u s a n d w h i c h w e are now considering. T h i r d , g i v e n the s e t of n e i g h b o r i n g a t o m s w h i c h a r e i m p o r t a n t i n d e t e r m i n i n g the f o r c e on the i t h a t o m , w e m u s t e v a l u a t e the f o r c e f u n c t i o n (r^ . . . f o r the i t h a t o m a n d i n t e g r a t e t h e p o s i t i o n j : - of t h e a t o m o n e s t e p f o r w a r d i n t i m e . T h i s c a l c u l a t i o n f o r a l l Ν a t o m s s c a l e s as N , and i s m o s t c o n v e n i e n t l y c a r r i e d out on a g e n e r a l p u r p o s e c o m p u t e r s i n c e f o r d i f f e r e n t a t o m s t h e JT^ c a n h a v e a v a r i e t y of a l g o r i t h m i c f o r m s . T h i s p a r t of t h e c a l c u l a t i o n w e t u r n o v e r t o a n e x p a n d a b l e s e t of p a r a l l e l a n d p i p e l i n e d f l o a t i n g p o i n t a r r a y p r o c e s s o r s w i t h c o n t r o l , coordination and c o m m u n i c a t i o n handled by a s u p e r v i s o r y c o m p u t e r , as i s s h o w n i n F i g . 1. A l l t h e p a r t s of t h i s m a n - m a c h i n e s y m b i o s i s m u s t w o r k s m o o t h l y t o g e t h e r , to e f f e c t t h e s t e e r e d s o l u t i o n to the c o u p l e d differential equations. It i s a n i n i t i a l v a l u e p r o b l e m w i t h m a n s u p p l y i n g the i n i t i a l v a l u e s i n r e a l h u m a n t i m e and r e l y i n g on r a p i d r e s p o n s e f r o m the m a c h i n e to g i v e h i m f e e d b a c k so he c a n t r i m h i s i n p u t . T h e m a c h i n e m u s t r e l y on m a n to h a n d l e the i n i t i a l v a l u e s e l e c t i o n (the N t h p o w e r p r o b l e m ) w h i c h i s b e y o n d m a c h i n e c a p a b i l i t y , a n d the m a n m u s t r e l y o n the m a c h i n e to s h o w h i m t h e c a l c u l a t e d r e s u l t s of h i s c h o i c e r a p i d l y e n o u g h s o h e c a n u s e the r e s u l t s to s t e e r the m o l e c u l e s i n t o the d e s i r e d initial pathway. W h e n the h u m a n c h e m i s t p u s h e s on c e r t a i n a t o m s , t h e r e s t of t h e m o l e c u l e m u s t f o l l o w , a n d t h u s t h e d i f f e r e n t i a l equations m u s t be s o l v e d r a p i d l y on a h u m a n t i m e
3.
WILSON
Molecular
Mechanics
33
scale. O u r p r e l i m i n a r y t e s t s i n d i c a t e t h a t to m a t c h m a n ' s v i s u a l a n d t o u c h p e r c e p t i o n s , the t i m e to s o l v e one s t e p i n t h e i n t e g r a t i o n s h o u l d be a m a x i m u m of a p p r o x i m a t e l y 0. 1 s e c o n d , and this sets m i n i m u m p e r f o r m a n c e standards for our m a c h i n e . 1. Molecular Manipulation - Touch Interface. Touchy F e e l y I, w h i c h i n p u t s 3D p o s i t i o n to a c o m p u t e r a n d o u t p u t s 3 D f o r c e , h a s b e e n b u i l t . T o u c h y F e e l y II, w h i c h i n p u t s 3D f o r c e and outputs 3D p o s i t i o n , i s b e i n g d e s i g n e d , a l o n g w i t h T o u c h y T w i s t y I w h i c h w i l l i n p u t t h r e e d i m e n s i o n s of p o s i t i o n a n d t h r e e of o r i e n t a t i o n a n d o u t p u t t h r e e d i m e n s i o n s of f o r c e a n d t h r e e of torque. T h e s e touch i n t e r f a c e s s h o u l d be sufficient f o r m o s t molecular applications. 2. Molecular P o r t r a y a l - Visual Interface. The v i s u a l i n t e r f a c e , the E v a n s & S u t h e r l a n d P i c t u r e S y s t e m , i s i n o p e r a t i o n and the software f o r this a p p l i c a t i o n is r u n n i n g . The P i c t u r e S y s t e m a l l o w s u s to b u i l d 3D m o l e c u l a r i m a g e s , to c o n t r o l a t o m a n d b o n d p o s i t i o n s f r o m e x t e r n a l c o m p u t e r s l i k e N E W T O N , to t r a n s l a t e and r o t a t e the m o l e c u l e s , to z o o m into s e l e c t e d p o r t i o n s , c l i p p i n g and w i n d o w i n g to see o n l y the c h o s e n r e g i o n , and to v i e w the m o l e c u l e s i f d e s i r e d i n p e r s p e c t i v e , s t e r e o a n d color. 3. Distributed M u l t i p r o c e s s o r N e t w o r k . A s shown in F i g . 1, the h a r d w a r e to i n t e g r a t e the c o u p l e d d i f f e r e n t i a l equations d i v i d e s into t h r e e p a r t s : the s u p e r v i s o r y p r o c e s s o r , the b a r r e l - r o l l d i s c r i m i n a t o r a n d a set of f l o a t i n g p o i n t processors. a) Supervisory Processor. The s u p e r v i s o r y p r o c e s s o r w i l l be r e s p o n s i b l e f o r s y s t e m s s o f t w a r e , f o r l o a d i n g and i n t e r r o g a t i n g the b a r r e l - r o l l d i s c r i m i n a t o r , f o r c o m p i l i n g and l o a d i n g m i c r o c o d e for the floating point a r r a y p r o c e s s o r s , for l o a d i n g t h e i r d a t a , f o r s u p e r v i s i n g c o m m u n i c a t i o n a m o n g the b a r r e l - r o l l d i s c r i m i n a t o r , the f l o a t i n g p o i n t p r o c e s s o r s , the v i s u a l and t o u c h i n t e r f a c e s and the h i e r a r c h i c a l s y s t e m and its n e t w o r k , a n d f o r c a r r y i n g out o r s u p e r v i s i n g o n - l i n e s u b s i d i a r y c a l c u l a t i o n s b a s e d on the t r a j e c t o r i e s . It n e e d s t o b e a r e l a t i v e l y f a s t p r o c e s s o r , to h a v e s u f f i c i e n t f a s t a n d a c c e s s i b l e m e m o r y to be a b l e to t r a n s f e r m i c r o c o d e a n d d a t a r a p i d l y e n o u g h to k e e p the d i s c r i m i n a t o r and a r r a y p r o c e s s o r s b u s y , a n d to h a v e enough f i x e d h e a d d i s k o r e q u i v a l e n t m e m o r y to r a p i d l y
34
COMPUTER
NETWORKING
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CHEMISTRY
store t r a j e c t o r y i n f o r m a t i o n for later o f f - l i n e analysis if desired, a n d a w a y , p e r h a p s a f l o p p y d i s k , to c o n v e n i e n t l y l o a d a n d s t o r e individual p r o g r a m s and data. b) D i s c r i m i n a t o r . A s shown i n F i g . 2, w h e n the n u m b e r of a t o m s , N , b e c o m e s s i z e a b l e , m o s t of the a r i t h m e t i c o p e r a t i o n s a r e t a k e n u p b y t h e p r o c e s s of l o c a t i n g the s u b s e t of a t o m s c l o s e enough to the a t o m u n d e r c o n s i d e r a t i o n to d i r e c t l y c o n t r i b u t e to the f o r c e it f e e l s . In a d y n a m i c s y s t e m the i d e n t i t i e s of t h e n e a r n e i g h b o r s c a n be c o n t i n u a l l y c h a n g i n g . We n e e d o n l y a f e w o u t of the s e v e r a l h u n d r e d o r a t h o u s a n d a t o m s for further consideration. The selection task, w h i c h increases as ~ Ν , s o o n d o m i n a t e s p r o c e s s i n g t i m e . T h i s p r o b l e m c o u l d b e h a n d l e d i n s e v e r a l w a y s : i) b y building an appropriate associative m e m o r y , ii) by building a s p e c i a l p r o c e s s o r , and iii) by being m o r e sophisticated and c o m p l e x i n the p r o g r a m m i n g to take into account " f r a m e c o h e r e n c e " , a s i n the v i s i b l e s u r f a c e p r o b l e m i n g r a p h i c s (30), t r y i n g to f i n d w a y s to u s e the f a c t that the i n t e g r a t i o n f r a m e s a r e n o t i n d e p e n d e n t so that w e d o n ' t h a v e to d o t h e w h o l e d i s c r i m i n a t i o n job o v e r a g a i n at e a c h s t e p . T h e s e c o n d a l t e r n a t i v e , b u i l d i n g a s p e c i a l p r o c e s s o r to do the d i s c r i m i n a t i o n , a p p e a r s the m o s t c o s t e f f e c t i v e . If w e a r r a n g e the c o o r d i n a t e d a t a ( p r o b a b l y c o n v e r t e d to f i x e d p o i n t n u m b e r s w h i c h w e n e e d to do a n y w a y f o r the P i c t u r e S y s t e m ) i n the f o r m of a t a b l e ,
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we can then load it into shift r e g i s t e r s or i n c r e m e n t a l l y a d d r e s s e d m e m o r y and s e q u e n t i a l l y p r o c e s s it to d i s c o v e r w h i c h a t o m s a r e w i t h i n a c u b e o f s i z e x^ ± Δ, y^ ± Δ, z^ ± Δ c e n t e r e d o n a t o m i a t (x^, y ^ , z^). A s a f i r s t a l t e r n a t i v e , w e c a n r o l l the table into a b a r r e l w i t h Xj^ f o l l o w i n g Xj,, yj^ f o l l o w i n g y^ a n d z j ^ f o l l o w i n g Z j a n d r o t a t e t h e b a r r e l b y s h i f t i n g t h e s h i f t r e g i s t e r s a r o u n d a h o r i z o n t a l a x i s s o t h a t t h e ( X J , y - , Zj) p a s s b y a set of p a r a l l e l c o m p a r a t o r s w h i c h c h e c k s i m u l t a n e o u s l y to see i f X j , y j a n d Zj f a l l w i t h i n the s i x l i m i t s . S e v e r a l s e t s of p a r a l l e l c o m p a r a t o r s l o a d e d w i t h c o o r d i n a t e s of t h e c u b e s s u r r o u n d i n g d i f f e r e n t i a t o m s c a n a l l s i m u l t a n e o u s l y b e f e d the
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Mechanics
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