PHONONS IN THE DNA DOUBLE HELIX

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PHONONS IN THE DNA DOUBLE HELIX

E. Prohofsky, L. van Zandt, M. Kohli, K. Lu, M. Mei, B. Putman

To cite this version:

E. Prohofsky, L. van Zandt, M. Kohli, K. Lu, M. Mei, et al.. PHONONS IN THE DNA DOUBLE HE- LIX. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-560-C6-562. �10.1051/jphyscol:19816162�.

�jpa-00221240�

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JOURNAL DE PHYSIQUE

CoZZoque C6, s u p p Z h e n t au n012, Tome 42, d6cembre 1981 page c6-560

PHONdNS I N THE DNA DOUBLE HELIX*

E.W. Prohofsky, L.L. Van Zandt, M. Kohli, K.C. Lu, M.N. Mei and B. Putman Dept. o f P h y s i c s , Pw,&e U n i v e r s i t y , W e s t L a f a y e t t e , I N 47907, U.S.A.

A b s t r a c t . - We have c a l c u l a t e d a model f o r t h e phonon modes of t h e DNA double h e l i x . We have used t h e s e modes i n a number of a p p l i c a t i o n s t o b i o l o g i c a l problems which u s e l a t t i c e concepts such a s s o f t modes, l o c a l modes and quasi- momen tum

.

1. Phonons.- The double h e l i x is a long c h a i n polymer made of u n i t s c a l l e d b a s e p a i r s . There a r e f o u r p o s s i b l e b a s e p a i r u n i t s and t h e s e u n i t s c o n t a i n two hydrogen bonded b a s e s and two backbone segments. The backbone segments a r e i d e n t i c a l . DNA can b e produced i n which t h e b a s e p a i r s have a r e p e a t i n g s t r u c t u r e . For long polymer DNA's a screw a x i s o p e r a t i o n i s a symmetry o p e r a t i o n , and t h e v i b r a t i o n a l normal modes can b e c h a r a c t e r i z e d a s t r a v e l i n g wave phonon bands. We have used s t a n d a r d l a t t i c e dynamics methods t o c a l c u l a t e t h e s e phonon bands. The polymers can c a r r y o u t many b i o l o g i c a l f u n c t i o n s and one can l e a r n much about t h e s e mechanisms by s t u d y i n g t h e polymers.

The u n i t c e l l i n t h e double h e l i x i s s t i l l l a r g e . We have used a common ap- proximation which assumes t h a t a l l hydrogen atoms a r e r i g i d l y bound t o t h e i r bonded atom. T h i s reduced t h e number of d e g r e e s of freedom by about h a l f , Even s o i n t h e s i m p l e s t polymers t h e s e c u l a r determinant i s : 120 X 120. More complicated homo- polymers e x i s t i n which t h e r e p e a t i n g u n i t c e l l h a s s e v e r a l b a s e p a i r s and t h e ma- t r i c e s h e r e a r e s e v e r a l times 120 X 120.

2. Force Constants.- An i n i t i a l e s t i m a t e of t h e f o r c e c o n s t a n t s was taken from r e - f i n e d v a l u e s f o r t h e s e p a r a t e chemical e n t i t i e s which make up t h e b a s e s , backbone, e t c . The c h o i c e of c o n s t a n t s followed t h e t r a d i t i o n a l v a l e n c e f o r c e f i e l d c h o i c e s . C a l c u l a t i o n s were made and t h e f o r c e f i e l d was r e f i n e d by f i t t i n g t o Raman and in- f r a r e d d a t a on t h e v i b r a t i o n a l modes of t h e h e l i x . The s i z e of t h e u n i t c e l l re- q u i r e d t h e development of new refinement procedures. The Raman and i n f r a r e d d a t a were l i m i t e d t o f r e q u e n c i e s above 200-300 cm -1 and only f a i r l y s t r o n g f o r c e con-

s t a n t s such a s compression and a n g l e bend c o n s t a n t s could b e r e f i n e d w i t h any con- f i d e n c e . I n a d d i t i o n t o t h e v a l e n c e f o r c e f i e l d c o n s t a n t s which a r e t i e d t o chemi- c a l bonds and l i n k nearby atoms, we have a l s o s t u d i e d "nonbonded" i n t e r a c t i o n s . These i n t e r a c t i o n s a r e important i n determining t h e conformation of t h e h e l i x . The a c o u s t i c v e l o c i t y a l o n g t h e h e l i x was determined by B r i l l o u i n s c a t t e r i n g . This v e l - o c i t y was f i t t e d f o r s e v e r a l models of t h e nonbonded f o r c e s . The r e s u l t s i n d i c a t e d

* T h i s work s u p p o r t e d by NSF DMR 7 8 2 0 6 0 2 , N I H GK 2 4 4 4 3 , FDA F D 0 0 9 4 9 and USAF S33615-78-D-0617.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19816162

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t h a t long range ( e l e c t r o s t a t i c l i k e ) f o r c e s were needed t o e x p l a i n t h e observed v e l o c i t y . These long range f o r c e s have a l s o been i n c o r p o r a t e d i n our c a l c u l a t i o n s of t h e phonon bands of t h e double h e l i x .

3 . S o f t Modes.- Conformation changes p l a y an important r o l e i n b i o l o g i c a l pro-

c e s s e s . We have used t h e method of s o f t mode a n a l y s i s t o e x p l o r e t h e o n s e t of conformation change. The double h e l i x undergoes a B -+ A conformation change when t h e p o l a r n a t u r e of i t s environment i s reduced. We have c a l c u l a t e d t h e e f f e c t of r e - duced p o l a r s h i e l d i n g on our e l e c t r o s t a t i c nonbonded i n t e r a c t i o n s and found t h a t a s o f t mode develops i n one DNA polymer t h a t does undergo t h e conformation change.

No s o f t mode developed i n a polymer t h a t does n o t undergo t h e t r a n s i t i o n . The s o f t mode displacements were a good p r e d i c t o r of t h e d i s p l a c i v e changes i n t h e t r a n s i - t i o n .

4. Melting.- I n some b i o l o g i c a l p r o c e s s e s t h e base message of DNA i s p a d . This r e q u i r e s a p a r t i a l s e p a r a t i o n of t h e two s t r a n d s and t h i s i s c a l l e d m e l t i n g of t h e double h e l i x . Using our c a l c u l a t e d e i g e n v a l u e s and e i g e n v e c t o r s we can p l o t t h e amplitude of t h e s t r e t c h of t h e hydrogen bonds t h a t hold t h e s t r a n d s t o g e t h e r a s a f u n c t i o n of temperature f o r s e v e r a l DNA polymers. We have e s t a b l i s h e d a n e m p i r i c a l Lindeman's law of h e l i x m e l t i n g based on t h e s e amplitudes and comparisons of observed m e l t i n g temperatures. We b e l i e v e t h a t t h i s can be used t o e x p l o r e whether phonon emission by enzymes can i n f l u e n c e l o c a l i z e d m e l t i n g w i t h o u t t h e c r e a t i o n and d i s r u p t i o n of s t r o n g chemical bonds. The modes involved i n s t r e t c h i n g t h e H-bonds a r e a t z 70 cm-' i n our c a l c u l a t i o n s .

5 . Local Modes.- The double h e l i x h a s many s p e c i a l s i t e s which a c t a s i n i t i a t o r s and t e r m i n a t o r s of r e a d i n g p r o c e s s e s . The p r o b a b i l i t y i s high t h a t t h e s e r e g i o n s have unique dynamic p r o p e r t i e s which can b r i n g about a l t e r e d conformations o r enhanced tendancy t o m e l t . Unique dynamic p r o p e r t i e s can on a s i m p l e r l e v e l a i d i n r e c o g n i t i o n by enzymes. By assuming t h e unique f e a t u r e t o be an i m p u r i t y i n an o t h e r w i s e p e r f e c t l a t t i c e t h e l o c a l mode Green f u n c t i o n method can be used t o d e t e r - mine t h e l o c a l modes a s s o c i a t e d w i t h t h e unique f e a t u r e s . We have c a r r i e d o u t a l o c a l mode a n a l y s i s of t h e terminus of a h e l i x by p u t t i n g i n t h e n e g a t i v e v a l u e s f o r a l l t h e f o r c e c o n s t a n t s t h a t connect a p a r t i c u l a r two b a s e p a i r s , End modes were found which were l o c a l i z e d t o t h e f i r s t few b a s e p a i r s from t h e terminus. The hydrogen bond s t r e t c h modes were e f f e c t e d and t h e r n s amplitude was : 2 times t h a t f o r a c e n t r a l b a s e p a i r i n d i c a t i n g an enhanced tendancy t o i n i t i a t e m e l t i n g from a terminus.

6 . Quasi-Momentum Conservation.- I n many b i o l o g i c a l p r o c e s s e s enzymes move a l o n g t h e double h e l i x . We have been i n t e r e s t e d i n what can be l e a r n e d about such pro- c e s s e s by a n a l y z i n g t h e way i n which r e a l momentum and quasi-momentum a r e conser- ved. One should be a b l e t o d e s c r i b e t h e p r o c e s s e s of p r o p u l s i o n i n terms of pro- c e s s e s by which enzymes emit phonons i n t o t h e h e l i x . One v e r y i n t e r e s t i n g b u t f a r o u t s p e c u l a t i o n h a s a r i s e n i n t h i s c o n t e x t . I n our c a l c u l a t i o n s on s e v e r a l DNA

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C6-562 JOURNAL DE PHYSIQUE

polymers we f i n d t h a t a few bands occur which have l a r g e amplitude of H-bond s t r e t c h a s s o c i a t e d w i t h melting. These modes have n e g a t i v e group v e l o c i t y a s w e l l . We have proposed t h a t t h e emission of wave p a c k e t s i n t h e s e bands by c e r t a i n en-

zymes may b e r e s p o n s i b l e f o r both t h e p r o p u l s i o n of t h e enzymes a s w e l l a s a i d i n g i n m a i n t a i n i n g and propagating a melted r e g i o n of h e l i x n e a r t h e enzyme. These phonons e m i t t e d p r e f e r e n t i a l l y i n t h e forward d i r e c t i o n would both i n c r e a s e t h e H-bond s t r e t c h amplitude and cause a forward r e c o i l i n t h e e m i t t i n g enzyme due t o t h e n e g a t i v e group v e l o c i t y . From t h e c a l c u l a t e d band energy one can e s t i m a t e t h e maxi- mum momentum v s energy and v e r y s m a l l amounts of energy c a n g i v e r i s e t o more t h a n enough motive power. The energy needed is much l e s s than energy known t o be de- graded d u r i n g p r o c e s s e s a s s o c i a t e d w i t h enzyme motion i n which h i g h energy bonds a r e d i s s o c i a t e d and lower energy chemical bonds formed.

7 . I n t e r a c t i o n w i t h Surroundings.- The double h e l i x i s always surrounded by vary- ing amounts of w a t e r and c o u n t e r i o n s . Removal of t h i s w a t e r and c o u n t e r i o n s c a u s e s t h e h e l i x t o d e n a t u r e and change t o a random c o i l conformation. We have c a r r i e d o u t s e v e r a l c a l c u l a t i o n s aimed a t t a k i n g i n t o account t h e e f f e c t s of i n t e r a c t i o n w i t h w a t e r and c o u n t e r i o n s on t h e v i b r a t i o n a l modes. The f i r s t approach h a s been t o t r e a t t h e w a t e r a s a continuous f l u i d whose reponse t o motion i s governed by t h e Navier-Stokes e q u a t i o n s . The h e l i x i s t r e a t e d a s a continuous c y l i n d e r w i t h v i b r a - t i o n a l p r o p e r t i e s determined by our l a t t i c e s o l u t i o n s . The motion of t h e water boundary l a y e r i s made t o conform t o t h e motion of t h e h e l i x boundary and t h e s e l f c o n s i s t e n t s o l u t i o n s of t h e complex a r e solved f o r . The r e s u l t s i n d i c a t e t h a t t h e l o n g i t u d i n a l a c o u s t i c mode f o r one h e l i x i n much water i s c r i t i c a l l y damped below 200 GHz. S i m i l a r c a l c u l a t i o n s f o r many s t a c k e d h e l i c e s i n d i c a t e d reduced damping.

Another approach we u s e i s t o c a l c u l a t e t h e behavior of water n e a r a h e l i x by u s i n g molecular dynamics methods. The w a t e r i s found t o o r d e r , We p l a n t o determine t h e w a t e r behavior f o r a d i s t o r t e d h e l i x which mimics t h e o s c i l l a t o r y motion of t h e h e l i x . Such c a l c u l a t i o n s have been done w i t h f r e e c o u n t e r i o n s i n t h e system a s w e l l .

8. Microwave Absorption.- The a c o u s t i c modes of t h e h e l i x span t h e microwave r e g i o n and w e have c a l c u l a t e d t h e probable a b s o r p t i o n because of t h e concern over g e n e t i c hazard of microwave r a d i a t i o n . Using our s o l u t i o n s f o r DNA i n water t h e s e overdamped modes g i v e r i s e t o a broad a b s o r p t i o n 1: 40 times t h a t of w a t e r p e r equi- v a l e n t mass. Observations i n good agreement have been r e p o r t e d . I n chromosomes t h e DNA i s wound i n t o nucleosomes which can b e r e s o n a n t s t r u c t u r e s f o r a b s o r p t i o n i n t o a c o u s t i c modes. L i t t l e w a t e r is p r e s e n t and t h e damping i s s m a l l . We calcu- l a t e t h a t nucleosomes could r e s o n a n t l y a b s o r b a t s 50 GHz. The a c t u a l r a t e of ab- s o r p t i o n i s s t i l l unknown a s t h e behavior of t h e w a t e r i n such a c o n c e n t r a t e d system is unknown.