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 HELIX. Journal de Physique Colloques, 1981, 42 (C6), pp.C6-560-C6-562.
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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.
Dept. o f P h y s i c s , Pw,&e
Lu, M.N.
Mei and B. Putman
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.
Abstract.- 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 quasimomen 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 base
There a r e f o u r p o s s i b l e base 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
pairs.
bonded bases and two backbone segments.
The backbone segments a r e i d e n t i c a l .
can b e produced i n which t h e base 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 .
DNA
For long poly-
mer 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.
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.
We have used standard
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
studying 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.
This reduced t h e number of degrees of freedom by about h a l f ,
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.
Even s o i n t h e
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 has s e v e r a l base p a i r s and t h e mat r i c e s h e r e a r e s e v e r a l times 120
2.
X
120.
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 re-
f i n e d values 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 bases, backbone,
etc.
The choice 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 valence f o r c e f i e l d choices.
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 inf 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-
quired t h e development of new refinement procedures. The Raman and i n f r a r e d d a t a
-1
and only f a i r l y s t r o n g f o r c e conwere l i m i t e d t o f r e q u e n c i e s above 200-300 cm
s t a n t s such a s compression and angle bend c o n s t a n t s could be r e f i n e d w i t h any confidence.
I n a d d i t i o n t o t h e valence 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 .
a c o u s t i c v e l o c i t y along 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 .
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
This vel-
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
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
velocity.
These long range f o r c e s have a l s o been incorporated i n our c a l c u l a t i o n s
of the phonon bands of t h e double h e l i x .
3.
S o f t Modes.-
cesses.
Conformation changes play an important r o l e i n b i o l o g i c a l pro-
We have used t h e method of s o f t mode a n a l y s i s t o explore t h e o n s e t of con-
formation 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 re-
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 tion.
4.
Melting.-
I n some b i o l o g i c a l processes 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 melting of t h e
double h e l i x .
Using our c a l c u l a t e d eigenvalues and eigenvectors 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 melting based on t h e s e amplitudes and comparisons of observed melting temperatures.
We b e l i e v e t h a t t h i s can be used t o explore whether
phonon emission by enzymes can i n f l u e n c e l o c a l i z e d melting without 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.
a r e a t z 70 cm-'
5.
Local Modes.-
The modes involved i n s t r e t c h i n g t h e H-bonds
i n our c a l c u l a t i o n s .
The double h e l i x has 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 terminators of reading processes.
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 bring about a l t e r e d conformations o r enhanced tendancy t o melt.
r e c o g n i t i o n by enzymes.
Unique dynamic p r o p e r t i e s can on a simpler l e v e l a i d i n
By assuming t h e unique f e a t u r e t o be an impurity i n an
otherwise 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 base 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 base 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 base 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 melting from a
terminus.
6.
Quasi-Momentum Conservation.-
t h e double h e l i x .
I n many b i o l o g i c a l processes enzymes move along
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 analyzing t h e way i n which r e a l momentum and quasi-momentum a r e conserved.
One should be a b l e t o d e s c r i b e t h e processes of propulsion 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 .
o u t s p e c u l a t i o n has a r i s e n i n t h i s context.
One very i n t e r e s t i n g b u t f a r
I n our c a l c u l a t i o n s on s e v e r a l DNA
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 packets i n t h e s e bands by c e r t a i n enzymes may be r e s p o n s i b l e f o r both t h e propulsion of t h e enzymes a s w e l l a s a i d i n g i n
maintaining and propagating a melted r e g i o n of h e l i x near t h e enzyme.
These phonons
emitted 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 very small amounts of energy can g i v e r i s e t o more than
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 processes a s s o c i a t e d with enzyme motion i n which high 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 water and counterions.
Removal of t h i s water and counterions causes
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
out s e v e r a l c a l c u l a t i o n s aimed a t taking 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 water and counterions on t h e v i b r a t i o n a l modes.
The f i r s t approach has been
t o t r e a t t h e water a s a continuous f l u i d whose reponse t o motion i s governed by t h e
Navier-Stokes
equations.
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 stacked h e l i c e s i n d i c a t e d reduced damping.
Another approach we use i s t o c a l c u l a t e t h e behavior of water near a h e l i x by using
molecular dynamics methods.
The water i s found t o o r d e r ,
We plan t o determine t h e
water 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
helix.
Such c a l c u l a t i o n s have been done with f r e e counterions i n t h e system a s
well.
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 we 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
v a l e n t mass.
1:
40 times t h a t of water per equi-
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 be resonant 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 water is p r e s e n t and t h e damping i s small.
l a t e t h a t nucleosomes could r e s o n a n t l y absorb a t s 50 GHz.
We calcu-
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 water i n such a concentrated
system is unknown.