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SOLVENT NETWORKS IN NUCLEOTIDE CRYSTAL HYDRATES
P. Howell, J. Goodfellow
To cite this version:
P. Howell, J. Goodfellow. SOLVENT NETWORKS IN NUCLEOTIDE CRYSTAL HYDRATES.
Journal de Physique Colloques, 1984, 45 (C7), pp.C7-211-C7-218. �10.1051/jphyscol:1984723�. �jpa-
00224288�
SOLVENT NETWORKS I N NUCLEOTIDE CRYSTAL HYDRATES
P.L. Howell and J.M. Goodfellow
Department o f CrystaZZography, Birkbeck CoZZege, Malet S t r e e t , London WC1E 7HX, U.K.
~ 6 s u m 6 - Nous savons que le solvant joue un r81e dans la stabilisation et les transitions des hklices dlacides nuclgiques. Ici nous utilisons des techniques de simulation surordinateur pour Gtudier la structure de lleau dans les cristaux dvacides nuclgiques, ce qui permet une comparaison d6taill)ee des structures prgdites du solvant avec celles r6ve/l6es par des moyens cristallographiques. Dans le but d1arn61iorer les prgdictions des simulations, nous avons 6tudi6 llutilisation des positions obtenues dlune part de faqon experimentale et dlautre part par calculs, des atomes d1hydrog8ne placEs soit sur llensemble de la mol6cule du solutg soit aeulement sur les groupes polaires de cette molgcule en se servant de deux champs de forces diffgrents pour les atomes du solute/.
Abstract - Solvent is known to play a role in stability and transitions of nucleic acid helices. We are using computer
simulation techniques to study the structure and energetics of water at nucleic acid interfaces in crystals, which enables a detailed comparison of the predicted solvent molecules to be compared with well characterised experimental data from crystallographic studies.
In an effort to improve the predictive power of computer simulation we have been studying the explicit use of both experimentally derived and calculated hydrogen atomic positions on either all solute atoms or on polar solute atoms alone using two different force fields for the solute atoms.
INTRODUCTION
The importance of water in all biological systems is now well established.
The folding, structural stability and dynamics of proteins are thought to be be extensively controlled by solvent interactions as are the helical
transitions of nucleic acids. A review by Texter / I / describes various experiments that look at the interaction of water with nucleic acids and concludes that water activity or relative humidity strongly influences conformational stability. In his final paragraphhe suggests that "future research should focus on successes in modern Monte Carlo techniques ... as...
the application of such statistical techniques will permit truly detailed molecular hypotheses to be tested in modelling nucleic acid-water
interactions1'. Before such techniques can be applied to large biological systems (especially in solution), it is necessary to ascertain the accuracy of such the computer simulation techniques and to discover to what extent the input requirements affect the accuracy.
Monte Carlo simulation is a form of numerical statistical mechanics from
which structural and energetic properties of solvent networks can be
predicted. The technique requires a knowledge of the molecular coordinates
of a system and also a set of potential functions which model the various
types of atom-atom interaction. The choice of these potential functions is
not a simple one, not least because of the variety of models that exist for
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984723
C7-212 JOURNAL DE PHYSIQUE
not a simple one, not l e a s t because of t h e v a r i e t y of models t h a t e x i s t f o r l i q u i d water /2/. Moreover, t h e parameters needed t o d e s c r i b e t h e s o l u t e atoms ( i . e . charge and non-bonded i n t e r a c t i o n s ) a r e known imprecisely.
Goodfellow e t a 1 /3/ showed t h a t s t r u c t u r a l r e s u l t s p r e d i c t e d by Monte Carlo simulation ( f o r small amino a c i d h y d r a t e s ) were s e n s i t i v e t o t h e values used i n t h e p o t e n t i a l f u n c t i o n s . An optimized s e t of parameters was obtained from t h i s study using t h e p o l a r i s a b l e e l e c t r o p o l e (PE) water model /4,5/ and t h i s was extended t o d e s c r i b e n u c l e i c acid...water i n t e r a c t i o n s / 6 / ,
Detailed comparisons of s o l v e n t networks i n c r y s t a l hydrates / 6 , 7 , 8 , 9 / have shown t h a t only moderate agreement is obtained between simulated and experimental d a t a . Use of agreement f a c t o r s t o measure t h e l e v e l of
s i m i l a r i t y between p r e d i c t e d and experimental networks and between different;
p r e d i c t i o n s of t h e same networks has shown t h a t f u r t h e r improvements would be expected i f t h e p o t e n t i a l f u n c t i o n s could be s u i t a b l y modified.
A major assumption i n previous work /6/ has been t h a t s o l u t e hydrogen atoms can be represented i m p l i c i t l y by i n c l u s i o n i n t o t h e n e a r e s t heavy atom, (e.g. t h e p o t e n t i a l s f u n c t i o n s used s o f a r d e s c r i b e t h e i n t e r a c t i o n s between water and a methyl group ( C H , ) and not between water...carbon and
water ... hydrogen atoms s e p a r a t e l y ) . The s t u d i e s of Vovelle e t a 1 /8/
i n d i c a t e d t h a t t h i s s i m p l i f i c a t i o n might be l e a d i n g t o i n a c c u r a c i e s i n t h e p r e d i c t e d r e s u l t s . Moreover, Kollman and colleagues / l o / have r e c e n t l y published a complete s e t of p o t e n t i a l s f o r n u c l e i c a c i d s and amino a c i d s i n which they found i t necessary t o include polar hydrogen atoms e x p l i c i t l y . The aim of t h i s s t u d y has been t o look a t t h e use of e x p l i c i t s o l u t e hydrogen atoms f o r ( a ) a l l hydrogens and ( b ) polar hydrogens alone a t c a l c u l a t e d and experimental p o s i t i o n s i n order t o a s c e r t a i n i f improvement i n t h e accuracy of s o l v e n t networks can be obtained
METHODS ( A ) P o t e n t i a l Energy Functions
( i ) Water-Water I n t e r a c t i o n s
These a r e represented by t h e P o l a r i z a b l e E l e c t r o p o l e (PE) model, / 4 , 5 / which has t h r e e p a r t s t o t h e energy f u n c t i o n :
( a ) The e l e c t r o p o l e energy, is obtained by t h e i n t e r a c t i o n of
e l e c t r o p o l e s centred on t h e oxygen atom of t h e water molecules and i n c l u d e s terms a s high a s t h e octupole-dipole i n t e r a c t i o n s .
( b ) The non-bonded energy, t a k e s t h e form of a Lennard-Jones (6-9) p o t e n t i a l , and
( c ) The p o l a r i z a t i o n energy. Each water molecule d i p o l e experiences t h e f i e l d of a l l t h e surrounding atoms, s o t h a t i t is increased from t h e monomer value (1.85 Debye) t o a value which depends on i t s environment / 1 1 / . The increased d i p o l e moments a r e c a l c u l a t e d i t e r a t i v e l y u n t i l s e l f - c o n s i s t e n t values a r e obtained. Thus
( i i ) Water-Solute I n t e r a c t i o n s
Each s o l u t e atom is represented by a charge and two non-bonded Lennard-Jones
c o e f f i c i e n t s . The charges a r e c a l c u l a t e d using a standard semi-empirical
quantum mechanical method, CND0/2. This method f o r c a l c u l a t i n g atomic
close, and (b) the charges for the complete solute molecule can be obtained (by successive overlapping fragments) in the experimentally obtained conformation. More sophisticated quantum mechanical calculations would require the use of charges calculated from small fragments in standard conformations.
The two non-bonded coefficients were in a (6-9) Lennard-Jones form in order to be compatible with the water model. The coefficients were taken from two different sources, from work by Lifson et a1 /13/ (Potential I) and Weiner et a1 /lo/ (Potential II), the latter potentials are not in a (6-9) form and therefore a fitting procedure was used. Thus
and
( B ) Crystal Systems
Two crystal systems have been studied:
(i) Adenosine-3'-phosphate dihydrate /lo/, and (ii) Gaunosine-5'-phospate trihydrate /15/.
These are chosen not only because they had been crystallised without the presence of counterions, (thus simplifying the variety of interactions for which potential energy functions are needed), but because they are well defined experimentally. In both systems hydrogen atomic positions were defined to an estimated standard deviation of 0.068 and 0.138 respectively.
More importantly the water positions are ordered (unit occupancy and low B values) and can therefore be used as a trial system, against which the predicted results can be tested without the added difficulties of comparing partially disordered solvent networks /8,9/.
(C) Representation of hydrogen atoms
We have used several methods for representing the solute atoms. The alternative methods are as follows:
(i) Explicity defined. All hydrogen positions are included in the system, with coordinates taken from one of two sources.
(a) Experimental positions; obtained from the crystal structure data /14,15/.
( b )
Calculated positions; estimated for each crystal system using
standard bond angles and a bond length of 1.08.
(ii) Semi-explicitly. All polar hydrogen atoms (e.g. NH, and COH) have defined positions. All other hydrogen positions are included in the nearest 'heavyt atom i.e. the implicit united atom approach. We have used both experimental positions, and calculated positions as described above. The previous work by Goodfellow /6/ on G~anosine-5~-phosphate using the united atom approach has been included for comparison.
(D) Monte-Carlo simulations
Monte-Carlo simulations using the metropolis algorithm /16/ are performed on
on the whole unit cell with periodic boundary conditions. The solute atoms
are kept fixed and the water molecules, placed initially at their crystal
C7-214 JOURNAL DE PHYSIQUE
positions, are allowed to move randomly, i.e. independent of the space group symmetry. A minimum of 200K configurational moves for each system was used to check that the system had equilbrated, through monitoring of the potential energy at every 5000th configurations. Average properties of the system, (such as the mean water oxygen positions), were calculated over the last lOOK configurations. All data was generated on either the CRAY-IS computer at ULCC or the NAS 7000 at the SERC, Daresbury laboratory. 75K configurations took approximately ten minutes on the NAS 7000.
RESULTS AND DISCUSSION
From previous studies /3,6,9/, it appears that one of the most useful, but difficult to,define parameters for comparison is that of the environment of each water molecule. In this study, we have used three different methods, each of which attempts to take a different approach to the assessment of how well a simulation reproduces the experimental solvent hydrogen bonding networks.
Table 1
Average properties
1. No. of assymetric unitdunit cell 2. No. of solute molecules/unit cell 3. No. of water molecules/unit cell 4. Mean dipole moment for all the
water molecules in the unit cell (a) Guanosine-5'-phosphate trihydrate (b) Adenosine-3'-phosphate dihydrate (A) Computer Graphical Representation
The average water oxygen positions are calculated by taking an average of the positions found at regular sampling intervals over the second 100K configurations. These positions can then be compared with the experimental crystallographic positions for an ordered solvent network. We have used an Evans and Sutherland computer graphics system to visualise, in three dimensions, the changes which occur between the predicted and crystal solvent positions. We have centred on predicted and experimental water oxygen positions for each solvent molecule and highlighted all nearest neighbours within a 3.28 sphere of the central solvent molecule. Thus changes in hydrogen bonded contacts could easily be noted.
We present here an example of this type of representation for the fourth
molecule in the unit cell of Adenosine-3'-phosphate dihydrate. We emphasise
that interactive computer graphics provides a much better view of the three
dimensional similarities and differences in positions and environment than
can be represented by a projection or two dimensional diagram presented
herein. In figures l(a) and l(b) we are comparing the experimental data
with that obtained from a simulation in which all all solute hydrogen atoms
were included explicitly in calculated standard positions. These hydrogen
atoms have been omitted from this diagram for clarity.
'%, /--
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