A Molecular Dynamics Study of Conformational Changes and Hydration of left-Handed d ( CGCGCCCGCGCC)2 in a Nonsalt Solution MATS A. 1. ERIKSSON and AATTO LAAKSONEN Division of Physical Chemistry, Arrhenius Laboratory, University of Stockholm, S-106 91 Stockholm, Sweden

SYNOPSIS

Twelve dinucleotides (one complete turn) of left-handed, flexible, double-helix poly (dGdC) Z-DNA have been simulated in aqueous solution with K + counterions for 70 ps. Most of the d(GpC) phosphates have rotated in accordance with a ZI + ZII transition. The ZII conformation was probably partly stabilized by counterions, which coordinate one of the anionic oxygens and the guanine-N7 of the next ( 5 ’ + 3’ direction) base. The presence of base-coordinating ions close to the helical axis rotated and pulled about half of the d ( CpG) phosphates further into the groove. These ions also gave rise to rather large deviations from the crystal structure (Z,) with their tendency of pulling the bases closer toward the helical axis. A flipping of the orientation about the glycosyl bond from the +sc to the -sc region was observed for one guanosine, also leading to deviations from the crystal structure. Many bridges containing one or two water molecules were found, with a dominance for the latter. They essentially formed a network of intra- and interstrand bridges between anionic and esterified phosphate oxygens. A “spine” of water molecules could be distinguished as a dark zig-zag pattern in the water density map. The lifetime of a bridge containing one water was about twice as long as that of a two-water bridge and it lasted 5-15 times longer than a hydrogen bond in water. The lifetimes were also calculated for a selection of bridge types, in order of decreasing stability: 0 1 P / 0 2 P - * * W. - 0 ; 0 1 P / 0 2 P * * * W e * guanine-N, > 0 1 P / 0 2 P . * -We * * 01P/02P. The reorientational motion of water molecules in the first hydration shell around selected groups was slowed down considerably compared to bulk water and the decreasing order of correlation times was guanine-N2 > 0 ; > O ; / 0; > o l P / 0 2 P . 0 1992 John Wiley & Sons, Inc.

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INTRODUCTION It is a well-established fact that water plays a dominant role in stabilizing the DNA structure, through intra- and interstrand bridges, and by its screening effect upon the highly charged polyion.’ The activity (effective concentration) of water is believed to be the most important factor determining the DNA c o n f ~ r m a t i o n . The ~ ~ ~ dominant conformation in vivo, B-DNA, is stable in solutions with high water activity. With DNA in this conformation, almost all possible water bridges are formed between the polar groups, with many of the bridges consisting of two water molecules.*The distance between free oxygens Biopolymers, Val. 32, 103.5-1059 (1992) Q 1992 John Wiley & Sons, Inc.

CCC 0006-3525/92/081035-25$04.00

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of adjacent phosphate groups is too great2 (>6.6 A ) for water bridging, and the oxygens will be individually hydrated.’ When the water activity is reduced by adding salt or alcohol, B-DNA transforms into the A or into the left-handed Z form. T h e Z form is preferred if the salt concentration is high5 (0.7M MgC12 or 2.5M NaC1) and the sequence is preferentially alternating in guanosines and c y t o ~ i n e s . ~ The DNA responds by adopting a conformation with a more economic hydration of the polar groups.’ The distances between the free oxygens of adjacent phosphate groups are now reduced’ (5.3-5.7 A for A-DNA and 4.4-4.8 A for Z-DNA), making it possible for the oxygens to “share” bridging water molecules; these bridges form strings along the backbone.* T h e solvent structure around B-DNA is thus more dynamic and less distinct than around Z1035

1036

ERIKSSON AND LAAKSONEN

DNA.l Two other characteristics of the hydration of Z-DNA are as follows: ( a ) the bridges between a guanosine-N2 and an anionic phosphate oxygen on the 3' side of the and ( b ) the "spine" of water molecules between adjacent cytosine-02 in the gr~ove.~ These , ~ . ~two characteristics are believed to be important for the preferential stabilization of ZDNA by GC pairs.g Many other factors are known to stabilize Z-DNA so that the equilibrium favors Z- over B-DNA. Methylation of cytosines at the C5 position of poly (dG-dC ) is a common covalent modification stabilizing Z-DNA.5,10The methyl groups fill a hydrophobic region that is exposed to water in unmethylated Z-DNA. When the methylated DNA is in the B form, the methyl groups protrude into the major groove, where they are surrounded by water molecules. Because of the unfavorable environment of the methyl groups in B-DNA, the B t-f Z equilibrium is shifted toward Z-DNA." Methylation of the cytosine-C, in eukaryotic DNA at GC-rich sequences is one of the most common base modifications and the reaction is believed to be involved in the regulation of the gene transcription process. It is thus plausible that methylation of cytosine-C, causes a transition of DNA into the Z form, which may serve as a regulation mechanism for the gene transcription in u ~ u o . ~Two " other factors enhancing the stability of Z-DNA are addition of di- and multivalent cations such as Mg" and spermidine3+ and negative supercoiling of DNA plasmids." In the past decade, a large number of Monte Carlo (MC ) , molecular dynamics ( MD ) ,15-27 and Brownian dynamics (BD)28 simulations have been performed on DNA systems at different levels of approximations. If the interest is focused on the dynamical behavior over a longer time scale, such as the slow counter ion dynamics,2' it is often appropriate to use BD. With this method, the water molecules are treated as a stochastic force field, and the time step can therefore be considerably (about 100 times) longer than in an MD simulation. In MC and MD simulations, the system is usually described in more detail, and the time scale for MD studies is normally less than 0.5 ns. Depending on what aspect the interest is focused on, a division into two groups of treatments can be made. In the first group, the interest is focused on the behavior of the intramolecular structure of the DNA helix. The usual approach is then to model the flexible DNA in U ~ C U O15*21325or in a solvent medium that is included in an implicit way.12,18,24,27 The solvent effects can, in the latter case, be mimicked by introducing distance-dependent dielectric constants.

One problem connected with this kind of approximation is that the dielectric constant in the close vicinity of the helix can be very different from that of bulk water, with a complicated distance variation. Another problem concerns the description of the counterion atmosphere; the difficulty can be overcome by reducing the charge of the phosphate g r o ~ p s as ~ ~a ,way ~ ~ to incorporate the effective screening due to the counterions. Another approach is to include a model of hydrated ions24,25 as a large Lennard-Jones radius parameter ( u N 5 A). In the second group, the structure (MC, MD) and/or dynamics (MD) of the surrounding water molecules and ions are instead of interest. The DNA is then most often modeled as rigid with counterions and water explicitly included, 13~19,20,26or with explicit water and reduced phosphates instead of counterThe most obvious disadvantage with this approach is that DNA is a highly dynamic polymer with a conformation heavily dependent on the water activity and ion c~ncentration.~ As the development of computers with increased power proceeds, a growing number of simulations are being reported16,17.22,23 that take both the flexibility of the helix and the molecular influence of the solvent into account. Modeling flexible DNA in a solution of explicitly included water and ions makes it possible to study both of the aspects mentioned above: DNA conformation and hydration. More importantly, it is also possible to combine these aspects: How do the solvent molecules affect the conformation of the DNA helix? In our MD simulation, we modeled Z-DNA in a water solution without the addition of salt (i.e., with counterions only), where DNA should preferentially adopt the right-handed B form because of the high water activity. The purpose of this work was, by investigation of the behavior of the intramolecular structure and the surrounding water molecules and counterions, to see whether Z-DNA would undergo any rapid conformational changes, or possibly show tendencies toward adopting the B form of DNA. Because of the short simulation time (70 ps) ,only some initial rearrangements toward such a transition could be observed. Results and discussion concerning counterion distribution, and hydration of DNA and the counterions, can be found in our previous paper." This article is organized in the following way: the next section describes the DNA model and the computational details. The third section is devoted to the analysis of the results, starting with the intramolecular structure and dynamics, going on to an analysis of the hydration of the helix, with emphasis

CONFORMATIONAL CHANGES A N D HYDRATION OF d ( CGCGCGCGCGCGh

on the one- and two-water bridges. The effects of the counterions are discussed in connection with both parts of this section. Finally, in the last section, some conclusions are drawn from the analysis.

DNA MODEL AND COMPUTATIONAL

DETAILS A simulation of one turn of flexible double-helix ZDNA with alternating cytosines and guanosines has been reported earlier.22All 756 atoms of the 12 dinucleotides were explicitly included, 24 K + counterions were added, and 2279 flexible SPC-water molecules29provided the solvent medium (see Table I ) . The simulation cell was cubic with an edge of 44.58 A, i.e., the pitch of one turn of Z-DNA. Periodic boundary conditions were used in all three directions, thereby making the helix pseudo-infinite. This was done to avoid (often rather complicated) end corrections to the helix. Without end corrections, the helix model would start falling apart, due to the solvating waters and the ions. An apparent drawback in using the periodic boundary conditions is that the helix is prevented from unwinding and overall bending. The conformational changes of the ends of the helix will also be correlated. Considering the short simulation time and the size of the simulated system, the use of periodic boundary conditions is not deemed a serious problem in the present study. The interaction potential for DNA was taken from Weiner et al.,30for DNA-water, DNA-K+, and K+-K+ from Clementi and G ~ r o n g i uand , ~ ~for water-K+ from Mackay et al.32A 10-12-type potential was used for the base-pair hydrogen bonds. The intramolecular force field for water was taken from Kuchitsu and M ~ r i n o . ~ ~ The long-range electrostatic interactions were treated with the Ewald summation technique and the equations of motion were solved using a double Table I Data of the MD Simulation’’ No. of H,O molecules No. of K f counterions Atomic charges cutoff (A) Box dimension (A3) Periodic boundary conditions Algorithm for solving the equations of motion Time steps (fs) Simulation time (ps)

2279 24 K + Full 10 Ewald summation 44.583 In all three directions Fourth-order double time-step predictorcorrector 1.0/0.1 70

+

1037

time-step predictor-corrector algorithm.34 The shorter time step (0.1 fs) was used for the fast intramolecular bond-stretching and angle-bending motions and the longer time step (1.0 fs) for the motion due to torsional stress and nonbonded interactions in the system. The simulation covered 10 ps of equilibration followed by a production run of 60 ps. For more details of the simulation, see Ref. 22. The intramolecular structure of the DNA was analyzed with the program “Dials and Windows,”’l which is based on another program “Curves,” developed by R. Lavery and H. Sklenar.35In “Curves,” a function is defined that describes the difference in orientation between successive nucleotides and the kinks between adjacent local helical axis segments. Minimization of this function produces the global helix axis that best fits the conformation in question. The description of geometrical irregularity is then distributed between the helicoidal parameter variation and axis curvature in the smoothest possible way. The time evolution of the helicoidal parameters is displayed in “windows” (see, for example, Figure 6) ; the start of the simulation, after equilibration, corresponds to the bottom of a window. The tipangle parameters (TIP, Figure 8) calculated by the original program, have values centered around -180” for the C. - G pairs and +Moo for the G C pairs. For better visualization, 360” has been added to the negative values of the tip angles. The program also calculates the time evolution of the backbone torsional angles (for definition, see Figure 1)displayed as “dials” (Figure 3 ) , with the start of the production run corresponding to the center of the dials. The “north” direction of a dial corresponds to a torsional angle of 0”) and the angle increases clockwise around the dial. The left- (LHS) and right- (RHS) hand strand designations are used arbitrarily to distinguish the strands. The bases are numbered in the 0; 0;direction, starting with the bases of the LHS. The straight lines in the dials and windows represent the crystal values for ZIDNA, which was the starting conformation of the simulation. Finally, the time evolution of some inter strand distances was followed with the program. One conformation every picosecond was included in the analysis of the intramolecular structure. The structure of the surrounding water molecules and counterions was analyzed as follows: The region within 11 A from the crystal axis was divided into volume elements with dimensions (in cylindrical coordinates): Az = 0.3 A, Ar = 1 A, and A 4 = 2”. A density map was calculated by assigning each water and counterion in each configuration to one of the

---

--f

1038

ERIKSSON AND LAAKSONEN

Base

* *P

Figure 1. Definition of the torsional angles of the

backbone.

volume elements. The density map was then normalized by dividing the volume elements with the number of configurations. We limited the averaging time to 20 ps, since further averaging would have lead to such great displacements of the DNA atoms that no preferential sites for water or ions in the helix could have been seen. For water bridges with one and two water molecules, the criteria for a H-bond X - * -HY, was an X-Y distance < 3.5 A and an XHY angle > 135". Because of the great number of bridges formed, only those with > 20% probability of occurring were taken into account. The probability was calculated as the number of occurrences of a certain bridge, divided by the total number of configurations.

(the X angle, see Figure 1) ,which is in the syn region ( x 70") for guanosine and in the anti region ( x 200" ) for cytosine ( see, for example, Ref. 5 ) . In B-DNA, all bases adopt the anti conformation about the glycosyl bond. We will use the Klyne and Prelog n ~ m e n c l a t u r efor ~ ~the torsional angle ranges. The sugar pucker of the Z-DNA cytosines is in the C;-endo region and the guanosines adopt the Ch-endo (or Ci-exo for the "high-salt" form, Z'DNA3v5)conformation, while the sugar pucker is C;-endo for all nucleotides in B-DNA. The difference between ZI- and ZII-DNA is most easily seen in changes of the torsional angles about the P-Oj bond ( a ) and about the 05-P bond caused by a rotation of the phosphate group in a d ( GpC) s e q u e n ~ e .In ~ .Zl-DNA ~ the phosphate group faces the groove, while it is rotated away from the groove in ZII-DNA. The crystal structure values of the backbone torsional angles of ZI-, ZII-, and BDNA are shown in Table 11. S I X Correlation. In our analysis, two distinct regions for the values of the 6 angle (rotation about the C2-C; bond) plotted against the x angle (rotation about the Ci-N1 glycosyl bond), can be distinguished in Figure 2. One region is centered around 6 x 80' and x NN 50°, and belongs to the guanosine backbone. These values correspond to a sugar pucker in the Ci-endo range ( 6 is directly correlated with the endocyclic torsional angle CL-C;-Ci-Oi and thus determines endocyclic sugar torsional angles, which in turn describe the sugar pucker, see Ref. 5, Fig. 46 ) and a syn conformation of the rotation about the glycosyl bond. There are also some conformations with a x angle of about 300". The guanosine responsible for these values is G2 (Figure 3 ) , which has flipped from the initial +syn to an angle in the

(r),

Table I1 Crystal Structure Values of the Backbone Torsional Angles' (The Values Are Given in Degrees) ZI-DNA

RESULTS AND DISCUSSION

a

Intramolecular Structure

P Y

Torsional Angles of the Backbone. The torsional

6

angles of the backbone serve as sensitive parameters for distinguishing the different subfamilies of ZDNA. A similar feature of all these subfamilies is the rotation of the bases about the glycosyl bond

t

iX a

ZIL-DNA

PC

PG

PC

PG

B-DNA"

223 221 56 138 266 80 201

47 179 191 99 256 291 68

146 164 66 147 260 74 212

92 193 157 94 181 55 62

314 214 36 156 155 264 260

Data for B-DNA from fiber d i f f r a ~ t i o n . ~ ~

CONFORMATIONAL CHANGES AND HYDRATION OF d ( CGCGCGCGCGCG)2

1039

6 / ~c o r r e l a t i o n

X

X

X

x x x X

0 0 00

0

0 0

0 0 0

@?gog

:8 00 0

0 00%

Figure 2. Correlationplot of the 6- and X-torsionalangles. Cross-bars:guanosines; circles: cytosines.

--sc range. The cytosines are also quite well clustered in a region with S / X values of about 145"/190", corresponding to a sugar pucker of C;-endo and a rotation about the glycosyl bond in the anti range. Some points deviate from this region, with a 6 value of around 90") corresponding to an 0;-endo sugar pucker. Cytosine C7 (Figure 3 ) is the base that has undergone this C;-endo =+ 0;-endo transition. On sterical ground^,^ the X angle should be less variable for the guanosines than for the cytosines, which can be seen in the 6 / x diagram. The situation for the 6 angle is expected to be the r e v e r ~ e dThis . ~ is, however, not the case here; the d values have an equal spread for the guanosines and cytosines. ( / a Correlation. Because of the different backbone characters of the d ( GpC) and d ( CpG) sequences, it is appropriate to study the sequences separately. For the d ( GpC) sequences (Figure 4, above) the angle values fall into two distinct regions. One region

is centered around (/a values of 50"/170°, which is close to the crystal structure values of ZII-DNA (see Table 11. Note that the {angle for this sequence is assigned to the guanosine, while the a angle belongs to the next ( 5 ' + 3' direction) cytosine, see Figure 1).There are some points in this region with relatively low a values. Cytosine C7 (Figure 3) is responsible for these deviating points. The other region, which is centered around 300°/200", corresponds to the d ( GpC) sequences that have remained in the ZI conformation. These are dG2pC3 and the bases that they form base pairs with: d (G22pC23) and possibly dG18pC19 (Figure 3 ) . In the counterion distribution (Figure 5 ) , many of the peripheral ions (shaded gray) have come rather close (3-5 A ) to one of the rotated phosphate oxygens and even closer (3-4 A ) to guanosine-N-, of the next residue. This kind of ion coordination has been found experimentally,8 with magnesium as counterion. Mg2+

1040

ERIKSSON AND LAAKSONEN

P

a

Y

6

&

c 1

G

2

c3 Q 8 190

c 3

0 63 @ Q 0@ Q 8 8 c";" @Q 8 @ 0 (3"5 @Q 0 88 @ GI Q 88 @Q 8

222

G 4

221

@55

190

c 5

222

G

6

9955

221

190

c 7

222

GEI

221

190

c 9

222

G

10

221

@55

190

c

11

222

G 12

221

@55

190

Figure 3. Time evolution of the backbone torsional angles, ( a ) LHS; (b) RHS (see text). The bases are numbered in the 5' + 3' direction. The values beside the "dials" are the starting ( = Z,) values of the simulation.

interacted directly with guanosine-N7 and through a water molecule with the anionic phosphate oxygen, and it served as a stabilizer for the ZIIconformation.' It is probable that the ions in Figure 5 have the same kind of stabilizing effect of the Z I I form. The interpretation of the < / a correlation in the

d ( CpG) sequences (Figure 4, below) is less straightforward. It is possible to distinguish two preferred angle ranges for fy and f . One region has fy and f values both between 60" and loo", corresponding to a mixture of ZI- and ZII-DNA (in this case, j- values belong to cytosines and a values to

CONFORMATIONAL CHANGES A N D HYDRATION OF d ( CGCGCGCGCGCGL

P

a

Y

6

c

E

x

1041

4)

Q egg

G 24

190

C 23

8

222

G 22

221@

QQ Q 221Q Q8 190

@47

c

21

@55

222

G 20

190

@47

c

19

6)

222

G 18 @47

C 17

0

222

G 16

221@

G 14

@47

291@

190

221@

2h66 Qe0 2ob66 Q52

Q52

@55

Q 8 8"" @ Q8

222

0" @

055

Q8

291

190

@47

C 15

8"5

221Q

190

C 13 Figure 3. (continued from the previous page)

following guanosines, see Figure 1) For about half of the d ( CpG) sequences, the j- angle has changed from 80" to a value in the up region, while the a angles have remained relatively unchanged, corresponding to the other region of [ / a values. Correlated with this increase in the [ angles are changes in the E angle to values in the up region and in the @ angle to around 270" (see Figure 3 ) . Inspection

of a model of Z-DNA showed that the most pronounced effect of these changes was a rotation of the phosphate group in the d ( CpG) sequence. The group was rotated through about go", as to make one of the anionic oxygens point toward the groove (and the other one away from the groove). One possible explanation for this behavior is found when looking at the counterion distribution around the

1042

ERIKSSON AND LAAKSONEN

(la - c o r r e l a t i o n f o r t h e d(GpC)-sequences 225

1.3 ps. The estimated correlation times are in the range 6-12 ps for r1and 3-6 ps for T ~The . motion is slowed down by a factor of 2-6, compared to 7 2 values from a MD simulation of pure, flexible SPC-~ater.~' This is a consequence of the preferential orientation of the dipole vector of hydrating water, which is not present in bulk water. The reorientational motion is further slowed down because many of the hydrating waters are also in bridging positions. The

reorientational motion around the guanine N2 and sugar 0 is slower than around anionic and esterified phosphate oxygens (Table IV) . This might reflect the fact that the latter groups are more exposed to the exterior water, being at the outer part of the minor groove. The other two groups are positioned deeper in the groove, where a greater portion of the water are in bridging positions and are thus reorienting more slowly. In a similar calculation,20a set of subcylinders around the helix axis were defined and correlation times of 7 2 from 0.88 to 3.08 ps were calculated depending on subcylinder. Our correlation times are generally longer, probably because we have chosen water molecules around groups, which constrain the dynamics of the water molecules. The results can also be compared with 72 values from a simulation of rigid B-DNA in SPC-water.26 Here, the space around DNA was divided into solvent shells, and T~ values around 1.0 ps for NaDNA were estimated, independent of solvent shell. These gen-

1058

ERIKSSON AND LAAKSONEN

Table IV Correlation Times Found from the Orientational Correlation Functions of Water MoIecuIes in the First Hydration Shell Around Different Groups

01P/02P 0 3

/o;

0 4

Guanine-N2

6.8 8.0 11.2 12.1

3.2 3.7 5.2 5.6

2.1 2.2 2.2 2.2

erally lower values could be a reflection of the more dynamic structure of the water in B- than in Z-DNA.’

CONCLUSIONS The changes of the torsional angles of the backbone of d(GpC) sequences indicates that most of the bases changed their conformation from ZI- to ZIIDNA. The final ZII-conformationwas probably stabilized to a large extent by ion coordination with one of the anionic oxygens of the d(GpC) phosphates and a guanine-N7 of the next guanosine. The coordination possibly occurred through a bridging water molecule to the anionic phosphate oxygens. The behaviour of the d ( CpG) sequences was influenced by the presence of base-coordinating counterions near the helical axis. About half of the d ( CpG) phosphates were rotated and pulled toward the interior of the groove, making it more narrow at these sequences. The rather large deviations of the helicoidal parameters from the crystal ( Z I ) values was partly caused by the presence of the ions near the helical axis. An interesting feature is the flipping from the +sc to the -sc region of the orientation about the glycosyl bond of one of the guanosines. This also gave rise to rather great deviations from the crystal values of the helicoidal parameters, since the base pairs in the vicinity of this guanosine accommodated to this flipping. Other trends during the simulation were an increase of the rise and the distance between the phosphates across the helix for the d(GpC) sequences, while the opposite was observed for the d ( CpG) sequences. The water bridges that were found in the system, showed quite poor agreement with experimental finding^.^^^,^" This might be explained by the fact that Z-DNA is simulated in a surrounding where the water activity is too high (no added salt) for ZDNA to be stable, resulting in formation of water

bridges that are not found in stable Z-DNA. The DNA conformation is also different from the crystal structures found by x-ray experiment^.^-^ The behavior of about half of the d ( CpG) phosphates (see above) resulted in formation of bridges that have not been found experimentally. Examples are the bridge between guanine-N2 and an anionic phosphate oxygen on the 5’ side and between anionic phosphates of different strands. Moreover, the criteria for defining a hydrogen bond are ambiguous; it can be defined on the basis of either geometry or energetics. The dynamics of the water bridges was much slower than that of H bonds in bulk water, with many of the bridges persisting throughout the whole simulation. The same applies for the reorientational dynamics of the water molecules around the selected polar groups in the DNA. This dynamics was slowed down because of the preferential direction of the dipole vector in the water molecule around the groups and by the fact that many of these water molecules were also held in bridging positions. The water molecules that contributed to the hydration of DNA formed a rather rigid network in the helix, showing that they could be considered as belonging to the “superstructure” of DNA. One of us ( M E ) would like to thank Dr. G. Ravishanker for his patience when installing “Dials and Windows” at our computer and his assistance when we made the program work for left-handed helices. ME would also like to thank Dr. R. Lavery for the program “Curves” and for valuable discussions. We are grateful to C. Ribbing for preparing a nice stereoview of the counterion distribution. Finally, we would like to thank Dr. L. G. Nilsson for wellorganized trajectories. This work has been supported by the Swedish Natural Science Research Council ( N F R ).

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CONFORMATIONAL CHANGES A N D HYDRATION OF d ( CGCGCGCGCGCG)*

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Received November 12, 1991 Accepted January 22, 1992

A molecular dynamics study of conformational changes and hydration of left-handed d(CGCGCGCGCGCG)2 in a nonsalt solution.

Twelve dinucleotides (one complete turn) of left-handed, flexible, double-helix poly(dG-dC) Z-DNA have been simulated in aqueous solution with K+ coun...
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