ABSTRACT
Molecular modelling with Jumna is used to study extreme stretching of the DNA
double helix. The results, which correlate well with recent nanomanipulation
experiments, show how the double helix can be extended to twice its normal
length before its base pairs break. Depending on the way the duplex is
stretched two types of conformation can occur, either an unwound flat ribbon or a narrow fibre with negatively inclined base pairs. The energetics of both types of deformation are similar
and existing structures show that at least the flat ribbon form can exist
locally under biological conditions.
DNA is known to be a very flexible molecule and there is already considerable
experimental data showing that important deformations of the double helix occur
in biological environments. Amongst these one can site helix bending and
kinking, base pair opening and strand separation, allomorphic transitions,
supercoiling and so on. As structural data on DNA-protein complexes accumulate, it has also become clear that proteins,
either in recognising the double helix or as part of their functional role,
often induce important local distortions and multiple protein binding, as in
the case of RecA (
1
), can extend such deformations over long tracts of DNA. It is thus important to understand the mechanics of conformational changes
which take us into the rarely studied area far from the canonical forms of the
double helix.
Before making such studies on specific protein-DNA complexes it seems important to understand the behaviour of the DNA
itself. Unfortunately, until recently this was not an easy task. Two
developments have however changed this situation. First, the invention of
techniques for manipulating individual DNA molecules have made it possible to
obtain direct physical data on at least certain types of extreme deformation (
2
-
6
). Secondly, development of the Jumna program (
7
) for modelling nucleic acids has made it possible to simulate large
conformational changes in reasonable amounts of computer time. We have taken
advantage of both these developments to study one important aspect of DNA
deformation, namely helix stretching.
DNA stretching has been studied in two types of nanomanipulation experiment. In
the so-called molecular combing experiments of Bensimon
et al.
(
2
,
3
), DNA molecules are attached by their ends to a glass surface, while suspended
in a droplet of solution. This droplet is then allowed to evaporate, causing
the retreating meniscus to exert a traction on the molecule and resulting in
its extension as it becomes bound to the glass surface. Maximum extensions of
roughly two times the original length of the DNA molecule have been measured.
In the case where both ends of a given molecule are attached, the force exerted
by the retreating meniscus is sufficient to lead to double-strand breakage (estimated to occur at ~500 picoNewtons). Measurement of DNA stretching in solution rather
than on a surface has also been possible through the use of a novel
nanomanipulation apparatus which enables a single DNA molecule (~15 [mu]m in length) to be fixed to a glass fibre at one end and to a microbead
at the other. Pulling the bead using a micropipette leads to a deflection of
the glass fibre. Passing a laser beam through the fibre and onto a
photosensitive detector enables the force applied to the DNA molecule to be
measured as a function of its extension (
4
, see also
5
,
6
). This experiment shows that a plateau occurs in the force curve for extensions
of ~1.3-1.6 times the original contour length of the DNA molecule, implying
the presence of a structural transition.
Such experiments provide very valuable data on the physical properties of DNA
molecules, but give little insight into the conformational changes taking place
at the molecular level. In order to probe these mechanisms we have used the
Jumna program (
7
). By employing a combination of helical and internal variables, and by
optionally including helical symmetry constraints, this program greatly
facilitates energy minimisation and allows large scale conformational changes
to be mapped out. Preliminary studies in collaboration with one of the groups
carrying out the nanomanipulation experiments on DNA have shown that Jumna
modelling is capable of reproducing both the plateau observed in the force
versus extension curve as well as the limiting extension of the molecule (
4
). On this basis, we now take a further step and investigate the underlying
mechanism of the extreme stretching of DNA. We also provide evidence that the resulting conformations are within the realms
of biological possibility and have indeed already been observed for short
tracts of DNA.
DNA modelling has been carried out using Jumna (JUnction Minimisation of Nucleic
Acids) (
7
). This program differs from most molecular modelling approaches in that it
represents DNA using internal and helicoidal coordinates, rather than Cartesian
atomic coordinates. All bond lengths are taken to be fixed and valence angle
changes are limited to the phosphodiester backbone and the sugar rings. These
choices enable the total number of variables representing a nucleic acid
fragment to be reduced by roughly a factor of 10. If, in addition, helical
symmetry is imposed, then a further factor can be gained. Whereas one turn of
double helical DNA (~650 atoms) is normally represented by nearly 2000 Cartesian variables,
Jumna requires ~300 variables without symmetry and a minimum of only 30 variables with
symmetry. This significant reduction, coupled with the use of chemically meaningful
variables (single bond rotations and valence angle deformations), greatly
improves energy minimisation.
Helicoidal coordinates are introduced by breaking the nucleic acid into a series
of 3'-monophosphate nucleotides. Each nucleotide is positioned with
respect to the helical axis system, using three translational (Xdisp, Ydisp,
Rise) and three rotational (Inclination, Tip, Twist) variables. The internal
movements of the nucleotide are represented by sugar puckering (four
independent variables), the glycosidic bond and bond rotations and valence
angles within the phosphodiester backbone. Inter-nucleotide links (O5'-C5') are maintained using quadratic distance constraints,
causing the bond rotations involving this linkage to become dependent
variables.
Helical symmetry can be imposed by simply equating all symmetrically equivalent
variables (rather than by introducing extra constraints, as would be the case
with Cartesian coordinates). Using symmetry, it becomes possible to model
effectively infinitely long polymeric nucleic acids by optimising the energy
per monomer unit in the presence of a sufficient number of neighbouring
monomers. This procedure saves computational effort and avoids the end-effects associated with studies of oligomeric fragments.
Jumna uses the Flex force field, developed specifically for nucleic acids (
7
-
8
), which includes Lennard-Jones and electrostatic terms between non-bonded atoms (including an angle dependent hydrogen bonding term) in
addition to valence angle and bond torsion contributions. Solvent damping of
electrostatic interactions is treated using a sigmoidal distance dependent
dielectric function (
8
,
9
) and counterion damping is mimicked by a reduction of the net phosphate charge
to -0.5e. Although this is a rather simple model, which ignores detailed
solvent and salt effects, it has been found to yield double helical structures,
and to predict conformational transitions, in good agreement with experimental
data (
10
,
11
). Lastly, this representation of DNA enables any structural feature of the
model to be controlled very simply. This feature has already been extensively
used to map the energy changes associated with changes in sugar pucker and with
backbone or helical conformations (
8
,
12
). Here we use adiabatic mapping as a function of chosen distance constraints to
stretch the DNA double helix, successive energy minimisations being carried out
with regular steps of 0.5 Å.
We have used the possibilities offered by Jumna to map the conformational and
energetic effects of stretching duplex DNA. Following recent nanomanipulation
experiments (
2
-
6
) described in the Introduction, we have stretched DNA to its limit when, in our
modelling study, strand separation occurs by rupture of the Watson-Crick hydrogen bonds. We also investigate the effects of base sequence
and of allomorphic form and, in particular, show that the conformational
changes induced are sensitive to the way the duplex is stretched.
Since the double helix contains two anti-parallel strands (whose direction is conventionally defined as 5' -> 3' on the basis of the sugar linkages of each
nucleotide), stretching can be carried out in four different ways: (i) using
the two 3'-termini; (ii) using the two 5'-termini; (iii) using the 5' and 3' termini of one strand or (iv) using the
5' and 3' termini of both strands simultaneously (Fig.
1
). Each of these techniques is topologically distinct and could lead to a
different type of DNA deformation. Notably, it can be seen that the first two
pathways should tend to induce positive and negative base inclination
respectively (positive inclination is defined as right-handed rotation of the base pairs around a pseudodyad axis pointing into
the major groove of the duplex) (
13
). The result of 5'3' stretching of one or both strands is less clear since base pair
inclination is not necessarily generated. It is also probable that the
deformation resulting from each of these pathways will be modulated by the
twist of the double helix, which, under physiological conditions, is right-handed.
We began our studies of these different stretching processes using polymeric DNA
with three regular base sequences: poly(dC-dG)[middot]poly(dC-dG), poly(dT-dA)[middot]poly(dT-dA) and poly(dC-dA)[middot] poly(dT-dG). Due to the choice of repeating sequences
we can impose helical symmetry on the DNA duplex and, by considering 16 base
pair interactions on either side of a double-stranded dinucleotide unit cell, we can effectively model an infinite
length polymer. This approach simplifies the conformational space to be studied
by strongly reducing the number of independent variables in the system. A
comparison with unconstrained simulations is presented in a following section.
Using this approach, the deformation energy as a function of stretching an
alternating CG sequence is shown in Figure
2
a. Stretching can be conveniently measured as a relative extension, RE, that is
equal to the actual length of DNA divided by the length of the corresponding
relaxed conformation. The energy cost of fully stretching the DNA duplex turns
out to be roughly similar whichever way the pulling is performed. All energy
curves show that ~30 Kcal/mol per nucleotide pair is necessary to stretch the duplex to a
little more than twice its normal length, although the 3'3' pathway is less favourable for extensions [lsim]1.5. Beyond an extension of ~2.1 times the initial length, the base pairs are
completely broken and the two strands slip with respect to one another. All the
energy curves in Figure
2
show sharp jumps in the energy during the stretching process (most pronounced
for the 5'5' and 5'3' curves). These jumps correspond to sudden
conformational rearrangements induced during stretching. This effect is
necessarily amplified by using regular repeating base sequences and imposing
symmetry constraints on DNA (
vide infra
).
a
If we now consider 5'5' stretching shown in Figure
3
b, early stages of the stretch again induce base pair buckling coupled with
partial unwinding. However, the inclination of the base pairs is now negative,
as expected, and the minor groove width is reduced with extension. As
stretching continues, no intercalation sites appear, the buckling remains and
the bases pairs adopt an increasingly negative inclination. In contrast to the
3'3' pathway, only moderate unwinding occurs (~5o-10o per base pair step). Beyond a relative
extension of 1.7, the base pairs break open towards the major groove side of
the duplex, losing successively their G(O6)-C(N4) and G(N1)-C(N3) hydrogen
bonds. This brings together the phosphodiester strands on the minor groove side
of the duplex and improves the interstrand stacking of the guanines. Finally,
clusters of CGGC bases are formed, two intrastrand CG (or GC) stacks being
coupled with an interstrand GG stack. This deformation leads to a very narrow
duplex with bases thrust outwards on the side of the major groove and almost
aligned with the axis of the duplex, quite unlike the flat ribbon obtained by
the 3'3' stretch (Fig.
4
b). Once again, changes in backbone conformation are limited to more negative
values of [xi], an [alpha][gamma] g
-
g
+
-> tt transition at both CpG and GpC steps and changes in the glycosidic
angles which become more negative, again showing a strong correlation with
inclination. (Negative inclination however pushes the nucleotides further into
the anti domain and can consequently continue without resistance from either
purines or pyrimidines.) We can see from these results that the intrinsic
handedness of the DNA duplex does indeed strongly modify deformation as a
function of the stretching pathway.
Lastly, what happens when we only stretch one strand of the duplex? The
conformation obtained for the alternating CG sequence (Fig.
4
c) in fact strongly resemble those along the 5'5' pathway and consequently lead to the narrow fibre-like conformation with negatively inclined bases. Even the
energy jumps occurring along the stretching pathway, corresponding to sudden
conformational rearrangements, are almost identical for the 5'3' and 5'5' energy profiles, apart from an offset of roughly RE
= 0.1 (Fig.
2
a). Since this type of deformation, and notably the negative inclination, is not
imposed by pulling a single strand, this result confirms the energetic
preference for this pathway, at least for relative extensions <= 1.5 (Fig.
2
a).
The deformation energy curves for the AT alternating sequence are shown in
Figure
2
b and have a similar appearance to those obtained with the alternating CG
sequence. However, the total energy needed to fully stretch DNA drops to ~15 Kcal/mol, only half the value found for the alternating CG sequence. The
3'3' pathway again leads to a ribbon-like structure, similar to that obtained with the CG
sequence, although unwinding is still not complete at a relative extension of
1.9 (Fig.
4
a). This conformation however has very different hydrogen bonding. Relatively
early in the stretching pathway, alternate AT base pairs become very distorted
and finally rupture. In consequence, alternate thymines interact with a total
of three other bases-their usual paired adenine, via a single A(N6)-T(O4) hydrogen bond, and
with both of the bases of the disrupted neighbouring pair-thymine via a T(O4)-T(N3) bond and adenine through an intrastrand
A(N6)-T(O2) hydrogen bond. Despite these deformations, backbone modifications
are again limited to more negative [xi] and [chi] values and no [alpha][gamma] transitions are observed.
The 5'5' and 5'3' pathways again resemble one another with strong
negative base pair inclination leading to a narrow fibre with the bases on the
major groove side and the phosphodiester strands close together on the minor
groove side (Fig.
4
b and c). These conformations are dominated by interstrand stacking, involving
TT and AA pairs on the 5'5' pathway and TAAT clusters on the 5'3' pathway, very similar to the CGGC clusters seen
with the CG alternating sequence. Also in common with the CG sequence, the
hydrogen bond on the major groove side of the base pairs, here an A(N6)-T(O4)
bond, is the first to break, allowing the bases to open outwards to the major
groove. The fact that the 5'3' and 5'5' pathways resemble one another is again in line with
the lower deformation energy of the latter pathway compared to the formation of
the 3'3' ribbon structure (Fig.
2
b).
Lastly, we consider the alternating sequence CA whose stretched conformations
are also shown in Figure
4
. This sequence behaves similarly to the others studied for both 3'3' and 5'5' stretching. The final 3'3' conformation is once more a flat
ribbon, although it is narrower than those of either the CG or TA sequences due
to the formation of interstrand AG and CT stacking. The 5'5' pathway, as expected, forms a narrow fibre with negatively
inclined bases, involved in stacked CAGT clusters. The surprise with this sequence comes from the 5'3' pathway which, unlike the former sequences, forms a ribbon
conformation most closely resembling the 3'3' ribbon of the TA alternating sequence. This result, which can be
related to the relative stability of the 3'3' stretching pathway for small relative extensions (results not
shown), demonstrates that pulling on a single strand of the DNA duplex can lead
to either of the characteristic conformations obtained by pulling both 3' or 5' extremities.
In order to test the effect of symmetry constraints upon these calculations, we
have firstly repeated the various stretching pathways for the alternating CG
and TA sequences replacing the normal dinucleotide constraint with a
decanucleotide constraint. This change, while allowing us to continue to
simulate an infinitely long polymeric DNA, increases the number of degrees of
freedom in the system by a factor of five. The results obtained in this way
yield very similar conformations for both the 3'3' and 5'5' stretching pathways, whichever base sequence is
considered. The deformation energies per base pair are however smaller, for any
given relative extension, and the energy curves are smoother, since sudden
conformational changes are not obliged to occur at the same moment within every
dinucleotide step. For the 5'3' pathway, the results with the TA sequence are again very similar
to the dinucleotide symmetry results, however, the CG sequence now goes to a
ribbon conformation almost identical to that of the 3'3' pathway. This once more emphasises that stretching a single
strand of the duplex does not predetermine the type of deformation pathway that
will be followed. Since the deformation energy curves are relatively smooth
under decanucleotide symmetry constraints it is possible to make a polynomial
fit and to derive these polynomials to obtain the force necessary to stretch
the DNA. The resulting curves either show a force plateau or a sinusoidal
variation of the force in the region between relative extensions of ~1.3-1.7 with forces varying between 150 and 350 pN. These values are
higher than the recent experimental result of 70 pN (
4
), but exact agreement cannot be expected given the sensitivity of the force to
the exact shape of the deformation energy curve and the limitations of the
simplified model presently being used.
In order to take a final step towards simulating a long unconstrained DNA
fragment with an inhomogeneous base sequence, we have carried out calculations
on a 15 base pair oligomer with the sequence GCGTATATAAAACGC. This oligomer was
stretched to a relative extension of 2.0 using both the 5'5' and 3'3' stretching pathways. The conformations obtained
along these pathways again resemble respectively the fibre and ribbon
structures discussed above although the deformation develops inhomogeneously,
the GC-rich ends deforming first along the 5'5' pathway and the central AT-rich segment deforming earlier along the 3'3' pathway. There is also some
irregularity in the fully stretched structures, with partial base pair breakage
being limited the 3-5 central nucleotide pairs. Energetically, the 5'5' stretching pathway is preferred, leading to a deformation
energy per nucleotide pair of 2 Kcal/mol at RE = 1.6, which is the same as the
value obtained by fitting to the experimental results (
4
). In contrast, 3'3' stretching to the same relative extension requires 5.7 Kcal/mol
(and leads to a force plateau at ~300 pN). The energetic preference for the fibre structure is again
confirmed by the fact that stretching a single strand of this oligomer again
leads to the fibre-like conformation.
It is worth briefly considering whether different allomorphic forms of the
double helix respond in the same way to this type of stress. We have addressed
this question with some preliminary calculations on A-DNA. Studies were made of both CG and TA alternating sequences by the 3'3' and 5'5' pathways. The final conformations of these
four simulations (Fig.
5
) show that changing the allomorphic form indeed affects stretching
deformations. The 3'3' structures differ principally by an increase in positive
inclination, while the 5'5' pathway leads to smaller negative inclination and less unwinding.
The bases remain between the phosphodiester strands rather than being pushed
out to form a fibre-like structure. These change can be linked to the natural preference of A-DNA for a positive inclination, which apparently continues to be
felt in the stretched forms. Inclination is once again directly coupled to the
glycosidic torsions and the high positive values at the end of the 3'3' pathway lead the purine nucleotides of both sequences to enter
the syn domain. Lastly, both pathways also show [alpha][gamma] transitions (g
-
g
+
-> tt), partial g
-
-> t transitions in [xi] and, for the CG sequence, 5'5' stretching forces the cytidine sugar to change from C3'-endo to C2'-endo. All these modifications
help in lengthening the phosphodiester backbone of the A-form which is initially ~1 Å shorter per nucleotide step than that of B-DNA.
The modelling we have carried out shows that DNA can be stretched, largely by
base pair reorientation, to roughly two times its original length before its
base pairs must be broken. This result is in good agreement with the maximal
extension observed in so-called DNA combing experiments, where strand breakage occurred beyond a
relative extension of 2.14 +- 0.2 (
2
,
3
). It is remarked that the ~1.7 times stretching limit of recent nanomanipulation experiments on single
DNA molecules (
4
) is due to breaking the molecular `scotch-tape' holding DNA, rather than to the rupture of the DNA molecule itself.
The energetics of stretching show only a minor dependence on the way the duplex
is pulled, but base sequence does have an influence, GC pairs leading to
greater resistance than AT pairs. The force versus extension curves deduced
from our modelling correlate well with the experimental measurements on single
DNA molecules and show a force plateau between relative extensions of ~1.3 -> 1.7. The height of the theoretical plateau decreases when helical
symmetry is relaxed, but remains at least twice the experimental value of 70
picoNewtons.
The most striking result of these studies is that there are two distinct
conformational pathways for stretching duplex DNA. Which path is followed
depends on which ends of the DNA duplex are pulled: pulling the 3' ends leads to a flat ribbon conformation, whereas pulling the 5' ends leads to a narrow fibre with strongly negatively inclined
bases. Still more surprisingly, pulling both ends of a single strand of the
duplex also leads to one of these two forms and the same is true when both
strand of the duplex are pulled simultaneously. The latter result can be explained by the fact that the relatively rigid base
pairs forming the centre of the duplex transmit stress very effectively from
one strand to the other. However, in order to understand why there are only two
routes for stretching, it is worth considering a little geometry.
We have already remarked that stretching occurs largely by repositioning the
base pairs within the duplex and that relatively little deformation is seen
within the phosphodiester strands. If, to a first approximation, we assume that
the inter-phosphate distance L within each strand remains constant then, as Figure
6
shows, there are indeed two ways to increase the rise R of the duplex in order
to double its length. This requires reducing the base of the triangle [theta]P roughly to zero so that R becomes equal to L. (In canonical B-DNA, L is ~7 Å and R is ~3.4 Å. Setting R = L therefore implies
stretching the duplex by slightly more than two times.) [theta]P can be made zero either by unwinding the helix ([theta] -> 0) or by reducing its radius (P -> 0).
The authors wish to thank the Institut de Développement et des Resources en Informatique Scientifique (Orsay,
France) for their allocation of computer resources and the Association for
International Cancer Research (St Andrews, UK) for their support of this
research.
REFERENCES
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