Topological Aspects of DNA Function and Protein Folding
Comparison of linear and ring DNA
macromolecules moderately and strongly
confined in nanochannels
Zuzana Benková*† and Peter Cifra*1
*Polymer Institute, Slovak Academy of Sciences, Dúbravská cesta 9, 842 36 Bratislava, Slovakia, and †REQUIMTE, Chemistry Department, University of Porto,
Rua do Campo Alegre 687, 4169-007 Porto, Portugal
Abstract
Understanding the mechanism of DNA extension in nanochannels is necessary for interpretation of
experiments in nanofluidic channel devices that have been conducted recently with both linear and ring
chains. The present article reviews the situation with linear chains and analyses the experimental results and
simulations for channel-induced extension (linearization) of ring chains. Results for confined rings indicate
a transition between moderate and strong confinement similar to that of linear chains. Owing to stronger
self-avoidance in confined rings, the transition and chain extension is shifted relative to linear DNA. We
suggest that a relationship similar to that used for the extension of linear chains may also be used for
circular DNA.
Introduction
The constraints due to the chain closure in combination
with geometrical constraints of a DNA molecule are
inevitable for many biological processes. In the present
article, we review the structural properties of flexible and
semi-flexible cyclic chains and their linear analogues confined
in nanochannels as studied in single-molecule experiments in
microfuidic channel devices used to detect, analyse and
visualize genomic macromolecules or their fragments
[1–7]. Particular attention is paid to comparison with
polymer theory [8–15] and to molecular simulations [16–27]
that mimic these single-molecule experiments and which both
help in the understanding and interpretation of underlying
phenomena. In biological systems, macromolecules usually
adopt conformations perturbed by the constraints invoked
by a crowded cellular environment. Because of the reduced
conformational freedom, the structure of a confined chain
appreciably differs from the structure of a free chain in bulk.
Exploring the structural changes triggered by confinement
is important for understanding biological properties and
functions of DNA and other biomacromolecules as well
as for manufacturing nanopores and nanochannels used to
investigate and manipulate DNA. The free space achievable
for a confined biomacromolecule is usually of micro- or nanoscale dimensions, which often means order of magnitude
smaller dimensions than the unperturbed size of
free biomacromolecules. Depending on the dimensionality
of the confining object, classified according to the number of
dimensions in which a chain is prevented from relaxation
as uni-, bi- or tri-axial geometries (slit, channel or spherical
pore respectively), structural and dynamic properties of
Key words: DNA stretching, linear and ring chain topology, nanochannel, nanofluidic device.
Abbreviation used: ds, double-stranded.
1
To whom correspondence should be addressed (email [email protected]).
Biochem. Soc. Trans. (2013) 41, 625–629; doi:10.1042/BST20120279
confined macromolecules are substantially modified. Reports
on channel confinement are abundant and mostly concentrate on linear macromolecules. In the present article, we
focus on the comparison of linear and ring chains in a
nanochannel.
DNA analysis through confinement in
nanofluidic devices
Recent advances in visualization and manipulation of
semi-flexible biopolymers in experimental techniques have
recorded a great improvement in providing information on
single-chain systems. This topic was reviewed recently for
linear DNA by Reisner et al. [28]. Of special relevance to
nanotechnology are the experimental approaches based on the
chip-based micro- and nano-fluidic devices combined with
florescence microscopy [1–3,6]. In these experimental setups,
the extension and dynamics of solvated chains, for example
DNA molecules being very often scrutinized, are affected.
Achievements in nanofluidics and the development of lab-onchip devices have had a significant impact in biotechnology
and on clinical diagnostics. The new technology enables one
to perform several laboratory tasks in combination with
automated data analysis in one process on a single platform.
In nanofluidic devices, the channels of precise geometry are
fabricated which allows the study of principal biopolymers
such as DNA. The properties of DNA molecules measured in channels depend on the strength and geometry
of confinement. The ability of DNA molecule to adapt
its conformation to the confinement is crucial for packing
exceptionally long DNA molecules into a chromosome. On
the other hand, the natural highly organized arrangement of
DNA complicates its structural analysis; genetic information
stored along the DNA backbone is difficult to be read
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off because of extensive DNA folding in channels under
moderate confinement.
Stretching of ds (double-stranded) DNA in nanofabricated
channels has emerged as an innovative technique to
access genetic information. The nanochannel-induced DNA
elongation (linearization) is now being developed along
the route to robust devices for biological bioassays [6].
In sufficiently narrow channels, DNA molecules will
spontaneously stretch to the dimension (span) R approaching
their contour length L. To facilitate the loading of DNA
into channels, moderately wide channels are used in practice.
As a result, instead of a fully stretched conformation, DNA
chains in nanochannels may be quite coiled, or, at least, they
may involve various loops, knots and folds of the chain on
itself, depending on the channel widths. It is thus important
to understand the extent of stretching of confined DNA
molecules as a function of the channel dimension D and
recognize the underlying regimes in the chain elongation
against confinement dependences. In this effort, singlemolecule DNA experiments are combined with theories of
confined polymers and mesoscale molecular simulations. The
experiments are usually carried out under moderate or strong
confinement. Recently, chains with other topologies have
been investigated in nanochannels. The extension of ring
DNA (usually relatively short rings such as plasmids) in
channels differs from linear DNA and poses new challenges
for measurement and interpretation [7,22–24].
Role of molecular simulations
Although the single-molecule experiments are crucial in
this field, the comparison with the theoretical prediction
and independent molecular simulations improve our understanding of processes involved. Molecular Monte Carlo
simulations or methods of molecular dynamics are suitable
to explore properties of dsDNA molecules in slits, channels
and cavities. The simulations are usually based on the coarsegrained worm-like chain model, where DNA is represented
by a thread of beads connected by springs. A very similar
molecular model, typical for soft matter simulation studies,
comprising the FENE (finite extensible non-linear elastic)
potential for springs connecting the beads, the potential due
to non-bonded interactions and the bending potential
accounting for the real chain stiffness, is used by several
research groups [18–25]. Often, the studies are restricted
to flexible macromolecules and/or electrostatics is included
implicitly. In the present article, results for chains of 300 beads
are shown. The relative chain elongation R/L is computed as
a function of the channel diameter D and the chain bending
rigidity related to the persistence length P (50 nm at high salt
concentration) [18–20,26,27]. The deflection, transition and
blob regime are identified on the DNA extension profiles R/L
against D and rationalized by the blob and Odijk [8] theories
of confined polymers [28]. From several quantities used to
assess the DNA extension in a channel, the chain span or the
radius of gyration Rg is found to agree with the blob scaling
theory [21].
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nanochannel against confinement
Radius of gyration Rg reduced by the corresponding maximal feasible
√
√
extension L/(2 12) and L/ 12 for cyclic (closed symbols) and linear
chains (open symbols) respectively as a function of reduced confinement
D/P for chain stiffness L/P = 15 (open or closed DNA fragments of
2200 bp) and a for more flexible chains of L/P = 30. The broken lines
are the fits according to Odijk-type equation [8] in the text and the
snapshots illustrate the conformation of semi-flexible cyclic chains under
the strong and moderate confinements.
Elucidation of the effect of chain topology
Experiments with ring macromolecules produced deviations
from the behaviour of their linear analogues in the chain
extension along channels [7]. Extensive molecular simulations
of semi-flexible rings (comprising only a few persistence
lengths P per chain contour length L, as applies to plasmid
mini-rings) and their linear analogues confirmed the observed
trends [20]. The radius of gyration Rg of chains satisfactorily
represents the longitudinal stretching of both linear and
ring chain topology in a channel. Apart from the focus on
moderate confinement, usually investigated in experiments,
simulations show that also strong confinement regime exists
for semi-flexible rings. This regime is unanticipated for
relatively stiff rings in contrast with their linear analogues,
where it is well described as Odijk’s deflection regime [8].
A transition between the moderate and strong confinement
regimes of semi-flexible rings is reported for the first time.
Whereas for linear chains in a tube, the abrupt transition
between the blob and deflection regimes was found at
R/L≈0.8 and D≈P [21], the transition for rings is shifted
to a weaker confinement. Qualitatively similar response of
the chain elongation to the confinement strength variation
Rg (D) is obtained in the case of rings compared with
the linear chains (Figure 1). However, the relative chain
extension in a channel is larger for rings, Odijk’s strong
confinement regime [8] is extended to the larger channel
diameters D and, under the moderate confinement, the chain
extension declines less steeply for cyclic chains. All three
findings are explained in terms of a strong self-avoidance of
Topological Aspects of DNA Function and Protein Folding
Figure 2 Orientation correlations along DNA
Figure 3 Structure factor of linear and cyclic DNA confined in
Dependence of the orientation correlations <ui uj > on the segment
separation n = |i − j| along the chain backbone for cyclic DNA chains
nanochannel
Static structure factor S(q) against wave vector q for cyclic (A) and
of L/P = 15 confined in a cylindrical channel of indicated diameters
D reduced by persistence length P. The curved arrows point from the
free chain to strongly confined conformation. For comparison, a strongly
linear (B) DNA chains of L/P = 15 in the channel of indicated reduced
diameters D/P. The continuous straight line in both graphs is a guide
for the eye representing the slope of − 1 for the rod-like regime [20]
confined linear chain is also included.
in a general q − 1/ν -type behaviour for a polymer coil, where ν is the
Flory exponent. The arrow in (A) indicates the increasing confinement
strength for a ring.
confined chains relative to their linear analogues, stemming
from the increased local density in narrow channels due to
looping of a cycle [20,22–24]. The latter finding is consistent
with the reported experimental measurements [7]. Of
importance, the relative extension for rings in the Odijk
regime [8] is governed by the same analytical function as for
linear chains provided half of the contour length for a cyclic
chain is considered at the full extension. Whereas for the
end-to-end distance of linear chains the established relation
due to Odijk [8], R = L[1 − A(D/P)2/3 ], has generally been
used, for rings, an analogical
relation, but for the radius of
√
gyration, Rgc = (L/2 12)[1 − A(D/P)2/3 ], can be used [20],
with very similar numerical constants A. This is shown clearly
by broken lines in Figure 1. Overall, the simulation results
for the channel-induced DNA elongation R/L for linear and
ring polymers are in harmony with measurements of confined
DNA at high salt concentrations [20,21].
Besides the chain extension profiles Rg (D), the orientation
correlation function and static structure factor for chains of
both architectures have also been studied and have pointed
out the characteristic features responsible for the recognition
of a cyclic architecture either from molecular simulations [20]
or from experiments analysing fluorescence images [29]. The
orientation correlations for a cyclic chain in narrow channels
are characterized by a typical sharp central minimum. Upon
increasing the channel cross-sectional area, the minimum is
broadened, turns into the negative maximum and, ultimately,
the orientation correlations merge with those for a free
cycle (Figure 2). As seen, the difference in the orientation
correlations in a ring and linear chain differs notably,
especially for stiff chains and for the strong confinement.
Confined flexible and less stiff chains resemble their linear
analogues more readily [20].
The structure factor usually evaluated from scattering
techniques in experiments for multichain systems also helps
to resolve the structural differences between confined rings
and linear polymers. Figure 3 shows that the impact of
increasing confinement in a channel on structural behaviour
is better resolved for DNA rings than for the linear polymer
and more for strong confinement [20]. The broader region
with slope − 1 (rod-like behaviour) at high wavelength q (i.e.
more locally) indicates a more extensive rod-like behaviour
for linear chains which are able to extend freely in a narrow
channel relative to rings which in turn loops due to the cyclic
chain topology.
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Furthermore, the role of chain backfolding in techniques
of DNA linearization for linear chains was examined by
simulations [21,27]. Since the folded structures are much
shorter than the straight forms, they tend to reduce
significantly the extension R. The distinctive events of the
transition to shorter folded structures of DNA were detected
on the simulation traces as a function of time. The abundance
of DNA chains folded at the chain ends and in the chain
interior was computed as a function of the channel width
D. The terminal chain regions, because of their enhanced
flexibility, were found to be most prone to the local folding
sketched as the J- or U-type hairpins. The backfolding in
the DNA chain interior into the Z-hairpins or loops is
relatively abundant in the blob regime, significantly restricted
in the transition region and practically absent from the
deflection regime [21]. One should account properly for
the local folding, which represents long-lived metastable
structures, in order to interpret the nanochannels DNA
experiments. Currently, no established theory is available for
the description of DNA conformation in channels with the
diameter comparable with the chain persistence length [27].
Similar events are still to be investigated for the case of ring
topology. In addition, for confined rings, the theory is less
developed than for linear polymers. Both experiment [7] and
early theoretical predictions [22–24] are interpreted on the
basis of stronger self-exclusion in confined rings.
The study of cylindrically confined polymers is not
only of practical importance, but also the first step
towards understanding several biological processes, such as
a bacterial chromosome segregation [17]. The combination
of confinement with crowding in dense macromolecular
systems in the tubular capsids that facilitates the segregation
in bacterial chromosomes is mostly investigated so far
only for flexible chains [30–32]. Recently, an increased
interest appears also in the role of knots under the channel
confinement or in chain unknotting just before the channel
translocation [25]. In this situation, molecular simulations of
channel-confined DNA play an important role in evaluation
of the effects including backfolding, loops, knots and
in the confined rings, where the theoretical picture is
underdeveloped.
Concluding remarks
The molecular simulations using the mesoscopic model
offer a powerful option to obtain an insight into the
behaviour of DNA in nanofluidic devices and to assist in
their development. Mutual comparison of the experimental
and simulation single-chain data presents an opportunity to
test and modify the current theories of confined polymers.
Comparing linear and ring DNA in nanochannels shows
similarities as well as deviations between the two different
chain topologies. Surprisingly, the strong confinement regime
appears also for stiff rings and a similar relation as in the Odijk
regime [8] for the linear polymer describes the extension
of a ring in a channel. The larger relative extension and
more extensive strong confinement regime for DNA rings
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than in linear chains. The structural events in a channel such
as chain backfolding, hairpins or knots, all contributing to
complications in channel linearization experiments, can now
be analysed by simulations. However, an effort to simulate
longer chains is necessary.
Funding
We gratefully acknowledge the support from the Slovak Research
and Development Agency [grant number SRDA-0451-11] and the
Scientific Grant Agency of the Ministry of Education of the Slovak
Republic [VEGA grant numbers 2/0093/12 and 2/0079/12] and
by a postdoctoral position (Z.B.) co-financed by the European Social
Fund [grant number SFRH/BPD/63568/2009].
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Received 24 October 2012
doi:10.1042/BST20120279
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