(484e) Conformational Thermodynamics of DNA Strands within Electrically Charged Nanopores

Conformational Thermodynamics of DNA Strands
within Electrically Charged Nanopores

Fernando J.A.L. Cruz, Jos? P.B. Mota

LAQV/REQUIMTE, Department of Chemistry, Universidade Nova de Lisboa,
2829-516 Caparica, Portugal

fj.cruz@fct.unl.pt

I.
Introduction

Deoxyribonucleic acid (DNA) and
single-walled carbon nanotubes (SWCNTs) are prototypical one-dimensional
structures, the former in chemical biology and the latter in nanotechnology
[1-3]; a plethora of applications currently envisage carbon nanotubes as
next-generation encapsulation media for biological polymers, such as proteins
and nucleic acids [1]. The interactions between both have been the subject of
intense investigation, nonetheless, the corresponding
molecular-level phenomena remain rather unexplored. Recently we have shown
that, given a sufficiently large hydrophobic nanotube, the confinement of a DNA
dodecamer is thermodynamically favourable under physiological environments (134
mM, 310 K, 1 bar), leading to DNA@nanotube
hybrids with lower free energy than the unconfined biomolecule [4]. To
accommodate itself within the D = 4nm
nanopore, DNA's end-to-end length increases from 3.85 nm up to approximately
4.1 nm, via a 0.3 nm elastic expansion of the strand termini. The canonical Watson-Crick H-bond network is essentially
preserved throughout encapsulation, showing that contact between the DNA
dodecamer and the hydrophobic carbon walls results in minor rearrangements of
the nucleotides H-bonding. A diameter threshold of 3 nm was established below
which encapsulation is inhibited.

It is well known
that nanotubes can be electrically charged, either using an
AFM tip and applying a voltage bias or by chemically doping the solids
with p-type dopants to obtain positively charged solids [5,6]. The effect of
charge density upon the energetics and dynamics of confinement needs to be
addressed; because DNA's outer surface is negatively charged (phosphate
moieties), its interaction with a positively charged solid might lead to the
occurrence of encapsulation which is prohibited for purely hydrophobic nanopores. We address this issue using enhanced
sampling algorithms (metadynamics,
umbrella sampling) to probe the
encapsulation mechanism of an atomistically detailed DNA dodecamer (5'-D(*CP*GP*CP*GP*AP*AP*TP*TP*CP*GP*CP*G)-3'),
onto positively charged (q = + 0.05 e^–/C)
SWCNTs of different diameters (3 – 4 nm). In order to allow the
extrapolation of results for in vivo
systems, precise physiological conditions are employed ([NaCl]=134
mM, 310 K, 1 bar).

II.
Results & Discussion

In contrast with a purely hydrophobic
(40,0) topology (D = 3 nm), the
existence of an overall positive charge density on the solid favours the
encapsulation of the DNA segment. To probe the thermodynamical stability
associated with encapsulation, free-energy landscapes are built using the
well-tempered metadynamics scheme [7] and two order parameters relating the
distance between centres of mass of DNA and SWCNT,  f₁, and the end-to-end length of the
biomolecule, f₂. The corresponding Gibbs free-energy maps
recorded in Figure 1 show that: i) the nanopore
endohedral volume ( f₁ < 2) is the thermodynamically
preferred region, by comparison with the bulk (f₁ > 2), ii) encapsulated DNA retains its translational mobility, diffusing
freely between adjacent free-energy minima located within the solid and iii) DNA maintains a quasi B-form end-to-end length within
the charged topologies (D = 3 –
4 nm). The end-to-end length, Q, probability distributions, P( Q), have been independently probed by
umbrella sampling calculations and the results are recorded in Figure 2 for
both charged topologies, (40,0) and (51,0), along with the previous results
obtained for a purely hydrophobic (51,0) SWCNT [4]. It now becomes clear that
charge density on the solid plays a paramount role upon the encapsulation
mechanism; the elastic expansion of the double-strand observed for the (51,0)
hydrophobic pore (Q = 4.01 nm) is annihilated when the solid
becomes electrically charged, resulting in a maximum probability DNA end-to-end
length of Q = 3.73 nm, consistent with the canonical
B-DNA form [8]. The bimodal symmetry associated with the electrostatically
charged nanotubes clearly identify the probability maxima corresponding to the
equilibrium conformations (Q = 3.73-3.75 nm), but also two other forms of DNA,
at Q = 3.51 nm (40,0) and Q = 4.29 nm (51,0), where the former corresponds to a
compressed conformation of the double-strand.

A nanoscopic picture of
the encapsulated DNA molecule is produced by calculating the corresponding
number density maps, as indicated in Figure 3 and obtained from atomically
detailed mass histograms (binwidth = 2«10^–3 nm). Figure 3 reveals the
existence of a cylindrical exclusion volume centred along the (51,0) main axis,
where molecular density is  r Å 0, which can be attributed to the
strong electrostatic attraction between DNA (phosphate ions) and the solid, pulling
the former towards the walls and away from the nanopore center. Entropic
effects caused by the pore narrowness of the (40,0) SWCNT force the DNA
molecule to cluster tightly around the nanopore center, where it exhibits the
region of highest molecular density.

As far as we are aware these observations
are the first of their kind, and they come to pave the way for the design of
smart nanotube based devices for in vivo
DNA encapsulation.

Acknowledgements. This
work makes use of results produced with the support of the Portuguese National
Grid Initiative (https://wiki.ncg.ingrid.pt). F.J.A.L. Cruz gratefully
acknowledges financial support from FCT/MCTES (Portugal) through grants
SFRH/BPD/45064/2008 and EXCL/QEQ-PRS/0308/2012.

References.  ADDIN EN.REFLIST [1] H. Kumar
et al., Soft Matter 7 (2011) 5898. [2] B.M. Venkatesan and
R. Bashir, Nature Nano. 6 (2011) 615. [3] A.D. Franklin et al., Nano Lett. 12 (2012)
758. [4] F.J.A.L. Cruz et al., J. Chem. Phys. 140
(2014) 225103. [5] X. Zhao and J.K. Johnson, J. Am. Chem. Soc. 129 (2007) 10438. [6] F.J.A.L. Cruz et al., RSC Advances 4
(2014) 1310. [7] A. Barducci et al., Phys. Rev. Lett. 100 (2008) 020603. [8] J.M. Vargason et al., Proc. Nat. Acad. Sci.
98 (2001) 7265.

FIGURE 1 – Gibbs free-energy maps of
encapsulated DNA. f₁ is the distance between centres of mass of DNA and
the SWCNT, projected along the nanopore main axis (z), and f₂ corresponds to the DNA end-to-end length measured
between opposite (GC) termini.
Low-lying free-energy valleys, evidenced as dark blue regions, are always
distributed along the nanopore internal volume, f₁ < 2.1 nm, and the absolute minima are observed
at the following (f₁, f₂) pair values:
,
,
.

FIGURE
2 – Probability distribution and potential of mean force
(PMF) profiles of encapsulated DNA. Because Q was
built as the double-strand end-to-end length, the bimodal symmetry associated
with the electrostatically charged nanotubes clearly identify the probability
maxima corresponding to the equilibrium conformations (Q=3.73-3.75 nm), but also two other two other forms of DNA,
at Q = 4.29 nm and a non-canonical
conformation at Q = 3.51 nm.
Symbols are the results obtained using umbrella sampling and red lines
corresponding to numerical fittings using Gaussian statistics: black) (51,0) q = 0, green) (51,0) q = +0.05 e^-/C and blue) (40,0) q = +0.05 e^-/C. The Gaussian curve for the (40,0) topology was determined in the
range Q > 3.5
nm.

FIGURE
3 – 2D molecular density maps of DNA at the charged topologies. The dashed lines in the middle figures indicate the
boundaries of the single-walled carbon nanotubes. The black lines recorded on
the inset graphs are 1D density profiles obtained along the corresponding
dimension.