Conformational Thermodynamics of DNA Strands within Electrically Charged Nanopores

Conformational Thermodynamics of DNA Strands within Electrically Charged Nanopores

Fernando J.A.L. Cruz, JosŽ 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.