THE JOURNAL OF CHEMICAL PHYSICS 140, 225103 (2014)

Endohedral confinement of a DNA dodecamer onto pristine carbonnanotubes and the stability of the canonical B form

Fernando J. A. L. Cruz,1,2,a) Juan J. de Pablo,2,3 and José P. B. Mota1

1Requimte/CQFB, Departamento de Química, Faculdade de Ciências e Tecnologia,Universidade Nova de Lisboa, Caparica 2829-516, Portugal2Department of Chemical and Biological Engineering, University of Wisconsin-Madison,Madison, Wisconsin 53706, USA3Institute of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, USA

(Received 21 February 2014; accepted 12 May 2014; published online 13 June 2014)

Although carbon nanotubes are potential candidates for DNA encapsulation and subsequent deliveryof biological payloads to living cells, the thermodynamical spontaneity of DNA encapsulationunder physiological conditions is still a matter of debate. Using enhanced sampling techniques,we show for the first time that, given a sufficiently large carbon nanotube, the confinement ofa double-stranded DNA segment, 5′-D(∗CP∗GP∗CP∗GP∗AP∗AP∗TP∗TP∗CP∗GP∗CP∗G)-3′, isthermodynamically favourable under physiological environments (134 mM, 310 K, 1 bar), leadingto DNA-nanotube hybrids with lower free energy than the unconfined biomolecule. A diameterthreshold of 3 nm is established below which encapsulation is inhibited. The confined DNA segmentmaintains its translational mobility and exhibits the main geometrical features of the canonical Bform. To accommodate itself within the nanopore, the DNA’s end-to-end length increases from3.85 nm up to approximately 4.1 nm, due to a ∼0.3 nm elastic expansion of the strand termini.The canonical Watson-Crick H-bond network is essentially conserved throughout encapsulation,showing that the contact between the DNA segment and the hydrophobic carbon walls results inminor rearrangements of the nucleotides H-bonding. The results obtained here are paramount to theusage of carbon nanotubes as encapsulation media for next generation drug delivery technologies.© 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4881422]

I. INTRODUCTION

Deoxyribonucleic acid (DNA) and single-walled car-bon nanotubes (SWCNTs) are prototypical one-dimensionalstructures; the former plays a central role in chemical bi-ology and the latter holds promise for nanotechnologyapplications.1–3 From the point of view of biological pur-poses and DNA manipulation, carbon nanotubes have beenproposed to be used as templates for DNA encapsulation,4, 5

intracellular penetration via endocytosis and delivery of bio-logical payloads,6, 7 and ultrafast nucleotide sequencing.2, 8, 9

While structure in its natural form and environment is wellestablished (e.g., B-DNA in aqueous solution), their interac-tions have been the subject of intense investigation,4, 5, 8, 10–16

nonetheless, the corresponding molecular-level phenomenaremain rather unexplored. Is confinement thermodynamicallyspontaneous (free-energy)? How important are the conforma-tional properties of the encapsulated double-strand (entropy)?How does the confinement process depend on nanotube di-ameter? Moreover, previous work has focused almost exclu-sively on exoadsorption of DNA on the external surface ofSWCNTs,8, 11, 17–19 overlooking the possibility of endohedralconfinement. Nonetheless, it is well known that the confor-mational properties of biopolymers under confinement are ofcrucial relevance in living systems (e.g., DNA packing in eu-karyotic chromosomes, viral capsids).

a)Author to whom correspondence should be addressed. Electronic mail:fj.cruz@fct.unl.pt.

DNA encapsulation is a phenomenon that remains ut-terly unmapped. Most of the earlier work focused on tem-peratures markedly distinct from the physiological value,precluding extrapolation of results to in vivo conditions. Thepioneer work of Lau et al.5 showed that a small DNA strand,initially confined in a 4 nm diameter nanotube, exhibits dy-namics similar to the unconfined molecule, but that behaviouris drastically altered when diameter is decreased to 3 nm. Be-cause the DNA had been artificially inserted, no informationabout the encapsulation process itself, e.g., its thermodynam-ical spontaneity and kinetics, was provided. Previous exper-iments and calculations indicate that the biomolecule can beconfined onto D = 2.7 nm SWCNTs13 and D = 3–4 nm multi-walled carbon nanotubes (MWCNTs),20, 21 however, the cor-responding working temperatures (350–400 K) were far toohigh to have any physiological relevance. Furthermore, theexperimental observations of Iijima et al. indicated that en-capsulation of DNA onto MWCNTs was a competing mech-anism with wrapping of the biomolecule around the externalwall;20 their reported data failed to identify the relevant condi-tions upon which the confinement process is favoured, such asionic strength of the media and temperature. Recently, Mogu-rampelly and Maiti addressed22 the encapsulation of dsDNAand siRNA onto SWCNTs, and established a critical diameterof D = 2.67 nm and D = 2.4 nm for the former and the latter,respectively, below which confinement was completely inhib-ited, and attributed it to a large free-energy barrier associatedwith the nanopore entrance.

0021-9606/2014/140(22)/225103/10/$30.00 © 2014 AIP Publishing LLC140, 225103-1

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225103-2 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

Our results obtained under precise physiological condi-tions (310 K, 1 bar, [NaCl] = 134 mM) show that an atom-ically detailed DNA dodecamer can be encapsulated onto aD = 4 nm SWCNT, resulting in a decrease of the system’sfree energy. Encapsulation kinetics is fast (<16 ns) and thedouble strand retains its translational mobility within the nan-otube. Very interestingly, our data indicate that the encap-sulated molecule free-energy minima correspond to a DNAconformation similar to the bulk canonical B form,23 witha pitch length of 3.4 nm (10 bps repeating unit) and a dou-ble strand end-to-end length of approximately 4.1 nm. Thecanonical Watson-Crick H-bonds network is roughly main-tained throughout confinement, exhibiting probability dis-tributions essentially corresponding to more than 75% ofhydrogen bonds existence. As far as we are aware these ob-servations are the first of their kind, and they come to pavethe way for the design of smart nanotube-based devices for invivo DNA encapsulation.

II. MODELS AND METHODS

A. Molecular models

All molecules in this work are described using atomisti-cally detailed force fields, including electrostatic charges ineach atom. The dispersive interactions are calculated withthe Lennard-Jones (12,6) potential, cross parameters be-tween unlike particles determined by the classical Lorentz-Berthelot mixing rules, and electrostatic energies describedby Coulomb’s law. DNA is modelled as a completely flex-ible molecule within the framework of the AMBER99sb-ildn force-field,24, 25 the corresponding potential energiesassociated with bond stretching and angle bending are cal-culated with harmonic potentials, whilst the dihedral ener-gies, U(ϕ), are computed via Ryckaert-Bellemans functions,

U (ϕ) = ∑dihedrals

5∑n=0

Cn[cos(ϕ − 180◦)]; we have included in

the potential the refinements recently proposed by Lindorff-Larsen et al.,25 which result in improved accuracy of the DNAbackbone dihedrals. The Na+ and Cl− ions are describedusing the parameterization of Aqvist and Dang26 and thewater molecules by the TIP3P force field of Jorgensen and co-workers;27 a recent discussion on the NaCl force-field influ-ence upon the static and dynamic properties of nucleic acidsunder physiological conditions can be found elsewhere.26, 28

To maintain computational tractability, we have chosen thedouble-stranded B-DNA Dickerson dodecamer,29, 30 exhibit-ing a pitch31 of ∼3.4 nm corresponding to an average of 10–10.5 base-pairs per turn over the entire helix,23 and with adouble-strand end-to-end length of ∼3.8 nm measured be-tween terminal (GC) base pairs; the well-known A-DNA formhas a pitch length of ∼2.6 nm with an average of 11 base-pairsper turn.23 Considering that the B-DNA backbone phospho-rus atoms lie on a cylindrical surface, the average diameter ofthe double-strand corresponds to ∼2 nm.31 Although explic-itly smaller in length than genomic DNA, the Dickerson do-decamer main structural features resemble those of genomicλ-bacteriophage DNA,32 namely, in the radius of gyration

and double-strand backbone diameter, Rg ≈ 0.7–1 nm andD ≈ 2 nm.

Recently, large diameter (D ≈ 4 nm) single-walled car-bon nanotubes have been prepared using supported-catalystchemical vapour deposition.33 In order to probe the confine-ment of DNA into such large, hollow nanostructures, we haveadopted two different diameter SWCNTs with zig-zag sym-metry, both with length L = 8 nm; the skeletal diameters, mea-sured between carbon centres on opposite sides of the wall,are D = 4 nm (51,0) and D = 3 nm (40,0). The walls are builtup of hexagonally arranged sp2 graphitic carbon atoms, witha C–C bond length34, 35 of 1.42 Å, whose Lennard-Jones po-tential is given by Steele’s parameterization (σ = 0.34 nm,ε = 28 K).36 The positions of all solid atoms are fixedthroughout the calculations.

B. Methodology and algorithms

Large simulation cells with dimensions (x, y, z) = 11× 11 × 15 nm were built according to the following stepwiseprocedure: (i) initially the solid was placed inside the emptycell, aligned along the z-axis, and the DNA molecule insertedat a distance of 0.5 nm away from the nanopore entrance, (ii)the whole cell was solvated with H2O (ρ = 1 g/cm3) and theappropriate number of Na+ and Cl− ions were added to en-sure physiological ionic strength, [NaCl] = 134 mM, (iii) thenthe whole system was energy-minimized and equilibrated dur-ing at least 0.8 ns, first in the canonical ensemble and then inthe isothermal–isobaric ensemble, resulting in a fully equili-brated simulation cell, as observed by the constancy of themain thermodynamical parameters (potential energy, temper-ature, volume, and pressure). During minimization and equi-libration the DNA position was constrained; once these stepswere completed, the biomolecule was unconstrained, produc-tion runs were started and data collected over a time intervalof 0.07–0.1 μs. The box dimensions were chosen in order toaccommodate a 3.5 nm solvation shell in all directions aroundthe nanotube.

Molecular dynamics (MD) simulations in the isothermal–isobaric ensemble (NpT) were performed using the Gromacsset of routines.37 Newton’s equations of motion were inte-grated with a time step of 1 fs and using a Nosé–Hooverthermostat38, 39 and a Parrinello–Rahman barostat40 to main-tain temperature and pressure at 310 K and 1 bar, respec-tively. A potential cut-off of 1.5 nm was employed for boththe van der Waals and Coulombic interactions, and the long-range electrostatics were calculated with the particle-meshEwald method41, 42 using cubic interpolation and a maximumFourier grid spacing of 0.12 nm. Three-dimensional peri-odic boundary conditions were applied. The well-temperedmetadynamics scheme of Barducci and Parrinello43 was em-ployed to obtain the free-energy landscape associated with theconfinement mechanism. The well-tempered algorithm biasesNewton dynamics by adding a time-dependent Gaussian po-tential, V(ζ ,t), to the total (unbiased) Hamiltonian, prevent-ing the system from becoming permanently trapped in localenergy minima and thus leading to a more efficient explo-ration of the phase space. The potential V(ζ ,t) is a functionof the so-called collective variables (or order parameters),

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225103-3 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

ζ (q) = [ξ 1(q), ξ 2(q), . . . , ξ n(q)], which in turn are related tothe microscopic coordinates of the real system, q, accordingto Eq. (1):

V (ζ (q), t) = W

t ′≤t∑t ′=0

exp

(−V (ζ (q(t ′)), t ′)

T

)

× exp

(−

n∑i=1

(ζi(q) − ξi(q(t ′)))2

2σ 2i

), (1)

where t is the simulation time, W = τGω is the height of asingle Gaussian, τG is the time interval at which the contri-bution for the bias potential, V(ζ ,t), is added, ω is the ini-tial Gaussian height, T is a parameter with dimensions oftemperature, σ i is the Gaussian width, and n is the num-ber of collective variables in the system; we have consideredτG = 0.1 ps, ω = 0.1 kJ/mol, T = 310 K, and σ = 0.1nm. The parameter T determines the rate of decay for theheight of the added Gaussian potentials and when T → 0the well-tempered scheme approaches an unbiased simula-tion. The SWCNTs are primarily one-dimensional symmet-ric, therefore, we decided to construct the free-energy land-

scape in terms of two collective variables, ξ1 =−→R

DNA

z −−→R

SWCNT

z

and ξ2 = |−→R GC

1 − −→R

GC

12 |, where−→R is the positional vec-

tor of the centre of mass of the biomolecule (−→R

DNA

z ) and

of the nanotube (−→R

SWCNT

z ), projected along the z-axis, or ofthe terminal (GC) nucleobase pairs at the double-strand ter-

mini, (−→R

GC

1 ) and (−→R

GC

12 ). According to our definition of col-lective variables, ξ 1 corresponds to the z-distance betweenthe biomolecule and the nanopore centre and ξ 2 can be in-terpreted as the DNA end-to-end length. The characteris-tic lengths of the nanotube and Dickerson dodecamer are,respectively, L = 8 nm and L = 3.8 nm, and thereforeany value ξ1 = L = (LSWCNT − LDNA) / 2 < 2.1 nm cor-responds to a DNA–SWCNT hybrid in which the biomoleculeis completely encapsulated within the solid; the thresholdξ 1 > 5.9 nm obviously indicates the absence of confine-ment. At the end of the simulation, the three-dimensionalfree-energy surface is constructed by summing the accumu-lated time-dependent Gaussian potentials according to F (ζ, t)= − T +T

TV (ζ, t). A discussion of the algorithm’s conver-

gence towards the correct free-energy profile is beyond thescope of this work and can be found in Refs. 43 and 44; suf-fices to say that it in the long time limit, (∂V (ζ, t) / ∂t) →0, the well-tempered method leads to a converged free-energy surface. An alternative approach to obtain the time-independent free-energy surface relies on integrating F(ζ , t)at the final portion of the metadynamics run.44 The convergedfree-energy can thus be mathematically obtained from Eq. (2),

F (ζ ) = − 1

τ

ttot∫ttot−τ

V (ζ, t), (2)

where ttot is the total simulation time and τ is the time windowover which averaging is performed. We have implementeda convergence analysis for each collective variable, ξ 1 andξ 2, splitting the last 40 ns of simulation time into τ = 4 nswindows,30 and the results show that the bias potential V(ζ , t)

has converged, and thus the three-dimensional surface ofFigure 2 is a good estimator of the free-energy changes as-sociated with molecular encapsulation.

Independent calculations were performed using the um-brella sampling technique.45, 46 For a system composed of Nparticles, the method consists in biasing the classical (un-biased) Hamiltonian that depends on the potential, U(rN),and kinetic energies, Ekin(pN), by introducing a time in-dependent harmonic potential, V ( i) = 1

2k( i − 0i )2, ac-

cording to H (rN , pN, i) = U (rN ) + Ekin(pN ) + V ( i); kis the harmonic force constant, i is an order parameter and 0

i corresponds to the position of the umbrella restrain; in

the present case, 1 = |−→R DNA − −→R

SWCNT | corresponds tothe absolute three-dimensional distance between the centresof mass of the double-strand and the SWCNT, and 2 =|−→R r1r24 − −→

Rr12r13| is equivalent to the DNA end-to-end dis-

tance measured between termini. We have adopted 01 = 0

and 02 = 4.1 nm, in direct analogy with the collective vari-

ables defined in the well-tempered metadynamics algorithm,ξ 1 and ξ 2. When such a biasing potential is used, the biasedprobability distribution of the system, Pb( i), can be obtainedfrom a Boltzmann weighted average along the i order pa-rameter and, therefore, assuming that the system is ergodic,46

P b( i) =∫

exp{−β[U (r) + V ( ′i(r))]}δ[ ′

i(r) − i]dNr∫exp{−β[U (r) + V ( ′

i(r))]}dNr,

(3)where β = (1 / kBT), kB is the Boltzmann constant, δ is theDirac delta function, and N is the total number of particles inthe system. Because the biasing potential depends only on theorder parameter i, and the integration in the numerator isperformed over all degrees of freedom except , the unbiasedprobability of the real system, Pu( i), can be evaluated fromEq. (4),

P u( i) = P b( i)expβV ( i )�, (4)

where � = −(1 / β)ln〈e−βV ( )〉 is independent of i and thetriangular brackets denote an ensemble average. The recon-struction of the true (unbiased) free energy profile or po-tential of mean force,47 consistent with the Gibbs free en-ergy, PMF( ) = −kBTlnPu( ), is accomplished using theweighted histogram analysis method.47–49

C. Parametric analysis

The radius of gyration, Rg, gives a measure of amolecule’s compactness and is defined by Eq. (5),

Rg =√√√√(

N∑i

‖ri‖2 mi

) /N∑i

mi, (5)

where N = 758 is the total number of atoms in the DNAmolecule, mi is the mass of atom i, and ri is the positionalvector of the atom relative to the molecular center of mass.The root mean squared deviation, RMSD, is obtained by cal-culating the distance rij between atoms i and j at time t, andcomparing with the same distance observed at time t = 0,

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225103-4 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

according to

RMSD =√√√√(1 /N2)

N∑i=1

N∑j=1

‖rij (t) − rij (0)‖2. (6)

III. RESULTS AND DISCUSSION

Confinement of double-stranded DNA (dsDNA30) into a(51,0) nanotube (D = 4 nm) is fast and becomes completewithin the first 16 ns of observation time. Initially, the doublestrand is in the bulk (0–2 ns) and as it diffuses towards theSWCNT entrance undergoes structural rearrangements lead-ing to minor increases in pitch length, P, and end-to-end dis-tance, L (Fig. 1(a)). After 2 ns, the dodecamer is already at thenanopore entrance, where it experiences strong van der Waalsattractions towards the solid,30 resulting in complete encap-sulation at 15.4 ns, after which the double-strand relaxes to

P ≈ 3.4 nm and L ≈ 4–4.1 nm. It is very interesting to observethat confinement appears to be permanent, i.e., the DNA frag-ment never returns to the bulk solution during the observationtime window, maintaining direct local contact with the solidwall at a distance of closest approach of ca. 2.6 Å. Nonethe-less, the encapsulated molecule clearly retains its transla-tional mobility, diffusing freely along the nanopore main axis(Fig. 1(b)). The encapsulation mechanism can be divided intoa three-step process: (I) fast diffusion of DNA towards thenanopore entrance (0–2 ns), (II) strong van der Waals attrac-tions towards the solid, leading to confinement of terminus 1at 2.33 ns, followed by structural rearrangements of the wholedouble strand occurring in bulk solution (t < 15 ns), and fi-nally (III) penetration of terminus 2 into the confining volumeresulting in complete encapsulation of the biomolecule.

In contrast, the narrowness of a (40,0) topology (D= 3 nm) completely inhibits encapsulation even over an ob-servation time of 0.1 μs. Instead, the DNA contact with the

Confinement@(51,0) (a) (b)

15.42 ns15.42 ns

-8-8 -4-4 0

IIIIIIIIII

I

56.64 ns

(d)

(c)P P = 3.4 nm= 3.4 nm L L = 4.1 nm= 4.1 nm

FIG. 1. Encapsulation of double-stranded DNA into a (51,0) SWCNT at T = 310 K and [NaCl] = 134 mM. (a) Kinetics: Encapsulation is complete after15.4 ns after which the double strand never returns to the bulk solution during the observation time window; nonetheless, DNA maintains its translationalmobility within the nanopore: (black) distance between centres of mass (c.o.m.s) of DNA and the (51,0) SWCNT, (dark red) distance between c.o.m.s of DNAand the (40,0) SWCNT, (green) distance between opposite GC termini in the double strand, e.g., DNA end-to-end length, L, (blue) DNA pitch length, (grey)minimum distance between any DNA atom and the SWCNT. A 2 nm c.o.m. distance between the biomolecule and the solid corresponds to the threshold belowwhich complete encapsulation is considered to occur. (b) State diagram of the encapsulation mechanism: Lines represent distances between terminal nucleobasepairs and the SWCNT entrance through which encapsulation takes place, projected along the nanotube main axis: (black) terminus 1 and (red) terminus 2. Thehorizontal dashed lines correspond to the SWCNT boundaries and the inset magnification depict the first instant just after complete encapsulation occurs,representing the terminus 1 atoms in black and the terminus 2 atoms in red. Note that the confined molecule maintains its translational mobility along thenanopore’s axial axis. (c) Probability distribution profiles of DNA encapsulated into a (51,0) SWCNT: Pitch (blue dots) and DNA length (green dots); red linescorrespond to Gaussian fittings of simulation data. (d) DNA characteristic lengths: (black) radius of gyration, Rg, (grey) z-component of the radius of gyration,Rz

g, (blue) root mean-squared deviation, RMSD. After confinement, molecular conformation deviates minimally from the canonical B-DNA form, RMSDaver

= 0.36 ± 0.002 nm, and maintains a quasi-linearity about the nanopore main axis.

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225103-5 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

smaller nanopore results in the occurrence of two distinctstates: (i) exoadsorption onto the external surface of the nan-otube via a π–π stacking mechanism of a terminal (GC)nucleobase pair onto the graphitic surface, and threading ofthe biomolecule along the hydrophobic cylinder similar toprevious observations,11 or (ii) trapping of the DNA at thenanopore entrance, with partial melting of the double-strandterminus closest to the solid; Mogurampelly et al.22 observedthat encapsulation onto a (20,20) tube (D = 2.67 nm) is ther-modynamically prohibited due to a large free-energy barrierlocated at the nanopore entrance. The decomposition of theinteraction energies between DNA and the surrounding envi-ronment, solid and solution,30 can help to throw some lightonto this issue. Upon confinement onto the (51,0) topology,the dodecamer becomes less solvated by the H2O moleculesthan in the bulk, as indicated by a decrease of the DNA/H2Ointeraction energy of 1327 kJ/mol, and leading to a thin hydra-tion shell of ca. 1–2 water molecules between the biomoleculeand the solid walls. However, this instabilization is roughlycompensated by an increase of the DNA/ions interactionsof −851 kJ/mol and also by the intrinsic effect exerted bythe hydrophobic solid upon the DNA van der Waals cloudof −442 kJ/mol. On the other hand, molecular exoadsorp-tion onto the (40,0) nanotube prevents stabilization of thebiomolecule from the dispersive interaction with the graphiticwalls, leading to a diminished DNA/(40,0) interaction en-ergy of −170 kJ/mol, clearly insufficient to overcome theenergetic penalty of a decreased solvation effect caused byencapsulation.

At physiological conditions the canonical B-form is ds-DNA most stable configuration;31, 50 however, little is knownwhen the molecule is confined into a strongly hydropho-bic solid, such as a carbon nanotube. The data recorded inFig. 1(a) suggest that this is also the case for encapsulateddsDNA. In fact, when simulation results are used to deter-mine distribution histograms, the corresponding frequenciesare well correlated by Gaussian statistics exhibiting a pitchlength of P = 3.4 nm, for a 10 nucleobase pair repeating unit,and a double strand length of L = 4.1 nm (Fig. 1(c)), con-sistent with the geometrical characteristics of B-DNA in bulksolution.23 We have determined the biomolecular characteris-tic lengths—radius of gyration (Rg, Eq. (5)) and its projectionalong the nanotube main axis (Rz

g) as well as the root-meansquared deviation (RMSD, Eq. (6)) from the B-DNA Dicker-son dodecamer used as starting configuration30—and plottedthem in Fig. 1(d). Because the RMSD compares the structureat any time t with the original DNA structure (t = 0), the bluecurve in Fig. 1(d) indicates a minor relaxation of the double-strand from the crystal structure to accommodate liquid stateflexibility, whilst maintaining the relative average distancebetween each atom in the double-strand. After 20 ns, thedata converged smoothly to average values of RMSD = 0.36± 0.002 nm and Rz

g = 1.02 ± 0.0015 nm; the latter value indi-cates an alignment of the biomolecule along the axial axis ofthe nanopore. The Rz

g = 0.8 nm depression observed at 56.6ns is transient and matches a total number of Watson-Crick Hbonds of 28.

The thermodynamical stability of molecular encapsula-tion is probed by the free-energy (F) differences associated

with the process, using well-tempered metadynamics.43, 44 Wehave chosen two order parameters to construct the free-energylandscape, ξ 1 and ξ 2, where ξ 1 is the distance between centresof mass of DNA and SWCNT, projected along the nanoporemain axis (z), and ξ 2 is the absolute distance between the(GC) termini on opposite sides of the double-strand, equiva-lent to the DNA end-to-end length (cf. Sec. II). An inspectionof the resulting 3D surface (Figure 2) reveals the existence offive distinct free-energy minima, sharing in common the factthat all are located at discrete positions along the internal vol-ume of the nanopore, ξ 1 < 1.8 nm; the absolute minimum atξ 1 = 0.117 nm indicates that the center of the nanotubeis the most energetically stable region for the encapsulatedbiomolecule, which results in the strongest concentration ofmolecular density at that location.30 Owing to their thermo-dynamical similarity, the five free-energy minima along ξ 1

provide a minimum free-energy path along which DNA cantranslate within the pore, visiting maximum probability con-figurations as indicated by the dotted line in Figure 2. In or-der to escape from those deep free-energy valleys, F (ξ 1, ξ 2)∼ −40 kJ/mol−1, DNA has to overcome large energetic bar-riers, rendering the exit process towards the bulk solutionthermodynamically expensive. The reversibility of encapsula-tion is discussed in the Conclusions, where different ejectionmechanisms are tackled to externalize the biomolecule.

It is remarkable to observe that the exact position ofthe free-energy minima is almost invariant at ξ 2 ∼ 4.1 nm,consistent with the end-to-end length of L = 3.8 nm of aB-DNA conformation. We have performed independent um-brella sampling calculations, using an harmonic bias, to de-termine the potential of mean force (PMF) and the system’sthermodynamical probability distribution, P( i), employingtwo order parameters to describe the distance between cen-tres of mass (c.o.m.s) of DNA and the solid, 1, and theend-to-end length of the double-strand, 2. The calculationswith 1 clearly corroborate the main findings revealed by themetadynamics analysis, namely, that the system has proba-bility maxima at 1 = (0.21, 1.62, 1.92) nm (Figure 3); theDNA molecule is fairly mobile inside the nanopore, easilymoving from one free-energy minimum to an adjacent one.The thermodynamical robustness of the canonical B-formunder confinement is illustrated by the Gaussian profile as-sumed by the probability distribution regarding the DNA end-to-end length, Figure 3. P( 2) is well described by P ( 2)= ϕexp[− 1

2 ( 2 − 02 / σ )2], with a Gaussian peak width at

half height of σ = 0.16 nm, φ = 4.32 × 10−2, and a peakcentered at 0

2 = 4.01 nm ± 0.001 nm corresponding to theequilibrium (unbiased) end-to-end distance of encapsulateddsDNA, L. It now becomes clear that a perturbation of thedouble strand towards non-equilibrium values of L, leading toeither a contraction ( 2 < 4.01) or a stretching ( 2 > 4.01) ofB-DNA, results in a rapid increase of the associated potentialof mean force rendering the perturbation process thermody-namically unstable.

In spite of the thermodynamical stability of the encap-sulated B-form, the geometric characteristics of the dou-ble strand naturally oscillate about their equilibrium val-ues, such as the angles between each individual strandtermini, ϕij. Postulating that C corresponds to the DNA

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225103-6 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

0 0.5 1 1.5 2 2.5 3

3

43.5

54.5

-10

-20

-30

-40

0

1 (nm)

2 (nm)

F (

kJ/m

ol)

(a)

1=0.117

(c)

1=1.307

(b)

1=0.621

(d)

1=1.796ξ

ξ

ξ

ξ

ξ

ξ

FIG. 2. Free energy landscape of DNA@(51,0) SWCNT hybrid. The thermodynamical surface is built using two macroscopic descriptors, ξ1 and ξ2, whereξ1 is the distance between centres of mass of the dsDNA and nanotube, projected along the nanopore main axis (z), and ξ2 is the absolute distance between the(GC) termini on opposite sides of the double-strand, equivalent to the dsDNA end-to-end length. The several adjacent free-energy minima along ξ1 demonstratethat the molecule is relatively mobile to translocate along the nanotube, however, the absolute minimum at ξ1 = 0.117 nm indicates that the nanopore center isthe energetically favoured region upon confinement. All the ξ1 minima are located along a quasi-linear path defined by ξ2 ≈ 4.1 nm highlighting the enhancedthermodynamic stability associated with the canonical B form. The snapshots were taken at different time intervals corresponding to (ξ1, ξ2) nm: (a) (0.117,4.112), (b) (0.621, 4.164), (c) (1.307, 4.164), and (d) (1.796, 4.115). H2O molecules and Na+ and Cl− ions are omitted for clarity sake.

molecular center and is given by the average axes bridg-ing the individual strands (Figure 4), then ϕij = � ( ri · C · rj )= arccos[(‖ ri‖2 + ‖ rj‖2 − ‖ ri − rj‖2) / (2‖ ri‖‖ rj‖)], where ri is the positional vector, with origin at C, of a terminalphosphorus atom belonging to nucleotide i. To simplify thenotation, let φ1 = φ2 24 = � (r2 · C · r24) and φ2 = φ12 14

= � (r12 · C · r14), which for the crystalline form of pure B-DNA assume the values ϕ1 = 55.9◦ and ϕ2 = 56.6◦ as mea-sured by Dickerson and co-workers.29 The anisotropy of theterminal angles is simply given by φ = (φ1 − φ2). The

local elevation of ϕ observed in the 10−20 ns time window,an interval during which DNA is being confined, falls back tonegligible values (ϕ ≈ 0.35◦) indicating that the anisotropicdeformation of the double strand is reversible once confine-ment is complete. Because the molecule undergoes encap-sulation from the ϕ2 termini, the fact that ϕ1 > ϕ2 whileconfinement takes place indicates a slight compression at theϕ2-end, which is replicated on the other side of the chain (ϕ1)as it penetrates into the SWCNT. This previously unobservedcompression phenomenon is an entropic effect arising from

1

Po

ten

tial

of

Mea

n F

orc

e (k

J/m

ol)

Pro

bab

ility

Po

ten

tial

of

Mea

n F

orc

e (k

J/m

ol)

Pro

bab

ility

FIG. 3. Potential of mean force, PMF (black), and probability distribution (blue line, blue dots). 1 is the order parameter defined by the distance betweencentres of mass of DNA and the nanotube and 2 is the end-to-end distance of the double-strand. The 2 probability distribution curve is Gaussian shaped andthe red line is the best fit of P ( 2) = ϕexp[− 1

2 ( 2 − 02 / σ )2] to the umbrella data.

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225103-7 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

(d)

X-perspectiveZ-perspective

y

x

(a)

(b)

(d)(c)

Δϕ (

deg

)

ϕ i (

deg

) Δϕmax=16.5º20

40

6080

100t (ns)

-15

0

20

20 30 40 50 60

ϕϕ1ϕ2 C

n2n12

n24n14

(c)

(a)

(b)

y

z

(e)(e)

FIG. 4. (Top) Quasi-isotropic individual axis distribution for confined DNA. (grey) axis corresponding to strand A, running from nucleotide 2 up to nucleotide12, (red) axis corresponding to strand B (n14-n24). The double-helix representation is as follows: (ochre), DNA backbone, (grey and red), single-strand axis,(pink) double-strand average axes; (a) (ϕ1, ϕ2) = (55.9, 56.6)◦, crystalline B-DNA Dickerson structure, t = 0 ns; (b) (ϕ1, ϕ2) = (48.36, 31.84)◦, t = 12.47 ns;(c) (ϕ1, ϕ2) = (41.5, 37.9)◦ t = 17.5 ns (during confinement); (d) (ϕ1, ϕ2) = (40.7, 37.4)◦, t = 30 ns; (e) (ϕ1, ϕ2) = (39.8, 38.5)◦, t = 70 ns. Notice the almostparallel alignment of the individual strand axis observed in the crystalline Dickerson dodecamer. H2O molecules and NaCl ions are omitted for clarity. (Bottom)Temporal evolution of the inter-strand terminal angles. The double-strand backbone is coloured ochre and the single-strand individual axes are coloured greyand red. The log-scale on the left reads the individual double-strand terminal angles, ϕ1 (grey) and ϕ2 (red), whilst the linear right-hand-side scale indicates thenominal difference between both angles, ϕ = (ϕ1 − ϕ2) (black).

the constriction caused by the pore walls, but also an energeticeffect given that the interaction energy between DNA and thenanotube only stabilizes once encapsulation is complete.30 Toaccommodate itself in the endohedral volume, the double-strand skeletal diameter slightly decreases and is balancedby an end-to-end length increase from L = 3.85 nm toL = 4−4.1 nm (Figure 1(a)).

Upon encapsulation the dodecamer maintains its kineticmobility, exploring a region whose boundaries are located atthe nanotube termini and correspond to minima in the over-all free-energy landscape (Figure 2). Translocation within thesolid occurs via a self-translational diffusion process alongthe central axis and also via a mechanism of self-rotationabout the biomolecular axis. The conformational ensembleof individual strand axes recorded in Figure 4 resembles atoroid in the yz-plane (parallel to the nanotube main axis),whose centre is largely unpopulated. On the other hand,even though the double strand is flexible, it cannot be over-stretched along the z-axis without a drastic increase of thecorresponding PMF, and thus the yx-projection shows sym-metrical opposite regions at the boundaries (corresponding todomains close to the wall), where the density of the axes issmaller.

The internal structure of the double-helix, �, is probedby measuring the minimum distance of closest approach be-tween each nucleotide, d(� i, � j)i,j = 1−24. The resulting con-tact maps in Figure 5 indicate that � is essentially maintainedinvariant, prior to, during, and after DNA encapsulation. It

should be noted that the contact map recorded at t = 0 nscorresponds to the pure crystalline form of the B-DNA Dick-erson dodecamer. Because the distance between a nucleotideand itself is null, the dark blue diagonal is related withthe intrastrand structure; adjacent nucleotides that belongto the same strand are always at a distance d(� i, � j)j= i+1

< 0.4 nm. The light blue diagonal represents the stability ofthe interstrand structure, determined by H-bonding betweencomplementary nucleotides located in different strands. At15.42 ns there is a slight increase in contact distance aroundan area defined by the terminal pair (12-13), in direct cor-respondence with the anisotropic deformation highlighted inFigure 4. This lateral opening of the chain, resulting in anencapsulation anisotropy of ϕmax = 16.5◦, is clearly a re-versible process because d(�12, �13) falls back to the purelycrystalline B-DNA values during the observed time win-dow. The two symmetrical shoulders located at regions de-fined by nucleotide indices (20–22) and (8–10), evidencing aslight distance decrease between contacts, need to be carefullyanalysed.

The conformational stability of DNA is markedly in-fluenced by the canonical Watson-Crick H-bonds network,which is also paramount to maintain double-strand integrityand avoiding melting into single strands. In crystals, the dis-tance between a donor (D) and the acceptor (A), dD–A, ismaximum for the N6–O4 H-bond of (AT) pairs correspond-ing to dD−A = 2.95 Å (Figure 6(a)), however, in the liq-uid phase dD−A slightly increases to accommodate transient

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225103-8 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

4

8

12

16

20

24 0 ns 2.33 ns 15.42 ns

4 8 12 16 20 24

4

8

12

16

20

24 20 ns

4 8 12 16 20 24

30 ns

Nu

cleo

tid

e in

dex

4 8 12 16 20 24

0

1.5(12,13)

Min

imu

m d

ista

nce

(n

m)

70 ns

(13,12)

Nucleotide index

FIG. 5. Contact maps between the DNA nucleotides. The distance between two nucleotides � iand � j is defined as the minimum distance between any pair ofatoms (i, j: i ∈ � i, j ∈ � j); by definition d(� i, � j) = d(� j, � i). The terminal nucleotide pairs, defining the DNA persistence length, are the first nucleotideH-bonded to the 24th nucleotide and nucleotide 12 H-bonded to the 13th one. Strand A is formed from nucleotides 1 to 12 and the (complementary) B strandruns from nucleotides 13 to 24. Adjacent nucleotides that belong to the same strand are always at a distance d(� i, � j) < 0.4 nm. Notice the slight increase incontact distance around the terminal pair (12-13).

thermal fluctuations and molecular flexibility. Accordinglywith previous studies18, 19, 31 we postulate that an H-bondexists when the donor and acceptor are not separated bymore than dD−A = 3.5 Å and with a characteristic angle19

of � D–H–A ≤ 35◦. In order to probe the complete Watson-Crick network, we have determined the number of H-bonds

of each donor-acceptor type occurring in the DNA dodecamerand represented them in terms of the corresponding proba-bility of occurrence computed by histogram weighting. Theresults in Figure 6(a) are represented in terms of the nor-malized probability of occurrence, P (%), where the normal-ization

∫ 100%0 P (%)d% = 1 is performed for the maximum

Stacked pair index

2

G GC C A A T T C CG G

G GCC C T T A A G GC C

24 23 22 21 20 19 18 17 16 15 14 13

12111098765431

stacking angle cosine

stacking distance

Ma

xim

um

pro

ba

bil

ity

occ

urr

en

ce (b)

Dis

tan

ce (

nm

), c

os(

Θ)

No

rma

lize

d p

rob

ab

ilit

y

N

A N1

N6H2

TNHN3

O

O4

N

G N1H CNN3

O2

O6

N2H2

H2N4

1009287.5

83.5

(a)

FIG. 6. (a) Canonical Watson-Crick H-bonds. Normalized probability distributions,∫ 100%

0 P (%)d% = 1, of the percentage of canonical H-bonds present inthe encapsulated DNA molecule, considering the last 20 ns of observation time: for the N1–N3 pair, %H bonds = 100% corresponds to the existence of 12H-bonds throughout the dodecamer, %H bonds = 92% to 11 H-bonds, %H bonds = 83.5% to 10 H-bonds, and so on. The probability maxima are indicated inthe graph by the corresponding %-value: (dark blue) H-bonds between N2–O2, (red) H-bonds between N4–O6, (green) H-bonds between N6–O4, and (black)H-bonds between N1–N3. (b) Intrastrand stacking geometry. (Dark red) strand 1, (grey) strand 2. The stacking distance (helical rise) is measured between thegeometrical centres of the molecular planes30 belonging to two consecutive nucleobases of the same strand (e.g., stacked NB pair 1 corresponds to C1–G2 andalso G24–C23), and the stacking angle is calculated between the normal vectors of those two planes (two perfectly stacked bases, with their rings parallel toeach other, have a stacking angle of 0◦ corresponding to cos (0◦) = 1).

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225103-9 Cruz, de Pablo, and Mota J. Chem. Phys. 140, 225103 (2014)

number of allowed H-bonds for a particular donor-acceptorpair. The H-bond between N1 and N3, characteristic of both(AC) and (GC) base pairs, has a maximum occurrence al-lowance of 12, and therefore the peak at 92% with a nor-malized probability of P(92%) = 0.574 corresponds to theexistence of 11 H-bonds; the other occurrences are locatedat 100% with P(100%) = 0.095 (12 H-bonds), at 83.5%with P(83.5%) = 0.264 (10 H-bonds), at 75% with P(75%)= 0.061 (9 H-bonds), and at 67% with P(67%) = 0.006 (8H-bonds). Occurrences below 50% have negligible probabil-ities for all H-bonds in the double-strand. For occurrenceshigher than 75%, the accumulated probabilities correspondto P(% > 75) ≥ 0.87−0.91; thus, Figure 6(a) indicates thatthe canonical Watson-Crick H-bond network is essentiallyconserved when the molecule becomes encapsulated underphysiological conditions. This comes to show that the contactbetween the DNA dodecamer and the hydrophobic inner sur-face of the carbon nanotube results in rather minor rearrange-ments of the nucleotides H-bonding, which is of the utmostrelevance to maintain double-strand integrity for drug deliv-ery techniques currently exploring SWCNT-based media asencapsulating agents.6, 7

The N2–O2 bond in (GC) pairs shows an accumulatedprobability of P(%>75) ∼ 0.87, suggesting that H-bondbreaking/formation occurs essentially in the double-strandtermini, richer in (GC) moieties, leaving intact the (AT) richinner tract. This is clearly consistent with the intrastrand datarecorded in Figure 6(b), where consecutive nucleotides havebeen probed for their stacking distance (helical rise) and nor-mal vector angle between molecular planes. From the corre-sponding distribution histograms, the maximum probabilityof occurrence has been obtained for both geometric param-eters and plotted as function of the stacked pair index. Thecrystallographic studies of Vargason et al.23 indicate that thetransition from pure B-DNA to an A-DNA conformation isaccomplished via a monotonical decrease of the intrastrandstacking distance from 3.4 Å to ca. 2.6 Å for the pure A-form.Apart from the severe deformation induced by basepairs 1 and11 upon the double-strand, our results indicate a helical risebetween nucleotides of ∼3.8 Å, resulting in L = 4.18 nm.We have observed (Figure 1(a)) that encapsulation of DNAleads to a slight increase of L from the pure B-form, and arenow able to attribute this increase to a 1D anisotropic stretch-ing of the molecule located essentially at the end of the (GC)tracts. From an energetical point of view this is somehow un-expected, bearing in mind that (AT) pairs form two H-bondsinstead of the characteristic three H-bonds of (GC) duos; theinteraction energies between purines and pyrimidines favourthe stability of (GC) pairs against their (AT) counterparts, EGC

= −291.9 kJ/mol and EAT = −110.2 kJ/mol.30 The explana-tion for this apparent inconsistency lies in entropic causes.Because the termini are more flexible than the inner core, theformer are more prone to adaption to the local environment,thus being more able to accommodate elastic deformation.

IV. CONCLUSIONS AND PROSPECTS

DNA can be encapsulated onto the purely hydrophobic(51,0) topology but not so at the (40,0) analogue, indicating

that a 1 nm decrease of diameter might prevent confinement.This observation is encouraging for technologies using pris-tine SWCNTs as drug delivery agents, however, needs to bewisely put in perspective. It is known that nanotubes can beelectrically charged, either using an AFM tip and applying avoltage bias or by chemically doping the solids with p-typedopants to obtain positively charged nanotubes.11, 51 The ef-fect of charge density upon the energetics and dynamics ofconfinement needs to be carefully addressed in the future;because DNA’s outer surface is negatively charged (phos-phates), its interaction with a positively charged (40,0) solidmight indeed lead to the occurrence of encapsulation with en-hanced thermodynamical stability. The latter is of paramountimportance, for any technological application to find its wayinto the industrial production line, the confinement of DNAmolecules needs to be a thermodynamically reversible pro-cess, and subsequent ejection possible towards the nanotubeexterior. Xue et al. used filler agents (C60) and mechanical ac-tuators (Ag) to eject ssDNA from hydrophobic SWCNTs,52

and related the feasibility of the ejection process with theenhanced dispersive interactions resulting from DNA exter-nalization; their C60 agents evidenced interaction energieswith the nanotube of ∼−1800 kJ/mol (∼−7000 kJ/mol forthe Ag nanowires), an order of magnitude higher than theones we observe for the (51,0) encapsulated DNA,30 leadingus to believe that similar externalization mechanisms can beemployed to revert DNA encapsulation.

ACKNOWLEDGMENTS

The authors would like to acknowledge Requimte/CQFB(Universidade Nova de Lisboa, Portugal) and NSEC (Uni-versity of Wisconsin – Madison, USA) for generous CPUtime. This work was partially supported by Grant No.PTDC/CTM/104782/2008 (Portugal) and makes use of re-sults produced with the support of the Portuguese NationalGrid Initiative (https://wiki.ncg.ingrid.pt). F. J. A. L. Cruzgratefully acknowledges financial support from FCT/MCTES(Portugal) through Grant No. SFRH/BPD/45064/2008.

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