Conformational Thermodynamics of DNA Strands in Hydrophilic

Article pubs.acs.org/JPCC

Conformational Thermodynamics of DNA Strands in Hydrophilic Nanopores Fernando J. A. L. Cruz* and José P. B. Mota LAQV-REQUIMTE, Department of Chemistry, Faculdade de Ciências e Tecnologia, Universidade NOVA de Lisboa, 2829-516 Caparica, Portugal S Supporting Information *

ABSTRACT: Enhanced sampling techniques spanning a submicrosecond time scale reveal that a double-stranded DNA dodecamer can be spontaneously encapsulated into (51, 0) and (40, 0) single-walled carbon nanotubes under the influence of an electric field, leading to hybrids with a 40 kJ/mol enhanced freeenergy. The confinement mechanism allows the nucleic acid to retain its mobility, diffusing anisotropically along the endohedral volume, visiting regions of space determined by entropic factors (diameter, free volume) and linked by a thermodynamical highway. In spite of the energetic similarities between both topologies (4.1 × 103 kJ/mol), the biomolecule favors positioning either parallel to the nanopore central axis (40, 0) or in close contact with the solid walls (51, 0), encasing a hollow cylindrical domain of diameter 1−1.5 nm in the latter. Precise physiological conditions allow the extrapolation of results to in vivo systems and constitute a novel and thorough contribution to nanotube technology in the areas of nucleic acid encapsulation/delivery and personalized therapeutics.

1. INTRODUCTION Ever since Watson and Crick unraveled the structure of the deoxyribonucleic acid (DNA) double helix,1 it has been considered as the building block of biological organisms. Because DNA is responsible for carrying genetic information across generations, the knowledge of its physical, chemical, and biological properties is paramount for human life. In the early 1990s, single-walled carbon nanotubes (SWCNTs) were prepared in the laboratory by the groups of Iijima and Bethune:2−4 because these are entities belonging to the nanometer domain, they are able to selectively interact with other species almost at the atomic level. SWCNTs share a common one-dimensional (1D) symmetry with DNA, rendering both systems ideal candidates to probe biomolecular encapsulation for nanotechnology purposes.5−8 It is well known that biological drugs such as insulin and nucleic acids are particularly sensitive to the harsh environment in the gastrointestinal tract, rendering a therapeutic alternative to oral ingestion more adequate and desirable. The confinement of genetic cargo into carbon nanotubes (CNTs), preventing direct contact of the confined biodrug with bacteria and the extreme pH characteristics on oral intake, can help protect against in vivo degradation of the drug, thus enhancing delivery to the cell.9 A plethora of applications currently envisage CNTs as nextgeneration encapsulation media for biological polymers, such as proteins and nucleic acids.10 Owing to several appealing features, for example, well-defined physicochemical properties and hydrophobic nature of their pristine structure, CNTs are considered ideal candidates to be used as nanopores for biomolecular confinement. Present day potential applications © XXXX American Chemical Society

span different purposes and objectives, such as intracellular penetration via endocytosis and delivery of biological cargoes,5,11 ultrafast nucleotide sequencing,12−15 and gene and DNA delivery to living cells. 5,9 The remarkable experimental work by Geng et al.5 has shown that nanotubes can spontaneously penetrate the lipid bilayer of a liposome and the corresponding hybrid incorporated into live mammalian cells to act as a nanopore through which H2O, ions, and DNA are delivered to the cellular interior; the underlying mechanism relies on differences in osmotic pressure across the cellular membrane.16 Besides their biological relevance, DNA molecules confined in nanoscopic geometries are of fundamental importance for polymer physics.17,18 For an efficient and cost-effective industrial fabrication of CNT-based systems for DNA encapsulation/delivery, the interactions between the solid and the biomolecule need to be thoroughly understood under precise physiological conditions (310 K, [NaCl] = 134 mM); nonetheless, the corresponding molecular-level details remain rather obscure. Previous theoretical and experimental work has focused almost exclusively on DNA exoadsorption at the external surface of the nanotubes,14,19−24 overlooking the possibility of endohedral confinement, or was conducted at temperatures unreasonably distinct from the physiological value to allow extrapolation of results for in vivo systems. The studies of Gao et al.25 for T = 400 K revealed that, depending on nanopore diameter, a small (eight nucleobases) single-stranded DNA (ssDNA) segment Received: June 20, 2016 Revised: August 17, 2016

A

DOI: 10.1021/acs.jpcc.6b06234 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C can be spontaneously confined into SWCNTs. Nonetheless, there is a critical diameter of 1.08 nm,26 below which molecular confinement is inhibited by an energy barrier of ca. 130 kJ/mol, arising essentially from strong van der Waals repulsions.27 These findings were extended for intratubular confinement of a 2 nm long ssDNA.28 The pioneering work of Lau et al.29 showed that a small double-stranded DNA (dsDNA) molecule, which had been previously confined into a 4 nm nanotube, exhibits kinetics similar to that of the unconfined nucleic acid, but its behavior is drastically reduced as the nanotube diameter approaches D = 3 nm. Cruz et al.30−32 demonstrated that molecular diffusion inside SWCNTs can exhibit deviations from the classical Fickian behavior. Earlier experiments and calculations have shown that DNA can be confined into single- (D = 2.7 nm)33 and multi-walled CNTs (D = 3−4 nm);34,35 however, the system temperature (350−400 K) was too high to have a significant physiological relevance. Moreover, the experimental measurements by Iijima et al.34 indicated that DNA encapsulation into MWCNTs can compete with biomolecular wrapping around the solid’s external surface, but, unfortunately, their reported data failed to identify the relevant conditions under which the confinement process is favored, for example, ionic strength of the medium and temperature. Recent calculations36 established SWCNT critical diameters of D = 2.67 and 2.4 nm, below which dsDNA and ssRNA encapsulations, respectively, are completely prohibited, and this was attributed to a large freeenergy barrier located at the nanopore entrance. Indeed, our own work showed that a dsDNA dodecamer can be spontaneously encapsulated into a purely hydrophobic SWCNT of D = 4 nm.37 As far as we are aware, this was the first study to demonstrate the thermodynamic spontaneity associated with the encapsulation of a full dsDNA molecule into SWCNTs, under precise physiological conditions, 310 K, 1 bar, and [NaCl] = 134 mM. The fast encapsulation rate ( 5.9 nm indicates absolute lack of confinement. The 3D Gibbs free-energy surface is built by summing the time-dependent Gaussian potentials according to F(Φ,t) = −{[(T + ΔT)]/ΔT}V(Φ,t). A discussion on the algorithm’s convergence toward the correct free-energy landscape can be found elsewhere;63,64 in the long time limit, (∂V(Φ, t)/∂t) → 0, and the well-tempered technique indeed leads to a converged free-energy surface. An alternative approach leading to a time-independent freeenergy relies on integrating F(Φ, t) at the final portion of a metadynamics run;64 therefore, the converged free-energy can be mathematically obtained from eq 2, where ttot is the total simulation time and υ is the time window over which averaging is performed. A convergence analysis of the individual order parameters, ϕ1 and ϕ2, has been implemented, using eq 2 with υ = 10 ns time windows (Figure S3 in the Supporting Information (SI)), and the procedure indicates that convergence is attained after ca. 40 ns. F(Φ) = − 1 ϑ

∫t

t tot

V (Φ , t ) d t

(3)

where β = (1/kBT), kB is the Boltzmann constant, δ is the Dirac delta function, and N is the total number of particles in the system. Because the biasing potential depends only on the order parameter, Θ, and the integration in the numerator is performed over all degrees of freedom except Θ, the unbiased probability of the real system, Pu(Θ), can be evaluated from eq 4 P u(Θ) = P b(Θ) exp βV (Θ) Γ

(4)

−βV(Θ)

where Γ = −(1/β) ln⟨e ⟩ is independent of Θ and the triangular brackets denote an ensemble average. The reconstruction of the real (unbiased) free-energy profile, or potential of mean force (PMF),67 consistent with the Gibbs free-energy, PMF(Θ) = −kBT ln Pu(Θ), is accomplished using the weighted histogram analysis method (WHAM).67−69 For each individual umbrella simulation, a spring constant of k = 1 kJ/mol was employed and the histogram reweighting occurred within 0−5 nm boundaries, using a total number of 300 bins with 1.666 × 10−2 nm length each and employing a 1 × 10−12 convergence tolerance for the WHAM calculations. Both the well-tempered metadynamics and the umbrella calculations were performed on the fly, by patching the original molecular dynamics code with the Plumed 1.2.2 plugin for freeenergy calculations.70

3. RESULTS AND DISCUSSION Initially placed in a bulk physiological-like solution containing an NaCl buffer and located at a distance of 5 Å from the closest nanotube terminii (Figure 2A), the DNA molecule diffuses toward the solid entrance as a consequence of strong Coulombic attractions. These dominate the total energy of the system, Etot = ELJ (dispersive) + ECoul (electrostatic), for at the nanopore entrance, the ratio ELJ/ECoul corresponds to ca. 0.15 for D = 4 nm and 0.18−0.2 for D = 3 nm (Figure 2D). The 130 kJ/mol energy barrier preventing encapsulation observed by Lim et al.27 vanishes when the nanopore is electrically charged, as in the case of the nanotubes employed in the present work. It is interesting to observe that the energetic interactions between DNA and the solid are quite similar, either dispersive or electrostatic in nature, suggesting that conformation/entropy plays a dominant role in the encapsulation mechanism. Indeed, Figure 2D reveals that regardless of the particular SWCNT topology, typical equilibrium energies are roughly invariant with respect to diameter and correspond to ELJ ≈ − 6.5 ×102 kJ/mol and ECoul ≈ − 3.5 × 103 kJ/mol. Molecular encapsulation occurs with fast kinetics, and after a few nanoseconds, the dodecamer is already trapped at the pore entrance (Figure 2B), where it undergoes structural rearrangements to penetrate the endohedral volume. After 3.4−4.3 ns, depending on the particular topology, the biomolecule is completely confined (Figure 2C) and never returns back to the bulk within an observation time window of 0.1−0.2 μs. It is possible that this fast kinetics becomes slower with an increase

(2)

tot −ϑ

∫ exp{−β[U (r ) + V (Θ′(r ))]}δ[Θ′(r ) − Θ]d N r ∫ exp{−β[U (r ) + V (Θ′(r ))]}d N r

65,66

Using the umbrella sampling technique, we have also performed independent calculations. Considering a system composed of N identical particles, the method biases the classical Hamiltonian that depends on the potential, U(rN), and kinetic energies, E(pN), by introducing a time-independent harmonic bias, V(Θ) = (k/2)(Θ − Θ0)2, according to H(rN, pN, Θ) = U(rN) + E(pN) + V(Θ); here, k is the harmonic force constant, Θ is an order parameter, and Θ0 = 4.1 nm corresponds to the position of the umbrella restrain. In the present case, Θ = |R⃗ GC,1 − R⃗ GC,12| is the DNA end-to-end distance measured between GC termini, analogous to the ϕ2 order parameter used in the metadynamics algorithm. When a D


Article

The Journal of Physical Chemistry C

The internal arrangement of the double strand is probed by the RMSD profiles, recorded as red lines in Figure 2E, which show that interatomic displacements occur to accommodate molecular flexibility. Ensemble-averaged profiles of both RMSD and RGyr have been histogram-reweighted using bin widths of 4 × 10−2 nm (Figure 2F), and although the results for the (40, 0) solid evidence some minor scattering, both topologies are satisfactorily described by Gaussian statistics. It becomes clear that both geometrical signatures show a unique maximum probability of occurrence at RMSD = 0.34 nm and RGyr = 1.48 nm and RMSD = 0.18 nm and RGyr = 1.34 nm for the (51, 0) and (40, 0) topologies, respectively, corroborating small deviations away from the canonical B-form as measured throughout the entire double strand (RMSD ≪ 1). 3.2. Thermodynamical Landscapes. Free-energy landscapes associated with encapsulated DNA are obtained using the well-tempered metadynamics technique63,64 and are recorded in Figure 3, highlighting the energetically most stable domains. The corresponding two-dimensional (2D) color maps are built in terms of two nanoscopic descriptors, corresponding to the distance between the centers of mass of the biomolecule and the nanotube, ϕ1, projected along the solid’s main axis (z), and the double-strand end-to-end length as measured between opposite (GC) termini, ϕ2. Keeping in mind that results were obtained under isothermal and isobaric conditions (310 K, 1 bar), the free energies recorded in Figure 3 are equivalent to the classical Gibbs free-energy; furthermore, the thermodynamical reference state corresponds to a bulk DNA system, where encapsulation has still not occurred. It is clear that both the larger (51, 0) topologies possess several consecutive free-energy minima located along the nanopore main axis and contained within an endohedral volume of 0 < ϕ1 < 2 nm, demonstrating that encapsulation is thermodynamically very favorable while leading to a marked decrease of the systems’ free-energy, which can reach ca. −40 kJ/mol when the biomolecule is positioned at the local minima. Consecutive local minima are linked amongst themselves by a minimum free-energy path of roughly 5 kJ/mol; this path can be understood as a thermodynamical highway through which DNA translates along the nanotube, visiting the minimum freeenergy regions, with only minor energetic penalties. In spite of the overall similarity of behavior observed for the (51, 0) topologies, the existence of electric charges on the graphitic walls induces several transformations upon the energetic landscape, which are worthwhile to discuss. The most relevant of which are essentially twofold, namely, (1) molecular mobility is somewhat reduced, as indicated by a decrease in the maximum value spanned by ϕ1, from 2.7 to 2.2 nm, and suggesting that molecular translation becomes restricted to a narrower domain of space located closer to the SWCNT center; this arises from a strong electrostatic attraction between the biomolecule and the charged solid (∼3.5 × 103 kJ/ mol), which is completely reversed when the electric gradient is switched off (q = 0), thus inducing a repulsion between the hydrophobic nanotube and the negatively charged DNA backbone (phosphates); and (2) the exact position of the absolute free-energy minimum increases from (ϕ1, ϕ2) = (0.1, 4.1) to (1.7, 4.1) nm when q = +0.05 e−/C, showing that the nanopore center is no longer the thermodynamically most favorable site for molecular positioning; however, the local minimum located exactly at the pore center, ϕ1 = 0.1 nm, still exists and is only slightly less stable (∼0.4 kJ/mol) than the absolute one at ϕ1 = 1.7 nm. The slight increase in DNA length

in the double-strand length as it approaches genomic DNA (kbps), as a larger nucleic acid requires more time to diffuse from the bulk and approach the solid entrance; however, such an effect should be counterbalanced by enhanced electrostatic attraction between the backbone phosphates and solid walls. Naturally, the encapsulated nucleic acid diffuses along the nanopore’s internal volume, either approaching the center of the nanotube or getting close to the symmetrically equivalent termini; those thresholds are never crossed as indicated by the horizontal dashed line at 2 nm depicted in Figure 2E. 3.1. Double-Strand Geometry. To obtain a detailed insight into the confinement mechanism, a conformational analysis of the nucleic acid is implemented based on two geometric signatures: radius of gyration (RGyr) and RMSD. Even though the Dickerson segment is smaller in length than genomic DNA, it is well known that its main structural features are similar to those of genomic λ-bacteriophage DNA,53 specifically the radius of gyration and double-strand backbone diameter, RGyr ≈ 0.7−1 nm and D ≈ 2 nm (Figure 1). Briefly, the radius of gyration N

R Gyr =

N

(∑ |ri|2 mi)/∑ mi i

(5)

i

is a measure of molecular compactness; here, N = 758 is the total number of atoms in the DNA molecule, mi is the mass of atom i, and ri is the positional vector of the same atom relative to the molecular c.o.m. On the other hand, the RMSD corresponds to a time-averaged measure of intrastrand atomic displacements obtained by determining the distance, rij, between atoms i and j at time t and relating it with the same distance observed at time t = 0 N

RMSD =

N

(1/N 2)∑ ∑ |rij(t ) − rij(0)|2 i=1 j=1

(6)

By definition, at t = 0, the DNA dodecamer corresponds to the crystalline structure of the canonical B-form as obtained by Xray crystallography.43 The corresponding results are recorded in Figure 2E and, overall, indicate that DNA encapsulation leads to minor structural rearrangements of the canonical B-form; this is a natural consequence arising from increased molecular flexibility characteristic of a liquid phase. Reference signatures corresponding to a bulk DNA system, where the nanotube has been removed, are graphically recorded in Figure S1. The molecular RGyr spans a domain of 1.2−1.5 nm, suggesting that the encapsulated molecule essentially maintains a linear-like conformation; nonetheless, the (51, 0) nanopore induces DNA to assume a slightly less linear configuration with RGyr = 1.49 and 1.34 nm (40, 0). The RGyr projection onto the z axis for the (51, 0) topology indicates an enhanced parallel alignment of the DNA molecule with the nanotube as compared to that in the (40, 0) solid (Figure S2). Because the (40, 0) nanotube (D = 3 nm) is entropically more constraining than its (51, 0) analogue (D = 4 nm), in the narrower nanopore, the dodecamer assumes a conformation whose length is closer to the canonical value of L = 3.8 nm, whereas the less restricting (51, 0) topology allows the molecule to slightly expand toward a noncanonical length. This issue will be re-addressed further when the umbrella sampling results are discussed. E


Article


existence of an electric field on the walls now favors biomolecular confinement as clearly evidenced by the corresponding Gibbs free-energy landscape (Figure 3, bottom). Furthermore, and by contrast with the larger (51, 0) topology, the ϕ2 phase space spans a broader range now including nonstable (transient) DNA forms with highly compressed double-strand lengths (ϕ2 < 3 nm). To corroborate the metadynamics findings, independent umbrella sampling calculations65,66 were also performed adopting a macroscopic descriptor, Θ, measuring the end-toend distance of the double strand and analogous to the ϕ2 order parameter employed in the well-tempered technique. As a result, the probability distribution thus obtained is used to reconstruct a free-energy profile or PMF; the corresponding results for the electrically charged nanotubes are graphically recorded in Figure 4, along with data for a purely hydrophobic solid of D = 4 nm.37

Figure 3. Gibbs free-energy maps of encapsulated DNA. ϕ1 is the distance between the centers of mass of DNA and the SWCNT, projected along the nanopore’s main axis (z), and ϕ2 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, ϕ1 < 2 nm, and linked amongst themselves via a thermodynamical highway with a freeenergy penalty of ≤5 kJ/mol. The complete ensemble of free-energy minima is as follows ((ϕ1, ϕ2) nm): (0.12, 4.11), (0.62, 4.16), (1.31, 4.16), and (1.80, 4.12) for (51, 0; q = 0); (0.1; 3.78), (0.67; 4), and (1.75; 4.1) for (51,0; q = +0.05 e−/C); and (0.1; 3.31), (0.4; 3.25), (0.65; 3.25), (0.85; 3.6), (1.05; 3.25), and (1.2; 3.25) for (40,0; q = +0.05 e−/C).

Figure 4. Probability distribution and PMF profiles of encapsulated DNA. Because the Θ order parameter was built as the double-strand end-to-end length, the bimodal symmetry associated with the electrostatically charged nanotubes clearly identifies the probability maxima corresponding to the equilibrium conformations (Θ = 3.73− 3.75 nm) but also two other noncanonical forms of DNA, at Θ = 4.29 and 3.51 nm. Symbols are the results obtained using umbrella sampling calculations, and red lines correspond 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 for the range Θ > 3.5 nm.

from 3.8 nm (corresponding to the canonical B-form) to 4.1 nm, as indicated in Figure 3 by the ϕ2 order parameter, occurs via a reversible and elastic expansion of the double-strand termini.37 When the nanotube diameter is decreased from 4 to 3 nm, while maintaining a positive charge distribution, the absolute free-energy minimum now appears at (ϕ1, ϕ2) = (1.05, 3.25) nm, although it reflects only a 0.4 kJ/mol enhanced stability compared to that of the valley observed at the nanopore center and located at (ϕ1, ϕ2) = (0.1, 3.31) nm. Very interestingly, and contrary to what happens with its hydrophobic analogue, the

The profiles are Gaussian shaped around Θ, with peak maxima in the range 3.73− 3.75 nm in line with the ϕ2 minima observed in the free-energy maps of Figure 3 and in striking agreement with a B-DNA length of 3.8 nm. Although these probability maxima completely dominate the energetic landscape, accounting for more than 90% of the integrated region underneath the curves, the onset of two other forms of DNA is worth noting, located on opposite sides of the Gaussian peaks F


Article


Figure 5. Time-averaged 2D molecular density maps of DNA at the charged topologies. The yellow and red domains where density approaches its maximum value, spanning large endohedral volumes, indicate that DNA maintains its translational mobility within the nanopores; the dashed lines in the middle figures indicate the boundaries of the SWCNTs and the black lines recorded on the inset graphs are 1D density profiles obtained along the corresponding dimension. Density maps determined for the molecular c.o.m. by histogram reweighting and using a bin width of 2 × 10−3 nm. Note the hollow volume at the (51, 0) topology seating along the nanopore main axis and with a cylindrical diameter of ∼1−1.5 nm.

at Θ = 4.29 nm (51, 0) and Θ = 3.51 nm (40, 0): the nanotube diameter plays a role in the effective length assumed by an encapsulated nucleic acid. We have observed before that DNA confinement into a pristine (51, 0) SWCNT leads to an elastic expansion of the double strand of roughly 0.3 nm, essentially located on opposite termini; however, neither the effect of nanotube charging nor narrower topologies were probed. As far as we are aware, the present thermodynamical analysis is the first of its kind, establishing a direct relationship between the nanotube diameter and double-strand end-to-end length.

The probability distribution curves obtained by umbrella sampling unmistakably echo upon the conformational results previously discussed regarding the radius of gyration of DNA (Figure 2F), for it is thermodynamically possible for the biomolecule to assume a more/less stretched conformation depending on the larger/narrower nanopore diameter, RGyr = 1.49 nm (51, 0) and RGyr = 1.34 nm (40, 0). The existence of such a relationship between length and diameter, LDNA = f(DSWCNT), seems to be in contrast with the recent umbrella studies of Bascom and Andricioaei,23 who probed the exoadsorption of poly(AT) and poly(GC) DNA segments G


Article


biomolecule. When the nanopore diameter increases to 4 nm, the available free volume follows a similar trend and the nucleic acid is no longer subjected to such harsh entropic constraints, being freer to move along the directions perpendicular to the main axis, x and y, which had been severely restricted in the (40, 0) topology. Indeed, the 1D density profiles recorded in Figure 5 become binodal for the (51, 0) solid, with a peak-topeak distance of 1.5 nm, leading to the existence of a hollow cylindrical volume at the pore main axis, where density approaches 0. Moreover, these two maximum density peaks are in close contact with the charged walls, indicating that DNA is now fully mobile within the (x, y) space. 3.4. Single-Strand Axis Ensembles. Molecular mobility within the solid boundaries occurs via a self-diffusion process along the central axis and the perpendicular (x, y) plane, but the nucleic acid also makes use of a mechanism that involves selfrotation about the molecular axis. To probe deeper into this matter, the Dickerson dodecamer has been split into its two constituent single strands, and each of the latter has been employed to monitor the conformational phase space. Coloring each individual strand axis differently, the results are graphically illustrated in Figure 6 for different perspectives upon the DNA@SWCNT systems (3D animations 1 and 2 in the Supporting Information show individual strand axis ensemble rotation about the y axis). It is worth remembering that the nanotube is oriented along the z direction. The ensembles obtained for the two topologies are markedly distinct. Overall, the data obtained for the (51, 0) nanotube is distributed in a quasi-isotropic fashion, in clear contrast with the anisotropic ensemble distribution obtained for the (40, 0) solid. This can be rationalized in terms of entropic penalties that DNA is subject to while encapsulated within the narrower pore, that are mitigated once the available free volume increases. In this last case, the conformational ensembles recorded in Figure 6 resemble a toroid in the (x, y) plane, whose center is largely unpopulated. Nonetheless, even though the dodecamer is flexible, it cannot be overstretched without a corresponding increase of the associated PMF (Figure 4); thus, the (x, y) projection shows symmetrical opposite regions at the boundaries (domains close to the wall), where the density of axes is smaller. Molecular density maps revealed that DNA tends to occupy a region of space centrally located regarding the (40, 0) nanopore inner volume; thus, the corresponding distribution of axis ensembles is heavily populated in that endohedral domain. Additionally, for DNA to accommodate itself in the (x, y) plane of the highly constraining 3 nm pore, its double strand (L = 3.8 nm) would have to undergo major elastic deformation, forcing the bending of the phosphates backbone towards the pore center and causing electrostatic repulsions between them.74

onto hydrophobic (10, 0) nanotubes and concluded that, regardless of the particular biomolecular sequence, the canonical B-form is mostly favored over the shorter Aconformation by several kilojoule/mole. However, the present results complement and extend their findings, addressing for the first time the influence of an electric field across the solid while probing the endohedral volume. 3.3. Molecular Density Maps. A nanoscopic picture of the systems containing the encapsulated DNA dodecamer is obtained by determining time-averaged histograms of molecular density, computed for the molecular c.o.m. and using a bin width of 2 × 10−3 nm. These are plotted in Figure 5 as 2D maps along a plane, containing both the bulk solution and the encapsulating nanotube, and the vast dark blue domains where density is null are unmistakably attributed to the bulk solution that DNA never revisits after penetrating the SWCNT. It has been discussed above that subsequent to encapsulation although the nucleic acid is able to explore the endohedral volume between the solid termini, it remains within the nanopore and is unable to exit and return to the bulk solution where it resided at t = 0 (Figure 2E). That encapsulated DNA retains translational mobility now becomes clear by inspecting the yellow and red areas (Figure 5), where density approaches its maximum, and spanning large portions of the cylindrical volume contained within the nanotubes. Employing a (51, 0) topology identical to ours, but where the electric field has been turned off, it has recently been shown31 that, initially (t < 4 ns), DNA travels along the nanopore according to Fick’s law (D = 1.713 × 10−9 m2/s), after which the mean-squared c.o.m. displacement assumes a single-file-type behavior71 becoming proportional to t1/2. Such nonlinear relationships are characteristic of anisotropic phases, as when a 1D nanoconfining solid surface is introduced into a purely liquid system.72 As such, molecular displacement becomes anisotropic, following a preferential path parallel to the nanopore’s main axis, and the DNA molecule diffuses along the endohedral volume by moving between adjacent freeenergy minima; we have shown that several of them exist for both topologies (Figure 3), separated by no more than a 5 kJ/ mol penalty. In spite of mobility conservation, the density maps in Figure 5 reveal that diffusion is markedly influenced by the nanopore diameter: with a skeletal diameter of ca. 2 nm (Figure 1), the nucleic acid is less constrained in a D = 4 nm nanopore, and, for entropic reasons (free volume), the corresponding molecular displacement becomes more inhibited in a SWCNT of D = 3 nm. Another consequence of free-volume restriction in the narrower topology is the constraining of molecular density within a cylindrical volume centered along the nanopore axis, pushing the DNA’s c.o.m. away from the solid walls, as demonstrated by the single peak displayed in both the x- and ydensity profiles and exactly located at the center, (x, y)Density,max = 5.5 nm. Bearing in mind that the Dickerson dodecamer has a skeletal diameter of 2 nm, encapsulation into a D = 3 nm pore leaves but 1 nm between the biomolecule and the solid walls, where the water molecules can form a slab to intermediate energetic interactions. Finney discussed the behavior of H2O at the molecular level,73 both in a pure liquid form and in solution, and although no consensus was attained regarding its absolute diameter, a value in the range 0.275−0.3 nm usually provides a satisfactory description of the corresponding physicochemical properties, meaning that the DNA solvation slab can roughly accommodate two H2O molecules in opposite sides of the

4. CONCLUSIONS AND OUTLOOK In the presence of an electric field acting on the nanotubes, complete encapsulation of a DNA dodecamer occurs with fast kinetics (≤4.3 ns) and is thermodynamically spontaneous, as demonstrated by a 40 kJ/mol decrease in the system’s Gibbs free-energy. The confinement process itself is driven by strong electrostatic attractions between the nucleic acid and solid, which in the early stages of confinement accounts for at least 80% of the total interaction energy. The end-to-end length of encapsulated DNA is similar to that of the canonical B-form (ca. 3.8 nm) in the two topologies under consideration, (51, 0) and (40, 0); however, consecutive free-energy minima occur in H


Article


obtained for the molecular density maps and single-strand individual axis ensembles indicate that the biomolecule favors positioning in close contact with the nanopore walls in the (51, 0) topology, in contrast with what is observed for the (40, 0) nanotube where the DNA’s c.o.m. is preferentially located along the pore central axis, (x, y) ≈ (0,0). As far as we are aware, the present thermodynamical analysis is the first of its kind, establishing a direct relationship between the nanotube diameter and double-strand conformational properties.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b06234. Bulk DNA geometric signatures (Figure S1), log−log plot of the radius of gyration and its projection along the z axis (Figure S2), convergence profiles of the metadynamics order parameters (Figure S3) (PDF) 3D animations with the individual strand axis ensemble rotation about the y axis (MPG, MPG)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +351 212948300. Author Contributions

F.J.A.L.C. designed the numerical experiments, performed the calculations, analyzed data, and interpreted the results. F.J.A.L.C. and J.P.B.M. wrote the manuscript. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Associate Laboratory for Green Chemistry LAQV, which is financed by national funds from FCT/MEC (UID/QUI/50006/2013) and co-financed by the ERDF under the PT2020 Partnership Agreement (POCI01-0145-FEDER - 007265); it also 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/QEQPRS/0308/2012.

Figure 6. Ensemble space of single-strand individual axes for confined DNA. Each strand individual axis runs from a terminal phosphorus atom to the last one located on the same corresponding strand; thus, each strand axis is represented by a different color: strand A (blue) and strand B (red). Note that the CNTs are parallelly aligned along the z axis with diameters D(51,0) = 4 nm and D(40,0) = 3 nm.

■

REFERENCES

(1) Watson, J. D.; Crick, F. H. C. Molecular Structure of Nucleic Acids: A Structure for Deoxyribose Nucleic Acid. Nature 1953, 171, 737−738. (2) Iijima, S. Helical Microtubules of Graphitic Carbon. Nature 1991, 354, 56−58. (3) Bethune, D. S.; Kiang, C. H.; Vries, M. S. d; Gorman, G.; Savoy, R.; Vasquez, J.; Beyers, R. Cobalt-Catalysed Growth of Carbon Nanotubes with Single-Atomic-Layer Walls. Nature 1993, 363, 605− 607. (4) Iijima, S.; Ichihashi, T. Single-Shell Carbon Nanotubes of 1-nm Diameter. Nature 1993, 363, 603−605. (5) Geng, J.; Kim, K.; Zhang, J.; Escalada, A.; Tunuguntla, R.; Comolli, L. R.; Allen, F. I.; Shnyrova, A. V.; Cho, K. R.; Munoz, D.; et al. Stochastic Transport through Carbon Nanotubes in Lipid Bilayers and Live Cell Membranes. Nature 2014, 514, 612−615. (6) Kostarelos, K.; Bianco, A.; Prato, M. Promises, Facts and Challenges for Carbon Nanotubes in Imaging and Therapeutics. Nat. Nanotechnol. 2009, 4, 627−633.

the thermodynamical landscapes, located within the endohedral volume, and corresponding to a 0.25−0.5 nm deviation away from the canonical form; these observations are corroborated by independent atomically detailed techniques. The effects exerted by the confining solid upon the nucleic acid exhibit a marked dependence on nanopore diameter, and this is attributed to entropic reasons arising from free-volume considerations. Nonetheless, the encapsulated DNA maintains translational mobility inside the nanotube and is able to translocate within a cylindrical volume comprised between termini, according to a (x, y, z) anisotropic self-diffusion mechanism that also involves molecular translation caused by a self-rotation of the double-strand axis. The nanoscopic pictures I


Article

The Journal of Physical Chemistry C (7) Squires, A.; Meller, A. DNA Capture and Translocation through Nanoscale Poresa Fine Balance of Electrophoresis and Electroosmosis. Biophys. J. 2013, 105, 543−544. (8) Nel, A. E.; Mädler, L.; Velegol, D.; Xia, T.; Hoek, E. M. V.; Somasundaran, P.; Klaessig, F.; Castranova, V.; Thompson, M. Understanding Biophysicochemical Interactions at the Nano−Bio Interface. Nat. Mater. 2009, 8, 543−557. (9) Wu, Y.; Phillips, J. A.; Liu, H.; Yang, R.; Tan, W. Carbon Nanotubes Protect DNA Strands During Cellular Delivery. ACS Nano 2008, 2, 2023−2028. (10) Kumar, H.; Lansac, Y.; Glaser, M. A.; Maiti, P. K. Biopolymers in Nanopores: Challenges and Opportunities. Soft Matter 2011, 7, 5898−5907. (11) Canton, I.; Battaglia, G. Endocytosis at the Nanoscale. Chem. Soc. Rev. 2012, 41, 2718−2739. (12) Venkatesan, B. M.; Bashir, R. Nanopore Sensors for Nucleic Acid Analysis. Nat. Nanotechnol. 2011, 6, 615−624. (13) Liu, H.; He, J.; Tang, J.; Liu, H.; Pang, P.; Cao, D.; Krstic, P.; Joseph, S.; Lindsay, S.; Nuckolls, C. Translocation of Single-Stranded DNA through Single-Walled Carbon Nanotubes. Science 2010, 327, 64−67. (14) Meng, S.; Maragakis, P.; Papaloukas, C.; Kaxiras, E. DNA Nucleoside Interaction and Identification with Carbon Nanotubes. Nano Lett. 2007, 7, 45−50. (15) Gui, E. L.; et al. DNA Sensing by Field-Effect Transistors Based on Networks of Carbon Nanotubes. J. Am. Chem. Soc. 2007, 129, 14427−14432. (16) Kim, K.; Geng, J.; Tunuguntla, R.; Comolli, L. R.; Grigoropoulos, C. P.; Ajo-Franklin, C. M.; Noy, A. OsmoticallyDriven Transport in Carbon Nanotube Porins. Nano Lett. 2014, 14, 7051−7056. (17) Jun, S.; Thirumalai, D.; Ha, B.-Y. Compression and Stretching of a Self-Avoiding Chain in Cylindrical Nanopores. Phys. Rev. Lett. 2008, 101, No. 138101. (18) Chang, R.; Jo, K. DNA Conformation in Nanochannels: Monte Carlo Simulation Studies Using a Primitive DNA Model. J. Chem. Phys. 2012, 136, No. 095101. (19) Zhao, X.; Johnson, J. K. Simulation of Adsorption of DNA on Carbon Nanotubes. J. Am. Chem. Soc. 2007, 129, 10438−10445. (20) Johnson, R. R.; Johnson, A. T. C.; Klein, M. L. Probing the Structure of DNA-Carbon Nanotube Hybrids with Molecular Dynamics. Nano Lett. 2008, 8, 69−75. (21) Alegret, N.; Santos, E.; Rodriguez-Fortea, A.; Rius, F. X.; Poblet, J. M. Disruption of Small Double Stranded DNA Molecules on Carbon Nanotubes: A Molecular Dynamics Study. Chem. Phys. Lett. 2012, 525−526, 120−124. (22) Santosh, M.; Panigrahi, S.; Bhattacharyya, D.; Sood, A. K. Unzipping and Binding of Small Interfering RNA with Single Walled Carbon Nanotube: A Platform for Small Interfering RNA Delivery. J. Chem. Phys. 2012, 136, No. 065106. (23) Bascom, G.; Andricioaei, I. Single-Walled Carbon Nanotubes Modulate the B- to a-DNA Transition. J. Phys. Chem. C 2014, 118, 29441−29447. (24) Shiraki, T.; Tsuzuki, A.; Toshimitsu, F.; Nakashima, N. Thermodynamics for the Formation of Double-Stranded DNA− Single-Walled Carbon Nanotube Hybrids. Chem. − Eur. J. 2016, 22, 4774−4779. (25) Gao, H.; Kong, Y.; Cui, D. Spontaneous Insertion of DNA Oligonucleotides into Carbon Nanotubes. Nano Lett. 2003, 3, 471− 473. (26) Pei, Q. X.; Lim, C. G.; Cheng, Y.; Gao, H. Molecular Dynamics Study on DNA Oligonucleotide Translocation through Carbon Nanotubes. J. Chem. Phys. 2008, 129, No. 125101. (27) Lim, M. C. G.; Zhong, Z. W. Effects of Fluid Flow on the Oligonucleotide Folding in Single-Walled Carbon Nanotubes. Phys. Rev. E 2009, 80, No. 041915. (28) Zimmerli, U.; Koumoutsakos, P. Simulations of Electrophoretic RNA Transport through Transmembrane Carbon Nanotubes. Biophys. J. 2008, 94, 2546−2557.

(29) Lau, E. Y.; Lightstone, F. C.; Colvin, M. E. Dynamics of DNA Encapsulated in a Hydrophobic Nanotube. Chem. Phys. Lett. 2005, 412, 82−87. (30) Cruz, F. J. A. L.; Müller, E. A. Behavior of Ethylene/Ethane Binary Mixtures within Single-Walled Carbon Nanotubes. 2Dynamical Properties. Adsorption 2009, 15, 13−22. (31) Cruz, F. J. A. L.; de Pablo, J. J.; Mota, J. P. B. Nanoscopic Characterization of DNA within Hydrophobic Pores: Thermodynamics and Kinetics. Biochem. Eng. J. 2015, 104, 41−47. (32) Cruz, F. J. A. L.; Müller, E. A.; Mota, J. P. B. The Role of the Intermolecular Potential on the Dynamics of Ethylene Confined in Cylindrical Nanopores. RSC Adv. 2011, 1, 270−281. (33) Gao, H.; Kong, Y. Simulation of DNA-Nanotube Interactions. Annu. Rev. Mater. Res. 2004, 34, 123−150. (34) Iijima, M.; Watabe, T.; Ishii, S.; Koshio, A.; Yamaguchi, T.; Bandow, S.; Iijima, S.; Suzuki, K.; Maruyama, Y. Fabrication and STMCharacterization of Novel Hybrid Materials of DNA/Carbon Nanotube. Chem. Phys. Lett. 2005, 414, 520. (35) Ghosh, S.; Dutta, S.; Gomes, E.; Carroll, D.; D’Agostino, R. J.; Olson, J.; Guthold, M.; Gmeiner, W. H. Increased Heating Efficiency and Selective Thermal Ablation of Malignant Tissue with DNAEncased Multiwalled Carbon Nanotubes. ACS Nano 2009, 3, 2667− 2673. (36) Mogurampelly, S.; Maiti, P. K. Translocation and Encapsulation of SiRNA inside Carbon Nanotubes. J. Chem. Phys. 2013, 138, No. 034901. (37) Cruz, F. J. A. L.; de Pablo, J. J.; Mota, J. P. B. Endohedral Confinement of a DNA Dodecamer onto Pristine Carbon Nanotubes and the Stability of the Canonical B Form. J. Chem. Phys. 2014, 140, No. 225103. (38) Franklin, R. E.; Gosling, R. G. Molecular Configuration in Sodium Thymonucleate. Nature 1953, 171, 740−741. (39) Kreupl, F. Carbon Nanotubes Finally Deliver. Nature 2012, 484, 321−322. (40) Heller, I.; Janssens, A. M.; Mannik, J.; Minot, E. D.; Lemay, S. G.; Dekker, C. Identifying the Mechanism of Biosensing with Carbon Nanotube Transistors. Nano Lett. 2008, 8, 591−595. (41) Ding, J.; Li, Z.; Lefebvre, J.; Cheng, F.; Dubey, G.; Zou, S.; Finnie, P.; Hrdina, A.; Scoles, L.; Lopinski, G. P.; et al. Enrichment of Large-Diameter Semiconducting SWCNTs by Polyfluorene Extraction for High Network Density Thin Film Transistors. Nanoscale 2014, 6, 2328−2339. (42) Elder, R. M.; Pfaendtner, J.; Jayaraman, A. Effect of Hydrophobic and Hydrophilic Surfaces on the Stability of DoubleStranded DNA. Biomacromolecules 2015, 16, 1862−1869. (43) Drew, H. R.; Wing, R. M.; Takano, T.; Broka, C.; Tanaka, S.; Itakura, K.; Dickerson, R. E. Structure of a B-DNA Dodecamer: Conformation and Dynamics. Proc. Natl. Acad. Sci. U.S.A. 1981, 78, 2179−2183. (44) Salmon, L.; Yang, S.; Al-Hashimi, H. M. Advances in the Determination of Nucleic Acid Conformational Ensembles. Annu. Rev. Phys. Chem. 2014, 65, 293−316. (45) Cruz, F. J. A. L.; de Pablo, J. J.; Mota, J. P. B. Free-Energy Landscapes of the Encapsulation Mechanism of DNA Nucleobases onto Carbon Nanotubes. RSC Adv. 2014, 4, 1310−1321. (46) Valsson, O.; Tiwary, P.; Parrinello, M. Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint. Annu. Rev. Phys. Chem. 2016, 67, 159−184. (47) Wang, J.; Cieplak, P.; Kollman, P. A. How Well Does a Restrained Electrostatic Potential (Resp) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules? J. Comput. Chem. 2000, 21, 1049−1074. (48) Lindorff-Larsen, K.; Piana, S.; Palmo, K.; Maragakis, P.; Klepeis, J. L.; Dror, R. O.; Shaw, D. E. Improved Side-Chain Torsion Potentials for the Amber Ff99sb Protein Force Field. Proteins 2010, 78, 1950− 1958. (49) Musiani, F.; Rossetti, G.; Capece, L.; Gerger, T. M.; Micheletti, C.; Varani, G.; Carloni, P. Molecular Dynamics Simulations Identify Time Scale of Conformational Changes Responsible for ConformaJ


Article

The Journal of Physical Chemistry C tional Selection in Molecular Recognition of Hiv-1 Transactivation Responsive RNA. J. Am. Chem. Soc. 2014, 136, 15631−15637. (50) Noy, A.; Soteras, I.; Luque, F. J.; Orozco, M. The Impact of Monovalent Ion Force Field Model in Nucleic Acids Simulations. Phys. Chem. Chem. Phys. 2009, 11, 10596−10607. (51) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.; Klein, M. L. Comparison of Simple Potential Functions for Simulating Liquid Water. J. Chem. Phys. 1983, 79, 926−935. (52) Joung, I. S.; Cheatham, T. E. Determination of Alkali and Halide Monovalent Ion Parameters for Use in Explicitly Solvated Biomolecular Simulations. J. Phys. Chem. B 2008, 112, 9020−9041. (53) Wang, Y.; Tree, D. R.; Dorfman, K. D. Simulation of DNA Extension in Nanochannels. Macromolecules 2011, 44, 6594−6604. (54) Elliott, J. A.; Sandler, J. K. W.; Windle, A. H.; Young, R. J.; Shaffer, M. S. P. Collapse of Single-Wall Carbon Nanotubes Is Diameter Dependent. Phys. Rev. Lett. 2004, 92, No. 095501. (55) Kobayashi, K.; Kitaura, R.; Nishimura, F.; Yoshikawa, H.; Awaga, K.; Shinohara, H. Growth of Large-Diameter (4 nm) SingleWall Carbon Nanotubes in the Nanospace of Mesoporous Material Sba-15. Carbon 2011, 49, 5173−5179. (56) Lv, W. The Adsorption of DNA Bases on Neutral and Charged (8, 8) Carbon-Nanotubes. Chem. Phys. Lett. 2011, 514, 311−316. (57) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435−447. (58) Nosé, S. A Unified Formulation of the Constant Temperature Molecular Dynamics Methods. J. Chem. Phys. 1984, 81, 511−519. (59) Hoover, W. G. Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, 1695−1697. (60) Parrinello, M.; Rahman, A. Polymorphic Transitions in Single Crystals: A New Molecular Dynamics Method. J. Appl. Phys. 1981, 52, 7182−7190. (61) Darden, T.; York, D.; Pedersen, L. Particle Mesh Ewald: An NLog(N) Method for Ewald Sums in Large Systems. J. Chem. Phys. 1993, 98, 10089−10092. (62) Essmann, U.; Perera, L.; Berkowitz, M. L.; Darden, T.; Lee, H.; Pedersen, L. G. A Smooth Particle Mesh Ewald Potential. J. Chem. Phys. 1995, 103, 8577−8592. (63) Barducci, A.; Bussi, G.; Parrinello, M. Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method. Phys. Rev. Lett. 2008, 100, No. 020603. (64) Laio, A.; Gervasio, F. L. Metadynamics: A Method to Simulate Rare Events and Reconstruct the Free-Energy in Biophysics, Chemistry and Material Science. Rep. Prog. Phys. 2008, 71, No. 126601. (65) Torrie, G. M.; Valleau, J. P. Nonphysical Sampling Distributions in Monte Carlo Free-Energy Estimation: Umbrella Sampling. J. Comput. Phys. 1977, 23, 187−199. (66) Kästner, J. Umbrella Sampling. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2011, 1, 932−942. (67) Roux, B. The Calculation of the Potential of Mean Force Using Computer Simulations. Comput. Phys. Commun. 1995, 91, 275−282. (68) Kumar, S.; Bouzida, D.; Swendsen, R. H.; Kollman, P. A.; Rosenberg, J. M. The Weighted Histogram Analysis Method for FreeEnergy Calculations on Biomolecules. J. Comput. Chem. 1992, 13, 1011−1021. (69) Grossfield, A. WHAM: The Weighted Histogram Analysis Method, version 2.0.6; University of Rochester Medical Center: Rochester, NY, 2015. (70) Bonomi, M.; et al. Plumed: A Portable Plugin for Free-Energy Calculations with Molecular Dynamics. Comput. Phys. Commun. 2009, 180, 1961−1972. (71) Bird, R. B.; Stewart, W. E.; Lightfoot, E. N. Transport Phenomena, 2nd ed.; John Wiley & Sons: New York, 2002. (72) Chen, Q.; Moore, J. D.; Liu, Y.-C.; Roussel, T. J.; Wang, Q.; Wuan, T.; Gubbins, K. E. Transition from Single-File to Fickian Diffusion for Binary Mixtures in Single-Walled Carbon Nanotubes. J. Chem. Phys. 2010, 133, No. 094501.

(73) Finney, J. L. The Water Molecule and Its Interactions: The Interaction between Theory, Modelling and Experiment. J. Mol. Liq. 2001, 90, 303−312. (74) Qiu, X.; Rau, D. C.; Parsegian, V. A.; Fang, L. T.; Knobler, C. M.; Gelbart, W. M. Salt-Dependent DNA−DNA Spacings in Intact Bacteriophage Reflect Relative Importance of DNA Self-Repulsion and Bending Energies. Phys. Rev. Lett. 2011, 106, No. 028102.

K


Conformational Thermodynamics of DNA Strands in Hydrophilic

Recommend Documents