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Dynamics of B-DNA in Electrically Charged Solid Nanopores Fernando J.A.L. Cruz, and Jose P.B. Mota J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b03167 • Publication Date (Web): 13 Jul 2017 Downloaded from http://pubs.acs.org on July 21, 2017

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The Journal of Physical Chemistry

Dynamics of B-DNA in Electrically Charged Solid 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. * [email protected]

ACS Paragon Plus Environment

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Abstract. Delivery of genetic cargo to a cell via nanopore encapsulation relies on the assumption that, subsequent to confinement, the biological load can diffuse along the endohedral volume to reach the desired exit point. Probing the corresponding kinetics is therefore of fundamental importance for nanopore-based technology to achieve cellular delivery. Atomically detailed computer experiments are used to probe the dynamics of canonical B-DNA double strands (5'D(*CP*GP*CP*GP*AP*AP*TP*TP*CP*GP*CP*G)-3') encapsulated into electrically charged carbon nanotubes (D = 3 – 4 nm), under physiological conditions; nucleic acid translation obeys Fick’s law (∝ t) only during a short initial time-window (2 ns), being followed by an apparent transition to a single-file regime (∝ t1/2) in which DNA exhibits preferential diffusion paths. The nucleic acid disfavours positioning at the nanopore termini, and whilst in the D = 4 nm tube DNA diffuses anisotropically, in the smaller diameter solid the preferred mode of translation is a self-rotation about the double-helix axis. This anisotropicity is attributed to free-volume, for instantaneous velocities are identical, max ≈ 27 m/s. The short time Fickian self-diffusivities determined, Deff = 0.537×10–9 – 0.954×10–9 m2/s, reveal, for the first time, that electrostatic attraction between the walls and DNA induces a slowing down of molecular diffusion in hydrophilic

nanotubes

as

compared

to

pristine

topologies.


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1. Introduction Unlike their pristine analogues,1-3 electrically charged single-walled carbon nanotubes (SWCNTs) are hydrophilic and biocompatible, thus highly soluble in aqueous electrolytic solutions4 and particularly so in the case of physiological-like liquids exhibiting high ionic strengths. Although carbon nanotubes are usually prepared via chemical vapour deposition or electric-arc discharge techniques2, 5-6 resulting in purely hydrophobic surfaces, it is well known that a positive charge distribution can be obtained by: i) chemically doping the graphene lattice with p-type dopants, ii) applying an electrical field across the system or iii) employing tailormade chemical functionalization strategies.4, 7-8 Upon charging, SWCNTs are able to selectively interact with biological macromolecules, such as nucleic acids and proteins, in a fashion similar to biomolecular threading through cellular membrane channels like the α-hemolysin pore.9-10 The experimental work by Geng et. al.11-12 demonstrated that nanotubes can spontaneously pierce across the lipid bilayer of a liposome, forming an hybrid that is incorporated into live mammalian cells to act as a nanopore through which ions and DNA flow towards the cellular interior; the overall mechanism relies heavily on osmotic pressure differences across the cellular membrane.12 Precise delivery of biological cargo to a cell employing carbon nanotubes as encapsulation media13-14 helps circumventing the classical problems associated with oral intake, that usually lead to drug degradation caused by the drastic pH conditions of the oral and gastrointestinal tract. The encapsulation of nucleic acids in SWCNTs and the corresponding equilibrium properties have been probed before, mostly for hydrophobic topologies11, 15-17 and more recently employing hydrophilic nanotubes.18 Although thermodynamically favourable, DNA confinement is markedly dependent on nanopore diameter and electrostatic environment, for the resulting


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nucleic acid can be elastically deformed away from the canonical B-form, predominant in living cells. The whole mechanism14, 19 can be rationalized in terms of a 3 – step kinetics, starting with i) biomolecular encapsulation into the nanotube, followed by ii) translocation/diffusion along the pore and finally iii) escape from the endohedral volume leading to release of the biological payload towards the cell. The intermediate step, involving molecular translation within the solid, remains mostly uncharted. Using an hydrophobic and large diameter nanotube (D = 4 nm), we have recently shown17 that the kinetics of a 12-nucleotide long DNA double-helix is consistent with Fick’s law only during the initial moments after encapsulation. Because narrower topologies prevented the latter, our previous work is but an initial stepping stone into the issue, and a more abridging and selfconsistent analysis is urgently needed. This issue is addressed here employing two distinct SWCNTs, while probing the dynamics of a confined Dickerson B-DNA dodecamer20 (Figure S1 in Supporting Information) onto those electrically charged topologies. For this purpose, a system is built containing the nucleic acid and the carbon nanotube and solvated with H2O and NaCl buffer (Fig. 1a). As a consequence of strong electrostatic attraction, DNA approaches the nanopore entrance (Fig. 1b) and becomes completely encapsulated within the solid lattice after 2 – 5 ns (Fig. 1c). Following encapsulation the nucleic acid diffuses along the endohedral volume (Fig. 1 d–g), exploring a region of space contained between nanopore termini: previously unexplored but remarkably significant, this phenomenon is the core subject of the present work.


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Figure 1. Nucleic acid trajectory after exposure to an electrically charged D = 4 nm nanotube. (a) Initial system setup showing DNA at a 0.5 nm distance away from the nanopore entrance; (b) encapsulation begins as a consequence of strong electrostatic attractions between the nucleic acid and the solid, leading to (c) complete confinement of the biomolecule, (d–g) which results in molecular translation within the endohedral volume. Colour key: ochre) DNA double-strand, light grey) (51,0) hydrophilic nanotube, red) H2O and blue) Na+ and Cl– ions.)


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2. Methodology, Molecules and Algorithms Classical molecular dynamics (CMD) is used to effectively sample the phase space and record temporal trajectories,21-22 along side with an atomically detailed descriptor23-24 of the DNA@SWCNT system seldom paralleled before. Initially, DNA is placed inside an orthorhombic cell containing the SWCNT, (x × y × z) = (11 × 11 × 15) nm, aligned with the nanotube main axis (z) and at a distance of 0.5 nm away from the closest terminii (Fig. 1a). The cell is H2O–solvated at ρ = 1 g/cm3, the media ionic strength adjusted with an NaCl buffer (134 mM) and an equilibration in the NVT ensemble followed by an NPT run is performed during at least 0.8 ns. Subsequently the whole system is monitored until encapsulation occurred (Fig. 1c), after which independent CMD runs were performed with a time length of 0.1 µs (one per nanotube diameter) to study the kinetics; encapsulation was determined by visual inspection of the molecular trajectories and calculating the c.o.m. distance between DNA and the nanotube.18 Technical implementation was performed using the Gromacs 4.6.7 CMD engine22 and the Verlet scheme to integrate Newton’s equations of motion with a 2 fs timestep; visualization of molecular trajectories was accomplished using VMD 1.9.3.25 In order to enforce physiological conditions upon the systems, we employed a Nosé-Hoover thermostat (310 K)26-27 and a Parrinello-Rahman barostat (1 bar),28 in aqueous solution with the NaCl ionic buffer. For both the van der Waals and Coulombic interactions a potential cut-off of 1.5 nm was employed, and the long-range electrostatics calculated with the particle-mesh Ewald method29-30 using cubic interpolation and a maximum Fourier grid spacing of 0.12 nm; full 3-D periodic boundaries were applied; physiological-like conditions are imposed throughout the numerical experiments.


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Molecules are described with atomically detailed force fields, including partial electrostatic charges in each atom; according to the atomically detailed nature of our study, a typical simulation cell contains ~ 1.8 x 105 particles. Dispersive energies are calculated with the Lennard-Jones (12,6) potential and using Lorentz-Berthelot mixing rules. DNA is modelled as a completely flexible entity within the framework of the AMBER99sb-ildn force-field;24,

31

we

have included in the potential the refinements proposed by Lindorff-Larsen et al.,24 resulting in an improved accuracy of the DNA backbone dihedrals. Recent simulation work with HIV1 proteins has been validated against experimental data (residual dipolar couplings, order parameter S2), and Musiani and co-workers have concluded that the AMBER99 force field performs better than the CHARM36 potential to describe nucleic acids.32 The classical parameterization of Aqvist and Dang33 is used to account for the buffer ions, Na+ and Cl–, and H2O molecules are dealt with the TIP3P force field of Jorgensen and co-workers;34 the adequacy of the NaCl force field within the context of biomolecular simulations under physiological conditions has been addressed before.33,

35

B-DNA is the predominant conformation in living

cells, and we have thus employed the double-stranded Dickerson dodecamer,20 5'D(*CP*GP*CP*GP*AP*AP*TP*TP*CP*GP*CP*G)-3' (Fig. S1). In spite of being smaller in length than its genomic-based analogue, the Dickerson dodecamer structural features exhibit similarities with genomic length λ-bacteriophage DNA,36 such as the radius of gyration and double-strand backbone diameter, RGyr ≈ 0.7 – 1 nm and D ≈ 2 nm, rendering it as an ideal candidate for biological purposes. Previous theoretical calculations37 with SWCNT bundles established a nanotube limiting diameter of D = 4.16 nm, beyond which the solids would collapse when exposed to atmospheric hydrostatic pressure. Recently, Kobayashi et al.38 experimentally validated that upper threshold


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by using supported-catalyst chemical vapour deposition to produce large diameter SWCNTs, D ≈ 4 nm, thus obtaining much larger diameter solids than the ones synthesized by conventional CVD. Building up on these previous works, two different diameter (D) nanotubes have been adopted herein, both with zig-zag symmetry and length L = 8 nm, namely D = 4 nm (51,0) and D = 3 nm (40,0). The effect of electrical charge density upon the encapsulation kinetics is addressed employing nanotubes with nominal electric charges of q = + 0.05 e–/C,7-8,

18, 39

effectively mimicking p-type doped solids and pristine nanotubes exposed to an electric field; Carbon atoms are described by Steele’s Lennard-Jones potential40 for graphite (σ = 0.34 nm, ε = 28 K), with a Carbon-Carbon bond length of 1.42 Å39, 41 and kept fixed in space throughout the simulations.

3. Results and Discussion The resulting nanopores exhibit a total net charge of Q = +156 e– (40,0) and Q = +199 e– (51,0) which is neutralized in H2O solution by adding an equivalent amount of NaCl buffer to obtain physiological ionic strength. The DNA@SWCNT hybrids evidence clear separation of electrical charge density, Γ(x,y) (Figure 2a), with dominant contributions from the nanotube itself but also from the Na+Cl– ionic pair; charge distribution is essentially symmetrical about the (x, y) centre, demonstrating that the hybrids are in a state of equilibrium.


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Figure 2. Electrical charge density. Boxes containing the DNA@SWCNT hybrids were divided into 100 slabs of 0.11 nm width, and each slab integrated along the x or y direction to obtain a


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volumetric charge density, Γ (x, y) (R is the SWCNT radius). a) NaCl (blue), DNA (red), complete (DNA@SWCNT+H2O+NaCl) systems (grey): the illustration representing concentric nanotubes is a guide to the eye; b) NaCl charge density, with the peaks location in the (x, y) space (nm), and c) complete system charge density (cf. Figure. S2 in SI for orthographic projections). The nanotubes are represented by their van der Waals volumes or C – C bonds, DNA as an ochre surface, H2O by its O atoms (red) and Cl– by blue spheres. Light and dark colours correspond to the (40,0) and (51,0) topologies, respectively. Notice that SWCNTs are aligned along the z-direction and thus their main axis is perpendicular to the (x, y) plane; the whole systems dimensions correspond to a volume of (x × y × z) = (11 × 11 × 15) nm (dashed lines indicate the (51,0) external boundaries).

Bearing in mind that the solids are positively charged (q = +0.05 e–/C), the sharp peaks in Figure 2b are attributed to the Cl– buffer ions clustering in direct contact with the walls and mediating the interactions between the latter and the nucleic acid; it is interesting to note the slight asymmetry associated with the peaks’ outer walls, arising essentially from the enhanced curvature of the (40,0) topology which induces a squeezing out effect upon the electrostatic cloud from the graphitic mesh (∼ 0.1 nm). The electrostatic profiles obtained for the ionic buffer produce a nanoscopic picture around the solid walls, revealing effective screening lengths between the bulk and the endohedral environment. Considering ζ = (ξ1 – ξ2), where ξ1 is the distance between the external wall peaks, 7.8 nm and 3.1 nm (51,0) and 7.4 nm and 3.5 nm (40,0), and ξ2 the same property regarding the inner walls, 7 nm and 3.8 nm (51,0) and 6.6 nm and 4.3 nm (40,0), then we obtain shielding constants ζ(51, 0) = 1.5 nm and ζ(40, 0) = 1.6 nm; ζ has


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no parallel in the Debye-Hückel formulation of an electrolyte screening length, but instead can be understood as the electrostatic distance (experienced by NaCl) separating the outer and inner walls, arising obviously from the graphitic Carbon atoms electrostatic clouds. Owing to the atomically detailed nature of our study, the multiple splitting of the Γ (x, y) peaks in Figure 2c marks the distinction between the outer and inner graphitic walls, the latter of which contacts directly with DNA (orthographic projections of the insets are recorded in Fig. S2 of Supporting Information). Being strongly correlated with the walls, charge density at the endohedral domain corresponds essentially to the nucleic acid and Cl– ions employed as buffer to counterbalance the solid’s positive charge. It is interesting to observe that, depending on the particular diameter, the DNA charge density is heavily located at the walls (D = 4 nm) or clustered around the nanopore centre (D = 3 nm); notice the sharp negative electrical signal associated with the whole DNA@SWCNT+H2O+NaCl system (Figure 2c) exactly located at the (40,0) centre, (x, y)/R = 0 (individual (x, y) DNA curves, as well as the corresponding z profile, are magnified in Fig. S3 of Supporting Information). This finding is attributed to available freevolume, for the nucleic acid/solid interaction energies are very similar for both topologies18 under equilibrium (~ 4.1 × 103 kJ/mol): DNA has no entropic degree of freedom to accommodate itself along the (40,0) solid except the z direction parallel to the pore main axis, an inhibition that is switched-off in the (51,0) solid, allowing the nucleic acid to elastically deform itself and explore the x and y dimensions. This observation echoes a similar issue in viral biophysics, for it is well known that conformational properties play a key role in the packaging/ejection of genomic material during viral infection.42-44 Following DNA confinement onto a viral capsid (assembled from highly charged protein building-blocks), bending energy is the dominant contribution affecting DNA conformation, essentially because the electrostatic forces rely largely


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on the DNA density that can reach 60% of the inner capsid volume.45 Electrostatic repulsions and entropic penalties are the dominant contributions to the free-energy of packaging, accounting for 90% in the case of a φ29 capsid. In the present work, the electrostatic environment of packaged DNA is probed via the NaCl charge distribution; Na+ and Cl– are used as electric probes not only for the surfaces (Figure 2b) but also for the biomolecule. Number density maps obtained for the Na+Cl– ionic pair are recorded in Figure 3, separating the contributions from negative and positively charged particles. Apart from the exclusion volume located at the nanotube walls, Na+ density is quasihomogeneously distributed between the pore and the bulk media, with a slightly enhanced density close to the biomolecule, forming essentially a continuous positive charge distribution. A completely different picture is observed for Cl–, arising from the existence of inhomogeneous domains. The presence of an electrical double hydration shell around the nanotubes is evident, and, most significantly, an enhanced clustering of negative charge along the inner wall that fades away as the nanotubes (x, y) centre is approached. That volume is already strongly populated by negative charge from the DNA double-strand.


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Figure 3. Number density maps for the Na+Cl– buffer. Notice the 2nd hydration shell of Cl- ions around the inner and outer walls. Dashed lines are pictorial representations of the nanopores’ boundaries.

When the SWCNTs main axis (z) is concerned, it becomes evident that there is a second exclusion volume, modestly populated by Cl–, and particularly notorious for the (40,0) solid; it has already been discussed that the nucleic acid favours positioning along the nanopore z centre (Figure S3b, Supporting Information). Cl– ions are of the same electric charge as the phosphate groups along the DNA backbone, therefore constituting simultaneously exclusive moieties, and thus are pushed towards the nanopores’ termini where DNA charge density → 0. Unseen before, this nanoscopic feature results in striking effects upon the nucleic acid diffusion along the solid. The time dependent analysis of molecular trajectories is performed within the framework of the Stokes-Einstein or the Green-Kubo equations,21, 46 which have become the de facto method to obtain self-diffusion coefficients; both formalisms are mathematically equivalent.47 Baidakov and Kozlova determined the self-diffusion coefficients of stable and meta-stable Lennard-Jones


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fluids tracking the particle mean-squared displacement (Einstein equation) and velocity autocorrelation functions (Green-Kubo equation), and concluded that both methodologies produce self-consistent results within the calculation error (0.5 – 1.0%).48 Transport data obtained from CMD runs are analysed herein calculating the DNA self-diffusion coefficient, Deff, using the Stokes-Einstein equation49 to relate Deff with the molecular center of mass meansquared displacement (MSD) according to Equation 1, where r(t) is the positional vector at time t, and the triangular brackets denote an ensemble average over all configurations.

= lim→ 〈 − 0 〉

(1)

Because r(t) is a three-dimensional (3D) positional vector, self-diffusivities thus calculated are the result of a 3D mapping of phase space, therefore constituting effective translational properties. To accurately sample CMD trajectories, special care was taken to achieve statistically significant results, and therefore small time delays between origins were used,21 separating 2100 – 2400 total origins by a 1 ps temporal delay. The corresponding 3D results are plotted in Figure 4, as well as the individual components of MSD along the x, y and z directions. For comparison purposes, the classical diffusion regimes are indicated as grey lines, namely ballistic (MSD ∝ t2), Fick (MSD ∝ t) and single-file (MSD ∝ t1/2).


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Figure 4. Log-log plot of mean-squared displacement, ⁄ = − 0⁄ (R is the SWCNT radius), and relative contribution curves (MSD(x),(y),(z)/MSD3D). Grey lines correspond to classical diffusion regimes, ballistic (MSD ∝ t2), Fick (MSD ∝ t) and single-file (MSD ∝ t1/2) translation, and the dotted black lines indicate a 0.33 threshold for the contribution profiles. Normalized time (τ) corresponds to τ = t/ttot, where t is the measurement time and ttot is the total simulation time. Colour key: black) 3D, purple) x, dark red) y, blue) z.

A careful inspection of MSD data in Figure 4 reveals that biomolecular translation starts in the Fickian regime and lasts for a relatively short initial time window (≤ 2 ns), during which the Einstein relation leads to Deff(51,0) = 0.954 × 10–9 m2/s and Deff (40,0) = 0.537 × 10–9 m2/s. The


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magnitude of these values is half that of the corresponding data for an hydrophobic (51,0) topology17 with Deff = 1.713 × 10–9 m2/s; electrostatic attraction between the walls and the nucleic acid induces a slowing down of molecular diffusion in hydrophilic topologies as compared to pristine nanotubes. Beyond the Fickian domain (t > 2 ns), a transition to a single-file regime seems to occur and DNA diffusion follows a t1/2 law, particularly evident for the (40,0) solid (Figure S4, Supporting Information). Furthermore, normalizing the one-directional MSD profiles with the corresponding 3D quantity according to MSD(x),(y),(z)/MSD3D, reveals a previously unobserved mechanism: diffusion is highly anisotropic in the (51,0) nanopore but no so in the (40,0) equivalent. Indeed, the curve of normalized MSD(z) (Figure 4) ends up contributing with more than 66% to the corresponding MSD3D value, whilst in the (40,0) pore it contributes with slightly less than 33%. It has already been discussed above that there is an exclusion volume along the nanotube z axis pushing Cl– towards opposite terminii, and leaving DNA responsible for the negative charge density in the endohedral domain (Figure S3b, Supporting Information); the latter domain is larger for (51,0) than for (40,0), thus enabling an enhanced z mobility of the nucleic acid in the (51,0) topology. This Cl– exclusion volume is also accountable for two distinct mechanisms of translation between topologies: whilst in the (51,0) solid DNA moves along the pore favouring the z direction, when diameter narrows down to 3 nm a self-rotation about the double-helix axis is the preferred mode of translocation within the pore (Animations 1-2 in Supporting Information). In a general fashion the mean-squared displacement, MSD = 〈 − 0 〉 , can be described by a power law according to MSD ∝ tκ, where the exponent is an indicator of the predominant mode of translation, namely κ = 2 (ballistic), κ = 1 (Fickian) and κ = 1/2 (singlefile). This latter case, where MSD increases less than linearly with time, falls in the general


16

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category of sub-diffusion, and it is trivial to demonstrate that, incorporation of the tκ power law in eqn. (1) leads to ∝ !!" ∝ MSD!

#$% %

. It now becomes apparent that the effective

diffusivity decreases with increasing time and displacement, as a natural consequence of resistance to translation arising from the existence of pore walls; for nanopores, only in the very long time limit (µs) does this sub-diffusive regime changes back to normal diffusion.49 Thus, the self-diffusivities obtained from MSD data recorded in Figure 4 should be taken with care, and employed as estimators for the diffusion of genetically-long nucleic acids in electrically charged nanotubes. A nanoscopic picture of the DNA’s mobility mechanism is obtained probing the corresponding instantaneous velocities, as indicated in Figure 5. Velocity data were histogram weighted with a bin width of 2 × 10–3 nm/ps to obtain probability densities, and analysed using the Maxwell-Boltzmann distribution50 for three-dimensional (equation 2) or one-dimensional translation (equation 3):

*

0

&' = ()+, ./ 42' 3

-

*

&'= = (+,

-.

3

!

456 > 67- 8

!

456 67- 8

' = '9, ;,

Dynamics of B-DNA in Electrically Charged Solid ... - ACS Publications

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