Simulations of Electrophoretic RNA Transport Through Transmembrane
Urs Zimmerli and Petros Koumoutsakos
Computational Science and Engineering Laboratory, ETH Zu ¨rich, Switzerland
ecules, is fundamental for the rational design of nanodevices interfacing with biological systems. In this work, we use molecular
dynamics simulations to study the electrophoretic transport of RNA through carbon nanotubes embedded in membranes.
Decorated and naked carbon nanotubes are inserted into a dodecane membrane and a dimyristoylphosphatidylcholine lipid
bilayer, and the system is subjected to electrostatic potential differences. The transport properties of this artificial pore are deter-
mined by the structural modifications of the membrane in the vicinity of the nanotube openings and they are quantified by the
nonuniform electrostatic potential maps at the entrance and inside the nanotube. The pore is used to transport electrophoretically
a short RNA segment and we find that the speed of translocation exhibits an exponential dependence on the applied potential
differences. The RNA is transported while undergoing a repeated stacking and unstacking process, affected by steric interactions
with the membrane headgroups and by hydrophobic interaction with the walls of the nanotube. The RNA is structurally reorganized
inside the nanotube, with its backbone solvated by water molecules near the axis of the tube and its bases aligned with the nano-
tube walls. Upon exiting the pore, the RNA interacts with the membrane headgroups and remains attached to the dodecane mem-
brane while it is expelled into the solvent in the case of the lipid bilayer. The results of the simulations detail processes of molecular
transport into cellular compartments through manufactured nanopores and they are discussed in the context of applications in
biotechnology and nanomedicine.
The study of interactions between carbon nanotubes and cellular components, such as membranes and biomol-
Recent advances at the interface of nanotechnology and mo-
lecular biology present us with new opportunities for the
development of devices such as nanoscale biosensors, mo-
lecular motors, and nanosyringes for application domains
ranging from bioengineering to nanomedicine (1,2). Biologi-
cal cells rely on nanoscale components such as ion channels
and pumps that regulate key transport processes across cell
membranes (3,4). Molecular transport across membranes may
also be inflicted by actions of external agents such as viruses
binding and puncturing the cell membrane to transfect it with
their nucleic acids (5).
The critical role of transmembrane channels and pores in
structures (1,6), with characteristics such as ion and mem-
brane selectivity, voltage and ligand gating, and blockage.
Several techniques have been developed for the synthesis of
artificial channels based on unimolecular macromolecules,
micellar pores, and barrel-stave and barrel-hoop supramo-
lecules (6). The requirements for these channels include
structural stability, appropriate trans-membrane orientation,
and regulated channel activity (1). These requirements are
not always easy to achieve by self-organizing structures; at
the same time, the activity regulation of these channels
remains an ambitious goal. Alternatively, we may consider
the implantation of artificial channels and pores in cell
membranes by processes such as conjugation of biological
molecules and synthetic polymers as well as by and in situ
forming implants (7).
The requirements for structural reliability and low reac-
tivity are met by silica and carbon nanotubes, which are en-
visioned as prototypes of artificial transmembrane channels
and nanosyringes for targeted drug delivery (2). Trans-
membrane transport in natural ion channels, however, is
largely controlled by the structure of membrane proteins
whose structure and precise molecular actions may not be
easily reproducible with today’s nanofabrication techniques.
Simpler structures, such as silica-based nanopores (8), can
be manufactured, which may provide us with enhanced ca-
pabilities for molecular sequencing and selective molecular
transport. This possibility has been thoroughly investigated
in a series of recent articles (9–13) that reported on the
electrophoretically driven transport of DNA in nanometer-
size silica pores. In Fyta et al. (14), the molecular dynamics
models to study DNA translocation through a pore for ex-
tended timescales. The interface between biological systems
and artificial nanopores was recently assessed by means
of coarse-grained simulations (15–17). These simulations
demonstrated that a generic, hydrophobic nanotube func-
tionalized with hydrophilic ends can be spontaneously in-
serted into a lipid bilayer. In this work, we consider a specific
carbon nanotube and we analyze the detailed molecular in-
teractions of the membrane components with the nanotube
using molecular dynamics.
Submitted December 4, 2006, and accepted for publication November 9,
Address reprint requests to Petros Koumoutsakos, Tel.: 41-44-632-5258;
Editor: Tamar Schlick.
? 2008 by the Biophysical Society
2546Biophysical JournalVolume 94 April 20082546–2557
Carbon nanotubes are consistent with the requirements for
a model nanopore (17), as they are hydrophobic and can be
decorated for insertion in membranes. Their low reactivity
and DNA gene delivery (20) and storage (21). In addition,
CNTs can withstand a broad range of voltages and they have
been suggested as artificial membranes for DNA sequencing
and as stabilizing pores in biological membranes during
electroporation. Several recent studies have assessed the in-
teraction of small CNTs with water (22–26), ions (27,28),
and nucleic acids (29–31). The regulated channel activity by
nanotubes remains a challenge, however, because it requires
the integration of suitable gating molecules during their
manufacturing. At the same time, the relatively simple struc-
ture of the nanotubes, reminiscent of pores consisting of uni-
molecular macromolecules, can help us to assess the role of
complex gating structures in biological channels.
In this study, we use MD simulations to characterize the
behavior of decorated and naked CNTs embedded in mem-
branes and assess the role of the CNT decoration for its sta-
bilization in the membrane. We analyze the electrophoretic
transport of RNA through these CNTs and quantify interac-
tions of the membrane constituents with the carbon nano-
tubes. We find that the interplay between the lipid heads and
the opening of the nanotube characterizes the electrostatic
potential of the CNT, particularly during the electrophoretic
transport of biomolecules. The article is structured as fol-
lows: In Methods, we describe the setup of the molecular
dynamics simulations and present a novel method for in-
serting and stabilizing CNTs in membranes. In The Elec-
trostatic Potential, we discuss the electrostatics of the CNT
embedded in the dodecane membrane and the lipid bilayer,
followed by RNA Translocation in Transmembrane CNTs
with results from the simulations of the electrophoretic
transport of RNA across a membrane-mimetic and a lipid
bilayer. In the final section, we conclude with a summary of
our findings and their implications for applications at the
interface of biology and nanotechnology.
Molecular dynamics is a key methodology for the evaluation of new tech-
nologies and biological systems at the nanoscale (32). In this study, we
employed the MD package FASTTUBE (33), developed in our group for the
simulation of carbon nanotubes in aqueous environments, and we visualized
the results using VMD (34). The electrostatic interactions were computed
using the smooth particle-mesh Ewald method (35). A 32 3 32 3 48 grid
was used and validation studies using a 48 3 48 3 64 grid did not show any
significant differences in quantities such as the electrostatic potential maps
and the structure and speed of translocation of the RNA. The van der Waals
interactions and the real-space contribution to the Coulomb interaction
were calculated using a cutoff of 1 nm. All systems were kept at a tem-
perature of 323 K by applying a Berendsen thermostat and equilibrated to
atmospheric conditions using a Berendsen barostat with a characteristic
timestep of 0.1 ps (36).
These MD simulations rely on potentials from the AMBER 96 force field
(37) with the extensions proposed in Smondyrev and Berkowitz (38) for
modeling phospholipids. Dodecane was modeled using a united atom ap-
proach similar to the modeling of lipid tails in Smondyrev and Berkowitz
(38). All membrane simulations were carried out at constant area and tem-
perature.Atime step of 2 fs was usedandall bondsinvolvinghydrogenwere
kept rigid throughout the simulations. Water was modeled using the TIP3P
water model (39). The carbon nanotubes were modeled using the Lennard-
Jones parameters for aromatic sp2-carbon of the AMBER 96 force field (37).
The bond, angle, and dihedral interaction potentials for the CNT were
modeled following Walther et al. (40). In the case of decorated CNTs, the
hydroxyl and hydrogen termini are modeled according to corresponding
groups in tyrosine in the AMBER 96 force field (37). The charges of the
hydroxyl and hydrogen termini were locally balanced on the carbon atoms
where the terminal groups are attached to the CNT (0.159 e for the hydroxyl
groups and ?0.166 for the hydrogen termini).
We note that, even though charged molecules are being transported
through the nanotube, we did not model polarizability effects. In an earlier
work (25), we have found that the inclusion of dipole terms in the potentials
of the nanotubes can alter drastically the transport of water molecules. These
effects were found to be significant near the entrance of short nanotubes,
leading to L-defects in the water chains, but they were negligible for nano-
tubes with a diameter wider than 2.5 nm. Several works have considered the
polarizability of carbon nanotubes interacting with water (41) and peptides
(42). In Lu et al. (41), the polarizability of CNTs has been empirically
modeled using atomic partial charges, derived from DFT calculations and a
tight-binding model to describe the dielectric response of the CNT. This
model was applied to the transport of a nonpolarizable water molecule
demonstrating that polarizability influences the water molecules and polar
solutes as they are transported by CNTs. In Tomasio and Walsh (42), a
polarizable force field has been developed for the interactions of CNTs and
peptides and it has been validatedby DFT calculations and experiments. The
inclusion of polarizability effects was shown to be important for describing
the stacking interactions between the aromatic peptide side groups and the
CNT. In that work, however, the effects of water were modeled by using an
effective continuum solvent. At the moment, there is no force field that has
been shown to adequately represent the interaction of the membrane mole-
cules used in this study with the carbon nanotube and the RNA. In addition,
as we consider the molecular description of water, nanotubes, RNA, and
membranes, the inclusion of polarizability effects in this study would have
amounted to prohibitively costly simulations. The absence of polarizability
in our modeling is further discussed in RNA Translocation in Transmem-
brane CNTs, when we present the results of the simulations.
The dodecane membrane mimetic was set up in a 6.1 nm 3 6.1 nm 3 10 nm
computational box. A slab of 192 dodecane molecules in random orientation
with a height of 2.5 nm were placed between two slabs of 3610 water
molecules, each ;3.1 nm thick. After energy minimization, this system was
equilibrated by a Berendsen thermostat and a Berendsen barostat acting only
in the direction orthogonal to the membrane for 180 ps (36) each, with
characteristic times of 0.1 ps. Using the Berendsen barostat, after equili-
bration, the system was relaxed at constant temperature for another 20 ps.
The final extent of the computational domain was 6.1 nm 3 6.1 nm 3 8.214
nm. The coordinates for the dimyristoylphosphatidylcholine (DMPC) lipid
bilayer were obtained from the Tieleman group (PDB file dmpc_npat.pdb
from http://moose.bio.ucalgary.ca/index.php?page¼Downloads). These co-
ordinates are the result of a 1-ns-long simulation of 128 DMPC molecules
solvated in 3655 water molecules.
The carbon nanotubes are based on a (14,14) armchair-CNT with a length
size of ;1.5 nm (29). We considered two variations of this CNT: The
‘‘naked’’ CNT (with unfilled valences at the ends) and a decorated/doped
CNT, where alternating hydroxyl and hydrogen termini were added at its
edges (H/OH CNT). The CNT diameter is comparable with the constriction
RNA Transport through Transmembrane CNTS2547
Biophysical Journal 94(7) 2546–2557
region of the a-hemolysin channel (9,29,43,) and the CNT length is selected
so that it minimizes the hydrophobic mismatch with the DMPC membrane
(44,45). Due to the limited size of the computational domain, the membrane
destabilization of the lipid bilayer structure.
In these simulations, we considered the transport of single-stranded RNA
consisting of 20 adenosine nucleotides. The RNA is hydroxylated at both
ends and the charge of the whole system is neutralized by randomly adding
potassium counterions to the solvent.
Membrane-CNT setup and equilibration
We present a snapshot (Fig. 1) from the simulations of the insertion of the
RNA into the CNT to define the geometry of the configuration. Using a
cylindrical coordinatesystem(r,u, z), thenanotubeaxis isnominallyaligned
along the z axis while the membrane surface is largely parallel to the (r, u)
Embedding the CNT in a membrane
The embedding of a CNT in a membrane is hindered by the irregular, un-
steady distribution of the lipids. To address this difficulty, Faraldo-Gomez
et al. (46) presented a two-stage method, first generating a cavity in a lipid
bilayer and then using steered molecular dynamics to insert in it a protein
We introduce a novel technique for the insertion of CNTs into pre-
equilibrated membranes. As a first step, the solvent around the membrane is
removed and the bilayer structure is adjusted to accommodate the CNT. In
the case of the DMPC bilayer, 14 lipid molecules were removed from the
central area of the bilayer corresponding to the nominal volume that would
be occupied by a (14,14) CNT. No molecules were removed from the do-
decane membrane. Subsequently, a scaling technique was used to insert the
CNT: the CNT was initially contracted to a single line of carbon atoms,
threaded into the cavity opened in the DPMC bilayer or into the unaltered
dodecanemembrane.Thelength-scaleparameterss of alltheLennard-Jones
interactions of the CNT molecules were initially set to zero and then linearly
scaled to their original value during a period of 2 ps. In the next 28 ps, the
radius of the CNT was grown back to its original size. During this process,
the positions of the CNT atoms were adjusted so that they correspond to a
linear scaling of the CNT radius. Furthermore, the motion of the membrane
atoms was restricted to the two in-plane dimensions and the respective
of 0.3 nm ps?1. The system was equilibrated for 1 ns and subsequently
samples were taken every 1 ps during the course of 1 ns.
Wenote thatthis approach differs from theinsertion technique presented in
Faraldo-Go ´mez et al.(46) in that it does not require any surface triangulation
and it relies on quantities that are computed routinely in MD simulations.
After the insertion of CNT into the membrane, the system is solvated by two
slabs of ;1 molar potassium chloride solution. In both cases, 150 potassium
and 150 chlorine ions were added to 8127 (for the dodecane membrane) and
8211 (for the DMPC bilayer) water molecules.
For the DMPC bilayer, during the first 40 ps of solvation all phosphorous
atoms are kept fixed and the water is relaxed to wet the membrane. This is
followed by 4 ps of dynamics where the phosphorous atoms are restricted to
move only within the plane of the membrane. After further relaxation and
a total simulation time of 60 ps, the system is relaxed using a Berendsen
barostat during 200 ps. This is followed by a further relaxation at constant
volume for 40 ps.
In the case of the dodecane membrane, its molecules were kept fixed
during the first 40 ps of simulation and the water was relaxed to wet the
membrane. Subsequently, the velocity of the dodecane molecules was cap-
ped at 0.3 nm ps?1for 4 ps. After a total simulation time of 80 ps, the system
was coupled to a Berendsen barostat for 120 ps. The system was further
equilibrated at constant volume for another 100 ps to obtain a total of 300 ps
for solvation, relaxation, and equilibration.
Insertion of RNA into CNTs
The simulations of RNA transport through the CNT were initialized by
terminus is situated 0.8 nm outside the CNT and on the tube axis. The whole
RNA was initially restrained for 46 ps and subsequently only the first
phosphorous atom from the 39-terminus was restrained, while the rest of the
RNA was allowed to move freely. Both, the RNA and the membrane were
After solvation and relaxation, the RNA was steeredinto the CNT (47). A
harmonic guiding potential with a force constant of 30,000 kJ nm?2mol?1
was applied to the first phosphorous atom from the 39-terminus. The RNA
was threaded into the CNT by moving the reference point of the steering
potential along the CNT axis during 280 ps. After the steering, the phos-
phorous atom was restrained at the opening of the CNT to allow for relax-
ation of structural strain imposed during the steering.
THE ELECTROSTATIC POTENTIAL
The electrostatic potential maps are used to characterize the
transport in transmembrane pores (48). We study naked and
H/OH-decorated carbon nanotubes, embedded in a dodecane
spheres) into the CNT (black spheres). The CNT is embedded in a DMPC
lipid bilayer. The whole system is solvated in a 1 M potassium chloride
aqueoussolution. In a cylindrical coordinate system (r, u, z) the membrane is
largely parallel to the (r, u)-plane while the axis of the nanotube is nominally
parallel to the z-axis.
Illustration of the system after the insertion of RNA (colored
2548Zimmerli and Koumoutsakos
Biophysical Journal 94(7) 2546–2557
membrane andalipidbilayer andsubjectedtoanelectrostatic
potential difference. The random distribution of dodecane
molecules and theorderedstructure ofthe lipid molecules are
reflected on the electrostatic potential of the system. In the
interior of the membrane, the lipid tails of the DMPC have a
composition similar to that of the molecules in the dodecane
membrane, but their lipid headgroups carry partial charges.
The headgroups interact with the decorated rims of the CNT
and alter the electrostatic potential in the vicinity of the
membrane and near the openings of the transmembrane pore,
as detailed later.
The electrostatic potential is assessed following the ap-
potential using the method of SPME (33,35). The instanta-
neous electrostatic potential is radially averaged over 1 ns
and presented as an axisymmetric electrostatic potential map.
In the related figures, the electrostatic potential map is com-
plemented with the contour lines of the number density for
characteristic atoms of the respective setup. These density
profiles serve to illustrate the location and mobility of the
membrane and the carbon nanotubes.
Electrostatics of a CNT in a membrane
We first present the electrostatic characteristics of a CNT
embedded in a membrane without the application of an ex-
ternal potential. The distribution of the electrostatic potential
helps us to assess the characteristics of the CNT as a trans-
CNT in a dodecane membrane
The electrostatic potential map of an H/OH-CNT in an ;2.5
nm thick dodecane membrane is presented in Fig. 2 along
with radially averaged density profiles of their constituent
atoms. The hydroxyl and hydrogen termini stabilize the CNT
in its transmembrane position and the hydrophilic interaction
between the water solution and the termini prevents the do-
decane molecules from creeping around the tube rim. The
CNT interior forms a channel of low electrostatic potential
across the membrane. The electrostatic potential map ex-
hibits distinct zones of high and low potential that are highly
correlated with the location of the membrane and the CNT.
of the ionic solution and the interior of the dodecane mem-
brane, in close agreement with the potential difference found
between bulk water and the interior of a lipid bilayer (38).
CNT in DMPC bilayer
The electrostatic potential maps for the decorated H/OH-CNT
and for the naked CNT in a DMPC lipid bilayer are shown in
potential connecting both sides of the membrane. On both
ends of the membrane, zones of high electrostatic potential
protrude into the nanotube and constrict the effective channel
opening by 50%, to ;1 nm in diameter. For the naked CNT
these effects are more pronounced, and we observe zones
of high electrostatic potential extending across the whole
channel and forming barriers (Fig. 3).
The CNT-DMPC electrostatic potential maps are signifi-
cantly different from the ones reported for the CNT in the
dodecane membrane. The differences are attributed to the
DMPC lipid heads that extend further into the solution to
access water molecules to satisfy their hydrophilicity. The
lipid molecules are arranged into an hourglass shape around
the CNT, widening above the area of constriction, while the
lipid headgroups are fanning out over the tube rims partially
covering the pore openings. This effect is well illustrated by
the radially averaged density profiles shown in Fig. 3.
The differences between the naked and theH/OH-CNTare
attributed to the solvation of the ester groups of the lipids.
The ester groups are stabilized by forming hydrogen bonds
with the hydrogen and the hydroxyl groups at the decorated
tube rim (Fig. 4). In the case of the naked CNT, this inter-
action is lacking and the lipids slide along the CNT and to-
ward the water phase, so that the ester groups come into
contact with the water at the tube rim (Fig. 4). This config-
uration is energetically more favorable, allowing for solva-
tion of the carbonyl groups, while at the same time the lipid
headgroups extend further over the tube rim, allowing the
ammonium groups to leap into the area of the tube opening
(Figs. 3 and 4).
The fanning of the lipid heads into the tube opening is
reflected in the distribution of the standard deviation of the
sity profile (left) on the (r, z) plane for a CNT in a dodecane membrane and
in the absence of an imposed transmembrane potential difference. The radi-
ally averaged density profile indicatesthe dodecane molecules (blue) and the
Radially averaged electrostatic potential map (right) and den-
RNA Transport through Transmembrane CNTS2549
Biophysical Journal 94(7) 2546–2557
electrostatic potential (Fig. 5) having large values in the zone
occupied by the lipid headgroups. The charge separation
of the choline group promotes significant fluctuations (of
;5 ns?1) of the electrostatic potential, which are more pro-
nounced for the naked CNT than for the H/OH-CNT. These
oscillations are attributed to the strongly correlated reorien-
tation of the lipid headgroups (Fig. 6).
We note that the hydrophilicity of membrane heads and
the corresponding CNT rim decorations are critical in de-
termining the access to the nanotube entrance. This finding
hints at possible regulation and gating mechanisms that may
be accomplished by specifying the molecules for the CNT
rims so as to control their interactions with the corresponding
Application of a transmembrane
A transmembrane voltage difference (8,9,48) is applied to
drive a single-stranded RNA segment of 20 adenosine nu-
cleotides through the CNT pore embedded in the membrane.
We first demonstrate that the electrostatic voltage differ-
ences induce an asymmetry on the lipid head arrangement on
the entrance and on the end-side of the CNT, and affect the
overall electrostatic potential maps. We then discuss the
electrophoretic transport of the RNA through the CNT and
identify a stacking process that depends on steric interactions
with lipid heads at the tube entrance and hydrophobic inter-
actions with the walls of the nanotube.
CNT in a dodecane and a DMPC membrane
An electrostatic potential of 0.95 V is applied across the
system of the H/OH-CNT embedded in the dodecane mem-
brane. The electrostatic potential (Fig. 7) is largely uniform
on either side of the membrane, although it changes sharply
within the transmembrane nanopore. The potential maps are
qualitatively similar to the corresponding maps of solid-state
nanopores presented by Heng et al. (10).
In the case of the DMPC membrane, an electrostatic po-
tential difference of 1.05 V is applied, resulting in the elec-
OH CNTs. We observe a constant electrostatic potential for
the H/OH-CNT on both sides of the membrane accompanied
outside the opening of the CNT (Fig. 8). On the side of low
electrostatic potential, a similar barrier is absent for the H/
OH-CNT, leading to an opening reflected in a bay of low
electrostatic potential extending into the pore. This distribu-
tion is due to the absence of lipid headgroups in the area of
that tube opening, which is also confirmed by the radially
averaged density profiles (Fig. 8).
A high barrier on the side of the high potential is also
observed in the case of the naked CNT. In contrast, however,
with the H/OH-CNT, this barrier is inside the CNT opening.
The asymmetry of the electrostatic potential map of the H/
OH-CNT is attributed to a reorientation of the membrane,
subject to theelectrostatic potential differences inthe vicinity
of the tube entrance. The positively charged ammonium
groups of the lipids (38) on the side of high electrostatic
potential are pushed by ;0.7 nm into the area of the H/OH-
CNT opening (compare Fig. 9). For the naked CNT, we
observe a similar effect with an ammonium density peak just
and a decorated H/OH-CNT (right). The membrane lipids in the vicinity of
the naked CNT leap farther into solution and into the tube area. For the H/
OH-CNT the hydroxyl groups form hydrogen bonds with the lipids, thus
satisfying their solvation requirements and preventing them from fanning
over the entrance of the CNT.
Sample snapshot of the lipids at the rims of a naked CNT (left)
z)-plane for a naked CNT (left panel) and a decorated H/
OH CNT (right panel) acting as nanopores in a DMPC
lipid bilayer in the absence of an imposed electrostatic
transmembrane potential difference. The electrostatic po-
tential map (right half in each figure), and density profile
(left half in each figure) are plotted to demonstrate corre-
lations between the distribution of the lipid heads and the
resulting potential. The density profiles indicate the CNT-
carbon atoms (red) and the DMPC-nitrogen atoms (blue).
There is no electrostatic potential difference acting across
the membrane. Zones of high electrostatic potential pro-
trude slightly into the pore area for the decorated CNT
(left), whereas for the case of a naked CNT (right) they
form a barrier across the entrance of the tube.
Potential maps and density profiles on the (r,
2550Zimmerli and Koumoutsakos
Biophysical Journal 94(7) 2546–2557
outside the tube openingthat ispushed ;0.7 nm into the tube
(Figs. 3 and 8) On the membrane side with low electrostatic
potential, the ammonium groups are subject to electrostatic
forces which, in turn, pull them away from their equilibrium
position, leading to their upright position close to the tube
entrance (Fig. 9).
In the case of the H/OH-CNT, the lipid headgroups are
hardly leaping into the tube area even in the absence of an
electrostatic potential difference (Fig. 4). As a consequence,
the electrostatic potential difference has a negligible effect on
their density distribution on the side of low electrostatic po-
tential (Figs. 3 and 8). Contrastingly, for the naked CNT in
the absence of an electrostatic potential difference, the lipid
headgroups are leaping into the area of the tube opening (3).
As the electrostatic potential difference is applied, the am-
monium density retracts by ;0.5 nm away from the tube axis.
The electrostatic barrier reported in the absence of an elec-
trostatic potential difference across the membrane is weaker
but still persists in the presence of a potential difference.
We note that the electrostatic potential maps persist for
potential differences between 0.2 V and 1.5 V and they are
significantly different from the maps obtained for a CNT in a
dodecane membrane (Fig. 7) and for solid-state nanopores
(11). The lipid headgroups reorient when they are subjected
to an electrostatic potential difference leading to different
barriers of electrostatic potential for H/OH and naked CNTs.
These differences are an essential feature of the steric inter-
actions between an artificial nanopore and a lipid bilayer, and
they need to be taken into consideration when designing the
The sensitivity of the lipid head arrangement in naked and
decorated CNTS can provide guidance for the design of
suitable unsteady voltage differences across the CNT that
may regulate access to its entrance. The interplay of nano-
tube-based pores and the lipid heads is further exemplified in
the following section presenting the translocation of RNA
through a CNT.
RNA TRANSLOCATION IN
The translocationof ions, DNA,and RNA throughbiological
and synthetic pores has been investigated recently by large-
scale MD simulations (10,11,27,32,49) to provide guidance
for the design of innovative sequencing devices. In this ar-
ticle, we present MD simulations of RNA transport through a
CNT embedded in a dodecane membrane and a DMPC bi-
layer to study the interplay of the lipid bilayers and the CNT
electrostatic potential map (right half of each snapshot)
and density profiles (left half of each snapshot) of the am-
monium group of the dodecane (blue) and the CNT (red)
molecules, on the (r, z) plane. The results indicate that the
averaged electrostatic potential in the tube opening corre-
lates with the density of the headgroups. As the density is
shifted from the center of the tube toward the tube rims, the
strength of the electrostatic potential in the tube center
diminishes, while the electrostatic potential protruding into
the tube area retracts.
Two snapshots of the radially averaged
CNT (left panel) and decorated H/OH CNT (right panel),
acting as nanopores in a DMPC lipid bilayer. Standard
deviation (right half of each figure) and averaged mean
value (left half of each figure) of the electrostatic potential
the area occupied by the lipid heads, indicating their
enhanced fanning in the presence of the CNT and lowest
in the center of the lipid bilayer.
Potential maps on the (r, z)-plane for a naked
RNA Transport through Transmembrane CNTS2551
Biophysical Journal 94(7) 2546–2557
in the translocation of RNA molecules. These simulations
provide insight for applications ranging from drug delivery
(50) to molecular machines (1,51), where artificial pores are
implanted in lipid bilayers.
RNA across a dodecane membrane
A single-stranded piece of RNA consisting of 20 adenosine
nucleotides is transported through a naked and H/OH-CNT
embedded in a dodecane membrane. The transport is driven
by transmembrane potential differences of 1.50–2.10 V in
steps of 0.1 V. The potential differences employed in this
study are significantly lower than potential differences em-
ployed for DNA translocation across synthetic pores (27,49)
as the bilayer membrane is ruptured for potential differences
of 2.4 V and beyond.
During the translocation, the entrance and exit of the RNA
bases in the nanotube is affected by steric interactions of the
CNT with the heads of the lipid bilayers, with the RNA bases
folding backward with regard to the direction of transloca-
tion (52). The transport inside the pore is characterized by
hydrophobic interactions between the nucleotide bases
(29,30) and the walls of the carbon nanotube (Fig. 10).
Inside the tube, the RNA bases maximize contact with the
CNT, sliding across the pore with their plane largely parallel
to the tube walls (Fig. 11). Single and stacked pairs of nu-
cleotide bases are observed, unstacking at the entrance of the
CNT, while small groups of RNA bases are observed to re-
stack at their exit from theCNT.During the translocation,the
RNA backbone is exposed toward the tube center (Fig. 12),
solvating the phosphate and sugar groups of the backbone by
the water inside the CNT. This arrangement of the RNA is
persistent throughout the simulations and suggests the pos-
sibility of using functionalized nanotubes to identify and
interact with the RNA bases.
We quantify the translocation of the RNA by relating the
speed of translocation with the potential differences applied
across the membrane. The speed of translocation is defined
the exit of nucleotide 16. This definition was chosen to ex-
clude contributions by end-effects such as nucleotides being
expelled from the tube entrance and reduced hydrophobic
interactions at the end of the simulation when the RNA is not
extended across the whole CNT. For potential differences of
1.20 V and beyond, the RNA was driven through the CNT in
relatively short time spans of ;10 ns. For potential differ-
ences between 1.20 and 2.15 V we observe a correlation with
the speed of translocation measured in nucleotides per
nanosecond (Fig. 11). The measurements were fitted with an
diffusion models of molecular translocations in pores (29).
The parameters of this exponential were determined by a
least-squares fit resulting in an empirical relation between
the activation voltage difference (DV) and the translocation
speed (v), v ¼ 0:087ðNuc=nsÞexpð2:57DVÞ: The speed of
translocation exhibits large fluctuations (Fig. 12) and a
tial map (right), and the corresponding radially averaged density profile for
the dodecane (blue) and the CNT (red) molecules on the (r, z) plane. A
potential difference of 0.955 V acts across the dodecane membrane.
CNT in a dodecane membrane. Averaged electrostatic poten-
CNT (right panel) in a DMPC membrane subject to a
electrostatic potential difference of 1.05 V. Radially aver-
aged electrostatic potential map (right half of each figure)
and density profile (left side of each figure) on the (r, z)
plane of the nitrogen of the DMPC (blue) and the CNT
A naked CNT (left panel) and a decorated
2552Zimmerli and Koumoutsakos
Biophysical Journal 94(7) 2546–2557
staircase pattern for potential differences ,1.55 V with the
longest stop of translocation lasting for ;1.2 ns. These
events are attributed to repeated conformational changes of
the RNA during its transport through the CNT. The RNA
bases form stacks as they approach the entrance of the CNT,
as their hydrophobic interactions intensify. This layering of
the RNA chain is broken when a base enters the CNT and the
interfacial area is hydrated. In turn, a secondary hydrophobic
interaction takes place between the base and the walls of the
CNT. The base approaches the CNT wall and aligns itself
parallel to it while, at the same time, water molecules are
being expelled from that region. The RNA bases are folding
backward with regard to the direction of transport, leading to
short temporal trappings. This is manifested in the steplike
behavior of the trajectories as the RNA bases overcome the
energy barrier and unstack.
The strength of the electrostatic potential difference con-
trols the stacking and unstacking of the bases, and the switch
between their hydrophobic interaction outside the entrance
of the CNT and their hydrophobic alignment with the walls
inside the CNT. At electrostatic potential differences of
RNA translocating insidea H/OH-CNT embedded in a dodecanemembrane.
In the top view, only the RNA fragments within the tube are shown. The
with respect to the direction of transport. The RNA backbone is exposed
toward the center of the tube.
Cross section (left) and top view (right) of a single-stranded
versus the potential difference across the membrane. Both translocations in
an H/OH-CNT (1) and a naked CNT (s) are plotted. An exponential is
fitted to the data.
Translocation speed in nucleotides per nano second plotted
CNT. The two ends of the CNT are indicated by dashed lines. A bold dashed
line indicates a steplike motion between 2 ns and 3.5 ns. Afterwards, the
RNA gets trapped for a relatively long time span from ;4 ns until 5.2 ns.
The trajectories of the RNA phosphate groups within the
the lipids close to the carbon nanotube, due to the application of the trans-
membrane electric field. On the side where the electric field points away
from the membrane, the ammonium group of the phospholipid (black) is
pushed toward the membrane and thus also over the carbon nanotube rim
(indicated by an arc). On the other side, the headgroups of the lipids are
stretched and the ammonium group is pulled away from the membrane. The
phosphate group is indicated by a white sphere.
Schematic indicating the reorientation of the headgroups of
RNA Transport through Transmembrane CNTS 2553
Biophysical Journal 94(7) 2546–2557
0.955 V, the RNA gets trapped after 1 ns, as the first two
nucleotides are expelled from the tube. In the next eight
nanoseconds, no noticeable motion was observed, although
the RNA inside the CNT exhibits spatial fluctuations of
;0.2 nm along the tube axis. The RNA outside the entrance
of the CNT moves similarly to free RNA in solution, until,
after another seven nanoseconds, one of the terminal attaches
to the membrane and remains attached to the membrane
throughout the rest of the simulation.
bases do not leave the CNT spontaneously, but are eventually
pushed away by the remaining RNA bases sliding down
within the CNT. One of the first nucleotides, however, usually
reattaches quickly to the outside of the tube or the dodecane
membrane. The RNA leaving the tube, buckles and forms a
loop, which eventually turns into a coiled-up structure. The
expelled RNA remains coiled-up at the tube exit during these
limited simulation times of 5–10 ns. The RNA was not de-
tached completely from the CNT in any of the simulations
conducted in this study that had one or two of the terminal
bases always hydrophobically attached to the CNT. (This is
similar to the results reported in (8) for synthetic pores.)
For larger potential differences, we observe similar trap-
pings and attachments of the RNA with intermittent periods
of fast translocation with speeds of four nucleotides per
nanosecond for an electrostatic difference of 1.2 V. For po-
tential differences larger that 1.55 V, we observe trapping of
nucleotides leaving a stacked geometry and entering the tube
could beidentifiedbya stepliketrajectoryasfound for smaller
potential differences (Fig. 12). The strong driving forces at
large potential differences mask the signature ofthe sequential
breaking of the stacking.
RNA across a DMPC bilayer
Simulations of RNA transport are performed for a tube em-
bedded in a DMPC bilayer, to study the effects induced by
the structure of the lipid bilayer membrane. The same single-
stranded piece of RNA consisting of 20 adenosine nucleo-
tides is transported through a naked CNT and an H/OH-CNT
embedded in a DMPC bilayer, which was subject to a po-
tential difference of 1.6 V.
The lipid headgroups of the DMPCmembrane extend over
the CNT and interact with the RNA (Fig. 13), slowing down
its translocationinthe tube.Inaddition,themotionofthe RNA
is sterically hindered as the lipid heads obstruct the pore open-
ing, similar to the effect described by de Groot et al. (53) and
comparable to the entropic barriers reported in Lim et al. (54).
The RNA structure within the CNT in the DMPC lipid
bilayer does not significantly differ from the structure in the
case of the dodecane membrane. The RNA bases are folded
bases towardthe centerofthe tube.Thetranslocation(Fig. 14)
of the RNA through the tube takes ;12 ns with an average
speed of translocation of 1.5 nucleotides/ns. This speed is
significantly lower than the one observed in the case of the
dodecane membrane, for similar voltage differences. This
effect is attributed to the increased steric interactions of the
lipid heads with the RNA. And contrary to the case of dode-
molecules shield the exterior of the CNT. The RNA leaves the
exit area and protrudes into solution while after ;10 ns the
foremost nucleotides get into contact with the lipid bilayer.
The RNA, however, is not adsorbed on the lipid bilayer sur-
face but readily diffuses back into solution.
It is important to recall here that polarizability effects have
not been accounted for in these simulations, largely due to
their computational expense. We estimate, however, based
on previous findings (41,42), that the inclusion of polariz-
ability effects in this configuration would have increased the
affinity of the RNA with the walls of the CNT, thus further
enhancing hydrophobic effects and further delaying the
transport of the RNA through the CNT. The study of polar-
izability effects in the electrophoretic translocation of RNA
in pores and channels, and the embedding of the MD simu-
lations in a multiscale framework where solvation effects are
accounted for by these mean-field theories, is a subject of our
SUMMARY AND CONCLUSIONS
of a short, single-stranded RNA segment through naked and
decorated carbon nanotubes embedded in lipid bilayer and
dodecane membranes. These simulations rely on a novel
method to insert nanotubes in bilayers. The results enable
observations with molecular detail for the interactions of the
nanotube with the membrane components. Simulations with
that lipid heads, and their coordination with the molecules at
the rim of the nanotube, determine to a large extent the
a transmembrane H/OH-CNT (black/red/white). The lipids are indicated
with a colored stick model, and the phosphorous (gold) and nitrogen (blue)
atoms within 7 A˚of the RNA are indicated with spheres. Both figures show
the same snapshot at an angle of 90?.
Snapshot of lipid headgroups interacting with RNA (gray) in
2554Zimmerli and Koumoutsakos
Biophysical Journal 94(7) 2546–2557
transport properties of the nanotube. These properties are
further quantified by presenting electrostatic potential maps
in the vicinity of the nanotube with and without electrostatic
potential differences. We note in particular that the lipid
heads of the DMPC bilayer extend above the CNT rims to be
solvated by water, thus blocking the entrance of the nanotube
and forming an electrostatic potential barrier. This effect may
help explain the structure of biological transmembrane pores
that exited into the solution.
The transport properties of the CNTs were further quan-
tified by measuring the speed of translocation of a short,
single-stranded RNA segment. During the electrophoretic
transport of RNA, the lipid heads in the DMPC membrane
were found to interact sterically with the transported RNA
bases and reduce by half its speed of translocation when
compared to the case where the CNT is embedded in a do-
decane membrane. In addition, the RNA was found to stay
attached to the dodecane membrane, after its exit from the
CNT, similar to a behavior that has been observed for other
artificial pores. In contrast, it appears that the DMPC lipid
heads help the RNA to overcome an entropic barrier so that it
enters the solvent after its exit from the CNT. We note,
however, that even at strong transmembrane potential dif-
ferences a few of the terminal nucleotide bases remain hy-
drophobically attached to the CNT. Chemical modifications
to the CNT interior and the tube rims that weaken the hy-
drophobic interaction of RNA bases and the CNT could
promote the detachment of the RNA from the CNT. Possible
applications may, however, benefit from the fact that RNA
may allow the retraction of the RNA after exposing it to the
cell interior. The transport of RNA across a carbon nanotube
transmembrane pore compares well with results reported on
synthetic silica nanopores (10) and the effects of constriction
are similar to results on a-hemolysin (11). While transport
velocities in transmembrane CNTs seem to exceed those of
an a-hemolysin, they seem to be slower than those observed
in synthetic silica pores (10).
Inside the nanotube, the CNT exhibits a strong hydro-
phobic interaction with the RNA bases, which align them-
selves to the walls of the nanotube, leading to a stacking and
unstacking process during the transport of the RNA. The
preferential orientation of the RNA bases inside the nanotube
may form the basis of rational functionalization of the CNT
interior for rapid sequencing protocols and the development
of novel molecular assembly scaffolds.
The results of these simulations help to demonstrate that
embedding carbon nanotubes inside membranes requires a
careful consideration of their functionalization and their in-
teractions with the surrounding membrane components. The
interaction of suitably decorated CNT rims and membrane
components may be exploited to regulate the transport
properties of the nanotube, an important feature for bio-
medical applications such as artificial nanosyringes, con-
trolled release drugs (50), and vectors for transfection (55).
Finally, we note that the design of devices based on the
interface of biological molecules with carbon nanotubes has
to take into account the toxicity of the nanotubes and identify
processes by which the administered CNTs (56) and fuller-
enes (57,58) will leave the body. Recent studies have shown
that water-soluble fullerenes do not enter membranes. The
results of these simulations indicate that decorated CNTs are
FIGURE 14 Translocation of RNA through an H/OH-CNT in a DMPC lipid bilayer. The snapshots are taken every 1.4 nanoseconds from 1.4 ns until 11.2 ns.
RNA Transport through Transmembrane CNTS 2555
Biophysical Journal 94(7) 2546–2557
well accommodated in lipid bilayers, resulting in well-
defined transmembrane channels that, at the same time, may
lead to increased toxicity and cell lysis.
Current work is geared toward modeling and assessing po-
larizability effects in membrane-CNT systems and the embed-
ding ofthese MD simulations in a multiscaling framework. As
imaging technologies are progressing toward capturing the
entering an era where the results of MD simulations of trans-
locating molecules may be validated by experimental works.
We wish to thank Professor Andrew Pohorille (UCSF) for many helpful
discussions at the inception of this project.
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