Interaction of Pristine and Functionalized Carbon Nanotubes with

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Interaction of Pristine and Functionalized Carbon Nanotubes with Lipid Membranes Svetlana Baoukina, Luca Monticelli, and D. Peter Tieleman J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/jp405732k • Publication Date (Web): 11 Sep 2013 Downloaded from http://pubs.acs.org on September 25, 2013

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The Journal of Physical Chemistry

Interaction of Pristine and Functionalized Carbon Nanotubes with Lipid Membranes Svetlana Baoukina1, Luca Monticelli2,3,4, D. Peter Tieleman1* 1. Department of Biological Sciences and Institute for Biocomplexity and Informatics, University of Calgary, Calgary, Canada 2. DSIMB, INSERM, Paris, France 3. Université Paris Diderot − Paris 7 4. INTS, Paris, France * corresponding author: [email protected], 1-403-220-2966. Abstract Carbon nanotubes are widely used in a growing number of applications. Their interactions with biological materials, cell membranes in particular, is of interest in applications including drug delivery and for understanding the toxicity of carbon nanotubes. We use extensive molecular dynamics simulations with the MARTINI model to study the interactions of model nanotubes of different thickness, length, and patterns of chemical modification with model membranes. In addition, we characterize the interactions of small bundles of carbon nanotubes with membrane models. Short pristine carbon nanotubes readily insert into membranes and adopt an orientation parallel to the plane of the membrane in the center of the membrane. Larger aggregates and functionalized nanotubes exhibit a range of possible interactions. The distribution and orientation of carbon nanotubes can be controlled by functionalizing the nanotubes. Free energy calculations provide thermodynamic insight into the preferred orientations of different nanotubes and quantify structural defects in the lipid matrix. Keywords free energy, insertion, molecular dynamics simulation, membrane perturbation, aggregation, carbon nanotube toxicity

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Introduction Carbon nanotubes (CNTs) are among the most widely studied nanomaterials. Their unique mechanical, thermal and electronic properties make them attractive for a vast number of applications in different areas of science and technology. CNTs can be used in high-strength composite materials,1 energy storage devices,2 various kinds of electronic devices3 and more 4. Applications in imaging and therapeutics have also been explored, reviewed in ref.5 Large scale production and use of CNTs have raised health and environmental concerns, as CNTs may be toxic, particularly for lung tissue.6 The study of CNT interactions with biological membranes is of paramount importance both towards the design of functionalized CNTs for biomedical applications and for understanding the physical and chemical basis of nanomaterial toxicity. CNT interaction with lipid membranes has been investigated using experimental, computational and theoretical approaches. Experimentally, it has been shown that CNTs induce the formation of reactive oxygen species in vitro and in vivo,7-8 and induce oxidative damage to lipids in lung membranes.9 Single-walled CNTs have been found to enter both plant and animal cells,10-13 but the internalization mechanism is not understood. In model systems, it has been shown that synthetic detergents, lysolipids and natural lipids form stable supramolecular assemblies with single-wall and multi-wall carbon nanotubes.14-16 Functionalized multi-walled CNTs are able to cross plasma membranes, with at least a significant fraction through an energy-independent mechanism.17 They can be transported between cells through a vesicle-mediated mechanism.18 Simulation studies so far have focused on simple model systems, including either detergents or lipid bilayers with only one or two different kinds of lipids.19 In a pioneering study in 2004, Klein and co-workers used MD simulations to characterize the passive insertion of purely hydrophobic and functionalized nano-sized tube-shaped molecules into a model membrane.20 Lysolipid-CNT self-assembled structures were studied by Qiao and Ke using atomistic MD simulations,21 and by Wallace and Sansom using larger scale, coarse-grained MD simulations.22 Sansom and Wallace also simulated lipid-CNT self-assembled structures,23 as well as the process of CNT penetration through a lipid membrane by pulling uncapped CNTs of different size at different speed.24 Modest atomistic simulations based on non-equilibrium pulling of carbon nanotubes into the bilayer along the bilayer normal have been reported by Gangupomu and Capaldi25 and by Raczynski et al. 26 Other recent atomistic simulations include the study of Zhao et al, who simulated a double-walled nanotube doped with different amounts of nitrogen atoms oriented along the membrane normal, and of Parthasarathi et al., who characterized by atomistic simulations the perturbation of lipids near a 6 nm carbon nanotube embedded in the membrane in either a parallel or perpendicular orientation as well as a bundle of seven nanotubes 27. Ban and Kopelevich studied the effect of carbon nanotubes on the structure and elastic properties of lipid membranes using simulations at the coarse-grained level with the Martini force field.28 Also using Martini, Lee simulated the interactions of a carbon nanotube wrapped in either lysolipids and shorter PEG (Mw=550) or phospholipids with longer PEG (Mw=2000)29. Insertion into the membrane was observed in the first but not the second scenario. Detailed understanding of membrane-CNT interaction requires an assessment of the energetics of CNT penetration into lipid membranes. Although some of the studies mentioned above have attempted this based on non-equilibrium pulling simulations, getting converged free energies and investigating a number of scenarios remains challenging for atomistic simulations. In a recent study, Kraszewski used both large scale equilibrium simulations and free energy calculations to study the interactions of a POPC bilayer with a number of different nanotubes, with either open or closed ends and with different degrees of coverage by functionalized groups (amino derivatives)30. The equilibrium simulations combined to over 3 microseconds, while a


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free energy profile was determined for the insertion of a closed pristine CNT, showing a free energy difference of ca. -21 kcal/mol between water and membrane interior. Larger-scale free energy calculations are possible with coarse-grained models. Pogodin and Baulin used a meanfield theory and simplified models of lipids and nanotubes.31 Their results suggested that hydrophilic NTs would encounter high energy barriers entering a lipid membrane in a perpendicular orientation (on the order of 100 kT); hydrophobic NTs, on the other hand, would spontaneously enter lipid membranes, but would find a significant barrier to translocation to the opposite aqueous compartment. In their study, NTs were represented as rigid cylinders with a chemically homogeneous surface, and only the perpendicular mode of entrance was considered. Using the MARTINI model, Nangia and Sureshkumar studied the effects of nanoparticle charge and shape on translocation through a model membrane. Although these were not nanotubes but gold particles of different shapes, this is a very interesting qualitative study of distributions and permeation rates that turn out to depend very strongly on both shape and, less surprisingly, charge density. Here we report results from extensive coarse-grained molecular dynamics and free energy calculations of nanotubes in the presence of lipid membranes (Figure 1). We model 4 different types of NTs: pristine, hydrophobic NTs; homogeneously functionalized NTs of intermediate polarity; and cap-functionalized NTs, with either partial (caps) or complete (caps and terminal rings) coatings; the length and diameter of hydrophobic NTs are also varied (Figure 2). Simulations are performed using the MARTINI coarse-grained force field32-35. For each type of CNT we carried out unbiased simulations and free energy calculations, which allowed determining the preferred mode of partitioning and the direction of insertion of CNTs in the membrane. Although these simulations are a significant step forward in terms of a quantitative assessment of interactions between nanotubes and biological membranes, they are based on simulations of individual carbon nanotubes. Hydrophobic nanotubes are likely to aggregate, complicating their interactions with membranes. We have addressed a similar question previously for fullerenes36 but the length of nanotubes makes this more challenging. As an initial step towards a better understanding of the interactions between aggregated nanotubes and membranes we also performed a number of equilibrium simulations of bundled CNTs near a membrane. A summary of all simulations is given in Tables 1 and 2.

Methods System setup. We simulated a bilayer in water with monomeric nanotubes (NT) or their aggregates. These systems are shown in Figure 1. We used seven different types of NT, varying, summarized in Figure 2. To study the effect of NT hydrophobicity, a carbon NT (Figure 2a), a functionalized NT (Figure 2b), a carbon NT with functionalized caps (Figure 2c), and a carbon NT with functionalized caps and terminal rings (Figure 2d) were simulated. To study the effect of NT size, a carbon NT of a smaller diameter 1.23 nm and three lengths: 4.1 nm, short (Figure 2e), 6.5 nm, medium (Figure 2a), and 9.7 nm, long (Figure 2f), and also a carbon NT of medium length and a larger diameter of 2.4 nm (Figure 2g) were simulated. All NTs were singlewalled and capped. To study the NT partitioning into a bilayer and perturbation of bilayer properties, we performed unbiased simulations on a single NT, and NT aggregates of four and sixteen. To characterize the energies of transfer from water to bilayer for monomeric NTs, umbrella sampling (US) and thermodynamic integration (TI) were employed. Two alternative thermodynamic cycles were considered (see schemes in Figure 3a-b). Potentials of mean force (PMFs) were calculated from US simulations for NTs of various types in thermodynamic cycle 1 (Figure 3a). Thermodynamic cycle 2 (Figure 3b) as well as unbiasing of restraints in cycle 1 was performed for selected systems as a control test. To compare the energies of transfer from bilayer center to water, a single NT in the oil-water system was also simulated. Bulk



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hexadecane was used to model oil. Note that in MARTINI, NT beads have the same interaction energy with alkanes and with lipid chain particles. Force field and models. We used the MARTINI coarse-grained force field33-34 for all simulations. The MARTINI model was originally developed for lipids33-34 and then extended to proteins37, carbohydrates38, various polymers39-41 and fullerene.36, 42 DOPC lipids are standard components of the force field; anti-freeze particles are typically added in concentration ~10% to prevent water crystallization in a confined geometry. The parameters of the NT model can be found in the Supplementary Material. Briefly, the hydrophobic (carbon) NT consists of CNP type particles,36, 42 forming a ring of 8 (or 16 for a wider NT). The small, medium and long NTs are comprised of 8, 14 and 22 rings, respectively. In NTs with smaller diameter, the caps consist of a ring of four particles plus a particle at the tip. In wider NTs, eight and four particles constitute the two cap rings. Uniformly functionalized NT groups are represented by particles of intermediate polarity (SNda type in MARTINI). Capfunctionalized NTs contain SNda particles either in the caps (partial coating) or in the caps and terminal rings (complete coating). An individual Nda bead type in MARTINI is used to represent 1-butanol. Therefore, we can argue that replacement of the CNP bead type with SNda corresponds to hydroxylation with approximately 1:3 OH:C ratio. Neighboring particles in the ring and between proximal rings are connected by harmonic bonds with an equilibrium length of 0.47 nm with a force constant of 5000 kJ mol-1 nm-2. Longer bonds with the same force constant and length n*0.404, where n is the number of rings, are applied between distal rings to increase NT rigidity. Bond angles are described by a cosine based angle potential with a force constant of 350 kJ mol-1 and an equilibrium angle of 135 degrees in the rings (157 degrees in the wider NT), and 90 and 180 degrees between the rings. The geometry of the caps is maintained with improper dihedrals with a force constant of 350 kJ mol-1 rad-2. A wider NT was modeled by an elastic network with a force constant 20,000 kJ mol-1 nm-2 and a cutoff of 1 nm, Due to the coarse-grained nature of the model, NT chirality is not represented. Simulation details. Simulations were performed with the Gromacs software package, version 4.43 The smaller systems consisted of 648 DOPC lipids, 27419 water particles, and 1400 antifreeze water particles, to which a NT was added. Simulations of the larger bilayer included 4608 lipids, solvated with 110000 water particles. In all setups, the simulation temperature was kept constant at 310 K using the Berendsen (weak coupling) algorithm,44 with a time constant of 1 ps. Lipids, water and NT were coupled separately. The pressure was kept at 1 bar using the Berendsen algorithm, with a time constant of 4 ps and a semi-isotropic coupling scheme. For non-bonded interactions, the standard cutoffs for the MARTINI force field were used: the Lennard-Jones interactions were shifted to zero between 0.9 and 1.2 nm, the Coulomb potential was shifted to zero between 0 and 1.2 nm. The relative dielectric constant was 15, which is the default for this force field. A time step of 20 fs was used; the neighbor list was updated every 10 steps. Unbiased simulations were 2 µs long for the systems with a single NT, and 10 µs long for aggregates. Four independent simulations for each system were performed, with different starting configurations. In two of them, the NT or its aggregate was placed in water. In two others, a single NT was placed in the bilayer oriented either parallel or perpendicular to the bilayer normal. The bilayer perturbation and NT orientation were characterized for the last 200 ns of one of the trajectories. The NT aggregates were initially placed in the bilayer by pulling them into the bilayer center by applying a harmonic restraint.


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The umbrella sampling (US) method45 was used to calculate PMFs for transfer of the NTs from water to the bilayer center. Due to limited sampling of NT rotations on the accessible simulation time scale, even within 2-10 µs, we fixed the NT orientation to discrete values, corresponding to angles of 0, 45, and 90 degrees between the NT long axis and the bilayer normal. To achieve this, an angle restraint defined between the terminal particles of the tips and z-axis with a force constant of 1000 kJ mol-1 deg-2 was included in the [ angle_restraints_z ] section of the NT topology. All US simulations were 300 ns long, of which the initial 100 ns were discarded as equilibration. Umbrella potentials with a force constant of 1000 kJ mol-1 nm-2 were applied to the NT center of mass (COM) and distributed with 0.1 nm spacing along the bilayer normal. Lipids near the NT were used as a reference group to determine the umbrella position. To dynamically select this bilayer patch close to the NT, we identified lipids within a cylinder with a radius of 1.5 nm. Lipids particles between 1.5 and 2.0 nm were counted in a weighted manner, with a weight starting at 1 at 1.5 nm and going to 0 at 2.0 nm. This pulling geometry minimized bilayer bending. Other tested setups included different cylinder radii, the whole bilayer as a reference group for pulling, or two biasing potentials applied to the NT tips at different distances from the bilayer such that the NT orientation is set to 0, 45 and 90 degrees. In the last two these setups, strong bilayer bending was observed. Bilayer bending was driven by the proximity of the NT to the bilayer surface imposed by a restraining potential, and was the strongest for the orientation parallel to the bilayer plane. Bilayer bending led to a significant underestimate of the calculated free energy of the NT transfer from water to the bilayer. In all US calculations, positional restraints were unbiased using the weighted histogram analysis method (WHAM).46 Orientational restraints in the US calculations were unbiased using the thermodynamic cycle 1 (Figure 7a), see below. The thermodynamic integration (TI) method47 was employed (a) to unbias orientational restraints (cycle 1, Figure 7a) and (b) to calculate the free energy of converting a NT into a dummy particle in the bilayer and in solution, used in thermodynamic cycle 2 (Figure 7b). Dummy particles have the same bonded interactions as regular particles, but their non-bonded interactions are set to zero. A soft-core potential with a=1.3 and s=0.47 was used for nonbonded interactions to avoid singularities as the NT particles were turned into dummies.48 In case (b), 2 independent simulations were performed for each system. Both in case (a) and (b), the free energy contribution is calculated as the integral of the average Hamiltonian derivative, ∆ G =

∫

1

0

∂H / ∂λ d λ . We used a series of simulations in which the intervals between

the parameter λ varied based on an initial estimate of the slope of the ∂ H / ∂ λ curve. For each λ value, the production run was 500 ns long. For unbiasing angle restraints, the first 500 ns of trajectory were used for initial equilibration. Unbiasing orientational restraints included in the NT topology was performed by changing the force constant of the angle restraints from 1000 kJ mol-1 deg-2 (in state A) to zero (in state B).

Free energies of transfer of NTs from water to bilayer, ∆ G BNT→ W , can be calculated using the thermodynamic cycle 1 (Figure 3a): B B→ W W ∆GBNT→ W = ∆GNT →NT + AR + ∆GNT + AR (PMF) + ∆GNT + AR →NT

(1)

or the thermodynamic cycle 2 (Figure 3b): B W ∆GBNT→ W = ∆GNT →D (TI) − ∆GNT →D (TI)


(2)


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where AR stands for angle restraints, D for dummy, B for bilayer, W for water. To estimate the enthalpic ( ∆H ) and entropic ( −T∆S ) contributions for decoupling the NT interactions with the bilayer and oil, ∆GBNT,O→D (TI) , in the TI calculations in the equation above, we used the following formula:

∆GBNT,O→D (TI) = ∆H − T∆S

(3)

The enthalpic contribution is calculated directly from the total energy, the free energy from either umbrella sampling or thermodynamic integration, and the entropy from these other two quantities.

Results and Discussion Equilibrium simulations of individual carbon nanotubes We first investigated the partitioning of the NTs monomers of different polarity and length into the DOPC bilayer. The results are summarized in Table 3. Hydrophobic NTs (Figure 2a) entered lipid bilayer spontaneously from water. For the three considered NT lengths (see Methods), penetration occurred between 100 and 200 ns in one of the two independent simulations. Penetration started with adsorption of a tip in the headgroup region in all three systems, followed by NT translocation into the membrane, during which the tip moved to the distal leaflet, and the NT adopted a tilted orientation spanning the bilayer. This is consistent with both experimental49 and computational results30, 49. Subsequently, the NT reoriented parallel to the bilayer plane and positioned in the hydrocarbon chain region in the center of the bilayer. Reorientation time decreased from 500 ns to 50 ns and 30 ns with increasing the NT length from small to medium and long. For a wider NT, spontaneous bilayer penetration was not observed. In additional simulations, the NTs were placed in the bilayer center in parallel or perpendicular orientations to the bilayer plane. In all cases, the NTs adopted a parallel orientation in the bilayer center (see Figure 3a-d). Uniformly functionalized NTs (Figure 2b) adsorbed readily on the bilayer surface in the headgroup region, and oriented parallel to the bilayer plane. Adsorption started from one of the tips in contact with the bilayer, and occurred between 100 and 200 ns. Adsorption completed with NTs assuming an orientation parallel to the bilayer plane (Figure 3e), which occurred in tens of nanoseconds (20 ns in one case, 68 ns in the second case). Differences in the reorientation time originated from different NT tilts upon tip adsorption, but this will be a stochastic process with a large range of time scales. When placed in the bilayer center oriented parallel to the bilayer plane, the NT moved to the headgroup region and remained parallel. When placed perpendicular to the bilayer plane, the NT reoriented to assume a tilted orientation with its COM remaining in the bilayer center (Figure 3f). Both this result and the previous result on the pristine NTs show that equilibrium simulations rapidly become problematic as reorientation of large NTs or strongly functionalized NTs is a slow process on time scales of MD simulations. Carbon NTs with functionalized caps (Figure 2c) spontaneously entered the bilayer in one of the two simulations in a manner similar to carbon NTs. Unlike the hydrophobic NTs, the capfunctionalized ones remained tilted with their COM in the bilayer center (Figure 3g). When placed in the bilayer center in either a parallel or a perpendicular orientation, the NTs became tilted with the functionalized caps positioned in the headgroup regions of opposite leaflets. 6 ACS Paragon Plus Environment

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Increasing the polarity of the caps did not lead to noticeable differences (results not shown). However, expanding functionalized groups to the rings proximal to the caps (terminal rings; Figure 2d) resulted in a somewhat different behavior. The NTs adsorbed to the bilayer surface and assumed a parallel orientation similar to the functionalized NTs (Figure 3h). Here, the time required to assume a parallel orientation was much shorter, ca. 6 ns, and the NTs moved deeper into bilayer into the glycerol-ester region. When placed in the bilayer center, both parallel and perpendicular oriented NTs became tilted (Figure 3i), with a smaller tilt angle compared to NTs with functionalized caps only. The NT tilt angle with respect to bilayer normal decreases with decreasing its hydrophobic length (increasing the number of functionalized groups). The tilt angle is affected by polar/apolar interactions on one hand, and degree of bilayer perturbation on the other hand. Thus the behavior of these NTs can be tuned to obtain a range of desired outcomes. Density profiles for the NT in lipid bilayer are shown in Figure 4. Double peaks in the NT profiles result from the concentration of particles on the NT surface. For functionalized NT and carbon NT with functionalized caps and terminal rings, there are two preferred positions: on the bilayer surface in a parallel orientation and in the bilayer center in a tilted orientation. To characterize the energies associated with these positions we calculated the PMFs for NT transfer from water to bilayer at different tilt angles (see below). Bilayer perturbation induced by monomeric NTs is shown in Figure 5. Hydrophobic NTs induced local bilayer thickening, which decayed with increasing distance from the NT in an approximately exponential fashion. A similar perturbation has been predicted for integral membrane proteins.50 The thickening increases slightly with increasing the NT length and significantly with increasing the NT diameter (see Figure 4). For the NT with functionalized caps, a tilted orientation also induced local bilayer thickening, resulting from hydrophobic mismatch. In contrast, fully functionalized NTs in tilted orientation in the bilayer center induced local bilayer thinning. Bilayer thinning is likely caused by unfavorable contacts of the bilayer hydrophobic core with the functionalized NT walls. Adsorption of the hydrophobic NT with functionalized caps and terminal rings and of the functionalized NT leads to local bilayer bending. Bilayer bending deformation is larger in the case of fully functionalized NTs (see Figure 3).

Distribution of individual NTs from free energy calculations Using the umbrella sampling method, we calculated PMFs for NT transfer from water to the bilayer center for fixed orientations. Results for various NT types at tilt angles of 0, 45 and 90 degrees with respect to the bilayer normal are shown in Figure 6. The free energy profile for a pure carbon NT (Figure 6a) has a minimum in the bilayer center for all three orientations tested here, with the lowest free energy at 90 degrees (with respect to the bilayer normal). This is in agreement with unbiased simulations, in which the NT partitioned into the bilayer center and oriented parallel to the bilayer plane. The parallel orientation is expected to be more favorable as it provides burying of the hydrophobic NT in the apolar environment. The free energy difference between water and the bilayer center equals 428 kJ/mol. Insertion in the membrane in the perpendicular orientation involves a free energy gain of 369 kJ/mol. While these energies are higher than reported in previous works (e.g by Pogodin and Baulin for a hydrophobic NT31), their magnitudes are expected given the large size of the NT (compared e.g. to a fullerene with a free energy gain of 110 kJ/mol36). The energy barrier for entering bilayer is the highest for parallel (90 deg) and the lowest for the tilted (45 deg) orientation, and equals 14 and 5 kJ/mol, respectively. In the unbiased simulations, NT entered the bilayer in the tilted orientation. The energy barrier is located at the headgroup/water boundary and appears to



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originate from the perturbation of the densely packed polar headgroup region by a hydrophobic NT. Barriers of a few kT can account for the mixed results of the equilibrium simulations as these are not easy to sample, but provide no practical barrier on physiological time scales. Increasing the length of the carbon NT does not change the energy difference between the bilayer and water for the normal orientation (0 deg), but significantly increases it (720 kJ/mol) for the parallel orientation (Figure 6b), as expected, due to a larger buried hydrophobic surface. Decreasing the NT length has the opposite effect (Figure 6c). In all three cases, the initial part of the PMF as the NT approaches the membrane is least favorable for a parallel orientation relative to the membrane surface, consistent with a preferred tilted insertion also found in the equilibrium simulations above, experimental measurements, and computational studies that allowed this degree of freedom.30, 49 Less hydrophobic, uniformly functionalized NTs show a qualitatively different behavior (Figure 6d). The free energy minimum is reached when the NT is parallel to the bilayer plane (90 degrees tilt) and lies in the lipid headgroup region. This position provides the optimal orientation of the NT of the given polarity (see Methods) with the densely packed hydrophilic headgroup region. The energy difference between water and bilayer is 60 kJ/mol, significantly lower than for the hydrophobic NT. Other orientations also have a shallow minimum as the NT tip enters the headgroup and glycerol-ester region. Further translocation into the hydrophobic bilayer interior is unfavorable and the energy increases. In the bilayer center, there is a local shallow minimum in the free energy profile. This position corresponds to a metastable state, as confirmed by unbiased simulations. As also follows from unbiased simulations, the preferred tilt angle is ca. 12 deg (see Table 3). The energy difference between water and the bilayer center is ~ - 87 kJ/mol. Due to an almost flat energy landscape in the bilayer center, the NT position and orientation fluctuate around this metastable state (increased standard deviation in Table 3). The NT is, however, trapped in this state (on the simulation time scale) due to the presence of local energy maxima. The free energy profile for the carbon NT with functionalized caps has a minimum in the bilayer center (Figure 6e). In contrast with what we observed for the pristine NT, the most favorable orientation for this NT is tilted. As follows from unbiased simulations, the equilibrium tilt angle is ca. 50 deg. The energy difference between water and the bilayer center is 407 kJ/mol (at 45 deg); smaller than that of the hydrophobic NT, likely resulting from its tilt and associated bilayer perturbations. The energy barrier for bilayer penetration in the tilted orientation is 3 kJ/mol, slightly lower that that for the hydrophobic NT. Carbon NTs with functionalized caps and terminal rings (Figure 6f) present a behavior somewhat intermediate between the hydrophobic and functionalized NTs. In orientation parallel to the interface, the free energy minimum corresponds to the NT on the bilayer surface. Compared to the functionalized NT, the location of the minimum is shifted towards the bilayer center, in the glycerol-ester region, due to a large fraction of hydrophobic groups. The free energy difference for this minimum is 203 kJ/mol. This metastable state is also observed in the unbiased simulations. The equilibrium state is in the bilayer center, with a tilt angle of ca. 36 deg relative to the bilayer normal. The free energy difference between water and the bilayer is 400 kJ/mol. No barrier for entering the bilayer at the tilt of 0 and 45 deg is present. The normal orientation has a local minimum corresponding to burying the functionalized tip into the headgroup region.


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The calculated PMFs provide information on the location of the free energy minima along the bilayer depth for a particular NT type. Yet they do not represent the total energy of NT transfer from the bilayer center to water, due to the presence of orientational restraints. To unbias the restraints, we consider the thermodynamic cycle 1, represented in Figure 7a. In the first step of the cycle, we fix the orientation of the NT by applying angular restraints to the NT in the membrane interior (see Methods). The PMFs calculated with the US technique and restraints presented above constitute the second step of the cycle. In the last step, we remove the restraints to the NT in bulk water. For carbon NT of medium length, the free energy of transfer at 0 deg tilt is 369 kJ/mol. Applying angular restrains to maintain this orientation has a free energy cost of 145 kJ/mol in the center of the bilayer, and 25 kJ/mol in water. Using formula (1), the resulting free energy cost of transferring the NT from bilayer center to water is 489 kJ/mol. As an additional control, we calculated the energy of transfer using thermodynamic cycle 2 (Figure 7b). Here, we start with the NT in the center of the membrane and decouple its interactions with the environment (i.e., the lipid membrane); we then re-couple the interactions of the NT with water. The calculated values are 709 and -190 kJ/mol, respectively. Using formula (2) in Methods, the total energy of transfer is 519 kJ/mol. This value is somewhat higher than the result of the thermodynamic cycle 1 using umbrella sampling. The difference in the free energies of NT transfer from bilayer to water calculated using the two cycles can be used as an error estimate as these are as independent as is feasible. It includes contributions from both statistical and systematic errors, in as far as they are different for the two cycles, for the simulation setups in this work. NT rotations in particular around the bilayer normal in both the TI and PMF calculations are undersampled on the simulations time scales. We estimate the contribution of the incomplete sampling of NT rotations using eq. 9 from ref. 51 to be of order of several kJ/mol. Upon unbiasing angular restraints, NT reorientation occurs on a time scale of hundreds of nanoseconds; it is difficult to assess errors of these calculations without performing much more extensive simulations. The proximity of the hydrophobic NT restrained by a harmonic potential in the PMF calculations leads to bilayer bending. Bilayer perturbation is the strongest for the parallel (90 deg) NT orientation, leading to even lower total free energy of transfer of 421 kJ/mol. Applying lateral tension to the bilayer indeed reduced bilayer bending and increases the energy difference between water and bilayer center calculated with the US method (results not shown). While we were able to minimize the effect of bilayer bending (by using a specific geometry in the US calculations, see Methods), due to the relatively large size of the hydrophobic nanotube it was not possible to prevent it completely. However, the PMFs provide qualitative information on the location of the equilibrium and metastable positions, as well as on NT orientations. As an additional control and to gain insight in the molecular basis of the free energies calculated for the bilayer system, we also calculated the free energy of transfer of a hydrophobic NT of medium length from bulk hexadecane to water using two different thermodynamic cycles: cycle 1, based on umbrella sampling, and cycle 2, based on thermodynamic integration (see Figure 7c,d). The free energy of transfer obtained using thermodynamic cycle 2 (Figure 7d) is 681 kJ/mol. The calculated PMF at 0 deg NT tilt with respect to the normal to the oil-water interface gives the energy gain of 651 kJ/mol. Applying angular restrains to maintain 0 deg NT orientation in oil has a free energy cost of 32 kJ/mol. Combined with the cost of applying orientation restraints in water (25 kJ/mol, see above), the total energy of NT transfer from oil to water using the thermodynamic cycle 1 (Figure 7c) is 658 kJ/mol. Similar to the membrane-water transfer, the value obtained in the thermodynamic cycle 1 is smaller than that in cycle 2 for the oil-water transfer. In the PMF calculations, the NT proximity to the oil phase causes perturbations of the



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oil-water interface, similar to bilayer bending, which likely leads to an underestimated free energy of transfer. Based on the results for the two systems, the NT partitioning to oil is more favorable than partitioning into the membrane, although the properties of the membrane hydrophobic interior are similar to oil. To understand the origin of this difference, we calculated the enthalpic and entropic contributions for decoupling the NT interactions with the bilayer and the oil, see formula (3) in Methods. Removing the NT from the bilayer and oil has a favorable entropic contribution of -249 and -195 kJ/mol, respectively. This is likely a result of the ordering of alkane chains due to the interactions with the NT. The enthalpic contribution for removing the NT is more unfavorable in oil (1074 kJ/mol) than in the bilayer (958 kJ/mol). This is mainly because NT solvation causes a stronger decrease of the Lennard-Jones lipid-lipid interactions (~900 kJ/mol) compared to the Lennard-Jones oil-oil interactions (~750 kJ/mol). The latter can be explained by the difference between the isotropic, disordered nature of the oil phase and the lamellar, ordered nature of the lipid bilayer: hexadecane chains can reorient freely and optimize dispersion interactions, while lipid chain reorientation is restricted and results in sub-optimal dispersion interactions in the presence of the nanotube.

Nanotube aggregates To study the effect of NT aggregates on lipid bilayers, we simulated systems containing 4 and 16 NTs of different types, selected based on the partitioning of the monomeric NTs described above (see Table 2). Carbon NTs placed separately in water aggregated in ~100 ns in two independent simulations. In the aggregate of 4, the NTs were parallel to each other and aligned (Figure 1b). In one case, the aggregate remained in water throughout the simulation (10 µs). In the second case, the aggregate entered the lipid bilayer in ~ 6 µs in a tilted orientation, moved to the bilayer center, and then adopted a parallel orientation (Figure 8a). This partitioning induced moderate distortion of the bilayer, which manifested as a local increase of bilayer thickness as its leaflets wrapped around the hydrophobic NT walls. A larger preformed aggregate of 16 parallel and aligned NTs (Figure 1c) did not enter the lipid bilayer. When placed in the bilayer center, the aggregate adopted a tilted orientation inducing significant perturbation of the bilayer, but did not cause bilayer rupture. In both cases, one NT detached from the aggregate on the simulation time scale. Although we do not have free energies to compare, this behavior is qualitatively similar to what we predicted for fullerene, which aggregates in solution but dissolves into individual molecules and small aggregates (dimers, trimers) inside the membrane.36 NTs with functionalized caps formed a parallel-aligned aggregate in water in one case. In the second case the center of mass of one NT was shifted with respect to the rest. This latter aggregate partitioned into the bilayer and assumed a tilted orientation (Figure 8c). When the aligned aggregate was placed in the bilayer center, it adopted a tilted orientation and started disaggregating on the simulation time scale. NTs with functionalized caps and terminal rings aggregated only partially in water as monomers rapidly (~ 100 ns) adsorbed to the bilayer surface. During simulations, all NTs and aggregates partitioned to the bilayer, either to one or both leaflets. NTs in one leaflet aggregated on the bilayer surface, and induced significant perturbation of the proximal leaflet (Figure 8d), which wrapped around the hydrophobic part of the aggregate. In contrast, when the aggregate was placed in the bilayer interior in the starting configuration, it adopted a tilted orientation with its center of mass positioned in the bilayer center.


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Larger pre-formed aggregates of NTs with functionalized caps (and terminal rings) adsorbed onto the bilayer surface on the simulation time scale. Adsorption occurred somewhat faster ( ~ 1µs) for the NTs with functionalized caps and terminal rings. Lipids from the proximal leaflet then wrapped the hydrophobic sides of the aggregate, which was accompanied by noticeable bending of the distal leaflet and thus strong perturbation of the whole bilayer (Figure 8e,f). We then performed simulations of larger aggregate of NTs with functionalized caps and terminal rings using a larger lipid bilayer (see Table 3). As the aggregate diffused to a close proximity to the bilayer, the bilayer bent towards it and wrapped the aggregate in the manner similar to a smaller bilayer setup.

Conclusions We have calculated free energies for transfer for a range of NTs to a model biological membrane. Free energy methods are essential as barriers of several kT make direct sampling difficult to achieve, and the presence of several local energy minima leads to metastable states. Small CNTs enter the membrane spontaneously and partition to the center in the parallel orientation; the energy gain increases with the NT length. This configuration is not expected to be favorable for longer CNTs comparable to the cell size, which would lead to perturbations of the membrane (and cell) structure. Functionalized NTs can be designed to have quite different partitioning behavior and preferred orientations for specific applications. Fully functionalized (with hydrophilic groups) NTs can be tuned to adsorb to a membrane with a low probability of insertion and transfer across the membrane. CNT bundles form in solution but their interactions with the bilayer are slow to sample. Simulations suggest smaller aggregates may dissolve inside the membrane. Lipids wrap around the hydrophobic parts of the bundle, and the distortion of the membrane leaflets increases with the aggregate size.

Acknowledgements This work was supported by the Natural Sciences and Engineering Research Council (Canada). DPT is an Alberta Innovates Health Solutions Scientist and Alberta Innovates Technology Futures Strategic Chair in (Bio)Molecular Simulation. Calculations were carried out on Compute Canada/WestGrid facilities.



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Table 1 Summary of unbiased simulations of single NTs. α, deg n 0 2 90 1 0 1 carbon short C1 w 0 2 b 90 1 0 1 carbon long C2 w 0 2 b 90 1 0 1 functionalized medium CF w 0 2 caps b 90 1 0 1 functionalized medium CR w 0 2 caps and terminal b 90 1 rings 0 1 functionalized medium F w 0 2 b 90 1 0 1 carbon wide, C3 w 0 2 medium b 90 1 0 1 Here z is initial NT position, α is NT initial orientation with respect to bilayer normal, n is number of independent simulations; w stands for water, b – bilayer center; *see Methods for details. NT type carbon

NT size* medium

notation z C w b

Table 2 Summary of unbiased simulations of NT aggregates. NT type C

# of NTs 4

# of z lipids 648 w b 16 w b CF 4 w b 16 w b CR 4 w b 16 w b 4608 w Notations are as in Table 1.

n 2 2 2 2 2 2 2 2 2 2 2 2 2



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Table 3 Properties of nanotubes inserted into a lipid bilayer. D, 10-7 t0, ns cm2/s C 0.0±0.1 87±4 2.5 620 C1 0.0±0.1 85±6 6.5 95 C2 0.0±0.1 88±3 1.1 1000 CF 0.0±0.1 50±5 3.8 170 CR 0.0±0.2 36±5 4 120 1.7±0.2* 85±6 3.8 540 F 2.7±0.2 86±5 3 310 0.0±0.4* 12±6 3.5 10 C3 0.0±0.1 87±3 3.3 Here z0 is position with respect to bilayer center, α0 - orientation with respect to bilayer normal, D –diffusion coefficient of NTs in the bilayer plane; t0 is in-plane rotational autocorrelation time calculated using a single exponential fit, other notations are as in Table 1. *Metastable position. NT type

z0, nm

α0, deg


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Figure captions Figure 1. System setup: a lipid bilayer in water with (a) a single NT; (b) an aggregate of 4 NTs; (c) an aggregate of 16 NTs. NTs are shown in silver, water in light blue, the polar moiety of lipids in green, the apolar tails in orange, the unsaturated bonds in the hydrocarbon chains in white. Figure 2. An overview of the different NTs in this study and notations used: (a) carbon (C), (b) functionalized (F), (c) carbon with functionalized caps (CF), (d) carbon with functionalized caps and terminal rings (CR), (e) small (C1), (f) long (C2), and (g) wide (C3) carbon NTs. Hydrophobic (carbon) groups are colored in silver, functionalized groups in yellow. Figure 3. NTs inserted into a lipid bilayer: equilibrium and metastable positions and orientations: (a) C; (b) C1; (c) C2; (d) C3; F in stable (e) and metastable (f) positions; CF (g), CR in stable (h) and metastable (i) positions. Symbols are as in Figure 2. Color scheme as in Figures 1,2; lipids are shown transparent, water not shown. Figure 4. Density profiles for different NTs in a lipid bilayer in equilibrium position: (a) C; (b) C1; (c) C2 ; (d) F; (e) CF; (f) CR. Profiles correspond to parallel orientation of the nanotube with respect to the bilayer plane, except for (e) showing tilted orientation. NT symbols are as in Figure 2; other symbols: NT – nanotube, W – water, HG – lipid headgroups, G – lipid glycerolester moiety, T – lipid tails. Figure 5 Perturbation of bilayer thickness induced by different NTs: (a) C, C1, and C2; (b) CF and CR in different orientations; (c) F in parallel and tilted orientation (dashed and dash-dotted lines, respectively). Perturbation is characterized by the displacement of the phosphate groups along the bilayer normal with respect to an unperturbed position as a function of distance from the NT. Figure 6. Potential of mean force (PMF) at a fixed NT orientation with respect to bilayer normal (of 0, 45 and 90 deg) for NTs of varying length and hydrophobicity: (a) C, (b) C1 and (c) C2; (d) F, (e) CF, and (f) CR. Symbols are as in Figure 2. Figure 7. A schematic view of the two thermodynamic cycles used for the calculation of the free energy of transfer of the nanotube from bilayer to water, and from oil to water. Abbreviations are as follows: B- bilayer, W- water, O – oil, AR – angular restraints; bilayer polar groups are shown in green, apolar in orange, oil in orange, NT in purple, NT dummy in white, water in blue. .Figure 8. Perturbation of lipid bilayer induced by NT aggregates (a) 4 and (b) 16 NTs type C; (c) aggregate of 4 NTs of type CF; and (d) CR; aggregates of 16 CR NTs, front (e) and side (f) views. Color scheme is as in Figure 4, symbols are as in Figure 2.



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Figures Figure 1.

Figure 2.


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Figure 3.



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Figure 5.


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Interaction of Pristine and Functionalized Carbon Nanotubes with

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