Translocation of Bioactive Molecules through Carbon Nanotubes

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Translocation of Bioactive Molecules through Carbon Nanotubes Embedded in Lipid Membrane Anil K. Sahoo, Subbarao Kanchi, Taraknath Mandal, Chandan Dasgupta, and Prabal K. Maiti ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b18498 • Publication Date (Web): 26 Jan 2018 Downloaded from http://pubs.acs.org on January 27, 2018

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ACS Applied Materials & Interfaces

Translocation of Bioactive Molecules through Carbon Nanotubes Embedded in Lipid Membrane Anil Kumar Sahoo*, Subbarao Kanchi, Taraknath Mandal, Chandan Dasgupta and Prabal K. Maiti* Center for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India

ABSTRACT: One of the major challenges of nanomedicine and gene therapy is the effective translocation of drugs and genes across cell membranes. In this study, we describe a systematic procedure that could be useful for efficient drug and gene delivery into the cell. Using fully atomistic molecular dynamics (MD) simulations, we show that molecules of various shape, size and chemistry can be spontaneously encapsulated in a single-walled carbon nanotube (SWCNT) embedded in a 1palmitoyl-2-oleoylphosphatidylcholine (POPC) lipid bilayer, as we have exemplified with dendrimers, asiRNA, ssDNA and ubiquitin protein. We compute the free energy gain by the molecules upon their entry inside the SWCNT channel to quantify the stability of these molecules inside the channel as well as to understand the spontaneity of the process. The free energy profiles suggest that all the molecules can enter the channel without facing any energy barrier but experience a strong energy barrier (≫ ) to translocate across the channel. We propose a theoretical model for the estimation of encapsulation and translocation time of the molecules. While the model predicts the encapsulation times to be of the order of few nanoseconds, which match reasonably well with those obtained from the simulations, it predicts the translocation time to be astronomically large for each molecule considered in this study. This eliminates the possibility of passive diffusion of the molecules through the CNTnanopore spanning across the membrane. To counter this, we put forward a mechanical method of ejecting the encapsulated molecules by pushing them with other free-floating SWCNTs of diameter smaller than the pore diameter. The feasibility of the proposed method is also demonstrated by performing MD simulations. The generic strategy described here should work for other molecules as well and hence could be potentially useful for drug and gene delivery applications.

KEYWORDS: lipid bilayer, carbon nanotubes, diffusion, nanopores, encapsulation, dendrimers

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INTRODUCTION: The fate of the small interfering RNA (siRNA) therapeutics and the practice of nanomedicine depend on efficient delivery of single molecule drugs and biomolecules such as, siRNA, DNA and proteins into living cells to regulate their biological functions. Generally, due to large free energy cost for rupture, these macromolecules cannot directly pass through the cell membrane without any “active” process. So, the development of novel techniques for introducing bioactive molecules inside the living cells is an active area of research1,2, and has broad implications in nanobiotechnology research. Recently there has been progress in delivering nucleic acids intracellularly.3,4,5 Several studies have demonstrated that carbon nanotubes (CNTs) hold a great promise for effective delivery of biomolecules into cells6,7,8 and as a cellular endoscope.9 CNTs have been used in biomedical applications (for treatment of diseases and optical detection of molecules) owing to their unique thermal, electrical and spectroscopic properties.10 Due to their large outer surface, CNTs have been exploited as nanovectors for efficient delivery of drugs and biomolecules by covalent or non-covalent attachment of biomolecules to its outer surface.11,12 There are reports that the interactions between carbon-based materials and biomolecules can lead to conformational changes of the biomolecules, which in turn can affect their biological functions.13,14

CNTs can be made biocompatible by chemical functionalization and functionalized CNTs can be biodegraded15, which further vindicate the use of CNTs as biomaterials.16 Besides, due to the free volume available inside CNTs, they can host guest molecules as well. There are reports of spontaneous encapsulation of biomolecules such as, siRNA,17 DNA,18,19,20 proteins21 and drugs22 into CNTs. There are also studies on encapsulation of linear polymers into CNTs and wrapping of linear polymers at the outer surface of CNTs.23 However, for star polymers and dendrimers, most investigations have concentrated on surface wrapping24,25 without paying much attention to the competitive phenomenon of encapsulation. Functionalized CNTs have been found to puncture cell membranes.26,27,28 Simulation studies have revealed that CNTs with a length comparable to the thickness of a lipid bilayer can spontaneously enter into the bilayer.29 It has been shown that short CNTs inserted into membranes can be used as biosensors.30 A recent experimental study has shown that short CNTs can spontaneously insert into live cell membranes and lipid bilayers to form channels, which can transport water, ions, protons and DNAs stochastically.31 There are many studies that focus on the unloading of drugs and biomolecules from CNTs.22 A recent study has investigated the ejection of molecules out of CNTs with the help of fullerenes and nanowires.32 Moreover, simulations show that a CNT can self-insert into another CNT of larger diameter to form a multiwalled carbon nanotube.33

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In this study, we propose a scheme for efficient nano-delivery across cell membranes. We use fully atomistic MD simulations along with free energy calculations to show the spontaneous uptake of various molecules, such as protein, ssDNA, asiRNA, PAMAM and PETIM dendrimers (see Figure S1 in the supporting information (SI)), into SWCNTs embedded in a POPC lipid bilayer. We also investigate the structural or conformational changes of these confined biomolecules inside the nanopore as the changes induced by the CNT-biomolecules interactions can affect their biological functions. The diffusion coefficients of the encapsulated molecules are computed and compared with their free diffusion coefficients in bulk water. We propose a model for theoretical estimation of the spontaneous encapsulation time and the translocation time of the molecules by passive diffusion across the nanopore. Both simulation results and the theoretical model suggest that the encapsulation times of the molecules are in the order of few nanoseconds whereas the theoretical model predicts the translocation time to be astronomically large. We finally describe a mechanical method, which involves spontaneous translocation of a smaller diameter CNT into the pore that pushes the encapsulated molecule out of the pore. The ejection time of the molecules by this mechanical method is much shorter.

RESULTS AND DISCUSSION: Structure of the CNT Channel Embedded in the Lipid Bilayer Membrane: We first demonstrate the equilibrium structure of a CNT channel embedded in a model POPC membrane. We refer the reader to the METHODS section for the details of the channel construction protocol. To investigate the stability of a CNT channel, we consider SWCNTs of various lengths. The initial structure of the channel is constructed in a way such that the channel axis remains perpendicular to the membrane plane as shown in Figures 1a, 1b and 1c. The final structures of the channels after 100 ns long unrestrained MD simulations are also presented in Figures 1a, 1b and 1c. Our results suggest that the axis of the pore remains perpendicular to the membrane plane if the length of the SWCNT is comparable to the membrane thickness (~ 5 nm). In contrast, the longer CNTs are not able to maintain their perpendicular orientation to the bilayer plane and tilt towards the membrane plane as shown in Figure 1c. This is so because the hydrophobic CNT surface strongly interacts with the hydrophobic lipid tails. As a result, the CNT tilts toward the membrane plane and ultimately immerse itself to minimize the surface energy. The tilt angle (θz) of the CNT axis with respect to the normal to the bilayer plane as a function of simulation time is shown in Figure 1d. These observations are consistent with previous coarsegrained simulation results.29 Thus the length of the CNT is a crucial parameter for the current application which should be close to the membrane thickness. The thermodynamic stability of CNTs in lipid bilayer environment has also been discussed in detail with coarse-grained model.34 We calculate the lipid tail order parameter ( ), defined in equation 7 (see METHODS), to characterize the change in the lipid bilayer properties in the presence of stable trans-

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membrane CNT pores (see Figure 1e). There is more ordering of lipid tails close to (within 10 Å distance) the CNT walls, which can be attributed to the strong interactions between the lipid tails and the CNT surface. Spontaneous Encapsulation of the Molecules into the Nanopores: In this section, we discuss about the encapsulation process of the molecules into the CNT nanopore. We consider various biomolecules such as, asiRNA, ssDNA and ubiquitin protein, which have been used for biomedical applications. We also investigate the encapsulation process of few synthetic hyperbranched polymers such as, G2 PAMAM and G3 PETIM dendrimers, which also have been used as drugs, as well as drug carriers. We first demonstrate the encapsulation process of the dendrimers followed by that of other biomolecules as described below. The radius of gyration ( ), defined in equation 8 in the METHODS section, of the G2 PAMAM dendrimer is around 1 nm (see Table 1) and the hydrodynamic diameter is around 2.9 nm.35 Thus we select a (20,20) CNT having diameter of approximately 2.7 nm to construct the channel. The dendrimer is placed near one end of the channel as shown in Figure 3a at the beginning of the simulation. During the simulation, the dendrimer gradually enters the channel spontaneously. To confirm the robustness of the spontaneous encapsulation, we run three independent simulations with different initial positions of the dendrimer. In each case, the dendrimer enters the channel within ~5 ns of the simulations and remains inside the channel for the rest of the 100 ns long simulations. Figure 2a shows the distance (Zcom) between the center of the pore and the center of mass (COM) of the PAMAM dendrimer projected along the axis of the pore for three different simulation runs. The value of Zcom fluctuates around zero suggesting that the dendrimer remains stable near the center of the nanopore. In the encapsulation process, the dendrimer-nanopore van der Waals (VDW) interaction energy decreases (by ~200 kcal/mol), which is the driving force for the encapsulation process. Note that the dendrimer should face an entropic barrier because of its confinement inside the CNT channel. However, the gain in the VDW energy upon its entry inside the channel helps overcome the entropic loss due to the confinement, as we shall show later that the change in the total free energy is negative for the encapsulation process. We also calculate the number of contacts (Nc) of the dendrimer with the nanopore inner wall, which increases during the encapsulation process and saturates at ~120 as the dendrimer gets completely encapsulated. This indicates that the dendrimer has been adsorbed on the inner wall of the CNT, which should decrease its diffusivity significantly. Later, we shall show that the diffusion coefficient of the dendrimer indeed decreases inside the channel compared to the diffusion coefficient of a free– floating dendrimer. We next consider a G3 PETIM dendrimer, which is comparable in size but more hydrophobic than the G2 PAMAM36, to check the effect of hydrophobicity on the encapsulation process of

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the molecules. We consider the same (20,20) CNT nanopore. Like the PAMAM dendrimers, the PETIM dendrimers also spontaneously enter the nanopore (Figure 3b), but more rapidly than the PAMAM dendrimers as we observe from three independent simulations. Figure 2b (Zcom plot) shows that the PETIM dendrimer gets completely encapsulated within 3 ns in all three cases and then it stays inside the nanopore while remaining mobile. The gain in VDW energy in this case is ~300 kcal/mol, which is ~100 Kcal/mol higher than the PAMAM dendrimer case, suggesting that hydrophobic interaction favors the encapsulation process as reported in previous studies.10 The number of contacts (~220) between the PETIM and CNT is also more than that between the PAMAM and CNT, suggesting that the PETIM interacts with the CNT more strongly. We have also performed simulations of protonated G2 PAMAM and protonated G3 PETIM dendrimers (see Figure S2 in the SI and the discussions there) to study how the results are modified by changing the pH of the solvent. Although, both protonated PAMAM and PETIM dendrimers enter into the nanopore spontaneously, the encapsulation times are increased for both cases compared to their non-protonated counterpart. The ubiquitin protein, although being similar in size to G2 PAMAM and G3 PETIM dendrimers (see the Rg values in Table 1), cannot enter completely into a (20,20) CNT nanopore. Note that the diameter of a (20,20) CNT nanopore is bigger than the size (twice the Rg value) of the protein. However, we verify that both the G2 PAMAM and G3 PETIM dendrimers spontaneously enter the (16,16) CNT nanopore, whose diameter (~ 2.1 nm) is similar to the size of the dendrimers (see Figure S3 in the SI for details). The inability of ubiquitin to enter inside a (20,20) CNT channel is probably due to the structural rigidity of the protein in comparison to dendrimers. As described in a recent study of electric field driven transport of PAMAM dendrimers through an α-hemolysin pore35, the size of a molecule is not the only criterion for predicting its spontaneous encapsulation inside the CNT nanopore, the structural flexibility of molecules also plays an important role. So, we calculate the root mean square fluctuation (RMSF) values (see Table 1), defined in equation 9 in the METHODS section, to quantify the relative flexibility of the dendrimers and the ubiquitin protein. The RMSF values of both the PAMAM and PETIM dendrimers are two to three times larger than that of the ubiquitin. We believe that higher flexibility in the chemical structure helps the dendrimer to spontaneously enter the narrower nanotube channel, whereas the structurally rigid protein cannot enter the channel easily even when the diameter of the channel is larger than that of the protein. However, if the diameter of the CNT channel is large enough, ubiquitin can spontaneously enter the channel, as we have verified with a bigger (28,28) CNT of diameter 3.8 nm (Figure 3c). Ubiquitin enters the nanopore within 20 ns in each of the three-independent simulation runs, as reflected in the Zcom values shown in Figure 2c. As in the previous cases, ubiquitin stays inside the nanopore for the rest of the simulation time. The VDW energy gain and the numbers of contacts are 100 kcal/mol and 35, respectively which are much lower than that of the dendrimers. 5



We also investigate the encapsulation process of asiRNA and ssDNA into the CNT channel. As shown in Figures 2e and 3e, the ssDNA can spontaneously enter into the narrower pore ((16,16) CNT), embedded in the bilayer, which is consistent with previous studies of ssDNA encapsulation into pristine CNTs.18, 20 However, for the entry of asiRNA, an wider pore ((20,20) CNT) is required which is the critical diameter for siRNA translocation.17 This is due to the wider diameter of the double stranded asiRNA than the ssDNA diameter. In contrast to the other cases, ssDNA enters the nanopore in steps, as is clear from the Zcom plots for all three simulations (Figure 2e) and each step represents moving a variable number of bases of the ssDNA into the pore. The VDW energy gains due to the encapsulation are 300 Kcal/mol and 460 Kcal/mol for the ssDNA and asiRNA, respectively. Higher gain in the VDW energy of the asiRNA compared to the ssDNA is due to larger number of contacts of the former (~260) with the CNT than the later (~80). Further, we study the effect of ionic strength on the encapsulation process of both asiRNA and ssDNA, whose details are provided in the SI (see Figure S4 and the discussions there). As these molecules are charged, some effect might be expected due to screening of charges at higher salt concentrations. We find that the encapsulation time decreases upon increasing the salt concentration for both cases. To check the initial structure dependency on the simulation results, we have performed additional simulations for each of the above discussed cases taking initial structures that are very different in orientations as well as distances relative to the nanopore (see Figure S5 in the SI). The molecule spontaneously enters into the nanopore in every case. The kinetics of spontaneous insertion into the nanopore for one of the cases for asiRNA is shown in Movie S1. We find the relative orientations of the molecule with the nanopore do not affect the results qualitatively, which show robustness of the spontaneous encapsulation process. Structure of the Molecules inside the Nanopores and in Water: Studies of polymer conformations under confinement are important, especially for the biomolecules, for better understanding of their structure-function relationship. We have, therefore, characterized the structural changes due to confinement for all the molecules considered in this study. Structural properties of the molecule such as, size (radius of gyration Rg), shape (asphericity δ), aspect ratios (Iz/Ix, Iz/Iy) and conformational fluctuations (quantified by RMSF value) are calculated and the values are reported in Table 1. The methods to calculate these quantities are described in the METHODS section. The size (Rg) of the PAMAM dendrimer inside the pore remains almost the same as the size of the dendrimer in bulk water, whereas the size of the PETIM dendrimer increases inside the channel, indicating that the PETIM dendrimer interacts with the CNT wall more strongly than the PAMAM dendrimer. The equilibrated structures of PAMAM and PETIM inside the pore are shown in Figures 3a and 3b, respectively. As one can see from these figures, most of the

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residues of PETIM (compared to PAMAM) are adsorbed to the inner wall of the CNT nanopore. This can be seen more quantitatively in the number of contacts plots (Figures 2a and 2b) for the two cases. Note that the asphericity (δ) of the PAMAM dendrimer decreases inside the channel compared with its value in bulk solution, as the rough surface of the PAMAM dendrimer becomes more spherical due to the symmetry of the pore. However, the asphericity (δ) of the PETIM dendrimer does not decrease much as it is already more spherical in the bulk solution. The equilibrated structures of ubiquitin in bulk water and inside the pore are shown in Figure S1c in the SI and Figure 3c, respectively. Both the size (Rg) and shape (δ, Iz/Ix and Iz/Iy) of the protein remain almost similar in confinement and in the bulk, indicating that the protein does not interact strongly with the CNT wall which can also be seen in Figure 3c. The dihedral angle distribution (see Figure S6 in the SI) of the protein also remains similar for both cases. Also, we do not find any major change in the secondary structure of the protein confined inside the nanopore, compared to bulk water (see Table S1 in the SI). The equilibrated structures of asiRNA in bulk water and inside the pore are shown in Figure S1d in the SI and Figure 3d, respectively. From the figure for the confined case, only the two free terminal bases of the anti-sense strand (not hydrogen bonded to any base of the sense strand) stack on the inner surface of the CNT nanopore and other bases maintain the double helix structure. The equilibrated structures of ssDNA in bulk water and inside the nanopore are shown in Figure S1e in the SI and Figure 3e, respectively. As one can see from the figure, most of the bases stack to the inner wall of the pore when the ssDNA is inside the pore. The RMSF values of all the molecules decrease inside the nanotube as compared to their values in the bulk solution (see Table 1). Decrease in the RMSF suggests that the molecules are adsorbed on the inner wall of the CNT and/or they do not have much freedom to fluctuate due to the confinement. Both should affect the diffusion properties of the molecules, which we discuss in the next section. Estimation of Diffusion Coefficients of the Molecules inside the Nanopores and Comparison with their Bulk Values: The diffusion coefficient ( ) of a molecule freely moving in water can be calculated from the slope of mean square displacement (MSD) of its center of mass (COM) as a function of time and is given by the Einstein relation 〈| − 0| 〉 , 1 → 2

= lim

where and 0 are the positions of the COM of the molecule at times and zero respectively, (=3) is the dimensionality of the space, and the angular bracket represents 7



average over time origins. The fits of MSD versus for different cases are depicted in Figure S7 in the SI and corresponding values in water are reported in Table 2.

The above procedure is not suitable to measure the effective diffusion coefficient of a molecule inside the pore because the MSD along the pore axis as a function of time saturates at a finite value (see Figure S8 in the SI).37 Also as one can see from the Zcom values in Figure 2, the position of the molecule fluctuates around the center of the pore. Here the presence of the pore acts as a confining potential. So, we model the process as one-dimensional diffusion of the molecule in the presence of a potential "#. For analytical tractability, we take the confining

potential to be harmonic i.e. "# = %&' # , where % is the mass and &' is the frequency of $

oscillation of the trapped molecule. The expression for the MSD is given by38 〈∆# 〉 = 〈# 〉 − 〈#〉 =

1 − )*+,− 2&' ⁄- /, 2 %&'

where is the Boltzmann constant, is the absolute temperature and - is the friction coefficient. The above expression for the MSD has been fitted to the MSD data obtained from simulations (Figure S8 in the SI) to get the values of &' and -. Then, the diffusion coefficient is given by

=

. 3 %-

The diffusion coefficient thus obtained is given in Table 2. As one might expect, is smaller inside the pore than in bulk water, by factors ranging from ~1.5 to ~2.5 for different cases. Free Energy (FE) Profiles: We also compute the free energy profile of the individual molecule for better understanding of the encapsulation process. From the free energy profile, the free energy barriers for the encapsulation and translocation process can be estimated. The potential of mean force (PMF) is computed using the Umbrella Sampling technique where the distance between z-center of mass of the molecule and z-center of the nanopore is considered as the reaction coordinate (RC). The details of the calculation are given in the METHODS section. Since the pore diameter is the same across the bilayer, the PMF should be symmetric with respect to the center of the bilayer. Hence, we have computed the PMF for one side of the bilayer, starting from its center. The FE profiles for PAMAM and PETIM dendrimers along the RC are shown in Figures 4a and 4b, respectively. We note that there is no free energy barrier faced by the dendrimer as the molecule enters the channel suggesting that the dendrimers can spontaneously enter the CNT pore. However, a barrier of 164 and 185 Kcal/mol must be overcome for the complete translocation of a PAMAM and PETIM dendrimer, respectively. Thus, the nanopore behaves like

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a trap for the dendrimers. The presence of such a high energy barrier (≫ ) suggests that the spontaneous translocation of the dendrimers across the channel is unlikely. Note that the free energy gain (-185 Kcal/mol) upon the entry of a PETIM dendrimer is -21 Kcal/mol higher than that for the PAMAM dendrimer, which could be due to the more hydrophobic nature of the PETIM dendrimer than the PAMAM dendrimer.24 Thus the driving force for the encapsulation process into a hydrophobic channel is higher for the PETIM dendrimer, which is also reflected in the faster encapsulation time of PETIM (~2 ns) compared to that for PAMAM (~5 ns) as we have already discussed before. Note that the free energy profile is comparatively flat near the center of the pore (-10 to +10 Å) suggesting that the dendrimers can freely oscillate in this region as we have mentioned earlier. The PMF profile for ubiquitin along the RC is shown in Figure 4c. The PMF profile suggests that ubiquitin is thermodynamically more stable inside the pore and hence we observe the spontaneous encapsulation of this protein. The free energy gain by the protein inside the pore is 84 Kcal/mol, which is much lower compared to the free energy gain by the dendrimers. This is so as the protein, being less flexible can maintain its structural integrity inside the pore. As a result, the hydrophobic core residues of the protein are not exposed to the CNT wall. In contrast, due to the flexibility of the dendrimers, they can undergo large structural deformations to maximize their interaction with the hydrophobic pore by exposing their hydrophobic cores and increasing the number of contacts with the pore wall. Figures 4d and 4e show the PMF profiles of the asiRNA and ssDNA, respectively. The free energy gain by the asiRNA (342 Kcal/mol) is higher than that gained by the ssDNA (228 Kcal/mol) as the number of close contacts of the asiRNA with the CNT pore is much higher. However, the PMF profiles suggest that both the asiRNA and ssDNA20 can spontaneously enter into the CNT channel but their translocation across the channel is unlikely as they face a high energy barrier. Note that there is almost no flat region near the centers of the PMF profiles of asiRNA and ssDNA as the lengths of these molecules are almost similar to the length of the channel. Thus, they cannot freely diffuse as much as the dendrimers and ubiquitin diffuse inside the channel. Another interesting feature of the ssDNA PMF profile is that, there is a region (highlighted by the magenta line) where the PMF increases linearly up to the outside of the pore. This resembles constant force kinetics (force plateaus) as found recently both in pulling experiment39 and in steered molecular dynamics (SMD) simulations.40,41 A linear increment in the PMF profile indicates a constant force 2 is required to pull the ssDNA out of the pore along the RC (here z-axis). We also compute the corresponding force profile as a function of the RC. The force plateau along the RC obtained from the numerical derivative of the FE as a function of z is shown in Figure S10 in the SI. This constant force kinetics is the consequence of frictionless sliding of ssDNA bases along the inner wall of CNT pore and the unfavorable DNA solvation energy.39 We also find quantitative agreement between the values of the extraction work of

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ssDNA from the pore obtained from our simulation (= 19 kcal/mol per base) and from the experiment (= 22 ± 10 kcal/mol per base).39

Entropic Barrier for Entry inside the Nanopore: In the previous section, we have demonstrated that the molecules do not face any free energy barrier to enter the CNT nanopores, although one expects them to face an entropic barrier for entering the pore, which is the confining volume for the molecules. We have used two phase thermodynamics (2PT)42,43 method to evaluate the entropic cost for the molecules to enter inside the nanopore. The entropic cost for each molecule, which is the difference between the entropy of the molecule inside and outside the nanopore, is reported in Table 3. For each case we find a decrease in entropy, while encapsulated inside the nanopore as anticipated. The PETIM dendrimer shows the highest decrease in entropy per atom, for which the entropic term () as a function of 4567 distance (the reaction coordinate taken for the PMF calculations) is plotted in Figure 4f. Note that the entropic cost is much smaller compared to the free energy change (reported in the same Table 3) for each case. The entropic cost is more than compensated by the huge gain in energy (see the time evolution of the VDW energy in Figure 1) of the molecule upon entering the nanopore, which makes the free energy change negative in each case. Hence the spontaneous encapsulation process described here is driven by energetics. Theoretical Estimation of the Encapsulation and Translocation Time: We have shown that all the molecules studied here can spontaneously enter the nanopore. However, the PMF profile suggests that each of the molecules must overcome a very high energy barrier (≫ ) to come out of the nanopore. Therefore, the probability of passive diffusion of the molecules through the pore from one side of the membrane to the other side is extremely small. This process is a rare event, which takes place on timescale that are beyond the reach of ordinary MD simulations. Thus, to estimate the time required for the encapsulation and translocation process, we employed a theoretical method described below.

We consider a particle diffusing in the presence of a potential 8%2#. The backward Smoluchowski equation for 8# 9 , |#, 0, the probability of finding the particle at # 9 at time , given that the particle was at # at the initial time = 0, is given by : 2# : : 8 = 8 + 8 4 : %- :# :#

where 2# = −

=

=>

8%2# is the mean force on the particle due to the potential 8%2#, and

other symbols are the same as those used before.

We define the encapsulation time # as the time required for a particle starting from # to go to the center of the nanopore for the first time. Similarly, the exit time ? # is defined as the 10


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time the particle takes to completely come out of the nanopore once it has gone inside. Both # and ? # can be treated as mean first passage times (MFPT) with appropriate boundary condition. We consider two boundaries “α” and “β” at points that are inside and outside the nanopore, respectively. The specific values of α and β for different cases along the axis of the pore are marked by dashed lines in the respective plots in Figure 4. For calculating #, absorbing and reflecting boundary conditions are taken at α and β, respectively, and vice versa for calculating ? #. Initially the particle is located at # (α ≤ # ≤ β) and with the above boundary conditions, # and ? # are given by 44 # =

C 1 > 9 A # )*+,8%2# 9 ⁄ / A # 99 )*+,−8%2# 99 ⁄ / 5

E >D

> 1 C 9 9 ⁄ # / ? = A # )*+,8%2# A # 99 )*+,−8%2# 99 ⁄ / 6

> E D

where is the diffusion constant of the molecule. In general, is position dependent. But, for simplicity, we consider as a constant, taken to be equal to the diffusion coefficient obtained in the confinement (see Table 2). The value of # is taken as β for the calculation of , and α for the calculation of ? . The values for and ? for different cases obtained by numerical integration, using equation 5 and equation 6, respectively are reported in Table 4. Also values, calculated from three different simulations for each case, are given in that table. Note that the values obtained from theory and simulations agree reasonably well except for the ssDNA, which may be due to the difficulty in extracting the diffusion constant correctly inside the pore as discussed earlier. Since ? given in the table is much larger than , ? is equivalent to the time required to translocate the molecule across the nanopore. Note that ? is an astronomically large number for each case. Forced Ejection of the Molecules from the Nanopores: As the previous calculations preclude the possibility of spontaneous translocation of molecules through the pore spanning across the membrane, one needs to apply an external force or add some active ingredient to move the molecules out of the pore to the desired location. This is an extremely challenging job and is an active area of research. Here we put forward an easy solution for this process and demonstrate the feasibility of the method using MD simulations. In the proposed method, we put another free-floating CNT of diameter smaller than that of the pore at the mouth of the pore. Strong van der Waals attraction between the CNT and the hydrophobic pore ensures that the CNT of smaller diameter spontaneously enters the nanopore and displaces the molecules encapsulated in it. Like the cases for the entry of different molecules inside the nanopore, we have calculated the energy and the entropy contributions to the process of insertion of the small CNT inside the nanopore (see Figure S11 in the SI). The

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decrease in the entropy (~25 kcal/mol) of the small CNT upon entry into the nanopore is more than compensated by the much larger decrease in its energy (~2300 kcal/mol), so that its free energy decreases monotonically as it enters the nanopore. As a result, the small CNT enters inside the nanopore spontaneously without facing any free energy barrier. The ejection of the asiRNA molecule is shown in Figure 5a (see Movie S2 also) as a representative example. In Figure 5b, we plot the COM distances of the molecules (see inset), and ejectors from the center of the nanopore as a function of time. As seen in the figure, the molecules can be ejected within few nanoseconds of the simulation time. Effect of Ends Functionalization of the CNT Nanopore: Sometimes CNTs may be present with negatively charged ends, where the ends are functionalized with some acidic groups.45 We consider -COOH functionalized CNT, where both the open ends of the CNT are terminated with -COOH functional groups. The procedure is given in the METHODS section, and in Figure S12 in the SI. We first demonstrate that the ends functionalization of CNTs do not affect the transorientation of the CNT in the bilayer membrane. The angle (G> ) between the long axis of the CNT and the bilayer normal is plotted in Figure S13 for (20,20) and (16,16) CNTs with diameters 2.7 nm and 2.16 nm, respectively. For both cases G> does not change much throughout 100 ns of simulation time. Then, we consider non-protonated G2 PAMAM and G3 PETIM dendrimers (charge neutral), and ssDNA (negatively charged) to study how the charged functional group present at the ends of the nanopore affects the dynamics of these molecules to enter the nanopore. The entry dynamics of PAMAM, PETIM and ssDNA are depicted in Figures S14 and S15 in the SI, and Figure 6, respectively. We observe, like in the case of the nanopore with neutral ends (see Figure 3), all the molecules enter the functionalized nanopore spontaneously. All the three molecules take longer time to spontaneously enter the end functionalized nanopore (see Figures S14a and S15a in the SI, and Figure 6a) compared to the time taken to enter the nanopore with neutral ends (see Figure 2). So, all the processes described for the CNT nanopore with neutral ends in this work can also be qualitatively demonstrated for the -COOH functionalized CNT nanopore, although some quantitative differences are expected depending on the end functionalization groups.

CONCLUSIONS: In summary, using fully atomistic simulations, we investigate the encapsulation and translocation process of bioactive molecules through a CNT channel embedded in a model cell membrane. In the recent past, CNTs have been used to form artificial channels across the cell membrane and the transport mechanism of small molecules like water and ions have been investigated both in experiments and simulations. However, the transport properties of larger biomolecules potentially used for drug and gene delivery have not been investigated in detail. In this study, we find that all the bioactive molecules studied here are spontaneously

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encapsulated into the channels, but they cannot translocate spontaneously as they face very high energy barriers, which we confirm by computing the free energy profiles of the molecules along the pore axis. We propose a theoretical model to estimate the encapsulation and translocation time for the molecules. The estimated encapsulation time agrees well with the simulation results and the estimated translocation time is astronomically large, which cannot be verified with simulations. However, we did not observe spontaneous translocation of any of the molecules during 100 ns long simulations suggesting this phenomenon to be very unlikely which qualitatively agrees with the theoretically predicted translocation time. So, the CNT pore acts as a trapping potential indicating an external force or some active ingredient is required to translocate the molecules out of the nanopore. In this context the physical displacement method described above can be used to eject the molecules out of the nanopore. So, the method demonstrated in this study can be exploited to transfer molecules into the interior of cells. Owing to the capability of CNTs to successfully encapsulate different molecules and their distinctive electrical, thermal and mechanical properties, different CNT based molecular complexes may also find applications in molecular sensing, sequencing and energy storage devices.

METHODS: System Building and Force Field Parameters: Initial structures of both PAMAM and PETIM dendrimers were built using the dendrimer building toolkit (DBT)46 and those of asiRNA and ssDNA were built using the nucleic acid builder (NAB) tool.47 The initial structure for the ubiquitin protein was obtained from the crystal structure (protein data bank (PDB) ID code 1UBQ). POPC lipid bilayers were constructed using the CHARMM-GUI membrane builder 48 and converted to Lipid 14 PDB format using the charmmlipid2amber.py script of AMBER14 tools.49 The SWCNTs were generated using ‘carbon nanostructure builder’ plug-in of visual molecular dynamics (VMD) software.50 A 12x12 nm2 patch of the bilayer containing 174 lipid molecules per leaflet was built. Then a pore was created in the bilayer by removing the entire lipid if any of its constituent atom’s x, y coordinates satisfied the condition * + H < , where was the radius of the pore, and SWCNTs were inserted in the pores using Tcl scripting interface of VMD.50 In our previous study51, we used a similar method to build a protein channel inserted into the bilayer. GAFF force field52 parameters were used to model PAMAM and PETIM dendrimers while ff10 force field, which includes ff99SB53 parameters for proteins along with the parmbsc0 correction54 for nucleic acids, was used to model asiRNA, ssDNA and the protein. Carbon atoms of SWCNTs were modeled as type CA atoms of the ff10 force field. Lipids were modeled using AMBER LIPID 14 force field55 parameters. For functionalization of CNT, the dangling bonds present at the two ends of the CNT are terminated by -COOH groups and H atoms with 50% from each type (see Figure S12 in the SI).

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We have followed the standard procedure in AMBER, which is described in detail in our earlier publication46, for extracting the charges and parameters for this non-standard residue. The restraint electrostatic potential (RESP) charges along with GAFF force field parameters are used to model the functionalized CNT. Equilibrium MD Simulation Protocols: All the equilibrium simulations were carried out using PMEMD module of AMBER14 package.56 Periodic boundary condition (PBC) along with a rectangular box as the unit cell was used for all the simulations. All systems were solvated with TIP3P57 water using the xleap module of AMBER14 tools in a way such that there exists at least 15 Å solvation shell in between the solute and simulation box wall. The charge neutrality of the solvated systems was maintained by adding the appropriate number of counter ions (JKL / NO P ), which were modeled using Joung and Cheatham parameters.58 The solvated systems were then subjected to 5000 steps of steepest decent minimization, followed by 5000 steps of conjugate gradient minimization to remove bad contacts present in the initially built systems. The energy minimized systems were slowly heated from 0 K to 100 K in 5 ps and then from 100 K to 300 K in the next 100 ps. The solute particles were restrained to their initial position using harmonic restraints with a force constant of 10 kcalmol-1Å-2 during the heating period and for the next 500 ps of MD simulations. All the simulations (heating, restrained equilibration and several ns of production run) were performed in the NPT ensemble using 2 fs time step for integration. Temperature of the system was maintained at 300 K using a Langevin thermostat59 with collision frequency 1.0 ps-1. The Berendsen weak coupling method 60 was used to apply a pressure of 1 atm with anisotropic pressure scaling with a pressure relaxation time constant of 1.0 ps. Bonds involving hydrogen atoms were constrained using the SHAKE algorithm.61 The particle mesh Ewald (PME)62 sum was used to compute the long range electrostatic interactions with a real space cutoff of 10 Å. The van der Waals and direct electrostatic interactions were truncated at the cutoff. The direct sum non-bonded list was extended to cutoff + “nonbond skin” (10 + 3 Å). PMF Calculations: Umbrella sampling63 method was used to calculate the PMF. All simulations for the free energy calculation were performed using NAMD-2.10 software64 with the collective variables module.65 Simulations were restarted by taking the AMBER equilibrated restart files. Simulations were performed in the NPT ensemble using 1 fs time step for integration. The temperature of the systems was maintained at 300 K using Langevin thermostat59 with collision frequency of 1.0 ps-1. Nose-Hoover Langevin pressure control (see section 7.5.2 of NAMD manual, Ref: http://www.ks.uiuc.edu/Research/namd/2.10b1/ug.pdf) was used to apply a pressure of 1 atm with a piston period of 0.2 ps and damping time constant of 0.05 ps, and constant ratio (x/y) was maintained. PME62 was used to compute the long range electrostatic interactions with a real space cutoff 12 Å. The van der Walls interaction was truncated at a cutoff of 12 Å by using a switch function (switchdist = 10 Å). The reaction coordinate is defined

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along the z axis (the axis of the pore) ranging from -10 to >50 Å with the bilayer center at z=0. Due to the symmetry of the pore about the z=0 plane, we considered negative values of z only till -10 Å. More than 60 windows were defined along the z axis for each case, with 1 Å distance between successive windows. A biasing harmonic potential was applied to the z coordinates of all atoms of the molecules (asiRNA, ssDNA, ubiquitin, PAMAM, PETIM) with a force constant of 4 kcal mol-1Å-2. The simulation was carried out for 2 ns for each window and the data obtained in the last 1 ns were considered for the PMF calculations. PMFs were computed using the weighted histogram analysis method (WHAM).66, 67 Analysis: All the analyses are performed either using home written codes or using AMBER14 tools.49 Images and movies are processed using VMD.50 To describe order of the lipid bilayer membrane, one can calculate an order parameter for every CH2 group present in the two tails (tail-1 and tail-2) of a POPC lipid molecule. The tail-1 and tail-2 contain fifteen and seventeen carbon atoms (CH2 groups), respectively. The order parameter is defined as follows: 1 = 3〈QRS G 〉 − 1, 7 2

where G is the angle between the CH-bond vector and the normal to the membrane. The angular brackets indicate average over all lipids and time. The radius of gyration is a measure of the size of a molecule and is defined as: 1 = U V WX |X − 5 | , 8 % Y

XZ$

where 5 is the center of mass and % is the total mass of the molecule, X is the position and WX is the mass of the \th atom.

The root mean square fluctuation is defined by the following equation:

1 1 %2 = V U VX − 〈X 〉 , 9 J X

]

Z'

where J is the total number of heavy atoms of the molecule, is the time period over which the positional fluctuations being averaged upon, X is the position of the \th atom at time and 〈X 〉 is the time average of the position of the same atom. 15



To characterize the shape of molecules one can calculate the shape tensor, whose elements are defined as follows: _`a

1 = V WX b`X − ` cbaX − a c; p, q = x, y, z, 10 % Y

XZ$

where M is the total mass and vector is the position of the center of mass of the molecule, WX is the mass and `X is the p coordinate of the \th atom. The three eigenvalues of the shape tensor (G) are the principal moments of inertia denoted by j> , jk , and jl in descending order. The ratios of these three principal moments provide information about the shape of the molecule. Another quantity called asphericity provides more quantitative information about the shape of the molecule and is defined as: 〈j 〉 m = 1 − 3 n o, 11 〈j$ 〉

where j$ and j are defined as: j$ = jl + jk + j> and j = jl jk + jk j> + jl j> , and the angular bracket represents time average. The time correlation function of the normalized end-to-end distance is defined as: N2 =

〈p0 ∙ p〉 , 12 〈p0 ∙ p0〉

where p and p0 are the end-to-end distance of the molecule at time and zero, respectively and the angular bracket represents average over time origins.

ASSOCIATED CONTENT: The Supporting Information is available free of charge. Snapshots for equilibrated structure of different molecules in water; effect of pH of the solution, diameter of the CNT, salt concentration, initial structures on the spontaneous encapsulation process; dihedral angle distributions of ubiquitin in water and inside the nanopore; MSD of the molecule in water and inside the nanopore; N2 plot; force profile of the ssDNA along the reaction coordinate; entropy and energy terms for the small diameter CNT entry inside the nanopore; results for -COOH functionalized CNTs; and table for secondary structure of ubiquitin in water and inside the nanopore (PDF) Movies for spontaneous encapsulation of the asiRNA, and its ejection (MPEG)

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AUTHOR INFORMATION: Corresponding Authors *E-mail: [email protected] *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS: We thank Supercomputer Education and Research Centre (SERC), IISc, for providing supercomputer time @SAHASRAT machine, where most of the simulations were performed. A.K.S thanks MHRD for generous fellowship.

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Figures and Tables:

Figure 1. The equilibrated structures of CNTs of different lengths, embedded in POPC lipid bilayer: (a) (20,20) CNT with length of 4.5 nm, (b) (28,28) CNT with length of 5nm, and (c) (20,20) CNT with length of 9 nm. The water molecules are not shown here for clarity. (d) Time evolution of the angle (θz) between the CNT axis and the normal to the bilayer plane. (e) The order parameters of the two tails of the lipids (upper panel tail-1 and lower panel tail-2), which are close (filled symbols) and far away (empty symbols) from the CNT wall.

21



Figure 2. The Zcom distance (upper panel), the number of close contacts (middle panel) and the VDW interaction energy (lower panel) between the CNT and (a) PAMAM, (b) PETIM, (c) ubiquitin, (d) asiRNA, and (e) ssDNA as a function of simulation time. Three colors in the upper panels show the results of three independent simulations. Close contacts and the VDW interaction energy are shown for single simulation only.

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Figure 3. Cross sectional views of initially built system (top panel) and equilibrated structures after 100 ns long MD simulations (middle panel). The top views of the equilibrated structures are shown in the lower panel. Here (a), (b), (c), (d) and (e) show the cases of PAMAM, PETIM, ubiquitin, asiRNA and ssDNA molecules, respectively. The water molecules and ions are not shown here for clarity.

23



Figure 4. PMF profile for (a) PAMAM, (b) PETIM, (c) ubiquitin, (d) asiRNA, and (e) ssDNA. The shaded areas in the figures correspond to regions inside the nanopores. The error bars calculated using MC bootstrapping are smaller than the symbols sizes used to represent the mean values. Hence error bars are not shown. (f) The entropic term () as a function of the reaction coordinate is plotted for the PETIM dendrimer, which shows the maximum decrease in entropy per atom in the process of encapsulation inside the nanopore.

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Figure 5. (a) Procedure for ejection of the asiRNA from the nanopore using another smaller diameter CNT. The CNT enters spontaneously inside the nanopore and displaces the molecule, present inside, out of the pore lumen. Top-left and bottom-right figures represent the initial and final configurations, respectively. The water molecules and ions are not shown here for clarity. (b) Time evolution of the center of mass distances between the nanopores and the ejectors. The inset of the figure represents the same between the nanopores and the molecules.

25



Figure 6. The entry dynamics of ssDNA into the -COOH end-functionalized CNT nanopore. (a) The time evolution of the Zcom distance is plotted. (b) and (c) The snapshots of the system at different instances of time are shown for simulation 1 and 2, respectively. The water molecules and ions are not shown here for clarity.

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Table 1. Size, shape and structural fluctuation for all systems in confinement (inside the nanopore) and in bulk water. (Å) %2 (Å) 10.18 ± 0.21 1.54 ± 0.04

asphericity 0.064 ± 0.007

10.79 ± 0.23 2.24 ± 0.04

0.079 ± 0.008

11.70 ± 0.05 0.87 ± 0.02

0.071 ± 0.002

13.54± 0.40

1.27 ± 0.01

0.557± 0.071

14.46± 3.04

asiRNA in 15.90 ± 0.07 confinement asiRNA in water 17.38 ± 0.60

0.47±0.02

0.378±0.008

5.90±0.09

system G2 PAMAM in confinement G2 PAMAM in water G3 PETIM in confinement G3 PETIM in water ubiquitin in confinement ubiquitin in water ssDNA in confinement ssDNA in water

10.74 ± 0.32 3.64 ± 0.09 9.20 ± 0.24

3.06 ± 0.04

11.71 ± 0.06 1.08 ± 0.02 10.05±0.21

1.29 ± 0.10

jr /jt 1.35 ± 0.13

2.66 ± 0.52

1.61 ± 0.34

0.253 ± 0.048

6.05 ± 1.48

0.091 ± 0.013

2.99 ± 0.60

0.052 ± 0.002

2.17 ± 0.10

0.310± 0.034

1.84±0.07

jr /js 2.58 ± 0.30

0.420± 0.070

2.33 ± 0.10

7.91± 1.83 7.36±1.05

2.96 ± 1.06 1.58 ± 0.32 1.87 ± 0.06 1.57 ± 0.08 7.38± 0.57 3.30±0.31 5.69±0.09

5.83± 0.79

Table 2. Diffusion coefficient of the molecules in bulk water and in confinement (inside the nanopore). system

× 10Pv QW ⁄S in water

× 10Pv QW ⁄S in confinement

G2 PAMAM 1.227

G3 PETIM 1.250

ubiquitin 0.649

ssDNA 1.154

asiRNA 0.555

0.794

0.639

0.377

0.468

0.219

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Table 3. The entropic cost (−∆) from 2PT calculation for the molecule to enter the nanopore. The free energy change (∆2) in this process obtained from the PMF calculation is also tabulated. system −∆ (in kcal/mol) ∆2 (in kcal/mol)

G2 PAMAM 8.96 ± 1.00

G3 PETIM 14.20 ± 1.17

ubiquitin 5.33 ± 1.06

−165.82 ± .07 −189.78 ± .17 −81.44 ± .07

ssDNA 7.73 ± 2.01

asiRNA 27.35 ± 1.27

−231.98 ± .09 −347.56 ± .18

Table 4. Encapsulation time ( ) obtained from the simulations and predicted from the theoretical model. Translocation time ( ? ) estimated from the theoretical model. system from simulation (in ns) from theory (in ns) ? from theory (in ns)

G2 PAMAM 7.1 ± 1.5

G3 PETIM 6.9 ± 2.9

ubiquitin 25.6 ± 9.4

ssDNA 60.6 ± 11.4

asiRNA 29.5 ± 8.9

2.27 × 10$'

5.96 × 10$wx

9.04 × 10xy

5.31 × 10$vy

1.32 × 10xw

10.0

7.6

28

40.7


13.6

28.2

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TOC:

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Translocation of Bioactive Molecules through Carbon Nanotubes

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