Carbon Nanotubes Mediate Fusion of Lipid Vesicles - ACS Publications

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Carbon Nanotubes Mediate Fusion of Lipid Vesicles Ramachandra Moorthy Bhaskara, Stephanie M. Linker, Martin Vögele, Juergen Koefinger, and Gerhard Hummer ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.6b05434 • Publication Date (Web): 19 Jan 2017 Downloaded from http://pubs.acs.org on January 20, 2017

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Carbon Nanotubes Mediate Fusion of Lipid Vesicles Ramachandra M. Bhaskara,†,¶ Stephanie M. Linker,†,¶ Martin Vögele,† Jürgen Köfinger,† and Gerhard Hummer∗,†,‡ †Department of Theoretical Biophysics, Max Planck Institute of Biophysics, Max-von-Laue Straße 3, D-60438 Frankfurt am Main, Germany ‡Institute for Biophysics, Goethe University Frankfurt, 60438 Frankfurt am Main, Germany ¶Contributed equally to this work E-mail: [email protected] Abstract The fusion of lipid membranes is opposed by high energetic barriers. In living organisms, complex protein machineries carry out this biologically essential process. Here we show that membrane-spanning carbon nanotubes (CNTs) can trigger spontaneous fusion of small lipid vesicles. In coarse-grained molecular dynamics simulations, we find that a CNT bridging between two vesicles locally perturbs their lipid structure. Their outer leaflets merge as the CNT pulls lipids out of the membranes, creating an hourglass-shaped fusion intermediate with still intact inner leaflets. As the CNT moves away from the symmetry axis connecting the vesicle centers, the inner leaflets merge, forming a pore that completes fusion. The distinct mechanism of CNT-mediated membrane fusion may be transferable, providing guidance in the development of fusion agents, e.g., for the targeted delivery of drugs or nucleic acids. Keywords: Membrane fusion; vesicle; carbon nanotube; membrane staples; coarse grained simulations.

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In living organisms, the fusion of lipid membranes is essential for cellular transport and communication. 1,2 To overcome its multiple free energy barriers, 3 complex protein machineries have evolved that carry out this challenging task in a controlled and efficient manner. 1,2,4–8 Several non-biological factors induce fusion, such as osmotic stress, 9 dehydration by addition of polymers, 10 cations, 11,12 amphiphiles, 12–14 electric fields, 15 surface tension 16 and irradiating membrane-attached gold nanoparticles. 17 They act by bringing vesicles together and by destabilizing the vesicle surfaces, thereby promoting fusion-stalk formation. By contrast, specifically designed molecules for initiating and regulating vesicle-fusion reactions are few. 12,18–20 Here we show with unbiased computer simulations that carbon nanotubes (CNTs) can induce spontaneous vesicle fusion. Previously, membrane fusion has been studied theoretically using a range of methods, from membrane elastic models 21,22 over field theoretic descriptions 23,24 to computer simulations. Inducing fusion in coarse-grained 7,25–27 or atomistic simulation models 21 required the imposition of constraints or the addition of bridging lipids with tails anchored in opposing membranes. By contrast, CNTs may offer a route to fusion realizable to both experiment and simulation. CNTs have already been used as delivery system for specific and localized targeting of anti-cancer drugs. 28 Exploiting the chemistry of end-group functionalization, multiple chemical compounds are tethered to CNTs for targeted delivery and localized actions. 29 Several experiments and all-atom molecular dynamics (MD) simulations have shown that CNTs can interact favorably 30–32 with lipid bilayers, penetrate into them, 32–34 and embed into them spontaneously. 35,36 Furthermore, mammalian cells actively take up CNTs either by endocytosis or passive diffusion. 33 CNTs can also mimic membraneprotein channels and contribute to passive transport, 35 high-efficiency proton conduction, 37,38 and sensing 39 across membranes. Recently, Geng et al. 35 were able to reconstitute CNTs in lipid vesicles of ∼200 nm diameter. Using cryo-transmission electron microscopy (cryo-TEM), they showed that CNTs are embedded into lipid vesicles, spanning both membrane leaflets, with their axes approx-

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imately perpendicular to the membrane. In their micrographs, several images show CNTstapled vesicles, with single CNTs bridging two vesicles. Furthermore, the images contain unusual, elongated lipid vesicle structures that could have resulted from fusion. 40,41 Putting these two observations together, we hypothesize that bridging CNTs could mediate vesicle fusion, which would result in larger, elongated vesicles. In the present study, we use MD simulations to explore this hypothesis of vesicle fusion induced by bridging CNTs. We base our initial simulation setup on the structures seen in the EM images by Geng et al. 35 Starting from states with CNT-stapled vesicles, we performed extensive MD simulations of hundreds of fusion events to characterize the molecular details of the CNT-mediated fusion reaction. A comparison of CNT-mediated fusion with the current picture of free fusion identifies key differences that are likely responsible for the speed-up of fusion. In particular, we highlight the role of CNTs in lowering the distinct barriers for merging first outer and then inner leaflets. We also show that the rate of fusion decreases with increasing vesicle size.

RESULTS To explore the possibility of CNT-mediated membrane fusion, we simulated vesicles stapled together by bridging CNTs (Figure 1). We considered vesicles of three different sizes (11.5 nm, 15 nm and 28 nm diameter) composed of three different lipids (POPC, DOPC and DSPC) with varying degrees of unsaturation. CNT-stapled vesicles of similar size and shape can be seen in cryo-TEM images (Figure S1). We used the coarse-grained MARTINI model, which has been instrumental in modeling vesicles and fusion processes, 42 and a flexible CNT model with modified parameters for polar end groups to mimic end group functionalization (see Methods). We performed multiple simulation runs in two different system setups with 40 000 to 330 000 particles, accumulating more than 370 µs of total simulation time. In setup A, we simulated CNT-mediated fusion of two vesicles in explicit water (Figure 1a). In the

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reduced setup B (Figure S2), we exploited periodic boundary conditions for fusion. 43,44 In a box containing only one vesicle, a CNT, and coarse-grained water, we simulated self-fusion between a vesicle and its periodic image. In the simulations, we observed more than 400 events of spontaneous CNT-mediated vesicle fusion (Figure 1b; Supplementary Movies SM1 and SM2; Table 1). These events share a common sequence of steps as detailed below (Figure 2). In a first phase, the CNTstapled vesicles rearrange to minimize water exposure of the hydrophobic CNT surface in the gap between the two vesicles (Figure 2a). To minimize this hydrophobic mismatch, the CNT pulls the two vesicles together. Lipids of the outer leaflets slide along the CNT and coat its entire outer surface (Figure 2a, bottom). To quantify these interactions, we count the number of lipid tail-beads within 1 nm of each CNT bead and color the CNT accordingly (Supplementary Text S1 and Figure S3). In a second phase, tilting of the CNT promotes the formation of a fusion stalk. By tilting away from the symmetry axis connecting the centers of the lipid vesicles, the CNT buries even more of its hydrophobic surface in the lipid environment (Figure 2b). As the entire CNT surface becomes lipid-coated, tails of lipids in the two outer leaflets are brought into contact (Figure 2b; bottom). This causes the outer leaflets to merge, creating the pre-fusion stalk with a continuous outer leaflet enveloping both vesicles (Figure 2b; Supplementary Movies SM1 and SM2). Lipids of the fused outer leaflet (Figure 2b, blue and green tails) coat a continuous ring around the center of the CNT, flanked by lipids of the still intact inner leaflets of the two vesicles (Figure 2b, red and yellow tails). This arrangement maximizes interactions between the hydrophobic exterior of the CNT and the lipid tails, while maintaining interactions of the functionalized ends of the CNT with polar head-groups of lipids in the inner leaflets (red and yellow beads in Figure 2) and with water inside the vesicles. This stalk structure constitutes a metastable intermediate along the fusion pathway. Further CNT-lipid rearrangements promote the transition from the fusion stalk to an hourglass-shaped structure (Figure 2c). In the fusion stalk, the CNT ends (at ± 4-6 nm 4


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from the center) are predominantly coated by lipids from inner leaflets (Figure 2b). In the transition to the hourglass shape, the two continuous rings of outer leaflet tails around the CNT center open up (green and blue tails in Figure 2b-c). Driven by hydrophobic interactions, the acyl chains of lipids in the inner leaflets now protrude towards the center of the CNT (Figure 2c bottom; Supplementary Movie SM1). These interactions (red and yellow lipid tails) on opposite sides of the CNT bring the inner leaflets into close contact and cause deformations of the inner water-filled cavities from spherical into teardrop-shaped structures (Figure 2c, bottom). At this stage, the tilt angle of the CNT relative to the symmetry axis connecting the vesicle centers has risen to nearly 45 degrees (Figure S4). The delicately balanced hourglass-shaped metastable intermediate has formed. The subsequent opening of the fusion pore is associated with further CNT movement (Figure 2d). As the CNT moves away from the symmetry axis (Figure 2c-d), it pulls lipid tails of the two inner leaflets together. A continuous line of inner leaflet-CNT contacts develops along the length of the CNT (Figure 2d, red and yellow tails; Figure S3d center, right). These interactions are spirally arranged around the CNT axis. In Figure 2d, the CNT is coated by lipids of the upper vesicle (red tails; top and front), which merge with lipids of the lower vesicle (yellow tails; bottom and back). The teardrop-shaped protrusions of the inner cavities are pulled together and the two inner leaflets merge. As a result, the seal between the two vesicles breaks. Opening of the fusion pore allows the first water molecules to pass through (Figure 2d). The two vesicles have thus fused into one. After the pore has formed, the interior volumes of the two vesicles merge and their water contents mix (Figure 2e). The fusion pore expands, allowing lipids from each vesicle to diffuse freely within the membrane of a single large vesicle. Note that during fusion, the two outer leaflets merge first (fusion stalk; Figure 2b, mixing of blue and green tails), and the two inner leaflets merge later (pore formation; Figure 2d, mixing of red and yellow tails). There is no exchange of lipids between outer and inner leaflets. The lipid surface area and volume of the post-fusion vesicle are roughly those of the two initially spherical vesicles combined,

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A12 = A1 + A2 and V12 = V1 + V2 . The reduced area of a12 = A12 /(V12 )2/3 thus exceeds that of a sphere by up to a factor of 21/3 . The fused vesicle therefore adopts a prolate axisymmetric structure (Figures 1b; 2e and S1c-d). 40 Its membrane is perturbed further by an imbalance of the numbers of lipids in post-fusion inner and outer leaflets as a result of the finite membrane thickness. A lack of lipids in the inner leaflet is compensated in part by the CNT. Owing to the large desolvation cost of the functionalized CNT ends and the strong hydrophobic interactions of the inner leaflet and CNT, the CNT sticks to the inside of the fused vesicles for extended times in our simulations. On a much longer timescale, we expect that the CNT will reestablish a membrane-spanning orientation to bring its polar rims into better contact with water, to reduce the disturbance of the bilayer structure, and to establish a more favorable lipid coat of the CNT surface. This process is likely associated with the flipping of lipids between the two leaflets. Major fusion steps are associated with distinct transitions in lipid coating patterns of the CNT (Figure 2). These are quantified as CNT-lipid interactions and mapped onto the cylindrical surface of the CNT to build interaction maps (Figure S3). During fusion, the character of the interaction map changes (Supplementary Movie SM1), as old symmetries break and new ones emerge (Supplementary Text S1). All simulations with small and medium-sized CNT-stapled vesicles showed fusion events (Table 1). Fusion events occurred in all three different lipid environments, making CNTmediated fusion lipid-type independent (Table 1). As negative control, we performed long simulations of systems with two vesicles without CNTs. In the absence of CNTs, vesicles simulated at near-contact for long times (10 µs) did not fuse, showing that the CNT clearly lowered the barrier for fusion. The kinetics of the process and the rate of CNT-mediated fusion is dictated by the system sizes and the ease of transiting through key intermediate stages. We find that the overall fusion process of 15 nm CNT-stapled vesicles can take anywhere from hundreds of nanoseconds to 1-2 µs. To characterize the time-scales associated with transitions into these

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intermediate states, we determined waiting times to arrive at the fusion stalk, the hourglass shape, and the fusion pore from repeated fusion simulations (Figure S5). To estimate the characteristic times associated with the three distinct transitions along the fusion pathway, we fit the waiting time distributions to convolutions of single exponential functions, with added lag times (see Methods). The lag times represent the drift of the system towards a particular intermediate state before the next stochastic event. We find three distinct characteristic times along the fusion pathway corresponding to the formation of the fusion stalk, the teardrop shape, and the fusion pore, starting from CNT-stapled vesicles (Figure S5). The formation of the fusion stalk with a tilted CNT is a fast process, requiring only ∼10-70 ns in our simulations (characteristic time, τStalk = 18 ns). The next process involves the transition into an hourglass shaped intermediate with teardrop shaped inner cavities. In 90% of our simulations, this transition occurred within the first 200 ns (τHourglass = 23 ns). Finally, pore formation takes ∼80-800 ns (τFusion = 116 ns). Small vesicles stapled by CNTs fuse faster (Figure S6). The high curvature of their membranes causes lipid packing defects, which facilitate the formation of the fusion stalk. The finite thickness of the membrane, and the difference in curvature of its two leaflets in both magnitude and sign cause further perturbations to the lipid organization. These perturbations ease CNT tilting and fusion-stalk formation. By contrast, larger vesicles face higher barriers to fusion. 45 Their bilayers are relatively more ordered. As a result, CNTmediated fusion of large vesicles exhibits longer pauses in the hourglass intermediate. Indeed, for the largest vesicles studied (28 nm diameter; Table 1), fusion did not complete on the MD timescale even at elevated temperature (50 µs of aggregate simulation time). This corresponds to a > 50-fold drop in the estimated rate of fusion upon doubling the vesicle size. The disruption of inner leaflet packing and reorganization into teardrop shaped structures eases formation of hourglass shapes in small vesicles. In larger vesicles the disruption of the inner leaflets by CNTs is small and hence delays the transition towards hourglass shapes. We explored the effect of CNT length on fusion kinetics with additional simulations in

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setup A (Supplementary Text S2 and Table S1). We found that vesicles stapled by CNTs longer than 10 nm fuse readily (Figure S8; Table S1). By contrast, CNTs shorter than the combined thickness of the two bilayers are unable to staple two vesicles completely. 7-10 nm long CNTs form fusion stalks, but the vesicles do not transition to hourglass structures within the simulation time (Figure S8; Table S1). The distortions of the inner leaflets that can be induced by the long CNTs, but not the shortest ones, appear to aid fusion. From the MD simulation results, we can also make at least a rough estimate on how much a bridging CNT lowers the free energy barrier to fusion of two vesicles at near-contact. With a CNT bridging two 15 nm vesicles, we found fusion to complete in the MD simulations after about 200 ns on average. By contrast, two 15 nm vesicles without CNT restrained to near contact did not fuse during 2 × 5 µs of MD. From the ratio of these two times we can estimate a lower bound on the drop in the activation free energy for fusion with CNT, ∆∆G‡ > kB T ln(10 000/200) ≈ 3 kB T . We obtain an even sharper bound of ∆∆G‡ > 6 kB T by noting that free fusion did not even proceed to the fusion-stalk state, which occurred with bridging CNTs on a 25-ns time scale. In Supplementary Text S3 and Figure S9, we also provide a rough estimate of the free energy landscape of fusion, extracted from the MD simulations with the help of a 1D diffusion model 46 (Supplementary Text S3). On this free energy profile, the fusion-stalk and hourglass states appear as local minima, and the fused state as the global minimum (Figure S9).

DISCUSSION Our simulations started from a single CNT-bridging two vesicles, as a model of the structures seen in the experimental images by Geng et al. 35 The formation of these structures requires membrane insertion of CNTs, as studied for bilayers 33,47,48 and vesicles 49 using a range of computational methods. The effect of CNT length on orientations of functionalized CNTs has also been studied. 50 In Supplementary Text S4 and Figure S10, we examine two possible

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routes of CNT insertion into vesicles. We show that CNTs can insert both concomitantly with vesicle formation (Figure S10a) and subsequently into an already formed vesicle (Figure S10b). Coarse-grained MD and dissipative particle dynamics simulations have already been used to study CNT coating 51 and transmembrane insertion 52 mechanisms. However, in the small simulation systems studied over limited times, compared to experiment, we did not observe simultaneous CNT embedding into multiple vesicles, which is likely a rare process favored by longer tubes (Text S4). The cryo-TEM images by Geng et al. 35 are suggestive of CNT-mediated fusion, as observed in our simulations. Most notably, several of their images show vesicles with the axisymmetric prolate shapes (Figure S1; and Extended Data Figures 4 and 5 of ref 35), as expected for post-fusion states from our simulations (Figures 1b and 2e) and from elastic theory. 40 Indeed, the occurrence of prolate-shaped vesicles in EM micrographs has previously been used as a reporter of vesicle fusion. 41 We note that CNTs are visible in some of the prolate vesicles (Figure S1c-d), reinforcing the possibility that they resulted from CNT-mediated fusion. The elongated shapes of some structures indicates multiple fusion events. Alternatively, prolate vesicles in EM images could also be explained by (a) volume changes through water transport, (b) solution extrusion through filters and (c) crowding effects in thin films promoting free fusion during EM sample preparations. (a) Osmotically driven water transport out of the vesicle through membrane embedded CNTs could have resulted in vesicle volume shrinkage. This would be possible only under conditions of severe osmotic shock and hypertonic solution exterior of vesicles, which seems unlikely because the hydration process used deionized water. 35 (b) Extrusion of hydrated lipid solutions through 200 nm polycarbonate filters was reported to have initially formed large, multi-lamellar vesicles. 35 After repeated passes through the polycarbonate filters, a unimodal distribution of unilamellar spherical vesicles was obtained. The EM micrographs in Geng et al. 35 were obtained after 10 cycles of extrusion, which would decrease the chances of obtaining long prolate shaped vesicles after extrusion. 35 (c) Finally, EM grid preparation could have induced fusion. The

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samples to be imaged were trapped in thin-films on Cu grids and dried by hand with filter paper. The film thickness is therefore variable and depends on the extent of excess water removal. This could have resulted in artificially high concentrations of lipid vesicles, which would have favored both CNT-mediated and direct fusion and could have resulted in prolate vesicles. However, a recent study of the effect of α-synuclein on vesicle fusion also showed prolate vesicles in the presence of the protein and almost spherical vesicles in the absence of protein, using similar techniques for EM sample preparation, i.e., film formation by blotting for 2.5 s using filter paper. 41 The large spherical vesicles stapled by CNTs (Figure S1a-b) in the cryo-TEM images are indicative of trapped intermediates during the fusion of large vesicles. Our finding that fusion slows down with increasing vesicle size (Table 1) provides a possible explanation. We tested this further by performing simulations of a flat bilayer (effectively an infinite-size vesicle) stapled to a 15 nm vesicle by a single CNT (Figure S11). Formation of the hourglassshaped intermediate was slow (≈1.5 µs) by comparison to small vesicles, and fusion did not complete on the MD timescales (>6 µs), consistent with our findings for large vesicles. Alternatively, CNT-stapled but unfused vesicles in the cryo-TEM images could have been caused by defects in the CNT that prevented lipids from sliding along the hydrophobic CNT surface to form the fusion stalk. Bending, buckling, and breaking defects often arise on CNT surfaces due to mechanical shearing during sonication cutting, sidewall oxidation defects 53 could attract water and prevent efficient lipid coating essential for fusion. 53 To test these different hypotheses will require additional experimentation, e.g., by studying the effects of CNT processing. Moreover, to decouple the contributions of the CNT fusogenic activity and of vesicle curvature stress would require the calculation of accurate maps of the underlying free energy surfaces from extensive biased simulations.

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branes come into close proximity, allowing their proximal outer leaflets to interact. 27,54 Interaction also requires local dewetting to destabilize the surface bilayer interactions at a single point. 22 This defect then grows with time and allows the proximal leaflets to merge and form the fusion stalk, while the distal leaflets remain intact. This so-called hemifusion intermediate adopts an hourglass shape. 4 Subsequently, the stalk grows and forms the hemifusion diaphragm where the distal leaflets come in close contact. The hemifusion diaphragm facilitates the formation of a fusion pore. Finally, the fusion pore opens and expands, connecting the two vesicle compartments. We note mechanistic differences between CNT-mediated and free fusion. First, stalk formation is rapid, in stark contrast to protein-free fusion. The lipid molecules slide along the hydrophobic surface of the CNT to form a continuous coat that eases stalk formation. We find that CNT-stapled vesicles are able to spontaneously transit to the fusion-stalk state in all simulation runs, indicating that CNTs greatly reduce the barrier for fusion-stalk formation. By contrast, in conventional free fusion, the stalk-formation step is very slow, thought to be associated with the expansion of small surface defects on the proximal leaflets. 3 Second, no hemifusion is observed. Free fusion can occur with or without a hemifusion diaphragm intermediate. 3,55–57 The size and stability of the hemifusion diaphragm is dependent on several factors such as the size of the fusion stalk and the ability of lipids to spontaneously splay. 58 In the hourglass shaped intermediate of CNT-mediate fusion, the bridging CNT itself blocks the passage of solvent between the two cavities, instead of either a disc-shaped bilayer diaphragm or a small bilayer-shaped pre-pore rim in the free-fusion pathways. Pore formation is a result of the CNT moving away from the central axis of the delicately balanced hourglass shape, whereas in free fusion, pore formation is dictated by bilayer diaphragm stability. The relative ease with which CNTs can induce fusion, at least of small vesicles, also provides guidance for the design of fusogenic molecules. Our results show that hydrophobic rods penetrating into fusing membranes can dramatically enhance fusion efficiency. For large

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vesicles, these hydrophobic spikes should be combined with factors that enhance the local membrane curvature to facilitate point-like contacts between local membrane protrusions. Fusion constructs that exploit the mechanisms highlighted here could result in more facile and controlled fusion of vesicles, addressing two major challenges in the targeted delivery of drugs or nucleic acids. CNTs themselves serve as potential tools to direct and regulate fusion of small vesicles. It is also conceivable that biology exploits at least aspects of the powerful downhill CNT fusion mechanism, e.g., by using the hydrophobic surface of rodshaped viral fusion proteins exposed in their extended state 59 to connect host and viral membranes. 60 Aspects of CNT-mediated fusion may prove relevant for problems ranging from protein reconstitution into membranes to the inhibition of membrane fusion in viral infections.

METHODS System Setup and Simulations. All molecular dynamics simulations were performed using Gromacs 4.5.6 61–64 with the MARTINI force field (version 2.3). 65 Two kinds of systems were set up to study CNT-mediated vesicle fusion. Setup A comprises two vesicles stapled by a CNT (Figure 1a). The vesicles were initially placed at a distance of 16.5 nm from each other, so that the line connecting their centers was parallel to the z-axis of the box. The CNT was then added to connect the interior cavities of the two vesicles, leaving a gap of 1-1.5 nm between the head groups of the outer leaflets of the two vesicles. Lipids overlapping with the CNT envelope were removed. The smaller setup B contains only a single vesicle, with a CNT embedded in such a way that it staples the vesicle with its periodic image along the z-axis (Figure S2). These systems were then solvated with coarse-grained water beads, energy minimized, and equilibrated with position restraints on the CNT under NPT conditions for 5 ns, followed by ∼1 µs production runs. Simulations were performed using a 20 fs time step. Coordinates 15


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were saved every 200 ps. The system pressure was held at 1 bar using the Berendsen coupling scheme 64 with a coupling constant of 3 ps during the equilibration phase, and the Parrinello-Rahman barostat 66 for the production phase with a coupling constant of 12 ps. The compressibility parameter was set to 3 × 10−4 bar-1 during both phases. 63 In setup A and setup B, the CNT was placed initially along the z-axis and the pressure was coupled differently along the xy plane and the z-axis using a semi-isotropic barostat. Test simulations with isotropic barostats also showed vesicle fusion events. Temperature was maintained at 295 K throughout the simulation by velocity rescaling with an added noise term to obtain a canonical ensemble. 67 The center-of-mass motion of the entire system was removed. The long range cut-off distance was 1.2 nm with a switching distance of 1 nm and a pair-list distance of 1.4 nm. All stiff bonds and ring systems were constrained using the LINCS algorithm. 62 Vesicle Generation. To obtain vesicles with properly balanced numbers of lipids in the inner and outer leaflets, we simulated spontaneous bilayer-to-vesicle transitions using three different types of lipids (POPC, 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, 16:0-18:1 PC; DOPC, 1,2-dioleoyl-sn-glycero-3-phosphocholine, 18:1 PC; and DSPC, 1,2dioctadecanoyl-sn-glycero-3-phosphocholine, 18:0 PC) of varying degree of unsaturation. POPC and DOPC are unsaturated lipids with one and two double bonds in their tails, respectively, while DSPC is a completely saturated lipid with no double bonds. Discontinuous square lipid bilayer patches (23 × 23 nm2 , 25 × 25 nm2 , and 50 × 50 nm2 ) of lipids were generated using the script insane.py (MARTINI version 2.3), 65 immersed in much larger cubic boxes (30 × 30 × 30 nm3 , 32 × 32 × 32 nm3 , and 60 × 60 × 60 nm3 ) and solvated using the coarse-grained water model. The systems were first energy minimized and equilibrated at 295 K for 10 ns. The x- and y-axis of the boxes were fixed and pressure was only coupled to the z-axis at 1 bar, to keep the bilayer patches from merging with its periodic images. The systems were then simulated for ∼1 µs using a 20-fs time step. During these simulations, the bilayer patches spontaneously curved to form spherical vesicles (11.5 nm, 15 nm, and

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28 nm diameter). For POPC lipids, the 11.5 nm vesicle contained 1250 lipids (395 in the inner leaflet and 855 in the outer leaflet) and the 15 nm vesicle contained 2048 lipids (726 in the inner leaflet and 1322 in the outer leaflet). Larger vesicles of 28 nm diameter were made only with DOPC lipids and contained 6728 lipid molecules (2815 in the inner leaflet and 3913 in the outer leaflet). These large vesicles were used for fusion simulations at higher temperatures (350 K) only in setup B. Carbon Nanotubes. Coarse-grained MARTINI models generally use a 4:1 mapping for interaction sites (beads). For ring structures, special beads with a 2:1 mapping are used. 65 Here, all carbon-only interaction sites of CNTs were mapped to CNP interaction sites used previously for fullerenes. 68 A similar mapping has also been employed previously for capped carbon nanotubes. 50 We modeled open CNTs with a polar end-group functionalization (typically -OH groups) by employing a more polar interaction site (SNda beads) for the rims (Figure S7). 69 Bonded interactions between neighboring beads were modeled with a bond length of a = 0.47 nm and a force constant of 5000 kJ mol−1 nm−2 , similar to the model for capped nanotubes. 50 The CNTs consist of 30 rings with 10 beads each, resulting in a total length of 11.8 nm and a diameter of 1.5 nm. Angle potentials along the rings were modeled with a force constant of 350 kJ mol−1 rad−2 . The equilibrium angle α = π(N − 2)/N depends on the diameter of the CNT, as determined by number N of beads per ring (here: N = 10). Previous CNT models had additional long-range bonds between distal rings to account for the stiffness of capped CNTs. We found that in the absence of capped structures, they failed to maintain the equilibrium shapes and were bent in lipid simulations. Here, stiffness along the tube was maintained by introducing improper dihedral angle potentials that maintain √ the angle between two adjacent triangles near the target value of β = 2 cos−1 [tan(π/2N )/ 3] with a force constant of 350 kJ mol−1 rad−2 (Figure S7). 69

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Table 1: Simulation setups in studies of CNT-mediated vesicle fusion. In the control simulations, POPC vesicles were simulated at close proximity with and without harmonic restraints on their center of mass-distance. setup

lipid type

lipid molecules

total beads

simulation time (ns)

Setup A

POPC DOPC DSPC POPC POPC POPC POPC DSPC DOPC DOPCa POPC POPC

4031 4032 4035 2438 4031 1183 1980 1983 2016 6666 2500 4096

202480 202587 231039 124042 219603 39632 85810 75844 115152 329881 102451 215234

1000 1000 1000 500 1000 500 500 220 500 5000 10000 5000

Setup B

Control a

vesicle diameter (nm) 15 15 15 11.5 15 11.5 15 15 15 28 11.5 15

simulations

fusion events

10 1 1 100 100 100 100 1 1 10 2 2

10 1 1 100 99 97 95 1 1 0 0 0

simulations at 350 K.

Kinetics of CNT-mediated fusion. For the small vesicles studied here, the whole fusion process was completed in a few hundreds of nanoseconds to a couple of microseconds (see Supplementary Movie S1 and S2). Owing to the smoother energy landscape of the MARTINI model, diffusion and other dynamic processes tend to speed up by factors of four to eight when compared with experiments and atomic simulations. 42 Here, we always refer to simulation ("MARTINI”) time, without rescaling, when discussing timescales. We record the times of forming the fusion-stalk (t1 ), the hourglass shape (t2 ), and the fusion pore (t3 ). Since the transit through these phases is sequential and directional (i.e., t1 < t2 < t3 ), we modeled the kinetics of each of the three sequential transitions between the states along the fusion pathway as independent Poisson processes (see, e.g., ref 70) with added lag times. Stalks form at times t1 = τ1 + t′1 ; hourglass shapes at times t2 = t1 + τ2 + t′2 ; and fusion pores at t3 = t2 + τ3 + t′3 . The constant lag times τi (i = 1, 2, 3) capture initial relaxation phases. The times t′i (i = 1, 2, 3) for the three Poisson processes are distributed exponentially with rates ki . The resulting distributions of the times ti are thus

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p1 (t1 ) = k1 e−k1 (t1 −τ1 ) , p2 (t2 ) = k1 k2 [e−k1 (t2 −τ12 ) − e−k2 (t2 −τ12 ) ]/(k2 − k1 ), and p3 (t3 ) =

k1 k2 k3 e−k1 (t3 −τ123 ) k1 k2 k3 e−k2 (t3 −τ123 ) k1 k2 k3 e−k3 (t3 −τ123 ) + + (k1 − k2 )(k1 − k3 ) (k2 − k1 )(k2 − k3 ) (k3 − k1 )(k3 − k2 )

where t1 ≥ τ1 , t2 ≥ τ12 , and t3 ≥ τ123 with τ12 = τ1 + τ2 and τ123 = τ1 + τ2 + τ3 . We determined the characteristic times of forming fusion stalks (τStalk = 1/k1 ), hourglass shapes (τhourglass = 1/k2 ), and fusion pores (τFusion = 1/k3 ), and the associated lag times (τ1 , τ2 , and τ3 ), by sequential fits of the cumulative distribution functions for the above probability densities to the observed waiting time distributions. Corresponding Author *E-mail: (G.H.) [email protected] Author Contributions S.L., R.M.B., J.K. and G.H. designed the study. S.L. and R.M.B. performed the simulations and made figures. M.V. designed the coarse-grained CNT model. R.M.B., J.K. and G.H. wrote the manuscript. S.L. and R.M.B. contributed equally. All authors reviewed the manuscript. Notes The authors declare no competing financial interest.

Acknowledgement We thank Prof. A. Noy, Dr. A. Bahrami and Dr. R. Covino for inspiring and insightful discussions. This work was supported by the Max Planck Society.

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Supporting Information Available Supplementary Figures S1-S11 with legends and Supplementary Texts S1-S4, Supplementary Movies SM1 and SM2 are provided in a separate files.

This material is available free of

charge via the Internet at http://pubs.acs.org/.

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