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Impact of Shock-Induced Lipid Nanobubble Collapse on a Phospholipid Membrane Dan-dan Sun, Xubo Lin, Zuoheng Zhang, and Ning Gu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b04086 • Publication Date (Web): 03 Aug 2016 Downloaded from http://pubs.acs.org on August 4, 2016

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The Journal of Physical Chemistry

Impact of Shock-Induced Lipid Nanobubble Collapse on a Phospholipid Membrane Dandan Sun†‡, Xubo Lin†§, Zuoheng Zhang†‡ and Ning Gu†‡*

†State Key Laboratory of Bioelectronics and Jiangsu Key Laboratory for Biomaterials and Devices, School of Biological Science & Medical Engineering, Southeast University, Nanjing 210096, China ‡Collaborative Innovation Center of Suzhou Nano-Science and Technology, Suzhou Key Laboratory of Biomaterials and Technologies, Suzhou 215123, China §Department of Integrative Biology & Pharmacology, Medical School, The University of Texas Health Science Center at Houston, Texas 77030, USA

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ABSTRACT：Lipid-shelled nanobubbles have shown great potentials in drug or gene therapy. In order to better understanding the ultrasound-mediated interactions of lipid nanobubbles with plasma membranes at the molecular level, we investigated the effect of shock-induced lipid nanobubble collapse on a lipid bilayer using coarse-grained molecular dynamics simulations. We observed the collapse of lipid nanobubbles and the formation of water nanojets. The water nanojets could induce structural changes in membranes. When shock velocities were large enough, the deformed bilayers were hemispherical and water pores were generated. Both the nanojets and the membrane deformations depended on the shock velocity and the initial lipid nanobubble diameter. In the recovery simulations, the bilayers were able to heal themselves, indicating that the bilayer poration was temporary. Besides, compared with the cases of vacuum nanobubbles, the lipid nanobubbles could weaken the effects of shock waves. All these molecular-level information from simulations will be useful for better biomedical applications of lipid nanobubbles.

INTRODUCTION As an important and widely used technique, ultrasound has been increasingly utilized in biomedical fields, such as ultrasonic imaging and hyperthermia.1-3 Nano- or microbubbles can serve as effective contrast agents to enhance the resolution of ultrasonic images.4-6 Besides, ultrasound in combination with nano- or microbubbles have been used to mediate drug or gene delivery.7-11 Ultrasound can enhance the uptake of molecules by increasing membrane


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permeability and generating temporary pores in membranes, which is defined as “sonoporation”. As reported in experiments, ultrasound intensity determines the mechanisms for bubble-induced sonoporation.10 At lower ultrasound intensity, bubbles oscillate steadily, which is known as stable or non-inertial cavitation. The forming micro-streams around bubbles exert shear stresses on membranes, leading to membrane poration. At higher ultrasound intensity, bubbles prefer expansion rather than contraction, which induces the bubbles rupture together with inrushing fluid. This phenomenon is called transient or inertial cavitation. During the violent and asymmetrical collapse of bubbles, shock waves are generated and liquid jets form. Experiments have proved that shock wave and liquid jets could generate high pressure and further induce membrane poration.12 Compared with stable cavitation, transient cavitation can induce larger pores, which facilitates the translocation of molecules with larger size across membranes.10 In addition, pore size is correlated with acoustic pressure and bubble size.10 The bubble shells also affect the sonoporation efficiency, and lipid-shelled bubble may be more efficient in drug delivery.13-16 It is reported that nanobubbles are more promising than microbubbles.17 Therefore, we attempt to clarify the interactions between lipid-shelled nanobubbles and cell membranes. Numerous experiments and simulations have concentrated on the collapse behavior of bubbles.18-23 High-intensity ultrasound will produce shock waves and liquid jets. The shock waves progress and act on the surrounding objects. Although it is difficult to model the ultrasound in molecular dynamics (MD) simulations, computational tools have been used to study the effects of shock wave on nanobubbles and lipid membranes.24-33 Koshiyama et al.


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firstly simulated shock waves by adding additional uniform momentum to water molecules, and further study the interactions of shock waves with membranes.24 The results showed that shock waves induced large structural changes to membranes and facilitated water molecules to cross the bilayers. Furthermore, all-atom (AA) MD simulations were applied to explore the poration of lipid bilayers by shock-induced nanobubble collapse.26 They created shock wave using a momentum mirror approach and reported the formation of nanojets and the poration of bilayers. In addition, Santo et al. constructed larger scale systems by coarse-grained (CG) models, making a thorough inquiry into the poration of membranes by shock-induced nanobubble collapse.27,28 Adhikari et al. performed MD simulations and calculated pressure distributions to understand the mechanism of membrane poration in the presence or absence of nanobubbles.29 Using simulated results of nano-scale systems, Fu et al. built a quantitative model to bridge the microscopic simulations and the macroscopic experiments.30 However, to the best of our knowledge, there are no MD simulations that concentrate on the role of shock wave in the interactions of lipid nanobubbles and lipid membranes. Given the remarkable advantages of lipid-shelled bubbles in drug or gene delivery10, we use CGMD simulations to fill this gap, and try to put forward a perspective on the applications of lipid nanobubbles. In the current work, details about the preparation of lipid nanobubbles are described in the Supplementary Information (Figure S1). Effects of shock waves with various intensities on the interactions between lipid nanobubbles of different sizes and lipid membranes were


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systematically studied. Our results well capture the influence of lipid shell of bubbles, which may provide useful insights for the potential biomedical applications of lipid nanobubbles.

SIMULATION METHODS CGMD simulations can access larger time and length scales compared with AAMD simulations. For all our simulations, MARTINI CG force field34,35 was employed. MARTINI model is one of the most appealing CG models for biomolecular systems36,37, especially for biomembrane systems34. We chose a simple lipid molecule, dipalmitoylphosphatidylcholine (DPPC), to constitute lipid membranes and lipid nanobubbles. DPPC and water molecules have been defined in MARTINI force field.34 Shock waves were generated by using the methods of Choubey et al21,26. A 2 nm vacuum layer was inserted at the distal side of the simulation box in the z direction. Then all the particles were set a constant velocity (up) in the -z direction towards the momentum mirror positioned at z = 0 nm. When molecules reached the momentum mirror, the velocities of the molecules were reversed, inducing a shock wave propagating along the +z direction. Pressure and temperature coupling were turned off in the shock simulations. Periodic boundary conditions (PBC) were imposed in the x and y directions and turned off in the z direction. We employed shock simulations of pure water system to validate the feasibility of the MARTINI force field. A system containing 178963 CG water molecules was equilibrated in the isothermal-isobaric (NPT) ensemble. The dimension of the equilibrated water system was 20.5 ×


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20.58 × 51.45 nm3. Then the system was subjected to shock wave with particle velocities up (= 0.4 - 3.0 km/s), respectively. The shock front was defined as the discontinuity in mass density of water molecules along the z direction. The lipid shells of lipid microbubbles were monolayer in experiments.38,39 In our simulations, lipid nanobubbles with diameters 20 nm or 30 nm were created by aligning lipid molecules in homogeneous spherical configurations (Figure S1). We used an experiment value of area per lipid of a DPPC bilayer40, 0.63 nm2, to estimate the number of DPPC molecules at the surface of the lipid nanobubble with diameter 20 nm and it was about 1993. These DPPC molecules were homogeneously distributed with a monolayer configuration at a spherical surface, constituting a lipid nanobubble. The simulation box was 32 × 32 × 32 nm3 and solvated with water molecules. After solvating, we would delete some water molecules to insure no water molecules in the cavity of the nanobubble. Energy minimization and equilibration simulations in the canonical (NVT) ensemble were performed. However, the nanobubble distorted and parts of lipid molecules spilled, indicating that the molecular density was high. Subsequently, we reduced the DPPC molecule numbers and conducted multiple pre-equilibration simulations to determine the appropriate number of lipid molecules. The final equilibrated system contained 1815 DPPC molecules and 267997 CG water molecules. A lipid nanobubble with diameter 30 nm containing 4102 DPPC molecules was obtained as well.


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Table 1. Details of shock simulations. The initial system without lipid nanobubbles contained 4608 DPPC molecules and 1117919 water molecules. For the simulation where D = 20 nm and up = 0.1 km/s, the lipid nanobubble didn’t collapse, thus its simulation parameters were not shown here.

A lipid bilayer system containing 4608 DPPC molecules and 1117919 CG water molecules was assembled by enlarging a 128 DPPC bilayer to 36 fold and solvating with water molecules. The system was energy-minimized and subjected to an equilibration simulation of 200 ns. The equilibration simulation was under the NPT ensemble and periodic boundary conditions. The temperature was controlled with Berendsen coupling, keeping at 323 K, and the coupling time was 1.0 ps. The pressure was controlled with semiisotropic pressure coupling (Berendsen


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coupling scheme, a coupling constant of 4 ps, and a compressibility constant of 3×10-5 bar-1). The dimension of the final equilibrated system was 38.12 × 38.12 × 97.73 nm3. To study the interaction between a lipid nanobubble and a lipid bilayer exposed to shock wave, two sizes of lipid nanobubbles were embedded respectively in the vicinity of the lipid bilayer by deleting overlapped water molecules. Lipid nanobubbles were about 3 nm away from the surface of the bilayers (Figure S2). Afterwards, two equilibrated systems containing a DPPC bilayer and different sized lipid nanobubbles were prepared, respectively. We conducted a number of non-equilibrium shock simulations with two sizes of lipid nanobubbles (D = 20, 30 nm) and variant particle velocities (0.1 -1.0 km/s). Shock waves were instantly generated as soon as the simulations started, propagated in the +z direction and hit the lipid nanobubbles. The lipid nanobubbles collapsed gradually, producing liquid nanojets to affect the bilayers. Details of the shock simulations are summarized in Table 1. We observed that water jets caused the formation of pores in the bilayers when the shock velocities were large enough. However, no membrane poration appeared in the simulations with smaller shock velocities. Moreover, we carried out recovery simulations to evaluate the deformations of the bilayers. We cut out parts of the after-shocked systems containing the bilayer sandwiched between 2 layers of water molecules to constitute new recovery systems. Recovery simulations in the NPzAT ensemble (constant normal pressure, constant lateral area, and constant temperature) were performed to keep the lateral dimensions and the pressure along the z direction constant. Berendsen coupling schemes for both pressure and temperature (323 K; 1.0 ps


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coupling time) were used. The pressure in the z direction was 1 bar and the compressibility in the lateral direction was zero. A time step of 20 fs and a simulation of 90 ns were adopted. Table 2 displays the details of the recovery simulations.

Table 2. Details of recovery simulations. We implemented recovery simulations for the systems which had obvious bilayer deformations.

All simulations were carried out by the GROMACS 4.5.4.41 All simulations were visualized using Visual Molecular Dynamics (VMD).42 All graphs were plotted using MATLAB software.

RESULTS AND DISCUSSION Planar shock waves were generated and traveled along the +z direction in the shock simulations of pure water systems. As Santo et al.27 reported, we calculated the shock velocity (us) to


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determine its relationship with the particle velocity (up). Figure 1 shows the correlation between us and up from the experiments43, AA simulation26, CG simulations by Santo et al.27 and Ours. When up is below 1.0 km/s, our results are in reasonable agreement with experiments43 and simulations26,27. The following simulations were performed in this range of velocities. Even though there is a discrepancy between CG and experimental results, the CG results still satisfy the Rankine-Hugoniot relationship44.

Figure 1. Shock velocity (us) as a function of particle velocity (up). Red, blue, green, and magenta curves represent CG simulation (Ours), CG simulation (by Santo et al.27), experimental (by Rybakov43) and AA simulation (by Choubey et al.26) results, respectively.


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After confirming the validity of the MARTINI force field in shock simulations, we investigated the effect of shock-induced lipid nanobubble collapse on lipid bilayers. Multiple pre-equilibration simulations were performed to obtain lipid nanobubbles with diameters 20 nm or 30 nm. The diameter of 20 nm or 30 nm, called outer diameter, was defined as twice the average distances between the phosphate beads (PO4, Figure S2) and the center of mass of the nanobubbles. A lipid bilayer containing 4608 DPPC molecules was prepared. The bilayer thickness was 4.04 nm and the area per lipid was 0.63 nm2, which were agreed with the experimental values40,45. Lipid nanobubbles were placed near the lipid bilayer and two equilibrated systems were obtained, each of which contained a lipid nanobubble (D = 20 nm or 30 nm) and a lipid bilayer. We performed a series of shock simulations as detailed in Table 1. Shock waves were realized by a momentum mirror and the particle velocities ranging from 0.1 - 1.0 km/s. The shock waves would accelerate the surrounding water molecules toward the center of the lipid nanobubbles and promote the implosion of the lipid nanobubbles, inducing the formation of water nanojets. The liquid jetting phenomenon caused by the shrinkage of bubbles has been remarked in experiments18,19 and simulations26,27. In the system where D = 20 nm and up = 0.1 km/s, we couldn’t observe the collapse of the nanobubble until the shock simulation terminated. Table 1 didn’t show the data for this case. Oppositely, lipid nanobubbles completely ruptured in other systems. Table 1 summarizes the nanobubble collapse times in various systems, inferring


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that the collapse of lipid nanobubbles depend on the shock velocities and the initial lipid nanobubble diameters.

Figure 2. Velocity distributions of water particles in the yz plane for the system with D = 30 nm and up = 0.7 km/s. Arrows indicate the directions of particle velocities and colors indicate the velocity magnitudes. White regions represent the location of lipid molecules (the lipid nanobubble or the lipid bilayer). (a) 19 ps, just before the complete collapse of the lipid nanobubble; (b) 23 ps, the water nanojet hit the bilayer.

Figure 2 displays the velocity distributions of water particles for the system with D = 30 nm and up = 0.7 km/s. The processed region was 1 nm slab in the middle of the system. The velocities were averaged in voxels of dimension 1 nm. Figure 2a shows that water molecules


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around the shrinking lipid nanobubble changed directions and gathered toward the distal edge of the nanobubble. The gathering water molecules formed a water nanojet. As the nanojet moved towards the bilayer, the velocities of particles in the nanojet increased. Once the particles in the nanojet encountered the bilayer, their velocities reduced. The velocities of the particles in the nanojets are influenced by the shock velocities and the initial lipid nanobubble diameters. Table 1 presents the maximum particle velocities in nanojets. For these systems with D = 30 nm, as up increased from 0.4 km/s to 1.0 km/s, the maximum velocities of particles in nanojets increased from 2.55 km/s to 3.93 km/s; similar values were submitted by Santo et al.27. Furthermore, the averaged nanojet velocities increased with the increase of initial nanobubble diameters and shock velocities (see the Supplementary Information). Figure 2b manifests the impact of the nanojet on the lipid bilayer and also shows a spreading flow. Figure 3 is the water density distributions along the yz plane for the system with D = 30 nm and up = 0.7 km/s. The density values were averaged over a 10 nm slab in the middle of the system. The left blue region suggests the morphological evolution of the lipid nanobubble. The right blue region presents the lipid bilayer. The discontinuity in the density distributions is identified as the shock wave front and the red regions represent the shocked regions. Figure 3a depicts that the shock wave travelling along the +z direction arrived at the proximal edge of the lipid nanobubble and started to pressure the lipid nanobubble. Obviously, the densities of the particles in the water nanojet are higher than that of the unshocked regions. Figure 3b shows that the lipid nanobubble completely collapsed. When the proximal side of the lipid nanobubble


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bended and ran into the distal side, we defined that the lipid nanobubble completely collapsed. At this moment, the intracavity of the lipid nanobubble disappeared and the lipid nanobubble ruptured as a distorted lipid sheet. We also observed that the lipid nanobubble had a shielding effect on the lipid bilayer, resulting in a concave shock wave front. The similar shield phenomenon has been put forward by Santo et al., where the bubble 1 acted as a shield for the bubble 2 and the membrane.28 The formed water nanojet hit and deformed the lipid bilayer. When D = 20 nm, up < 0.6 km/s or D = 30 nm, up < 0.4 km/s, the bilayers experienced slight compression, but they didn’t show obvious deformation. Apart from these systems, other bilayers deformed evidently and membrane pores formed. Figure 3c shows the lipid bilayer deformed with a hemispherical shape. As a result of the secondary shock26,28, the shock wave had a convex front. Nevertheless, the shock front regained a planar surface at 33 ps. The deformations in the bilayers included the bending of bilayers and the formation of holes in the bilayers. Table 1 displays the particle velocities and the initial nanobubble diameters that bilayer deformations required. When D = 20 nm, up ≥ 0.6 km/s or D = 30 nm, up ≥ 0.4 km/s, the bilayer deformations were visible and holes appeared in the bilayers. Santo et al. proposed that the deformation of a 12800 DPPC bilayer occurred when D = 20 nm and up ≥ 0.4 km/s27, however, our 4608 DPPC bilayers deformed when D = 20 nm and up ≥ 0.6 km/s. The nanobubble shell influences the interactions between bubbles and cell membranes, which has been involved in experiments13.


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Figure 3. Two-dimensional density distributions of water particles in the yz plane for the system with D = 30 nm and up = 0.7 km/s. (a) 6 ps, just before the shock wave compressed the lipid nanobubble; (b) 19 ps, the lipid nanobubble completely collapsed; (c) 29 ps, shock wave had passed through the bilayer.

Figure 4 offers the deformed bilayers for two systems with up = 1.0 km/s and D = 20 nm or 30 nm. The lipid nanobubbles became distorted lipid sheets and the impacted lipid membranes presented hemispheres. The larger nanobubble (Figure 4b) induced a more serious deformation than the smaller one (Figure 4a). The top views (Figures 4c - d) distinctly visualize the pores in


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the bilayers. The regions in red boxes are enlarged to provide highlight of the pores. Besides, we did an analysis of the Voronoi Tessellation for enlarged regions to identify the pores. Numerically, Table 1 provides the estimated areas of holes in the bilayers after shock wave passed across the bilayers. The areas of pores were calculated by dividing the impacted region of the bilayer into pixels of 0.2 nm and counting the number of empty pixels having no lipid molecules. The area values suggest that the deformations of bilayers relate with the shock velocities and the initial nanobubble diameters. In the system where D = 30 nm and up = 1.0 km/s, the area of the largest pores was 133.08 nm2, which was 9.1% of the total bilayer area. For the system where D = 30 nm and up = 1.0 km/s, the bilayer had the largest deformation, however it was still integrated. We also studied the recovery of the systems after the shock simulations. The new recovery systems containing the bilayer and the collapsed nanobubble and adjacent water layers were took out from the after-shocked systems. During the recovery simulations under the NPzAT ensemble, membrane holes became larger very quickly, then shrank slowly, and finally disappeared, inducing stable planar bilayers. Table 2 lists the maximum sizes of holes and the recovery time of the distorted bilayers. The results reveal that the more strongly the shock wave impacted, the slower the bilayer recovered. In our simulations, no lipid molecules were divorced from the bilayers and dissociated in the solutions, which was different from Santo et al.27. It may be attributed to the presence of lipid molecules at the surface of lipid nanobubbles. Santo et al. created vacuum nanobubbles by removing water molecules from a spherical region, whereas, our


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nanobubbles were hollow lipid nanobubbles. Although our results are nearly identical with Santo et al.27, the role of lipid molecules is non-negligible. Our ruptured lipid nanobubbles became distorted lipid sheets, affecting the intensity of the nanojets. It should be responsible for smaller deformations of the bilayers compared with Santo et al.27. As expected, the smaller membrane pores also demonstrated the role of lipid molecules in relieving the impact of shock wave.

Figure 4. Snapshots of lipid bilayers after shock wave impacted. (a) and (c), 28 ps of the shock simulation with D = 20 nm and up = 1.0 km/s; (b) and (d), 29 ps of the shock simulation with D = 30 nm and up = 1.0 km/s. (a) and (b) are cross-sectional views; (c) and (d) are top views.


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For three systems where D = 30 nm and up = 0.8 - 1.0 km/s, we found that some lipid molecules left the collapsed lipid nanobubbles and integrated into the lipid bilayers. Figures 5a c record the phenomenon that some lipid molecules of the nanobubbles became a part of the bilayers. The reason is that the central lipid molecules of the severe distorted nanobubbles squeezed into the bilayers owing to the systems expanded in the z direction. The number of lipid molecules which integrated into the bilayers were 3, 39 and 144 for the systems with D = 30 nm and up = 0.8 - 1.0 km/s, respectively. Since the number of lipid molecules was small compared with the 4608 DPPC molecules of the bilayers, the bilayers were planar on the whole. The area per lipid (APL) of the bilayer can be simply estimated by dividing the cross-sectional area of the simulation box by the molecule number of the monolayer. The maximum decrease of the APL was in the proximal monolayer of the system with up = 1.0 km/s and D = 30 nm and it was 4.8%. We also calculated the local curvature27of the bilayer in the system with up = 1.0 km/s and D = 30 nm (Figure S4). The lipid molecules integrated into the bilayer did not cause a drastic change for the local curvature of the bilayer. Additionally, we followed the recovery of lipid nanobubbles in the NPzAT ensemble. We found that the distorted lipid sheets slowly inflated to notched chambers, and eventually resealed as lipid vesicles. In our simulation of 90 ns, the lipid vesicles were stabilized and no disruption. For two systems, Figure 5 clearly presents the formation of lipid vesicles for the corrupted lipid nanobubbles.


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Figure 5. Snapshots of recovery simulations with D = 30 nm and up =1.0 km/s at (a) 0 ns, (b) 20 ns, (c) 50 ns. For (a) - (c), two colors are used to distinguish the lipid molecules of the lipid nanobubble and the lipid bilayer. The lipid molecules belonging to the lipid nanobubbles are represent as blue beads, and those belonging to lipid bilayers as cyan beads. Snapshots of recovery simulations with D = 20 nm and up = 1.0 km/s at (d) 0 ns, (e) 10 ns, (f) 21 ns. For (d) (f), the lipid tail groups are shown as cyan beads, GLY as green beads, the lipid head groups as the tan and blue beads. All the water molecules are pink beads.

Though the holes transiently existed in the recovery of lipid bilayers, water molecules could diffuse through those large enough holes. We tracked the water molecules initially located at one side of the bilayers. Figure 6 shows the headgroups of the bilayer and water molecules which were initially between the origin and the bilayer in the system with D = 30 nm and up = 1.0 km/s. Figure 6a is the initial configuration before shock simulation. The bilayer bended and water


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molecules appeared in the hydrophobic tails region at 29 ps of the shock simulation (Figure 6b). Figure 6c is the snapshot at 2 ns of the recovery simulation, exhibiting 2742 water molecules permeated through the bilayer. The number of migratory water molecules increased with the increase of shock velocities and initial nanobubble diameters. Table 2 posts the number of permeated molecules for different systems. As mentioned above, lipid molecules at the surface of the nanobubbles also induced a smaller amount of transported water molecules.

Figure 6. The headgroups of the DPPC bilayers and the water molecules initially located at the left of the bilayer are displayed. The headgroups are shown in blue, and water molecules are shown in pink. Here D is 30 nm and up equals to 1.0 km/s. (a) The initial configuration before shock simulation, 0 ps. (b) 29 ps of the shock simulation when shock wave had passed the bilayer. (c) 2 ns of the recovery simulation.


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The influence of ultrasound or shock wave on membranes has been discussed extensively in both experiments and simulations, in absence or presence of bubbles. Koshiyama et al. examined the structural changes of bilayers under the action of shock wave. However, they didn’t observed pores in membrane.24 As a key factor, bubbles play a vital role in the interaction of membranes with shock wave. Both AAMD and CGMD simulations have revealed the poration of membranes by shock-induced nanobubble collapse.26,27 Why is there no pores formation in the membrane with only shock wave, but the membrane poration occurs when a bubble is added? The reason explained by Adhikari et al. was that an unequal distribution of pressure would create an unbalanced stress on the membrane, inducing membrane poration.29 Currently, we introduce the lipid nanobubble to probe its impact on membranes under shock wave exposures. We found that weaker membrane poration than Santo et al.27 when the shock impulse and the bubble dimension were the same. The presence of lipid molecules at the surface of lipid nanobubbles may be a reasonable interpretation that undermines the pressure of nanojets on membranes. Experiments have also explicated a higher acoustic intensities for lipid-shelled bubbles to respond compared with gas bubbles.10,46 On the other hand, attention should be paid to the difference between the theoretical simulations and the macroscopic experiments. It has been reported that the impulse of ultrasound could determine the quantity of drug/gene transported across membranes.12,47 In experiments, the bubble diameters range from 10 to 100 µm, but it is prohibitively expensive to model such bubbles in simulations. In view of nano-scale bubbles and a small patch of model membranes in


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simulations, the impulse of shock wave (i.e., the pressure integrated over time) used in simulations is relatively weak compared with that in experiments.24,30 Therefore, further investigations should been proposed to bridge the microscopic simulations and macroscopic experiments. Fu et al. used the simulation results in nano-scale systems to built a quantitative model (IA = 0.0033D1.15; IA, the average impulse per unit area; D, the nanobubble diameter), rationalizing experimental measurements.30 For our systems, more different sizes of nanobubles will be simulated to establish a reasonable model, which is applicable to both simulations and experiments.

CONCLUSIONS In the current work, we performed CGMD simulations to study the effects of shock-induced lipid nanobubble collapse on model membrane. When the planar shock fronts hit the proximal side of the lipid nanobubbles, the lipid nanobubbles were forced to collapse and ambient water molecules were accelerated toward the center of the bubbles, forming water nanojets. Since the lipid bilayers were close to the lipid nanobubbles, the water nanojets caused membrane deformations. The nanojets and the deformations of bilayers enhanced as shock velocities and lipid nanobubble diameters increased. Pores appeared in bilayers when the shock velocities were large enough. Lipid-shelled nanobubbles would soften the nanojets and the effects on lipid bilayers compared with Santo et al.27. Such poration in membranes allowed water molecules to cross the bilayers. Moreover, we performed recovery simulations and observed that the


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membranes could heal. In particular, there were water molecules transporting through the transient holes. The number of diffused water molecules was correlated with the shock velocity and the initial nanobubble diameter. The study may provide insights into the biomedical applications of lipid nanobubbles.

ASSOCIATED CONTENT

Supporting Information The preparation of lipid nanobubbles, the schematic of simulation systems, the calculation of averaged nanojet velocity and the local curvature of bilayers are described in detail. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

Corresponding Author *Tel: +86(0)25-83272476. Fax: +86(0)25-83272460. E-mail: [email protected]. Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS


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The research was supported by grants from the National Key Basic Research Program of China (2013CB934400), the National High Technology Research and Development Program (“863” Program) of China (2013AA032205), the National Natural Science Foundation of China (NSFC) for Key Project of International Cooperation (61420106012), the Natural Science Foundation of Jiangsu Province BK20130608.

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