Numerical evaluations of membrane poration by shockwave induced multiple nanobubble collapse in presence of electric fields for transport through cells

Electric pulses can be used to create pores in biological cell membranes, which then function as pathways for cellular material transport. This effect was termed “electroporation”, and technically dates back about two hundred years.¹ Over time, several researchers hypothesized that membrane electroporation may also explain the electrical conductivity changes in nerves.² Much later, Neumann and colleagues³ used pulsed electric fields to temporarily permeabilize cell membranes to deliver DNA into cells. Progress was much faster thereafter, and in the following decade, novel clinical applications such as electrochemotherapy,^4,5 drug/gene delivery^6,7 and controlled immuno-therapy⁸ emerged. Many recent applications involve the use of high intensity (∼50-100 kV/cm), nanosecond duration pulsed electric fields. This modality has been shown to help shrink tumors,⁹ triggered intra-cellular calcium release,¹⁰ activate platelets for wound healing,¹¹ and temporary block action potential in nerves.¹² The non-thermal nature of this excitation affords treatment in close proximity to sensitive organs.¹³ Furthermore, the use of such short-duration, high-field pulses circumvents issues such as muscle contraction, burns, and unpleasant sensations when applied in vivo.

The interaction of shock waves with biological cells is a relative recent area of active research.^14–16 Examples include water purification and desalination,^17,18 and bacterial decontamination.¹⁹ Controlled shock waves also have great potential for biomedical use, since they can also permeabilize cell membranes thereby allowing for the transport of various macromolecules, drugs and genetic material into cells.²⁰ Other uses of shock waves include extracorporeal shock wave lithotripsy (ESWL) to treat kidney stones below 20 mm in size, or destruction of cancer cells.¹⁹ Shockwaves which carry high energy, promote nanobubble collapse in fluids, which can then generate “nanojets” at very high speeds.^21–23 The nanojets impinging on cell membranes facilitate poration within picosecond time scales. The presence of a nanobubble presents a site of scattering and pressure amplification in a directed manner. The incident energy, which initially is spread over a planar volume, squeezes the bubble leading to its collapse, and creates a localized microsource. Thus, a conversion into a spatially nonuniform pressure distribution takes place, with generation of concentrated force on the membrane for more efficient poration. The effect of shock waves could be enhanced or engineered by varying the bubble sizes and/or their distances from the vicinity of the membrane. However, this aspect is beyond the present scope.

A recent report analyzed a potentially synergistic scheme of porating cell membranes through the use of both electric fields and shockwaves.²⁴ The dual input could in principle, speed up the poration, or lead to larger nanopores, or help reduce time delays, and/or the electric field magnitudes required for poration. An important point in this regard is that fields associated with electric pulses are generally better able to penetrate cells at locations close to the electrodes. This occurs because the field magnitudes tend to fall off quickly with distance. On the other hand, pressure waves incident on nano-bubbles could be used to generate nanojets at desired locations, and be a modality for supplemental directed effects. Furthermore, the shockwave based sonoporation could even be used for “pretreating” cell membranes for a greater electroporative response. Advantages of such a dual strategy would be to reduce voltage requirements on the circuitry, mitigate collateral electrical damage, and possibly create larger pores more quickly. Furthermore, a dual strategy would lower the pressure requirement for shockwaves, and circumvent the potential for irreversible large area poration.

Simulations and predictions of such a dual strategy²⁴ were carried out for cases of a single nanobubble. In this contribution, Molecular Dynamics (MD) simulations are performed to probe the poration with multiple nano-bubbles for the dual strategy. This would be a more realistic situation, since in practice, one would not expect a solitary bubble, but rather a distribution that might have been created or be pre-existing in the liquid. The evolution of membrane poration for non-overlapping bubbles, scenarios with bubbles having partial overlap above the membrane, and configurations with serial bubbles in tandem are all evaluated here. The simulation scheme, the results obtained, and related discussions are given in the following sections.

The MD method is superior to continuum approaches, and offers some advantages such as: (i) appropriate inclusion of the collective, many-body interaction potentials at the nanoscale level; (ii) dynamical screening; (iii) avoidance of the “mean-field” approximations; (iv) a natural inclusion of noise and statistical fluctuations; (v) self-consistent and dynamical transport calculations without arbitrary fitting parameters; and (vi) easy incorporation of arbitrary defects, nonuniformities and complex geometries. However, this technique does have its own shortcomings and cannot be applied for simulations in all situations. Some of the limitations of MD include: (i) Inability to simulate long time scales due to the computational complexity. At this time, simulations typically tend to over durations less than 100 ns. Hence, many of the important phenomena such as pore resealing or their stabilization, or biophysical changes in the cellular structure, morphology or cytoskeletal changes cannot be simulated. (ii) The computational burden similarly restricts the simulation size to nanometer length scales. Consequently, membrane patches are usually simulated, rather than complete cells or even sub-cellular structures. (iii) The atomic motion and interatomic interactions are classical in nature, based on Newtonian mechanics. Hence role of possible electron tunneling or dynamic changes in the energies of the system (as might be possible from techniques like Time Domain Density Functional Theory) are excluded.

Poration of the cell plasma membrane was probed based on atomistic Molecular Dynamics (MD) simulations. Both shock waves and an external electric field were included. Such a dual strategy has been suggested previously for enhancing gene transfer or anti-tumor treatment.²⁵ Since the method has been detailed elsewhere,²⁴ it is only reviewed here very briefly. The GROMACS simulator²⁶ was used with a with a 2 fs time step for a dipalmitoyl-phosphatidylcholine (DPPC) bilayer membrane patch. The MD cell for the numerical simulations were chosen to have dimensions of 13.51 nm x 13.56 nm x 32.98 nm, with over 0.5 million atoms in the system. The DPPC membrane system had 512 DPPC lipid and 172,302 SPC water molecules. A 13 nm thick layer of water was added to the system above the DPPC membrane to accommodate the creation of a nanobubble. The radius of the nanobubble was chose to be 4 nm. The pressure wave was initiated by assigning fixed velocities along the negative z-axis to the topmost two layers of water molecules. The downward motion of the water molecules comprising the shockwave, then creates pressure on the nanobubble, and leads to its subsequent collapse. A schematic of the simulation setup is shown in Figure 1. This, in turn, produces a nanojet incident on the DPPC membrane. With the nanobubble present, strong pressure distributions can be created.

Figure 2 shows a MD simulation result for the temporal evolution of the combined bubble-aqueous-membrane system, and the process of nanobubble collapse. The lipid membrane is located roughly over the central portion of the figure, and is surrounded by water. The central dark circular area above the membrane denotes a single bubble. The radius of the nanobubble was 4 nm. Snapshots at four different times of 0 ns, 1.8 ps, 2.6 ps, and 3 ps are shown in Figures 2(a)–2(d), respectively. The light blue areas represent the water density. Clearly over time, the bubble collapses, and the pressure wave propagates downwards onto the membrane. The bubble collapse generates a focused pressure wave and helps concentrate the mechanical energy onto the membrane.

Molecular Dynamics (MD) simulations of poration with multiple nano-bubbles were carried out. Since nanobubbles might be pre-existing or can be created by external means, one would practically expect a distribution of these entities, rather than the occurrence of an isolated bubble. One can envision three separate scenarios: (a) separated and non-overlapping bubbles, (b) bubbles with partial overlap above the membrane region, and (c) serial bubbles located in tandem above the membrane. Figure 3 shows MD results obtained starting with two 3 nm bubbles side to side (i.e., in a parallel configuration) at the same height from the membrane patch. There was thus no overlap between the two bubbles. The initial velocity of the water molecules was taken to be -4 km/s (a representative value associated with the shockwave), and an electric field of 0.2 V/nm was applied after passage of the shockwave. The snapshots of the lipid membrane patch at time instants of 0 ns, 1 ns, 2 ns, and 4 ns from the start of the electric pulsing, are shown in Figures 3(a)–3(d), respectively. At the 1 ns instant, the beginnings of two nanopores can be seen in Figures 3(b). The result at 2 ns reveals the pores becoming more prominent and better defined. The state at t=4ns shown in Figure 3(d) clearly reveal two distinct pores of dissimilar shape and size. The dimensions of the left pore in Fig. 3(d) were 2.8nm x 1.6 nm, while that on the right had dimensions of 4.7 nm x 2.8 nm. It is thus apparent that within a relatively short time of 4 ns, two nanopores spaced quite close to each other can be formed. This scenario of multiple nanopores close to each other, is in keeping with the notion of “supraporation”.²⁷ It is, therefore, expected that the use of multiple bubbles will likely enhance the pore density and hence, lead to stronger material throughout into cells. Furthermore, it may be noted that almost all other MD simulations of electroporation in the literature have only yielded a single nanopore in a membrane patch! The difference here in Fig. 3 was the presence of two separated bubbles which led to two nanojets incident on the membrane, and represents a new result. Hence, this combined strategy clearly seems to offer the high pore-density advantage.

Next, simulations were carried out for a serial (in tandem) nanobubble configuration. Qualitatively, one would not expect a significant advantage in having two 3 nm bubbles placed in tandem, since such a configurational geometry would effectively still provide one nanojet source. Results obtained from the MD results are shown in Figure 4. Snapshots obtained from simulation with both a shockwave with the -4 km/s initial velocity and a subsequent 0.2 V/nm electric field. The initial snapshot of Figure 4(a) shows two serial nanobubbles above the membrane patch. Figure 4(b) at a slightly later time of 1.6 ps, reveals the upper nanobubble collapsing, as a pressure wave begins to descend on the second bubble below. Results at the 22 ps instant show the perturbation and partial collapse of the membrane. Figure 4(d) is a 4 ns snapshot showing a single pore formation in the membrane with a size of 4.9 nm x 3.1 nm.

Finally, simulations were carried out for two nanobubbles having partial overlap. The initial bubble configuration is shown in Figure 5(a), and a slight off-set can be seen. At 20 ps pore initiation due to the incident shockwave begins as shown in Figure 5(b). The sideview at 20 ps reveals membrane bending and shockwave exiting the bilayer bottom. (d) A 1 ns snapshot, with the external electric field turned on, shows a slightly enlarged pore. This process continues as seen in Figure 5(e). Finally, the result of Figure 5(f) at 4 ns shows a much bigger pore having dimensions of 5.02 nm by 3.27 nm.

In the microscopic analyses discussed above, the shockwave was applied prior to electric pulsing. This sequence is similar to an actual sonoporation-electroporation technique reported for in vivo gene transfer.²⁸ Their result was an increased transgene expression, although the pulse durations were much longer than simulated here. Though quite dissimilar in pulse duration and with different objectives, the result by Yamashita et al. is mentioned here to underscore the potential benefit of the dual approach in a simple, qualitative way. It may be mentioned that the reversed sequence of an initial use of electric fields (rather than the shockwave) may not be the most effective strategy in the context of nanosecond pulsing. In this revered sequence, the shorter nanosecond pulsing would be applied first. It would help achieve a nonthermal response, and lead to a high density of small nanopores.²⁹ However, due to the smaller pore sizes, such pulsing would not easily facilitate the direct entry of drugs, external agents, genes, or large molecules into a cell. Furthermore, due to the short timescales, some of the nanopores might reseal prior to the onset of the pressure wave. Furthermore, with spatially confined field profiles, such nanosecond pulsing would not be very effective at herding molecules, genes, plasmid DNA, etc. from a large volume within the aqueous medium, towards the cell membrane. Instead, multiple pulses may have to be used to facilitate a more robust transport towards the cells. However, this might lead to heating and collateral thermal effects. On the other hand, the first-use of a pressure wave, might be helpful in initially herding larger amounts of materials towards the cell, thus better positioning them for cellular entry with guidance by subsequent electric pulsing.

Furthermore, a simultaneous combination of a pressure wave and electric stimulus might lead to even stronger benefits. However, since the electrical stimulation in the present case relies on ultrashort, nanosecond pulsing; this would require careful synchronization of the shockwave with the electrical input. This scenario, however, is beyond the present scope and would be studied separately. It may be added for completeness that the current experimental techniques are not at a stage and level, where some of the quantities (such as nanopores in this case), can be measured or imaged. Hence, the scientific development in this domain is usually guided by the physics and mechanistic-based processes and predictive outcomes, as presented in our contribution.

A final point that must be mentioned for completeness, is that the present simulations were carried out in a lipid membrane patch taken to be uniform without any inclusions. However, seminal work some years ago by the Ljubljana group^30,31 clearly showed that the presence of inclusions in cellular lipid membrane could work to stabilize pores. Without such inclusions, the pores would tend to shrink because of the line tension present at the pore rim. However, it was shown based on a mean-field approach that the presence of inclusions reduces the line tension and alters the free-energy through their interactions with the membrane.³⁰ In particular, anisotropic inclusions were shown to have a stronger stabilization effect. For small pores, the free-energy was shown to reduce by a few kT, while for charged membranes more dramatic reductions (leading to pore stability) were predicted on the basis of anisotropic inclusions in charged membranes. So it is conceivably that suitable introduction of inclusions could engineer even greater cellular throughput, by tailoring the degree of anisotropy inherent in the inclusions and/or the membrane charge.

This contribution builds on a previous report of using a dual strategy for material transport in biological cells that could reduce the voltage requirements and allow more compact electrical circuitry. It was shown that shockwaves could be used for “pretreatment” of cell membranes for electroporation. The possible role of multiple nanobubbles in strengthening the shockwave impact was probed. It has also been shown that not only would the multiple nanobubbles make it possible to create larger pores, but also increase the pore density on the surface of biological cells. The multi-pore scenario would be useful practically in enhancing material throughout into cells. Further optimizations could be envisioned by tailoring the shockwave and electrical pulsing parameters. Using bipolar versus monopolar pulses, or series versus simultaneous application of pulse trains,³² could be useful aspects to study in the future. In a similar vein, membrane engineering through introduction of inclusions^30,31 for longer lived nanopores could also be probed for even higher cellular throughputs.