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Interpretation of the molecular mechanism of the electroporation induced by symmetrical bipolar picosecond pulse trains
BBA - Biomembranes 1862 (2020) 183213
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Interpretation of the molecular mechanism of the electroporation induced by symmetrical bipolar picosecond pulse trains
T
Jingchao Tanga,b, Jialu Maa, Lianghao Guoa, Kaicheng Wanga, Yang Yanga, Wenfei Boa, ⁎ Lixia Yangc, Zhao Wanga, Haibo Jiangd, Zhe Wua, Baoqing Zenga, Yubin Gonga, a
School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan Province, China CNRS, UMR 7565, F-54506 Vandoeuvre les Nancy, France c School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore d Chengdu Institute of Biology, Chinese Academy of Sciences, Chengdu, Sichuan Province, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Electroporation Molecular dynamics Picosecond bipolar cancellation Symmetrical bipolar picosecond pulse trains
Picosecond pulse trains (psPTs) are emerging as a new characteristic diagnostic and therapeutic tool in biomedical fields. To specifically determine the stimulus provided to cells, in this article, we use a molecular dynamics (MD) model to show the molecular mechanisms of electroporation induced by symmetrical bipolar psPTs and predict a bipolar cancellation for the studied picosecond pulses. Electric field conditions that do not cause electroporation reveal that the interfacial water molecules continuously flip and redirect as the applied bipolar psPT reverses, and the molecules cannot keep moving in one direction or leave the lipid-water interface. Based on our simulation results, we determine the threshold for electroporation with symmetrical bipolar psPTs. For a fixed electric field intensity, a lower repetition frequency leads to more rapid electroporation. For a fixed repetition frequency, a higher electric field intensity leads to more rapid electroporation. We found that the water dipole relaxation time decreases as the electric field magnitude increases. Additionally, the influences of the symmetrical bipolar psPT intensity and frequency on the pore formation time are presented. Discrete nanoscale pores can form with the applied psPT at terahertz (THz) repetition frequency. When the psPT amplitude increases or the frequency decreases, the number of water bridges will increase. Moreover, for the first time, the molecular mechanism of bipolar cancellation for the studied picosecond pulse is discussed preliminarily. Our results indicate that the influence of the unipolar picosecond pulse on the interfacial water dipoles will accumulate in one direction, but the bipolar picosecond pulse does not cause this effect.
1. Introduction Permeabilization of cell membranes or membrane breakdown induced by an external electric field is a phenomenon often referred to as electroporation or electropermeabilization [1–4]. Electroporation allows the transport of impermeant molecules across cell membranes, and a wide range of applications have been found in biotechnological and medical fields, e.g., cancer therapy, DNA vaccination, gene regulation, tissue ablation and microbial deactivation [5–7]. Over a decade ago, it was reported that ultrashort (hundreds of nanoseconds) pulsed electric fields can induce apoptosis in human cells [8]. Compared to classical electroporation, where μs and ms pulses are used, it was suggested that the shorter pulses were more likely to target the membranes of internal organelles of the cell than were the longer pulses [9,10]. It has, for instance, been shown that sub-nanosecond
⁎
pulses can not only kill cancer cells [11,12] but also directly affect the mitochondria in HeLa cells and cause cell apoptosis through a mitochondrial-mediated pathway [12]. In addition, an advantage of the sub-nanosecond pulses is that they can be noninvasively applied to the tissue by an impulse antenna, which is different from the methods required for traditional ms, μs and sub-μs pulses [10,12]. THz fields have been found to strongly interact with biomolecular systems [13–15] and to substantially affect cell function [16–18]. Picosecond pulsed electric fields overlap with the THz spectrum regions, and as such, they may present great potential for applications in biorelated fields. The experimental technology required to deliver highintensity bipolar ultrashort (picosecond) pulses has yet to emerge. However, few groups have investigated the molecular mechanism at play in membrane electroporation induced by sub-nanosecond bipolar electric pulses using MD simulations.
Corresponding author at: University of Electronic Science and Technology of China, No.4, Section 2, North Jianshe Road, 610054 Chengdu, Sichuan, China. E-mail address: [email protected] (Y. Gong).
https://doi.org/10.1016/j.bbamem.2020.183213 Received 4 August 2019; Received in revised form 17 January 2020; Accepted 3 February 2020 Available online 11 February 2020 0005-2736/ © 2020 Elsevier B.V. All rights reserved.
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simulations were conducted with a 2-fs time step, and a multiple time step algorithm was employed. The particle mesh Ewald (PME) algorithm [26,27] with 3D periodic boundary conditions was applied to calculate the long-range electrostatic forces. The direct space cut-off distance of electrostatic and van der Waals interactions was 1.2 nm. The simulation process was divided into two steps. First, we performed 40 ns MD simulations to equilibrate the model system without an external electric field. The model system was then subject to symmetrical bipolar electric pulse trains (see results for detail) covering a wide range of intensities and frequencies. The direction of the applied electric fields in all simulations was perpendicular to the membrane plane.
Hence, a few years ago, researchers found that an applied THz bipolar electric field triggered the formation of many small, disordered water defects in the hydrophobic core of lipid bilayers instead of the commonly observed occurrences of single nanoscale water bridges and columns [15], the hallmark of the early events leading to membrane electroporation [2,3]. Additionally, the study found that the electropore formation mechanism associated with picosecond pulses is similar to that of much longer pulses. Later, the effect of the repetition frequency of unipolar picosecond pulse trains on the average pore formation time was reported [19], and it was shown that no electroporation occurred in response to the applied bipolar (sinewave) psPTs when the field intensity was the same as that in the unipolar case. Simulations of MD can be used to directly observe the electroporation process at the atomic level [20]. These simulations can help us effectively understand the molecular mechanism of electroporation induced by symmetrical bipolar psPT. In this paper, we extend on previous studies to shed light on the key molecular properties of the system preventing electroporation from occurring under applied symmetrical bipolar psPT as well as the conditions required for the symmetrical bipolar psPT to induce electroporation. We also propose hypotheses about the molecular mechanism involved in bipolar cancellation for the studied picosecond pulses.
3. Results and discussion First, it should be noted that the previous work [19] has found that no pores appeared with the applied sinewave (bipolar) electric fields, while electroporation occurred with the applied picosecond electric pulses of the same intensity and same frequency. However, the detailed physical mechanism of this phenomenon is still unknown. Therefore, in Section 3.1, we describe the electric field conditions of bipolar psPTs that do not cause electroporation. Second, Section 3.2 shows that bipolar psPTs can also cause electroporation, and the conditions required for psPTs to induce electroporation are analyzed. The influences of intensity and frequency on the pore formation time are presented in Section 3.3. Finally, in Section 3.4, the electroporation induced by the symmetrical bipolar psPT and that produced by the unipolar psPT are compared.
2. Methods 2.1. Model system The membrane model system is displayed in Fig. 1. The system is composed of 164 POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid molecules arranged in a bilayer hydrated at 0.14 mol/ l KCl solution (9087 water molecules), totaling 49,171 atoms. The size of the system (~7.7 nm × 7.7 nm × 8.9 nm) is similar to those used in standard studies in the field [15,21].
3.1. Analysis and interpretation of the phenomenon in which no electroporation occurs with the applied symmetrical bipolar psPT In this section, simulations of the membrane system with the applied 0.4 THz 0.65 V/nm symmetrical bipolar psPT are described. The results show that no electroporation occurs, even if the calculation time lasts for 10 ns. The interfacial water dipole moment and the force on the interfacial water were analyzed to understand this phenomenon. The bipolar psPT waveform is displayed in Fig. 2A. In this work, we really need to understand the effect of electric field direction reversal on the membrane system, and particularly on the water dipole. The rapid reversal of electric field direction can help us analyze the effect of field direction variation on the water dipole as well as the underlying mechanism. To this end, a trapezoidal pulse was used and relatively short rising and falling edges of 60 fs were chosen. Additionally, because poration with 0.65 V/nm constant electric field was observed, this amplitude was chosen. The results reveal that no electroporation occurs in response to the applied 0.4 THz 0.65 V/nm symmetrical bipolar psPT. The water molecules are only distributed in the upper and lower regions of the system, and no water molecules enter the middle hydrophobic region. Water plays a key role in electroporation. In particular, interfacial water is regarded as the driver and initiator of electroporation during pore formation. To determine the mechanism preventing electroporation with the applied symmetrical bipolar psPT, the water dipole moment and the force on the water molecules were compared to the results obtained from a constant electric field. The direction of the constant electric field remained the same and was perpendicular to the membrane surface pointing upward. The constant electric field magnitude was also 0.65 V/nm. The Z-components of the average water dipole moments along the Z-axis with the applied 0.4 THz symmetrical bipolar psPT are shown in Fig. 2 and Fig. S1. A diagram that illustrates the Z-component of the average water dipole moment is provided in Fig. 2E. The blue frame represents the whole model, and the Z-axis is perpendicular to the membrane surface. First, the total dipole moment (blue arrow) of a water layer that is perpendicular to the Z-axis is calculated. Then, the
2.2. Simulation parameters All MD simulations were carried out using the CHARMM27 force field and the NAMD MD simulation software [22]. The system was kept at constant temperature (310 K) and constant pressure (1 atm) using the Langevin piston Nose-Hoover method [23,24]. The motion equations were integrated using the velocity Verlet integration method [25]. All
Fig. 1. The membrane system. Water molecules are in red and white. The lipid headgroups are indicated by yellow balls, and the lipid chains are shown in blue. 2
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Fig. 2. (A) The waveform of the 0.4 THz symmetrical bipolar psPT and locations of the six selected time points. (B) The summary of the Z-components of the average water dipole moment along the Z-axis with the applied 0.4 THz symmetrical bipolar psPT at the six selected time points. (C) The waveform of the constant electric field and locations of the six selected time points. (D) The summary of the Z-components of the average water dipole moments along the Z-axis with the applied constant electric field at the six selected time points. (E) Diagram illustrating the Z-component of the average water dipole moment along the Z-axis.
cannot leave the interface area.
total dipole moment divided by the total number of water molecules of the water layer is the average water dipole moment. Finally, the Zcomponent of the average water dipole moment is the desired result. The water dipole direction can be determined by the electricity of the dipole moment. Six time points with a same interval of 1.2 ps were selected, and the direction of the bipolar electric field alternates at these six time points, as illustrated in Fig. 2A. When the field direction periodically reverses, the Z-component of the dipole moment of the interfacial water molecule (z = ~10 Å) also reverses (Fig. S1), and this finding is most clearly shown in Fig. 2B. This result suggests that the interfacial water molecule dipoles periodically flip around the bilayerwater interface area with the applied symmetrical bipolar psPT. Moreover, the interfacial water molecules vary more dramatically than the bulk water molecules because they are bound differently. Unlike the result for the symmetrical bipolar psPT, the average interfacial water dipole moment remains positive in response to the applied constant electric field, as shown in Fig. 2D and Fig. S2. This finding indicates that the arrangement direction of the interfacial water molecules is always consistent with the applied constant electric field direction. This phenomenon is in stark contrast to that for the bipolar psPT. Similar differences could be observed by examining the total water dipole moment and force on water molecules (Supplementary Material Figs. S3–7). In brief, when the external symmetrical bipolar psPT does not meet the conditions to cause electroporation, the interfacial water molecules keep flipping and vibrating around the bilayer-water interface area. This process occurs because the half-period of the electric field is not larger than the relaxation time of the dipole, and the water dipoles continue to redirect when the external psPT direction continues to reverse. The molecules cannot complete the reorientation and keep moving in one direction within a half-period (the electric field direction remains unchanged in a half-period). As a result, the water molecules
3.2. Conditions required for the symmetrical bipolar psPT to induce electroporation The conditions for membrane electroporation induced by the symmetrical bipolar psPT are given in this section. The psPT repetition frequency needs to be less than the threshold when the applied psPT magnitude is determined, and the psPT magnitude needs to be greater than the threshold when the applied psPT repetition frequency is determined. In other words, a long half-cycle duration (corresponding to a small repetition frequency) is needed when the psPT magnitude is fixed, and a large psPT magnitude is needed when the half-cycle duration of the electric field (repetition frequency) is fixed. Only in this way can water protrusions occur in a half-cycle. Otherwise, the water molecules will continue redirecting and flipping in response to the bipolar psPT. First, electroporation can occur when the applied symmetrical bipolar psPT repetition frequency decreases (the half-cycle length increases). Membrane systems with applied 1 V/nm symmetrical bipolar psPTs of 1.5 THz, 1 THz, 0.3 THz and 0.1 THz were simulated. The results show that no electroporation occurs with the applied 1.5 THz (half-cycle length: 0.33 ps) and 1 THz (half-cycle length: 0.5 ps) 1 V/nm psPTs, while water bridges can form when the symmetrical bipolar psPT repetition frequency decreases to 0.3 THz (half-cycle length: 1.67 ps) and 0.1 THz (half-cycle length: 5 ps), as displayed in Fig. 3. In Fig. 3B, a water protrusion can be seen at 924 ps with the applied 0.3 THz 1 V/nm symmetrical bipolar psPT. Subsequently, the water protrusion height gradually increases. At 978 ps, the water protrusion reaches the opposite bilayer-water interface and a water bridge forms, as displayed in Fig. 3C. The moment that the water bridge forms is defined as the pore formation time. After the water bridge forms, the water bridge diameter gradually increases and water bridges become 3
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Fig. 3. (A) The waveform of the 0.3 THz 1 V/nm symmetrical bipolar psPT. (B–D) The electroporation process for the 0.3 THz 1 V/nm symmetrical bipolar psPT. (E) The waveform of the 0.1 THz 1 V/nm symmetrical bipolar psPT. (F–H) The electroporation process for the 0.1 THz 1 V/nm symmetrical bipolar psPT.
Here, the electroporation process is approximately divided into two stages. The first stage begins with the application of an external electric field and ends when water protrusion occurs. The second stage begins when water protrusion occurs and ends when a water bridge forms. The above simulation results indicate that the first stage of the symmetrical bipolar psPT yields two potential situations: one is the appearance of water protrusion from both the upper and lower interfaces, and the other is the appearance of water protrusion from only one interface. However, in the second stage, no matter which interface the protrusion appears from, the protrusion will grow normally with the applied symmetrical bipolar psPT. To determine the mechanism of the growth process of water protrusion after the electric field direction reverses, a simulation that begins with an upward (↑) constant electric field and is then followed by a downward (↓) constant electric field after water protrusions form was performed. The angle variation of the water molecule dipoles was also calculated. The results are displayed in Fig. 5. The magnitude of both the upward and downward constant electric fields is 0.65 V/nm. In Fig. 5B, water protrusions appear at 144 ps with the applied upward (↑) constant electric field. Then, the upward electric field is removed and the downward (↓) constant electric field is applied to the system, as shown in Fig. 5C–E. After the constant electric field direction reverses, water protrusions do not disappear and most continue to gradually grow. At the same time, because the electric field direction reverses, new water protrusions appear from the lower side of the bilayer. Through the average water dipole moments along the Z-axis, which are shown in Fig. S8A–C,
stabilized by lipid headgroups, as shown in Fig. 3D. This electroporation process is similar to the traditional electroporation process of a long-pulse electric field, and the nanoscale single water bridge forms as well. Then, an electroporation process with the applied 1 V/nm symmetrical bipolar psPT of a small frequency of 0.1 THz was investigated. In Fig. 3F, small water protrusions simultaneously appear from both the upper and lower interfaces at 198 ps. In Fig. 3G, the water protrusions reach the opposite bilayer-water interface and more than one water bridge forms. The results show that the number of water bridges increases, the size of the water bridge decreases, and water protrusions simultaneously appear from the upper and lower interfaces when the psPT repetition frequency decreases. In addition to the simulations of the symmetrical bipolar psPT at the same amplitude and different repetition frequencies, simulations of the symmetrical bipolar psPT with the same repetition frequency and different amplitudes were performed. The results indicate that electroporation will occur as the psPT amplitude increases. Electroporation cannot occur with the applied 0.4 THz symmetrical bipolar psPTs of 0.65 V/nm and 0.8 V/nm. However, as the field magnitude increases to 1 V/nm and 1.6 V/nm, pores form, as shown in Fig. 4. It is worth noting that when the field magnitude is relatively small (1 V/nm), the amount of water protrusion is very small and the single nanoscale pore forms. However, when the field magnitude increases to 1.6 V/nm, the number of water protrusions increases. A total of 25 duplicate simulations were performed under the same conditions, and the results presented in Fig. 3 and Fig. 4 are representative. 4
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Fig. 4. (A) The waveform of the 0.4 THz 1 V/nm symmetrical bipolar psPT. (B–D) The electroporation process for the 0.4 THz 1 V/nm symmetrical bipolar psPT. (E) The waveform of the 0.4 THz 1.6 V/nm symmetrical bipolar psPT. (F–H) The electroporation process for the 0.4 THz 1.6 V/nm symmetrical bipolar psPT.
constant electric field followed by no external electric field was also conducted, as shown in Fig. S9A–C. The simulation of no external electric field was also based on the results given in Fig. 5B. After the upward (↑) constant electric field was removed, the water protrusions immediately stopped growing and gradually disappeared, although the
the directions of the water protrusion dipoles are reversed, and they are the same as the direction of the applied downward (↓) constant electric field. Then, the reversed water protrusion dipoles continue to grow with the applied reversed electric field. For comparison, a simulation that began with an upward (↑)
Fig. 5. The variation in water protrusion after the constant electric field direction reverses from upward (↑) to downward (↓). (A–B) The simulation with the applied upward (↑) constant electric field. (C–E) The simulation with the applied downward (↓) constant electric field. 5
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dipoles. After the water molecules flip, although the alignment direction of the water molecules is consistent with the external electric field direction, the molecules will continue to move in the Z-axis direction with the applied electric field, and the polarization degree will increase accordingly. In addition, the variations in the average water protrusion dipole moment and angle θ with the applied reversed constant electric fields of different magnitudes were calculated, as shown in Fig. S12 and Fig. S13. The results show that the relaxation time of the water protrusion dipole is closely related to the electric field magnitude, and this time decreases as the external electric field intensity increases. In conclusion, when the symmetrical bipolar psPT repetition frequency is fixed, increasing the psPT magnitude can reduce the water molecule relaxation time so that the water molecules can redirect and move with the applied psPT within a half-period. However, if the psPT magnitude is not sufficiently large, the water molecules will not be able to complete the redirect before the next half-cycle begins, and the molecules will have to continue oscillating with the bipolar psPT. Hence, the psPT magnitude must be greater than the threshold when the repetition frequency is determined. For the same reason, when the psPT magnitude is fixed, the water molecule relaxation time can be determined. Then, decreasing the psPT repetition frequency can increase the half-period duration. When the half-period duration is longer than the water molecule relaxation time, the water molecules will have sufficient time to flip and reorient before the next half-cycle begins. As a result, the repetition frequency must be less than the threshold when the psPT magnitude is determined.
Fig. 6. The variation in the average angle θ of the water protrusion dipole after the 0.65 V/nm constant electric field direction changes from upward (↑) to downward (↓). The angle θ is between the water dipole moment direction and the positive Z-axis.
dipole directions remained roughly upward, as illustrated in Fig. S10A–C. At the same time, the Z-components of average water dipole moment gradually decrease after the upward constant electric field is removed. To better understand the process of water molecule variation after the external electric field direction reverses, the changes in the average water protrusion dipole moment and average water protrusion dipole angle θ were calculated. Fig. S11 shows that the average dipole moment of the water molecules first rapidly varies from positive to negative and then slowly decreases. Fig. 6 shows that the average angle θ of the water protrusion dipole varies from 180° to almost 0° when the field direction reverses from upward (↑) to downward (↓). Thus, the water molecules flip and redirect after the electric field direction reverses. After the water molecules flip, the angle θ only fluctuates within a small range around approximately 0°, which indicates that the water molecules are basically arranged in the same direction as the downward (↓) electric field. It should be noted that the dipole moment still decreases when the applied electric field reverses, whereas the angle θ is relatively stable. This phenomenon is related to the oriented polarization of the water
3.3. The effects of the symmetrical bipolar psPT repetition frequency and magnitude on the average pore formation time Although the effects of the symmetrical bipolar psPT magnitude and repetition frequency on the pore formation time were addressed in the previous section. Here, a more specific and explicit relationship between the average pore formation time and the psPT magnitude and repetition frequency is described. Twenty-five duplicate simulations were conducted under the same conditions to obtain the average values. The variations in the average dipole moment and average angle θ of the interfacial water molecules were also analyzed. Fig. 7 shows that the pore formation time increases from 123.8 ps to 3770.6 ps when the symmetrical bipolar psPT repetition frequency increases from 0.1 THz to 1.3 THz. The interfacial water is believed to play a key role in the
Fig. 7. (A) The waveforms of 0.1, 0.4, 0.7, 1 and 1.3 THz symmetrical bipolar psPTs. The magnitudes of all the psPTs are 1.3 V/nm. (B) The relationship between the pore formation time and symmetrical bipolar psPT repetition frequency. 6
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be contradictory, they are, in fact, governed by different conditions. When no electroporation occurs, because the applied symmetrical bipolar psPT amplitude is small or the half-period duration is too short, the force on the interfacial water molecules cannot have an effect. Thus, it is difficult for interfacial water molecules to enter the hydrophobic zone from the interface. The water molecules just flip and vibrate with the applied bipolar psPT. However, when electroporation is induced by symmetrical bipolar psPT, the interfacial water molecules can escape from the interface with the applied external forces in very short time. Then, every time the electric field direction reverses, the protrusion water molecules can flip quickly and continue moving. These molecules do more than flip and vibrate around the bilayer-water interface. 3.4. Comparison of electroporation induced by the symmetrical bipolar psPT and unipolar psPT Fig. 8. The Z-components of the average interfacial water dipole moments with the applied 0.1, 0.4 and 0.7 THz symmetrical bipolar psPTs of 1.3 V/nm (duration is 1500 ps).
In recent years, a new and interesting issue related to the electroporation phenomena induced by bipolar pulse trains has emerged: the so-called bipolar cancellation. In 2011, the use of bipolar pulse trains for tissue electroporation was first suggested, and the effect of pulse delay was also first studied [1]. Subsequently, it was discovered that bipolar electric nanosecond electric pulses were universally less efficient for membrane permeabilization than were monopolar pulses of equal voltage and width [28]. In this section, we predict a bipolar cancellation for the studied picosecond pulses. The electroporation with the applied symmetrical bipolar psPT and the unipolar psPT is compared. The magnitude of the bipolar psPT and the unipolar psPT is 0.65 V/nm, and the repetition frequency is 0.4 THz. First, a very significant difference between the two different psPTs is observed for the interfacial water dipole angle θ, as shown in Fig. 11. The water molecules with the applied bipolar psPTs flip and redirect continuously when the field direction periodically reverses. However, the water molecules with the applied unipolar psPT vary relatively little. Fig. 11B shows that before the external electric field is removed, the water dipole is aligned with the electric field. Then, the electric field is removed in the next half-period. No external electric field forces are applied to the water molecules, and the dipoles are not consistent with the direction of the electric field. However, it is remarkable that the water dipoles do not exhibit large angular variations, nor do they flip, instead displaying a relatively small deviation from the original direction. This finding is quite different from that in the case of the bipolar psPT. In Fig. 12A, when the external unipolar electric field is applied, water dipoles turn to be aligned with the electric field and the dipole moment immediately increases. After the external electric field is removed, the dipole moments rapidly decrease to a minimum. It should be noted that although the dipole moment is reduced to a minimum, it does not completely return to the initial value without an electric field, and it will take a relatively long time to fully return to the initial state. Moreover, this result has been confirmed in Fig. S9 and Fig. S10, in which the dipole moment does not immediately decrease to the initial value after the electric field is removed. After the electric field is removed, the effect of the electric field will still remain for approximately 70 ps (according to our simulations in Fig. S9). Then, the action of the unipolar psPT on the water dipoles will accumulate only in one direction. The water polarization degree continues to increase in response to the applied unipolar psPT, as shown in Fig. 12B. In the case of the symmetrical bipolar psPT, when the electric field is upward (↑), the dipole moment increases to the positive maximum. When the field direction reverses (↓), the dipole moment rapidly decreases to the negative maximum. In fact, the polarization effect of the upward (↑) electric field on the water molecules in the previous halfcycle will be eliminated, which is in contrast to the response for the unipolar psPT. The periodic reversal of the electric field direction destroys the polarization effect of the previous electric field. Additionally, the action of the bipolar psPT on the water dipoles will not accumulate
electroporation process. To understand the relationship between the pore formation time and psPT repetition frequency, the effect of the repetition frequency on the interfacial water molecules polarization degree should be understood in detail. Fig. S14A shows that the water dipole moment increases as the psPT repetition frequency decreases. This response occurs because the water dipole moment magnitude depends on the duration of the half-period. Every time the electric field direction changes, the water dipole redirects (as shown in Fig. S14B) and the dipole moment has to increase from the minimum value. The dipole moment will continue to increase with the applied external electric field when the field direction is constant. As a result, when the psPT repetition frequency decreases, the half-period duration increases; then, the duration of the continued increase in the water dipole moment becomes longer and the interfacial water polarization degree increases. Notably, the polarization discussed here refers to the oriented polarization. For clarity, only three frequencies (0.1, 0.4 and 0.7 THz) are selected as examples. Fig. 8 clearly shows (calculation time is extended to 1500 ps) that the interfacial water polarization degree increases as the symmetrical bipolar psPT repetition frequency decreases. Additionally, the interfacial water dipole moment increases considerably after pore formation. In addition to the influence of the symmetrical bipolar psPT repetition frequency on the pore formation time, the effect of the symmetrical bipolar psPT magnitude on pore formation time was also investigated, as displayed in Fig. 9. The pore formation time decreases with increasing applied psPT magnitude. This phenomenon can also be understood through the interfacial water polarization degree. Fig. S15A and Fig. 10 show that the interfacial water dipole moment increases as the applied symmetrical bipolar psPT magnitude increases. This trend is expected because the polarization degree will increase as the external electric field magnitude increases. Fig. S15B shows that the larger the psPT magnitude is, the shorter the water dipole flip time will be, which is consistent with the results presented in the last section. Thus, the water molecules are rapidly redirected, and the water dipole moment increases when the psPT magnitude increases. In conclusion, the interfacial water polarization degree increases and the pore formation time becomes shorter when the symmetrical bipolar psPT repetition frequency decreases. At the same time, the interfacial water polarization degree increases and the pore formation time decreases when the symmetrical bipolar psPT magnitude increases. It should be noted that in the previous analysis of the case in which no electroporation occurs, the reason for the lack of electroporation was attributed to the continuous flipping and oscillation of interfacial water molecules. However, here, even though the pores form, the dipole moment is still periodically reversed. Although these actions appear to 7
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Fig. 9. (A) The waveforms of the 1, 1.3, 1.6, 1.9 and 2.2 V/nm symmetrical bipolar psPTs. The repetition frequencies of all psPTs are 0.4 THz. (B) The relationship between the pore formation time and symmetrical bipolar psPT magnitude.
in one direction. According to the previous analysis of the conditions required for the symmetrical bipolar psPT to induce electroporation, only when the field amplitude is sufficiently large and the half-cycle is sufficiently long will water protrusion be produced within half a cycle. However, if the unipolar psPT has a high amplitude and a wide half-period, water protrusion will appear in a very short time due to the existence of effect accumulation. In addition, the average pore formation times of unipolar psPT and bipolar psPT were calculated and compared, and the results are displayed in Fig. S16 and Fig. S17. These findings show that the times of the unipolar psPT are shorter than those of the bipolar psPT at the same frequency and intensity. As a result, it is speculated that the reason for bipolar cancellation for picosecond pulses may be related to the phenomenon in which the influence of unipolar picosecond pulses on interfacial water dipoles will accumulate in one direction, whereas the bipolar picosecond pulses do not cause this effect.
Fig. 10. The Z-components of the average interfacial water dipole moments with the applied 1, 1.3, 1.6, 1.9 and 2.2 V/nm symmetrical bipolar psPTs of 0.4 THz (duration is 1500 ps).
4. Conclusion In summary, the phenomenon of no electroporation with the
Fig. 11. The variation in the average angle θ of the interfacial water dipole with the applied 0.65 V/nm 0.4 THz symmetrical bipolar psPT and unipolar psPT. (A) The water angle θ for the symmetrical bipolar psPT. (B) The water angle θ for the unipolar psPT. 8
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Fig. 12. The Z-components of the average interfacial water dipole moments with the applied 0.65 V/nm 0.4 THz symmetrical bipolar psPT and unipolar psPT. (A) The total duration is 7.5 ps. (B) The total duration is 6000 ps.
applied symmetrical bipolar psPT and the conditions required for the symmetrical bipolar psPT to induce electroporation are analyzed and discussed. Moreover, it is discovered that the pore formation time becomes shorter when the symmetrical bipolar psPT repetition frequency decreases and the pore formation time becomes longer when the psPT magnitude decreases. Additionally, a bipolar cancellation for the studied picosecond pulses is predicted. Our findings may provide new insight and theoretical guidance for the application of psPTs in the biomedical field.
[8]
[9]
[10]
[11]
Transparency document [12]
The Transparency document associated this article can be found, in online version.
[13] [14]
Author contributions
[15]
Y.G. and J.T. designed the research and wrote the article. J.T. performed the simulations and analysis. L.Y., J.M., L.G., K.W., Y.Y., W.B., Z.W., H.J., Z.W. and B.Z. revised the article. All authors participated in scientific discussions.
[16]
Declaration of competing interest
[17]
None.
[18]
Appendix A. Supplementary data [19]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.bbamem.2020.183213.
[20] [21]
References
[22] [1] C.B. Arena, M.B. Sano, J.H. Rossmeisl, J.L. Caldwell, P.A. Garcia, M.N. Rylander, R.V. Davalos, High-frequency irreversible electroporation (H-FIRE) for non-thermal ablation without muscle contraction, Biomed. Eng. Online 10 (1) (2011) 102. [2] M. Casciola, M. Tarek, A molecular insight into the electro-transfer of small molecules through electropores driven by electric fields, Biochim. Biophys. Acta Biomembr. 1858 (10) (2016) 2278–2289. [3] T. Kotnik, L. Rems, M. Tarek, D. Miklavčič, Membrane electroporation and electropermeabilization: mechanisms and models, Annu. Rev. Biophys. 48 (2019). [4] I. Semenov, C. Zemlin, O.N. Pakhomova, S. Xiao, A.G. Pakhomov, Diffuse, nonpolar electropermeabilization and reduced propidium uptake distinguish the effect of nanosecond electric pulses, Biochim. Biophys. Acta Biomembr. 1848 (10) (2015) 2118–2125. [5] S.J. Beebe, K.H. Schoenbach, R. Heller, Bioelectric applications for treatment of melanoma, Cancers 2 (3) (2010) 1731–1770. [6] M.L. Yarmush, A. Golberg, G. Serša, T. Kotnik, D. Miklavčič, Electroporation-based technologies for medicine: principles, applications, and challenges, Annu. Rev. Biomed. Eng. 16 (2014) 295–320. [7] C.B. Arena, C.S. Szot, P.A. Garcia, M.N. Rylander, R.V. Davalos, A three-
[23] [24]
[25] [26] [27] [28]
9
dimensional in vitro tumor platform for modeling therapeutic irreversible electroporation, Biophys. J. 103 (9) (2012) 2033–2042. S.J. Beebe, P.M. Fox, L.J. Rec, E.L.K. Willis, K.H. Schoenbach, Nanosecond, highintensity pulsed electric fields induce apoptosis in human cells, FASEB J. 17 (11) (2003) 1493–1495. T. Kotnik, D. Miklavčič, Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields, Biophys. J. 90 (2) (2006) 480–491. S. Xiao, S. Guo, V. Nesin, R. Heller, K.H. Schoenbach, Subnanosecond electric pulses cause membrane permeabilization and cell death, IEEE Trans. Biomed. Eng. 58 (5) (2011) 1239–1245. J.T. Camp, Y. Jing, J. Zhuang, J.F. Kolb, S.J. Beebe, J. Song, K.H. Schoenbach, Cell death induced by subnanosecond pulsed electric fields at elevated temperatures, IEEE Trans. Plasma Sci. 40 (10) (2012) 2334–2347. Y.Y. Hua, X.S. Wang, Y.U. Zhang, C.G. Yao, X.M. Zhang, Z.A. Xiong, Intense picosecond pulsed electric fields induce apoptosis through a mitochondrial-mediated pathway in HeLa cells, Mol. Med. Rep. 5 (4) (2012) 981–987. H. Fröhlich, The biological effects of microwaves and related questions, Advances in Electronics and Electron Physics, vol. 53, Academic Press, 1980, pp. 85–152. P.H. Siegel, Terahertz technology in biology and medicine, IEEE Trans. Microwave Theory Tech. 52 (10) (2004) 2438–2447. P.T. Vernier, Z.A. Levine, M.C. Ho, S. Xiao, I. Semenov, A.G. Pakhomov, Picosecond and terahertz perturbation of interfacial water and electropermeabilization of biological membranes, J. Membr. Biol. 248 (5) (2015) 837–847. G.J. Wilmink, B.L. Ibey, C.L. Roth, R.L. Vincelette, B.D. Rivest, C.B. Horn, W.P. Roach, Determination of death thresholds and identification of terahertz (THz)-specific gene expression signatures, Optical Interactions with Tissues and Cells XXI, 7562 International Society for Optics and Photonics, 2010, February, p. 75620K. G.J. Wilmink, J.E. Grundt, Invited review article: current state of research on biological effects of terahertz radiation, J. Infrared Millim. Terahertz Waves 32 (10) (2011) 1074–1122. M. Borovkova, M. Serebriakova, V. Fedorov, E. Sedykh, V. Vaks, A. Lichutin, M. Khodzitsky, Investigation of terahertz radiation influence on rat glial cells, Biomed. Opt. Express 8 (1) (2017) 273–280. J. Tang, H. Yin, J. Ma, W. Bo, Y. Yang, J. Xu, Y. Gong, Terahertz electric fieldinduced membrane electroporation by molecular dynamics simulations, J. Membr. Biol. 251 (5–6) (2018) 681–693. R.L. Andrew, Molecular Modeling Principles and Applications, Prentice Hall, London, 2001. F. Castellani, J. Teissié, P.T. Vernier, Permeabilizing phospholipid bilayers with non-normal electric fields, J. Membr. Biol. 251 (2) (2018) 229–236. L. Kalé, R. Skeel, M. Bhandarkar, R. Brunner, A. Gursoy, N. Krawetz, K. Schulten, NAMD2: greater scalability for parallel molecular dynamics, J. Comput. Phys. 151 (1) (1999) 283–312. G.J. Martyna, D.J. Tobias, M.L. Klein, Constant pressure molecular dynamics algorithms, J. Chem. Phys. 101 (5) (1994) 4177–4189. S.E. Feller, Y. Zhang, R.W. Pastor, B.R. Brooks, Constant pressure molecular dynamics simulation: the Langevin piston method, J. Chem. Phys. 103 (11) (1995) 4613–4621. M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford university press, 2017. T. Darden, D. York, L. Pedersen, Particle mesh Ewald: an N· log (N) method for Ewald sums in large systems, J. Chem. Phys. 98 (12) (1993) 10089–10092. U. Essmann, L. Perera, M.L. Berkowitz, T. Darden, H. Lee, L.G. Pedersen, A smooth particle mesh Ewald method, J. Chem. Phys. 103 (19) (1995) 8577–8593. A.G. Pakhomov, I. Semenov, S. Xiao, O.N. Pakhomova, B. Gregory, K.H. Schoenbach, B.L. Ibey, Cancellation of cellular responses to nanoelectroporation by reversing the stimulus polarity, Cell. Mol. Life Sci. 71 (22) (2014) 4431–4441.
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BBA - Biomembranes journal homepage: www.elsevier.com/locate/bbamem
Interpretation of the molecular mechanism of the electroporation induced by symmetrical bipolar picosecond pulse trains
T
Jingchao Tanga,b, Jialu Maa, Lianghao Guoa, Kaicheng Wanga, Yang Yanga, Wenfei Boa, ⁎ Lixia Yangc, Zhao Wanga, Haibo Jiangd, Zhe Wua, Baoqing Zenga, Yubin Gonga, a
School of Electronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan Province, China CNRS, UMR 7565, F-54506 Vandoeuvre les Nancy, France c School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore d Chengdu Institute of Biology, Chinese Academy of Sciences, Chengdu, Sichuan Province, China b
A R T I C LE I N FO
A B S T R A C T
Keywords: Electroporation Molecular dynamics Picosecond bipolar cancellation Symmetrical bipolar picosecond pulse trains
Picosecond pulse trains (psPTs) are emerging as a new characteristic diagnostic and therapeutic tool in biomedical fields. To specifically determine the stimulus provided to cells, in this article, we use a molecular dynamics (MD) model to show the molecular mechanisms of electroporation induced by symmetrical bipolar psPTs and predict a bipolar cancellation for the studied picosecond pulses. Electric field conditions that do not cause electroporation reveal that the interfacial water molecules continuously flip and redirect as the applied bipolar psPT reverses, and the molecules cannot keep moving in one direction or leave the lipid-water interface. Based on our simulation results, we determine the threshold for electroporation with symmetrical bipolar psPTs. For a fixed electric field intensity, a lower repetition frequency leads to more rapid electroporation. For a fixed repetition frequency, a higher electric field intensity leads to more rapid electroporation. We found that the water dipole relaxation time decreases as the electric field magnitude increases. Additionally, the influences of the symmetrical bipolar psPT intensity and frequency on the pore formation time are presented. Discrete nanoscale pores can form with the applied psPT at terahertz (THz) repetition frequency. When the psPT amplitude increases or the frequency decreases, the number of water bridges will increase. Moreover, for the first time, the molecular mechanism of bipolar cancellation for the studied picosecond pulse is discussed preliminarily. Our results indicate that the influence of the unipolar picosecond pulse on the interfacial water dipoles will accumulate in one direction, but the bipolar picosecond pulse does not cause this effect.
1. Introduction Permeabilization of cell membranes or membrane breakdown induced by an external electric field is a phenomenon often referred to as electroporation or electropermeabilization [1–4]. Electroporation allows the transport of impermeant molecules across cell membranes, and a wide range of applications have been found in biotechnological and medical fields, e.g., cancer therapy, DNA vaccination, gene regulation, tissue ablation and microbial deactivation [5–7]. Over a decade ago, it was reported that ultrashort (hundreds of nanoseconds) pulsed electric fields can induce apoptosis in human cells [8]. Compared to classical electroporation, where μs and ms pulses are used, it was suggested that the shorter pulses were more likely to target the membranes of internal organelles of the cell than were the longer pulses [9,10]. It has, for instance, been shown that sub-nanosecond
⁎
pulses can not only kill cancer cells [11,12] but also directly affect the mitochondria in HeLa cells and cause cell apoptosis through a mitochondrial-mediated pathway [12]. In addition, an advantage of the sub-nanosecond pulses is that they can be noninvasively applied to the tissue by an impulse antenna, which is different from the methods required for traditional ms, μs and sub-μs pulses [10,12]. THz fields have been found to strongly interact with biomolecular systems [13–15] and to substantially affect cell function [16–18]. Picosecond pulsed electric fields overlap with the THz spectrum regions, and as such, they may present great potential for applications in biorelated fields. The experimental technology required to deliver highintensity bipolar ultrashort (picosecond) pulses has yet to emerge. However, few groups have investigated the molecular mechanism at play in membrane electroporation induced by sub-nanosecond bipolar electric pulses using MD simulations.
Corresponding author at: University of Electronic Science and Technology of China, No.4, Section 2, North Jianshe Road, 610054 Chengdu, Sichuan, China. E-mail address: [email protected] (Y. Gong).
https://doi.org/10.1016/j.bbamem.2020.183213 Received 4 August 2019; Received in revised form 17 January 2020; Accepted 3 February 2020 Available online 11 February 2020 0005-2736/ © 2020 Elsevier B.V. All rights reserved.
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simulations were conducted with a 2-fs time step, and a multiple time step algorithm was employed. The particle mesh Ewald (PME) algorithm [26,27] with 3D periodic boundary conditions was applied to calculate the long-range electrostatic forces. The direct space cut-off distance of electrostatic and van der Waals interactions was 1.2 nm. The simulation process was divided into two steps. First, we performed 40 ns MD simulations to equilibrate the model system without an external electric field. The model system was then subject to symmetrical bipolar electric pulse trains (see results for detail) covering a wide range of intensities and frequencies. The direction of the applied electric fields in all simulations was perpendicular to the membrane plane.
Hence, a few years ago, researchers found that an applied THz bipolar electric field triggered the formation of many small, disordered water defects in the hydrophobic core of lipid bilayers instead of the commonly observed occurrences of single nanoscale water bridges and columns [15], the hallmark of the early events leading to membrane electroporation [2,3]. Additionally, the study found that the electropore formation mechanism associated with picosecond pulses is similar to that of much longer pulses. Later, the effect of the repetition frequency of unipolar picosecond pulse trains on the average pore formation time was reported [19], and it was shown that no electroporation occurred in response to the applied bipolar (sinewave) psPTs when the field intensity was the same as that in the unipolar case. Simulations of MD can be used to directly observe the electroporation process at the atomic level [20]. These simulations can help us effectively understand the molecular mechanism of electroporation induced by symmetrical bipolar psPT. In this paper, we extend on previous studies to shed light on the key molecular properties of the system preventing electroporation from occurring under applied symmetrical bipolar psPT as well as the conditions required for the symmetrical bipolar psPT to induce electroporation. We also propose hypotheses about the molecular mechanism involved in bipolar cancellation for the studied picosecond pulses.
3. Results and discussion First, it should be noted that the previous work [19] has found that no pores appeared with the applied sinewave (bipolar) electric fields, while electroporation occurred with the applied picosecond electric pulses of the same intensity and same frequency. However, the detailed physical mechanism of this phenomenon is still unknown. Therefore, in Section 3.1, we describe the electric field conditions of bipolar psPTs that do not cause electroporation. Second, Section 3.2 shows that bipolar psPTs can also cause electroporation, and the conditions required for psPTs to induce electroporation are analyzed. The influences of intensity and frequency on the pore formation time are presented in Section 3.3. Finally, in Section 3.4, the electroporation induced by the symmetrical bipolar psPT and that produced by the unipolar psPT are compared.
2. Methods 2.1. Model system The membrane model system is displayed in Fig. 1. The system is composed of 164 POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid molecules arranged in a bilayer hydrated at 0.14 mol/ l KCl solution (9087 water molecules), totaling 49,171 atoms. The size of the system (~7.7 nm × 7.7 nm × 8.9 nm) is similar to those used in standard studies in the field [15,21].
3.1. Analysis and interpretation of the phenomenon in which no electroporation occurs with the applied symmetrical bipolar psPT In this section, simulations of the membrane system with the applied 0.4 THz 0.65 V/nm symmetrical bipolar psPT are described. The results show that no electroporation occurs, even if the calculation time lasts for 10 ns. The interfacial water dipole moment and the force on the interfacial water were analyzed to understand this phenomenon. The bipolar psPT waveform is displayed in Fig. 2A. In this work, we really need to understand the effect of electric field direction reversal on the membrane system, and particularly on the water dipole. The rapid reversal of electric field direction can help us analyze the effect of field direction variation on the water dipole as well as the underlying mechanism. To this end, a trapezoidal pulse was used and relatively short rising and falling edges of 60 fs were chosen. Additionally, because poration with 0.65 V/nm constant electric field was observed, this amplitude was chosen. The results reveal that no electroporation occurs in response to the applied 0.4 THz 0.65 V/nm symmetrical bipolar psPT. The water molecules are only distributed in the upper and lower regions of the system, and no water molecules enter the middle hydrophobic region. Water plays a key role in electroporation. In particular, interfacial water is regarded as the driver and initiator of electroporation during pore formation. To determine the mechanism preventing electroporation with the applied symmetrical bipolar psPT, the water dipole moment and the force on the water molecules were compared to the results obtained from a constant electric field. The direction of the constant electric field remained the same and was perpendicular to the membrane surface pointing upward. The constant electric field magnitude was also 0.65 V/nm. The Z-components of the average water dipole moments along the Z-axis with the applied 0.4 THz symmetrical bipolar psPT are shown in Fig. 2 and Fig. S1. A diagram that illustrates the Z-component of the average water dipole moment is provided in Fig. 2E. The blue frame represents the whole model, and the Z-axis is perpendicular to the membrane surface. First, the total dipole moment (blue arrow) of a water layer that is perpendicular to the Z-axis is calculated. Then, the
2.2. Simulation parameters All MD simulations were carried out using the CHARMM27 force field and the NAMD MD simulation software [22]. The system was kept at constant temperature (310 K) and constant pressure (1 atm) using the Langevin piston Nose-Hoover method [23,24]. The motion equations were integrated using the velocity Verlet integration method [25]. All
Fig. 1. The membrane system. Water molecules are in red and white. The lipid headgroups are indicated by yellow balls, and the lipid chains are shown in blue. 2
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Fig. 2. (A) The waveform of the 0.4 THz symmetrical bipolar psPT and locations of the six selected time points. (B) The summary of the Z-components of the average water dipole moment along the Z-axis with the applied 0.4 THz symmetrical bipolar psPT at the six selected time points. (C) The waveform of the constant electric field and locations of the six selected time points. (D) The summary of the Z-components of the average water dipole moments along the Z-axis with the applied constant electric field at the six selected time points. (E) Diagram illustrating the Z-component of the average water dipole moment along the Z-axis.
cannot leave the interface area.
total dipole moment divided by the total number of water molecules of the water layer is the average water dipole moment. Finally, the Zcomponent of the average water dipole moment is the desired result. The water dipole direction can be determined by the electricity of the dipole moment. Six time points with a same interval of 1.2 ps were selected, and the direction of the bipolar electric field alternates at these six time points, as illustrated in Fig. 2A. When the field direction periodically reverses, the Z-component of the dipole moment of the interfacial water molecule (z = ~10 Å) also reverses (Fig. S1), and this finding is most clearly shown in Fig. 2B. This result suggests that the interfacial water molecule dipoles periodically flip around the bilayerwater interface area with the applied symmetrical bipolar psPT. Moreover, the interfacial water molecules vary more dramatically than the bulk water molecules because they are bound differently. Unlike the result for the symmetrical bipolar psPT, the average interfacial water dipole moment remains positive in response to the applied constant electric field, as shown in Fig. 2D and Fig. S2. This finding indicates that the arrangement direction of the interfacial water molecules is always consistent with the applied constant electric field direction. This phenomenon is in stark contrast to that for the bipolar psPT. Similar differences could be observed by examining the total water dipole moment and force on water molecules (Supplementary Material Figs. S3–7). In brief, when the external symmetrical bipolar psPT does not meet the conditions to cause electroporation, the interfacial water molecules keep flipping and vibrating around the bilayer-water interface area. This process occurs because the half-period of the electric field is not larger than the relaxation time of the dipole, and the water dipoles continue to redirect when the external psPT direction continues to reverse. The molecules cannot complete the reorientation and keep moving in one direction within a half-period (the electric field direction remains unchanged in a half-period). As a result, the water molecules
3.2. Conditions required for the symmetrical bipolar psPT to induce electroporation The conditions for membrane electroporation induced by the symmetrical bipolar psPT are given in this section. The psPT repetition frequency needs to be less than the threshold when the applied psPT magnitude is determined, and the psPT magnitude needs to be greater than the threshold when the applied psPT repetition frequency is determined. In other words, a long half-cycle duration (corresponding to a small repetition frequency) is needed when the psPT magnitude is fixed, and a large psPT magnitude is needed when the half-cycle duration of the electric field (repetition frequency) is fixed. Only in this way can water protrusions occur in a half-cycle. Otherwise, the water molecules will continue redirecting and flipping in response to the bipolar psPT. First, electroporation can occur when the applied symmetrical bipolar psPT repetition frequency decreases (the half-cycle length increases). Membrane systems with applied 1 V/nm symmetrical bipolar psPTs of 1.5 THz, 1 THz, 0.3 THz and 0.1 THz were simulated. The results show that no electroporation occurs with the applied 1.5 THz (half-cycle length: 0.33 ps) and 1 THz (half-cycle length: 0.5 ps) 1 V/nm psPTs, while water bridges can form when the symmetrical bipolar psPT repetition frequency decreases to 0.3 THz (half-cycle length: 1.67 ps) and 0.1 THz (half-cycle length: 5 ps), as displayed in Fig. 3. In Fig. 3B, a water protrusion can be seen at 924 ps with the applied 0.3 THz 1 V/nm symmetrical bipolar psPT. Subsequently, the water protrusion height gradually increases. At 978 ps, the water protrusion reaches the opposite bilayer-water interface and a water bridge forms, as displayed in Fig. 3C. The moment that the water bridge forms is defined as the pore formation time. After the water bridge forms, the water bridge diameter gradually increases and water bridges become 3
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Fig. 3. (A) The waveform of the 0.3 THz 1 V/nm symmetrical bipolar psPT. (B–D) The electroporation process for the 0.3 THz 1 V/nm symmetrical bipolar psPT. (E) The waveform of the 0.1 THz 1 V/nm symmetrical bipolar psPT. (F–H) The electroporation process for the 0.1 THz 1 V/nm symmetrical bipolar psPT.
Here, the electroporation process is approximately divided into two stages. The first stage begins with the application of an external electric field and ends when water protrusion occurs. The second stage begins when water protrusion occurs and ends when a water bridge forms. The above simulation results indicate that the first stage of the symmetrical bipolar psPT yields two potential situations: one is the appearance of water protrusion from both the upper and lower interfaces, and the other is the appearance of water protrusion from only one interface. However, in the second stage, no matter which interface the protrusion appears from, the protrusion will grow normally with the applied symmetrical bipolar psPT. To determine the mechanism of the growth process of water protrusion after the electric field direction reverses, a simulation that begins with an upward (↑) constant electric field and is then followed by a downward (↓) constant electric field after water protrusions form was performed. The angle variation of the water molecule dipoles was also calculated. The results are displayed in Fig. 5. The magnitude of both the upward and downward constant electric fields is 0.65 V/nm. In Fig. 5B, water protrusions appear at 144 ps with the applied upward (↑) constant electric field. Then, the upward electric field is removed and the downward (↓) constant electric field is applied to the system, as shown in Fig. 5C–E. After the constant electric field direction reverses, water protrusions do not disappear and most continue to gradually grow. At the same time, because the electric field direction reverses, new water protrusions appear from the lower side of the bilayer. Through the average water dipole moments along the Z-axis, which are shown in Fig. S8A–C,
stabilized by lipid headgroups, as shown in Fig. 3D. This electroporation process is similar to the traditional electroporation process of a long-pulse electric field, and the nanoscale single water bridge forms as well. Then, an electroporation process with the applied 1 V/nm symmetrical bipolar psPT of a small frequency of 0.1 THz was investigated. In Fig. 3F, small water protrusions simultaneously appear from both the upper and lower interfaces at 198 ps. In Fig. 3G, the water protrusions reach the opposite bilayer-water interface and more than one water bridge forms. The results show that the number of water bridges increases, the size of the water bridge decreases, and water protrusions simultaneously appear from the upper and lower interfaces when the psPT repetition frequency decreases. In addition to the simulations of the symmetrical bipolar psPT at the same amplitude and different repetition frequencies, simulations of the symmetrical bipolar psPT with the same repetition frequency and different amplitudes were performed. The results indicate that electroporation will occur as the psPT amplitude increases. Electroporation cannot occur with the applied 0.4 THz symmetrical bipolar psPTs of 0.65 V/nm and 0.8 V/nm. However, as the field magnitude increases to 1 V/nm and 1.6 V/nm, pores form, as shown in Fig. 4. It is worth noting that when the field magnitude is relatively small (1 V/nm), the amount of water protrusion is very small and the single nanoscale pore forms. However, when the field magnitude increases to 1.6 V/nm, the number of water protrusions increases. A total of 25 duplicate simulations were performed under the same conditions, and the results presented in Fig. 3 and Fig. 4 are representative. 4
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Fig. 4. (A) The waveform of the 0.4 THz 1 V/nm symmetrical bipolar psPT. (B–D) The electroporation process for the 0.4 THz 1 V/nm symmetrical bipolar psPT. (E) The waveform of the 0.4 THz 1.6 V/nm symmetrical bipolar psPT. (F–H) The electroporation process for the 0.4 THz 1.6 V/nm symmetrical bipolar psPT.
constant electric field followed by no external electric field was also conducted, as shown in Fig. S9A–C. The simulation of no external electric field was also based on the results given in Fig. 5B. After the upward (↑) constant electric field was removed, the water protrusions immediately stopped growing and gradually disappeared, although the
the directions of the water protrusion dipoles are reversed, and they are the same as the direction of the applied downward (↓) constant electric field. Then, the reversed water protrusion dipoles continue to grow with the applied reversed electric field. For comparison, a simulation that began with an upward (↑)
Fig. 5. The variation in water protrusion after the constant electric field direction reverses from upward (↑) to downward (↓). (A–B) The simulation with the applied upward (↑) constant electric field. (C–E) The simulation with the applied downward (↓) constant electric field. 5
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dipoles. After the water molecules flip, although the alignment direction of the water molecules is consistent with the external electric field direction, the molecules will continue to move in the Z-axis direction with the applied electric field, and the polarization degree will increase accordingly. In addition, the variations in the average water protrusion dipole moment and angle θ with the applied reversed constant electric fields of different magnitudes were calculated, as shown in Fig. S12 and Fig. S13. The results show that the relaxation time of the water protrusion dipole is closely related to the electric field magnitude, and this time decreases as the external electric field intensity increases. In conclusion, when the symmetrical bipolar psPT repetition frequency is fixed, increasing the psPT magnitude can reduce the water molecule relaxation time so that the water molecules can redirect and move with the applied psPT within a half-period. However, if the psPT magnitude is not sufficiently large, the water molecules will not be able to complete the redirect before the next half-cycle begins, and the molecules will have to continue oscillating with the bipolar psPT. Hence, the psPT magnitude must be greater than the threshold when the repetition frequency is determined. For the same reason, when the psPT magnitude is fixed, the water molecule relaxation time can be determined. Then, decreasing the psPT repetition frequency can increase the half-period duration. When the half-period duration is longer than the water molecule relaxation time, the water molecules will have sufficient time to flip and reorient before the next half-cycle begins. As a result, the repetition frequency must be less than the threshold when the psPT magnitude is determined.
Fig. 6. The variation in the average angle θ of the water protrusion dipole after the 0.65 V/nm constant electric field direction changes from upward (↑) to downward (↓). The angle θ is between the water dipole moment direction and the positive Z-axis.
dipole directions remained roughly upward, as illustrated in Fig. S10A–C. At the same time, the Z-components of average water dipole moment gradually decrease after the upward constant electric field is removed. To better understand the process of water molecule variation after the external electric field direction reverses, the changes in the average water protrusion dipole moment and average water protrusion dipole angle θ were calculated. Fig. S11 shows that the average dipole moment of the water molecules first rapidly varies from positive to negative and then slowly decreases. Fig. 6 shows that the average angle θ of the water protrusion dipole varies from 180° to almost 0° when the field direction reverses from upward (↑) to downward (↓). Thus, the water molecules flip and redirect after the electric field direction reverses. After the water molecules flip, the angle θ only fluctuates within a small range around approximately 0°, which indicates that the water molecules are basically arranged in the same direction as the downward (↓) electric field. It should be noted that the dipole moment still decreases when the applied electric field reverses, whereas the angle θ is relatively stable. This phenomenon is related to the oriented polarization of the water
3.3. The effects of the symmetrical bipolar psPT repetition frequency and magnitude on the average pore formation time Although the effects of the symmetrical bipolar psPT magnitude and repetition frequency on the pore formation time were addressed in the previous section. Here, a more specific and explicit relationship between the average pore formation time and the psPT magnitude and repetition frequency is described. Twenty-five duplicate simulations were conducted under the same conditions to obtain the average values. The variations in the average dipole moment and average angle θ of the interfacial water molecules were also analyzed. Fig. 7 shows that the pore formation time increases from 123.8 ps to 3770.6 ps when the symmetrical bipolar psPT repetition frequency increases from 0.1 THz to 1.3 THz. The interfacial water is believed to play a key role in the
Fig. 7. (A) The waveforms of 0.1, 0.4, 0.7, 1 and 1.3 THz symmetrical bipolar psPTs. The magnitudes of all the psPTs are 1.3 V/nm. (B) The relationship between the pore formation time and symmetrical bipolar psPT repetition frequency. 6
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be contradictory, they are, in fact, governed by different conditions. When no electroporation occurs, because the applied symmetrical bipolar psPT amplitude is small or the half-period duration is too short, the force on the interfacial water molecules cannot have an effect. Thus, it is difficult for interfacial water molecules to enter the hydrophobic zone from the interface. The water molecules just flip and vibrate with the applied bipolar psPT. However, when electroporation is induced by symmetrical bipolar psPT, the interfacial water molecules can escape from the interface with the applied external forces in very short time. Then, every time the electric field direction reverses, the protrusion water molecules can flip quickly and continue moving. These molecules do more than flip and vibrate around the bilayer-water interface. 3.4. Comparison of electroporation induced by the symmetrical bipolar psPT and unipolar psPT Fig. 8. The Z-components of the average interfacial water dipole moments with the applied 0.1, 0.4 and 0.7 THz symmetrical bipolar psPTs of 1.3 V/nm (duration is 1500 ps).
In recent years, a new and interesting issue related to the electroporation phenomena induced by bipolar pulse trains has emerged: the so-called bipolar cancellation. In 2011, the use of bipolar pulse trains for tissue electroporation was first suggested, and the effect of pulse delay was also first studied [1]. Subsequently, it was discovered that bipolar electric nanosecond electric pulses were universally less efficient for membrane permeabilization than were monopolar pulses of equal voltage and width [28]. In this section, we predict a bipolar cancellation for the studied picosecond pulses. The electroporation with the applied symmetrical bipolar psPT and the unipolar psPT is compared. The magnitude of the bipolar psPT and the unipolar psPT is 0.65 V/nm, and the repetition frequency is 0.4 THz. First, a very significant difference between the two different psPTs is observed for the interfacial water dipole angle θ, as shown in Fig. 11. The water molecules with the applied bipolar psPTs flip and redirect continuously when the field direction periodically reverses. However, the water molecules with the applied unipolar psPT vary relatively little. Fig. 11B shows that before the external electric field is removed, the water dipole is aligned with the electric field. Then, the electric field is removed in the next half-period. No external electric field forces are applied to the water molecules, and the dipoles are not consistent with the direction of the electric field. However, it is remarkable that the water dipoles do not exhibit large angular variations, nor do they flip, instead displaying a relatively small deviation from the original direction. This finding is quite different from that in the case of the bipolar psPT. In Fig. 12A, when the external unipolar electric field is applied, water dipoles turn to be aligned with the electric field and the dipole moment immediately increases. After the external electric field is removed, the dipole moments rapidly decrease to a minimum. It should be noted that although the dipole moment is reduced to a minimum, it does not completely return to the initial value without an electric field, and it will take a relatively long time to fully return to the initial state. Moreover, this result has been confirmed in Fig. S9 and Fig. S10, in which the dipole moment does not immediately decrease to the initial value after the electric field is removed. After the electric field is removed, the effect of the electric field will still remain for approximately 70 ps (according to our simulations in Fig. S9). Then, the action of the unipolar psPT on the water dipoles will accumulate only in one direction. The water polarization degree continues to increase in response to the applied unipolar psPT, as shown in Fig. 12B. In the case of the symmetrical bipolar psPT, when the electric field is upward (↑), the dipole moment increases to the positive maximum. When the field direction reverses (↓), the dipole moment rapidly decreases to the negative maximum. In fact, the polarization effect of the upward (↑) electric field on the water molecules in the previous halfcycle will be eliminated, which is in contrast to the response for the unipolar psPT. The periodic reversal of the electric field direction destroys the polarization effect of the previous electric field. Additionally, the action of the bipolar psPT on the water dipoles will not accumulate
electroporation process. To understand the relationship between the pore formation time and psPT repetition frequency, the effect of the repetition frequency on the interfacial water molecules polarization degree should be understood in detail. Fig. S14A shows that the water dipole moment increases as the psPT repetition frequency decreases. This response occurs because the water dipole moment magnitude depends on the duration of the half-period. Every time the electric field direction changes, the water dipole redirects (as shown in Fig. S14B) and the dipole moment has to increase from the minimum value. The dipole moment will continue to increase with the applied external electric field when the field direction is constant. As a result, when the psPT repetition frequency decreases, the half-period duration increases; then, the duration of the continued increase in the water dipole moment becomes longer and the interfacial water polarization degree increases. Notably, the polarization discussed here refers to the oriented polarization. For clarity, only three frequencies (0.1, 0.4 and 0.7 THz) are selected as examples. Fig. 8 clearly shows (calculation time is extended to 1500 ps) that the interfacial water polarization degree increases as the symmetrical bipolar psPT repetition frequency decreases. Additionally, the interfacial water dipole moment increases considerably after pore formation. In addition to the influence of the symmetrical bipolar psPT repetition frequency on the pore formation time, the effect of the symmetrical bipolar psPT magnitude on pore formation time was also investigated, as displayed in Fig. 9. The pore formation time decreases with increasing applied psPT magnitude. This phenomenon can also be understood through the interfacial water polarization degree. Fig. S15A and Fig. 10 show that the interfacial water dipole moment increases as the applied symmetrical bipolar psPT magnitude increases. This trend is expected because the polarization degree will increase as the external electric field magnitude increases. Fig. S15B shows that the larger the psPT magnitude is, the shorter the water dipole flip time will be, which is consistent with the results presented in the last section. Thus, the water molecules are rapidly redirected, and the water dipole moment increases when the psPT magnitude increases. In conclusion, the interfacial water polarization degree increases and the pore formation time becomes shorter when the symmetrical bipolar psPT repetition frequency decreases. At the same time, the interfacial water polarization degree increases and the pore formation time decreases when the symmetrical bipolar psPT magnitude increases. It should be noted that in the previous analysis of the case in which no electroporation occurs, the reason for the lack of electroporation was attributed to the continuous flipping and oscillation of interfacial water molecules. However, here, even though the pores form, the dipole moment is still periodically reversed. Although these actions appear to 7
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Fig. 9. (A) The waveforms of the 1, 1.3, 1.6, 1.9 and 2.2 V/nm symmetrical bipolar psPTs. The repetition frequencies of all psPTs are 0.4 THz. (B) The relationship between the pore formation time and symmetrical bipolar psPT magnitude.
in one direction. According to the previous analysis of the conditions required for the symmetrical bipolar psPT to induce electroporation, only when the field amplitude is sufficiently large and the half-cycle is sufficiently long will water protrusion be produced within half a cycle. However, if the unipolar psPT has a high amplitude and a wide half-period, water protrusion will appear in a very short time due to the existence of effect accumulation. In addition, the average pore formation times of unipolar psPT and bipolar psPT were calculated and compared, and the results are displayed in Fig. S16 and Fig. S17. These findings show that the times of the unipolar psPT are shorter than those of the bipolar psPT at the same frequency and intensity. As a result, it is speculated that the reason for bipolar cancellation for picosecond pulses may be related to the phenomenon in which the influence of unipolar picosecond pulses on interfacial water dipoles will accumulate in one direction, whereas the bipolar picosecond pulses do not cause this effect.
Fig. 10. The Z-components of the average interfacial water dipole moments with the applied 1, 1.3, 1.6, 1.9 and 2.2 V/nm symmetrical bipolar psPTs of 0.4 THz (duration is 1500 ps).
4. Conclusion In summary, the phenomenon of no electroporation with the
Fig. 11. The variation in the average angle θ of the interfacial water dipole with the applied 0.65 V/nm 0.4 THz symmetrical bipolar psPT and unipolar psPT. (A) The water angle θ for the symmetrical bipolar psPT. (B) The water angle θ for the unipolar psPT. 8
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Fig. 12. The Z-components of the average interfacial water dipole moments with the applied 0.65 V/nm 0.4 THz symmetrical bipolar psPT and unipolar psPT. (A) The total duration is 7.5 ps. (B) The total duration is 6000 ps.
applied symmetrical bipolar psPT and the conditions required for the symmetrical bipolar psPT to induce electroporation are analyzed and discussed. Moreover, it is discovered that the pore formation time becomes shorter when the symmetrical bipolar psPT repetition frequency decreases and the pore formation time becomes longer when the psPT magnitude decreases. Additionally, a bipolar cancellation for the studied picosecond pulses is predicted. Our findings may provide new insight and theoretical guidance for the application of psPTs in the biomedical field.
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Transparency document [12]
The Transparency document associated this article can be found, in online version.
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Author contributions
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Y.G. and J.T. designed the research and wrote the article. J.T. performed the simulations and analysis. L.Y., J.M., L.G., K.W., Y.Y., W.B., Z.W., H.J., Z.W. and B.Z. revised the article. All authors participated in scientific discussions.
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Declaration of competing interest
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None.
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Appendix A. Supplementary data [19]
Supplementary data to this article can be found online at https:// doi.org/10.1016/j.bbamem.2020.183213.
[20] [21]
References
[22] [1] C.B. Arena, M.B. Sano, J.H. Rossmeisl, J.L. Caldwell, P.A. Garcia, M.N. Rylander, R.V. Davalos, High-frequency irreversible electroporation (H-FIRE) for non-thermal ablation without muscle contraction, Biomed. Eng. Online 10 (1) (2011) 102. [2] M. Casciola, M. Tarek, A molecular insight into the electro-transfer of small molecules through electropores driven by electric fields, Biochim. Biophys. Acta Biomembr. 1858 (10) (2016) 2278–2289. [3] T. Kotnik, L. Rems, M. Tarek, D. Miklavčič, Membrane electroporation and electropermeabilization: mechanisms and models, Annu. Rev. Biophys. 48 (2019). [4] I. Semenov, C. Zemlin, O.N. Pakhomova, S. Xiao, A.G. Pakhomov, Diffuse, nonpolar electropermeabilization and reduced propidium uptake distinguish the effect of nanosecond electric pulses, Biochim. Biophys. Acta Biomembr. 1848 (10) (2015) 2118–2125. [5] S.J. Beebe, K.H. Schoenbach, R. Heller, Bioelectric applications for treatment of melanoma, Cancers 2 (3) (2010) 1731–1770. [6] M.L. Yarmush, A. Golberg, G. Serša, T. Kotnik, D. Miklavčič, Electroporation-based technologies for medicine: principles, applications, and challenges, Annu. Rev. Biomed. Eng. 16 (2014) 295–320. [7] C.B. Arena, C.S. Szot, P.A. Garcia, M.N. Rylander, R.V. Davalos, A three-
[23] [24]
[25] [26] [27] [28]
9
dimensional in vitro tumor platform for modeling therapeutic irreversible electroporation, Biophys. J. 103 (9) (2012) 2033–2042. S.J. Beebe, P.M. Fox, L.J. Rec, E.L.K. Willis, K.H. Schoenbach, Nanosecond, highintensity pulsed electric fields induce apoptosis in human cells, FASEB J. 17 (11) (2003) 1493–1495. T. Kotnik, D. Miklavčič, Theoretical evaluation of voltage inducement on internal membranes of biological cells exposed to electric fields, Biophys. J. 90 (2) (2006) 480–491. S. Xiao, S. Guo, V. Nesin, R. Heller, K.H. Schoenbach, Subnanosecond electric pulses cause membrane permeabilization and cell death, IEEE Trans. Biomed. Eng. 58 (5) (2011) 1239–1245. J.T. Camp, Y. Jing, J. Zhuang, J.F. Kolb, S.J. Beebe, J. Song, K.H. Schoenbach, Cell death induced by subnanosecond pulsed electric fields at elevated temperatures, IEEE Trans. Plasma Sci. 40 (10) (2012) 2334–2347. Y.Y. Hua, X.S. Wang, Y.U. Zhang, C.G. Yao, X.M. Zhang, Z.A. Xiong, Intense picosecond pulsed electric fields induce apoptosis through a mitochondrial-mediated pathway in HeLa cells, Mol. Med. Rep. 5 (4) (2012) 981–987. H. Fröhlich, The biological effects of microwaves and related questions, Advances in Electronics and Electron Physics, vol. 53, Academic Press, 1980, pp. 85–152. P.H. Siegel, Terahertz technology in biology and medicine, IEEE Trans. Microwave Theory Tech. 52 (10) (2004) 2438–2447. P.T. Vernier, Z.A. Levine, M.C. Ho, S. Xiao, I. Semenov, A.G. Pakhomov, Picosecond and terahertz perturbation of interfacial water and electropermeabilization of biological membranes, J. Membr. Biol. 248 (5) (2015) 837–847. G.J. Wilmink, B.L. Ibey, C.L. Roth, R.L. Vincelette, B.D. Rivest, C.B. Horn, W.P. Roach, Determination of death thresholds and identification of terahertz (THz)-specific gene expression signatures, Optical Interactions with Tissues and Cells XXI, 7562 International Society for Optics and Photonics, 2010, February, p. 75620K. G.J. Wilmink, J.E. Grundt, Invited review article: current state of research on biological effects of terahertz radiation, J. Infrared Millim. Terahertz Waves 32 (10) (2011) 1074–1122. M. Borovkova, M. Serebriakova, V. Fedorov, E. Sedykh, V. Vaks, A. Lichutin, M. Khodzitsky, Investigation of terahertz radiation influence on rat glial cells, Biomed. Opt. Express 8 (1) (2017) 273–280. J. Tang, H. Yin, J. Ma, W. Bo, Y. Yang, J. Xu, Y. Gong, Terahertz electric fieldinduced membrane electroporation by molecular dynamics simulations, J. Membr. Biol. 251 (5–6) (2018) 681–693. R.L. Andrew, Molecular Modeling Principles and Applications, Prentice Hall, London, 2001. F. Castellani, J. Teissié, P.T. Vernier, Permeabilizing phospholipid bilayers with non-normal electric fields, J. Membr. Biol. 251 (2) (2018) 229–236. L. Kalé, R. Skeel, M. Bhandarkar, R. Brunner, A. Gursoy, N. Krawetz, K. Schulten, NAMD2: greater scalability for parallel molecular dynamics, J. Comput. Phys. 151 (1) (1999) 283–312. G.J. Martyna, D.J. Tobias, M.L. Klein, Constant pressure molecular dynamics algorithms, J. Chem. Phys. 101 (5) (1994) 4177–4189. S.E. Feller, Y. Zhang, R.W. Pastor, B.R. Brooks, Constant pressure molecular dynamics simulation: the Langevin piston method, J. Chem. Phys. 103 (11) (1995) 4613–4621. M.P. Allen, D.J. Tildesley, Computer Simulation of Liquids, Oxford university press, 2017. T. Darden, D. York, L. Pedersen, Particle mesh Ewald: an N· log (N) method for Ewald sums in large systems, J. Chem. Phys. 98 (12) (1993) 10089–10092. U. Essmann, L. Perera, M.L. Berkowitz, T. Darden, H. Lee, L.G. Pedersen, A smooth particle mesh Ewald method, J. Chem. Phys. 103 (19) (1995) 8577–8593. A.G. Pakhomov, I. Semenov, S. Xiao, O.N. Pakhomova, B. Gregory, K.H. Schoenbach, B.L. Ibey, Cancellation of cellular responses to nanoelectroporation by reversing the stimulus polarity, Cell. Mol. Life Sci. 71 (22) (2014) 4431–4441.