Sonoporation at Small and Large Length Scales: Effect of Cavitation

Letter pubs.acs.org/JPCL

Sonoporation at Small and Large Length Scales: Effect of Cavitation Bubble Collapse on Membranes Haohao Fu,†,# Jeffrey Comer,‡,§,# Wensheng Cai,† and Christophe Chipot*,‡,∥,⊥ †

Collaborative Innovation Center of Chemical Science and Engineering (Tianjin), and Research Center for Analytical Sciences, College of Chemistry, Nankai University, Tianjin 300071, China ‡ Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana−Champaign, Unité Mixte de Recherche n°7565, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy cedex, France § Nanotechnology Innovation Center of Kansas State, Institute of Computational Comparative Medicine, Department of Anatomy and Physiology, Kansas State University, P-213 Mosier Hall, Manhattan, Kansas 66506, United States ∥ Theoretical and Computational Biophysics Group, Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, 405 North Mathews, Urbana, Illinois 61801, United States ⊥ Department of Physics, University of Illinois at Urbana−Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States S Supporting Information *

ABSTRACT: Ultrasound has emerged as a promising means to effect controlled delivery of therapeutic agents through cell membranes. One possible mechanism that explains the enhanced permeability of lipid bilayers is the fast contraction of cavitation bubbles produced on the membrane surface, thereby generating large impulses, which, in turn, enhance the permeability of the bilayer to small molecules. In the present contribution, we investigate the collapse of bubbles of different diameters, using atomistic and coarse-grained molecular dynamics simulations to calculate the force exerted on the membrane. The total impulse can be computed rigorously in numerical simulations, revealing a superlinear dependence of the impulse on the radius of the bubble. The collapse affects the structure of a nearby immobilized membrane, and leads to partial membrane invagination and increased water permeation. The results of the present study are envisioned to help optimize the use of ultrasound, notably for the delivery of drugs.

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and contraction become asymmetric, with gradual expansion followed by violent collapsea phenomenon generally referred to as inertial cavitation.4,9 The violent collapse of the bubbles produces a shock wave and fluid jets,12 which have been shown to cause dramatic changes in the cell membrane morphology.13 Regardless of the precise mechanism that underlies sonoporation, the impulse delivered to the membrane has been identified experimentally as a key parameter in determining the quantity of therapeutic agent transferred to the cell.14 One would expect this impulse to increase with increasing bubble sizea relationship that we explore here. Analytical work and simulations of continuum and molecular dynamics models have shed light on the process of bubble formation, oscillation, and collapse.15−21 However, only molecular dynamics can supply the level of detail required to determine the effect of shock waves on lipid bilayer structure.22−24 Although it yields exquisite detail and can be used to simulate the complete collapse of relatively small bubbles, atomistic molecular dynamics is limited in the size and time scales it can commonly access. Recently, Santo and

ltrasound is capable of increasing the permeability of cell membranes to pharmaceuticals, allowing even poorly bioavailable drugs to be delivered in sufficient quantity.1−5 Enhanced permeability of the otherwise impervious lipid environment is presumed to be the result of the reversible disruption of the membrane structurefor instance, through the generation of transient water-filled pores. For this reason, the phenomenon is referred to as “sonoporation.” Due to the relatively high compressibility of the gas phase, small bubbles suspended in a fluid subjected to an ultrasonic field undergo rapid oscillations in size, with singular or repeated periods of growth followed by contraction.6 Numerous studies have emphasized that such bubbles play a major role in sonoporation.4,5,7−11 Several distinct mechanisms for bubble-induced sonoporation have been proposed, some of which have been observed experimentally.4 At low acoustic intensities, cavitation bubbles undergo small oscillations in size with approximately symmetric expansion and contraction phases.4,9 These low-amplitude oscillations are referred to as stable cavitation, and cause rapid flow of liquid around the bubbles, which can induce shear stresses to membranes. These stresses can be much larger than those due to typical physiological phenomena, such as blood flow.4 At higher ultrasound intensities, the bubble expansion © 2015 American Chemical Society

Received: November 29, 2014 Accepted: January 14, 2015 Published: January 14, 2015 413

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Figure 1. Cross section of the mass density and mass flux of water during bubble collapse for an atomistic model. The mass density is characterized by the shade of cyan for each voxel, as specified by the color bar on the righthand side, while the red arrows depict the mass flux in the x and z directions for each voxel. The initial 20 nm-diameter bubble can be identified by its approximate circular cross section and near zero density, while the membrane appears as a ribbon of zero density just below it. Panels A, B, and C show averages of the data over the time intervals 0−40, 240−280, and 280−300 ps, respectively, after the initiation of the collapse. The significant fluctuations of the density in the plots are natural fluctuations on the size scale of the voxels (0.125 nm3).

Figure 2. Collapse of the bubble, and force and impulse on the membrane. (A) Diameter of the bubble as a function of time after initiation of collapse. The data correspond to the atomistic simulations of bubbles with initial diameters of 6, 8, and 20 nm. (B) Force exerted on the membrane as a function of time after initiation of collapse. So that the correspondence with the collapse can be clearly identified, only the first 0.5 ns of the data is shown. (C) Impulse on the membrane as a function of time after initiation of collapse. The data show the full duration of the simulations. (D) Distribution of the z-force on the surface of the lipid bilayer as a function of the distance from the center of the bubble projected onto the x,y-plane. The force is calculated per lipid and averaged over many lipids and over the time interval of 40−80 ps after initiation of the collapse.

Berkowitz23,24 employed the coarse-grained MARTINI model,25 in which each particle represents about four nonhydrogen atoms, to perform molecular dynamics simulations of bubbles of unprecedented size, while maintaining the ability to observe their effects on individual lipids. These simulations revealed the creation of water-filled pores in the bilayer, which heal over time, except for some lipids that appear to be more or less permanently expelled from the membrane. The MARTINI force field is parametrized to augment sampling in molecular simulations, while preserving moderate accuracy. Whereas the simulation of shock waves with the atomistic SPC water model26 yields results comparable to experiment,18 Santo and Berkowitz23,24 report a more modest agreement with the MARTINI water model. It still remains that this coarse-grained force field appears to be suitable to simulate the implosion of a bubble in a system formed of water and lipids. As is asserted in the original paper of the MARTINI force field,25 however, the use of standard masses  i.e., 72 Da per bead, sometimes leads to poor kinetics. In what follows, we will emphasize the importance of using correct masses in simulations where Newtonian kinetics plays a crucial role. Since the total impulse delivered to the membrane highly correlates with the enhanced permeation of drugs,14 in this work, we focus on the computation of this quantity from numerical simulations. We find that the impulse can be calculated in a rigorous fashion, assuming appropriate design of the atomistic or the coarse-grained simulations. In light of these

simulations, we put forth a relationship that establishes the dependence of the impulse on the size of the bubble. Because the bubbles in our simulations are separated from the membrane by a layer of water, all forces exerted on this membrane during collapse are transmitted through the water. Therefore, in Figure 1, we highlight the action of water during the process of bubble collapse for an atomistic model of a 20 nm-diameter bubble. A spherically symmetric potential was initially applied to expel water from the interior of the bubble (see “Computational details” in the Supporting Information (SI) for the precise mathematical form of the force). Upon removal of the force maintaining this bubble, the very low pressure within the latter is unable to withstand the external hydrostatic pressure, so that the interfacial water gushes rapidly inward, as can be seen in Figure 1A. Due to the speed of sound being on the order of 1 nm/ps, the effect of the flow reaches the nearby lipid bilayer in the first few picoseconds, while the collapse is in its early stages, and the water between the membrane and the surface of the bubble flows rapidly toward the latter. After 240 ps, the bubble has contracted to less than half its original diameter, and has become somewhat prolate, having a greater diameter along the z axis than that orthogonal to it, as is evidenced from Figure 1B. The shape of the bubble can be ascribed to the small gap between the surface of the cavitation bubble and the nearby membrane. Although water molecules are fewer below, adjacent water molecules can rapidly gush in to fill the void. As the bubble collapses, its 414

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appeared resilient to dramatic changes in the system geometry, corroborating the reliability of the impulses as predicted by molecular dynamics. The collapse of a bubble near the lipid bilayer results in changes in the structure of the latter, which become particularly dramatic as the size of the bubble increases. The collapse transiently reduces the local pressure above the membrane. The water below it, which remains at atmospheric pressure, exerts an upward force on the lipid bilayer, causing it to protrude in the direction of the collapsing bubble  a phenomenon evidenced in Figure 1B and Figure 1C. To determine the distribution of the force acting on the surface of the membrane, we repeated the simulation of the 8 nm-diameter bubble, with each lipid pertaining to the upper leaflet individually restrained about a fixed z value, instead of restraining the center of mass of the entire bilayer. The strength of the geometrical restraint was chosen to minimally affect the spatial distribution of the lipid bilayer at equilibrium, while eliminating large deformations. Figure 2D shows the radial distribution in the xy-plane of the z component of the force acting on the membrane. At this early stage of the collapse, a large force gradient can be observed, with a strong pull toward the bubble in a 1 nm radius nearest the bubble, and similarly, a strong force away from the bubble at radial distances between 1.3 and 2.0 nm. It is this force distribution that is responsible for the protuberance of the membrane visible in Figure 1B. We also quantify the deformation of the lipid bilayer by calculating the root-meansquare roughness of its surface, shown in Figure S4B. In all cases, the roughness rises rapidly at the beginning of the collapse and then gradually approaches its equilibrium value over many nanoseconds. For the 20 nm-diameter bubble, large undulations appear on the scale of the thickness of the membrane itself. The amplitude and the wavelength of these undulations likely depend on the size of the membrane patch equivalently its xy-dimensions, used in our simulations. Although atomistic simulations have revealed many aspects of bubble collapse, these simulations are somewhat limited in the sizes of the molecular assemblies and the lengths of time that can be simulated at an acceptable computational cost and within a reasonable amount of real, wall-clock time. Coarsegrained models were, therefore used to explore the effects of larger bubbles on the membrane. Following the standard protocol of the MARTINI coarse-grained models,25 we first assigned to each bead a mass of 72 Da. However, as stated by Marrink et al. in their reference article, for “accurate analysis of kinetic properties, more realistic masses should be used in the simulations”. Indeed, Figure S5 of the SI clearly shows that the 72 Da masses lead to prediction of higher impulses on the lipid bilayer, while more realistic masses yield similar results for atomistic and MARTINI coarse-grained models. It is worth noting that we arrive at this agreement without rescaling the time, as is sometimes done when the MARTINI model is employed.25 Beyond the methodological implications, the dependence of the impulse on the mass of the lipids would entail that the impulse be sensitive to the lipid composition, as well as other factors affecting membrane mechanics, including protein content and the presence of a cytoskeleton. Thus, while the present work represents a step forward in understanding the physical effect of collapsing cavitation bubbles on a membrane, future work may need to consider more realistic models of cell membranes. Using the coarse-grained model with realistic masses, four collapse simulations were performed for 15, 20, 30, and 40 nm-

center is displaced only slightly, moving by approximately 0.4, 0.5, and 1.2 nm before collapsing completely for the 6, 8, and 20 nm bubbles, respectively. The flow field near the bubble around 240 ps appears somewhat steady, albeit anisotropic, with a greater flow of water from above and from the sides than from below, owing to the presence of the membrane. As has been highlighted by Lugli et al.,15 the final stage of contraction is particularly violent. Continuum hydrodynamics predicts a diverging velocity for the infalling bubble surface as the bubble approaches complete collapse. The rate of change of the bubble diameter is given by −3/5 2D ⎛ t − t ⎞ dD = − 0⎜ c ⎟ dt 5tc ⎝ tc ⎠

(1)

where D is the diameter of the bubble at time t, D0 is the initial diameter, and tc is the time at which the bubble has completely collapsed. A similar behavior can be observed in Figure 2A, with D(t) displaying very large slopes near tc. Because the collapsing bubble did not remain precisely spherical, nor did it remain centered on its original position, the diameter was calculated by generating line segments in random directions that pass through the centroid of the void and begin and end on the water surface. The values shown in Figure 2A represent the average of the length of these line segments. Near the time of complete collapse, the flow field in the vicinity of the bubble, shown in Figure 1C, becomes distinctly nonuniform. As shown in Figure 2B, the force exerted on the restrained membrane rises rapidly at the beginning of collapse, but then plateaus and only rises slowly. The maximum of the force acting on the membrane occurs very near the time at which the diameter of the bubble reaches zero, i.e., when the bubble has collapsed completely. For the bubbles with initial diameters of 6, 8, and 20 nm, complete collapse transpires in a relatively short time framenamely, after 39, 145, and 305 ps, respectively. While the force on the membrane noticeably begins to drop after the complete collapse, it dissipates with a long tail. Indeed, Figure 2C reveals that the impulse, i.e., the time integral of the force, plateaus for the 6 and 8 nm-diameter bubbles only after about 5 nsthat is, more than 30 times longer than the time required for complete disappearance of the bubble. Furthermore, the impulse on the membrane from the collapse of the 20 nm bubble does not reach a steady value within the 33 ns duration of the simulation, which raises an important question. What is the origin of the persistence of the force? As described below, it appears to be due to a continued inflow of water as the density approaches its equilibrium value at 300 K and 1 atm. One might argue that the values of the impulse, or the time scale of the decay of the force might be artifacts due to the finite size of the simulated systems. To determine whether there were significant finite-size artifacts, we repeated the collapse of the 8 nm-diameter bubble, quadrupling the area in the xy-plane, or quintupling the height along the z axis of the volume of water containing the bubble. In both cases, the final value of the impulse on the membrane is remarkably similar to that of the original system (see Methods and Figure S4A of the SI). The force as a function of time is nearly identical in the original system and in the system that was extended along the z axis. Despite the similar final values of the impulse, the system featuring the largest area in the xy-plane displayed a somewhat reduced peak force and a somewhat slower rise and decay. In conclusion, the total impulse imparted to the membrane 415

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increase as the bubble implodes, peaking with the disappearance of the latter. Subsequently, the peak force decays gradually toward zero, and the impulse reaches a plateau. The deformation of the membrane induced by the collapse of the bubble results in an increased permeation of water molecules through the lipid bilayer, which is possible, even though a complete transmembrane water channel was not observed.22 The total number of water molecules permeating the membrane in different systems is shown in Figure 4C. Only a few hundred water molecules permeate the bilayer when the diameter of the bubble is 20 nm or smaller. However, the collapse of the 40 nm bubble was associated with the passage of thousands of water molecules through the lipid bilayer. Despite this massive increase in water permeation, no water filled pores are observed during the simulation, perhaps because the bubbles modeled in the present work are still too small to produce the required impulse. In experiments, the diameter of contractive bubbles ranges from 10 to 100 μm, which is hundreds of times larger than those examined in our simulations. Molecular simulation for bubbles of such size would be extremely costly. It is, therefore, necessary to build a quantitative model to bridge atomic-level simulations and the macroscopic experiments. It can be seen clearly in Figure 4A that the final value of the impulse on the membrane increases with the size of the bubbles. To establish a quantitative relationship, we performed least-squares fitting on the data obtained from both the atomistic and coarse-grained simulations. The fitted curve is shown in Figure 4D, and has a correlation coefficient greater than 0.98. The curve obeys the equation

diameter bubbles. Both the snapshots of the membrane and the time-evolution of the mass density of water beads obtained from the simulation trajectory indicate that the largest deformation of the membrane emerges within 2.4 ns, that is, slightly after the collapse of the bubble (see Figure 3 and Figure

Figure 3. Time-evolution of the mass density of the water beads in the xz-plane. The mass density decreases during the collapse of a 20 nmdiameter bubble, but fully recovers after approximately 30 ns. The deformation of the membrane occurs after the complete implosion of the bubble.

S6 of the SI). It is worth noting that the complete-collapse time of the bubble is nearly double that witnessed in the atomistic simulation (cf. Figure 1), notwithstanding the fact that the effective time in MARTINI simulations is usually assumed to be accelerated with respect to atomistic simulations.25 As shown in Figure 4A,B, the time-evolution of the forces and impulses on the lipid bilayer follow trends similar to those observed from the atomistic simulations. The forces initially undergo rapid

Itotal = cD2.15

(2)

where Itotal is the total impulse on the membrane in nN·ns, D is the diameter of the bubble in nm, and c = 0.063. This empirical equation, proposed for the first time, provides a quantitative analysis of the effect of the cavitation bubble collapse on a lipid bilayer. As suggested by Figure 2D, we assume that the impulse is concentrated on a particular portion of the membrane having area A, and that A is roughly proportional to the cross-sectional area of the bubble. Thus, the relationship between the average impulse per unit area, IA and the diameter, D, of the bubbles can be deduced as follows (see the SI for details):

IA = c0D1.15

(3)

where c0 is a coefficient depending on the definition of A and the minimum distance between the surface of the bubble and the membrane, h. For our simulations, we calculate c0 = 0.0033, for IA in nN·ns2. On one hand, in experiment, the size of the microbubbles observed on the surface of the membrane by microscope and high-speed camera ranges from 10 to 100 μm, and these bubbles have been shown to be capable of generating transient transmembrane water pores.12,27 Using eq 3, the corresponding value of IA for these microbubbles is estimated to range from 131 to 1856 Pa·s. On the other hand, experiments of shock-wave-induced permeation suggest that a 140 Pa·s shock can promote drug delivery.14 From the above analysis, it is apparent that the present model, bridging the size of the bubbles and the shock-wave strength on the membrane through eq 3, can rationalize experimental measurements. In light of the equations introduced herein, a number of phenomena observed in the macroscopic experiments can be well explained. For example, it is found that the transfection

Figure 4. (A) Time evolution of the impulse exerted on the membrane, using coarse-grained models. (Inset) Comparison of coarse-grained and atomistic simulations for the 20 nm bubble. (B) Time evolution of the force exerted on the membrane, using coarsegrained models. (C) Total number of water molecules permeating the membrane as a function of initial bubble diameter. (D) Total impulse as a function of initial bubble diameter with least-squares fit. The numbers from left to right are obtained from the molecular assemblies featuring 6, 8, 15, 20, 30, 40 nm-diameter bubbles, respectively. 416

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sizes, the membrane roughness, time-evolution of the impulses, mapping strategy of corrected masses for the coarse-grained model, membrane deformation, assumption of an effective action area, and calculation the of impulse per area. This material is available free of charge via the Internet at http:// pubs.acs.org/.

efficiency of genomic drugs and the cell viability are highly correlated with the ultrasound parameters, e.g., acoustic peak negative pressure and pulse repetition frequency.13,28 Different ultrasound parameters may induce different sizes of cavitation bubbles on the surface of the lipid bilayer. On one hand, excessively small bubbles cannot generate enough impulse per area to promote enhanced permeation, and, hence, may have difficulty in facilitating drug delivery. On the other hand, overly large bubbles may create impulses that irremediably disrupt the lipid bilayer and, thus, reduce cell viability. Applying the proper ultrasound parameters may ensure production of bubbles of the proper size, thereby enhancing transfection efficiency, while maintaining cell viability. Although eq 3 was derived based on the results from the collapse of cavitation bubbles at the nanoscale, by extrapolation on the basis of experimental data, we found that it also holds at the microscale. We have reasons to believe that our work can bridge the microscopic detail of numerical simulations with the macroscopic nature of experiments. It, nevertheless, should be made clear that the derivation of this equation was based on stringent assumptions, namely, (i) the impulse per area is the most important parameter in the analysis of the collapse of a bubble, and (ii) all the effect of the collapse is concentrated in a certain surface area of the membrane, and the distribution of the total impulse in this region is uniform. Further experiment and simulation may be needed to determine whether the partial violation of these assumptions will invalidate the predictions of the model. The high rate of attrition of pharmaceuticals due to their poor absorption and distribution constitutes a major obstacle for conventional administration routes. Sonoporation, an approach that consists in perturbing the membrane transiently by the collapse of small bubbles generated at its aqueous interface by means of ultrasound, represents a promising avenue to reposition potent drugs that have been disregarded on account of their mediocre bioavailability and possible cytotoxicity. In this contribution, the collapse of bubbles of different sizes on the surface of a lipid bilayer was simulated using both atomistic and coarse-grained descriptions. For the first time, a phenomenological formula relating the total impulse acting on the membrane to the diameter of the bubbles is reported. This equation has the potential to bridge macroscopic sonoporation experiments to the microscopic theory of bubble collapse. In addition to providing information that may help optimize the ultrasound parameters used in experiments, the present work also reveals the effects that bubble collapse or other strong hydrodynamic flows impose on membranes. Moreover, we provide herein what we hope will serve as a basis for further simulations of cavitation bubble collapse near membranes, in particular a theoretical framework for estimating the impulse delivered to the membrane and an assessment of how the latter quantity evolves with the size of the molecular assembly. Furthermore, our results highlight the need for correct masses in coarse-grained simulations of dynamic phenomena, as well as the difficulty of defining effective time scales in these simulations.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions #

(H.F., J.C.) Contributed equally to this work

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This study is supported by National Natural Science Foundation of China (No. 21373117). The CINES, Montpellier, France, is gratefully acknowledged for provision of generous amounts of computer time. The Cai Yuanpei program is also appreciatively acknowledged for its support of the international collaboration between the research groups of C.C. and W.C.

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ASSOCIATED CONTENT

S Supporting Information *

The methods, including the design of the simulations and the computational details, the effect of the thermostat, the simulations of bubble collapse, the effect of different system 417

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