Melittin-induced bilayer leakage depends on lipid material properties: evidence for toroidal pores

The membrane-lytic peptide melittin has previously been shown to form pores in lipid bilayers that have been described in terms of two different structural models. In the "barrel stave" model the bilayer remains more or less flat, with the peptides penetrating across the bilayer hydrocarbon region and aggregating to form a pore, whereas in the "toroidal pore" melittin induces defects in the bilayer such that the bilayer bends sharply inward to form a pore lined by both peptides and lipid headgroups. Here we test these models by measuring both the free energy of melittin transfer (DeltaG degrees ) and melittin-induced leakage as a function of bilayer elastic (material) properties that determine the energetics of bilayer bending, including the area compressibility modulus (K(a)), bilayer bending modulus (k(c)), and monolayer spontaneous curvature (R(o)). The addition of cholesterol to phosphatidylcholine (PC) bilayers, which increases K(a) and k(c), decreases both DeltaG degrees and the melittin-induced vesicle leakage. In contrast, the addition to PC bilayers of molecules with either positive R(o), such as lysoPC, or negative R(o), such as dioleoylglycerol, has little effect on DeltaG degrees , but produces large changes in melittin-induced leakage, from 86% for 8:2 PC/lysoPC to 18% for 8:2 PC/dioleoylglycerol. We observe linear relationships between melittin-induced leakage and both K(a) and 1/R(o)(2). However, in contrast to what would be expected for a barrel stave model, there is no correlation between observed leakage and bilayer hydrocarbon thickness. All of these results demonstrate the importance of bilayer material properties on melittin-induced leakage and indicate that the melittin-induced pores are defects in the bilayer lined in part by lipid molecules.     

Atomistic Simulations of Pore Formation and Closure in Lipid Bilayers

Cellular membranes separate distinct aqueous compartments, but can be breached by transient hydrophilic pores. A large energetic cost prevents pore formation, which is largely dependent on the composition and structure of the lipid bilayer. The softness of bilayers and the disordered structure of pores make their characterization difficult. We use molecular-dynamics simulations with atomistic detail to study the thermodynamics, kinetics, and mechanism of pore formation and closure in DLPC, DMPC, and DPPC bilayers, with pore formation free energies of 17, 45, and 78 kJ/mol, respectively. By using atomistic computer simulations, we are able to determine not only the free energy for pore formation, but also the enthalpy and entropy, which yields what is believed to be significant new insights in the molecular driving forces behind membrane defects. The free energy cost for pore formation is due to a large unfavorable entropic contribution and a favorable change in enthalpy. Changes in hydrogen bonding patterns occur, with increased lipid-water interactions, and fewer water-water hydrogen bonds, but the total number of overall hydrogen bonds is constant. Equilibrium pore formation is directly observed in the thin DLPC lipid bilayer. Multiple long timescale simulations of pore closure are used to predict pore lifetimes. Our results are important for biological applications, including the activity of antimicrobial peptides and a better understanding of membrane protein folding, and improve our understanding of the fundamental physicochemical nature of membranes.     

Interaction of hagfish cathelicidin antimicrobial peptides with model lipid membranes

Hagfish intestinal antimicrobial peptides (HFIAPs) are a family of polycationic peptides exhibiting potent, broad-spectrum bactericidal activity. In an attempt to unravel the mechanism of action of HFIAPs, we have studied their interaction with model membranes. Synthetic HFIAPs selectively bound to liposomes mimicking bacterial membranes, and caused the release of vesicle-encapsulated fluorescent markers in a size-dependent manner. In planar lipid bilayer membranes, HFIAPs induced erratic current fluctuations and reduced membrane line tension according to a general theory for lipidic pores, suggesting that HFIAP pores contain lipid molecules. Consistent with this notion, lipid transbilayer redistribution accompanied HFIAP pore formation, and membrane monolayer curvature regulated HFIAP pore formation. Based on these studies, we propose that HFIAPs kill target cells, at least in part, by interacting with their plasma membrane to induce formation of lipid-containing pores. Such a membrane-permeabilizing function appears to be an evolutionarily conserved host-defense mechanism of antimicrobial peptides.     

Atomistic Simulations of Pore Formation and Closure in Lipid Bilayers

Cellular membranes separate distinct aqueous compartments, but can be breached by transient hydrophilic pores. A large energetic cost prevents pore formation, which is largely dependent on the composition and structure of the lipid bilayer. The softness of bilayers and the disordered structure of pores make their characterization difficult. We use molecular-dynamics simulations with atomistic detail to study the thermodynamics, kinetics, and mechanism of pore formation and closure in DLPC, DMPC, and DPPC bilayers, with pore formation free energies of 17, 45, and 78 kJ/mol, respectively. By using atomistic computer simulations, we are able to determine not only the free energy for pore formation, but also the enthalpy and entropy, which yields what is believed to be significant new insights in the molecular driving forces behind membrane defects. The free energy cost for pore formation is due to a large unfavorable entropic contribution and a favorable change in enthalpy. Changes in hydrogen bonding patterns occur, with increased lipid-water interactions, and fewer water-water hydrogen bonds, but the total number of overall hydrogen bonds is constant. Equilibrium pore formation is directly observed in the thin DLPC lipid bilayer. Multiple long timescale simulations of pore closure are used to predict pore lifetimes. Our results are important for biological applications, including the activity of antimicrobial peptides and a better understanding of membrane protein folding, and improve our understanding of the fundamental physicochemical nature of membranes.     

Molecular dynamics simulations of hydrophilic pores in lipid bilayers

Hydrophilic pores are formed in peptide free lipid bilayers under mechanical stress. It has been proposed that the transport of ionic species across such membranes is largely determined by the existence of such meta-stable hydrophilic pores. To study the properties of these structures and understand the mechanism by which pore expansion leads to membrane rupture, a series of molecular dynamics simulations of a dipalmitoylphosphatidylcholine (DPPC) bilayer have been conducted. The system was simulated in two different states; first, as a bilayer containing a meta-stable pore and second, as an equilibrated bilayer without a pore. Surface tension in both cases was applied to study the formation and stability of hydrophilic pores inside the bilayers. It is observed that below a critical threshold tension of approximately 38 mN/m the pores are stabilized. The minimum radius at which a pore can be stabilized is 0.7 nm. Based on the critical threshold tension the line tension of the bilayer was estimated to be approximately 3 x 10(-11) N, in good agreement with experimental measurements. The flux of water molecules through these stabilized pores was analyzed, and the structure and size of the pores characterized. When the lateral pressure exceeds the threshold tension, the pores become unstable and start to expand causing the rupture of the membrane. In the simulations the mechanical threshold tension necessary to cause rupture of the membrane on a nanosecond timescale is much higher in the case of the equilibrated bilayers, as compared with membranes containing preexisting pores.     

Relationships between the orientation and the structural properties of peptides and their membrane interactions

Physical properties of membranes, such as fluidity, charge or curvature influence their function. Proteins and peptides can modulate those properties and conversely, the lipids can affect the activity and/or the structure of the former. Tilted peptides are short hydrophobic protein fragments characterized by an asymmetric distribution of their hydrophobic residues when helical. They were detected in viral fusion proteins and in proteins involved in different biological processes that need membrane destabilization. Those peptides and non lamellar lipids such as PE or PA appear to cooperate in the lipid destabilization process by enhancing the formation of negatively-curved domains. Such highly bent lipidic structures could favour the formation of the viral fusion pore intermediates or that of toroidal pores. Structural flexibility appears as another crucial property for the interaction of peptides with membranes. Computational analysis on another kind of lipid-interacting peptides, i.e. cell penetrating peptides (CPP) suggests that peptides being conformationally polymorphic should be more prone to traverse the bilayer. Future investigations on the structural intrinsic properties of tilted peptides and the influence of CPP on the bilayer organization using the techniques described in this chapter should help to further understand the molecular determinants of the peptide/lipid inter-relationships.     

Hemifusion between cells expressing hemagglutinin of influenza virus and planar membranes can precede the formation of fusion pores that subsequently fully enlarge

The chronological relation between the establishment of lipid continuity and fusion pore formation has been investigated for fusion of cells expressing hemagglutinin (HA) of influenza virus to planar bilayer membranes. Self-quenching concentrations of lipid dye were placed in the planar membrane to monitor lipid mixing, and time-resolved admittance measurements were used to measure fusion pores. For rhodamine-PE, fusion pores always occurred before a detectable amount of dye moved into an HA-expressing cell. However, with DiI in the planar membrane, the relationship was reversed: the spread of dye preceded formation of small pores. In other words, by using DiI as probe, hemifusion was clearly observed to occur before pore formation. For hemifused cells, a small pore could form and subsequently fully enlarge. In contrast, for cells that express a glycosylphosphatidylinositol-anchored ectodomain of HA, hemifusion occurred, but no fully enlarged pores were observed. Therefore, the transmembrane domain of HA is required for the formation of fully enlarging pores. Thus, with the planar bilayer membranes as target, hemifusion can precede pore formation, and the occurrence of lipid dye spread does not preclude formation of pores that can enlarge fully.     

Membrane permeability changes at early stages of influenza hemagglutinin-mediated fusion

While biological membrane fusion is classically defined as the leak-free merger of membranes and contents, leakage is a finding in both experimental and theoretical studies. The fusion stages, if any, that allow membrane permeation are uncharted. In this study we monitored membrane ionic permeability at early stages of fusion mediated by the fusogenic protein influenza hemagglutinin (HA). HAb2 cells, expressing HA on their plasma membrane, fused with human red blood cells, cultured liver cells PLC/PRF/5, or planar phospholipid bilayer membranes. With a probability that depended upon the target membrane, an increase of the electrical conductance of the fusing membranes (leakage) by up to several nS was generally detected. This leakage was recorded at the initial stages of fusion, when fusion pores formed. This leakage usually accompanied the "flickering" stage of the early fusion pore development. As the pore widened, the leakage reduced; concomitantly, the lipid exchange between the fusing membranes accelerated. We conclude that during fusion pore formation, HA locally and temporarily increases the permeability of fusing membranes. Subsequent rearrangement in the fusion complex leads to the resealing of the leaky membranes and enlargement of the pore.     

pH-triggered pore-forming peptides with strong composition-dependent membrane selectivity

Peptides that self-assemble into nanometer-sized pores in lipid bilayers could have utility in a variety of biotechnological and clinical applications if we can understand their physical chemical properties and learn to control their membrane selectivity. To empower such control, we have used synthetic molecular evolution to identify the pH-dependent delivery peptides, a family of peptides that assemble into macromolecule-sized pores in membranes at low peptide concentration but only at pH < ～6. Further advancements will also require better selectivity for specific membranes. Here, we determine the effect of anionic headgroups and bilayer thickness on the mechanism of action of the pH-dependent delivery peptides by measuring binding, secondary structure, and macromolecular poration. The peptide pHD15 partitions and folds equally well into zwitterionic and anionic membranes but is less potent at pore formation in phosphatidylserine-containing membranes. The peptide also binds and folds similarly in membranes of various thicknesses, but its ability to release macromolecules changes dramatically. It causes potent macromolecular poration in vesicles made from phosphatidylcholine with 14 carbon acyl chains, but macromolecular poration decreases sharply with increasing bilayer thickness and does not occur at any peptide concentration in fluid bilayers made from phosphatidylcholine lipids with 20-carbon acyl chains. The effects of headgroup and bilayer thickness on macromolecular poration cannot be accounted for by the amount of peptide bound but instead reflect an inherent selectivity of the peptide for inserting into the membrane-spanning pore state. Molecular dynamics simulations suggest that the effect of thickness is due to hydrophobic match/mismatch between the membrane-spanning peptide and the bilayer hydrocarbon. This remarkable degree of selectivity based on headgroup and especially bilayer thickness is unusual and suggests ways that pore-forming peptides with exquisite selectivity for specific membranes can be designed or evolved.     

Free energy analysis of membrane pore formation process in the presence of multiple melittin peptides

Understanding the molecular mechanism underlying pore formation in lipid membranes by antimicrobial peptides is of great importance in biological sciences as well as in drug design applications. Melittin has been widely studied as a pore forming peptide, though the molecular mechanism for pore formation is still illusive. We examined the free energy barrier for the creation of a pore in lipid membranes with and without multiple melittin peptides. It was found that six melittin peptides significantly stabilized a pore, though a small barrier (a few k_BT) for the formation still existed. With five melittin peptides or fewer, the pore formation barrier was much higher, though the established pore was in a local energy minimum. Although seven melittins effectively reduced the free energy barrier, a single melittin peptide left the pore after a long time MD simulation probably because of the overcrowded environment around the bilayer pore. Thus, it is highly selective for the number of melittin peptides to stabilize the membrane pore, as was also suggested by the line tension evaluations. The free energy cost required to insert a single melittin into the membrane is too high to explain the one-by-one insertion mechanism for pore formation, which also supports the collective melittin mechanism for pore formation.     

Defect formation of lytic peptides in lipid membranes and their influence on the thermodynamic properties of the pore environment

We present an experimental study of the pore formation processes of small amphipathic peptides in model phosphocholine lipid membranes. We used atomic force microscopy to characterize the spatial organization and structure of alamethicin- and melittin-induced defects in lipid bilayer membranes and the influence of the peptide on local membrane properties. Alamethicin induced holes in gel DPPC membranes were directly visualized at different peptide concentrations. We found that the thermodynamic state of lipids in gel membranes can be influenced by the presence of alamethicin such that nanoscopic domains of fluid lipids form close to the peptide pores, and that the elastic constants of the membrane are altered in their vicinity. Melittin-induced holes were visualized in DPPC and DLPC membranes at room temperature in order to study the influence of the membrane state on the peptide induced hole formation. Also differential scanning calorimetry was used to investigate the effect of alamethicin on the lipid membrane phase behaviour.     

Defect formation of lytic peptides in lipid membranes and their influence on the thermodynamic properties of the pore environment

We present an experimental study of the pore formation processes of small amphipathic peptides in model phosphocholine lipid membranes. We used atomic force microscopy to characterize the spatial organization and structure of alamethicin- and melittin-induced defects in lipid bilayer membranes and the influence of the peptide on local membrane properties. Alamethicin induced holes in gel DPPC membranes were directly visualized at different peptide concentrations. We found that the thermodynamic state of lipids in gel membranes can be influenced by the presence of alamethicin such that nanoscopic domains of fluid lipids form close to the peptide pores, and that the elastic constants of the membrane are altered in their vicinity. Melittin-induced holes were visualized in DPPC and DLPC membranes at room temperature in order to study the influence of the membrane state on the peptide induced hole formation. Also differential scanning calorimetry was used to investigate the effect of alamethicin on the lipid membrane phase behaviour.     

Minimum Membrane Bending Energies of Fusion Pores

Membranes fuse by forming highly curved intermediates, culminating in structures described as fusion pores. These hourglass-like figures that join two fusing membranes have high bending energies, which can be estimated using continuum elasticity models. Fusion pore bending energies depend strongly on shape, and the present study developed a method for determining the shape that minimizes bending energy. This was first applied to a fusion pore modeled as a single surface and then extended to a more realistic model treating a bilayer as two monolayers. For the two-monolayer model, fusion pores were found to have metastable states with energy minima at particular values of the pore diameter and bilayer separation. Fusion pore energies were relatively insensitive to membrane thickness but highly sensitive to spontaneous curvature and membrane asymmetry. With symmetrical bilayers and monolayer spontaneous curvatures of ?0.1 nm^?1 (a typical value) separated by 6 nm (closest distance determined by repulsive hydration forces), fusion pore formation required 43–65 kT. The pore radius of ~2.25 nm fell within the range estimated from conductance measurements. With bilayer separation >6 nm, fusion pore formation required less energy, suggesting that protein scaffolds can promote fusion by bending membranes toward one another. With nonzero spontaneous monolayer curvature, the shape that minimized the energy change during fusion pore formation differed from the shape that minimized its energy after it formed. Thus, a nascent fusion pore will relax spontaneously to a new shape, consistent with the experimentally observed expansion of nascent fusion pores during viral fusion.     

Mechanisms of leakage

Abstract

Two mechanisms of leakage from liposomes are discussed, (i) Cations such as Ca²⁺ induce graded release whose rate depends mainly on vesicle collisions and is associated in the case of several acidic phospholipids with fusion events. A certain degree of leakage also occurs in between collisions. Consequently, the leakage per fusion is reduced at larger lipid and Ca concentrations, (n) Certain peptides induce leakage by pore formation, which shows selectivity to the size of the entrapped molecules and occurs by an all or none mechanism; vesicles either leak or retain all of their contents. A model for final extents and kinetics of leakage due to pore forming peptides is described. This model assumes that pore forming peptides become incorporated into the vesicle bilayer and aggregate to form a pore. Recent developments in the model enable considerations of a reversible or irreversible surface aggregation of peptides. Results of final extents and kinetics of leakage induced by pore forming peptides can be well explained and predicted by this formalism. Studies demonstrate that Ca can play a dual role in affecting leakage. A case is presented where Ca ⁺ inhibits and can even arrest pore formation by a peptide, while promoting vesicle fusion. Conversely, formation of pore structures by a peptide can inhibit vesicle fusion.     

Protein Arcs May Form Stable Pores in Lipid Membranes

Electron microscopy and atomic force microscopy images of cholesterol-dependent cytolysins and related proteins that form large pores in lipid membranes have revealed the presence of incomplete rings, or arcs. Some evidence indicates that these arcs are inserted into the membrane and induce membrane leakage, but other experiments seem to refute that. Could such pores, only partially lined by protein, be kinetically and thermodynamically stable? How would the lipids be structured in such a pore? Using the antimicrobial peptide protegrin-1 as a model, we test the stability of pores only partially lined by peptide using all-atom molecular dynamics simulations in POPC and POPE/POPG membranes. The data show that, whereas pure lipid pores close rapidly, pores partially lined by protegrin arcs are stable for at least 300 ns. Estimates of the thermodynamic stability of these arcs using line tension data and implicit solvent calculations show that these arcs can be marginally stable in both zwitterionic and anionic membranes. Arcs provide an explanation for the observed ion selectivity in protegrin electrophysiology experiments and could possibly be involved in other membrane permeabilization processes where lipids are thought to participate, such as those induced by antimicrobial peptides and colicins, as well as the Bax apoptotic pore.     

Dynamics of fusion pores connecting membranes of different tensions

The energetics underlying the expansion of fusion pores connecting biological or lipid bilayer membranes is elucidated. The energetics necessary to deform membranes as the pore enlarges, in some combination with the action of the fusion proteins, must determine pore growth. The dynamics of pore growth is considered for the case of two homogeneous fusing membranes under different tensions. It is rigorously shown that pore growth can be quantitatively described by treating the pore as a quasiparticle that moves in a medium with a viscosity determined by that of the membranes. Motion is subject to tension, bending, and viscous forces. Pore dynamics and lipid flow through the pore were calculated using Lagrange's equations, with dissipation caused by intra- and intermonolayer friction. These calculations show that the energy barrier that restrains pore enlargement depends only on the sum of the tensions; a difference in tension between the fusing membranes is irrelevant. In contrast, lipid flux through the fusion pore depends on the tension difference but is independent of the sum. Thus pore growth is not affected by tension-driven lipid flux from one membrane to the other. The calculations of the present study explain how increases in tension through osmotic swelling of vesicles cause enlargement of pores between the vesicles and planar bilayer membranes. In a similar fashion, swelling of secretory granules after fusion in biological systems could promote pore enlargement during exocytosis. The calculations also show that pore expansion can be caused by pore lengthening; lengthening may be facilitated by fusion proteins.     

Protein Arcs May Form Stable Pores in Lipid Membranes

Electron microscopy and atomic force microscopy images of cholesterol-dependent cytolysins and related proteins that form large pores in lipid membranes have revealed the presence of incomplete rings, or arcs. Some evidence indicates that these arcs are inserted into the membrane and induce membrane leakage, but other experiments seem to refute that. Could such pores, only partially lined by protein, be kinetically and thermodynamically stable? How would the lipids be structured in such a pore? Using the antimicrobial peptide protegrin-1 as a model, we test the stability of pores only partially lined by peptide using all-atom molecular dynamics simulations in POPC and POPE/POPG membranes. The data show that, whereas pure lipid pores close rapidly, pores partially lined by protegrin arcs are stable for at least 300 ns. Estimates of the thermodynamic stability of these arcs using line tension data and implicit solvent calculations show that these arcs can be marginally stable in both zwitterionic and anionic membranes. Arcs provide an explanation for the observed ion selectivity in protegrin electrophysiology experiments and could possibly be involved in other membrane permeabilization processes where lipids are thought to participate, such as those induced by antimicrobial peptides and colicins, as well as the Bax apoptotic pore.     

Organizations of melittin peptides after spontaneous penetration into cell membranes

The antimicrobial peptide, melittin, is a potential next-generation antibiotic because melittin can spontaneously form pores in bacterial cell membranes and cause cytoplasm leakage. However, the organizations of melittin peptides in cell membranes remain elusive, which impedes the understanding of the poration mechanism. In this work, we use coarse-grained and all-atom molecular dynamics (MD) simulations to investigate the organizations of melittin peptides during and after spontaneous penetration into DPPC/POPG lipid bilayers. We find that the peptides in lipid bilayers adopt either a transmembrane conformation or a U-shaped conformation, which are referred to as T- and U-peptides, respectively. Several U-peptides and/or T-peptides aggregate to form stable pores. We analyze a T-pore consisting of four T-peptides and a U-pore consisting of three U-peptides and one T-peptide. In both pores, peptides are organized in a manner such that polar residues face inward and hydrophobic residues face outward, which stabilizes the pores and produces water channels. Compared with the U-pore, the T-pore has lower energy, larger pore diameter, and higher permeability. However, the T-pore occurs less frequently than the U-pore in our simulations, probably because the formation of the T-pore is kinetically slower than the U-pore. The stability and permeability of both pores are confirmed by 300 ns all-atom MD simulations. The peptide organizations obtained in this work should deepen the understanding of the stability, poration mechanism, and permeability of melittin, and facilitate the optimization of melittin to enhance the antibacterial ability.     

Interactions of peptides with liposomes: pore formation and fusion

Leakage from liposomes induced by several peptides is reviewed and a pore model is described. According to this model peptide molecules become incorporated into the vesicle bilayer and aggregate reversibly or irreversibly within the surface. When a peptide aggregate reaches a critical size, peptide translocation can occur and a pore is formed. With the peptide GALA the pores are stable and persist for at least 10 minutes. The model predicts that for a given lipid/peptide ratio, the extent of leakage should decrease as the vesicle diameter decreases, and for a given amount of peptide bound per vesicle less leakage would be observed at higher temperatures due to the increase in reversibility of surface aggregates of the peptide. Effect of membrane composition on pore formation is reviewed. When cholesterol was included in the liposomes the efficiency of inducation of leakage by the peptide GALA was reduced due to reduced binding and increased reversibility of surface aggregation of the peptide. Phospholipids which contain less ordered acyl-chains and have a slightly wedge-like shape, can better accommodate peptide surface aggregates, and consequently insertion and translocation of the peptide may be less favored. Demonstrations of antagonism between pore formation and fusion are presented. The choice of factors which promote vesicle aggregation, e.g., larger peptides, increased vesicle and peptide concentration results in enhanced vesicle fusion at the expense of formation of intravesicular pores. FTIR studies with HIV-1 fusion peptides indicate that in systems where extensive vesicle fusion occurred the beta conformation of the peptides was predominant, whereas the alpha conformation was exhibited in cases where leakage was the main outcome. Antagonism between leakage and fusion was exhibited by 1-palmitoyl-2-oleoylphosphatidylglycerol vesicles, where the order of addition of peptide (HIV(arg)) or Ca(2+)dictated whether pore formation or vesicle fusion would occur. The current study emphasizes that the addition of Ca(2+), which promotes vesicle aggregation can also reduce peptide translocation in isolated vesicles.     

Molecular dynamics simulations of pore formation dynamics during the rupture process of a phospholipid bilayer caused by high-speed equibiaxial stretching

Rupture of a phospholipid bilayer under mechanical stresses is triggered by pore formation in an intact bilayer. To understand the molecular details of the dynamics of pore formation we perform molecular dynamics simulations of a phospholipid bilayer under two different equibiaxial stretching conditions: first, unsteady stretching with various stretching speeds in the range of 0.1-1.0m/s, and second, quasistatic stretching. We analyze (i) patterns of pore formation, (ii) the critical area where a pore forms, (iii) the deformation of the bilayer, and (iv) the apparent breaking force. With stretching, the bilayer deforms anisotropically due to lipid chain packing and water penetrating into the hydrophilic region of the bilayer, and when the area exceeds a critical value, water filled pore structure penetrating the bilayer forms and develops into a large pore, resulting in rupture. For a high stretching speed, small pores (multipore) can temporarily form in a small area. It has been statistically determined that the probability of the multipore formation, the critical areal strain, and the apparent breaking force increase with the stretching speed in the range of 0-50%, 0.8-2.0, and 250-400 pN, respectively. The results qualitatively agree with the experimental and other simulation results, and rationalize the leakage of hemoglobin from erythrocytes in shock wave experiments.