Molecular Simulations of Aqueous Electrolytes: Role of Explicit Inclusion of Charge Transfer into Force Fields.

We describe here simulations of aqueous salt solutions that are performed using an explicit charge transfer force field. The emphasis of the discussion is on the calculation of a dynamical property of the solutions: self-diffusion of water. While force fields that are based on pairwise additive potentials or on potentials with explicit inclusion of polarization or with scaled charges can provide at best a qualitative agreement with experiments, force fields with explicit inclusion of charge transfer can produce quantitative agreement with experiment for NaCl and KCl solutions. We argue that a force field with explicit charge transfer contains new physics absent in the previously used force fields described in recent reviews of molecular simulations of aqueous electrolytes.

Stretch-Induced Cavitation: How Critical Cavity Radius and Barrier Energy, Radius, and Energy of a Stable Cavity Depend on the Stretching Factor.

Characteristics of tension-induced cavitation, such as free energy at the barrier for cavitation, the size of the critical (barrier) cavity, the stable cavity size, and the free energy of the stable cavity, depend on the amount of tension (stretch) and the initial size of the sample. In this work, we study how the characteristics of the cavitation mentioned above scale with the amount of applied tension. We consider two models characterizing the properties of cavitating liquid: (a) a simple model with a linear tension-strain relation and neglect of curvature dependence of cavity surface tension and (b) a more realistic model with a nonlinear tension-strain relation and curvature-dependent surface tension. For both models, we find the relevant scaling relations when we stretch the initial volume of the liquid sample in the interval between 1% and 20% of the initial volume. Specific numerical tests are performed for the case of liquid water when the initial volume of the sample is a sphere with a radius of 100 nm.

Damage to Polystyrene Polymer Film by Shock Wave Induced Bubble Collapse.

Metallic surfaces that are in contact with solutions are commonly used in numerous applications where these surfaces can be damaged by shock wave induced bubble collapse. Use of polymer films that coat such surfaces to prevent them from damage requires a better understanding of how much harm collapsing bubbles produce in the films. In this study, we report the results from coarse-grained molecular dynamics simulations to study the damage to polystyrene (PS) films coating a hard surface. The damage was caused by a collapsing nanobubble located in the proximity of the film and interacting with an impinging shock wave. This collapse produces a high-speed water jet that impacts the PS film with a greater force than the shock front and creates cavities/pits in the PS film. We observed that polymer molecules located in the jet vicinity undergo conformational extension in the direction perpendicular to the jet motion, while chain molecules in the rest of the film undergo compression. We also observed that damage to the film is sensitive to the strength of the shock wave.

Enhanced Cavitation and Hydration Crossover of Stretched Water in the Presence of C60.

We performed molecular dynamics simulations on systems containing stretched water and a C60 buckyball molecule. Our goals were to understand how the presence of the hydrophobic impurity influences the rate of cavitation in stretched water and how the change in pressure (an increase in the value of negative pressure) affects the nature of hydrophobic hydration. Our simulations show that the presence of a buckyball increases the rate of cavitation in water under negative pressure. When studying the influence of the degree of stretching on hydration, we observed that at pressures above -100 MPa the mechanism of hydrophobic hydration is the one that characterizes hydration of a small particle. At some pressure below -100 MPa, there is a crossover in the mechanism of hydration where dewetting occurs by forming cavities next to the surface of the buckyball, and this is characteristic of hydrophobic hydration of large particles.

Bubbles in water under stretch-induced cavitation.

When a finite sample of water experiences tension, it may develop voids (bubbles). We present here a result for the work (Helmholtz free energy change) that needs to be done for the creation of a bubble in fixed volume of water under tension and show that this result depends on the general form of stress-strain relationship. We observe that it is very important to include the curvature-dependent surface tension into consideration in order to explain bubble stability. The analytical result we obtained for the free energy allows us to make prediction for the values of critical and stable radii of the bubbles. We also performed simulations on the TIP4P/2005 water model and observed creation of bubbles in water under stretch. Combining analytical results obtained from our thermodynamic description with the results from computer simulations allowed us to determine the two parameters that describe the curvature-dependent surface tension and also to find the values of critical and stable bubble radii. We also determined the values of critical bubble radii by using mean first-passage time calculations.

A comparative computational study of coarse-grained and all-atom water models in shock Hugoniot states.

We performed molecular dynamics simulations to study how well some of the water models used in simulations describe shocked states. Water in our simulations was described using three different models. One was an often-used all-atom TIP4P/2005 model, while the other two were coarse-grained models used with the MARTINI force field: non-polarizable and polarizable MARTINI water. The all-atom model provided results in good agreement with Hugoniot curves (for data on pressure versus specific volume or, equivalently, on shock wave velocity versus "piston" velocity) describing shocked states in the whole range of pressures (up to 11 GPa) under study. If simulations of shocked states of water using coarse-grained models were performed for short time periods, we observed that data obtained for shocked states at low pressure were fairly accurate compared to experimental Hugoniot curves. Polarizable MARTINI water still provided a good description of Hugoniot curves for pressures up to 11 GPa, while the results for the non-polarizable MARTINI water substantially deviated from the Hugoniot curves. We also calculated the temperature of the Hugoniot states and observed that for TIP4P/2005 water, they were consistent with those from theoretical calculations, while both coarse-grained models predicted much higher temperatures. These high temperatures for MARTINI water can be explained by the loss of degrees of freedom due to coarse-graining procedure.

Nanobubbles, cavitation, shock waves and traumatic brain injury.

Collapse of bubbles, microscopic or nanoscopic, due to their interaction with the impinging pressure wave produces a jet of particles moving in the direction of the wave. If there is a surface nearby, the high-speed jet particles hit it, and as a result damage to the surface is produced. This cavitation effect is well known and intensely studied in case of microscopic sized bubbles. It can be quite damaging to materials, including biological tissues, but it can also be beneficial when controlled, like in case of sonoporation of biological membranes for the purpose of drug delivery. Here we consider recent simulation work performed to study collapse of nanobubbles exposed to shock waves, in order to understand the detailed mechanism of the cavitation induced damage to soft materials, such as biological membranes. We also discuss the connection of the cavitation effect with the traumatic brain injury caused by blasts. Specifically, we consider possible damage to model membranes containing lipid bilayers, bilayers with embedded ion channel proteins like the ones found in neural cells and also protein assemblies found in the tight junction of the blood brain barrier.

Behavior of P85 and P188 Poloxamer Molecules: Computer Simulations Using United-Atom Force-Field.

To study the interaction between poloxamer molecules and lipid bilayers using molecular dynamics simulation technique with the united-atom resolution, we augmented the GROMOS force-field to include poloxamers. We validated the force-field by calculating the radii of gyration of two poloxamers, P85 and P188, solvated in water and by considering the poloxamer density distributions at the air/water interface. The emphasis of our simulations was on the study of the interaction between poloxamers and lipid bilayer. At the water/lipid bilayer interface, we observed that both poloxamers studied, P85 and P188, behaved like surfactants: the hydrophilic blocks of poloxamers became adsorbed at the polar interface, while their hydrophobic block penetrated the interface into the aliphatic tail region of the lipid bilayer. We also observed that when P85 and P188 poloxamers interacted with damaged membranes that contained pores, the hydrophobic blocks of copolymers penetrated into the membrane in the vicinity of the pore and compressed the membrane. Due to this compression, water molecules were evacuated from the pore.

Properties of Poloxamer Molecules and Poloxamer Micelles Dissolved in Water and Next to Lipid Bilayers: Results from Computer Simulations.

To study the properties of poloxamer molecules P85 and P188 and micelles containing these poloxamers in bulk water and also next to lipid bilayers, we performed coarse-grained molecular dynamics computer simulations. We used MARTINI force-field and adjusted Lennard-Jones nonbonded interaction strength parameters for poloxamer beads to take into account the presence of polarizable water. Simulations of systems containing poloxamer molecules or micelles solvated in bulk water showed that structural properties, such as radii of gyration of the molecules and micelles, agree with the ones inferred from experiments. We observed that P85 micelle is almost spherical in shape, whereas the P188 micelle is distorted from being spherical. Simulations containing systems with the water-lipid bilayer interface showed that hydrophilic blocks of poloxamers interact with lipid headgroups of the bilayer and remain at the interface, whereas hydrophobic blocks prefer to insert into the central hydrophobic region of the bilayer. Simulations containing poloxamer micelles next to lipid bilayer showed no permeation of these micelles into the bilayer. To study the "healing" properties of P188 poloxamer, we performed simulations on a system containing a P188 micelle next to "damaged" lipid bilayer containing a pore. We observed that hydrophobic chains of poloxamers got inserted into the bilayer through the pore region, ultimately closing the pore.

Shock Wave-Induced Damage of a Protein by Void Collapse.

In this study, we report on a series of molecular dynamics simulations that were used to examine the effects of shock waves on a membrane-bound ion channel. A planar shock wave was found to compress the ion channel upon impact, but the protein geometry resembles the crystal structure as soon as the solvent density begins to dissipate. When a void was placed in close proximity to the membrane, the shock wave proved to be more destructive to the protein due to formation of a nanojet that results from the asymmetric collapse of the void. The nanojet was able to cause significant structural changes to the protein even at low piston velocities that are not able to directly cause poration of the membrane.

Opening of the blood-brain barrier tight junction due to shock wave induced bubble collapse: a molecular dynamics simulation study.

Passage of a shock wave across living organisms may produce bubbles in the blood vessels and capillaries. It was suggested that collapse of these bubbles imposed by an impinging shock wave can be responsible for the damage or even destruction of the blood-brain barrier. To check this possibility, we performed molecular dynamics computer simulations on systems that contained a model of tight junction from the blood-brain barrier. In our model, we represent the tight junction by two pairs of interacting proteins, claudin-15. Some of the simulations were done in the absence of a nanobubble, some in its presence. Our simulations show that when no bubble is present in the system, no damage to tight junction is observed when the shock wave propagates across it. In the presence of a nanobubble, even when the impulse of the shock wave is relatively low, the implosion of the bubble causes serious damage to our model tight junction.

Mechanism of membrane poration by shock wave induced nanobubble collapse: a molecular dynamics study.

We performed coarse-grained molecular dynamics simulations in order to understand the mechanism of membrane poration by shock wave induced nanobubble collapse. Pressure profiles obtained from the simulations show that the shock wave initially hits the membrane and is followed by a nanojet produced by the nanobubble collapse. While in the absence of the nanobubble, the shock wave with an impulse of up to 18 mPa s does not create a pore in the membrane, in the presence of a nanobubble even a smaller impulse leads to the poration of the membrane. Two-dimensional pressure maps depicting the pressure distributed over the lateral area of the membrane reveal the differences between these two cases. In the absence of a nanobubble, shock pressure is evenly distributed along the lateral area of the membrane, while in the presence of a nanobubble an unequal distribution of pressure on the membrane is created, leading to the membrane poration. The size of the pore formed depends on both shock wave velocity and shock wave duration. The results obtained here show that these two properties can be tuned to make pores of various sizes.

Communication: Modeling of concentration dependent water diffusivity in ionic solutions: Role of intermolecular charge transfer.

The translational diffusivity of water in solutions of alkali halide salts depends on the identity of ions, exhibiting dramatically different behavior even in solutions of similar salts of NaCl and KCl. The water diffusion coefficient decreases as the salt concentration increases in NaCl. Yet, in KCl solution, it slightly increases and remains above bulk value as salt concentration increases. Previous classical molecular dynamics simulations have failed to describe this important behavior even when polarizable models were used. Here, we show that inclusion of dynamical charge transfer among water molecules produces results in a quantitative agreement with experiments. Our results indicate that the concentration-dependent diffusivity reflects the importance of many-body effects among the water molecules in aqueous ionic solutions. Comparison with quantum mechanical calculations shows that a heterogeneous and extended distribution of charges on water molecules around the ions due to ion-water and also water-water charge transfer plays a very important role in controlling water diffusivity. Explicit inclusion of the charge transfer allows us to model accurately the difference in the concentration-dependent water diffusivity between Na(+) and K(+) ions in simulations, and it is likely to impact modeling of a wide range of systems for medical and technological applications.

Shock Wave Induced Collapse of Arrays of Nanobubbles Located Next to a Lipid Membrane: Coarse-Grained Computer Simulations.

We used molecular dynamics simulations to study creation of pores in lipid bilayer membranes by inducing shock waves in systems containing arrays of nanobubbles next to these membranes. Shock waves impinged on the bubbles imploding them and produced nanojets that subsequently hit the bilayers making pores in them. Our simulations were performed using the MARTINI coarse-grained force field. The emphasis in our study was on the interaction of shock waves with two-bubble arrays when the bubbles were placed in different alignments. We observed that the largest damage to the bilayer was produced when two bubbles were positioned in a serial alignment and the bubbles touched each other. When two touching each other bubbles were located parallel to the membrane surface and at the same distance from the surface, the membrane damage was reduced, compared to the damage done by explosion of two independent nanobubbles. When two nanobubbles were placed in slanted configurations, the damage was intermediate between damages produced by two bubbles in parallel or serial alignment. Damage to the membrane produced by arrays containing more than two bubbles can be understood as a combination of damage produced by all three alignments of two bubbles.

Local pressure changes in lipid bilayers due to adsorption of melittin and magainin-h2 antimicrobial peptides: results from computer simulations.

We performed a series of coarse-grained computer simulations in order to study how the placement of melittin and magainin-h2 antimicrobial peptides on the surface of the bilayer changes the local pressure profiles in the bilayer. The simulations were done using the NPT ensemble when the total stress on the bilayer was zero and also using the NP(z)AT ensemble, with a nonzero total stress. In the NPT ensemble, although the total stress was zero, each leaflet of the bilayer experienced a nonzero stress, and the stresses are equal by magnitude, but opposite in their direction. The observed stresses acting on the monolayers may cause the rupture of the monolayers to release the stress. Our simulations were done at different peptide to lipid ratio (P/L). When the P/L ratio was 1/50 there was no large difference in the local pressure profile for bilayers with melittin versus bilayers with magainin-h2. When simulations were performed in the NP(z)AT ensemble at P/L = 3/100 we observed a large difference in the pressure profiles in the bilayers with melittin peptides compared to the bilayer with magainin-h2. The observed in this case difference in stress may explain the difference in actions of melittin and magainin at high P/L.

Shock wave interaction with a phospholipid membrane: coarse-grained computer simulations.

We used MARTINI coarse-grained force field to study poration of a lipid bilayer by a shock wave induced nanobubble collapse. Different systems containing different sized nanobubbles that were exposed to shock waves propagating with different velocities were simulated. We observed creation of pores and damage to bilayers and also subsequent pore closing and the bilayer recovery after shock wave passed the bilayer. In all our systems where bilayers were damaged, they recovered; nevertheless we observed that a large amount of water crossed the pore that was temporarily created. We also observed that not every lipid molecule remained in the bilayer after recovery, some lipids moved out into water and created micelles.

Role of Charge Transfer in Water Diffusivity in Aqueous Ionic Solutions.

We performed molecular dynamics simulations on four types of systems containing ion and solvating water. Two systems contained a cation (Na(+) or K(+)), and two other systems an anion (Cl(-) or I(-)). Classical molecular dynamics simulations were performed using three different force fields: a fixed charge force field, a polarizable force field that includes explicit polarization, and also a recently developed force field that includes polarization and charge transfer. These simulations were then compared to first-principles molecular dynamics simulations. While the first-principles simulations showed that the anions accelerated water translational diffusion, the cations slowed it down. In simulations with the classical force fields, only the force field that incorporates explicit charge transfer reproduced this ion-specific behavior. Additional simulations performed to understand the effect of charge transfer demonstrated that two competitive factors determine the behavior of water translational diffusion: the ions diminished charge accelerates water, while the net charge acquired by water either accelerates or slows down its dynamics. Our results show that charge transfer plays a crucial role in governing the water dynamics in aqueous ionic solutions.

Free energy barrier for melittin reorientation from a membrane-bound state to a transmembrane state.

An important step in a phospholipid membrane pore formation by melittin antimicrobial peptide is a reorientation of the peptide from a surface into a transmembrane conformation. Experiments measure the fraction of peptides in the surface state and the transmembrane state, but no computational study exists that quantifies the free energy curve for the reorientation. In this work we perform umbrella sampling simulations to calculate the potential of mean force (PMF) for the reorientation of melittin from a surface-bound state to a transmembrane state and provide a molecular level insight in understanding the peptide-lipid properties that influence the existence of the free energy barrier. The PMFs were calculated for a peptide to lipid (P/L) ratio of 1/128 and 4/128. We observe that the free energy barrier is reduced when the P/L ratio increases. In addition, we study the cooperative effect; specifically we investigate if the reorientation barrier is smaller for a second melittin, given that another neighboring melittin was already in the transmembrane orientation. We observe that indeed the barrier of the PMF curve is reduced in this case, thus confirming the presence of a cooperative effect.

Restructuring of a model hydrophobic surface: Monte Carlo simulations using a simple coarse-grained model.

A lattice model is proposed to explain the restructuring of an ionic surfactant absorbed on a charged surface. When immersed in water, an ionic mica plate initially covered by a monolayer of surfactants rearranges to a surface inhomogeneously covered by patches of surfactant bilayer and bare mica. The model considers four species that can cover lattice sites of a surface. These species include (i) a surfactant molecule with its headgroup down, (ii) surfactant molecule with the headgroup up, (iii) a surfactant dimer arranged in a tail-to-tail configuration, which is a part of a bilayer, and (iv) a mica lattice site covered by water. We consider that only nearest neighbors on the lattice interact and describe the interactions by an interaction matrix. Using this model, we perform Monte Carlo simulations and study how the structure of the inhomogeneous surface depends on the interaction between water covered lattice site and its neighboring surfactant species covered sites. We observe that when this interaction is absent, the system undergoes phase separation into a bilayer phase and mica surface covered with water. When this interaction is taken into account, patches of surfactant bilayer and water are present in our system. The interaction between mica surfaces covered by patches of ionic surfactants is studied in experiments to understand the nature of long-ranged "hydrophobic" forces.

Melittin creates transient pores in a lipid bilayer: results from computer simulations.

To study the interaction between melittin peptides and lipid bilayer, we performed coarse-grained simulations on systems containing melittin interacting with a bilayer containing zwitterionic dipalmitoylphosphatidylcholine (DPPC) and anionic palmitoyloleoylphosphatidylglycerol (POPG) phospholipids in a 7:3 ratio. Eight different systems were considered: four at low and four at high peptide to lipid (P/L) ratios. In case of low P/L ratio we did not observe any pore creation in the bilayer. In two out of four of the simulations with the high P/L ratio, appearance of transient pores in the bilayer was observed. These pores were created due to an assembly of 3-5 melittin peptides. Not all of the peptides in the pores were in a transmembrane conformation; many of them had their termini residues anchored to the same leaflet, and these peptides assumed bent, U-shaped, conformations. We propose that when an assembly of melittin peptides creates pores, such an assembly acts as a "wedge" that splits the bilayer. To get a more detailed description of melittin on the bilayer surface and in transient pores, we performed coarse-grained to united-atom scale transformations and after that performed 50 ns molecular dynamics simulations using the united atom description of the systems. While these simulations did not show much of the change in the pore structure during the 50 ns time interval, they clearly showed the presence of water in the transient pores. The appearance of transient pores together with the translocation of peptides across the membranes is consistent with the mechanism proposed to explain graded dye leakage from large vesicles in the presence of melittin.