Pressure Profile Calculation with Mesh Ewald Methods

Mitochondrial membrane model: Lipids, elastic properties, and the changing curvature of cardiolipin

Mammalian and Drosophila melanogaster model mitochondrial membrane compositions are constructed from experimental data. Simplified compositions for inner and outer mitochondrial membranes are provided, including an asymmetric inner mitochondrial membrane. We performed atomistic molecular dynamics simulations of these membranes and computed their material properties. When comparing these properties to those obtained by extrapolation from their constituting lipids, we find good overall agreement. Finally, we analyzed the curvature effect of cardiolipin, considering ion concentration effects, oxidation, and pH. We draw the conclusion that cardiolipin-negative curvature is most likely due to counterion effects, such as cation adsorption, in particular of H3O+. This oft-neglected effect might account for the puzzling behavior of this lipid.

Understanding the Molecular Mechanism of Anesthesia: Effect of General Anesthetics and Structurally Similar Non-Anesthetics on the Properties of Lipid Membranes

General anesthesia can be caused by various, chemically very different molecules, while several other molecules, many of which are structurally rather similar to them, do not exhibit anesthetic effects at all. To understand the origin of this difference and shed some light on the molecular mechanism of general anesthesia, we report here molecular dynamics simulations of the neat dipalmitoylphosphatidylcholine (DPPC) membrane as well as DPPC membranes containing the anesthetics diethyl ether and chloroform and the structurally similar non-anesthetics n-pentane and carbon tetrachloride, respectively. To also account for the pressure reversal of anesthesia, these simulations are performed both at 1 bar and at 600 bar. Our results indicate that all solutes considered prefer to stay both in the middle of the membrane and close to the boundary of the hydrocarbon domain, at the vicinity of the crowded region of the polar headgroups. However, this latter preference is considerably stronger for the (weakly polar) anesthetics than for the (apolar) non-anesthetics. Anesthetics staying in this outer preferred position increase the lateral separation between the lipid molecules, giving rise to a decrease of the lateral density. The lower lateral density leads to an increased mobility of the DPPC molecules, a decreased order of their tails, an increase of the free volume around this outer preferred position, and a decrease of the lateral pressure at the hydrocarbon side of the apolar/polar interface, a change that might well be in a causal relation with the occurrence of the anesthetic effect. All these changes are clearly reverted by the increase of pressure. Furthermore, non-anesthetics occur in this outer preferred position in a considerably smaller concentration and hence either induce such changes in a much weaker form or do not induce them at all.

A perspective on the microscopic pressure (stress) tensor: History, current understanding, and future challenges

The pressure tensor (equivalent to the negative stress tensor) at both microscopic and macroscopic levels is fundamental to many aspects of engineering and science, including fluid dynamics, solid mechanics, biophysics, and thermodynamics. In this Perspective, we review methods to calculate the microscopic pressure tensor. Connections between different pressure forms for equilibrium and nonequilibrium systems are established. We also point out several challenges in the field, including the historical controversies over the definition of the microscopic pressure tensor; the difficulties with many-body and long-range potentials; the insufficiency of software and computational tools; and the lack of experimental routes to probe the pressure tensor at the nanoscale. Possible future directions are suggested.

A random batch Ewald method for charged particles in the isothermal-isobaric ensemble

We develop an accurate, highly efficient, and scalable random batch Ewald (RBE) method to conduct molecular dynamics simulations in the isothermal-isobaric ensemble (the NPT ensemble) for charged particles in a periodic box. After discretizing the Langevin equations of motion derived using suitable Lagrangians, the RBE method builds the mini-batch strategy into the Fourier space in the Ewald summation for the pressure and forces such that the computational cost is reduced to O(N) per time step. We implement the method in the Large-scale Atomic/Molecular Massively Parallel Simulator package and report accurate simulation results for both dynamical quantities and statistics for equilibrium for typical systems including all-atom bulk water and a semi-isotropic membrane system. Numerical simulations on massive supercomputing cluster are also performed to show promising central processing unit efficiency of the RBE.

Computer Simulation of the Surface of Aqueous Ionic and Surfactant Solutions

The surface of aqueous solutions of simple salts was not the main focus of scientific attention for a long while. Considerable interest in studying such systems has only emerged in the past two decades, following the pioneering finding that large halide ions, such as I^-, exhibit considerable surface affinity. Since then, a number of issues have been clarified; however, there are still several unresolved points (e.g., the effect of various salts on lateral water diffusion at the surface) in this respect. Computer simulation studies of the field have largely benefited from the appearance of intrinsic surface analysis methods, by which the particles staying right at the boundary of the two phases can be unambiguously identified. Considering complex ions instead of simple ones opens a number of interesting questions, both from the theoretical point of view and from that of the applications. Besides reviewing the state-of-the-art of intrinsic surface analysis methods as well as the most important advances and open questions concerning the surface of simple ionic solutions, we focus on two such systems in this Perspective, namely, the surface of aqueous mixtures of room temperature ionic liquids and that of ionic surfactants. In the case of the former systems, for which computer simulation studies have still scarcely been reported, we summarize the theoretical advances that could trigger such investigations, which might well be of importance also from the point of view of industrial applications. Computer simulation methods are, on the other hand, widely used in studies of the surface of surfactant solutions. Here we review the most important theoretical advances and issues to be addressed and discuss two areas of applications, namely, the inclusion of information gathered from such simulations in large scale atmospheric models and the better understanding of the airborne transmission of viruses, such as SARS-CoV-2.

Calcium Ions Promote Membrane Fusion by Forming Negative-Curvature Inducing Clusters on Specific Anionic Lipids

Vesicles enriched in certain negatively charged lipids, such as phosphatidylserine and PIP2, are known to undergo fusion in the presence of calcium ions without assistance from protein assemblies. Other lipids do not exhibit this propensity, even if they are negatively charged. Using our recently developed methodology, we extract elastic properties of a representative set of lipids. This allows us to trace the origin of lipid-calcium selectivity in membrane fusion to the formation of lipid clusters with long-range correlations that induce negative curvature on the membrane surface. Furthermore, the clusters generate lateral tension in the headgroup region at the membrane surface, concomitantly also stabilizing negative Gaussian curvature. Finally, calcium binding also reduces the orientational polarization of water around the membrane head groups, potentially reducing the hydration force acting between membranes. Binding calcium only weakly increases membrane bending rigidity and tilt moduli, in agreement with experiments. We show how the combined effects of calcium binding to membranes lower the barriers along the fusion pathway that lead to the formation of the fusion stalk as well as the fusion pore.

Contribution of Different Molecules and Moieties to the Surface Tension in Aqueous Surfactant Solutions. II: Role of the Size and Charge Sign of the Counterions

Understanding the role of the counterion species in surfactant solutions is a complicated task, made harder by the fact that, experimentally, it is not possible to vary independently bulk and surface quantities. Here, we perform molecular dynamics simulations at constant surface coverage of the liquid/vapor interface of lithium, sodium, potassium, rubidium, and cesium dodecyl sulfate aqueous solutions. We investigate the effect of counterion type and charge sign on the surface tension of the solution, analyzing the contribution of different species and moieties to the lateral pressure profile. The observed trends are qualitatively compatible with the Hofmeister series, with the notable exception of sodium. We point out a possible shortcoming of what is at the moment, in our experience, the most realistic nonpolarizable force field (CHARMM36) that includes the parametrization for the whole series of alkali counterions. In the artificial system where the counterion and surfactant charges are inverted in sign, the counterions become considerably harder. This charge inversion changes considerably the surface tension contributions of the counterions, surfactant headgroups, and water molecules, stressing the key role of the hardness of the counterions in this respect. However, the hydration free energy gain of the counterions, occurring upon charge inversion, is compensated by the concomitant free energy loss of the headgroups and water molecules, leading to a negligible change in the surface tension of the entire system.

Can we define a unique microscopic pressure in inhomogeneous fluids?

The estimation of a microscopic pressure tensor in an adsorbed thin film on a planar surface remains a challenge in both experiment and theory. While the normal pressure is well-defined for a planar surface, the tangential pressure at a point is not uniquely defined at the nanoscale. We report a new method that allows us to calculate the local pressure tensor and its spatial integral using an arbitrary contour definition of the "virial-route" local pressure tensor. We show that by integrating the local tangential pressure over a small region of space, roughly the range of the intermolecular forces, it is possible to define a coarse-grained tangential pressure that appears to be unique and free from ambiguities in the definition of the local pressure tensor. We support our argument by presenting the results for more than ten types of contour definitions of the local pressure tensor. By defining the coarse-grained tangential pressure, we can also find the effective thickness of the adsorbed layer and, in the case of a porous material, the statistical pore width. The coarse-grained in-layer and in-pore tangential pressures are determined for Lennard-Jones argon adsorbed in realistic carbon slit pores, providing a better understanding of the pressure enhancement for strongly wetting systems.

Microscopic Pressure Tensor in Cylindrical Geometry: Pressure of Water in a Carbon Nanotube

The microscopic pressure tensor plays an important role in understanding the mechanical stability, transport, and high-pressure phenomena of confined phases. The lack of an exact formulation to account for the long-range Coulombic contribution to the local pressure tensor in cylindrical geometries prevents the characterization of molecular fluids confined in cylindrical pores. To address this problem, we first derive the local cylindrical pressure tensor for Lennard-Jones fluids based on the Harasima (H) definition, which is expected to be compatible with the Ewald summation method. The test of the H-definition pressure equations in a homogeneous system shows that the radial and azimuthal pressure have unphysical radial dependence near the origin, while the axial pressure gives physically meaningful values. We propose an alternative contour definition that is more appropriate for cylindrical geometry and show that it leads to physically realistic results for all three pressure tensor components. With this definition, the radial and azimuthal pressures are of Irving-Kirkwood (IK) type, and the axial pressure is of Harasima type. Because of the practical interest in the axial pressure, we develop a Harasima/Ewald (H/E) method for calculating the long-range Coulombic contribution to the local axial pressure for rigid molecules. As an application, the axial pressure profile of water inside and outside a (20, 20) single-wall carbon nanotube is determined. The H/E method is compared to the IK method, which assumes a spherically truncated Coulombic potential. Detailed analysis of the pressure profile by both methods shows that the water confined in the nanotube is in a stretched state overall in the axial direction.

Hybrid particle-field molecular dynamics under constant pressure

Hybrid particle-field methods are computationally efficient approaches for modeling soft matter systems. So far, applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field interactions to represent systems coupled to constant external pressure. First, we show that the commonly used particle-field energy functional can be modified to model and parameterize the isotropic contributions to the pressure tensor without interfering with the microscopic forces on the particles. Second, we employ a square gradient particle-field interaction term to model non-isotropic contributions to the pressure tensor, such as in surface tension phenomena. This formulation is implemented within the hybrid particle-field molecular dynamics approach and is tested on a series of model systems. Simulations of a homogeneous water box demonstrate that it is possible to parameterize the equation of state to reproduce any target density for a given external pressure. Moreover, the same parameterization is transferable to systems of similar coarse-grained mapping resolution. Finally, we evaluate the feasibility of the proposed approach on coarse-grained models of phospholipids, finding that the term between water and the lipid hydrocarbon tails is alone sufficient to reproduce the experimental area per lipid in constant-pressure simulations and to produce a qualitatively correct lateral pressure profile.

Role of the Counterions in the Surface Tension of Aqueous Surfactant Solutions. A Computer Simulation Study of Alkali Dodecyl Sulfate Systems

We have investigated the surface tension contributions of the counterions, surfactant headgroups and tails, and water molecules in aqueous alkali dodecyl sulfate (DS) solutions close to the saturated surface concentration by analyzing the lateral pressure profile contribution of these components using molecular dynamics simulations. For this purpose, we have used the combination of two popular force fields, namely KBFF for the counterions and GROMOS96 for the surfactant, which are both parameterized for the SPC/E water model. Except for the system containing Na+ counterions, the surface tension of the surfactant solutions has turned out to be larger rather than smaller than that of neat water, showing a severe shortcoming of the combination of the two force fields. We have traced back this failure of the potential model combination to the unphysically strong attraction of the KBFF counterions, except for Na+, to the anionic head of the surfactants. Despite this failure of the model, we have observed a clear relation between the soft/hard character (in the sense of the Hofmeister series) and the surface tension contribution of the counterions, which, given the above limitations of the model, can only be regarded as an indicative result. We emphasize that the obtained results, although in a twisted way, clearly stress the crucial role the counterions of ionic surfactants play in determining the surface tension of the aqueous surfactant solutions.

Electromechanics of the liquid water vapour interface

Two collective properties distinguishing the thin liquid water vapour interface from the bulk liquid are the anisotropy of the pressure tensor giving rise to surface tension and the orientational alignment of the molecules leading to a finite dipolar surface potential. Both properties can be regarded as capillary phenomena and are likely to be coupled. We have investigated this coupling by determining the response of the tangential component of the surface tension to the application of an electric field normal to the surface using finite field molecular dynamics simulations. We find an upside down parabola with a maximum shifted away from zero field. Comparing the molecular dynamics results to a phenomenological electromechanical model we relate the zero field derivative of the tangential part of the surface tension to the electrostatic potential generated by the spontaneous interface polarization. When interpreted with this model our simulations also indicate that Kelvin forces due to electric field gradients at a polarized interface play an important role in the effective dielectric response.

Effect of general anesthetics on the properties of lipid membranes of various compositions

Computer simulations of four lipid membranes of different compositions, namely neat DPPC and PSM, and equimolar DPPC-cholesterol and PSM-cholesterol mixtures, are performed in the presence and absence of the general anesthetics diethylether and sevoflurane both at 1 and 600 bar. The results are analyzed in order to identify membrane properties that are potentially related to the molecular mechanism of anesthesia, namely that change in the same way in any membrane with any anesthetics, and change oppositely with increasing pressure. We find that the lateral lipid density satisfies both criteria: it is decreased by anesthetics and increased by pressure. This anesthetic-induced swelling is attributed to only those anesthetic molecules that are located close to the boundary of the apolar phase. This lateral expansion is found to lead to increased lateral mobility of the lipids, an effect often thought to be related to general anesthesia; to an increased fraction of the free volume around the outer preferred position of anesthetics; and to the decrease of the lateral pressure in the nearby range of the ester and amide groups, a region into which anesthetic molecules already cannot penetrate. All these changes are reverted by the increase of pressure. Another important finding of this study is that cholesterol has an opposite effect on the membrane properties than anesthetics, and, correspondingly, these changes are less marked in the presence of cholesterol. Therefore, changes in the membrane that can lead to general anesthesia are expected to occur in the membrane domains of low cholesterol content.

Mechanical properties of drug loaded diblock copolymer bilayers: A molecular dynamics study

In this work, we present results of coarse-grained simulations to study the encapsulation of prilocaine (PLC), both neutral and protonated, on copolymer bilayers through molecular dynamics simulations. Using a previously validated membrane model, we have simulated loaded bilayers at different drug concentrations and at low (protonated PLC) and high (neutral PLC) pH levels. We have characterized key structural parameters of the loaded bilayers in order to understand the effects of encapsulation of PLC on the bilayer structure and mechanical properties. Neutral PLC was encapsulated in the hydrophobic region leading to a thickness increase, while the protonated species partitioned between the water phase and the poly(ethylene oxide)-poly(butadiene) (PBD) interface, relaxing the PBD region and leading to a decrease in the thickness. The tangential pressures of the studied systems were calculated, and their components were decomposed in order to gain insights on their compensation. In all cases, it is observed that the loading of the membrane does not significantly decrease the stability of the bilayer, indicating that the system could be used for drug delivery.

Nonzero Ideal Gas Contribution to the Surface Tension of Water

Surface tension, the tendency of fluid interfaces to behave elastically and minimize their surface, is routinely calculated as the difference between the lateral and normal components of the pressure or, invoking isotropy in momentum space, of the virial tensor. Here we show that the anisotropy of the kinetic energy tensor close to a liquid-vapor interface can be responsible for a large part of its surface tension (about 15% for water, independent from temperature).