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We address the problem of the quantitative prediction of micelle formation in dilute aqueous solutions of ionic surfactants using sodium dodecyl sulfate (SDS) as a model system through a computational approach that involves three steps: (a) execution of coarse-grained simulations based on the MARTINI force field (with slightly modified parameters to afford the formation of large micelles); (b) reverse mapping of the final self-assembled coarse-grained configuration into an all-atom configuration; and (c) final relaxation of this all-atom configuration through short-time (on the order of a few tens of nanoseconds), detailed isothermal-isobaric molecular dynamics simulations using the CHARMM36 force field. For a given concentration of the solution in SDS molecules, the modified MARTINI-based coarse-grained simulations lead to the formation of large micelles characterized by mean aggregation numbers above the experimentally observed ones. However, by reintroducing the detailed chemical structure through a strategy that solves a well-defined geometric problem and re-equilibrating, these large micellar aggregates quickly dissolve to smaller ones and equilibrate to sizes that perfectly match the average micelle size measured experimentally at the given surfactant concentration. From the all-atom molecular dynamics simulations, we also deduce the surfactant diffusivity DSDS and the zero-shear rate viscosity, η0, of the solution, which are observed to compare very favorably with the few experimental values that we were able to find in the literature.

The skin surface, our first barrier against the external environment, is covered by the sebum oil, a lipid film composed of sebaceous and epidermal lipids, which is important in the regulation of the hydration level of our skin. Here, we investigate the pathways leading to the transfer of epidermal lipids from the skin lipid bilayer to the sebum. We show that the sebum triglycerides, a major component of sebum, interact strongly with the epidermal lipids and extract them from the bilayer. Using microsecond time scale molecular dynamics simulations, we identify and quantify the free energy associated with the skin lipid extraction process.

In recent years, sebum oil has been found to play a key role in the regulation of the hydration of the outermost layer of the skin, the stratum corneum. Understanding how a major component of the sebum oil, the triglyceride tri-cis-6-hexadecenoin (TG), interacts with water is an important step in gaining insight into the water regulation function of the sebum oil. Here we use molecular dynamics simulations to investigate the structural and interfacial properties of TG in bulk and at the air and water interface. Our model performs very well in reproducing experimental results, such as density, surface tensions and surface pressure area isotherms. We show that triglyceride molecules in the liquid phase assemble together, through the glycerol group, forming a single percolating network. TG-air interfaces orient the lipids with the interface enriched with the hydrophobic tails and the glycerol groups buried inside. When in contact with water, the TG molecules at the interface orient the glycerol group towards the water phase and adopt a characteristic trident conformation. Water is shown to penetrate the TG layer thanks to the interaction with the oxygen atoms of the TG molecules, which acts as a pathway for water diffusion. The activation energy for the passage of water is found to be ≈9.5kBT at 310 K, showing that the layer is permeable to water diffusion.

Monoglycerides and unsaturated fatty acids, naturally present in trace amounts in the stratum corneum (top layer of skin) lipid matrix, are commonly used in pharmaceutical, cosmetic and health care formulations. However, a detailed molecular understanding of how the oil additives get incorporated into the skin lipids from topical application and, once incorporated, how they affect the properties and integrity of the lipid matrix remains unexplored. Using ceramide 2 bilayers as skin lipid surrogates, we use a series of molecular dynamics simulations with six different natural oil ingredients at multiple concentrations to investigate the effect of the oils on the properties and stability of the bilayers. The six oils: monoolein, monostearin, monoelaidin, oleic acid, stearic acid and linoleic acid – all having the same length of the alkyl chain, C18, but a varying degree of saturation, allow us to systematically address the effect of unsaturation in the additives. Our results show that at low oil concentration (∼5%) the mixed bilayers containing any of the oils and ceramide 2 (CER2) become more rigid than pure CER2 bilayers due to more efficient lipid packing. Better packing also results in the formation of larger numbers of hydrogen bonds between the lipids, which occurs at the expense of the hydrogen bonds between lipids and water. The mixed bilayers with saturated or trans-unsaturated oils remain stable over the whole range of oil concentration. In contrast, the presence of the oils with at least one cis-double bond leads to bilayer instability and complete loss of bilayer structure at the oil content of about 50–65%. Two cis-double bonds in the lipid tail induce bilayer disruption at even lower concentration (∼30%). The mixed bilayers remain in the gel phase (without melting to a fluid phase) until the phase transition to a non-bilayer phase occurs. We also demonstrate that the stability of the bilayer strongly correlates with the order parameter of the lipid tails.

In this paper, we present protocols for simulating micelles using dissipative particle dynamics (and in principle molecular dynamics) that we expect to be appropriate for computing micelle properties for a wide range of surfactant molecules. The protocols address challenges in equilibrating and sampling, specifically when kinetics can be very different with changes in surfactant concentration, and with minor changes in molecular size and structure, even using the same force field parameters. We demonstrate that detection of equilibrium can be automated and is robust, for the molecules in this study and others we have considered. In order to quantify the degree of sampling obtained during simulations, metrics to assess the degree of molecular exchange among micellar material are presented, and the use of correlation times are prescribed to assess sampling and for statistical uncertainty estimates on the relevant simulation observables. We show that the computational challenges facing the measurement of the critical micelle concentration (CMC) are somewhat different for high and low CMC materials. While a specific choice is not recommended here, we demonstrate that various methods give values that are consistent in terms of trends, even if not numerically equivalent.

The stratum corneum is the uppermost layer of the skin and acts as a barrier to keep out contaminants and retain moisture. Understanding the molecular structure and behavior of this layer will provide guidance for optimizing its biological function. In this study we use a model mixture comprised of equimolar portions of ceramide NS (24:0), lignoceric acid, and cholesterol to model the effect of the addition of small amounts of oleic acid to the bilayer at 300 and 340 K. Five systems at each temperature have been simulated with concentrations between 0 and 0.1 mol % oleic acid. Our major finding is that subdiffusive behavior over the 200 ns time scale is evident in systems at 340 K, with cholesterol diffusion being enhanced with increased oleic acid. Importantly, cholesterol and other species diffuse faster when radial densities indicate nearest neighbors include more cholesterol. We also find that, with the addition of oleic acid, the bilayer midplane and interfacial densities are reduced and there is a 3% decrease in total thickness occurring mostly near the hydrophilic interface at 300 K with reduced overall density at 340 K. Increased interdigitation occurs independent of oleic acid with a temperature increase. Slight ordering of the long non-hydroxy fatty acid of the ceramide occurs near the hydrophilic interface as a function of the oleic acid concentration, but no significant impact on hydrogen bonding is seen in the chosen oleic acid concentrations.

The fatty acid oleic acid (OA) is known to modulate the structure of membranes, which forms the basis for a number of its important applications including its use as a therapeutic supplement to reduce the risk of cardiovascular disease, in molecule delivery systems such as liposomes, and as a skin permeability enhancer. While a number of studies have investigated the effect of OA on lipid membranes, our understanding of its mechanisms of action at the molecular level remains rudimentary. We have carried out molecular dynamics simulations using coarse-grained models to investigate the interactions of OA at a range of concentrations with a dipalmitoylphosphatidylcholine (DPPC) bilayer in the liquid-crystalline phase. We have also investigated the relative permeability of the bilayers to model hydrophilic and hydrophobic penetrants by means of chemical potential calculations. The results indicate that OA is able to disperse homogeneously into the bilayer at all concentrations without much perturbation. OA appears to slightly weaken the lateral forces between lipid headgroups, and as the concentration of OA increases this manifests itself as a slight decrease in the area compressibility modulus and a minor increase in the diffusion rate of the OA molecules. While the chemical potential profiles showed little or no variation as a function of OA concentration, the frequency of water permeation events was found to double, indicating some OA-induced permeability enhancement. The study suggests that physiological effects of OA are probably more subtle rather than via gross perturbation of the structure, or that its significant effects are restricted to more condensed membrane structures such as the gel phase.

The bulk thermodynamic properties of membrane proteins originate from a complex combination of molecular interactions. We propose a simple model based on the pair interactions between a model membrane protein, annexin V. The experimental observations of a honeycomb (p6) and a triangular (p3) phase are successfully reproduced with Monte Carlo computer simulations. Grand canonical simulations and a newly developed "strip"-move constant pressure technique reveal the stability of a dilute fluid phase and a dense solid phase, not observed with the current experimental technology. While this model is extremely simple in that it relies only on hard-body and short-range directional interactions, it nevertheless captures the essential physics of the interactions between the protein molecules and reproduces the phase behavior observed in experiments.

We present a systematic, top-down, thermodynamic parametrization scheme for dissipative particle dynamics (DPD) using water-octanol partition coefficients, supplemented by water-octanol phase equilibria and pure liquid phase density data. We demonstrate the feasibility of computing the required partition coefficients in DPD using brute-force simulation, within an adaptive semi-automatic staged optimization scheme. We test the methodology by fitting to experimental partition coefficient data for twenty one small molecules in five classes comprising alcohols and poly-alcohols, amines, ethers and simple aromatics, and alkanes (i.e. hexane). Finally, we illustrate the transferability of a subset of the determined parameters by calculating the critical micelle concentrations of selected alkyl ethoxylate surfactants, in good agreement with reported experimental values., Comment: 12 pages, 4 figures, 7 tables, RevTeX 4.1

We report a numerical simulation of the phase diagram of a simple model for membrane proteins constrained to move in a plane. In analogy with the corresponding three dimensional models, the liquid-gas transition becomes metastable as the range of attraction decreases. Spontaneous crystallization happens much more readily in the two dimensional models rather than in their three dimensional counterparts., Revtex, 9 pages, 7 figures

Although Enskog kinetic theory describes intermolecular collisional dynamics in terms of hard core molecular cross sections with inclusion of environmental crowding (excluded volume), more detailed analyses must incorporate the effects due to softness of the intermolecular potential and correlations of successive collisions. We present a simple model for the probability, pr(t), for a collision (defined as a velocity reversal) to occur at a time t after the last collision, that includes all the effects listed. Although the model incorporates correlated collisions, it does so only in the sense that such correlations affect pr(t), an intrinsically Markovian property since it carries memory only back to the last collision. We also examine the sign velocity autocorrelation function in order to identify the strictly Markovian contributions to the collisional dynamics.

We treat the competition between self-energy (single-micelle curvature preference) and interaction (interaggregate) effects on the evolution of micellar shapes and long-range ordering phase transitions in ternary systems of mixed surfactant and water. One surfactant prefers to satisfy the hydrophobic effect via formation of globular (positive curvature) micelles, whereas for the other we have in mind the phospholipids, for instance, which prefer to aggregate as planar bilayers. It follows that the preferred curvature in the ternary mixture case will depend sensitively on composition, i.e., on the relative numbers of the two surfactants. At high total concentrations of surfactant, however, the micellar shape is controlled as well by the relative efficiencies of packing aggregates of different curvature, independent of relative amphiphile mole numbers. By combining these self-energy and intermicellar interaction effects, then, we are able to generate “master” phase diagrams for the ternary systems, as a fun...

Stochastic cage models require a choice for the cage variables suitable to describe the restoring forces generated by the solvent on the solute. A set of cage variables is introduced from the parametrization of the cage potential which is defined as the solute–solvent interaction energy considered as a function of the solute position for a fixed solvent configuration. This is an operative definition of cage variables that allows their identification at each time step of molecular dynamics simulations. Therefore, quantitative information about the equilibrium properties and the dynamics of cage variables can be extracted from molecular dynamics simulations. This procedure is applied to liquid argon near the triple point, in order to recognize the different processes contributing to the cage diffusion. The equilibrium distribution and the characteristic correlation times are derived as ingredients for the stochastic cage model developed in part II of the work.

By means of molecular dynamics simulations we have investigated increasing configurational ordering and decreasing particle mobility with increasing density ρ of a two-dimensional equilibrated liquid composed of soft discs. An equaltime correlation function h 2 (3) (0) which includes three-body, as well as twobody, correlations is introduced as a measure of structural order; this function is related to the dipole-induced-dipole equal-time correlation function h 2 (4) (0), and its sensitivity to structural order in the liquid is associated with the cancellation effect, the cancellation of the positive contribution of the two-body correlations by the negative contribution of the three-body correlations

We report a numerical calculation of the melting point of NaCl. The solid–liquid transition was located by determining the point where the chemical potentials of the solid and liquid phases intersect. To compute these chemical potentials, we made use of free energy calculations. For the solid phase the free energy was determined by thermodynamic integration from the Einstein crystal. For the liquid phase two distinct approaches were employed: one based on particle insertion and growth using the Kirkwood coupling parameter, and the other involving thermodynamic integration of the NaCl liquid to a Lennard-Jones fluid. The latter approach was found to be significantly more accurate. The coexistence point at 1074 K was characterized by a pressure of –30±40 MPa and a chemical potential of –97.9±0.2kβT. This result is remarkably good as the error bounds on the pressure enclose the expected coexistence pressure of about 0.1 MPa (ambient). Using the Clausius–Clapyron relation, we estimate that dP/dT ≈3 MPa/K. This yields a melting point of 1064±14 K at ambient pressure, which encompasses the quoted range for the experimental melting point (1072.45–1074.4 K). The good agreement with the experimental melting-point data provides additional evidence that the Tosi–Fumi model for NaCl is quite accurate. Our study illustrates that the melting point of an ionic system can be calculated accurately by employing a judicious combination of free energy techniques. The techniques used in this work can be directly extended to more complex, charged systems.

We propose an extension of the law of corresponding states that can be applied to systems - such as colloidal suspensions - that have widely different ranges of attractive interactions. We argue that, for such systems, the ``reduced'' second virial coefficient is a convenient parameter to quantify the effective range of attraction. This procedure allows us to give a simple definition of the effective range of attraction of potentials with different functional forms. The advantage of the present approach is that it allows us to estimate the relative location of the liquid-vapor and solid-fluid coexistence curves exclusively on basis of the knowledge of the pair-potential., REVTeX, 5 pages, 2 figures