Massimo G. Noro

Extended corresponding-states behavior for particles with variable range attractions

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 the “reduced” second virial coefficient is a convenient parameter to quantify the effective range of attraction. Knowledge of the pair-potential alone allows one to estimate the relative location of the liquid–vapor and solid–fluid coexistence curves.

Calculation of the melting point of NaCl by molecular simulation

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.

Simulation Studies of Stratum Corneum Lipid Mixtures

We present atomistic molecular dynamics results for fully hydrated bilayers composed of ceramide NS-24:0, free fatty acid 24:0 and cholesterol, to address the effect of the different components in the stratum corneum (the outermost layer of skin) lipid matrix on its structural properties. Bilayers containing ceramide molecules show higher in-plane density and hence lower rate of passive transport compared to phospholipid bilayers. At physiological temperatures, for all composition ratios explored, the lipids are in a gel phase with ordered lipid tails. However, the large asymmetry in the lengths of the two tails of the ceramide molecule leads to a fluidlike environment at the bilayer midplane. The lateral pressure profiles show large local variations across the bilayer for pure ceramide or any of the two-component mixtures. Close to the skin composition ratio, the lateral pressure fluctuations are greatly suppressed, the ceramide tails from the two leaflets interdigitate significantly, the depression in local density at the interleaflet region is lowered, and the bilayers have lowered elastic moduli. This indicates that the observed composition ratio in the stratum corneum lipid layer is responsible for both the good barrier properties and the stability of the lipid structure against mechanical stresses.

The role of long-range forces in the phase behavior of colloids and proteins

The phase behavior of colloid-polymer mixtures, and of solutions of globular proteins, is often interpreted in terms of a simple model of hard spheres with short-ranged attraction. While such a model yields a qualitative understanding of the generic phase diagrams of both colloids and proteins, it fails to capture one important difference: the model predicts fluid-fluid phase separation in the metastable regime below the freezing curve. Such demixing has been observed for globular proteins, but for colloids it appears to be pre-empted by the appearance of a gel. In this paper, we study the effect of additional long-range attractions on the phase behavior of spheres with short-ranged attraction. We find that such attractions can shift the (metastable) fluid-fluid critical point out of the gel region. As this metastable critical point may be important for crystal nucleation, our results suggest that long-ranged attractive forces may play an important role in the crystallization of globular proteins. However, in colloids, where refractive index matching is often used to switch off long-ranged dispersion forces, gelation is likely to inhibit phase separation.

Bilayer Structure and Lipid Dynamics in a Model Stratum Corneum with Oleic Acid

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.

Simulations of Skin Barrier Function: Free Energies of Hydrophobic and Hydrophilic Transmembrane Pores in Ceramide Bilayers

Transmembrane pore formation is central to many biological processes such as ion transport, cell fusion, and viral infection. Furthermore, pore formation in the ceramide bilayers of the stratum corneum may be an important mechanism by which penetration enhancers such as dimethylsulfoxide (DMSO) weaken the barrier function of the skin. We have used the potential of mean constraint force (PMCF) method to calculate the free energy of pore formation in ceramide bilayers in both the innate gel phase and in the DMSO-induced fluidized state. Our simulations show that the fluid phase bilayers form archetypal water-filled hydrophilic pores similar to those observed in phospholipid bilayers. In contrast, the rigid gel-phase bilayers develop hydrophobic pores. At the relatively small pore diameters studied here, the hydrophobic pores are empty rather than filled with bulk water, suggesting that they do not compromise the barrier function of ceramide membranes. A phenomenological analysis suggests that these vapor pores are stable, below a critical radius, because the penalty of creating water-vapor and tail-vapor interfaces is lower than that of directly exposing the strongly hydrophobic tails to water. The PMCF free energy profile of the vapor pore supports this analysis. The simulations indicate that high DMSO concentrations drastically impair the barrier function of the skin by strongly reducing the free energy required for pore opening.

A cage model of liquids supported by molecular dynamics simulations. I. The cage variables

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.

Phase behavior of a simple model for membrane proteins

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.

Toward a Standard Protocol for Micelle Simulation.

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.

Complete Structure of an Epithelial Keratin Dimer: Implications for Intermediate Filament Assembly

Keratins are cytoskeletal proteins that hierarchically arrange into filaments, starting with the dimer sub-unit. They are integral to the structural support of cells, in skin, hair and nails. In skin, keratin is thought to play a critical role in conferring the barrier properties and elasticity of skin. In general, the keratin dimer is broadly described by a tri-domain structure: a head, a central rod and a tail. As yet, no atomistic-scale picture of the entire dimer structure exists; this information is pivotal for establishing molecular-level connections between structure and function in intermediate filament proteins. The roles of the head and tail domains in facilitating keratin filament assembly and function remain as open questions. To address these, we report results of molecular dynamics simulations of the entire epithelial human K1/K10 keratin dimer. Our findings comprise: (1) the first three-dimensional structural models of the complete dimer unit, comprising of the head, rod and tail domains; (2) new insights into the chirality of the rod-domain twist gained from analysis of the full domain structure; (3) evidence for tri-subdomain partitioning in the head and tail domains; and, (4) identification of the residue characteristics that mediate non-covalent contact between the chains in the dimer. Our findings are immediately applicable to other epithelial keratins, such as K8/K18 and K5/K14, and to intermediate filament proteins in general.