A fresh look at the vibrational and thermodynamic properties of liquids within the soft potential model.

Contrary to the case of solids and gases, where Debye theory and kinetic theory offer a good description for most of the physical properties, a complete theoretical understanding of the vibrational and thermodynamic properties of liquids is still missing. Liquids exhibit a vibrational density of states (VDOS) which does not obey Debye law, and a heat capacity which decreases monotonically with temperature, rather than growing as in solids. Despite many attempts, a simple, complete and widely accepted theoretical framework able to formally derive the aforementioned properties has not been found yet. Here, we revisit one of the theoretical proposals, and in particular we re-analyze the properties of liquids within the soft-potential model, originally formulated for glasses. We confirm that, at least at a qualitative level, many characteristic properties of liquids can be rationalized within this model. We discuss the validity of several phenomenological expressions proposed in the literature for the density of unstable modes, and in particular for its temperature and frequency dependence. We discuss the role of negative curvature regions and unstable modes as fundamental ingredients to have a linear in frequency VDOS. Finally, we compute the heat capacity within the soft potential model for liquids and we show that it decreases with temperature, in agreement with experimental and simulation data.

Membrane Phase Transitions in Lipid-Wrapped Nanoparticles.

A Landau theory is constructed for the gel/fluid transition of a lipid bilayer wrapped around a spherical nanoparticle (lipid-wrapped nanoparticle, LNP). The bilayer is regarded as a regular solution of gel and fluid lipids with distinct inter- and intralayer interactions plus the interaction of the core with the inner layer. It is required that both the inner and the outer surfaces of the bilayer are perfectly covered with lipids, with the gel and fluid lipids having different areas/lipid. The equilibrium state is found by minimizing the free energy as a function of the fractions of fluid lipids in the inner and outer layers. The transition has been studied extensively for lamellar membranes in the thermodynamic limit. LNP have significant curvature and are not in the thermodynamic limit. The increase of the gel energy with curvature, identified in our previous work as its most important effect, is included. The focus of the paper is the dependence of the transition on the core radius, R, controlling curvature, and the core-lipid interaction. With decreasing R, trends found in experiment are reproduced in a model calculation: (1) decrease of the transition temperature, Tm, (2) decoupling of the transitions in the inner and outer layers, and (3) possibility of lower Tm in the inner layer. The disruption of gel packing by curvature and the interaction of the core with the inner layer are highlighted as the most important determinants of deviation from bulk behavior.

Moltemplate: A Tool for Coarse-Grained Modeling of Complex Biological Matter and Soft Condensed Matter Physics.

Coarse-grained models have long been considered indispensable tools in the investigation of biomolecular dynamics and assembly. However, the process of simulating such models is arduous because unconventional force fields and particle attributes are often needed, and some systems are not in thermal equilibrium. Although modern molecular dynamics programs are highly adaptable, software designed for preparing all-atom simulations typically makes restrictive assumptions about the nature of the particles and the forces acting on them. Consequently, the use of coarse-grained models has remained challenging. Moltemplate is a file format for storing coarse-grained molecular models and the forces that act on them, as well as a program that converts moltemplate files into input files for LAMMPS, a popular molecular dynamics engine. Moltemplate has broad scope and an emphasis on generality. It accommodates new kinds of forces as they are developed for LAMMPS, making moltemplate a popular tool with thousands of users in computational chemistry, materials science, and structural biology. To demonstrate its wide functionality, we provide examples of using moltemplate to prepare simulations of fluids using many-body forces, coarse-grained organic semiconductors, and the motor-driven supercoiling and condensation of an entire bacterial chromosome.

Simulation of fluid/gel phase equilibrium in lipid vesicles.

Simulation of single component dipalmitoylphosphatidylcholine (DPPC) coarse-grained DRY-MARTINI lipid vesicles of diameter 10 nm (1350 lipids), 20 nm (5100 lipids) and 40 nm (17 600 lipids) is performed using statistical temperature molecular dynamics (STMD), to study finite size effects upon the order-disorder gel/fluid transition. STMD obtains enhanced sampling using a generalized ensemble, obtaining a flat energy distribution between upper and lower cutoffs, with little computational cost over canonical molecular dynamics. A single STMD trajectory of moderate length is sufficient to sample 20+ transition events, without trapping in the gel phase, and obtain well averaged properties. Phase transitions are analyzed via the energy-dependence of the statistical temperature, TS(U). The transition temperature decreases with decreasing diameter, in agreement with experiment, and the transition changes from first order to borderline first-second order. The size- and layer-dependence of the structure of both stable phases, and of the pathway of the phase transition, are determined. It is argued that the finite size effects are primarily caused by the disruption of the gel packing by curvature. Inhomogeneous states with faceted gel patches connected by unusual fluid seams are observed at high curvature, with visually different structure in the inner and outer layers due to the different curvatures. Thus a simple physical picture describes phase transitions in nanoscale finite systems far from the thermodynamic limit.

Membrane-wrapped nanoparticles probe divergent roles of GM3 and phosphatidylserine in lipid-mediated viral entry pathways.

Gold nanoparticles (NPs) wrapped in a membrane can be utilized as artificial virus nanoparticles (AVNs) that combine the large nonblinking or bleaching optical cross-section of the NP core with the biological surface properties and functionalities provided by a self-assembled lipid membrane. We used these hybrid nanomaterials to test the roles of monosialodihexosylganglioside (GM3) and phosphatidylserine (PS) for a lipid-mediated targeting of virus-containing compartments (VCCs) in macrophages. GM3-presenting AVNs bind to CD169 (Siglec-1)-expressing macrophages, but inclusion of PS in the GM3-containing AVN membrane decreases binding. Molecular dynamics simulations of the AVN membrane and experimental binding studies of CD169 to GM3-presenting AVNs reveal Na+-mediated interactions between GM3 and PS as a potential cause of the antagonistic action on binding by the two negatively charged lipids. GM3-functionalized AVNs with no or low PS content localize to tetherin+, CD9+ VCC in a membrane composition-depending fashion, but increasing amounts of PS in the AVN membrane redirect the NP to lysosomal compartments. Interestingly, this compartmentalization is highly GM3 specific. Even AVNs presenting the related monosialotetrahexosylganglioside (GM1) fail to achieve an accumulation in VCC. AVN localization to VCC was observed for AVN with gold NP core but not for liposomes, suggesting that NP sequestration into VCC has additional requirements beyond ligand (GM3)-receptor (CD169) recognition that are related to the physical properties of the NP core. Our results confirm AVN as a scalable platform for elucidating the mechanisms of lipid-mediated viral entry pathways and for selective intracellular targeting.

Lipid Packing in Lipid-Wrapped Nanoparticles.

Equilibrium simulations of lipid-wrapped nanoparticles (LNP) were performed using a hybrid molecular dynamics/Monte Carlo (MD/MC) approach. The radius, R, of a spherical nanoparticle (NP) core was adjusted with MC moves while a surrounding lipid bilayer was treated with MD. A wide range of LNP sizes, with the largest R ∼ 40 nm, were studied to determine the average NP radius for a given total number of lipids, N, the number of lipids in each layer, and configurational information. A three-bead lipid model was used to allow large N. A nonequilibrium Jarzynski free energy calculation of the optimal R for a given N, was also demonstrated validating the MD/MC method. An order/disorder transition was described, unique to LNP and distinct from lamellar bilayers, that is weak and continuous with small N, but sharpens to a first order transition with N > 10000 at T ≈ 1.1, shifting to higher T with increasing N. The radius and the overlap of the inner and outer layers were used as order parameters charactering the whole system, and the density vs distance from the origin served to describe the transition in individual layers. The ordering effect of the core on the inner layer, and the disordering effect of curvature, are evident. Excellent fits for the number of lipids in the inner and outer layers vs R are presented, based on the idea that the inner layer is described as usual by an area and area/lipid but that the outer layer is slaved to the inner. The most ordered states exhibit interdigitation of the inner head groups with themselves.

Membrane Fluidity Sensing on the Single Virus Particle Level with Plasmonic Nanoparticle Transducers.

Viral membranes are nanomaterials whose fluidity depends on their composition, in particular, the cholesterol (chol) content. As differences in the membrane composition of individual virus particles can lead to different intracellular fates, biophysical tools capable of sensing the membrane fluidity on the single-virus level are required. In this manuscript, we demonstrate that fluctuations in the polarization of light scattered off gold or silver nanoparticle (NP)-labeled virus-like-particles (VLPs) encode information about the membrane fluidity of individual VLPs. We developed plasmonic polarization fluctuation tracking microscopy (PFTM) which facilitated the investigation of the effect of chol content on the membrane fluidity and its dependence on temperature, for the first time on the single-VLP level. Chol extraction studies with different methyl-ß-cyclodextrin (MßCD) concentrations yielded a gradual decrease in polarization fluctuations as a function of time. The rate of chol extraction for individual VLPs showed a broad spread, presumably due to differences in the membrane composition for the individual VLPs, and this heterogeneity increased with decreasing MßCD concentration.

Enhanced Sampling of Phase Transitions in Coarse-Grained Lipid Bilayers.

Freezing and melting of dipalmitoylphosphatidylcholine (DPPC) bilayers are simulated in both the explicit (Wet) and implicit solvent (Dry) coarse-grained MARTINI force fields with enhanced sampling, via the isobaric, molecular dynamics version of the generalized replica exchange method (gREM). Phase transitions are described with the entropic viewpoint, based upon the statistical temperature as a function of enthalpy, TS(H) = 1/(dS(H)/dH), where S is the configurational entropy. Bilayer thickness, area per lipid, and the second-rank order parameter (P2) are calculated vs temperature in the transition range. In a 32-lipid Wet MARTINI system, transitions in the lipid and water subsystems are strongly coupled, giving rise to considerable structure in TS(H) and the need to specify the state of the water when reporting a lipid transition temperature. For gel lipid + liquid water → fluid lipid + liquid water, we find 292.4 K. The small system is influenced by finite-size effects, but it is argued that the entropic approach is well suited to revealing them, which will be particularly relevant for studies of finite nanosystems where there is no thermodynamic limit. In a 390-lipid Dry MARTINI system, two-dimensional analogues of the topographies of coexisting states ("subphases") seen in pure fluids are found. They are not seen in the 32-lipid Wet or Dry system, but the Dry lipids show a new type of state with gel in one leaflet and tilted gel in the other. Dry bilayer transition temperatures are 333.3 K (390 lipids) and 338 K (32 lipids), indicating that the 32-lipid system is not too small for a qualitative study of the transition. Physical arguments are given for Dry lipid system size dependence and for the difference between Wet and Dry systems.

Pathways through Equilibrated States with Coexisting Phases for Gas Hydrate Formation.

Under ambient conditions, water freezes to either hexagonal ice or a hexagonal/cubic composite ice. The presence of hydrophobic guest molecules introduces a competing pathway: gas hydrate formation, with the guests in clathrate cages. Here, the pathways of the phase transitions are sought as sequences of states with coexisting phases, using a generalized replica exchange algorithm designed to sample them in equilibrium, avoiding nonequilibrium processes. For a dilute solution of methane in water under 200 atm, initializing the simulation with the full set of replicas leads to methane trapped in hexagonal/cubic ice, while gradually adding replicas with decreasing enthalpy produces the initial steps of hydrate growth. Once a small amount of hydrate is formed, water rearranges to form empty cages, eventually transforming the remainder of the system to metastable ß ice, a scaffolding for hydrates. It is suggested that configurations with empty cages are reaction intermediates in hydrate formation when more guest molecules are available. Free energy profiles show that methane acts as a catalyst reducing the barrier for ß ice versus hexagonal/cubic ice formation.

Water Freezing and Ice Melting.

The generalized replica exchange method (gREM) is designed to sample states with coexisting phases and thereby to describe strong first order phase transitions. The isobaric MD version of the gREM is presented and applied to the freezing of liquid water and the melting of hexagonal and cubic ice. It is confirmed that coexisting states are well-sampled. The statistical temperature as a function of enthalpy, TS(H), is obtained. Hysteresis between freezing and melting is observed and discussed. The entropic analysis of phase transitions is applied and equilibrium transition temperatures, latent heats, and surface tensions are obtained for hexagonal ice ↔ liquid and cubic ice ↔ liquid with excellent agreement with published values. A new method is given to assign water molecules among various symmetry types. Pathways for water freezing, ultimately leading to hexagonal ice, are found to contain intermediate layered structures built from hexagonal and cubic ice.

Isobaric Molecular Dynamics Version of the Generalized Replica Exchange Method (gREM): Liquid-Vapor Equilibrium.

A prescription for sampling isobaric generalized ensembles with molecular dynamics is presented and applied to the generalized replica exchange method (gREM), which was designed to simulate first-order phase transitions. The properties of the isobaric gREM ensemble are discussed, and a study is presented for the liquid-vapor equilibrium of the guest molecules given for gas hydrate formation with the mW water model. Phase diagrams, critical parameters, and a law of corresponding states are obtained.

Entropic Description of Gas Hydrate Ice-Liquid Equilibrium via Enhanced Sampling of Coexisting Phases.

Metastable ß ice holds small guest molecules in stable gas hydrates, so its solid-liquid equilibrium is of interest. However, aqueous crystal-liquid transitions are very difficult to simulate. A new molecular dynamics algorithm generates trajectories in a generalized NPT ensemble and equilibrates states of coexisting phases with a selectable enthalpy. With replicas spanning the range between ß ice and liquid water, we find the statistical temperature from the enthalpy histograms and characterize the transition by the entropy, introducing a general computational procedure for first-order transitions.

Classical Description of the Vibrational Spectroscopy, Structure, and Electrostatics of the Halide Solvation Shell with the POLIR Potential.

POLIR (POLarizable for IR) (J. Chem. Phys. 2008, 129, 034504) is a polarizable, flexible, and transferable water potential which describes the IR spectrum in the O-H stretch region via the classical dipole correlation function with simple quantum corrections. POLIR also reproduces experimental spectral shifts in solutions of Ca(2+), Mg(2+), and Cu(2+) (J. Am. Chem. Soc. 2011, 133, 9441-9450). Here we present an extended investigation of POLIR water in the solvation shell of the halides F(-), Cl(-), Br(-), and I(-) using various interaction potentials, polarizabilities, and short-range electrostatic damping parameters. Our results indicate that the correlation of the first solvation shell dipoles produces IR spectra that are in agreement with experiment; that is, vibrational spectral shifts may be obtained with classical mechanics and simple corrections. Calculated ion induced dipoles agree with quantum simulations. Further analysis shows that ion-dependent shifts in the spectra may be attributed to the hydrogen bond O···O-H angle distribution within the first solvation shell, decomposed into ion-water and water-water contributions.

Replica exchange statistical temperature molecular dynamics algorithm.

The replica exchange statistical temperature molecular dynamics (RESTMD) algorithm is presented, designed to alleviate an extensive increase of the number of replicas required as system size increases in the conventional temperature replica exchange method (tREM), and to obtain improved sampling in individual replicas. RESTMD optimally integrates multiple STMD (Phys. Rev. Lett. 2006, 97, 050601) runs with replica exchanges, giving rise to a flat energy sampling in each replica with a self-adjusting weight determination. The expanded flat energy dynamic sampling range allows the use of significantly fewer STMD replicas while maintaining the desired acceptance probability for replica exchanges. The computational advantages of RESTMD over conventional REM and single-replica STMD are explicitly demonstrated with an application to a coarse-grained protein model. The effect of two different kinetic temperature control schemes on the sampling efficiency is explored for diverse simulation conditions.

The relation between the structure of the first solvation shell and the IR spectra of aqueous solutions.

The spectroscopic signatures of solvated anions and cations, in the O-H stretch region of water, are studied using the POLIR potential. Shifts in the spectra are shown to correlate very well with the distribution of a particular hydrogen bond angle for the waters in the first solvation shell. The results indicate that the spectral shifts might be predicted from MD simulations in a computationally convenient fashion, avoiding an explicit calculation of the spectra, as first suggested by Sharp et al. (J Chem Phys 114(4):1791-1796, 2001).

Classical simulations with the POLIR potential describe the vibrational spectroscopy and energetics of hydration: divalent cations, from solvation to coordination complex.

POLIR, a polarizable water potential optimized for vibrational and intermolecular spectroscopy in pure water but not optimized for solvation, is used to describe solutions of the divalent metal cations Ca(2+), Mg(2+), and Cu(2+). The spectral shifts in the O-H stretch region obtained from classical simulations are in agreement with experiment. The water-ion binding energies are dominated by classical electrostatics, even though the Cu(2+) case might be considered to involve an intermediate-strength chemical bond. Three-body energies of the ion with the first solvation shell are in agreement with ab initio calculations. Our results indicate the importance of polarization in the development of accurate, transferable, force fields and the power of classical methods when it is carefully included.

Extending classical molecular theory with polarization.

A classical, polarizable, electrostatic theory of short-ranged atom-atom interactions, incorporating the smeared nature of atomic partial charges, is presented. Detailed models are constructed for CO monomer and for CO interacting with an iron atom, as a first step toward heme proteins. A good representation is obtained of the bond-length-dependent dipole of CO monomer from fitting at the equilibrium distance only. Essential features of the binding of CO to myoglobin (Mb) and model heme compounds, including the binding energy, the position of the minimum in the Fe-C potential, the Fe-C frequency, the bending energy, the linear geometry of FeCO, and the increase of the Stark tuning rate and IR intensity, are obtained, suggesting that a substantial part of the Fe-CO interaction consists of a classical, noncovalent, "electrostatic bond ". The binding energy is primarily polarization energy, and the polarization energy of an OH pair in water is shown to be comparable to the experimental hydrogen bond energy.

Protein folding and confinement: inherent structure analysis of chaperonin action.

A coarse-grained model of the action of a chaperonin cage of tunable hydrophobicity, h, upon a protein with the possibility of misfolding is studied with inherent structure (IS) analysis and statistical temperature molecular dynamics (STMD) simulation. Near the folding temperature, the equilibrium properties of the system may be understood in terms of <10 IS. The known phenomenon of an optimal cage hydrophobicity for productive folding, found at h = 0.25, is seen to arise from a striking suppression of the occupations of IS in the misfolding funnel, which in turn arises from a decrease in translational entropy due to confinement to the region of the cage wall. The kinetics of folding is correspondingly fastest at h = 0.25, where a minimum is found in the h-dependent barrier height. While true kinetics is determined by conventional MD, it is shown that the accelerated dynamics of STMD provide a valuable quantitative perspective.

Classical molecular electrostatics: recognition of ligands in proteins and the vibrational Stark effect.

It is shown that classical electrostatics quantitatively describes both the binding of the diatomic ligands XO (X = C, N, O) to the heme group in myoglobin and the dependence of their vibrational frequencies upon an external field, the vibrational Stark effect. The key is a proper treatment of induced dipoles. The results suggest that ligand binding occurs via an "electrostatic bond", a generalization of the standard ionic bond to include induction, and, more generally, that classical electrostatics can replace quantum mechanics for a considerable simplification of some complex problems.