Symmetrized Drude Oscillator Force Fields Improve Numerical Performance of Polarizable Molecular Dynamics.

Drude oscillator potentials are a popular and computationally efficient class of polarizable models that represent each polarizable atom as a positively charged Drude core harmonically bound to a negatively charged Drude shell. We show that existing force fields that place all non-Coulomb forces on the Drude core and none on the shell inadvertently couple the dipole to non-Coulombic forces. This introduces errors where interactions with neutral particles can erroneously induce atomic polarization, leading to spurious polarizations in the absence of an electric field, exacerbating violations of equipartition in the employed Carr-Parinello scheme. A suitable symmetrization of the interaction potential that correctly splits the force between the Drude core and shell can correct this shortcoming, improving the stability and numerical performance of Drude oscillator-based simulations. The symmetrization procedure is straightforward and only requires the rescaling of a few force field parameters.

Ceramide-1-phosphate transfer protein enhances lipid transport by disrupting hydrophobic lipid-membrane contacts.

Cellular distributions of the sphingolipid ceramide-1-phosphate (C1P) impact essential biological processes. C1P levels are spatiotemporally regulated by ceramide-1-phosphate transfer protein (CPTP), which efficiently shuttles C1P between organelle membranes. Yet, how CPTP rapidly extracts and inserts C1P into a membrane remains unknown. Here, we devise a multiscale simulation approach to elucidate biophysical details of CPTP-mediated C1P transport. We find that CPTP binds a membrane poised to extract and insert C1P and that membrane binding promotes conformational changes in CPTP that facilitate C1P uptake and release. By significantly disrupting a lipid's local hydrophobic environment in the membrane, CPTP lowers the activation free energy barrier for passive C1P desorption and enhances C1P extraction from the membrane. Upon uptake of C1P, further conformational changes may aid membrane unbinding in a manner reminiscent of the electrostatic switching mechanism used by other lipid transfer proteins. Insertion of C1P into an acceptor membrane, eased by a decrease in membrane order by CPTP, restarts the transfer cycle. Most notably, we provide molecular evidence for CPTP's ability to catalyze C1P extraction by breaking hydrophobic C1P-membrane contacts with compensatory hydrophobic lipid-protein contacts. Our work, thus, provides biophysical insights into how CPTP efficiently traffics C1P between membranes to maintain sphingolipid homeostasis and, additionally, presents a simulation method aptly suited for uncovering the catalytic mechanisms of other lipid transfer proteins.

Tuning nonequilibrium phase transitions with inertia.

In striking contrast to equilibrium systems, inertia can profoundly alter the structure of active systems. Here, we demonstrate that driven systems can exhibit effective equilibrium-like states with increasing particle inertia, despite rigorously violating the fluctuation-dissipation theorem. Increasing inertia progressively eliminates motility-induced phase separation and restores equilibrium crystallization for active Brownian spheres. This effect appears to be general for a wide class of active systems, including those driven by deterministic time-dependent external fields, whose nonequilibrium patterns ultimately disappear with increasing inertia. The path to this effective equilibrium limit can be complex, with finite inertia sometimes acting to accentuate nonequilibrium transitions. The restoration of near equilibrium statistics can be understood through the conversion of active momentum sources to passive-like stresses. Unlike truly equilibrium systems, the effective temperature is now density dependent, the only remnant of the nonequilibrium dynamics. This density-dependent temperature can in principle introduce departures from equilibrium expectations, particularly in response to strong gradients. Our results provide additional insight into the effective temperature ansatz while revealing a mechanism to tune nonequilibrium phase transitions.

Static Disorder has Dynamic Impact on Energy Transport in Biomimetic Light-Harvesting Complexes.

Despite extensive studies, many questions remain about what structural and energetic factors give rise to the remarkable energy transport efficiency of photosynthetic light-harvesting protein complexes, owing largely to the inability to synthetically control such factors in these natural systems. Herein, we demonstrate energy transfer within a biomimetic light-harvesting complex consisting of identical chromophores attached in a circular array to a protein scaffold derived from the tobacco mosaic virus coat protein. We confirm the capability of energy transport by observing ultrafast depolarization in transient absorption anisotropy measurements and a redshift in time-resolved emission spectra in these complexes. Modeling the system with kinetic Monte Carlo simulations recapitulates the observed anisotropy decays, suggesting an inter-site hopping rate as high as 1.6 ps-1. With these simulations, we identify static disorder in orientation, site energy, and degree of coupling as key remaining factors to control to achieve long-range energy transfer in these systems. We thereby establish this system as a highly promising, bottom-up model for studying long-range energy transfer in light-harvesting protein complexes.

A Pair of 2D Quantum Liquids: Investigating the Phase Behavior of Indirect Excitons.

Long-lived indirect excitons (IXs) exhibit a rich phase diagram, including a Bose-Einstein condensate (BEC), a Wigner crystal, and other exotic phases. Recent experiments have hinted at a "classical" liquid of IXs above the BEC transition. To uncover the nature of this phase, we use a broad range of theoretical tools and find no evidence of a driving force toward classical condensation. Instead, we attribute the condensed phase to a quantum electron-hole liquid (EHL), first proposed by Keldysh for direct excitons. Taking into account the association of free carriers into bound excitons, we study the phase equilibrium between a gas of excitons, a gas of free carriers, and an EHL for a wide range of electron-hole separations, temperatures, densities, and mass ratios. Our results agree reasonably well with recent measurements of GaAs/AlGaAs coupled quantum wells.

Dielectric response of thin water films: a thermodynamic perspective.

The surface of a polar liquid presents a special environment for the solvation and organization of charged solutes, which differ from bulk behaviors in important ways. These differences have motivated many attempts to understand electrostatic response at aqueous interfaces in terms of a spatially varying dielectric permittivity, typically concluding that the dielectric constant of interfacial water is significantly lower than in the bulk liquid. Such analyses, however, are complicated by the potentially nonlocal nature of dielectric response over the short length scales of interfacial heterogeneity. Here we circumvent this problem for thin water films by adopting a thermodynamic approach. Using molecular simulations, we calculate the solvent's contribution to the reversible work of charging a parallel plate capacitor. We find good agreement with a simple dielectric continuum model that assumes bulk dielectric permittivity all the way up to the liquid's boundary, even for very thin (∼1 nm) films. This comparison requires careful attention to the placement of dielectric boundaries between liquid and vapor, which also resolves apparent discrepancies with dielectric imaging experiments.

Local Ice-like Structure at the Liquid Water Surface.

Experiments and computer simulations have established that liquid water's surfaces can deviate in important ways from familiar bulk behavior. Even in the simplest case of an air-water interface, distinctive layering, orientational biases, and hydrogen bond arrangements have been reported, but an overarching picture of their origins and relationships has been incomplete. Here we show that a broad set of such observations can be understood through an analogy with the basal face of crystalline ice. Using simulations, we demonstrate a number of structural similarities between water and ice surfaces, suggesting the presence of domains at the air-water interface with ice-like features that persist over 2-3 molecular diameters. Most prominent is a shared characteristic layering of molecular density and orientation perpendicular to the interface. Lateral correlations of hydrogen bond network geometry point to structural similarities in the parallel direction as well. Our results bolster and significantly extend previous conceptions of ice-like structure at the liquid's boundary and suggest that the much-discussed quasi-liquid layer on ice evolves subtly above the melting point into a quasi-ice layer at the surface of liquid water.

Trade-offs between Translational and Orientational Order in 2D Superlattices of Polygonal Nanocrystals with Differing Edge Count.

The goal of this work is to identify factors which modulate structural order in 2D self-assembled superlattices of polygon-shaped colloidal nanocrystals. Using combined experimental and simulation techniques, we quantify order in superlattices of hexagonal prism-shaped CdSe/CdS nanocrystals and cube-shaped CsPbBr3 nanocrystals. Superlattices derived from cube-shaped nanocrystals display less translational order compared to hexagonal prism-shaped nanocrystals both experimentally and in simulations. This effect can be attributed to geometric considerations inherent to the combined rotational and translational symmetries of different polygonal shapes and their superlattices. Cubes form a simple cubic lattice where nanocrystals can slide without steric overlap, whereas hexagonal prisms interlock, preventing translation. Regarding orientational order, cube assemblies display a narrower orientation distribution. Intuitively, hexagonal prisms are a more "spherical" shape compared to cubes. The results presented here outline a conceptual framework for identifying superlattice structures which favor translationally and orientationally ordered self-assembled superlattices.

Elastic forces drive nonequilibrium pattern formation in a model of nanocrystal ion exchange.

Chemical transformations, such as ion exchange, are commonly employed to modify nanocrystal compositions. Yet the mechanisms of these transformations, which often operate far from equilibrium and entail mixing diverse chemical species, remain poorly understood. Here we explore an idealized model for ion exchange in which a chemical potential drives compositional defects to accumulate at a crystal's surface. These impurities subsequently diffuse inward. We find that the nature of interactions between sites in a compositionally impure crystal strongly impacts exchange trajectories. In particular, elastic deformations which accompany lattice-mismatched species promote spatially modulated patterns in the composition. These same patterns can be produced at equilibrium in core/shell nanocrystals, whose structure mimics transient motifs observed in nonequilibrium trajectories. Moreover, the core of such nanocrystals undergoes a phase transition-from modulated to unstructured-as the thickness or stiffness of the shell is decreased. Our results help explain the varied patterns observed in heterostructured nanocrystals produced by ion exchange and suggest principles for the rational design of compositionally patterned nanomaterials.

The microscopic mechanism of bulk melting of ice.

We study the initial stages of homogeneous melting of a hexagonal ice crystal at coexistence and at moderate superheating. Our trajectory-based computer simulation approach provides a comprehensive picture of the events that lead to melting, from the initial accumulation of 5+7 defects, via the formation of L-D and interstitial-vacancy pairs, to the formation of a liquid nucleus. Of the different types of defects that we observe to be involved in melting, a particular kind of 5+7 type defect (type 5) plays a prominent role as it often forms prior to the formation of the initial liquid nucleus and close to the site where the nucleus forms. Hence, like other solids, ice homogeneously melts via the prior accumulation of defects.

Molecular Properties and Chemical Transformations Near Interfaces.

The properties of bulk water and aqueous solutions are known to change in the vicinity of an interface and/or in a confined environment, including the thermodynamics of ion selectivity at interfaces, transition states and pathways of chemical reactions, and nucleation events and phase growth. Here we describe joint progress in identifying unifying concepts about how air, liquid, and solid interfaces can alter molecular properties and chemical reactivity compared to bulk water and multicomponent solutions. We also discuss progress made in interfacial chemistry through advancements in new theory, molecular simulation, and experiments.

The Buckling Spectra of Nanoparticle Surfactant Assemblies.

Fine control over the mechanical properties of thin sheets underpins transcytosis, cell shape, and morphogenesis. Applying these principles to artificial, liquid-based systems has led to reconfigurable materials for soft robotics, actuation, and chemical synthesis. However, progress is limited by a lack of synthetic two-dimensional membranes that exhibit tunable mechanical properties over a comparable range to that seen in nature. Here, we show that the bending modulus, B, of thin assemblies of nanoparticle surfactants (NPSs) at the oil-water interface can be varied continuously from sub-kBT to 106kBT, by varying the ligands and particles that comprise the NPS. We find extensive departure from continuum behavior, including enormous mechanical anisotropy and a power law relation between B and the buckling spectrum width. Our findings provide a platform for shape-changing liquid devices and motivate new theories for the description of thin-film wrinkling.

Quadrupole-mediated dielectric response and the charge-asymmetric solvation of ions in water.

Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of the solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for basic length and energy scales of ion solvation, computer simulations indicate not only its quantitative inaccuracies but also its inability to capture some basic and important aspects of microscopic polarization response. Here, we consider one such shortcoming, a failure to distinguish the solvation thermodynamics of cations from that of otherwise-identical anions, and we pursue a simple, physically inspired modification of the dielectric continuum model to address it. The adaptation is motivated by analyzing the orientational response of an isolated water molecule whose dipole is rigidly constrained. Its free energy suggests a Hamiltonian for dipole fluctuations that accounts implicitly for the influence of higher-order multipole moments while respecting constraints of molecular geometry. We propose a field theory with the suggested form, whose nonlinear response breaks the charge symmetry of ion solvation. An approximate variational solution of this theory, with a single adjustable parameter, yields solvation free energies that agree closely with simulation results over a considerable range of solute size and charge.

Membrane hydrophobicity determines the activation free energy of passive lipid transport.

The collective behavior of lipids with diverse chemical and physical features determines a membrane's thermodynamic properties. Yet, the influence of lipid physicochemical properties on lipid dynamics, in particular interbilayer transport, remains underexplored. Here, we systematically investigate how the activation free energy of passive lipid transport depends on lipid chemistry and membrane phase. Through all-atom molecular dynamics simulations of 11 chemically distinct glycerophospholipids, we determine how lipid acyl chain length, unsaturation, and headgroup influence the free energy barriers for two elementary steps of lipid transport: lipid desorption, which is rate limiting, and lipid insertion into a membrane. Consistent with previous experimental measurements, we find that lipids with longer, saturated acyl chains have increased activation free energies compared to lipids with shorter, unsaturated chains. Lipids with different headgroups exhibit a range of activation free energies; however, no clear trend based solely on chemical structure can be identified, mirroring difficulties in the interpretation of previous experimental results. Compared to liquid-crystalline phase membranes, gel phase membranes exhibit substantially increased free energy barriers. Overall, we find that the activation free energy depends on a lipid's local hydrophobic environment in a membrane and that the free energy barrier for lipid insertion depends on a membrane's interfacial hydrophobicity. Both of these properties can be altered through changes in lipid acyl chain length, lipid headgroup, and membrane phase. Thus, the rate of lipid transport can be tuned through subtle changes in local membrane composition and order, suggesting an unappreciated role for nanoscale membrane domains in regulating cellular lipid dynamics.

Phase Diagram of Active Brownian Spheres: Crystallization and the Metastability of Motility-Induced Phase Separation.

Motility-induced phase separation (MIPS), the phenomenon in which purely repulsive active particles undergo a liquid-gas phase separation, is among the simplest and most widely studied examples of a nonequilibrium phase transition. Here, we show that states of MIPS coexistence are in fact only metastable for three-dimensional active Brownian particles over a very broad range of conditions, decaying at long times through an ordering transition we call active crystallization. At an activity just above the MIPS critical point, the liquid-gas binodal is superseded by the crystal-fluid coexistence curve, with solid, liquid, and gas all coexisting at the triple point where the two curves intersect. Nucleating an active crystal from a disordered fluid, however, requires a rare fluctuation that exhibits the nearly close-packed density of the solid phase. The corresponding barrier to crystallization is surmountable on a feasible timescale only at high activity, and only at fluid densities near maximal packing. The glassiness expected for such dense liquids at equilibrium is strongly mitigated by active forces, so that the lifetime of liquid-gas coexistence declines steadily with increasing activity, manifesting in simulations as a facile spontaneous crystallization at extremely high activity.

Breakage of Hydrophobic Contacts Limits the Rate of Passive Lipid Exchange between Membranes.

The maintenance of heterogeneous lipid compositions among cellular membranes is key to biological function. Yet, even the simplest process that could be responsible for maintaining proper lipid distributions, passive lipid exchange of individual molecules between membranes, has eluded a detailed understanding, due in part to inconsistencies between experimental findings and molecular simulations. We resolve these discrepancies by discovering the reaction coordinate for passive lipid exchange, which enables a complete biophysical characterization of the rate-limiting step for lipid exchange. Our approach to identify the reaction coordinate capitalizes on our ability to harvest over 1000 unbiased trajectories of lipid insertion, an elementary step of passive lipid transport, using all-atom and coarse-grained molecular dynamics simulations. We find that the reaction coordinate measures the formation and breakage of hydrophobic contacts between the membrane and exchanging lipid. Consistent with experiments, free energy profiles as a function of our reaction coordinate exhibit a substantial barrier for insertion. In contrast, lipid insertion was predicted to be a barrier-less process by previous computational studies, which incorrectly presumed the reaction coordinate to be the displacement of the exchanging lipid from the membrane. Utilizing our newfound knowledge of the reaction coordinate, we formulate an expression for the lipid exchange rate to enable a quantitative comparison with experiments. Overall, our results indicate that the breakage of hydrophobic contacts is rate limiting for passive lipid exchange and provide a foundation to understand the catalytic function of lipid transfer proteins.

Lattice Models for Protein Organization throughout Thylakoid Membrane Stacks.

Proteins in photosynthetic membranes can organize into patterned arrays that span the membrane's lateral size. Attractions between proteins in different layers of a membrane stack can play a key role in this ordering, as was suggested by microscopy and fluorescence spectroscopy and demonstrated by computer simulations of a coarse-grained model. The architecture of thylakoid membranes, however, also provides opportunities for interlayer interactions that instead disfavor the high protein densities of ordered arrangements. Here, we explore the interplay between these opposing driving forces and, in particular, the phase transitions that emerge in the periodic geometry of stacked thylakoid membrane disks. We propose a lattice model that roughly accounts for proteins' attraction within a layer and across the stromal gap, steric repulsion across the lumenal gap, and regulation of protein density by exchange with the stroma lamellae. Mean-field analysis and computer simulation reveal rich phase behavior for this simple model, featuring a broken-symmetry striped phase that is disrupted at both high and low extremes of chemical potential. The resulting sensitivity of microscopic protein arrangement to the thylakoid's mesoscale vertical structure raises intriguing possibilities for regulation of photosynthetic function.

Assessing long-range contributions to the charge asymmetry of ion adsorption at the air-water interface.

Anions generally associate more favorably with the air-water interface than cations. In addition to solute size and polarizability, the intrinsic structure of the unperturbed interface has been discussed as an important contributor to this bias. Here we assess quantitatively the role that intrinsic charge asymmetry of water's surface plays in ion adsorption, using computer simulations to compare model solutes of various size and charge. In doing so, we also evaluate the degree to which linear response theory for solvent polarization is a reasonable approach for comparing the thermodynamics of bulk and interfacial ion solvation. Consistent with previous works on bulk ion solvation, we find that the average electrostatic potential at the center of a neutral, sub-nanometer solute at the air-water interface depends sensitively on its radius, and that this potential changes quite nonlinearly as the solute's charge is introduced. The nonlinear response closely resembles that of the bulk. As a result, the net nonlinearity of ion adsorption is weaker than in bulk, but still substantial, comparable to the apparent magnitude of macroscopically nonlocal contributions from the undisturbed interface. For the simple-point-charge model of water we study, these results argue distinctly against rationalizing ion adsorption in terms of surface potentials inherent to molecular structure of the liquid's boundary.

Weak scaling of the contact distance between two fluctuating interfaces with system size.

A pair of flat parallel surfaces, each freely diffusing along the direction of their separation, will eventually come into contact. If the shapes of these surfaces also fluctuate, then contact will occur when their centers-of-mass remain separated by a nonzero distance ℓ. An example of such a situation is the motion of interfaces between two phases at conditions of thermodynamic coexistence, and in particular the annihilation of domain wall pairs under periodic boundary conditions. Here we present a general approach to calculate the probability distribution of the contact distance ℓ and determine how its most likely value ℓ^{*} depends on the surfaces' lateral size L. Using the Edward-Wilkinson equation as a model for interfaces, we demonstrate that ℓ^{*} scales weakly with system size, i.e., the dependence of ℓ^{*} on L for both (1+1)- and (2+1)-dimensional interfaces is such that lim_{L→∞}(ℓ^{*}/L)=0. In particular, for (2+1)-dimensional interfaces ℓ^{*} is an algebraic function of logL, a result that is confirmed by computer simulations of slab-shaped domains formed under periodic boundary conditions. This weak scaling implies that such domains remain topologically intact until ℓ becomes very small compared to the lateral size of the interface, contradicting expectations from equilibrium thermodynamics.

Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids.

Lattice mismatch can substantially impact the spatial organization of heterogeneous materials. We examine a simple model for lattice-mismatched solids over a broad range of temperature and composition, revealing both uniform and spatially modulated phases. Scenarios for coexistence among them are unconventional due to the extensive mechanical cost of segregation. Together with an adapted Maxwell construction for elastic phase separation, mean field theory predicts a phase diagram that captures key low-temperature features of Monte Carlo simulations.