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.

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.

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.

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.

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.

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.

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.

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.

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.

Robust nonequilibrium pathways to microcompartment assembly.

Cyanobacteria sequester photosynthetic enzymes into microcompartments which facilitate the conversion of carbon dioxide into sugars. Geometric similarities between these structures and self-assembling viral capsids have inspired models that posit microcompartments as stable equilibrium arrangements of the constituent proteins. Here we describe a different mechanism for microcompartment assembly, one that is fundamentally nonequilibrium and yet highly reliable. This pathway is revealed by simulations of a molecular model resolving the size and shape of a cargo droplet and the extent and topography of an elastic shell. The resulting metastable microcompartment structures closely resemble those of carboxysomes, with a narrow size distribution and faceted shells. The essence of their assembly dynamics can be understood from a simpler mathematical model that combines elements of classical nucleation theory with continuum elasticity. These results highlight important control variables for achieving nanoscale encapsulation in general and for modulating the size and shape of carboxysomes in particular.

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.

Mechanism of ion adsorption to aqueous interfaces: Graphene/water vs. air/water.

The adsorption of ions to aqueous interfaces is a phenomenon that profoundly influences vital processes in many areas of science, including biology, atmospheric chemistry, electrical energy storage, and water process engineering. Although classical electrostatics theory predicts that ions are repelled from water/hydrophobe (e.g., air/water) interfaces, both computer simulations and experiments have shown that chaotropic ions actually exhibit enhanced concentrations at the air/water interface. Although mechanistic pictures have been developed to explain this counterintuitive observation, their general applicability, particularly in the presence of material substrates, remains unclear. Here we investigate ion adsorption to the model interface formed by water and graphene. Deep UV second harmonic generation measurements of the SCN- ion, a prototypical chaotrope, determined a free energy of adsorption within error of that for air/water. Unlike for the air/water interface, wherein repartitioning of the solvent energy drives ion adsorption, our computer simulations reveal that direct ion/graphene interactions dominate the favorable enthalpy change. Moreover, the graphene sheets dampen capillary waves such that rotational anisotropy of the solute, if present, is the dominant entropy contribution, in contrast to the air/water interface.

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.

Necessity of capillary modes in a minimal model of nanoscale hydrophobic solvation.

Modern theories of the hydrophobic effect highlight its dependence on length scale, emphasizing the importance of interfaces in the vicinity of sizable hydrophobes. We recently showed that a faithful treatment of such nanoscale interfaces requires careful attention to the statistics of capillary waves, with significant quantitative implications for the calculation of solvation thermodynamics. Here, we show that a coarse-grained lattice model like that of Chandler [Chandler D (2005)Nature437(7059):640-647], when informed by this understanding, can capture a broad range of hydrophobic behaviors with striking accuracy. Specifically, we calculate probability distributions for microscopic density fluctuations that agree very well with results of atomistic simulations, even many SDs from the mean and even for probe volumes in highly heterogeneous environments. This accuracy is achieved without adjustment of free parameters, because the model is fully specified by well-known properties of liquid water. As examples of its utility, we compute the free-energy profile for a solute crossing the air-water interface, as well as the thermodynamic cost of evacuating the space between extended nanoscale surfaces. These calculations suggest that a highly reduced model for aqueous solvation can enable efficient multiscale modeling of spatial organization driven by hydrophobic and interfacial forces.

Near-optimal protocols in complex nonequilibrium transformations.

The development of sophisticated experimental means to control nanoscale systems has motivated efforts to design driving protocols that minimize the energy dissipated to the environment. Computational models are a crucial tool in this practical challenge. We describe a general method for sampling an ensemble of finite-time, nonequilibrium protocols biased toward a low average dissipation. We show that this scheme can be carried out very efficiently in several limiting cases. As an application, we sample the ensemble of low-dissipation protocols that invert the magnetization of a 2D Ising model and explore how the diversity of the protocols varies in response to constraints on the average dissipation. In this example, we find that there is a large set of protocols with average dissipation close to the optimal value, which we argue is a general phenomenon.

Exploiting Chromophore-Protein Interactions through Linker Engineering To Tune Photoinduced Dynamics in a Biomimetic Light-Harvesting Platform.

Creating artificial systems that mimic and surpass those found in nature is one of the great challenges of modern science. In the context of photosynthetic light harvesting, the difficulty lies in attaining utmost control over the energetics, positions and relative orientations of chromophores in densely packed arrays to transfer electronic excitation energy to desired locations with high efficiency. Toward achieving this goal, we use a highly versatile biomimetic protein scaffold from the tobacco mosaic virus coat protein on which chromophores can be attached at precise locations via linkers of differing lengths and rigidities. We show that minor linker modifications, including switching chiral configurations and alkyl chain shortening, lead to significant lengthening of the ultrafast excited state dynamics of the system as the linkers are shortened and rigidified. Molecular dynamics simulations provide molecular-level detail over how the chromophore attachment orientations, positions, and distances from the protein surface lead to the observed trends in system dynamics. In particular, we find that short and rigid linkers are able to sandwich water molecules between chromophore and protein, leading to chromophore-water-protein supracomplexes with intricately coupled dynamics that are highly dependent on their local protein environment. In addition, cyclohexyl-based linkers are identified as ideal candidates to retain rotational correlations over several nanoseconds and thus lock relative chromophore orientations throughout the lifetime of an exciton. Combining linker engineering with judicious placement of chromophores on the hydrated protein scaffold to exploit different chromophore-bath couplings provides a clear and effective path to producing highly controllable artificial light-harvesting systems that can increasingly mimic their natural counterparts, thus aiding to elucidate natural photosynthetic mechanisms.

Interfacial ion solvation: Obtaining the thermodynamic limit from molecular simulations.

Inferring properties of macroscopic solutions from molecular simulations is complicated by the limited size of systems that can be feasibly examined with a computer. When long-ranged electrostatic interactions are involved, the resulting finite size effects can be substantial and may attenuate very slowly with increasing system size, as shown by previous work on dilute ions in bulk aqueous solution. Here we examine corrections for such effects, with an emphasis on solvation near interfaces. Our central assumption follows the perspective of Hünenberger and McCammon [J. Chem. Phys. 110, 1856 (1999)]: Long-wavelength solvent response underlying finite size effects should be well described by reduced models like dielectric continuum theory, whose size dependence can be calculated straightforwardly. Applied to an ion in a periodic slab of liquid coexisting with vapor, this approach yields a finite size correction for solvation free energies that differs in important ways from results previously derived for bulk solution. For a model polar solvent, we show that this new correction quantitatively accounts for the variation of solvation free energy with volume and aspect ratio of the simulation cell. Correcting periodic slab results for an aqueous system requires an additional accounting for the solvent's intrinsic charge asymmetry, which shifts electric potentials in a size-dependent manner. The accuracy of these finite size corrections establishes a simple method for a posteriori extrapolation to the thermodynamic limit and also underscores the realism of dielectric continuum theory down to the nanometer scale.

The More the Tubular: Dynamic Bundling of Actin Filaments for Membrane Tube Formation.

Tubular protrusions are a common feature of living cells, arising from polymerization of stiff protein filaments against a comparably soft membrane. Although this process involves many accessory proteins in cells, in vitro experiments indicate that similar tube-like structures can emerge without them, through spontaneous bundling of filaments mediated by the membrane. Using theory and simulation of physical models, we have elaborated how nonequilibrium fluctuations in growth kinetics and membrane shape can yield such protrusions. Enabled by a new grand canonical Monte Carlo method for membrane simulation, our work reveals a cascade of dynamical transitions from individually polymerizing filaments to highly cooperatively growing bundles as a dynamical bottleneck to tube formation. Filament network organization as well as adhesion points to the membrane, which bias filament bending and constrain membrane height fluctuations, screen the effective attractive interactions between filaments, significantly delaying bundling and tube formation.

Dynamics of Seeded Aß40-Fibril Growth from Atomistic Molecular Dynamics Simulations: Kinetic Trapping and Reduced Water Mobility in the Locking Step.

Filamentous ß-amyloid aggregates are crucial for the pathology of Alzheimer's disease. Despite the tremendous biomedical importance, the molecular pathway of growth propagation is not completely understood and remains challenging to investigate by simulations due to the long time scales involved. Here, we apply extensive all-atom molecular dynamics simulations in explicit water to obtain free energy profiles and kinetic information from position-dependent diffusion profiles for three different Aß9-40-growth processes: fibril elongation by single monomers at the structurally unequal filament tips and association of larger filament fragments. Our approach provides insight into the molecular steps of the kinetic pathway and allows close agreement with experimental binding free energies and macroscopic growth rates. Water plays a decisive role, and solvent entropy is identified as the main driving force for assembly. Fibril growth is disfavored energetically due to cancellation of direct peptide-peptide interactions and solvation effects. The kinetics of growth is consistent with the characteristic dock/lock mechanism, and docking is at least 2 orders of magnitude faster. During initial docking, interactions are mediated by transient non-native hydrogen bonds, which efficiently catch the incoming monomer or fragment already at separations of about 3 nm. In subsequent locking, the dynamics is much slower due to formation of kinetically trapped conformations caused by long-lived non-native hydrogen bonds. Fibril growth additionally requires collective motion of water molecules to create a dry binding interface. Fibril growth is further retarded due to reduced mobility of the involved hydration water, evident from a 2-fold reduction of the diffusion coefficient.