Tunable assembly of host-guest colloidal crystals.

Entropy compartmentalization provides new self-assembly routes to colloidal host-guest (HG) structures. Leveraging host particle shape to drive the assembly of HG structures has only recently been proposed and demonstrated. However, the extent to which the guest particles can dictate the structure of the porous network of host particles has not been explored. In this work, by modifying only the guest shape, we show athermal, binary mixtures of star-shaped host particles and convex polygon-shaped guest particles assemble as many as five distinct crystal structures, including rotator and discrete rotator guest crystals, two homoporous host crystals, and one heteroporous host crystal. Edge-to-edge alignment of neighboring stars results in the formation of three distinct pore motifs, whose preferential formation is controlled by the size and shape of the guest particles. Finally, we confirm, via free volume calculations, that assembly is driven by entropy compartmentalization, where the hosts and guests contribute differently to the free energy of the system; free volume calculations also explain differences in assembly based on guest shape. These results provide guest design rules for assembling colloidal HG structures, especially on surfaces and interfaces.

Inverse design of triblock Janus spheres for self-assembly of complex structures in the crystallization slot via digital alchemy.

The digital alchemy framework is an extended ensemble simulation technique that incorporates particle attributes as thermodynamic variables, enabling the inverse design of colloidal particles for desired behavior. Here, we extend the digital alchemy framework for the inverse design of patchy spheres that self-assemble into target crystal structures. To constrain the potentials to non-trivial solutions, we conduct digital alchemy simulations with constant second virial coefficient. We optimize the size, range, and strength of patchy interactions in model triblock Janus spheres to self-assemble the 2D kagome and snub square lattices and the 3D pyrochlore lattice, and demonstrate self-assembly of all three target structures with the designed models. The particles designed for the kagome and snub square lattices assemble into high quality clusters of their target structures, while competition from similar polymorphs lower the yield of the pyrochlore assemblies. We find that the alchemically designed potentials do not always match physical intuition, illustrating the ability of the method to find nontrivial solutions to the optimization problem. We identify a window of second virial coefficients that result in self-assembly of the target structures, analogous to the crystallization slot in protein crystallization.

Using molecular simulation to understand the skin barrier.

Skin's effectiveness as a barrier to permeation of water and other chemicals rests almost entirely in the outermost layer of the epidermis, the stratum corneum (SC), which consists of layers of corneocytes surrounded by highly organized lipid lamellae. As the only continuous path through the SC, transdermal permeation necessarily involves diffusion through these lipid layers. The role of the SC as a protective barrier is supported by its exceptional lipid composition consisting of ceramides (CERs), cholesterol (CHOL), and free fatty acids (FFAs) and the complete absence of phospholipids, which are present in most biological membranes. Molecular simulation, which provides molecular level detail of lipid configurations that can be connected with barrier function, has become a popular tool for studying SC lipid systems. We review this ever-increasing body of literature with the goals of (1) enabling the experimental skin community to understand, interpret and use the information generated from the simulations, (2) providing simulation experts with a solid background in the chemistry of SC lipids including the composition, structure and organization, and barrier function, and (3) presenting a state of the art picture of the field of SC lipid simulations, highlighting the difficulties and best practices for studying these systems, to encourage the generation of robust reproducible studies in the future. This review describes molecular simulation methodology and then critically examines results derived from simulations using atomistic and then coarse-grained models.

Multiscale Simulation of Ternary Stratum Corneum Lipid Mixtures: Effects of Cholesterol Composition.

Molecular dynamics simulations of mixtures of the ceramide nonhydroxy-sphingosine (NS), cholesterol, and a free fatty acid are performed to gain molecular-level understanding of the structure of the lipids found in the stratum corneum layer of skin. A new coarse-grained force field for cholesterol was developed using the multistate iterative Boltzmann inversion (MS-IBI) method. The coarse-grained cholesterol force field is compatible with previously developed coarse-grained force fields for ceramide NS, free fatty acids, and water and validated against atomistic simulations of these lipids using the CHARMM force field. Self-assembly simulations of multilayer structures using these coarse-grained force fields are performed, revealing that a large fraction of the ceramides adopt extended conformations, which cannot occur in the single bilayer in water structures typically studied using molecular simulation. Cholesterol fluidizes the membrane by promoting packing defects, and an increase in cholesterol content is found to reduce the bilayer thickness due to an increase in interdigitation of the C24 lipid tails, consistent with experimental observations. Using a reverse-mapping procedure, a self-assembled coarse-grained multilayer system is used to construct an equivalent structure with atomistic resolution. Simulations of this atomistic structure are found to closely agree with experimentally derived neutron scattering length density profiles. Significant interlayer hydrogen bonding is observed in the inner layers of the atomistic multilayer structure that are not found in the outer layers in contact with water or in equivalent bilayer structures. This work highlights the importance of simulating multilayer structures, as compared to the more commonly studied bilayer systems, to enable more appropriate comparisons with multilayer experimental membranes. These results also provide validation of the efficacy of the MS-IBI derived coarse-grained force fields and the framework for multiscale simulation.

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices.

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote-and, in some cases, may be necessary for-the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

Shape-driven entropic self-assembly of an open, reconfigurable, binary host-guest colloidal crystal.

Entropically driven self-assembly of hard anisotropic particles, where particle shape gives rise to emergent valencies, provides a useful perspective for the design of nanoparticle and colloidal systems. Hard particles self-assemble into a rich variety of crystal structures, ranging in complexity from simple close-packed structures to structures with 432 particles in the unit cell. Entropic crystallization of open structures, however, is missing from this landscape. Here, we report the self-assembly of a two-dimensional binary mixture of hard particles into an open host-guest structure, where nonconvex, triangular host particles form a honeycomb lattice that encapsulates smaller guest particles. Notably, this open structure forms in the absence of enthalpic interactions by effectively splitting the structure into low- and high-entropy sublattices. This is the first such structure to be reported in a two-dimensional athermal system. We discuss the observed compartmentalization of entropy in this system, and show that the effect of the size of the guest particle on the stability of the structure gives rise to a reentrant phase behavior. This reentrance suggests the possibility for a reconfigurable colloidal material, and we provide a proof-of-concept by showing the assembly behavior while changing the size of the guest particles in situ. Our findings provide a strategy for designing open colloidal crystals, as well as binary systems that exhibit co-crystallization, which have been elusive thus far.

Examining Tail and Headgroup Effects on Binary and Ternary Gel-Phase Lipid Bilayer Structure.

The structural properties of two- and three-component gel-phase bilayers were studied using molecular dynamics simulations. The bilayers contain distearoylphosphatidylcholine (DSPC) phospholipids mixed with alcohols and/or fatty acids of varying tail lengths, with carbon chain lengths of 12, 16, and 24 studied. Changes in both headgroup chemistry and tail length are found to affect the balance between steric repulsion and van der Waals attraction within the bilayers, manifesting in different bilayer structural properties. Lipid components are found to be located at different depths within the bilayer depending on both chain length and headgroup chemistry. The highest bilayer ordering and lowest area per tail are found in systems with medium-length tails. While longer tails can enhance van der Waals attractions, the increased tail-length asymmetry is found to induce disorder and reduce tail packing. Bulkier headgroups further increase steric repulsion, as reflected in increased component offsets and reduced tail packing. These findings help explain how bilayer composition affects the structure of gel-phase bilayers.

Analysis of Self-Assembly Pathways with Unsupervised Machine Learning Algorithms.

Colloidal and nanoparticle systems display a rich and exciting phase behavior including the self-assembly of highly complex crystal structures. Nucleation and growth pathways toward crystallization have been studied both computationally and experimentally, but the mechanisms for the formation of the precritical nucleus and consequent crystal growth are yet to be fully understood. Recent advances in the application of machine learning algorithms applied to many-particle systems have led to significant breakthroughs in the ability for high-throughput analysis of phase transitions and the identification of crystal structures. We build upon these techniques to identify and analyze pathways for nucleation and growth in supercooled liquids of colloidal systems modeled with isotropic pair potentials. Our study involves the development of unsupervised machine learning models trained on spherical-harmonics-based descriptors. These models allow us to determine clusters of local environments that are present prior to and during crystallization. We analyze these environments to identify prevalent motifs and local order within the supercooled liquid prior to formation of the critical nucleus.

Influence of Single-Stranded DNA Coatings on the Interaction between Graphene Nanoflakes and Lipid Bilayers.

Using molecular dynamics simulations, it is demonstrated that a partial coating of single-stranded DNA (ssDNA) reduces the penetration depth of a graphene nanoflake (GNF) into a phospholipid bilayer by attenuating the hydrophobic force that drives the penetration. As the GNF penetrates the bilayer, the ssDNA remains adsorbed to the GNF outside of the bilayer where it shields the graphene from the surrounding water. The penetration depth is found to be controlled by the amount of ssDNA coating the GNF, with a sparser coating resulting in a deeper penetration since the ssDNA shields less of the GNF surface. As the coating density is increased, the likelihood of the GNF entering the bilayer is reduced where it instead tends to lie flat on the bilayer surface with the sugar phosphate backbone of ssDNA interacting with the hydrophilic lipid head groups. While no bilayer disruption is observed for a partially inserted ssDNA-coated GNF, a larger, bare, partially inserted GNF is found to preferentially extract phospholipids from the bilayer, offering further evidence of lipid extraction as a main cytotoxicity mechanism of GNFs. Therefore, a coating of ssDNA may reduce the cytotoxicity of GNFs by shielding the unfavorable graphene-water interaction, thus preventing graphene penetration and lipid extraction.

Composition Dependence of Water Permeation Across Multicomponent Gel-Phase Bilayers.

The permeability of multicomponent phospholipid bilayers in the gel phase is investigated via molecular dynamics simulation. The physical role of the different molecules is probed by comparing multiple mixed-component bilayers containing distearylphosphatidylcholine (DSPC) with varying amounts of either the emollient isostearyl isostearate or long-chain alcohol (dodecanol, octadecanol, or tetracosanol) molecules. Permeability is found to depend on both the tail packing density and hydrogen bonding between lipid headgroups and water. Whereas the addition of emollient or alcohol molecules to a gel-phase DSPC bilayer can increase the tail packing density, it also disturbed the hydrogen-bonding network, which in turn can increase interfacial water dynamics. These phenomena have opposing effects on bilayer permeability, which is found to depend on the balance between enhanced tail packing and decreased hydrogen bonding.

Effect of Ceramide Tail Length on the Structure of Model Stratum Corneum Lipid Bilayers.

Lipid bilayers composed of non-hydroxy sphingosine ceramide (CER NS), cholesterol (CHOL), and free fatty acids (FFAs), which are components of the human skin barrier, are studied via molecular dynamics simulations. Since mixtures of these lipids exist in dense gel phases with little molecular mobility at physiological conditions, care must be taken to ensure that the simulations become decorrelated from the initial conditions. Thus, we propose and validate an equilibration protocol based on simulated tempering, in which the simulation takes a random walk through temperature space, allowing the system to break out of metastable configurations and hence become decorrelated from its initial configuration. After validating the equilibration protocol, which we refer to as random-walk molecular dynamics, the effects of the lipid composition and ceramide tail length on bilayer properties are studied. Systems containing pure CER NS, CER NS + CHOL, and CER NS + CHOL + FFA, with the CER NS fatty acid tail length varied within each CER NS-CHOL-FFA composition, are simulated. The bilayer thickness is found to depend on the structure of the center of the bilayer, which arises as a result of the tail-length asymmetry between the lipids studied. The hydrogen bonding between the lipid headgroups and with water is found to change with the overall lipid composition, but is mostly independent of the CER fatty acid tail length. Subtle differences in the lateral packing of the lipid tails are also found as a function of CER tail length. Overall, these results provide insight into the experimentally observed trend of altered barrier properties in skin systems where there are more CERs with shorter tails present.

Molecular dynamics simulations of stratum corneum lipid mixtures: A multiscale perspective.

The lipid matrix of the stratum corneum (SC) layer of skin is essential for human survival; it acts as a barrier to prevent rapid dehydration while keeping potentially hazardous material outside the body. While the composition of the SC lipid matrix is known, the molecular-level details of its organization are difficult to infer experimentally, hindering the discovery of structure-property relationships. To this end, molecular dynamics simulations, which give molecular-level resolution, have begun to play an increasingly important role in understanding these relationships. However, most simulation studies of SC lipids have focused on preassembled bilayer configurations, which, owing to the slow dynamics of the lipids, may influence the final structure and hence the calculated properties. Self-assembled structures would avoid this dependence on the initial configuration, however, the size and length scales involved make self-assembly impractical to study with atomistic models. Here, we report on the development of coarse-grained models of SC lipids designed to study self-assembly. Building on previous work, we present the interactions between the headgroups of ceramide and free fatty acid developed using the multistate iterative Boltzmann inversion method. Validation of the new interactions is performed with simulations of preassembled bilayers and good agreement between the atomistic and coarse-grained models is found for structural properties. The self-assembly of mixtures of ceramide and free fatty acid is investigated and both bilayer and multilayer structures are found to form. This work therefore represents a necessary step in studying SC lipid systems on multiple time and length scales.

Structural Properties of Phospholipid-based Bilayers with Long-Chain Alcohol Molecules in the Gel Phase.

The structural properties of two-component gel-phase bilayers of distearylphosphatidylcholine (DSPC) and alcohol molecules with different compositions and chain lengths (12-24 carbons long) are studied via molecular dynamics simulations. Several bilayer properties, including area per lipid, tilt angle, chain interdigitation, and headgroup offset, are studied for each system and compared, revealing important structural implications depending upon headgroup size and chain length. While tail tilt is the primary mechanism for single-component bilayers to balance tail attraction and headgroup repulsion, our results demonstrate that the lipid mixtures studied adjust this balance via an offset between the depths of the different molecular species in the bilayer; this behavior is found to depend both on composition and on the length of alcohol molecules relative to the length of DSPC tails. It is shown that the structural properties of bilayers with asymmetric tail lengths depend strongly on the bilayer composition, while the composition has less influence on mixed-component bilayers with nearly symmetric tail lengths. These findings are explained on the basis of the interdigitation between bilayer leaflets and how interdigitation is related to other structural properties.

A Coarse-Grained Model of Stratum Corneum Lipids: Free Fatty Acids and Ceramide NS.

Ceramide (CER)-based biological membranes are used both experimentally and in simulations as simplified model systems of the skin barrier. Molecular dynamics studies have generally focused on simulating preassembled structures using atomistically detailed models of CERs, which limit the system sizes and time scales that can practically be probed, rendering them ineffective for studying particular phenomena, including self-assembly into bilayer and lamellar superstructures. Here, we report on the development of a coarse-grained (CG) model for CER NS, the most abundant CER in human stratum corneum. Multistate iterative Boltzmann inversion is used to derive the intermolecular pair potentials, resulting in a force field that is applicable over a range of state points and suitable for studying ceramide self-assembly. The chosen CG mapping, which includes explicit interaction sites for hydroxyl groups, captures the directional nature of hydrogen bonding and allows for accurate predictions of several key structural properties of CER NS bilayers. Simulated wetting experiments allow the hydrophobicity of CG beads to be accurately tuned to match atomistic wetting behavior, which affects the whole system, since inaccurate hydrophobic character is found to unphysically alter the lipid packing in hydrated lamellar states. We find that CER NS can self-assemble into multilamellar structures, enabling the study of lipid systems more representative of the multilamellar lipid structures present in the skin barrier. The coarse-grained force field derived herein represents an important step in using molecular dynamics to study the human skin barrier, which gives a resolution not available through experiment alone.

Investigating the Structure of Multicomponent Gel-Phase Lipid Bilayers.

Single- and multicomponent lipid bilayers of 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine (DPPC), 1,2-distearoyl-sn-glycero-3-phosphatidylcholine (DSPC), isostearyl isostearate, and heptadecanoyl heptadecanoate in the gel phase are studied via molecular dynamics simulations. It is shown that the structural properties of multicomponent bilayers can deviate strongly from the structures of their single-component counterparts. Specifically, the lipid mixtures are shown to adopt a compact packing by offsetting the positioning depths at which different lipid species are located in the bilayer. This packing mechanism affects the area per lipid, the bilayer height, and the chain tilt angles and has important consequences for other bilayer properties, such as interfacial hydrogen bonding and bilayer permeability. In particular, the simulations suggest that bilayers containing isostearyl isostearate or heptadecanoyl heptadecanoate are less permeable than pure 1,2-dipalmitoyl-sn-glycero-3-phosphatidylcholine or DSPC bilayers. Furthermore, hydrogen-bond analysis shows that the residence times of lipid-water hydrogen bonds depend strongly on the bilayer composition, with longer residence times for bilayers that have a higher DSPC content. The findings illustrate and explain the fundamental differences between the properties of single- and multicomponent bilayers.

Development of a coarse-grained water forcefield via multistate iterative Boltzmann inversion.

A coarse-grained water model is developed using multistate iterative Boltzmann inversion. Following previous work, the k-means algorithm is used to dynamically map multiple water molecules to a single coarse-grained bead, allowing the use of structure-based coarse-graining methods. The model is derived to match the bulk and interfacial properties of liquid water and improves upon previous work that used single state iterative Boltzmann inversion. The model accurately reproduces the density and structural correlations of water at 305 K and 1.0 atm, stability of a liquid droplet at 305 K, and shows little tendency to crystallize at physiological conditions. This work also illustrates several advantages of using multistate iterative Boltzmann inversion for deriving generally applicable coarse-grained forcefields.

Derivation of coarse-grained potentials via multistate iterative Boltzmann inversion.

In this work, an extension is proposed to the standard iterative Boltzmann inversion (IBI) method used to derive coarse-grained potentials. It is shown that the inclusion of target data from multiple states yields a less state-dependent potential, and is thus better suited to simulate systems over a range of thermodynamic states than the standard IBI method. The inclusion of target data from multiple states forces the algorithm to sample regions of potential phase space that match the radial distribution function at multiple state points, thus producing a derived potential that is more representative of the underlying interactions. It is shown that the algorithm is able to converge to the true potential for a system where the underlying potential is known. It is also shown that potentials derived via the proposed method better predict the behavior of n-alkane chains than those derived via the standard IBI method. Additionally, through the examination of alkane monolayers, it is shown that the relative weight given to each state in the fitting procedure can impact bulk system properties, allowing the potentials to be further tuned in order to match the properties of reference atomistic and/or experimental systems.

Simulation study of the structure and phase behavior of ceramide bilayers and the role of lipid head group chemistry.

Ceramides are known to be a key component of the stratum corneum, the outermost protective layer of the skin that controls barrier function. In this work, molecular dynamics simulations are used to examine the behavior of ceramide bilayers, focusing on non-hydroxy sphingosine (NS) and non-hydroxy phytosphingosine (NP) ceramides. Here, we propose a modified version of the CHARMM force field for ceramide simulation, which is directly compared to the more commonly used GROMOS-based force field of Berger (Biophys. J. 1997, 72); while both force fields are shown to closely match experiment from a structural standpoint at the physiological temperature of skin, the modified CHARMM force field is better able to capture the thermotropic phase transitions observed in experiment. The role of ceramide chemistry and its impact on structural ordering is examined by comparing ceramide NS to NP, using the validated CHARMM-based force field. These simulations demonstrate that changing from ceramide NS to NP results in changes to the orientation of the OH groups in the lipid headgroups. The arrangement of OH groups perpendicular to the bilayer normal for ceramide NP, verse parallel for NS, results in the formation of a distinct hydrogen bonding network, that is ultimately responsible for shifting the gel-to-liquid phase transition to higher temperature, in direct agreement with experiment.