Main phase transition in lipid bilayers: Phase coexistence and line tension in a soft, solvent-free, coarse-grained model

Optimizing Coarse-Grained Models for Large-Scale Membrane Protein Simulation

Coarse-grained (CG) models have been developed for studying membrane proteins at physiologically relevant scales. Such methods, including popular CG lipid models, exhibit stability and efficiency at moderate scales, but they can become impractical or even unusable beyond a critical size due to various technical issues. Here, we report that these scale-dependent issues can arise from progressively slower relaxation dynamics and become confounded by unforeseen instabilities observed only at larger scales. To address these issues, we systemically optimized a 4-site solvent-free CG lipid model that is suitable for conducting micron-scale molecular dynamics simulations of membrane proteins under various membrane properties. We applied this lipid model to explore the long-range membrane deformation induced by a large mechanosensitive ion channel, PIEZO. We show that the optimized CG models are powerful in elucidating the structural and dynamic interplay between PIEZO and the membrane. Furthermore, we anticipate that our methodological insights can prove useful for resolving issues stemming from scale-dependent limitations of similar CG methodologies.

Entanglements via Slip Springs with Soft, Coarse-Grained Models for Systems Having Explicit Liquid-Vapor Interfaces

Recent advances in nano-rheology require that new techniques and models be developed to precisely describe the equilibrium and non-equilibrium characteristics of entangled polymeric materials and their interfaces at a molecular level. In this study, a slip-spring (SLSP) model is proposed to capture the dynamics of entangled polymers at interfaces, including those between liquids, liquids and vapors, and liquids and solids. The SLSP model employs a highly coarse-grained approach, which allows for comprehensive simulations of entire nano-rheological characterization systems using a particle-level description. The model relies on many-body dissipative particle dynamics (MDPD) non-bonded interactions, which permit explicit description of liquid-vapor interfaces; a compensating potential is introduced to ensure an unbiased representation of the shape of the liquid-vapor interface within the SLSP model. The usefulness of the proposed MDPD + SLSP approach is illustrated by simulating a capillary breakup rheometer (CaBR) experiment, in which a liquid droplet splits into two segments under the influence of capillary forces. We find that the predictions of the MDPD + SLSP model are consistent with experimental measurements and theoretical predictions. The proposed model is also verified by comparison to the results of explicit molecular dynamics simulations of an entangled polymer melt using a Kremer-Grest chain representation, both at equilibrium and far from equilibrium. Taken together, the model and methods presented in this study provide a reliable framework for molecular-level interpretation of high-polymer dynamics in the presence of interfaces.

Excluded-Volume Interactions in Field-Theoretic Simulations: Multiconvolutions and Model Equivalence

To deal with divergences of functional integrals in field-theoretic simulations (FTS) of complex fluids, the microscopic density is often smeared by being replaced by a convoluted one, typically using a Gaussian masking function. The smearing changes radically the nature of nonbonded interactions of the original microscopic density and results in a regularized model that is free of ultraviolet (UV) divergences. In this work, we first resolve a few fundamental issues related with the use of masking functions for δ-interactions in FTS and then we detail a new methodology that builds on the concept of multiconvoluted inverse potentials and a principle of model equivalence for statistical weights to accommodate more physically relevant interactions in FTS. The capabilities of the new approach are highlighted by examining the Gaussian-regularized Edwards model (GREM) and the Yukawa potential. A successful test calculation of the excess chemical potential of a polymer chain in a good solvent with the GREM illustrates the power of the new theoretical framework.

Molecular Weight Dependent Morphological Transitions of Bottlebrush Block Copolymer Particles: Experiments and Simulations

The molecular weights and chain rigidities of block copolymers can strongly influence their self-assembly behavior, particularly when the block copolymers are under confinement. We investigate the self-assembly of bottlebrush block copolymers (BBCPs) confined in evaporative emulsions with varying molecular weights. A series of symmetric BBCPs, where polystyrene (PS) and polylactide (PLA) side-chains are grafted onto a polynorbornene (PNB) backbone, are synthesized with varying degrees of polymerization of the PNB (N_PNB) ranging from 100 to 300. Morphological transitions from onion-like concentric particles to striped ellipsoids occur as the N_PNB of the BBCP increases above 200, which is also predicted from coarse-grained simulations of BBCP-containing droplets by an implicit solvent model. This transition is understood by the combined effects of (i) an elevated entropic penalty associated with bending lamella domains of large molecular weight BBCP particles and (ii) the favorable parallel alignment of the backbone chains at the free surface. Furthermore, the morphological evolutions of onion-like and ellipsoidal particles are compared. Unlike the onion-like BBCP particles, ellipsoidal BBCP particles are formed by the axial development of ring-like lamella domains on the particle surface, followed by the radial propagation into the particle center. Finally, the shape anisotropies of the ellipsoidal BBCP particles are analyzed as a function of particle size. These BBCP particles demonstrate promising potential for various applications that require tunable rheological, optical, and responsive properties.

Mesoscale Simulations of Polymer Solution Self-Assembly: Selection of Model Parameters within an Implicit Solvent Approximation

Coarse-grained modeling is an outcome of scientific endeavors to address the broad spectrum of time and length scales encountered in polymer systems. However, providing a faithful structural and dynamic characterization/description is challenging for several reasons, particularly in the selection of appropriate model parameters. By using a hybrid particle- and field-based approach with a generalized energy functional expressed in terms of density fields, we explore model parameter spaces over a broad range and map the relation between parameter values with experimentally measurable quantities, such as single-chain scaling exponent, chain density, and interfacial and surface tension. The obtained parameter map allows us to successfully reproduce experimentally observed polymer solution assembly over a wide range of concentrations and solvent qualities. The approach is further applied to simulate structure and shape evolution in emulsified block copolymer droplets where concentration and domain shape change continuously during the process.

Efficient and realistic simulation of phase coexistence

We show how an existing concurrent multi-scale method named hybrid particle field-molecular dynamics (hPF-MD) can be adapted to enable the simulation of structure and/or structural dynamics in compressible systems. Implementing such new equations of state (EOS) into hPF-MD, while conserving the efficiency associated with treating intermolecular interactions in a continuum fashion, opens this method up to describe a new class of phenomena in which non-uniform densities play a role, for example, evaporation and crystallization. We carefully consider how compressible hPF-MD compares to its mean-field counterpart for two particular EOS, adopted from the Cell Model for polymers and the Carnahan-Starling expression for hard spheres. Here, we performed a very basic analysis for a single-component system, focusing on the significance of various particle-based parameters and the particle-to-field projection. Our results illustrate the key role of the particle density per field grid cell and show that projection based on a Gaussian kernel is preferred over the standard cloud-in-cell projection. They also suggest that the behavior of hPF-MD close to the critical point is non-classical, i.e., in agreement with a critical exponent for a pure particle description, despite the mean-field origin of the method.

Bottom-up coarse-grained models for external fields and interfaces

Bottom-up coarse-grained (CG) models accurately describe the structure of homogeneous systems but sometimes provide limited transferability and a poor description of thermodynamic properties. Consequently, inhomogeneous systems present a severe challenge for bottom-up models. In this work, we examine bottom-up CG models for interfaces and inhomogeneous systems. We first analyze the effect of external fields upon the many-body potential of mean force. We also demonstrate that the multiscale CG (MS-CG) variational principle for modeling the external field corresponds to a generalization of the first Yvon-Born-Green equation. This provides an important connection with liquid state theory, as well as physical insight into the structure of interfaces and the resulting MS-CG models. We then develop and assess MS-CG models for a film of liquid methanol that is adsorbed on an attractive wall and in coexistence with its vapor phase. While pair-additive potentials provide unsatisfactory accuracy and transferability, the inclusion of local-density (LD) potentials dramatically improves the accuracy and transferability of the MS-CG model. The MS-CG model with LD potentials quite accurately describes the wall-liquid interface, the bulk liquid density, and the liquid-vapor interface while simultaneously providing a much improved description of the vapor phase. This model also provides an excellent description of the pair structure and pressure-density equation of state for the bulk liquid. Thus, LD potentials hold considerable promise for transferable bottom-up models that accurately describe the structure and thermodynamic properties of both bulk and interfacial systems.

Boundary-directed epitaxy of block copolymers

Directed self-assembly of block copolymers (BCPs) enables nanofabrication at sub-10 nm dimensions, beyond the resolution of conventional lithography. However, directing the position, orientation, and long-range lateral order of BCP domains to produce technologically-useful patterns is a challenge. Here, we present a promising approach to direct assembly using spatial boundaries between planar, low-resolution regions on a surface with different composition. Pairs of boundaries are formed at the edges of isolated stripes on a background substrate. Vertical lamellae nucleate at and are pinned by chemical contrast at each stripe/substrate boundary, align parallel to boundaries, selectively propagate from boundaries into stripe interiors (whereas horizontal lamellae form on the background), and register to wide stripes to multiply the feature density. Ordered BCP line arrays with half-pitch of 6.4 nm are demonstrated on stripes >80 nm wide. Boundary-directed epitaxy provides an attractive path towards assembling, creating, and lithographically defining materials on sub-10 nm scales.

Density Field Thermodynamic Integration (DFTI): A "Soft" Approach to Calculate the Free Energy of Surfactant Self-Assemblies

Thermodynamic integration is one of the most established methods to quantify excess free energies between different metastable states. Excess intermolecular interactions in surfactant assemblies are on the scale of the energy of thermal fluctuations. Therefore, these materials can be deformed and topologically altered via relatively small mechanical stresses. It is thus intuitive to design reaction paths and associated order parameters that exploit the "soft" nature of these materials to mechanically rather than alchemically morph surfactant assemblies from state to state. Here, we propose a novel method coined "density field thermodynamic integration" (DFTI) that adopts the universality and transferability of alchemical methods while simultaneously exploiting the soft excess interactions between surfactant molecules. DFTI was designed for a rapid quantification of the free energy differences between different metastable structures in soft fluid materials. The DFTI method uses an external field coupled to the local density to mechanically morph the system between metastable states of interest. Here, we explored the capability of the DFTI method to swiftly and accurately calculate free energy differences between states. To this aim, we studied two different coarse-grained lipidic surfactant systems: (i) a fusion stalk and (ii) a worm-like micelle. Our results illustrate that DFTI can provide an efficient, versatile, and rather reliable method to calculate the free energy differences between surfactant assemblies.

Analysis of local density potentials

Low resolution coarse-grained (CG) models are widely adopted for investigating phenomena that cannot be effectively simulated with all-atom (AA) models. Since the development of the many-body dissipative particle dynamics method, CG models have increasingly supplemented conventional pair potentials with one-body potentials of the local density (LD) around each site. These LD potentials appear to significantly extend the transferability of CG models, while also enabling more accurate descriptions of thermodynamic properties, interfacial phenomena, and many-body correlations. In this work, we systematically examine the properties of LD potentials. We first derive and numerically demonstrate a nontrivial transformation of pair and LD potentials that leaves the total forces and equilibrium distribution invariant. Consequently, the pair and LD potentials determined via bottom-up methods are not unique. We then investigate the sensitivity of CG models for glycerol to the weighting function employed for defining the local density. We employ the multiscale coarse-graining (MS-CG) method to simultaneously parameterize both pair and LD potentials. When employing a short-ranged Lucy function that defines the local density from the first solvation shell, the MS-CG model accurately reproduces the pair structure, pressure-density equation of state, and liquid-vapor interfacial profile of the AA model. The accuracy of the model generally decreases as the range of the Lucy function increases further. The MS-CG model provides similar accuracy when a smoothed Heaviside function is employed to define the local density from the first solvation shell. However, the model performs less well when this function acts on either longer or shorter length scales.

Exploring the impact of proteins on the line tension of a phase-separating ternary lipid mixture

The separation of lipid mixtures into thermodynamically stable phase-separated domains is dependent on lipid composition, temperature, and system size. Using molecular dynamics simulations, the line tension between thermodynamically stable lipid domains formed from ternary mixtures of di-C16:0 PC:di-C18:2 PC:cholesterol at 40:40:20 mol. % ratio was investigated via two theoretical approaches. The line tension was found to be 3.1 ± 0.2 pN by capillary wave theory and 4.7 ± 3.7 pN by pressure tensor anisotropy approaches for coarse-grained models based on the Martini force field. Using an all-atom model of the lipid membrane based on the CHARMM36 force field, the line tension was found to be 3.6 ± 0.9 pN using capillary wave theory and 1.8 ± 2.2 pN using pressure anisotropy approaches. The discrepancy between estimates of the line tension based on capillary wave theory and pressure tensor anisotropy methods is discussed. Inclusion of protein in Martini membrane lipid mixtures was found to reduce the line tension by 25%-35% as calculated by the capillary wave theory approach. To further understand and predict the behavior of proteins in phase-separated membranes, we have formulated an analytical Flory-Huggins model and parameterized it against the simulation results. Taken together these results suggest a general role for proteins in reducing the thermodynamic cost associated with domain formation in lipid mixtures and quantifies the thermodynamic driving force promoting the association of proteins to domain interfaces.

Studying polymer solutions with particle-based models linked to classical density functionals: co-non-solvency

We demonstrate the potential of hybrid particle-based models, where interactions are introduced through functionals of local order parameters, in describing multicomponent polymer solutions. The link to a free-energy-like functional is advantageous for controlling the thermodynamics of the model. We focus on co-non-solvency - the collapse of polymer chains in dilute mixtures with two miscible good solvents, having different affinities towards the polymer. We employ a simple model where polymers and solvents are represented, respectively, by worm-like chains and single particles. Non-bonded interactions are captured by a polynomial which is third order in local densities and can, therefore, describe liquid-vapour coexistence. The parameterisation of the functional benefits from an elementary mean-field approximation to the statistical mechanics of the model. The model provides a framework for Monte Carlo simulations using a particle-to-mesh algorithm. Studies with conventional generic bead-spring and all-atom models have demonstrated that co-non-solvency is caused by preferential binding of the better solvent (termed cosolvent) with polymer. Hence, segmental loops bridged by cosolvent molecules are formed, initiating polymer collapse. The mesoscopic hybrid model differs conceptually from the conventional microscopic descriptions. Yet, it reproduces the same co-non-solvency mechanism supporting its universality. Films of adsorbed ternary solutions, showing co-non-solvency in the dilute regime, are considered at high concentrations. In this case, chains do not collapse. The properties of loops and tails of the adsorbed polymer agree with early theoretical predictions obtained for concentrated binary solutions.

Rupturing the hemi-fission intermediate in membrane fission under tension: Reaction coordinates, kinetic pathways, and free-energy barriers

Membrane fission is a fundamental process in cells, involved inter alia in endocytosis, intracellular trafficking, and virus infection. Its underlying molecular mechanism, however, is only incompletely understood. Recently, experiments and computer simulation studies have revealed that dynamin-mediated membrane fission is a two-step process that proceeds via a metastable hemi-fission intermediate (or wormlike micelle) formed by dynamin's constriction. Importantly, this hemi-fission intermediate is remarkably metastable, i.e., its subsequent rupture that completes the fission process does not occur spontaneously but requires additional, external effects, e.g., dynamin's (unknown) conformational changes or membrane tension. Using simulations of a coarse-grained, implicit-solvent model of lipid membranes, we investigate the molecular mechanism of rupturing the hemi-fission intermediate, such as its pathway, the concomitant transition states, and barriers, as well as the role of membrane tension. The membrane tension is controlled by the chemical potential of the lipids, and the free-energy landscape as a function of two reaction coordinates is obtained by grand canonical Wang-Landau sampling. Our results show that, in the course of rupturing, the hemi-fission intermediate undergoes a "thinning → local pinching → rupture/fission" pathway, with a bottle-neck-shaped cylindrical micelle as a transition state. Although an increase of membrane tension facilitates the fission process by reducing the corresponding free-energy barrier, for biologically relevant tensions, the free-energy barriers still significantly exceed the thermal energy scale k_BT.

Generalization of the swelling method to measure the intrinsic curvature of lipids

Via computer simulation of a coarse-grained model of two-component lipid bilayers, we compare two methods of measuring the intrinsic curvatures of the constituting monolayers. The first one is a generalization of the swelling method that, in addition to the assumption that the spontaneous curvature linearly depends on the composition of the lipid mixture, incorporates contributions from its elastic energy. The second method measures the effective curvature-composition coupling between the apposing leaflets of bilayer structures (planar bilayers or cylindrical tethers) to extract the spontaneous curvature. Our findings demonstrate that both methods yield consistent results. However, we highlight that the two-leaflet structure inherent to the latter method has the advantage of allowing measurements for mixed lipid systems up to their critical point of demixing as well as in the regime of high concentration (of either species).

Membrane phase transition during heating and cooling: molecular insight into reversible melting

With increasing temperature, lipid bilayers undergo a gel-fluid phase transition, which plays an essential role in many physiological phenomena. In the present work, this first-order phase transition was investigated for variable heating and cooling rates for a dipalmitoylphosphatidylcholine (DPPC) lipid bilayer by means of atomistic molecular dynamics simulations. Alternative methods to track the melting temperature [Formula: see text] are compared. The resulting [Formula: see text] is shown to be independent of the scan rate for small heating rates (0.05-0.3 K/ns) implying reversible melting, and increases for larger heating (0.3-4 K/ns) or cooling rates (2-0.1 K/ns). The reported dependency of the melting temperature on the heating rate is in perfect agreement with a two-state kinetic rate model as suggested previously. Expansion and shrinkage, as well as the dynamics of melting seeds is described. The simulations further exhibit a relative shift between melting seeds in opposing membrane leaflets as predicted from continuum elastic theory.

Combining cell-based hydrodynamics with hybrid particle-field simulations: efficient and realistic simulation of structuring dynamics

We have extended an existing hybrid MD-SCF simulation technique that employs a coarsening step to enhance the computational efficiency of evaluating non-bonded particle interactions. This technique is conceptually equivalent to the single chain in mean-field (SCMF) method in polymer physics, in the sense that non-bonded interactions are derived from the non-ideal chemical potential in self-consistent field (SCF) theory, after a particle-to-field projection. In contrast to SCMF, however, MD-SCF evolves particle coordinates by the usual Newton's equation of motion. Since collisions are seriously affected by the softening of non-bonded interactions that originates from their evaluation at the coarser continuum level, we have devised a way to reinsert the effect of collisions on the structural evolution. Merging MD-SCF with multi-particle collision dynamics (MPCD), we mimic particle collisions at the level of computational cells and at the same time properly account for the momentum transfer that is important for a realistic system evolution. The resulting hybrid MD-SCF/MPCD method was validated for a particular coarse-grained model of phospholipids in aqueous solution, against reference full-particle simulations and the original MD-SCF model. We additionally implemented and tested an alternative and more isotropic finite difference gradient. Our results show that efficiency is improved by merging MD-SCF with MPCD, as properly accounting for hydrodynamic interactions considerably speeds up the phase separation dynamics, with negligible additional computational costs compared to efficient MD-SCF. This new method enables realistic simulations of large-scale systems that are needed to investigate the applications of self-assembled structures of lipids in nanotechnologies.

Changes in physical and chemical properties of niosome membrane induced by cholesterol: a promising approach for niosome bilayer intervention

Recently, the self-assembly property of nonionic surfactants has been utilized to create vesicles as alternatives to liposomes.

Force Field Development for Lipid Membrane Simulations

With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Measuring the composition-curvature coupling in binary lipid membranes by computer simulations

The coupling between local composition fluctuations in binary lipid membranes and curvature affects the lateral membrane structure. We propose an efficient method to compute the composition-curvature coupling in molecular simulations and apply it to two coarse-grained membrane models-a minimal, implicit-solvent model and the MARTINI model. Both the weak-curvature behavior that is typical for thermal fluctuations of planar bilayer membranes as well as the strong-curvature regime corresponding to narrow cylindrical membrane tubes are studied by molecular dynamics simulation. The simulation results are analyzed by using a phenomenological model of the thermodynamics of curved, mixed bilayer membranes that accounts for the change of the monolayer area upon bending. Additionally the role of thermodynamic characteristics such as the incompatibility between the two lipid species and asymmetry of composition are investigated.

A hemi-fission intermediate links two mechanistically distinct stages of membrane fission

Fusion and fission drive all vesicular transport. Although topologically opposite, these reactions pass through the same hemi-fusion/fission intermediate^1,2, characterized by a ‘stalk’ in which only the inner monolayers of the two compartments have merged to form a localized non-bilayer connection^1-3. Formation of the hemi-fission intermediate requires energy input from proteins catalyzing membrane remodeling; however the relationship between protein conformational rearrangements and hemi-fusion/fission remains obscure. Here we analyzed how the GTPase cycle of dynamin, the prototypical membrane fission catalyst^4-6, is directly coupled to membrane remodeling. We used intra-molecular chemical cross-linking to stabilize dynamin in its GDP•AlF₄^--bound transition-state. In the absence of GTP this conformer produced stable hemi-fission, but failed to progress to complete fission, even in the presence of GTP. Further analysis revealed that the pleckstrin homology domain (PHD) locked in its membrane-inserted state facilitated hemi-fission. A second mode of dynamin activity, fueled by GTP hydrolysis, couples dynamin disassembly with cooperative diminishing of the PHD wedging, thus destabilizing the hemi-fission intermediate to complete fission. Molecular simulations corroborate the bimodal character of dynamin action and indicate radial and axial forces as dominant, although not independent drivers of hemi-fission and fission transformations, respectively. Mirrored in the fusion reaction^7-8, the force bimodality might constitute a general paradigm for leakage-free membrane remodeling.

Poly(N-isopropylacrylamide)-Based Mixed Brushes: A Computer Simulation Study

Temperature-sensitive poly(N-isopropylacrylamide) (PNIPAM) polymer brushes of fixed molecular weight and grafting density are modeled in the framework of a coarse-grained model with soft, nonbonded interactions and an implicit solvent. This model has been developed to address experimentally relevant, large invariant degrees of polymerization, and nonbonded interactions are expressed via a third-order (virial) expansion of the equation of state. The choice of interaction parameters is intended to mimic the swelling behavior of PNIPAM in water as the temperature increases toward the lower critical solution temperature (T(LCST)). Results of molecular dynamics simulations for one component brushes are compared to experimental data. Mixed brushes incorporating small and large amounts of grafted poly(ethylene glycol) polymers are then considered. The effects of mixing polymer components on the response of the mixed brushes to temperature changes are monitored, and the results are compared to experimental data. In the end, two design principles for biomolecule triggering using temperature-sensitive mixed polymer brushes with functional and switchable end-groups are proposed and studied. This work is in favor of establishing qualitative rules for the design, optimization, and comprehension of binary polymer brushes for bioengineering purposes.

Process-directed self-assembly of block copolymers: a computer simulation study

The free-energy landscape of self-assembling block copolymer systems is characterized by a multitude of metastable minima and concomitant protracted relaxation times of the morphology. Tailoring rapid changes (quench) of thermodynamic conditions, one can reproducibly trap the ensuing kinetics of self-assembly in a specific metastable state. To this end, it is necessary to (1) control the generation of well-defined, highly unstable states and (2) design the unstable state such that the ensuing spontaneous kinetics of structure formation reaches the desired metastable morphology. This process-directed self-assembly provides an alternative to fine-tuning molecular architecture by synthesis or blending, for instance, in order to fabricate complex network structures. Comparing our simulation results to recently developed free-energy techniques, we highlight the importance of non-equilibrium molecular conformations in the starting state and motivate the significance of the local conservation of density.

Coarse-grained simulation of dynamin-mediated fission

Fission is a process in which a region of a lipid bilayer is deformed and separated from its host membrane, so that an additional, topologically independent compartment surrounded by a continuous lipid bilayer is formed. It is a fundamental process in the organization of the compartmentalization of living organisms and carefully regulated by a number of membrane-shaping proteins. An important group within these is the dynamin family of proteins that are involved in the final severance of the hourglass-shaped neck, via which the growing compartment remains connected to the main volume until the completion of fission. We present computer simulations testing different hypotheses of how dynamin proteins facilitate fission by constriction and curvature. Our results on constraint-induced fission of cylindrical membrane tubes emphasize the importance of the local creation of positive curvature and reveal a complex picture of fission, in which the topological transformation can become arrested in an intermediate stage if the proteins constituting the fission machinery are not adaptive.

Simulation of Defect Reduction in Block Copolymer Thin Films by Solvent Annealing

Solvent annealing provides an effective means to control the self-assembly of block copolymer (BCP) thin films. Multiple effects, including swelling, shrinkage, and morphological transitions, act in concert to yield ordered or disordered structures. The current understanding of these processes is limited; by relying on a theoretically informed coarse-grained model of block copolymers, a conceptual framework is presented that permits prediction and rationalization of experimentally observed behaviors. Through proper selection of several process conditions, it is shown that a narrow window of solvent pressures exists over which one can direct a BCP material to form well-ordered, defect-free structures.

Perspective: Coarse-grained models for biomolecular systems

By focusing on essential features, while averaging over less important details, coarse-grained (CG) models provide significant computational and conceptual advantages with respect to more detailed models. Consequently, despite dramatic advances in computational methodologies and resources, CG models enjoy surging popularity and are becoming increasingly equal partners to atomically detailed models. This perspective surveys the rapidly developing landscape of CG models for biomolecular systems. In particular, this review seeks to provide a balanced, coherent, and unified presentation of several distinct approaches for developing CG models, including top-down, network-based, native-centric, knowledge-based, and bottom-up modeling strategies. The review summarizes their basic philosophies, theoretical foundations, typical applications, and recent developments. Additionally, the review identifies fundamental inter-relationships among the diverse approaches and discusses outstanding challenges in the field. When carefully applied and assessed, current CG models provide highly efficient means for investigating the biological consequences of basic physicochemical principles. Moreover, rigorous bottom-up approaches hold great promise for further improving the accuracy and scope of CG models for biomolecular systems.

Mechanisms of vesicle spreading on surfaces: coarse-grained simulations

Exposition of unilamellar vesicles to attractive surfaces is a frequently used way to create supported lipid bilayers. Although this approach is known to produce continuous supported bilayer coatings, the mechanism of their formation and its dependence on factors like surface interaction and roughness or membrane tension as well as the interplay between neighboring vesicles or the involvement of preadsorbed bilayer patches are not well understood. Using dissipative particle dynamics simulations, we assess different mechanisms of vesicle spreading on attractive surfaces, placing special emphasis on the orientation of the resulting bilayer. Making use of the universality of collective phenomena in lipid membranes, we employed a solvent-free coarse-grained model, enabling us to cover the relatively large system sizes and time scales required. Our results indicate that one can control the mechanism of vesicle spreading by tuning the strength and range of the interactions with the substrate as well as the surface's roughness, resulting in a switch from a predominant inside-up to an outside-up orientation of the created supported bilayer.

Simulations of nematic homopolymer melts using particle-based models with interactions expressed through collective variables

We develop a hybrid Monte Carlo approach for modelling nematic liquid crystals of homopolymer melts. The polymer architecture is described with a discrete worm-like chain model. A quadratic density functional accounts for the limited compressibility of the liquid, while an additional quadratic functional of the local orientation tensor of the segments captures the nematic ordering. The approach can efficiently address large systems parametrized according to volumetric and conformational properties, representative of real polymeric materials. The results of the simulations regarding the influence of the molecular weight on the isotropic-nematic transition are compared to predictions from a Landau-de Gennes free energy expansion. The formation of the nematic phase is addressed within Rouse-like dynamics, realized using the current model.

Main transition in the Pink membrane model: finite-size scaling and the influence of surface roughness

We consider the main transition in single-component membranes using computer simulations of the Pink model [D. A. Pink et al., Biochemistry 19, 349 (1980)]. We first show that the accepted parameters of the Pink model yield a main transition temperature that is systematically below experimental values. This resolves an issue that was first pointed out by Corvera and co-workers [Phys. Rev. E 47, 696 (1993)]. In order to yield the correct transition temperature, the strength of the van der Waals coupling in the Pink model must be increased; by using finite-size scaling, a set of optimal values is proposed. We also provide finite-size scaling evidence that the Pink model belongs to the universality class of the two-dimensional Ising model. This finding holds irrespective of the number of conformational states. Finally, we address the main transition in the presence of quenched disorder, which may arise in situations where the membrane is deposited on a rough support. In this case, we observe a stable multidomain structure of gel and fluid domains, and the absence of a sharp transition in the thermodynamic limit.

Systematic implicit solvent coarse-graining of bilayer membranes: lipid and phase transferability of the force field

We study the lipid and phase transferability of our recently developed systematically coarse-grained solvent-free membrane model. The force field was explicitly parameterized to describe a fluid 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer at 310 K with correct structure and area per lipid, while gaining at least three orders of magnitude in computational efficiency (see Wang and Deserno 2010 J. Phys. Chem. B 114 11207-20). Here, we show that exchanging CG tails, without any subsequent re-parameterization, creates reliable models of 1,2-dioleoylphosphatidylcholine (DOPC) and 1,2-dipalmitoylphosphatidylcholine (DPPC) lipids in terms of structure and area per lipid. Furthermore, all CG lipids undergo a liquid-gel transition upon cooling, with characteristics like those observed in experiments and all-atom simulations during phase transformation. These studies suggest a promising transferability of our force field parameters to different lipid species and thermodynamic state points, properties that are a prerequisite for even more complex systems, such as mixtures.