Effects of grafted polymers on the lipid membrane fluidity.

Since the membrane fluidity controls the cellular functions, it is important to identify the factors that determine the cell membrane viscosity. Cell membranes are composed of not only lipids and proteins but also polysaccharide chain-anchored molecules, such as glycolipids. To reveal the effects of grafted polymers on the membrane fluidity, in this study, we measured the membrane viscosity of polymer-grafted giant unilamellar vesicles (GUVs), which were prepared by introducing the poly (ethylene glycol) (PEG)-anchored lipids to the ternary GUVs composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and cholesterol. The membrane viscosity was obtained from the velocity field on the GUV generated by applying a point force, based on the hydrodynamic model proposed by Henle and Levine. The velocity field was visualized by a motion of the circular liquid ordered (Lo) domains formed by a phase separation. With increasing PEG density, the membrane viscosity of PEG-grafted GUVs increased gradually in the mushroom region and significantly in the brush region. We propose a hydrodynamic model that includes the excluded volume effect of PEG chains to explain the increase in membrane viscosity in the mushroom region. This work provides a basic understanding of how grafted polymers affect the membrane fluidity.

Reaction-induced morphological transitions in a blend of diblock copolymers and reactive monomers: dissipative particle dynamics simulation.

The dissipative particle dynamics (DPD) method is applied to the morphological transitions of microphase-separated domains in a mixture of symmetric AB-diblock copolymers and reactive C-monomers, where polymerization and cross-linking reactions take place among C-monomers. The initial structure for the DPD simulation is an equilibrated cylindrical domain structure prepared by the density-biased Monte Carlo method with density profiles obtained from the self-consistent field theory. By introducing a cross-linking reaction among reactive C-monomers, we confirmed that the DPD simulation reproduces the morphological transitions observed in experiments, where the domain morphology changes due to segregation between A-blocks of diblock copolymers and cross-linking networks of C-monomers. When the cross-linking reaction of C-monomers is sufficiently fast compared to the deformation of the domains, the initial cylindrical domains are preserved, while the distance between the domains increases. On the other hand, when the formation of the cross-linking network is slow, the domains can deform and reconnect with each other in the developing cross-linking network. In this case, we observe morphological transitions from the initial domain morphology with a large-curvature interface to another domain morphology with a smaller-curvature interface, such as the transition from the cylindrical phase to the lamellar phase. We calculated the spatial correlations in the microphase-separated domains and found that such correlations are affected by the speed of the formation of the cross-linking network depending on whether the bridging between microphase-separated domains occurs in a nucleation and growth process or in a spinodal decomposition process.

Synthesising a minimal cell with artificial metabolic pathways.

A "synthetic minimal cell" is considered here as a cell-like artificial vesicle reproduction system in which a chemical and physico-chemical transformation network is regulated by information polymers. Here we synthesise such a minimal cell consisting of three units: energy production, information polymer synthesis, and vesicle reproduction. Supplied ingredients are converted to energy currencies which trigger the synthesis of an information polymer, where the vesicle membrane plays the role of a template. The information polymer promotes membrane growth. By tuning the membrane composition and permeability to osmolytes, the growing vesicles show recursive reproduction over several generations. Our "synthetic minimal cell" greatly simplifies the scheme of contemporary living cells while keeping their essence. The chemical pathways and the vesicle reproduction pathways are well described by kinetic equations and by applying the membrane elasticity model, respectively. This study provides new insights to better understand the differences and similarities between non-living forms of matter and life.

Efficient compressed database of equilibrated configurations of ring-linear polymer blends for MD simulations.

To effectively archive configuration data during molecular dynamics (MD) simulations of polymer systems, we present an efficient compression method with good numerical accuracy that preserves the topology of ring-linear polymer blends. To compress the fraction of floating-point data, we used the Jointed Hierarchical Precision Compression Number - Data Format (JHPCN-DF) method to apply zero padding for the tailing fraction bits, which did not affect the numerical accuracy, then compressed the data with Huffman coding. We also provided a dataset of well-equilibrated configurations of MD simulations for ring-linear polymer blends with various lengths of linear and ring polymers, including ring complexes composed of multiple rings such as polycatenane. We executed 109 MD steps to obtain 150 equilibrated configurations. The combination of JHPCN-DF and SZ compression achieved the best compression ratio for all cases. Therefore, the proposed method enables efficient archiving of MD trajectories. Moreover, the publicly available dataset of ring-linear polymer blends can be employed for studies of mathematical methods, including topology analysis and data compression, as well as MD simulations.

Modeling of chemically active particles at an air-liquid interface.

The collective motion of chemically active particles at an air-liquid interface is studied theoretically as a dynamic self-organization problem. Based on a physical consideration, we propose a minimal model for self-propelled particles by combining hydrodynamic interaction, capillary interaction, driving force by Marangoni effect, and Marangoni flow. Our model has successfully captured the features of chemically active particles, that represent dynamic self-organized states such as crystalline, chain, liquid-like and spreading states.

Hybrid particle-field molecular dynamics under constant pressure.

Hybrid particle-field methods are computationally efficient approaches for modeling soft matter systems. So far, applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field interactions to represent systems coupled to constant external pressure. First, we show that the commonly used particle-field energy functional can be modified to model and parameterize the isotropic contributions to the pressure tensor without interfering with the microscopic forces on the particles. Second, we employ a square gradient particle-field interaction term to model non-isotropic contributions to the pressure tensor, such as in surface tension phenomena. This formulation is implemented within the hybrid particle-field molecular dynamics approach and is tested on a series of model systems. Simulations of a homogeneous water box demonstrate that it is possible to parameterize the equation of state to reproduce any target density for a given external pressure. Moreover, the same parameterization is transferable to systems of similar coarse-grained mapping resolution. Finally, we evaluate the feasibility of the proposed approach on coarse-grained models of phospholipids, finding that the term between water and the lipid hydrocarbon tails is alone sufficient to reproduce the experimental area per lipid in constant-pressure simulations and to produce a qualitatively correct lateral pressure profile.

Viscosity Landscape of Phase-Separated Lipid Membrane Estimated from Fluid Velocity Field.

In cell membranes, the functional constituents such as peptides, proteins, and polysaccharides diffuse in a sea of lipids as single molecules and molecular aggregates. Thus, the fluidity of the heterogeneous multicomponent membrane is important for understanding the roles of the membrane in cell functionality. Recently, Henle and Levine described the hydrodynamics of molecular diffusion in a spherical membrane. A tangential point force at the north pole induces a pair of vortices whose centers lie on a line perpendicular to the point force and are symmetrical with respect to the point force. The position of the vortex center depends on ηm/Rηw, where R is the radius of the spherical membrane, and ηm and ηw are the viscosities of the membrane and the surrounding medium, respectively. Based on this theoretical prediction, we applied a point force to a phase-separated spherical vesicle composed of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine/1,2-dioleoyl-sn-glycero-3-phosphocholine/cholesterol by means of a microinjection technique. The pathlines were visualized by trajectories of microdomains. We determined the position of the vortex center and estimated the membrane viscosity using the dependence of the position of the vortex center on ηm/Rηw. The obtained apparent membrane viscosities for various compositions are mapped on the phase diagram. The membrane viscosity is almost constant in the range of 0 <ϕLo ≤ 0.5 (ϕLo: area fraction of the liquid ordered phase), whereas that in the range of 0.5 ≤ ϕLo < 1.0 exponentially increases with increase of ϕLo. The obtained viscosity landscape provides a basic understanding of the fluidity of heterogeneous multicomponent membranes.

Mesoscale Electrostatics Driving Particle Dynamics in Nonhomogeneous Dielectrics.

We introduce a density functional-based formalism to compute the electrostatic energy and forces for a mesoscopic system in the condensed phase, described with molecular resolution. The dielectric permittivity is variable in space, and it is dependent on the density fields of the individual particles present in the system. The electrostatic potential is obtained from standard numerical solutions of the generalized Poisson equation. The presence of a particle-dependent varying dielectrics produces the appearance of mesoscopic polarization forces, which are dependent on the local fluctuations of the permittivity, as well as of the electrostatic field. The proposed implementation is numerically robust, with an error on the Coulomb forces that can be systematically controlled by the mesh of spatial grid used for solving the generalized Poisson equation. We show that the method presented here is able to reproduce the concentration-dependent partitioning of an ideal salt in water/oil mixtures, in particular, reproducing the ∝ 1/ϵ dependency of the partition coefficient for the free ions predicted by Born theory. Moreover, this approach reproduces the correct electrostatic features of both dipolar and charged lipid bilayers, with positive membrane and dipole potentials. The sum of both Coulomb and polarization interactions inside the membrane yields a globally repulsive potential of mean force for the ions, independently on their charge. The computational efficiency of the method makes it particularly suitable for the description of large-scale polyelectrolyte soft-matter systems.

Time-Resolved Structured Illumination Microscopy for Phase Separation Dynamics of Water and 2-Butoxyethanol Mixtures: Interpretation of "Early Stage" Involving Micelle-Like Structures.

Phase separation dynamics of a water/2-butoxyethanol (2BE) mixture was studied with newly developed time-resolved structured illumination microscopy (SIM). Interestingly, an employed hydrophobic fluorescent probe for SIM showed spectral shifts up to 500 ns after a laser-induced temperature jump, which suggests 2BE micellar-like aggregates become more hydrophobic at the initial stage of phase separation. This hydrophobic environment in 2BE aggregates, probably due to the ejection of water molecules, continued up to at least 10 µs. Time-resolved SIM and previously reported light scattering data clearly showed that the size of a periodic structure remained constant (ca. 300 nm) from 3 to 10 µs, and then the growth of periodic structures having the self-similarity started. We think that the former and the latter processes correspond to "early stage" (concentration growth) and "late stage" (size growth), respectively, in phase separation dynamics. Here we suggest that, in the early stage, the entity to bear 2BE phase be water-poor 2BE aggregates, and the number density of these aggregates would simply increase in time.

Molecular structure and multi-body potential of mean force in silica-polystyrene nanocomposites.

We perform a systematic application of the hybrid particle-field molecular dynamics technique [Milano, et al., J. Chem. Phys., 2009, 130, 214106] to study interfacial properties and potential of mean force (PMF) for separating nanoparticles (NPs) in a melt. Specifically, we consider Silica NPs bare or grafted with Polystyrene chains, aiming to shed light on the interactions among free and grafted chains affecting the dispersion of NPs in the nanocomposite. The proposed hybrid models show good performances in catching the local structure of the chains, and in particular their density profiles, documenting the existence of the "wet-brush-to-dry-brush" transition. By using these models, the PMF between pairs of ungrafted and grafted NPs in Polystyrene matrix are calculated. Moreover, we estimate the three-particle contribution to the total PMF and its role in regulating the phase separation on the nanometer scale. In particular, the multi-particle contribution to the PMF is able to give an explanation of the complex experimental morphologies observed at low grafting densities. More in general, we propose this approach and the models utilized here for a molecular understanding of specific systems and the impact of the chemical nature of the systems on the composite final properties.

Hybrid Particle-Field Molecular Dynamics Simulations of Charged Amphiphiles in an Aqueous Environment.

We develop and test specific coarse-grained models for charged amphiphilic systems such as palmitoyloleoylphosphatidylglycerol (POPG) lipid bilayer and sodium dodecyl sulfate (SDS) surfactant in an aqueous environment, to verify the ability of the hybrid particle-field method to provide a realistic description of polyelectrolytes. According to the hybrid approach, the intramolecular interactions are treated by a standard molecular Hamiltonian, and the nonelectrostatic intermolecular forces are described by density fields. Electrostatics is introduced as an additional external field obtained by a modified particle-mesh Ewald procedure, as recently proposed [Zhu et al. Phys. Chem. Chem. Phys. 2016 , 18 , 9799 ]. Our results show that, upon proper calibration of key parameters, electrostatic forces can be correctly reproduced. Molecular dynamics simulations indicate that the methodology is robust with respect to the choice of the relative dielectric constant, yielding the same correct qualitative behavior for a broad range of values. In particular, our methodology reproduces well the organization of the POPG bilayer, as well as the SDS concentration-dependent change in the morphology of the micelles from spherical to microtubular aggregates. The inclusion of explicit electrostatics with good accuracy and low computational cost paves the way for a significant extension of the hybrid particle-field method to biological systems, where the polyelectrolyte component plays a fundamental role for both structural and dynamical molecular properties.

Translocation of a vesicle through a narrow hole across a membrane.

We study the translocation process of a vesicle through a hole in a solid membrane separating two chambers by using the Onsager principle. By considering the stretching energy of the vesicle and the driving force due to pressure difference, we derive a free energy that shows clearly a decrease in the energy barrier as the pressure difference between two sides of the membrane increases. The difference between the reaction path obtained from the string method and the actual kinetic paths obtained from the Onsager principle is discussed when the friction parameter changes. The translocation time decreases as the pressure difference increases or the initial size of the vesicle decreases.

pH sensing by lipids in membranes: The fundamentals of pH-driven migration, polarization and deformations of lipid bilayer assemblies.

Most biological molecules contain acido-basic groups that modulate their structure and interactions. A consequence is that pH gradients, local heterogeneities and dynamic variations are used by cells and organisms to drive or regulate specific biological functions including energetic metabolism, vesicular traffic, migration and spatial patterning of tissues in development. While the direct or regulatory role of pH in protein function is well documented, the role of hydrogen and hydroxyl ions in modulating the properties of lipid assemblies such as bilayer membranes is only beginning to be understood. Here, we review approaches using artificial lipid vesicles that have been instrumental in providing an understanding of the influence of pH gradients and local variations on membrane vectorial motional processes: migration, membrane curvature effects promoting global or local deformations, crowding generation by segregative polarization processes. In the case of pH induced local deformations, an extensive theoretical framework is given and an application to a specific biological issue, namely the structure and stability of mitochondrial cristae, is described. This article is part of a Special Issue entitled: Emergence of Complex Behavior in Biomembranes edited by Marjorie Longo.

Onsager's variational principle for the dynamics of a vesicle in a Poiseuille flow.

We propose a systematic formulation of the migration behaviors of a vesicle in a Poiseuille flow based on Onsager's variational principle, which can be used to determine the most stable steady state. Our model is described by a combination of the phase field theory for the vesicle and the hydrodynamics for the flow field. The dynamics is governed by the bending elastic energy and the dissipation functional, the latter being composed of viscous dissipation of the flow field, dissipation of the bending energy of the vesicle, and the friction between the vesicle and the flow field. We performed a series of simulations on 2-dimensional systems by changing the bending elasticity of the membrane and observed 3 types of steady states, i.e., those with slipper shape, bullet shape, and snaking motion, and a quasi-steady state with zig-zag motion. We show that the transitions among these steady states can be quantitatively explained by evaluating the dissipation functional, which is determined by the competition between the friction on the vesicle surface and the viscous dissipation in the bulk flow.

Coarse-Grained Molecular Simulation Model for Gecko Feet Keratin.

The mechanical properties of gecko setae and spatulae are investigated with a coarse-grained model having two bead types. The two-bead model is based on both experimental information of the internal structure of setae and the chemical amino acid composition. Because the seta is composed of a stiff fibril region and a soft matrix region, we model each of the regions separately. Our model is parameterized in a bottom-up way, and it successfully predicts essential mechanical properties without optimization against the macroscopic properties of keratin. Young's modulus of the fibril area (13.2 ± 0.02 GPa) is 6 times stiffer than that of the pure matrix (2.13 ± 0.059 GPa). Because the volume fraction of the matrix decreases toward the top of a seta, its distal area should be stiffer than its proximal area. The anisotropy of the fibrils is clearly confirmed by the comparison between Young's modulus and the shear modulus of the fibril region. Our model also lends some support to the notion that water uptake selectively weakens the axial cohesion of the fibrils, which leads to the experimentally observed plateau in the stress-strain curves beyond 2% strain for setae under high relative humidity.

Migration of Phospholipid Vesicles Can Be Selectively Driven by Concentration Gradients of Metal Chloride Solutions.

We have investigated the migrations of phospholipid vesicles under the concentration gradients of metal ions. We microinjected metal chloride solutions, monovalent (NaCl and KCl), divalent (CaCl2 and MgCl2), and trivalent (LaCl3) salts, toward phospholipid giant vesicles (GVs) composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). For NaCl, CaCl2, and MgCl2 solutions, the GVs migrated straight toward the tip of the micropipette in response to the concentration gradients, whereas for KCl and LaCl3, GVs moved to the opposite direction. Our motion tracking of lipid domains in a vesicle membrane showed no unidirectional flow in the membrane during the vesicle migration, indicating that the Marangoni mechanism is not responsible for the observed vesicle migration. We calculated the diffusiophoretic velocities for symmetric and asymmetrical electrolytes by solving the Stokes' equation numerically. The theoretical diffusiophoretic velocities described the observed migration velocities well. Thus, we can control the migration of vesicle in response to the concentration gradient by adapting the electrolytes and the lipids.

Biomembrane solubilization mechanism by Triton X-100: a computational study of the three stage model.

The solubilization mechanism of lipid membranes in the presence of Triton X-100 (TX-100) is investigated at molecular resolution using molecular dynamics (MD) simulations. Thanks to the large time and length scales accessible by the hybrid particle-field formulation of the models employed here, the complex process of membrane solubilization has been studied, with the goal of verifying the three stage model reported in the literature. DPPC lipid bilayers and vesicles have been studied at different concentrations of the TX-100 detergent employing coarse grained (CG) models. Systems up to ∼600.000 beads, corresponding to more than 2 millions heavy atoms, have been simulated. Moreover, in order to clarify several experimental pieces of evidence, both slow and fast detergent partition scenarios have been investigated. Flat and curved (vesicles) lipid bilayer surfaces, interacting with TX-100, have been considered to study the curvature effects on the detergent partition rate in the membrane. Shape and conformational changes of mixed DPPC/TX-100 vesicles, as a function of TX-100 content, have also been studied. In particular, high curvature surfaces, corresponding to a higher local TX-100 content, promote a membrane rupture. In flat lipid surfaces, on the time scale simulated the detergent partition is almost absent, following a different pathway of the solubilization membrane mechanism.

Orientation-shape coupling between liquid crystal and membrane through the anchoring effect.

We perform a series of Monte Carlo simulations on an interface between a liquid crystal (LC) material in isotropic phase in its bulk and a surfactant membrane. These two objects are simulated using coarse-grained molecular models. We estimate physical properties of the membrane such as the interfacial tension and the bending rigidity, focusing on the anchoring effects of the membrane on the LC. According to our simulation results, when the strength of the homeotropic anchoring denoted by the anchoring parameter ξ is increased, the interfacial tension decreases and the bending rigidity first increases in ξ<ξ_{m}, and it then decreases in ξ_{m}<ξ. We explain these results by constructing a continuum field model based on the two order parameters: directional order of LC and the membrane shape. These order parameters are mutually interacting through the anchoring effect, the fluctuation coupling between the LC and the membrane, and the effect of the nematic layer.

Phase behavior of a binary fluid mixture of quadrupolar molecules.

We propose a model molecule to investigate microscopic properties of a binary mixture with a closed-loop coexistence region. The molecule is comprised of a Lennard-Jones particle and a uniaxial quadrupole. Gibbs ensemble Monte Carlo simulations demonstrate that the high-density binary fluid of the molecules with the quadrupoles of the same magnitude but of the opposite signs can show closed-loop immiscibility. We find that an increase in the magnitude of the quadrupoles causes a shrinkage of the coexistence region. Molecular dynamics simulations also reveal that aggregates with two types of molecules arranged alternatively are formed in the stable one-phase region both above and below the coexistence region. String structures are dominant below the lower critical solution temperature, while branched aggregates are observed above the upper critical solution temperature. We conclude that the anisotropic interaction between the quadrupoles of the opposite signs plays a crucial role in controlling these properties of the phase behavior.

Self-assembly of carbon nanotubes in polymer melts: simulation of structural and electrical behaviour by hybrid particle-field molecular dynamics.

Self-assembly processes of carbon nanotubes (CNTs) dispersed in different polymer phases have been investigated using a hybrid particle-field molecular dynamics technique (MD-SCF). This efficient computational method allowed simulations of large-scale systems (up to ∼1 500 000 particles) of flexible rod-like particles in different matrices made of bead spring chains on the millisecond time scale. The equilibrium morphologies obtained for longer CNTs are in good agreement with those proposed by several experimental studies that hypothesized a two level "multiscale" organization of CNT assemblies. In addition, the electrical properties of the assembled structures have been calculated using a resistor network approach. The calculated behaviour of the conductivities for longer CNTs is consistent with the power laws obtained by numerous experiments. In particular, according to the interpretation established by the systematic studies of Bauhofer and Kovacs, systems close to "statistical percolation" show exponents t ∼ 2 for the power law dependence of the electrical conductivity on the CNT fraction, and systems in which the CNTs reach equilibrium aggregation show exponents t close to 1.7 ("kinetic percolation"). The confinement effects on the assembled structures and their corresponding conductivity behaviour in a non-homogeneous matrix, such as the phase separating block copolymer melt, have also been simulated using different starting configurations. The simulations reported herein contribute to a microscopic interpretation of the literature results, and the proposed modelling procedure may contribute meaningfully to the rational design of strategies aimed at optimizing nanomaterials for improved electrical properties.