Nanoparticles insertion and dimerization in polymer brushes.

Molecular dynamics simulations are conducted to systematically investigate the insertion of spherical nanoparticles (NPs) in polymer brushes as a function of their size, strength of their interaction with the polymers, polymer grafting density, and polymer chain length. For attractive interactions between the NPs and the polymers, the depth of NPs' penetration in the brush results from a competition between the enthalpic gain due to the favorable polymer-NP interaction and the effect of osmotic pressure resulting from displaced polymers by the NP's volume. A large number of simulations show that the average depth of the NPs increases by increasing the strength of the interaction strength. However, it decreases by increasing the NPs' diameter or increasing the polymer grafting density. While the NPs' effect on the polymer density is local, their effect on their conformations is long-ranged and extends laterally over length scales larger than the NP's size. This effect is manifested by the emergence of laterally damped oscillations in the normal component of the chains' radius of gyration. Interestingly, we found that for high enough interaction strength, two NPs dimerize in the polymer brush. The dimer is parallel to the substrate if the NPs' depth in the brush is shallow. However, the dimer is perpendicular to the substrate if the NPs' are deep in the brush. These results imply that polymer brushes can be used as a tool to localize and self-assemble NPs in polymer brushes.

Membrane-mediated dimerization of spherocylindrical nanoparticles.

We present a numerical investigation of the modes of adhesion and endocytosis of two spherocylindrical nanoparticles (SCNPs) on planar and tensionless lipid membranes, using systematic molecular dynamics simulations of an implicit-solvent model, with varying values of the SCNPs' adhesion strength and dimensions. We found that at weak values of the adhesion energy per unit of area, ξ, the SCNPs are monomeric and adhere to the membrane in the parallel mode. As ξ is slightly increased, the SCNPs dimerize into wedged dimers, with an obtuse angle between their major axes that decreases with increasing ξ. However, as ξ is further increased, we found that the final adhesion state of the two SCNPs is strongly affected by the initial distance, d0, between their centers of mass, upon their adhesion. Namely, the SCNPs dimerize into wedged dimers, with an acute angle between their major axes, if d0 is relatively small. However, for relatively high d0, they adhere individually to the membrane in the monomeric normal mode. For even higher values of ξ and small values of d0, the SCNPs cluster into tubular dimers. However, they remain monomeric if d0 is high. Finally, the SCNPs endocytose either as a tubular dimer, if d0 is low or as monomers for large d0, with the onset value of ξ of dimeric endocytosis being lower than that of monomeric endocytosis. Dimeric endocytosis requires that the SCNPs adhere simultaneously at nearby locations.

Non-close-packed hexagonal self-assembly of Janus nanoparticles on planar membranes.

The adhesion modes of an ensemble of spherical Janus nanoparticles on planar membranes are investigated through large-scale molecular dynamics simulations of a coarse-grained implicit-solvent model. We found that the Janus nanoparticles adhering to planar membranes exhibit a rich phase behavior that depends on their adhesion energy density and areal number density. In particular, effective repulsive membrane-curvature-mediated interactions between the Janus nanoparticles lead to their self-assembly into an ordered hexagonal superlattice at intermediate densities and intermediate to high adhesion energy density, with a lattice constant determined by their areal density. The melting behavior of the hexagonal superlattice proceeds through a two-stage melting scenario in agreement with the Kosterlitz-Thouless-Halperin-Nelson-Young classical theory of two-dimensional melting.

Lipid vesicles induced ordered nanoassemblies of Janus nanoparticles.

Since many advanced applications require specific assemblies of nanoparticles (NPs), considerable efforts have been made to fabricate nanoassemblies with specific geometries. Although nanoassemblies can be fabricated through top-down approaches, recent advances show that intricate nanoassemblies can also be obtained through self-assembly, mediated for example by DNA strands. Here, we show, through extensive molecular dynamics simulations, that highly ordered self-assemblies of NPs can be mediated by their adhesion to lipid vesicles (LVs). Specifically, Janus NPs are considered so that the amount by which they are wrapped by the LV is controlled. The specific geometry of the nanoassembly is the result of effective curvature-mediated repulsion between the NPs and the number of NPs adhering to the LV. The NPs are arranged on the LV into polyhedra which satisfy the upper limit of Euler's polyhedral formula, including several deltahedra and three Platonic solids, corresponding to the tetrahedron, octahedron, and icosahedron.

Collective motion of cells modeled as ring polymers.

In this article, we use a coarse-grained model of disjoint semi-flexible ring polymers to investigate computationally the spatiotemporal collective behavior of cell colonies. A ring polymer in this model is self-propelled by a motility force along the cell's polarity, which depends on its historical kinetics. Despite the repulsive interaction between the cells, a collective behavior sets in as a result of cells pushing against each other. This cooperative motion emerges as the amplitude of the motility force is increased and/or their areal density is increased. The degree of collectivity, characterized by the average cluster size, the velocity field order parameter, and the polarity field nematic order parameter, is found to increase with increasing the amplitude of the motility force and area coverage of the cells. Furthermore, the degree of alignment exhibited by the cell velocity field within a cluster is found to be stronger than that exhibited by the cell polarity. Comparison between the collective behavior of elongated cells and that of circular cells, at the same area coverage and motility force, shows that elongated cells exhibit a stronger collective behavior than circular cells, in agreement with earlier studies of self-propelled anisotropic particles. An investigation of two-cell collisions shows that while two clustered cells move in tandem, their polarities are misaligned. As such the cells push against each other while moving coherently.

Modes of adhesion of two Janus nanoparticles on the outer or inner side of lipid vesicles.

Using molecular dynamics simulations of a coarse-grained model, in conjunction with the weighted histogram analysis method, the adhesion modes of two spherical Janus nanoparticles (NPs) on the outer or inner side of lipid vesicles are explored. In particular, the effects of the area fraction, J, of the NPs that interact attractively with lipid head groups, the adhesion strength and the size of the NPs on their adhesion modes are investigated. The NPs are found to exhibit two main modes of adhesion when adhered to the outer side of the vesicle. In the first mode, which occurs at relatively low values of J, the NPs are apart from each other. In the second mode, which occurs at higher values of J, the NPs form an in-plane dimer. Janus NPs, which adhere to the inner side of the vesicle, are always found to be apart from each other, regardless of the value of J and their diameter.

Modes of adhesion of spherocylindrical nanoparticles to tensionless lipid bilayers.

The adhesion modes and endocytosis pathway of spherocylindrical nanoparticles (NPs) are investigated numerically using molecular dynamics simulations of a coarse-grained implicit-solvent model. The investigation is performed systematically with respect to the adhesion energy density ξ, NP's diameter D, and NP's aspect ratio α. At weak ξ, the NP adheres to the membrane through a parallel mode, i.e., its principal axis is parallel to the membrane. However, for relatively large ξ, the NP adheres through a perpendicular mode, i.e., the NP is invaginated, such as its principal axis is nearly perpendicular to the membrane. The value of ξ at the transition from the parallel to the perpendicular mode decreases with increasing the D or α, in agreement with theoretical arguments based on the Helfrich Hamiltonian. As ξ is further increased, the NP undergoes endocytosis, with the value of ξ at the endocytosis threshold that is independent of the aspect ratio but decreases with increasing D. The kinetics of endocytosis depends strongly on ξ and D. While for low values of D, the NP first rotates to a parallel orientation then to a perpendicular orientation. At high values of ξ or D, the NP is endocytosed while in the parallel orientation.

Conformational behavior and self-assembly of disjoint semi-flexible ring polymers adsorbed on solid substrates.

The conformational behavior and spatial organization of self-avoiding semi-flexible ring polymers, that are fully adsorbed on solid substrates, are investigated via systematic coarse-grained molecular dynamics simulations. Our results show that both conformations and spatial organization of the polymers depend strongly on their bending stiffness, κ, and on their areal number density, ρ. For ρ < ρ*, where ρ* is the overlap density, and for low values of κ, thermal fluctuations lead to weakly anisotropic instantaneous conformations of the polymers. The interplay between thermal fluctuations and polymer stiffness leads to a non-monotonic dependence of the polymers elongation on κ with a maximum elongation at some intermediate κ. Regardless of κ, the polymers elongation is almost independent of ρ for ρ ⪅ ρ*, then increases with ρ. At ρ ≈ ρ* and high κ, the almost circularly-shaped polymers self-assemble into a triangular lattice with quasi-long range order. For ρ above ρ* and high κ, crowding of the polymers leads to their self-assembly into liquid-crystalline phases. In particular, for ρ moderately above ρ* and high κ, the polymer conformations are obround and self-assemble into domains with smectic-A-like order. At higher densities, the polymer have a biconcave geometry and self-assemble into domains with smectic-C-like order.

Binding, unbinding and aggregation of crescent-shaped nanoparticles on nanoscale tubular membranes.

Using molecular dynamics simulations of a coarse-grained implicit solvent model, we investigate the binding of crescent-shaped nanoparticles (NPs) on tubular lipid membranes. The NPs adhere to the membrane through their concave side. We found that the binding/unbinding transition is first-order, with the threshold binding energy being higher than the unbinding threshold, and the energy barrier between the bound and unbound states at the transition that increases with increasing the NP's arclength Lnp or curvature mismatch µ = Rc/Rnp, where Rc and Rnp are the radii of curvature of the tubular membrane and the NP, respectively. Furthermore, we found that the threshold binding energy increases with increasing either Lnp or µ. NPs with curvature larger than that of the tubule (µ > 1) lie perpendicularly to the tubule's axis. However, for µ smaller than a specific arclength-dependent mismatch µ*, the NPs are tilted with respect to the tubule's axis, with the tilt angle that increases with decreasing µ. We also investigated the self-assembly of the NPs on the tubule at relatively weak adhesion strength and found that for µ > 1 and high values of Lnp, the NPs self-assemble into linear chains, and lie side-by-side. For µ < µ* and high Lnp, the NPs also self-assemble into chains, while being tilted with respect to the tubule's axis.

Spatial arrangements of spherical nanoparticles on lipid vesicles.

We report results of a numerical investigation of the modes of adhesion of two spherical nanoparticles (NPs) on lipid vesicles based on molecular dynamics simulations, in conjunction with the weighted histogram analysis method, of an implicit-solvent model of self-assembled membranes. Our investigation shows that the NPs exhibit a sequence of three modes of adhesion. For low adhesive interactions, the adhering NPs are apart from each other. As the adhesive interaction is increased, the NPs dimerize into in-plane dimers. As the adhesive interaction is further increased for relatively large vesicles, the NPs dimerize into tubular dimers. However, for small vesicles, the tubular dimer state is not observed. For higher values of the adhesive interaction, four endocytosis modes are observed, depending on the initial locations of the NPs on the vesicle and the relative size of the NPs with respect to that of the vesicle. For relatively large vesicles, the NPs are endocytosed individually or as a dimer. For relatively small vesicles, only one NP is endocytosed if the initial distance between the NPs is large, while the second NP remains adhered to the outer leaflet of the vesicle. However, if the initial distance between the NPs is small, one NP is endocytosed, while the other is internalized in the vesicle through a pore.

Discontinuous wrapping transition of spherical nanoparticles by tensionless lipid membranes.

We present a numerical study of the wrapping of spherical nanoparticles by tensionless lipid membranes using molecular dynamics simulations of a coarse-grained implicit solvent model. We found that the degree of wrapping of small nanoparticles increases continuously with the adhesion strength for nanoparticles with diameter less than or about 15 nm. In contrast, the increase in the degree of wrapping becomes discontinuous for larger nanoparticles and exhibits a clear hysteresis when upward and downward annealing scans with respect to adhesion strength are performed. The gap in the degree of wrapping increases with the increase in the diameter of nanoparticles. These results are in qualitative agreement with the mean field prediction that large nanoparticles are either unbound or completely wrapped by tensionless lipid membranes.

Stability of membrane-induced self-assemblies of spherical nanoparticles.

The self-assembly of spherical nanoparticles, resulting from their adhesion on tensionless lipid membranes, is investigated through molecular dynamics simulations of a coarse-grained implicit-solvent model. Our simulations indicate that, with increasing adhesion strength, while reshaping the membrane, the nanoparticles aggregate into a sequence of self-assemblies corresponding to in-plane chains, two-row tubular (bitube) chains, annular (ring) chains, and single-row tubular (tube) chains. Annealing scans, with respect to adhesion strength, show that the transitions between the various phases are highly first-order with significant hystereses. Free energy calculations indicate that the gas and single-row tubular chains are stable over wide ranges of adhesion strength. In contrast, the in-plane chains are only stable for small aggregates of NPs, and the bitube and ring chains are long-lived metastable states over a wide range of adhesion strength.

Phase behavior of supported lipid bilayers: A systematic study by coarse-grained molecular dynamics simulations.

Solid-supported lipid bilayers are utilized by experimental scientists as models for biological membranes because of their stability. However, compared to free standing bilayers, their close proximity to the substrate may affect their phase behavior. As this is still poorly understood, and few computational studies have been performed on such systems thus far, here we present the results from a systematic study based on molecular dynamics simulations of an implicit-solvent model for solid-supported lipid bilayers with varying lipid-substrate interactions. The attractive interaction between the substrate and the lipid head groups that are closest to the substrate leads to an increased translocation of the lipids from the distal to the proximal bilayer-leaflet. This thereby leads to a transbilayer imbalance of the lipid density, with the lipid density of the proximal leaflet higher than that of the distal leaflet. Consequently, the order parameter of the proximal leaflet is found to be higher than that of the distal leaflet, the higher the strength of lipid interaction is, the stronger the effect. The proximal leaflet exhibits gel and fluid phases with an abrupt melting transition between the two phases. In contrast, below the melting temperature of the proximal leaflet, the distal leaflet is inhomogeneous with coexisting gel and fluid domains. The size of the fluid domains increases with increasing the strength of the lipid interaction. At low temperatures, the inhomogeneity of the distal leaflet is due to its reduced lipid density.

Membrane-mediated aggregation of anisotropically curved nanoparticles.

Using systematic numerical simulations, we study the self-assembly of elongated curved nanoparticles on lipid vesicles. Our simulations are based on molecular dynamics of a coarse-grained implicit-solvent model of self-assembled lipid membranes with a Langevin thermostat. Here we consider only the case wherein the nanoparticle-nanoparticle interaction is repulsive, only the concave surface of the nanoparticle interacts attractively with the lipid head groups and only the outer surface of the vesicle is exposed to the nanoparticles. Upon their adhesion on the vesicle, the curved nanoparticles generate local curvature on the membrane. The resulting nanoparticle-generated membrane curvature leads in turn to nanoparticle self-assembly into two main types of aggregates corresponding to chain aggregates at low adhesion strengths and aster aggregates at high adhesion strength. The chain-like aggregates are due to the fact that at low values of adhesion strength, the nanoparticles prefer to lie parallel to each other. As the adhesion strength is increased, a splay angle between the nanoparticles is induced with a magnitude that increases with increasing adhesion strength. The origin of the splay angles between the nanoparticles is shown to be saddle-like membrane deformations induced by a tilt of the lipids around the nanoparticles. This phenomenon of membrane mediated self-assembly of anisotropically curved nanoparticles is explored for systems with varying nanoparticle number densities, adhesion strength, and nanoparticle intrinsic curvature.

Partial wrapping and spontaneous endocytosis of spherical nanoparticles by tensionless lipid membranes.

Computer simulations of an implicit-solvent particle-based model are performed to investigate the interactions between small spherical nanoparticles and tensionless lipid bilayers. We found that nanoparticles are either unbound, wrapped by the bilayer, or endocytosed. The degree of wrapping increases with increasing the adhesion strength. The transition adhesion strength between the unbound and partially wrapped states decreases as the nanoparticle diameter is increased. We also observed that the transition adhesion strength between the wrapped states and endocytosis state decreases with increasing the nanoparticle diameter. The partial wrapping of the nanoparticles by the tensionless bilayer is explained by an elastic theory which accounts for the fact that the interaction between the nanoparticle and the bilayer extends beyond the contact region. The theory predicts that for small nanoparticles, the wrapping angle increases continuously with increasing the adhesion strength. However, for relatively large nanoparticles, the wrapping angle exhibits a discontinuity between weakly and strongly wrapped states. The size of the gap in the wrapping angle between the weakly wrapped and strongly wrapped states increases with decreasing the range of nanoparticle-bilayer interaction.

Kinetics of domain registration in multicomponent lipid bilayer membranes.

The kinetics of registration of lipid domains in the apposing leaflets of symmetric bilayer membranes is investigated via systematic dissipative particle dynamics simulations. The decay of the distance between the centres of mass of the domains in the apposing leaflets is almost linear during early stages, and then becomes exponential during late times. The time scales of both linear and exponential decays are found to increase with decreasing strength of interleaflet coupling. The ratio between the time scales of the exponential and linear regimes decreases with increasing domain size, implying that the decay of the distance between the domains' centres of mass is essentially linear for large domains. These numerical results are largely in agreement with the recent theoretical predictions of Han and Haataja [Soft Matter, 2013, 9, 2120-2124]. We also found that the domains become elongated during the registration process.

Combined effect of cortical cytoskeleton and transmembrane proteins on domain formation in biomembranes.

We investigate the combined effects of transmembrane proteins and the subjacent cytoskeleton on the dynamics of phase separation in multicomponent lipid bilayers using computer simulations of a particle-based implicit solvent model for lipid membranes with soft-core interactions. We find that microphase separation can be achieved by the protein confinement by the cytoskeleton. Our results have relevance to the finite size of lipid rafts in the plasma membrane of mammalian cells.

Highly Ordered Nanoassemblies of Janus Spherocylindrical Nanoparticles Adhering to Lipid Vesicles.

In recent years, there has been a heightened interest in the self-assembly of nanoparticles (NPs) that is mediated by their adsorption onto lipid membranes. The interplay between the adhesive energy of NPs on a lipid membrane and the membrane's curvature energy causes it to wrap around the NPs. This results in an interesting membrane curvature-mediated interaction, which can lead to the self-assembly of NPs on lipid membranes. Recent studies have demonstrated that Janus spherical NPs, which adhere to lipid vesicles, can self-assemble into well-ordered nanoclusters with various geometries, including a few Platonic solids. The present study explores the additional effect of geometric anisotropy on the self-assembly of Janus NPs on lipid vesicles. Specifically, the current study utilized extensive molecular dynamics simulations to investigate the arrangement of Janus spherocylindrical NPs on lipid vesicles. We found that the additional geometric anisotropy significantly expands the range of NPs' self-assemblies on lipid vesicles. The specific geometries of the resulting nanoclusters depend on several factors, including the number of Janus spherocylindrical NPs adhering to the vesicle and their aspect ratio. The lipid membrane-mediated self-assembly of NPs, demonstrated by this work, provides an alternative cost-effective route for fabricating highly engineered nanoclusters in three dimensions. Such structures, with the current wide range of material choices, have great potential for advanced applications, including biosensing, bioimaging, drug delivery, nanomechanics, and nanophotonics.

Collective vortical motion and vorticity reversals of self-propelled particles on circularly patterned substrates.

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction ϕ[over ¯], motility force F_{D}, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of F_{D}. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of F_{D}, the SPPs exclusion from the center is dominated by the confining boundary. At high values of ϕ[over ¯], the substrate pattern leads to reversals in the vorticity, which become quasiperiodic with increasing ϕ[over ¯]. We also found that the substrate pattern is able to separate SPPs based on their motilities.