Equilibrium structure and lateral stress distribution of amphiphilic bilayers from dissipative particle dynamics simulations

Clathrin-Mediated Endocytosis of Multiple Nanoparticles Tends to Be Less Cooperative: A Computational Study

The internalization of nanoparticles is of great significance for their biological applications. Clathrin-mediated endocytosis (CME) is one of the main endocytic pathways. However, there is still a lack of a fundamental understanding regarding the internalization of multiple nanoparticles via CME. Therefore, in this study, we conducted computational investigations to uncover detailed molecular mechanisms and kinetic pathways for differently shaped nanoparticles in the presence of clathrin. Particular focus is given to understanding the CME of multiple-nanoparticle systems. We found that unlike receptor-mediated endocytosis, multiple nanoparticles did not get cooperatively wrapped by the membrane but tended to undergo independent endocytosis in the presence of clathrin. To further investigate the endocytosis mechanism, we studied the effects of clathrins, nanoparticle shape, nanoparticle size, nanoparticle arrangement, and membrane surface tension. The self-assembly of clathrin prefers independent endocytosis for multiple nanoparticles. Besides, the cooperative behavior is weak with increasing nanoparticle-shape anisotropy. However, when the membrane tension is reduced, the endocytosis pathway for multiple nanoparticles is cooperative endocytosis. Moreover, we found that the self-assembly of clathrins reduces the critical size of nanoparticles to undergo cooperative wrapping by the cell membrane. Our results provide valuable insights into the molecular mechanisms of multiple nanoparticles through CME and offer useful guidance for the design of nanoparticles as drug/gene delivery carriers.

Multiscale remodeling of biomembranes and vesicles

Biomembranes and vesicles cover a wide range of length scales. Indeed, small nanovesicles have a diameter of a few tens of nanometers whereas giant vesicles can have diameters up to hundreds of micrometers. The remodeling of giant vesicles on the micron scale can be observed by light microscopy and understood by the theory of curvature elasticity, which represents a top-down approach. The theory predicts the formation of multispherical shapes as recently observed experimentally. On the nanometer scale, much insight has been obtained via coarse-grained molecular dynamics simulations of nanovesicles, which provides a bottom-up approach based on the lipid numbers assembled in the two bilayer leaflets and the resulting leaflet tensions. The remodeling processes discussed here include the shape transformations of vesicles, their morphological responses to the adhesion of condensate droplets, the instabilities of lipid bilayers and nanovesicles, as well as the topological transformations of vesicles by membrane fission and fusion. The latter processes determine the complex topology of the endoplasmic reticulum.

Molecular mechanisms and energetics of lipid droplet formation and directional budding

The formation and budding of lipid droplets (LDs) are known to be governed by the LD size and by membrane tensions in the endoplasmic reticulum (ER) bilayer and LD-monolayers. Using coarse-grained simulations of an LD model, we first show that ER-embedded LDs of different sizes can form through a continuous transition from wide LD lenses to spherical LDs at a fixed LD size. The ER tendency to relax its bilayer modulates the transition via a subtle interplay between the ER and LD lipid densities. By calculating the energetic landscape of the LD transition, we demonstrate that this size-independent transition is regulated by the mechanical force balance of ER and LD-tensions, independent from membrane bending and line tension whose energetic contributions are negligible according to our calculations. Our findings explain experimental observation of stable LDs of various shapes. We then propose a novel mechanism for directional LD budding where the required membrane asymmetry is provided by the exchange of lipids between the LD-monolayers. Remarkably, we demonstrate that this budding process is energetically neutral. Consequently, LD budding can proceed by a modest energy input from proteins or other driving agents. We obtain equal lipid densities and membrane tensions in LD-monolayers throughout budding. Our findings indicate that unlike LD formation, LD budding by inter-monolayer lipid exchange is a tension-independent process.

RE, Mocskos EE, Facelli JC, Pickholz M, Ferraro MB. Molecular dynamics study of the mechanical properties of drug loaded model systems: A comparison of a polymersome with a bilayer

In this work we implement a new methodology to study structural and mechanical properties of systems having spherical and planar symmetries throughout Molecular Dynamics simulations. This methodology is applied here to a drug delivery system based in polymersomes, as an example. The chosen model drug was the local anesthetic prilocaine due to previous parameterization within the used coarse grain scheme. In our approach, mass density profiles (MDPs) are used to obtain key structural parameters of the systems, and pressure profiles are used to estimate the curvature elastic parameters. The calculation of pressure profiles and radial MPDs required the development of specific methods, which were implemented in an in-house built version of the GROMACS 2018 code. The methodology presented in this work is applied to characterize poly(ethylene oxide)-poly(butadiene) polymersomes and bilayers loaded with the model drug prilocaine. Our results show that structural properties of the polymersome membrane could be obtained from bilayer simulations, with significantly lower computational cost compared to whole polymersome simulations, but the bilayer simulations are insufficient to get insights on their mechanical aspects, since the elastic parameters are canceled out for the complete bilayer (as consequence of the symmetry). The simulations of entire polymersomes, although more complex, offer a complementary approach to get insights on the mechanical behavior of the systems.

Probing the elastic response of lipid bilayers and nanovesicles to leaflet tensions via volume per lipid

Biological and biomimetic membranes are based on lipid bilayers, consisting of two monolayers or leaflets. One important but challenging physical parameter of these membranes is their tension. For a long time, this tension was explicitly or implicitly taken to be the bilayer tension, acting on the whole bilayer membrane. More recently, it has been realized that it is useful to decompose the bilayer tension into two leaflet tensions and that these tensions are accessible to molecular dynamics simulations. To divide the bilayer up into two leaflets, it is necessary to introduce a midsurface that defines the spatial extent of the two leaflets. In previous studies, this midsurface was obtained from the density profiles across the bilayer and was then used to compute the molecular area per lipid. Here, we develop an alternative approach based on three-dimensional Voronoi tessellation and molecular volume per lipid. Using this volume-based approach, we determine the reference states with tensionless leaflets as well as the optimal volumes and areas per lipid. The optimal lipid volumes have practically the same value in both leaflets, irrespective of the size and curvature of the nanovesicles, whereas the optimal lipid areas are different for the two leaflets and depend on the vesicle size. In addition, we introduce lateral volume compressibilities to describe the elastic response of the lipid volume to the leaflet tensions. We show that the outer leaflet of a nanovesicle is more densely packed and less compressible than the inner leaflet and that this difference becomes more pronounced for smaller vesicles.

Dynamics of fluid bilayer vesicles: Soft meshes and robust curvature energy discretization

Continuum models like the Helfrich Hamiltonian are widely used to describe fluid bilayer vesicles. Here we study the molecular dynamics compatible dynamics of the vertices of two-dimensional meshes representing the bilayer, whose in-plane motion is only weakly constrained. We show (i) that Jülicher's discretization of the curvature energy offers vastly superior robustness for soft meshes compared to the commonly employed expression by Gommper and Kroll and (ii) that for sufficiently soft meshes, the typical behavior of fluid bilayer vesicles can emerge even if the mesh connectivity remains fixed throughout the simulations. In particular, soft meshes can accommodate large shape transformations, and the model can generate the typical ℓ^{-4} signal for the amplitude of surface undulation modes of nearly spherical vesicles all the way up to the longest wavelength modes. Furthermore, we compare results for Newtonian, Langevin, and Brownian dynamics simulations of the mesh vertices to demonstrate that the internal friction of the membrane model is negligible, making it suitable for studying the internal dynamics of vesicles via coupling to hydrodynamic solvers or particle-based solvent models.

Leaflet Tensions Control the Spatio-Temporal Remodeling of Lipid Bilayers and Nanovesicles

Biological and biomimetic membranes are based on lipid bilayers, which consist of two monolayers or leaflets. To avoid bilayer edges, which form when the hydrophobic core of such a bilayer is exposed to the surrounding aqueous solution, a single bilayer closes up into a unilamellar vesicle, thereby separating an interior from an exterior aqueous compartment. Synthetic nanovesicles with a size below 100 nanometers, traditionally called small unilamellar vesicles, have emerged as potent platforms for the delivery of drugs and vaccines. Cellular nanovesicles of a similar size are released from almost every type of living cell. The nanovesicle morphology has been studied by electron microscopy methods but these methods are limited to a single snapshot of each vesicle. Here, we review recent results of molecular dynamics simulations, by which one can monitor and elucidate the spatio-temporal remodeling of individual bilayers and nanovesicles. We emphasize the new concept of leaflet tensions, which control the bilayers' stability and instability, the transition rates of lipid flip-flops between the two leaflets, the shape transformations of nanovesicles, the engulfment and endocytosis of condensate droplets and rigid nanoparticles, as well as nanovesicle adhesion and fusion. To actually compute the leaflet tensions, one has to determine the bilayer's midsurface, which represents the average position of the interface between the two leaflets. Two particularly useful methods to determine this midsurface are based on the density profile of the hydrophobic lipid chains and on the molecular volumes.

Membrane curvature sensing by model biomolecular condensates

Biomolecular condensates (BCs) are fluid droplets that form in biological cells by liquid-liquid phase separation. Their major components are intrinsically disordered proteins. Vast attention has been given in recent years to BCs inside the cytosol and nucleus. BCs at the cell membrane have not been studied to the same extent so far. However, recent studies provide increasingly more examples of interfaces between BCs and membranes which function as platforms for diverse biomolecular processes. Galectin-3, for example, is known to mediate clathrin-independent endocytosis and has been recently shown to undergo liquid-liquid phase separation, but the function of BCs of galectin-3 in endocytic pit formation is unknown. Here, we use dissipative particle dynamics simulations to study a generic coarse-grained model for BCs interacting with lipid membranes. In analogy to galectin-3, we consider polymers comprising two segments - one of them mediates multivalent attractive interactions between the polymers, and the other one has affinity for association with specific lipid head groups. When these polymers are brought into contact with a multi-component membrane, they spontaneously assemble into droplets and, simultaneously, induce lateral separation of lipids within the membrane. Interestingly, we find that if the membrane is bent, the polymer droplets localize at membrane regions curved inward. Although the polymers have no particular shape or intrinsic curvature, they appear to sense membrane curvature when clustered at the membrane. Our results indicate toward a generic mechanism of membrane curvature sensing by BCs involved in such processes as endocytosis.

A many-body dissipative particle dynamics parametrisation scheme to study behaviour at air-water interfaces

In this article, we present a general parametrisation scheme for many-body dissipative particle dynamics (MDPD). The scheme is based on matching model components to experimental surface tensions and chemical potentials. This allows us to obtain the correct surface and mixing behaviours of complex, multicomponent systems. The methodology is tested by modelling the behaviour of nonionic polyoxyethylene alkyl ether surfactants at an air/water interface. In particular, the influence of the number of ethylene oxide units in the surfactant head group is investigated. We find good agreement with many experimentally obtained parameters, such as minimum surface area per molecule; and a decrease in the surface tension with increasing surfactant surface density. Moreover, we observe an orientational transition, from surfactants lying directly on the water surface at low surface coverage, to surfactants lying parallel or tilted with respect to the surface normal at high surface coverage. The parametrisation scheme is also extended to cover the zwitterionic surfactant lauryldimethylamine oxide (LDAO), where we provide good predictions for the surface tension at maximum surface coverage. Here, if we exceed this coverage, we are able to demonstrate the spontaneous production of micelles from the surface surfactant layer.

Investigating anionic surfactant phase diagrams using dissipative particle dynamics: development of a transferable model

Dissipative particle dynamics (DPD) provides a powerful coarse-grained simulation technique for the study of a wide range of soft matter systems. Here, we investigate the transferability of DPD models to the prediction of anionic surfactant phase diagrams, taking advantage of fast parameter sweeps to optimise the choice of DPD parameters for these systems. Parameters are developed which provide a good representation of the phase diagrams of SDS (sodium dodecyl sulfate) and three different isomeric forms of LAS (linear alkylbenzene sulfonates) across an extensive concentration range. A high degree of transferability is seen, with parameters readily transferable to other systems, such as AES (alkyl ether sulfates). Excellent agreement is obtained with experimentally measured quantities, such as the lamellar layer spacing. Isosurfaces are produced from the surfactant head group, from which the second moment M of the isosurface normal distribution is calculated for different phase structures. Lyotropic liquid crystalline phases are characterised by a combination of the eigenvalues of M, radial distribution functions, and visual inspections.

Effects of Shape on Interaction Dynamics of Tetrahedral Nanoplastics and the Cell Membrane

Cellular uptake of nanoplastics is instrumental in their environmental accumulation and transfer to humans through the food chain. Despite extensive studies using spherical plastic nanoparticles, the influence of the morphological characteristics of environmentally released nanoplastics is understudied. Using dissipative particle dynamics simulations, we modeled the interactions between a cell membrane and hydrophobic nanotetrahedra, which feature high shape anisotropy and large surface curvature seen for environmental nanoplastics. We observe robust uptake of nanotetrahedra with sharp vertices and edges by the lipid membrane. Two local energy minimum configurations of nanotetrahedra embedded in the membrane bilayer were identified for particles of large sizes. Further analysis of particle dynamics within the membrane shows that the two interaction states exhibit distinct translational and rotational dynamics in the directions normal and parallel to the plane of the membrane. The membrane confinement significantly arrests the out-of-plane motion, resulting in caged translation and subdiffusive rotation. While the in-plane diffusion remains Brownian, we find that the translational and rotational modes decouple from each other as the particle size increases. The rotational diffusion decreases by a greater extent compared to the translational diffusion, deviating from the continuum theory predictions. These results provide fundamental insights into the shape effect on the nanoparticle dynamics in crowded lipid membranes.

Different pathways for engulfment and endocytosis of liquid droplets by nanovesicles

During endocytosis of nanoparticles by cells, the cellular membranes engulf the particles, thereby forming a closed membrane neck that subsequently undergoes fission. For solid nanoparticles, these endocytic processes have been studied in some detail. Recently, such processes have also been found for liquid and condensate droplets, both in vitro and in vivo. These processes start with the spreading of the droplet onto the membrane followed by partial or complete engulfment of the droplet. Here, we use molecular dynamics simulations to study these processes at the nanoscale, for nano-sized droplets and vesicles. For both partial and complete engulfment, we observe two different endocytic pathways. Complete engulfment leads to a closed membrane neck which may be formed in a circular or strongly non-circular manner. A closed circular neck undergoes fission, thereby generating two nested daughter vesicles whereas a non-circular neck hinders the fission process. Likewise, partial engulfment of larger droplets leads to open membrane necks which can again have a circular or non-circular shape. Two key parameters identified here for these endocytic pathways are the transbilayer stress asymmetry of the vesicle membrane and the positive or negative line tension of the membrane-droplet contact line.

Macromolecular Crowding Is Surprisingly Unable to Deform the Structure of a Model Biomolecular Condensate

The crowded interior of a living cell makes performing experiments on simpler in vitro systems attractive. Although these reveal interesting phenomena, their biological relevance can be questionable. A topical example is the phase separation of intrinsically disordered proteins into biomolecular condensates, which is proposed to underlie the membrane-less compartmentalization of many cellular functions. How a cell reliably controls biochemical reactions in compartments open to the compositionally-varying cytoplasm is an important question for understanding cellular homeostasis. Computer simulations are often used to study the phase behavior of model biomolecular condensates, but the number of relevant parameters increases as the number of protein components increases. It is unfeasible to exhaustively simulate such models for all parameter combinations, although interesting phenomena are almost certainly hidden in their high-dimensional parameter space. Here, we have studied the phase behavior of a model biomolecular condensate in the presence of a polymeric crowding agent. We used a novel compute framework to execute dozens of simultaneous simulations spanning the protein/crowder concentration space. We then combined the results into a graphical representation for human interpretation, which provided an efficient way to search the model's high-dimensional parameter space. We found that steric repulsion from the crowder drives a near-critical system across the phase boundary, but the molecular arrangement within the resulting biomolecular condensate is rather insensitive to the crowder concentration and molecular weight. We propose that a cell may use the local cytoplasmic concentration to assist the formation of biomolecular condensates, while relying on the dense phase to reliably provide a stable, structured, fluid milieu for cellular biochemistry despite being open to its changing environment.

Studying the Structure of Sodium Lauryl Ether Sulfate Solutions Using Dissipative Particle Dynamics

Sodium lauryl ether sulfate (SLES) is a common anionic surfactant used in a large number of personal care products. Commercial products typically contain a distribution in the number of ethoxy groups; despite this, there is limited existing work studying the effect of the ethoxy groups on the phase formation and structure. This is particularly important for the effect the structure has on the viscosity, an important consideration for commercial products. Dissipative particle dynamics is used to simulate the full phase diagram of SLES in water, including both micellar and lyotropic liquid crystal phases. Phase transitions occur at locations which are in good agreement with experimental data, and we find that these boundaries can shift as a result of varying the number of ethoxy groups. Varying the ethoxy groups has a significant effect on the micellar shape and crystalline spacing, with a reduction leading to more nonspherical micelles and decreased periodic spacing of the hexagonal and lamellar phases. Finally, while typical commercial products contain a distribution of ethoxy groups, computational work tends to focus on simulations containing a single chain length. We show that it is valid to use monodisperse simulations to infer behavior about solutions with a polydisperse chain length, based on its mean molecular length.

Understanding Interfacial Nanoparticle Organization through Simulation and Theory: A Review

Understanding the behaviors of nanoparticles at interfaces is crucial not only for the design of novel nanostructured materials with superior properties but also for a better understanding of many biological systems where nanoscale objects such as drug molecules, viruses, and proteins can interact with various interfaces. Theoretical studies and tailored computer simulations offer unique approaches to investigating the evolution and formation of structures as well as to determining structure-property relationships regarding the interfacial nanostructures. In this feature article, we summarize our efforts to exploit computational approaches as well as theoretical modeling in understanding the organization of nanoscale objects at the interfaces of various systems. First, we present the latest research advances and state-of-the-art computational techniques for the simulation of nanoparticles at interfaces. Then we introduce the applications of multiscale modeling and simulation methods as well as theoretical analysis to explore the basic science and the fundamental principles in the interfacial nanoparticle organization, covering the interfaces of polymer, nanoscience, biomacromolecules, and biomembranes. Finally, we discuss future directions to signify the framework in tailoring the interfacial organization of nanoparticles based on the computational design. This feature article could promote further efforts toward fundamental research and the wide applications of theoretical approaches in designing interfacial assemblies for new types of functional nanomaterials and beyond.

Model biomolecular condensates have heterogeneous structure quantitatively dependent on the interaction profile of their constituent macromolecules

Biomolecular condensates play numerous roles in cells by selectively concentrating client proteins while excluding others. These functions are likely to be sensitive to the spatial organization of the scaffold proteins forming the condensate. We use coarse-grained molecular simulations to show that model intrinsically-disordered proteins phase separate into a heterogeneous, structured fluid characterized by a well-defined length scale. The proteins are modelled as semi-flexible polymers with punctate, multifunctional binding sites in good solvent conditions. Their dense phase is highly solvated with a spatial structure that is more sensitive to the separation of the binding sites than their affinity. We introduce graph theoretic measures to quantify their heterogeneity, and find that it increases with increasing binding site number, and exhibits multi-timescale dynamics. The model proteins also swell on passing from the dilute solution to the dense phase. The simulations predict that the structure of the dense phase is modulated by the location and affinity of binding sites distant from the termini of the proteins, while sites near the termini more strongly affect its phase behaviour. The relations uncovered between the arrangement of weak interaction sites on disordered proteins and the material properties of their dense phase can be experimentally tested to give insight into the biophysical properties, pathological effects, and rational design of biomolecular condensates.

Changes in Ion Concentrations upon the Binding of Short Polyelectrolytes on Phospholipid Bilayers: Computer Study Addressing Interesting Physiological Consequences

This computer study was inspired by the experimental observation of Y. Qian et al. published in ACS Applied Materials and Interfaces, 2018 that the short positively charged β-peptide chains and their oligomeric analogues efficiently suppress severe medical problems caused by antimicrobial drug-resistant bacteria despite them not penetrating the bacterial membrane. Our coarse-grained molecular dynamics (dissipative particle dynamics) simulations confirm the tentative explanation of the authors of the experimental study that the potent antimicrobial activity is a result of the entropically driven release of divalent ions (mainly magnesium ions essential for the proper biological function of bacteria) into bulk solution upon the electrostatic binding of β-peptides to the bacterial membrane. The study shows that in solutions containing cations Na⁺, Ca²⁺ and Mg²⁺, and anions Cl⁻, the divalent cations preferentially concentrate close to the membrane and neutralize the negative charge. Upon the addition of positively charged oligomer chains (models of β-peptides and their analogues), the oligomers electrostatically bind to the membrane replacing divalent ions, which are released into bulk solvent. Our simulations indicate that the entropy of small ions (which controls the behavior of synthetic polyelectrolyte solutions) plays an important role in this and also in other similar biologically important systems.

Large stress asymmetries of lipid bilayers and nanovesicles generate lipid flip-flops and bilayer instabilities

Much effort has been devoted to lipid bilayers and nanovesicles with a compositional asymmetry between the two leaflets of the bilayer membranes. Here, we address another fundamental asymmetry related to lipid densities and membrane tensions. To avoid membrane rupture, the osmotic conditions must be adjusted in such a way that the bilayer membranes are subject to a relatively low bilayer tension. However, even for vanishing bilayer tension, the individual leaflets can still experience significant leaflet tensions if one leaflet is stretched whereas the other leaflet is compressed. Such a stress asymmetry between the two leaflets can be directly controlled in molecular dynamics simulations by the initial assembly of the lipid bilayers. This stress asymmetry is varied here over a wide range to determine the stability and instability regimes of the asymmetric bilayers. The stability regime shrinks with decreasing size and increasing membrane curvature of the nanovesicle. In the instability regimes, the lipids undergo stress-induced flip-flops with a flip-flop rate that increases with increasing stress asymmetry. The onset of flip-flops can be characterized by a cumulative distribution function that is well-fitted by an exponential function for planar bilayers but has a sigmoidal shape for nanovesicles. In addition, the bilayer membranes form transient non-bilayer structures that relax back towards ordered bilayers with a reduced stress asymmetry. Our study reveals intrinsic limits for the possible magnitude of the transbilayer stress asymmetry and shows that the leaflet tensions represent key parameters for the flip-flop rates.

Selective membrane wrapping on differently sized nanoparticles regulated by clathrin assembly: A computational model

Nanoparticles (NPs) enter cells via multiple pathways, all of which are NP size dependent. Previous studies indicated that the clathrin-mediated endocytosis has different selectivity for the NP size, but the regulatory mechanism remains unclear and difficult to study at the molecular scale in vivo. By means of computer simulation, here we design membrane wrapping on differently sized NPs with mimic clathrin assembly at the opposite membrane side. With relatively large NPs readily wrapped by a pure membrane as manifested, clathrin modulates the process and tunes the size selectivity. Although finite curvature can be generated by cage-like clathrin assembly to facilitate membrane wrapping on relatively small NPs, the clathrin assemblage has a certain range of size, which is mismatched with larger NPs. Besides, the local membrane patch is rigidified by clathrin to increase the barrier of membrane wrapping on larger NPs. Competition of these items determines whether membrane wrapping on NPs is promoted or suppressed, and can be tuned by the NP-membrane adhesion strength, clathrin concentration, and inter-NP distance. Our results highlight the significance of complex environment in altering the nature of NP interaction with cell membranes, and are expected to help design NPs for biomedical applications requiring precise control of NP uptake or cell membrane attachment.

Investigating the morphological transitions in an associative surfactant ternary system

Associative surfactants systems involving polar oils have recently been shown to stabilize immiscible liquids by forming nanostructures at the liquid interface and have been used to print soft materials. Although these associating surfactant systems show great promise for creating nanostructured soft materials, a fundamental understanding of the self-assembly process is still unknown. In this study, a ternary phase diagram for a system of cationic surfactant cetylpyridinium chloride monohydrate (CPCl), a polar oil (oleic acid), and water is established using experiment and simulation, to study the equilibrium phase behavior. A combination of visual inspection, small-angle X-ray scattering (SAXS), and rheological measurements was employed to establish the phase behavior and properties of the self-assembled materials. Dissipative particle dynamics (DPD) is used to simulate the formation of the morphologies in this system and support the experimental results. The ternary phase diagram obtained from the simulations agrees with the experimental results, indicating the robustness of the computational simulation as a supplement to the mesoscale experimental systems. We observe that morphological transitions (e.g., micelle-to-bilayer and vesicle-to-lamellar) are in agreement between experiments and simulations across the ternary diagram. DPD simulations correctly predict that associative surfactant systems form new nanoscale phases due to the co-assembly of the components. The established ternary phase diagram and the DPD model pave the way towards predicting and controlling the formation of different mesostructures like lamellar or vesicles, opening new avenues to tailor and synthesize desired morphologies for applications related to liquid-in-liquid 3D printing.

Coupling Bulk Phase Separation of Disordered Proteins to Membrane Domain Formation in Molecular Simulations on a Bespoke Compute Fabric

Phospholipid membranes surround the cell and its internal organelles, and their multicomponent nature allows the formation of domains that are important in cellular signalling, the immune system, and bacterial infection. Cytoplasmic compartments are also created by the phase separation of intrinsically disordered proteins into biomolecular condensates. The ubiquity of lipid membranes and protein condensates raises the question of how three-dimensional droplets might interact with two-dimensional domains, and whether this coupling has physiological or pathological importance. Here, we explore the equilibrium morphologies of a dilute phase of a model disordered protein interacting with an ideal-mixing, two-component lipid membrane using coarse-grained molecular simulations. We find that the proteins can wet the membrane with and without domain formation, and form phase separated droplets bound to membrane domains. Results from much larger simulations performed on a novel non-von-Neumann compute architecture called POETS, which greatly accelerates their execution compared to conventional hardware, confirm the observations. Reducing the wall clock time for such simulations requires new architectures and computational techniques. We demonstrate here an inter-disciplinary approach that uses real-world biophysical questions to drive the development of new computing hardware and simulation algorithms.

Non-monotonic fibril surface occlusion by GFP tags from coarse-grained molecular simulations

The pathological growth of amyloid fibrils in neurons underlies the progression of neurodegenerative diseases including Alzheimer's and Parkinson's disease. Fibrils form when soluble monomers oligomerise in the cytoplasm. Their subsequent growth occurs via nucleated polymerization mechanisms involving the free ends of the fibrils augmented by secondary nucleation of new oligomers at their surface. Amyloid fibrils possess a complex interactome with diffusing cytoplasmic proteins that regulates many aspects of their growth, seeding capacity, biochemical activity and transition to pathological inclusions in diseased brains. Changes to their surface are also expected to modify their interactome, pathogenicity and spreading in the brain. Many assays visualise fibril formation, growth and inclusion formation by decorating monomeric proteins with fluorescent tags such as GFP. Recent studies from our group suggest that tags with sizes comparable to the fibril radius may modify the fibril surface accessibility and thus their PTM pattern, interactome and ability to form inclusions. Using coarse-grained molecular simulations of a single alpha synuclein fibril tagged with GFP we find that thermal fluctuations of the tags create a non-monotonic, size-dependent sieve around the fibril that perturbs its interactome with diffusing species. Our results indicate that experiments using tagged and untagged monomers to study the growth and interactome of fibrils should be compared with caution, and the confounding effects of the tags are more complex than a reduction in surface accessibility. The prevalence of fluorescent tags in amyloid fibril growth experiments suggests this has implications beyond the specific alpha synuclein fibrils we model here.

Multiscale simulations of polyzwitterions in aqueous bulk solutions and brush array configurations

Zwitterionic polymers are very promising candidates for antifouling materials that exhibit high chemical stability as compared to polyethylene glycol-based systems. A number of simulation and experimental studies have emerged over recent years for the investigation of sulfobetaine-based zwitterionic polymers. Investigating the structural and thermodynamic properties of such polymers requires access to broad time and length regimes, thus necessitating the development of multiscale simulation strategies. The present article advocates a mesoscopic dissipative particle dynamics (DPD) model capable of addressing a wide range of time and length scales. The mesoscopic force field was developed hand-in-hand with atomistic simulations based on the OPLS force field through a bottom-up parameterization procedure that matches the atomistically calculated strand-length, strand-angle and pair distribution functions. The DPD model is validated against atomistic simulations conducted in this work, and against relevant atomistic simulation studies, theoretical predictions and experimental correlations from the literature. Properties examined include the conformations of SPE polymers in dilute bulk aqueous solution, the density profile and thickness of brush arrays as functions of the grafting density and chain length. In addition, we compute the potential of mean force of an approaching hydrophilic or hydrophobic foulant via umbrella sampling as a function of its position relative to the poly-zwitterion-covered surface. The aforementioned observables lead to important insights regarding the conformational tendencies of grafted polyzwitterions and their antifouling properties.

Structural properties of cationic surfactant-fatty alcohol bilayers: insights from dissipative particle dynamics

Bilayers, self-assembled by cationic surfactants and fatty alcohols in water, are the basic units of lamellar gel networks - creamy formulations extensively used in cosmetics and pharmaceutics. Mesoscopic modelling and study of the bilayers formed by single- or double-tail cationic surfactants (CTAC or DHDAC), and fatty alcohols (FAs) in the lamellar fluid and gel phases were employed. Fatty alcohols with alkyl tail equal to or greater than the surfactant alkyl tail, i.e., C₁₆FA or C₁₈FA and C₂₂FA, were considered. A model formulation was explored with the FA concentration greater than that of the surfactant and the structure of the fluid and gel bilayers in tensionless state characterised via the density profiles across the bilayers, orientational order parameters of the surfactant and FA chains, intrinsic analysis of the bilayer interfaces, and bending rigidity. The intrinsic analysis allows identification and quantification of the coexistence of the interdigitated and non-interdigitated phases present within the gel bilayers. The FA chains were found to conform the primary scaffolding of the bilayers while the surfactant chains tessellate bilayer monolayers from their water-hydrophobic interface. Further, the overlap of the FA chains from the apposed monolayers of the fluid bilayers rises with increasing FA length. Finally, the prevalence of the non-interdigitated phase over the interdigitated phase within the gel bilayers becomes enhanced upon the FA length increase with a preference of the surfactant chains to reside in the non-interdigitated phase rather than the interdigitated phase.

Interactions between poloxamer, PEOx-PPOy-PEOx, and non-ionic surfactant, sucrose monolaurate: A study on potential allergenic effect using model phospholipid membrane

Sugar-based surfactants are involved in skin related allergy cases in the past decade. Skin irritation starts with the interaction of the surfactant with the skin lipids leading to lipid emulsification and eventual barrier damage. Polymers or co-surfactants can be used to mitigate the allergenic effect but the mechanism of formulation mildness on skin remains unclear. We have used the quartz crystal microbalance (QCM) together with dissipative particle dynamics (DPD) simulation, small angle x-ray scattering (SAXS) as well as cell viability tests to decipher the interactions between poloxamers and sucrose monolaurate (SML), and how these interactions could prevent the disruption of a model supported phospholipid bilayer (SLB). Poloxamer addition to the SML solution can delay or totally prevent the disruption of the SLB depending on poloxamer type and concentration. Poloxamer P407 (Pluronic® F127) delays the onset of disruption while poloxamer P188 (Pluronic® F68) does not preserve the bilayer integrity even at high concentration of up to 15% w/w. Preservation of the SLB is likely due to the differences in the aggregates formation between SML-F127 and SML-F68 mixtures with corresponding retarded motion of SML micelles through the SML-F127 polymer matrix that improved cell viability.

Phase behaviour and structure of a model biomolecular condensate

Phase separation of immiscible fluids is a common phenomenon in polymer chemistry, and is recognized as an important mechanism by which cells compartmentalize their biochemical reactions. Biomolecular condensates are condensed fluid droplets in cells that form by liquid-liquid phase separation of intrinsically-disordered proteins. They have a wide range of functions and are associated with chronic neurodegenerative diseases in which they become pathologically rigid. However, it remains unclear how their material properties depend on the molecular structure of the proteins. Here we explore the phase behaviour and structure of a model biomolecular condensate composed of semi-flexible polymers with attractive end-caps using coarse-grained simulations. The model contains the minimal molecular features that are sufficient to observe liquid-liquid phase separation of soluble polymers into a porous, three-dimensional network in which their end-caps reversibly bind at junctions. The distance between connected junctions scales with the polymer length as a self-avoiding random walk over a wide range of concentration with a weak affinity-dependent prefactor. By contrast, the average number of polymers that meet at the junctions depends on the end-cap affinity but only weakly on the polymer length. The structured porosity of the condensed phase suggests a mechanism for cells to regulate biomolecular condensates. Protein interaction sites may be turned on or off to modulate the condensate's porosity and therefore the diffusion and interaction of additional proteins.

Kinetically-arrested single-polymer nanostructures from amphiphilic mikto-grafted bottlebrushes in solution: a simulation study

Solution self-assembly of molecular bottlebrushes offers a rich platform to create complex functional organic nanostructures. Recently, it has become evident that kinetics, not just thermodynamics, plays an important role in defining the self-assembled structures that can be formed. In this work, we present results from extensive molecular dynamics simulations that explore the self-assembly behavior of mikto-grafted bottlebrushes when the solvent quality for one of the side blocks is changed by a rapid quench. We have performed a systematic study of the effect of different structural parameters and the degree of incompatibility between side chains on the final self-assembled nanostructures in the low concentration limit. We found that kinetically-trapped complex nanostructures are prevalent as the number of macromonomers increases. We performed a quantitative analysis of the self-assembled morphologies by computing the radius of gyration tensor and relative shape anisotropy as the different relevant parameters were varied. Our results are summarized in terms of non-equilibrium morphology diagrams.

Polymer stiffness governs template mediated self-assembly of liposome-like nanoparticles: simulation, theory and experiment

This study suggests that the self-assembly of a template-mediated liposome (TML) can be utilized as a general method to produce liposomes with controlled sizes. A polymer tethered core is used here as a starting configuration of a TML. Lipids anchored to the free ends of the tethered polymers direct the self-assembly of surrounding free lipid molecules to form liposome-like nanoparticles. Characterizing the flexibility of polymers by their persistence lengths, we performed large scale molecular simulations to investigate the self-assembly process of TMLs with tethered polymers of different stiffness values. The stiffness of tethered polymer is found to play a crucial role in the self-assembly process of TMLs. The flexible and rigid-like polymers can accelerate and delay the self-assembly of TMLs, respectively. In addition, the critical grafting of tethered polymers and required lipid concentrations to from perfectly encapsulated TMLs are found to increase with the flexibility of tethered polymers. To scrutinize these simulation-based findings, we synthesized DNA-polyethylene glycol (PEG) TMLs and performed corresponding experiments. To this end we incorporate increasing concentrations of DNA as a proxy for increasing the rigidity of the tethered polymers. We find that the resulting structures are indeed consistent with the simulated ones. Finally, a theory is developed that allows one to estimate the required free lipid number (or lipid concentration) and grafting density analytically for polymers of a given persistence length. Through these combined computational, experimental, and theoretical studies, we present a predictive model for determining the effect of polymer stiffness on the self-assembly of TMLs, which can be used as a general approach for obtaining perfectly encapsulated TMLs as potential drug delivery vehicles.

Membrane Wrapping Pathway of Injectable Hydrogels: From Vertical Capillary Adhesion to Lateral Compressed Wrapping

Membrane wrapping pathway of injectable hydrogels (IHs) plays a vital role in the nanocarrier effectiveness and biomedical safety. Although considerable progress in understanding this complicated process has been made, the mechanism behind this process has remained elusive. Herein, with the help of large-scale dissipative particle dynamics simulations, we explore the molecular mechanism of membrane wrapping by systematically examining the IH architectures and hydrogel-lipid binding strengths. To the best of our knowledge, this is the first report on the membrane wrapping pathway on which IHs transform from vertical capillary adhesion to lateral compressed wrapping. This transformation results from the elastocapillary deformation of networked gels and nanoscale confinement of the bilayer membrane, and it takes long time for the IHs to be fully wrapped owing to the high energy barriers and wrapping-induced shape deformation. Collapsed morphologies and small compressed angles are identified in the IH capsules with a thick shell or strong binding strength to lipids. In addition, the IHs binding intensively to the membrane exhibit special nanoscale mixing and favorable deformability during the wrapping process. Our study provides a detailed mechanistic understanding of the influence of architecture and binding strength on the IH membrane wrapping efficiency. This work may serve as rational guidance for the design and fabrication of IH-based drug carriers and tissue engineering.

Pro-Nifuroxazide Self-Assembly Leads to Triggerable Nanomedicine for Anti-cancer Therapy

Transcription factor STAT3 has been shown to regulate genes that are involved in stem cell self-renewal and thus represents a novel therapeutic target of great biological significance. However, many small-molecule agents with potential effects through STAT3 modulation in cancer therapy lack aqueous solubility and high off-target toxicity, hence impeding efficient bioavailability and activity. This work, for the first time, reports a prodrug-based strategy for selective and safer delivery of STAT3 inhibitors designed toward metastatic and drug-resistant breast cancer. We have synthesized a novel lipase-labile SN-2 phospholipid prodrug from a clinically investigated STAT3 inhibitor, nifuroxazide (Pro-nifuroxazide), which can be regioselectively cleaved by the membrane-abundant enzymes in cancer cells. Pro-nifuroxazide self-assembled to sub 20 nm nanoparticles (NPs), and the cytotoxic ability was screened in ER(+)-MCF-7 and ER(-)-MD-MB231 cells at 48-72 h using 3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetra-zolium bromide proliferation assay. Results indicated that Pro-nifuroxazide NPs are multifold more effective toward inhibiting cancer cells in a time-dependent manner compared to parent nifuroxazide. A remarkable improvement in the local concentration of drugs to as high as ∼240 fold when assembled into NPs is presumably the reason for this functional improvement. We also introduced molecular dynamics simulations to generate Pro-nifuroxazide nano-assembly, as a model assembly from triggerable anti-cancer drugs, to provide molecular insights correlating physicochemical and anti-cancer properties. In silico properties of Pro-nifuroxazide including size, chemistry of NPs and membrane interactions with individual molecules could be validated by in vitro functional activities in cells of breast cancer origin. The in vivo anti-cancer efficiencies of Pro-nifuroxazide NPs in nude mice xenografts with MCF-7 revealed remarkable growth inhibition of as high as 400%. Histopathological analysis corroborated these findings to show significantly high nuclear fragmentation and retracted cytoplasm. Immunostaining on tumor section demonstrated a significantly lower level of pSTAT-3 by Pro-nifuroxazide NP treatment, establishing the inhibition of STAT-3 phosphorylation. Our strategy for the first time proposes a translatable prodrug agent self-assembled into NPs and demonstrates remarkable enhancement in IC50, induced apoptosis, and reduced cancer cell population through STAT-3 inhibition via reduced phosphorylation.

A new equation of state for homo-polymers in dissipative particle dynamics

A chain-revised Groot-Warren equation of state (crGW-EOS) was developed and tested to describe systems of homo-oligomeric chains in the framework of dissipative particle dynamics (DPD). First, thermodynamic perturbation theory is applied to introduce correction terms that account for the reduction in pressure with an increasing number of bonds at constant bead number density. Then, this EOS is modified by introducing a set of switching functions that yields an accurate second virial coefficient in the low-density limit. The crGW-EOS offers several improvements over the revised Groot-Warren equation of state and Groot-Warren equation of state for chain molecules. We tested the crGW-EOS by using it to predict the pressure of oligomeric systems and the B₂ virial coefficient of chain DPD particles for a range of bond lengths. Additionally, a method is developed for determining the strength of cross-interaction parameters between chains of different compositions and sizes and for thermal and athermal mixtures. We explored how different levels of coarse-graining affect the upper-critical solution temperature.

Dissipative particle dynamics simulation of critical pore size in a lipid bilayer membrane

We investigate with computer simulations the critical radius of pores in a lipid bilayer membrane. Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)) recently showed that nucleated pores in a homopolymer film can increase or decrease in size, depending on whether they are larger or smaller than a critical size which scales linearly with film thickness. Using dissipative particle dynamics, a particle-based simulation method, we investigate the same scenario for a lipid bilayer membrane whose structure is determined by lipid-water interactions. We simulate a perforated membrane in which holes larger than a critical radius grow, while holes smaller than the critical radius close, as in the experiment of Ilton et al. (Ilton et al. 2016 Phys. Rev. Lett. 117, 257801 (doi:10.1103/PhysRevLett.117.257801)). By altering key system parameters such as the number of particles per lipid and the periodicity, we also describe scenarios in which pores of any initial size can seal or even remain stable, showing a fundamental difference in the behaviour of lipid membranes from polymer films.

Tethering solvophilic blocks to the ends of polymer brushes: an effective method for adjusting surface patterns

The effect of different lengths of solvophilic A and C blocks on the assembled configuration of intermediate solvophobic B-blocks in both ABA and ABC polymer brush systems is investigated via dissipative particle dynamics simulations. For the AB diblock copolymer brush with solvophilic A-blocks being grafted to the surface, B-blocks self-assemble into spherical micelle structures that are immersed in a layer formed by the A-blocks. Tethering a very small solvophilic block A(C) at the free end of the polymer brush pulls the B-blocks toward the polymer brush/solvent interface and increases their local density which can significantly change the B-block self-assembled structure from spherical micelles to ripples. By increasing the length of the outermost solvophilic blocks, the lateral density distribution of B-blocks can be further changed, resulting in the domain size of the ripple structure first decreasing and then increasing. Compared to the ABA system, the incompatibility between the A and C blocks can effectively reduce the vertical domain separation caused by the fusion of the upper and lower A blocks. Then, based on an AB diblock copolymer brush system with self-assembled spherical micelles, we introduce extremely short free solvophilic blocks A(C) in dilute solution that can be tethered to the free ends of the polymer brush by using a reaction model [Liu et al., J. Chem. Phys., 2007, 127, 144903]. We find that the micelles' coalescence is mainly affected by the content of tethered reactive solvophilic blocks, and only weakly affected by the reaction rate of the reversible reactions. This strategy of tethering solvophilic blocks to the ends of polymer brushes can be an effective way for the fabrication of stimuli-responsive surfaces and for adjusting nanoscopic surface patterns.

Extracting lipid vesicles from plasma membranes via self-assembly of clathrin-inspired scaffolding nanoparticles

Single-cell analysis is a new and rapidly expanding field, the goal of which is obtaining fresh information from individual cells to understand the regulatory mechanisms of cell development and diseases. Conventional approaches generally rely on the cell lysis which, however, is destructive to cells and against multiple sampling from the living cell. Here, we propose and design a scaffolding nanoparticle (NP) system that enables us to sample cytoplasmic contents without rupturing the cellular membrane, by mimicking the unusual features of clathrin. Our simulation results reveal the design principles, following which scaffolding NPs can extract lipid vesicles from plasma membranes, with both the pathway and the mechanism resembling the clathrin-mediated endocytosis, i.e. multiple NPs deposit at the membrane, assembling into cage-like structures to deform the membrane into a vesicle shape. As important design parameters, the interaction between different NPs should be properly stronger than that between each NP and the membrane to ensure the cage formation, and optimal NP concentration and the membrane surface tension are also requisite for extracting lipid vesicles. Our results provide useful guidelines for design of bio-inspired scaffolding NPs as an intelligent machine for practical use in but not limited to the single-cell analysis.

Nanodroplets at Membranes Create Tight-Lipped Membrane Necks via Negative Line Tension

The response of biomembranes to aqueous-phase separation and to the resulting water-in-water droplets has been recently studied on the micrometer scale using optical microscopy and elasticity theory. When such a droplet adheres to the membrane, it forms a contact area that is bounded by a contact line. For a micrometer-sized droplet, the line tension associated with this contact line can usually be ignored compared with the surface tensions. However, for a small nanoscopic droplet, this line tension is expected to affect the membrane-droplet morphology. Here, we use molecular simulations to study nanodroplets at membranes and to gain insight into these line tension effects. The latter effects are shown to depend strongly on another key parameter, the mechanical tension experienced by the membrane. For a large membrane tension, a droplet adhering to the membrane is only partially engulfed by the membrane, and the membrane-droplet system exhibits an axisymmetric morphology. A reduction of the membrane tension leads to an increase in the contact area and a decrease in the interfacial area of the droplet, initially retaining its axisymmetric shape, which implies a circular contact line and a circular membrane neck. However, when the tension falls below a certain threshold value, the system undergoes a morphological transition toward a non-axisymmetric morphology with a non-circular membrane neck. This morphology persists until the nanodroplet is completely engulfed by the membrane and the membrane neck has closed into a tight-lipped shape. The latter morphology is caused by a negative line tension, which is shown to be a robust feature of membrane-droplet systems. A closed membrane neck with a tight-lipped shape suppresses both thermally activated and protein-induced scission of the neck, implying a reduction in the cellular uptake of nanodroplets by pinocytosis and fluid-phase endocytosis. Furthermore, based on our results, we can also draw important conclusions about the time-dependent processes corresponding to the surface nucleation and growth of nanodroplets at membranes.

Relationship between water permeation and flip-flop motion in a bilayer membrane

The lipid bilayer membrane facilitates various biological reactions and is thus an essential structure that sustains all higher forms of life. The unique local environment of the lipid bilayer plays critical roles for the diffusion of biomolecules as well as water molecules in biological reactions. Although fluctuation of the cell membrane is expected to allow for the transport of some water molecules, the flip-flop of lipid molecules corresponds to lipid transport between membrane leaflets, and is considered to be an important process to regulate the lipid composition of biological membranes. However, the relationship between these flip-flop phenomena and surrounding water molecules remains poorly understood. We hypothesized that the flip-flop is caused by water molecules permeating through the cell membrane. To test this hypothesis, we used millisecond-order coarse-grained molecular simulations (dissipative particle dynamics) to investigate the distance between water molecules and lipid molecules depending on the position of the lipid molecule. The results clearly showed that water molecules affect the flip-flop motion in the early stage, but have minimal contribution to the subsequent behavior. Moreover, based on the results of dissipative particle dynamics simulation, we computed several first-passage-time (FPT) quantities to describe the detailed dynamics of water permeation. We modeled arrangements in the middle of the flip-flop process, which were compared with the arrangement without lipid molecules. Overall, our results indicate that lipid molecules located both in perpendicular and parallel arrangements largely affect water permeation. These findings provide new insight into the detailed relationship between water permeation and the flip-flop motion.

Thinning Approximation for Calculating Two-Dimensional Scattering Patterns in Dissipative Particle Dynamics Simulations under Shear Flow

Modifications to improve thinning approximation (TA) were considered in order to calculate two-dimensional scattering patterns (2DSPs) for dissipative particle dynamics (DPD) simulations of polymer melts under a shear flow. We proposed multipoint TA and adaptive TA because the bond lengths in DPD chains vary widely when compared to those in Kremer⁻Grest (KG) chains, and the effectiveness of these two types of TA for the two major DPD parameter sets were investigated. In this paper, we report our findings on the original DPD model with soft bonds and that with rigid bonds. Based on the behavior of the 2DSPs and the distribution of orientations of the bond vectors, two spot patterns originating from the oriented chain correlations were observed when distinct distributions of the highly oriented bond vectors in the shear direction were obtained. For multipoint TA, we concluded that at least two additional midpoints ( n mid ≥ 2 ) are required to clearly observe the two spot patterns. For adaptive TA, a dividing distance of l ATA ≤ 0.4 is sufficient for clear observation, which is consistent with the requirement of n mid ≥ 2 for multipoint TA.

Multipoint segmental repulsive potential for entangled polymer simulations with dissipative particle dynamics

A model is developed for simulating entangled polymers by dissipative particle dynamics (DPD) using the segmental repulsive potential (SRP). In contrast to previous SRP models that define a single-point interaction on each bond, the proposed SRP model applies a dynamically adjustable multipoint on the bond. Previous SRP models could not reproduce the equilibrium properties of Groot and Warren's original DPD model [R. D. Groot and P. B. Warren, J. Chem. Phys. 107, 4423 (1997)] because the introduction of a single SRP induces a large excluded volume, whereas, the proposed multipoint SRP (MP-SRP) introduces a cylindrical effective excluded bond volume. We demonstrate that our MP-SRP model exhibits equilibrium properties similar to those of the original DPD polymers. The MP-SRP model parameters are determined by monitoring the number of topology violations, thermodynamic properties, and the polymer internal structure. We examine two typical DPD polymers with different bond-length distributions; one of them was used in the modified SRP model by Sirk et al. [J. Chem. Phys. 136, 134903 (2012)], whereas the other was used in the original DPD model. We demonstrate that for both polymers, the proposed MP-SRP model captures the entangled behaviors of a polymer melt naturally, by calculating the slowest relaxation time of a chain in the melt and the shear relaxation modulus. The results indicate that the proposed MP-SRP model can be applied to a variety of DPD polymers.

Lipids with bulky head groups generate large membrane curvatures by small compositional asymmetries

Glycolipids such as GM1 have bulky head groups consisting of several monosaccharides. When these lipids are added to phospholipid bilayers, they generate large membrane curvatures even for small compositional asymmetries between the two leaflets of the bilayers. On the micrometer scale, these bilayer asymmetries lead to the spontaneous tubulation of giant vesicles as recently observed by optical microscopy. Here, we study these mixed membranes on the nanometer scale using coarse-grained molecular simulations. The membrane composition is defined by the mole fractions ϕ₁ and ϕ₂ of the large-head lipid in the two leaflets of the bilayer. Symmetric membranes are obtained for ϕ₁ = ϕ₂ ≡ ϕ_le, and asymmetric ones for ϕ₁ ≠ ϕ₂. In both cases, we compute the density and stress profiles across the membranes. The stress profiles are used to identify the tensionless states of the membranes. Symmetric and tensionless bilayers are found to be stable within the whole composition range 0 ≤ ϕ_le ≤ 1. For these symmetric bilayers, both the area compressibility modulus and the bending rigidity are found to vary non-monotonically with the leaflet mole fraction ϕ_le. For asymmetric bilayers, we compute the product of bending rigidity and spontaneous curvature from the first moment of the stress profile and determine the bending rigidities of the asymmetric membranes using the ϕ_le-dependent rigidities of the single leaflets. When we combine these results, the compositional asymmetry ϕ₁ - ϕ₂ is found to generate the spontaneous curvature (ϕ₁ - ϕ₂)/(0.63 ℓ_me) with the membrane thickness ℓ_me ≃ 4 nm. Therefore, the spontaneous curvature increases linearly with the compositional asymmetry. Furthermore, the small compositional asymmetry ϕ₁ - ϕ₂ = 0.04 leads to the large spontaneous curvature 1/(63 nm) and the increased asymmetry ϕ₁ - ϕ₂ = 0.2 generates the huge spontaneous curvature 1/(13 nm). These large values of the spontaneous curvature will facilitate future simulation studies of various membrane processes such as bud formation and nanoparticle engulfment.

Fractal properties of biophysical models of pericellular brushes can be used to differentiate between cancerous and normal cervical epithelial cells

Fractal behavior is found on the topographies of pericellular brushes on the surfaces of model healthy and cancerous cells, using dissipative particle dynamics models and simulations. The influence of brush composition, chain stiffness and solvent quality on the fractal dimension is studied in detail. Since fractal dimension alone cannot guarantee that the brushes possess fractal properties, their lacunarity was obtained also, which is a measure of the space filling capability of fractal objects. Soft polydisperse brushes are found to have larger fractal dimension than soft monodisperse ones, under poor solvent conditions, in agreement with recent experiments on dried cancerous and healthy human cervical epithelial cells. Additionally, we find that image resolution is critical for the accurate assessment of differences between images from different cells. The images of the brushes on healthy model cells are found to be more textured than those of brushes on model cancerous cells, as indicated by the larger lacunarity of the former. These findings are helpful to distinguish monofractal behavior from multifractality, which has been found to be useful to discriminate between immortal, cancerous and normal cells in recent experiments.