One-particle-thick, solvent-free, coarse-grained model for biological and biomimetic fluid membranes

Discrete network models of endothelial cells and their interactions with the substrate

Endothelial cell monolayers line the inner surfaces of blood and lymphatic vessels. They are continuously exposed to different mechanical loads, which may trigger mechanobiological signals and hence play a role in both physiological and pathological processes. Computer-based mechanical models of cells contribute to a better understanding of the relation between cell-scale loads and cues and the mechanical state of the hosting tissue. However, the confluency of the endothelial monolayer complicates these approaches since the intercellular cross-talk needs to be accounted for in addition to the cytoskeletal mechanics of the individual cells themselves. As a consequence, the computational approach must be able to efficiently model a large number of cells and their interaction. Here, we simulate cytoskeletal mechanics by means of molecular dynamics software, generally suitable to deal with large, locally interacting systems. Methods were developed to generate models of single cells and large monolayers with hundreds of cells. The single-cell model was considered for a comparison with experimental data. To this end, we simulated cell interactions with a continuous, deformable substrate, and computationally replicated multistep traction force microscopy experiments on endothelial cells. The results indicate that cell discrete network models are able to capture relevant features of the mechanical behaviour and are thus well-suited to investigate the mechanics of the large cytoskeletal network of individual cells and cell monolayers.

Active osmoticlike pressure on permeable inclusions

We use a standard minimal active Brownian model to investigate the osmotic-like effective pressure generated by active fluids on fixed hollow inclusions. These inclusions are enclosed by a permeable (albeit nonflexible) membrane, and the interior and exterior regions of the inclusions have different particle motility strengths. We consider both rectangular and disklike inclusions and analyze the effects of various system parameters, such as excluded volume interaction between active particles, hardness of membrane, and active particle density, on the effective pressure produced on the enclosing membrane. We focus on the range of intermediate to high motility strengths and analyze the effective pressure in the steady state. Our findings for the active pressure produced in the interior and exterior regions of the inclusion indicate that the pressure is higher in the region with lower motility due to the relatively stronger accumulation of active particles.

Mitochondrial nucleoid condensates drive peripheral fission through high membrane curvature

Mitochondria are dynamic organelles that undergo fusion and fission events, in which the mitochondrial membrane and DNA (mtDNA) play critical roles. The spatiotemporal organization of mtDNA reflects and impacts mitochondrial dynamics. Herein, to study the detailed dynamics of mitochondrial membrane and mtDNA, we rationally develop a dual-color fluorescent probe, mtGLP, that could be used for simultaneously monitoring mitochondrial membrane and mtDNA dynamics via separate color outputs. By combining mtGLP with structured illumination microscopy to monitor mitochondrial dynamics, we discover the formation of nucleoid condensates in damaged mitochondria. We further reveal that nucleoid condensates promoted the peripheral fission of damaged mitochondria via asymmetric segregation. Through simulations, we find that the peripheral fission events occurred when the nucleoid condensates interacted with the highly curved membrane regions at the two ends of the mitochondria. Overall, we show that mitochondrial nucleoid condensates utilize peripheral fission to maintain mitochondrial homeostasis.

Extension of the iSoLF implicit-solvent coarse-grained model for multicomponent lipid bilayers

iSoLF is a coarse-grained (CG) model for lipid molecules with the implicit-solvent approximation used in molecular dynamics (MD) simulations of biological membranes. Using the original iSoLF (iSoLFv1), MD simulations of lipid bilayers consisting of either POPC or DPPC and these bilayers, including membrane proteins, can be performed. Here, we improve the original model, explicitly treating the electrostatic interactions between different lipid molecules and adding CG particle types. As a result, the available lipid types increase to 30. To parameterize the potential functions of the new model, we performed all-atom MD simulations of each lipid at three different temperatures using the CHARMM36 force field and the modified TIP3P model. Then, we parameterized both the bonded and non-bonded interactions to fit the area per lipid and the membrane thickness of each lipid bilayer by using the multistate Boltzmann Inversion method. The final model reproduces the area per lipid and the membrane thickness of each lipid bilayer at the three temperatures. We also examined the applicability of the new model, iSoLFv2, to simulate the phase behaviors of mixtures of DOPC and DPPC at different concentrations. The simulation results with iSoLFv2 are consistent with those using Dry Martini and Martini 3, although iSoLFv2 requires much fewer computations. iSoLFv2 has been implemented in the GENESIS MD software and is publicly available.

Wrapping Pathways of Anisotropic Dumbbell Particles by Giant Unilamellar Vesicles

Endocytosis is a key cellular process involved in the uptake of nutrients, pathogens, or the therapy of diseases. Most studies have focused on spherical objects, whereas biologically relevant shapes can be highly anisotropic. In this letter, we use an experimental model system based on Giant Unilamellar Vesicles (GUVs) and dumbbell-shaped colloidal particles to mimic and investigate the first stage of the passive endocytic process: engulfment of an anisotropic object by the membrane. Our model has specific ligand-receptor interactions realized by mobile receptors on the vesicles and immobile ligands on the particles. Through a series of experiments, theory, and molecular dynamics simulations, we quantify the wrapping process of anisotropic dumbbells by GUVs and identify distinct stages of the wrapping pathway. We find that the strong curvature variation in the neck of the dumbbell as well as membrane tension are crucial in determining both the speed of wrapping and the final states.

The patterned assembly and stepwise Vps4-mediated disassembly of composite ESCRT-III polymers drives archaeal cell division

ESCRT-III family proteins form composite polymers that deform and cut membrane tubes in the context of a wide range of cell biological processes across the tree of life. In reconstituted systems, sequential changes in the composition of ESCRT-III polymers induced by the AAA-adenosine triphosphatase Vps4 have been shown to remodel membranes. However, it is not known how composite ESCRT-III polymers are organized and remodeled in space and time in a cellular context. Taking advantage of the relative simplicity of the ESCRT-III-dependent division system in Sulfolobus acidocaldarius, one of the closest experimentally tractable prokaryotic relatives of eukaryotes, we use super-resolution microscopy, electron microscopy, and computational modeling to show how CdvB/CdvB1/CdvB2 proteins form a precisely patterned composite ESCRT-III division ring, which undergoes stepwise Vps4-dependent disassembly and contracts to cut cells into two. These observations lead us to suggest sequential changes in a patterned composite polymer as a general mechanism of ESCRT-III-dependent membrane remodeling.

Modelling membrane reshaping by staged polymerization of ESCRT-III filaments

ESCRT-III filaments are composite cytoskeletal polymers that can constrict and cut cell membranes from the inside of the membrane neck. Membrane-bound ESCRT-III filaments undergo a series of dramatic composition and geometry changes in the presence of an ATP-consuming Vps4 enzyme, which causes stepwise changes in the membrane morphology. We set out to understand the physical mechanisms involved in translating the changes in ESCRT-III polymer composition into membrane deformation. We have built a coarse-grained model in which ESCRT-III polymers of different geometries and mechanical properties are allowed to copolymerise and bind to a deformable membrane. By modelling ATP-driven stepwise depolymerisation of specific polymers, we identify mechanical regimes in which changes in filament composition trigger the associated membrane transition from a flat to a buckled state, and then to a tubule state that eventually undergoes scission to release a small cargo-loaded vesicle. We then characterise how the location and kinetics of polymer loss affects the extent of membrane deformation and the efficiency of membrane neck scission. Our results identify the near-minimal mechanical conditions for the operation of shape-shifting composite polymers that sever membrane necks.

Synergistic Entry of Individual Nanoparticles into Mammalian Cells Driven by Free Energy Decline and Regulated by Their Sizes

Cell entry is one of the common prerequisites for nanomaterial applications. Despite extensive studies on a homogeneous group of nanoparticles (NPs), fewer studies have been performed when two or more types of NPs were coadministrated. We previously described a synergistic cell entry process for two heterogeneous groups of NPs, where NPs functionalized with TAT (transactivator of transcription) peptide (T-NPs) stimulate the cellular uptake of coadministered unfunctionalized NPs (bystander NPs, B-NPs). Here, we show that the synergistic cell entry of NPs is driven by free energy decline and depends on B-NP sizes. Simulations showed that when separately placed initially, two NPs first move toward each other instead of initiating cell entry individually. Only T-NP invokes an inward bending of membrane mimicking endocytosis, which attracts the nearby NPs into the same "vesicle". A two-phase free energy decline of the entire system occurred as two NPs get closer until contact, which is likely the thermodynamic driver for synergistic NP coentry. Experimentally, we found that T-NPs increase the apparent affinity of B-NPs to plasma membrane, suggesting that T-NPs help B-NPs "trapped" in the endocytic vesicles. Next, we varied the sizes of B-NPs and found that bystander activity peaks around 50 nm. Simulations also showed that the size of B-NPs influences the free energy decline, and thus the tendency and dynamics of NP coentry. These efforts provide a system to further understand the synergistic cell entry among individual NPs or multiple NP types on a biophysical basis and shed light on the future design of nanostructures for intracellular delivery.

Spatiotemporal Tracing of the Cellular Internalization Process of Rod-Shaped Nanostructures

Endocytosis, as one of the main ways for nanostructures enter cells, is affected by several aspects, and shape is an especially critical aspect during the endocytosis of nanostructures. However, it has remained challenging to capture the dynamic internalization behaviors of rod-shaped nanostructures while also probing the mechanical aspects of the internalization. Here, using the atomic force microscopy-based force tracing technique, transmission electron microscopy, and molecular dynamic simulation, we mapped the detailed internalization behaviors of rod-shaped nanostructures with different aspect ratios at the single-particle level. We found that the gold nanorod is endocytosed in a noncontinuous and force-rebound rotation manner, herein named "intermittent rotation". The force tracing test indicated that the internalization force (∼81 pN, ∼108 pN, and ∼157 pN) and time (∼0.56 s, ∼0.66 s, and ∼1.14 s for a 12.10 nm × 11.96 nm gold nanosphere and 26.15 nm × 13.05 nm and 48.71 nm × 12.45 nm gold nanorods, respectively) are positively correlated with the aspect ratios. However, internalization speed is negatively correlated with internalization time, irrespective of the aspect ratio. Further, the energy analysis suggested that intermittent rotation from the horizontal to vertical direction can reduce energy dissipation during the internalization process. Thus, to overcome the energy barrier of internalization, the number and angle of rotation increases with aspect ratios. Our findings provide critical missing evidence of rod-shaped nanostructure's internalization, which is essential for fundamentally understanding the internalization mechanism in living cells.

Scale-invariance in miniature coarse-grained red blood cells by fluctuation analysis

To accurately represent the morphological and elastic properties of a human red blood cell, Fu et al. [Fu et al., Lennard-Jones type pair-potential method for coarse-grained lipid bilayer membrane simulations in LAMMPS, 2017, 210, 193-203] recently developed a coarse-grained molecular dynamics model with particular detail in the membrane. However, such a model accrues an extremely high computational cost for whole-cell simulation when assuming an appropriate length scaling - that of the bilayer thickness. To date, the model has only simulated "miniature" cells in order to circumvent this, with the a priori assumption that these miniaturised cells correctly represent their full-sized counterparts. The present work assesses the validity of this approach, by testing the scale invariance of the model through simulating cells of various diameters; first qualitatively in their shape evolution, then quantitatively by measuring their bending rigidity through fluctuation analysis. Cells of diameter of at least 0.5 μm were able to form the characteristic biconcave shape of human red blood cells, though smaller cells instead equilibrated to bowl-shaped stomatocytes. Thermal fluctuation analysis showed the bending rigidity to be constant over all cell sizes tested, and consistent between measurements on the whole-cell and on a planar section of bilayer. This is as expected from the theory on both counts. Therefore, we confirm that the evaluated model is a good representation of a full-size RBC when the model diameter is ≥0.5 μm, in terms of the morphological and mechanical properties investigated.

Physical mechanisms of ESCRT-III-driven cell division

Living systems propagate by undergoing rounds of cell growth and division. Cell division is at heart a physical process that requires mechanical forces, usually exerted by assemblies of cytoskeletal polymers. Here we developed a physical model for the ESCRT-III-mediated division of archaeal cells, which despite their structural simplicity share machinery and evolutionary origins with eukaryotes. By comparing the dynamics of simulations with data collected from live cell imaging experiments, we propose that this branch of life uses a previously unidentified division mechanism. Active changes in the curvature of elastic cytoskeletal filaments can lead to filament perversions and supercoiling, to drive ring constriction and deform the overlying membrane. Abscission is then completed following filament disassembly. The model was also used to explore how different adenosine triphosphate (ATP)-driven processes that govern the way the structure of the filament is changed likely impact the robustness and symmetry of the resulting division. Comparisons between midcell constriction dynamics in simulations and experiments reveal a good agreement with the process when changes in curvature are implemented at random positions along the filament, supporting this as a possible mechanism of ESCRT-III-dependent division in this system. Beyond archaea, this study pinpoints a general mechanism of cytokinesis based on dynamic coupling between a coiling filament and the membrane.

Membrane-Mediated Interactions Between Protein Inclusions

Integral or peripheral membrane proteins, or protein oligomers often get close to each other on cell membranes and carry out biological tasks in a collective manner. In addition to electrostatic and van der Waals interactions, those proteins also experience membrane-mediated interactions, which may be necessary for their functionality. The membrane-mediated interactions originate from perturbation of lipid membranes by the presence of protein inclusions, and have been the subject of intensive research in membrane biophysics. Here we review both theoretical and numerical studies of such interactions for membrane proteins and for nanoparticles bound to lipid membranes.

Modelling the dynamics of vesicle reshaping and scission under osmotic shocks

We study the effects of osmotic shocks on lipid vesicles via coarse-grained molecular dynamics simulations by explicitly considering the solute in the system. We find that depending on their nature (hypo- or hypertonic) such shocks can lead to bursting events or engulfing of external material into inner compartments, among other morphology transformations. We characterize the dynamics of these processes and observe a separation of time scales between the osmotic shock absorption and the shape relaxation. Our work consequently provides an insight into the dynamics of compartmentalization in vesicular systems as a result of osmotic shocks, which can be of interest in the context of early proto-cell development and proto-cell compartmentalisation.

Experimental and theoretical explorations of nanocarriers' multistep delivery performance for rational design and anticancer prediction

The poor understanding of the complex multistep process taken by nanocarriers during the delivery process limits the delivery efficiencies and further hinders the translation of these systems into medicine. Here, we describe a series of six self-assembled nanocarrier types with systematically altered physical properties including size, shape, and rigidity, as well as both in vitro and in vivo analyses of their performance in blood circulation, tumor penetration, cancer cell uptake, and anticancer efficacy. We also developed both data and simulation-based models for understanding the influence of physical properties, both individually and considered together, on each delivery step and overall delivery process. Thus, beyond finding that nanocarriers that are simultaneously endowed with tubular shape, short length, and low rigidity outperformed the other types, we now have a suit of theoretical models that can predict how nanocarrier properties will individually and collectively perform in the multistep delivery of anticancer therapies.

Domain Aggregation and Associated Pore Growth in Lipid Membranes

Recent experiments have shown that certain molecular agents can selectively penetrate and aggregate in bacterial lipid membranes, leading to their permeability and rupture. To help reveal and understand the underlying mechanisms, here we establish a theory to show that the deformation energy of the membrane tends to limit the growth of molecular domains on a lipid membrane, resulting in a characteristic domain size, and that the domain aggregation significantly reduces the energy barrier to pore growth. Coarse-grained molecular dynamics simulations are performed to validate such domain aggregation and associated pore formation. This study sheds light on how lipid membranes can be damaged through molecular domain aggregation and contributes to establish a theoretical foundation for the next-generation membrane-targeting nanomedicine.

Characterising the diffusion of biological nanoparticles on fluid and cross-linked membranes

Tracing the motion of macromolecules, viruses, and nanoparticles adsorbed onto cell membranes is currently the most direct way of probing the complex dynamic interactions behind vital biological processes, including cell signalling, trafficking, and viral infection. The resulting trajectories are usually consistent with some type of anomalous diffusion, but the molecular origins behind the observed anomalous behaviour are usually not obvious. Here we use coarse-grained molecular dynamics simulations to help identify the physical mechanisms that can give rise to experimentally observed trajectories of nanoscopic objects moving on biological membranes. We find that diffusion on membranes of high fluidities typically results in normal diffusion of the adsorbed nanoparticle, irrespective of the concentration of receptors, receptor clustering, or multivalent interactions between the particle and membrane receptors. Gel-like membranes on the other hand result in anomalous diffusion of the particle, which becomes more pronounced at higher receptor concentrations. This anomalous diffusion is characterised by local particle trapping in the regions of high receptor concentrations and fast hopping between such regions. The normal diffusion is recovered in the limit where the gel membrane is saturated with receptors. We conclude that hindered receptor diffusivity can be a common reason behind the observed anomalous diffusion of viruses, vesicles, and nanoparticles adsorbed on cell and model membranes. Our results enable direct comparison with experiments and offer a new route for interpreting motility experiments on cell membranes.

Exploring the Design Rules for Efficient Membrane-Reshaping Nanostructures

In this study, we investigate the role of the surface patterning of nanostructures for cell membrane reshaping. To accomplish this, we combine an evolutionary algorithm with coarse-grained molecular dynamics simulations and explore the solution space of ligand patterns on a nanoparticle that promote efficient and reliable cell uptake. Surprisingly, we find that in the regime of low ligand number the best-performing structures are characterized by ligands arranged into long one-dimensional chains that pattern the surface of the particle. We show that these chains of ligands provide particles with high rotational freedom and they lower the free energy barrier for membrane crossing. Our approach reveals a set of nonintuitive design rules that can be used to inform artificial nanoparticle construction and the search for inhibitors of viral entry.

On the shuttling across the blood-brain barrier via tubule formation: Mechanism and cargo avidity bias

The blood-brain barrier is made of polarized brain endothelial cells (BECs) phenotypically conditioned by the central nervous system (CNS). Although transport across BECs is of paramount importance for nutrient uptake as well as ridding the brain of waste products, the intracellular sorting mechanisms that regulate successful receptor-mediated transcytosis in BECs remain to be elucidated. Here, we used a synthetic multivalent system with tunable avidity to the low-density lipoprotein receptor-related protein 1 (LRP1) to investigate the mechanisms of transport across BECs. We used a combination of conventional and super-resolution microscopy, both in vivo and in vitro, accompanied with biophysical modeling of transport kinetics and membrane-bound interactions to elucidate the role of membrane-sculpting protein syndapin-2 on fast transport via tubule formation. We show that high-avidity cargo biases the LRP1 toward internalization associated with fast degradation, while mid-avidity augments the formation of syndapin-2 tubular carriers promoting a fast shuttling across.

An ESCRT-III Polymerization Sequence Drives Membrane Deformation and Fission

The endosomal sorting complex required for transport-III (ESCRT-III) catalyzes membrane fission from within membrane necks, a process that is essential for many cellular functions, from cell division to lysosome degradation and autophagy. How it breaks membranes, though, remains unknown. Here, we characterize a sequential polymerization of ESCRT-III subunits that, driven by a recruitment cascade and by continuous subunit-turnover powered by the ATPase Vps4, induces membrane deformation and fission. During this process, the exchange of Vps24 for Did2 induces a tilt in the polymer-membrane interface, which triggers transition from flat spiral polymers to helical filament to drive the formation of membrane protrusions, and ends with the formation of a highly constricted Did2-Ist1 co-polymer that we show is competent to promote fission when bound on the inside of membrane necks. Overall, our results suggest a mechanism of stepwise changes in ESCRT-III filament structure and mechanical properties via exchange of the filament subunits to catalyze ESCRT-III activity.

The proteasome controls ESCRT-III-mediated cell division in an archaeon

Sulfolobus acidocaldarius is the closest experimentally tractable archaeal relative of eukaryotes and, despite lacking obvious cyclin-dependent kinase and cyclin homologs, has an ordered eukaryote-like cell cycle with distinct phases of DNA replication and division. Here, in exploring the mechanism of cell division in S. acidocaldarius, we identify a role for the archaeal proteasome in regulating the transition from the end of one cell cycle to the beginning of the next. Further, we identify the archaeal ESCRT-III homolog, CdvB, as a key target of the proteasome and show that its degradation triggers division by allowing constriction of the CdvB1:CdvB2 ESCRT-III division ring. These findings offer a minimal mechanism for ESCRT-III-mediated membrane remodeling and point to a conserved role for the proteasome in eukaryotic and archaeal cell cycle control.

Coarse-Grained Modeling of Pore Dynamics on the Red Blood Cell Membrane under Large Deformations

Transient pore formation on the membrane of red blood cells (RBCs) under high mechanical tensions is of great importance in many biomedical applications, such as RBC damage (hemolysis) and mechanoporation-based drug delivery. The dynamic process of pore formation, growth, and resealing is hard to visualize in experiments. We developed a mesoscale coarse-grained model to study the characteristics of transient pores on a patch of the lipid bilayer that is strengthened by an elastic meshwork representing the cytoskeleton. Unsteady molecular dynamics was used to study the pore formation and reseal at high strain rates close to the physiological ranges. The critical strain for pore formation, pore characteristics, and cytoskeleton effects were studied. Results show that the presence of the cytoskeleton increases the critical strain of pore formation and confines the pore growth. Moreover, the pore recovery process under negative strain rates (compression) is analyzed. Simulations show that pores can remain open for a long time during the high-speed tank-treading induced stretching and compression process that a patch of the RBC membrane usually experiences under high shear flow. Furthermore, complex loading conditions can affect the pore characteristics and result in denser pores. Finally, the effects of strain rate on pore formation are analyzed. Higher rate stretching of membrane patch can result in a significant increase in the critical areal strain and density of pores. Such a model reveals the dynamic molecular process of RBC damage in biomedical devices and mechanoporation that, to our knowledge, has not been reported before.

Cellular Uptake of Active Particles

Active particles are widely recognized to potentially revolutionize technologies in numerous biomedical applications. However, the physical origin behind cellular uptake of these particles in the nonequilibrium state remains scarcely understood. Here we combine Brownian dynamics simulation as well as theoretical analysis to provide the criterion for cellular uptake of active particles, related to various physical attributes. Upon enhancing the activity, the uptake efficiency for the active particles with tilted orientation is examined to be nonmonotonic, in stark contrast to the monotonic dependence for active particles orientated normally to the membrane. This can be attributed to the interplay between membrane adhesion energy and kinetic energy of active particles, resulting in unique kinetic pathways. Furthermore, a theoretical model that captures the essential physics of the cellular endocytosis process is developed to reproduce this nonmonotonic feature. The results are of immediate interest to understand and tune activity-mediated cellular interaction and internalization of such emerging colloids.

Electrostatic interaction effects on the size distribution of self-assembled giant unilamellar vesicles

The influence of electrostatic conditions (salt concentration of the solution and vesicle surface charge density) on the size distribution of self-assembled giant unilamellar vesicles (GUVs) is considered. The membranes of GUVs are synthesized by a mixture of dioleoylphosphatidylglycerol and dioleoylphosphatidylcholine in a physiological buffer using the natural swelling method. The experimental results are presented in the form of a set of histograms. The log-normal distribution is used for statistical treatment of results. It is obtained that the decrease of salt concentration and the increase of vesicle surface charge density of the membranes increase the average size of the GUV population. To explain the experimental results, a theory using the Helmholtz free energy of the system describing the GUV vesiculation is developed. The size distribution histograms and average size of GUVs under various conditions are fitted with the proposed theory. It is shown that the variation of the bending modulus due to changing of electrostatic parameters of the system is the main factor causing a change in the average size of GUVs.

Interaction of Graphene Nanoparticles and Lipid Membranes Displaying Different Liquid Orderings: A Molecular Dynamics Study

Understanding the effects of graphene-based nanomaterials on lipid membranes is fundamental to determine their environmental impact and the efficiency of their biomedical use. By means of molecular dynamics simulations of simple model lipid bilayers, we analyze in detail the different interaction modes. We have studied bilayers consisting of lipid species (including cholesterol) which display different internal liquid orderings. Nanometric graphene layers can be transiently adsorbed onto the lipid membrane and/or inserted in its hydrophobic region. Once inserted, graphene nanometric flakes display a diffusive dynamics in the membrane plane, they adopt diverse orientations depending on their size and oxidation degree, and they show a particular aversion to be placed close to cholesterol molecules in the membrane. Addition of graphene to phase-segregated ternary membranes is also investigated in the context of the lipid raft model for the lipid organization of biological membranes. Our simulation results show that graphene layers can be inserted indistinctly in the ordered and disordered regions. Once inserted, nanometric flakes migrate to disordered and cholesterol-poor lipid phases.

Changes in ESCRT-III filament geometry drive membrane remodelling and fission in silico

BACKGROUND

ESCRT-III is a membrane remodelling filament with the unique ability to cut membranes from the inside of the membrane neck. It is essential for the final stage of cell division, the formation of vesicles, the release of viruses, and membrane repair. Distinct from other cytoskeletal filaments, ESCRT-III filaments do not consume energy themselves, but work in conjunction with another ATP-consuming complex. Despite rapid progress in describing the cell biology of ESCRT-III, we lack an understanding of the physical mechanisms behind its force production and membrane remodelling.

RESULTS

Here we present a minimal coarse-grained model that captures all the experimentally reported cases of ESCRT-III driven membrane sculpting, including the formation of downward and upward cones and tubules. This model suggests that a change in the geometry of membrane bound ESCRT-III filaments-from a flat spiral to a 3D helix-drives membrane deformation. We then show that such repetitive filament geometry transitions can induce the fission of cargo-containing vesicles.

CONCLUSIONS

Our model provides a general physical mechanism that explains the full range of ESCRT-III-dependent membrane remodelling and scission events observed in cells. This mechanism for filament force production is distinct from the mechanisms described for other cytoskeletal elements discovered so far. The mechanistic principles revealed here suggest new ways of manipulating ESCRT-III-driven processes in cells and could be used to guide the engineering of synthetic membrane-sculpting systems.

Wrapping of a nanowire by a supported lipid membrane

Internalization of particles by cells plays a crucial role for adsorbing nutrients and fighting infection. Endocytosis is one of the most important mechanisms of particle uptake, which encompasses multiple pathways. Although endocytosis is a complex mechanism involving biochemical signaling and active force generation, the energetic cost associated with the large deformations of the cell membrane wrapping around a foreign particle is an important factor controlling this process, which can be studied using quantitative physical models. Of particular interest is the competition between membrane-cytoskeleton and membrane-target adhesion. This competitive adhesion mechanism can be reproduced to some extent by studying particle wrapping by a membrane adhered to a substrate. We propose a theoretical analysis of this process. Here, we explore the wrapping of a lipid membrane around a long cylindrical object in the presence of a substrate mimicking the cytoskeleton. Using discretization of the Helfrich elastic energy, which accounts for the membrane bending rigidity and surface tension, we obtain a wrapping phase diagram as a function of the membrane-cytoskeleton and the membrane-target adhesion energy, which includes unwrapped, partially wrapped and fully wrapped states. We provide an analytical expression for the boundary between the different regimes. While the transition to partial wrapping is independent of the membrane tension, the transition to full wrapping is very much influenced by the membrane tension. We also show that target wrapping may proceed in an asymmetric fashion in the full wrapping regime.

Minimal coarse-grained models for molecular self-organisation in biology

The molecular machinery of life is largely created via self-organisation of individual molecules into functional assemblies. Minimal coarse-grained models, in which a whole macromolecule is represented by a small number of particles, can be of great value in identifying the main driving forces behind self-organisation in cell biology. Such models can incorporate data from both molecular and continuum scales, and their results can be directly compared to experiments. Here we review the state of the art of models for studying the formation and biological function of macromolecular assemblies in living organisms. We outline the key ingredients of each model and their main findings. We illustrate the contribution of this class of simulations to identifying the physical mechanisms behind life and diseases, and discuss their future developments.

Cytoskeleton Remodeling Induces Membrane Stiffness and Stability Changes of Maturing Reticulocytes

Reticulocytes, the precursors of erythrocytes, undergo drastic alterations in cell size, shape, and deformability during maturation. Experimental evidence suggests that young reticulocytes are stiffer and less stable than their mature counterparts; however, the underlying mechanism is yet to be fully understood. Here, we develop a coarse-grained molecular-dynamics reticulocyte membrane model to elucidate how the membrane structure of reticulocytes contributes to their particular biomechanical properties and pathogenesis in blood diseases. First, we show that the extended cytoskeleton in the reticulocyte membrane is responsible for its increased shear modulus. Subsequently, we quantify the effect of weakened cytoskeleton on the stiffness and stability of reticulocytes, via which we demonstrate that the extended cytoskeleton along with reduced cytoskeleton connectivity leads to the seeming paradox that reticulocytes are stiffer and less stable than the mature erythrocytes. Our simulation results also suggest that membrane budding and the consequent vesiculation of reticulocytes can occur independently of the endocytosis-exocytosis pathway, and thus, it may serve as an additional means of removing unwanted membrane proteins from reticulocytes. Finally, we find that membrane budding is exacerbated when the cohesion between the lipid bilayer and the cytoskeleton is compromised, which is in accord with the clinical observations that erythrocytes start shedding membrane surface at the reticulocyte stage in hereditary spherocytosis. Taken together, our results quantify the stiffness and stability change of reticulocytes during their maturation and provide, to our knowledge, new insights into the pathogenesis of hereditary spherocytosis and malaria.

Temperature- and rigidity-mediated rapid transport of lipid nanovesicles in hydrogels

Lipid nanovesicles are widely present as transport vehicles in living organisms and can serve as efficient drug delivery vectors. It is known that the size and surface charge of nanovesicles can affect their diffusion behaviors in biological hydrogels such as mucus. However, how temperature effects, including those of both ambient temperature and phase transition temperature (T _m), influence vehicle transport across various biological barriers outside and inside the cell remains unclear. Here, we utilize a series of liposomes with different T _m as typical models of nanovesicles to examine their diffusion behavior in vitro in biological hydrogels. We observe that the liposomes gain optimal diffusivity when their T _m is around the ambient temperature, which signals a drastic change in the nanovesicle rigidity, and that liposomes with T _m around body temperature (i.e., ∼37 °C) exhibit enhanced cellular uptake in mucus-secreting epithelium and show significant improvement in oral insulin delivery efficacy in diabetic rats compared with those with higher or lower T _m Molecular-dynamics (MD) simulations and superresolution microscopy reveal a temperature- and rigidity-mediated rapid transport mechanism in which the liposomes frequently deform into an ellipsoidal shape near the phase transition temperature during diffusion in biological hydrogels. These findings enhance our understanding of the effect of temperature and rigidity on extracellular and intracellular functions of nanovesicles such as endosomes, exosomes, and argosomes, and suggest that matching T _m to ambient temperature could be a feasible way to design highly efficient nanovesicle-based drug delivery vectors.

Effect of pressure profile of shock waves on lipid membrane deformation

Use of shock waves to temporarily increase the permeability of the cell membrane is a promising approach in drug delivery and gene therapy to allow the translocation of macromolecules and small polar molecules into the cytoplasm. Our understanding of how the characteristics of the pressure profile of shock waves, such as peak pressure and pulse duration, influences membrane properties is limited. Here we study the response of lipid bilayer membranes to shock pulses with different pressure profiles using atomistic molecular dynamics simulations. From our simulation results, we find that the transient deformation/disordering of the membrane depends on both the magnitude and the pulse duration of the pressure profile of the shock pulse. For a low pressure impulse, peak pressure has a dominant effect on membrane structural changes, while for the high pressure impulse, we find that there exists an optimal pulse duration at which membrane deformation/disordering is maximized.

Membrane Wrapping Efficiency of Elastic Nanoparticles during Endocytosis: Size and Shape Matter

Using coarse-grained molecular dynamics simulations, we systematically investigate the receptor-mediated endocytosis of elastic nanoparticles (NPs) with different sizes, ranging from 25 to 100 nm, and shapes, including sphere-like, oblate-like, and prolate-like. Simulation results provide clear evidence that the membrane wrapping efficiency of NPs during endocytosis is a result of competition between receptor diffusion kinetics and thermodynamic driving force. The receptor diffusion kinetics refer to the kinetics of receptor recruitment that are affected by the contact edge length between the NP and membrane. The thermodynamic driving force represents the amount of required free energy to drive NPs into a cell. Under the volume constraint of elastic NPs, the soft spherical NPs are found to have similar contact edge lengths to rigid ones and to less efficiently be fully wrapped due to their elastic deformation. Moreover, the difference in wrapping efficiency between soft and rigid spherical NPs increases with their sizes, due to the increment of their elastic energy change. Furthermore, because of its prominent large contact edge length, the oblate ellipsoid is found to be the least sensitive geometry to the variation in NP's elasticity among the spherical, prolate, and oblate shapes during the membrane wrapping. In addition, simulation results indicate that conflicting experimental observations on the efficiency of cellular uptake of elastic NPs could be caused by their different mechanical properties. Our simulations provide a detailed mechanistic understanding about the influence of NPs' size, shape, and elasticity on their membrane wrapping efficiency, which serves as a rational guidance for the design of NP-based drug carriers.

Flow plate separation of cells based on elastic properties: a computational study

Medical studies have consistently shown that the best defense against cancer is early detection. Due to this, many efforts have been made to develop methods of screening patient blood quickly and cheaply. These methods range from separation via differences in size, electrostatic potential, chemical potential, antibody-binding affinity, among others. We propose a method of separating cells which have similar size and outer coatings, but which differ in their elastic properties. Such a method would be useful in detecting cancerous cells, which may have similar properties to leukocytes or erythrocytes but differ in their stiffness and deformation response. Here, we use coarse-grained model of a cell with membrane, cytoskeleton, and inner fluid to determine how small changes in the cell stiffness may be used to quickly and efficiently separate out irregular cells such as circulating tumor cells from a sample of blood. We focus specifically on the effects of volumetric flux and plate geometry on the ability of a separation plate to differentiate cells of similar but disparate stiffnesses. We show that volumetric flux is crucial in determining the stiffness cutoff for separating out cells of similar sizes, while the angle of the separation plate plays a less important role. With this work, we provide a comprehensive approach to the design factors of cell separation via elastic properties and hope to offer a guideline for the development of novel cytometry devices for the detection of irregular cells such as circulating tumor cells.

Controlling Cargo Trafficking in Multicomponent Membranes

Biological membranes typically contain a large number of different components dispersed in small concentrations in the main membrane phase, including proteins, sugars, and lipids of varying geometrical properties. Most of these components do not bind the cargo. Here, we show that such "inert" components can be crucial for the precise control of cross-membrane trafficking. Using a statistical mechanics model and molecular dynamics simulations, we demonstrate that the presence of inert membrane components of small isotropic curvatures dramatically influences cargo endocytosis, even if the total spontaneous curvature of such a membrane remains unchanged. Curved lipids, such as cholesterol, as well as asymmetrically included proteins and tethered sugars can, therefore, actively participate in the control of the membrane trafficking of nanoscopic cargo. We find that even a low-level expression of curved inert membrane components can determine the membrane selectivity toward the cargo size and can be used to selectively target membranes of certain compositions. Our results suggest a robust and general method of controlling cargo trafficking by adjusting the membrane composition without needing to alter the concentration of receptors or the average membrane curvature. This study indicates that cells can prepare for any trafficking event by incorporating curved inert components in either of the membrane leaflets.

Rapid transport of deformation-tuned nanoparticles across biological hydrogels and cellular barriers

To optimally penetrate biological hydrogels such as mucus and the tumor interstitial matrix, nanoparticles (NPs) require physicochemical properties that would typically preclude cellular uptake, resulting in inefficient drug delivery. Here, we demonstrate that (poly(lactic-co-glycolic acid) (PLGA) core)-(lipid shell) NPs with moderate rigidity display enhanced diffusivity through mucus compared with some synthetic mucus penetration particles (MPPs), achieving a mucosal and tumor penetrating capability superior to that of both their soft and hard counterparts. Orally administered semi-elastic NPs efficiently overcome multiple intestinal barriers, and result in increased bioavailability of doxorubicin (Dox) (up to 8 fold) compared to Dox solution. Molecular dynamics simulations and super-resolution microscopy reveal that the semi-elastic NPs deform into ellipsoids, which enables rotation-facilitated penetration. In contrast, rigid NPs cannot deform, and overly soft NPs are impeded by interactions with the hydrogel network. Modifying particle rigidity may improve the efficacy of NP-based drugs, and can be applicable to other barriers.

Penetration of the mucus and tumor interstitial matrix is an important consideration for drug delivery devices. Here, the authors report on a study into the optimization of rigidity for the transport of nanoparticles through biological hydrogels using core-shell polymer-lipid nanoparticles.

Entropic elasticity based coarse-grained model of lipid membranes

Various models for lipid bilayer membranes have been presented to investigate their morphologies. Among them, the aggressive coarse-grained models, where the membrane is represented by a single layer of particles, are computationally efficient and of practical importance for simulating membrane dynamics at the microscopic scale. In these models, soft potentials between particle pairs are used to maintain the fluidity of membranes, but the underlying mechanism of the softening requires further clarification. We have analyzed the membrane area decrease due to thermal fluctuations, and the results demonstrate that the intraparticle part of entropic elasticity is responsible for the softening of the potential. Based on the stretching response of the membrane, a bottom-up model is developed with an entropic effect explicitly involved. The model reproduces several essential properties of the lipid membrane, including the fluid state and a plateau in the stretching curve. In addition, the area compressibility modulus, bending rigidity, and spontaneous curvature display linear dependence on model parameters. As a demonstration, we have investigated the closure and morphology evolution of membrane systems driven by spontaneous curvature, and vesicle shapes observed experimentally are faithfully reproduced.

Particle-based membrane model for mesoscopic simulation of cellular dynamics

We present a simple and computationally efficient coarse-grained and solvent-free model for simulating lipid bilayer membranes. In order to be used in concert with particle-based reaction-diffusion simulations, the model is purely based on interacting and reacting particles, each representing a coarse patch of a lipid monolayer. Particle interactions include nearest-neighbor bond-stretching and angle-bending and are parameterized so as to reproduce the local membrane mechanics given by the Helfrich energy density over a range of relevant curvatures. In-plane fluidity is implemented with Monte Carlo bond-flipping moves. The physical accuracy of the model is verified by five tests: (i) Power spectrum analysis of equilibrium thermal undulations is used to verify that the particle-based representation correctly captures the dynamics predicted by the continuum model of fluid membranes. (ii) It is verified that the input bending stiffness, against which the potential parameters are optimized, is accurately recovered. (iii) Isothermal area compressibility modulus of the membrane is calculated and is shown to be tunable to reproduce available values for different lipid bilayers, independent of the bending rigidity. (iv) Simulation of two-dimensional shear flow under a gravity force is employed to measure the effective in-plane viscosity of the membrane model and show the possibility of modeling membranes with specified viscosities. (v) Interaction of the bilayer membrane with a spherical nanoparticle is modeled as a test case for large membrane deformations and budding involved in cellular processes such as endocytosis. The results are shown to coincide well with the predicted behavior of continuum models, and the membrane model successfully mimics the expected budding behavior. We expect our model to be of high practical usability for ultra coarse-grained molecular dynamics or particle-based reaction-diffusion simulations of biological systems.

Ballistic impact response of lipid membranes

Therapeutic agent loaded micro and nanoscale particles as high-velocity projectiles can penetrate cells and tissues, thereby serving as gene and drug delivery vehicles for direct and rapid internalization. Despite recent progress in developing micro/nanoscale ballistic tools, the underlying biophysics of how fast projectiles deform and penetrate cell membranes is still poorly understood. To understand the rate and size-dependent penetration processes, we present coarse-grained molecular dynamics simulations of the ballistic impact of spherical projectiles on lipid membranes. Our simulations reveal that upon impact, the projectile can pursue one of three distinct pathways. At low velocities below the critical penetration velocity, projectiles rebound off the surface. At intermediate velocities, penetration occurs after the projectile deforms the membrane into a tubular thread. At very high velocities, rapid penetration occurs through localized membrane deformation without tubulation. Membrane tension, projectile velocity and size govern which phenomenon occurs, owing to their positive correlation with the reaction force generated between the projectile and the membrane during impact. Two critical membrane tension values dictate the boundaries among the three pathways for a given system, due to the rate dependence of the stress generated in the membrane. Our findings provide broad physical insights into the ballistic impact response of soft viscous membranes and guide design strategies for drug delivery through lipid membranes using micro/nanoscale ballistic tools.

Entry of nanoparticles into cells: the importance of nanoparticle properties

Knowledge of the interactions between nanoparticles (NPs) and cell membranes is of great importance for the design of safe and efficient nanomedicines.

Optimal multivalent targeting of membranes with many distinct receptors

Cells can often be recognized by the concentrations of receptors expressed on their surface. For better (targeted drug treatment) or worse (targeted infection by pathogens), it is clearly important to be able to target cells selectively. A good targeting strategy would result in strong binding to cells with the desired receptor profile and barely binding to other cells. Using a simple model, we formulate optimal design rules for multivalent particles that allow them to distinguish target cells based on their receptor profile. We find the following: (i) It is not a good idea to aim for very strong binding between the individual ligands on the guest (delivery vehicle) and the receptors on the host (cell). Rather, one should exploit multivalency: High sensitivity to the receptor density on the host can be achieved by coating the guest with many ligands that bind only weakly to the receptors on the cell surface. (ii) The concentration profile of the ligands on the guest should closely match the composition of the cognate membrane receptors on the target surface. And (iii) irrespective of all details, the effective strength of the ligand-receptor interaction should be of the order of the thermal energy [Formula: see text], where [Formula: see text] is the absolute temperature and [Formula: see text] is Boltzmann's constant. We present simulations that support the theoretical predictions. We speculate that, using the above design rules, it should be possible to achieve targeted drug delivery with a greatly reduced incidence of side effects.

The Effect of Thermal Fluctuation on the Receptor-Mediated Adhesion of a Cell Membrane to an Elastic Substrate

Mechanics of the bilayer membrane play an important role in many biological and bioengineering problems such as cell-substrate and cell-nanomaterial interactions. In this work, we study the effect of thermal fluctuation and the substrate elasticity on the cell membrane-substrate adhesion. We model the adhesion of a fluctuating membrane on an elastic substrate as a two-step reaction comprised of the out-of-plane membrane fluctuation and the receptor-ligand binding. The equilibrium closed bond ratio as a function of substrate rigidity was computed by developing a coupled Fourier space Brownian dynamics and Monte Carlo method. The simulation results show that there exists a crossover value of the substrate rigidity at which the closed bond ratio is maximal.

Formation and size distribution of self-assembled vesicles

When detergents and phospholipid membranes are dispersed in aqueous solutions, they tend to self-assemble into vesicles of various shapes and sizes by virtue of their hydrophobic and hydrophilic segments. A clearer understanding of such vesiculation processes holds promise for better elucidation of human physiology and disease, and paves the way to improved diagnostics, drug development, and drug delivery. Here we present a detailed analysis of the energetics and thermodynamics of vesiculation by recourse to nonlinear elasticity, taking into account large deformation that may arise during the vesiculation process. The effects of membrane size, spontaneous curvature, and membrane stiffness on vesiculation and vesicle size distribution were investigated, and the critical size for vesicle formation was determined and found to compare favorably with available experimental evidence. Our analysis also showed that the critical membrane size for spontaneous vesiculation was correlated with membrane thickness, and further illustrated how the combined effects of membrane thickness and physical properties influenced the size, shape, and distribution of vesicles. These findings shed light on the formation of physiological extracellular vesicles, such as exosomes. The findings also suggest pathways for manipulating the size, shape, distribution, and physical properties of synthetic vesicles, with potential applications in vesicle physiology, the pathobiology of cancer and other diseases, diagnostics using in vivo liquid biopsy, and drug delivery methods.

IMPETUS - Interactive MultiPhysics Environment for Unified Simulations

We introduce IMPETUS - Interactive MultiPhysics Environment for Unified Simulations, an object oriented, easy-to-use, high performance, C++ program for three-dimensional simulations of complex physical systems that can benefit a large variety of research areas, especially in cell mechanics. The program implements cross-communication between locally interacting particles and continuum models residing in the same physical space while a network facilitates long-range particle interactions. Message Passing Interface is used for inter-processor communication for all simulations.

On the dynamics of molecular self-assembly and the structural analysis of bilayer membranes using coarse-grained molecular dynamics simulations

We present a molecular dynamics simulation study of the self-assembly of coarse-grained lipid molecules from unbiased random initial configurations. Our lipid model is based on a well-tried CG polymer model with an additional potential that mimics the hydrophobic properties of lipid tails. We find that several stages of self-organization of lipid clusters are involved in the dynamics of bilayer formation and that the resulting equilibrium structures sensitively depend on the strength of hydrophobic interactions hc of the lipid tails and on temperature T. The obtained stable lipid membranes are quantitatively analyzed with respect to their local structure and their degree of order. At equilibrium, we obtain self-stabilizing bilayer membrane structures that exhibit a bending stiffness κB and compression modulus KC comparable to experimental measurements under physiological conditions. We present a phase diagram of our lipid model which covers a sol-gel transition, a liquid (or gel-like) phase including stable bilayer structures and vesicle formation, as well as a quasi-crystalline phase. We also determine the exact conditions for temperature T and degree of hydrophobicity hc for stable bilayer formation including closed vesicles.

Reversible host cell remodeling underpins deformability changes in malaria parasite sexual blood stages

The sexual blood stage of the human malaria parasite Plasmodium falciparum undergoes remarkable biophysical changes as it prepares for transmission to mosquitoes. During maturation, midstage gametocytes show low deformability and sequester in the bone marrow and spleen cords, thus avoiding clearance during passage through splenic sinuses. Mature gametocytes exhibit increased deformability and reappear in the peripheral circulation, allowing uptake by mosquitoes. Here we define the reversible changes in erythrocyte membrane organization that underpin this biomechanical transformation. Atomic force microscopy reveals that the length of the spectrin cross-members and the size of the skeletal meshwork increase in developing gametocytes, then decrease in mature-stage gametocytes. These changes are accompanied by relocation of actin from the erythrocyte membrane to the Maurer's clefts. Fluorescence recovery after photobleaching reveals reversible changes in the level of coupling between the membrane skeleton and the plasma membrane. Treatment of midstage gametocytes with cytochalasin D decreases the vertical coupling and increases their filterability. A computationally efficient coarse-grained model of the erythrocyte membrane reveals that restructuring and constraining the spectrin meshwork can fully account for the observed changes in deformability.

Modeling of band-3 protein diffusion in the normal and defective red blood cell membrane

We employ a two-component red blood cell (RBC) membrane model to simulate lateral diffusion of band-3 proteins in the normal RBC and in the RBC with defective membrane proteins. The defects reduce the connectivity between the lipid bilayer and the membrane skeleton (vertical connectivity), or the connectivity of the membrane skeleton itself (horizontal connectivity), and are associated with the blood disorders of hereditary spherocytosis (HS) and hereditary elliptocytosis (HE) respectively. Initially, we demonstrate that the cytoskeleton limits band-3 lateral mobility by measuring the band-3 macroscopic diffusion coefficients in the normal RBC membrane and in a lipid bilayer without the cytoskeleton. Then, we study band-3 diffusion in the defective RBC membrane and quantify the relation between band-3 diffusion coefficients and percentage of protein defects in HE RBCs. In addition, we illustrate that at low spectrin network connectivity (horizontal connectivity) band-3 subdiffusion can be approximated as anomalous diffusion, while at high horizontal connectivity band-3 diffusion is characterized as confined diffusion. Our simulations show that the band-3 anomalous diffusion exponent depends on the percentage of protein defects in the membrane cytoskeleton. We also confirm that the introduction of attraction between the lipid bilayer and the spectrin network reduces band-3 diffusion, but we show that this reduction is lower than predicted by the percolation theory. Furthermore, we predict that the attractive force between the spectrin filament and the lipid bilayer is at least 20 times smaller than the binding forces at band-3 and glycophorin C, the two major membrane binding sites. Finally, we explore diffusion of band-3 particles in the RBC membrane with defects related to vertical connectivity. We demonstrate that in this case band-3 diffusion can be approximated as confined diffusion for all attraction levels between the spectrin network and the lipid bilayer. By comparing the diffusion coefficients measured in horizontal vs. vertical defects, we conclude that band-3 mobility is primarily controlled by the horizontal connectivity.

Inter-tube adhesion mediates a new pearling mechanism

A common mechanism for intracellular transport is the controlled shape transformation, also known as pearling, of membrane tubes. Exploring how tube pearling takes place is thus of quite importance to not only understand the bio-functions of tubes, but also promote their potential biomedical applications. While the pearling mechanism of one single tube is well understood, both the pathway and the mechanism of pearling of multiple tubes still remain unclear. Herein, by means of computer simulations we show that the tube pearling can be mediated by the inter-tube adhesion. By increasing the inter-tube adhesion strength, each tube undergoes a discontinuous transition from no pearling to thorough pearling. The discontinuous pearling transition is ascribed to the competitive variation between tube surface tension and the extent of inter-tube adhesion. Besides, the final pearling instability is also affected by tube diameter and inter-tube orientation. Thinner tubes undergo inter-tube lipid diffusion before completion of pearling. The early lipid diffusion reduces the extent of inter-tube adhesion and thus restrains the subsequent pearling. Therefore, only partial or no pearling can take place for two thinner tubes. For two perpendicular tubes, the pearling is also observed, but with different pathways and higher efficiency. The finite size effect is discussed by comparing the pearling of tubes with different lengths. It is expected that this work will not only provide new insights into the mechanism of membrane tube pearling, but also shed light on the potential applications in biomaterials science and nanomedicine.