Simulations of stable pores in membranes: system size dependence and line tension

Transient pores in hemifusion diaphragms

Exchange of material across two membranes, as in the case of synaptic neurotransmitter release from a vesicle, involves the formation and poration of a hemifusion diaphragm (HD). The nontrivial geometry of the HD leads to environment-dependent control, regarding the stability and dynamics of the pores required for this kind of exocytosis. This work combines particle simulations, field-based calculations, and phenomenological modeling to explore the factors influencing the stability, dynamics, and possible control mechanisms of pores in HDs. We find that pores preferentially form at the HD rim, and that their stability is sensitive to a number of factors, including the three line tensions, membrane tension, HD size, and the ability of lipids to "flip-flop" across leaflets. Along with a detailed analysis of these factors, we discuss ways that vesicles or cells may use them to open and close pores and thereby quickly and efficiently transport material.

Membrane Binding Strength vs Pore Formation Cost─What Drives the Membrane Permeation of Nanoparticles Coated with Cell-Penetrating Peptides?

Cell-penetrating peptides (CPPs) enable the transport of nanoparticles through cell membranes. Using molecular simulations, we conduct an in-depth investigation into the thermodynamic forces governing the passive translocation of CPP-coated nanoparticles across lipid bilayers, contrasting their behavior with that of bare particles to dissect the contribution of the peptides. Our analysis unveils a distinctive two-stage translocation mechanism, where the adsorption energy of the particles overcomes the cost of forming a hydrophilic transmembrane pore. Proper evaluation of the translocation mechanisms is only possible when using two reaction coordinates, in particular, one that explicitly includes the density of the lipids on the binding site of the particle. An analysis of adsorption and activation free energies in terms of a simple kinetic model provides a clearer understanding of the CPP effect. Experimental validation using nonendocytic cells confirms the superior membrane permeation of CPP-coated particles. Our findings have implications for the rational design of more efficient cell-permeating particles.

Reaction-driven assembly: controlling changes in membrane topology by reaction cycles

Chemical reaction cycles are prototypical examples how to drive systems out of equilibrium and introduce novel, life-like properties into soft-matter systems. We report simulations of amphiphilic molecules in aqueous solution. The molecule's head group is permanently hydrophilic, whereas the reaction cycle switches the molecule's tail from hydrophilic (precursor) to hydrophobic (amphiphile) and vice versa. The reaction cycle leads to an arrest in coalescence and results in uniform vesicle sizes that can be controlled by the reaction rate. Using a continuum description and particle-based simulation, we study the scaling of the vesicle size with the reaction rate. The chemically active vesicles are inflated by precursor, imparting tension onto the membrane and, for specific parameters, stabilize pores.

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.

Impact of Lipid Peroxidation on the Response of Cell Membranes to High-Speed Equibiaxial Stretching: A Computational Study

The difference between diseased and healthy cellular membranes in response to mechanical stresses is crucial for biology, as well as in the development of medical devices. However, the biomolecular mechanisms by which mechanical stresses interact with diseased cellular components remain largely unknown. In this work, we focus on the response of diseased cellular membranes with lipid peroxidation to high-speed tensile loadings. We find that the critical areal strain (ξ_c, when the pore forms) is highly sensitive to lipid peroxidation. For example, ξ_c of a fully oxidized bilayer is only 64 and 69% of the nonoxidized one at the stretching speed of 0.1 and 0.6 m/s, respectively. ξ_c decreases with the increase in the oxidized lipid ratio, regardless of the speeds. Also, the critical rupture tension of membranes exhibits a similar change. It is obvious that the oxidized membranes are more easily damaged than normal ones by high-speed stretching, which coincides with experimental findings. The reason is that peroxidation introduces a polar group to the tail of lipids, increases the hydrophilicity of tails, and warps the tails to the membrane-water interface, which causes loose accumulation and disorder of lipid tails. This can be deduced from the variation in the area per lipid and order parameter. In addition, the lowering stretching modulus and line tension of membranes (i.e., softening) after lipid peroxidation is also a significant factor. We reveal the difference between the peroxidized (diseased) and normal membrane in response to high-speed stretching, give the ξ_c value in the pore formation of membranes and analyze the influence of the stretching speed, peroxidation ratio, and molecular structure of phospholipids. We hope that the molecular-level information will be useful for the development of biological and medical devices in the future.

Effects of Nanopillar Size and Spacing on Mechanical Perturbation and Bactericidal Killing Efficiency

Nanopatterned surfaces administer antibacterial activity through contact-induced mechanical stresses and strains, which can be modulated by changing the nanopattern's radius, spacing and height. However, due to conflicting recommendations throughout the theoretical literature with poor agreement to reported experimental trends, it remains unclear whether these key dimensions-particularly radius and spacing-should be increased or decreased to maximize bactericidal efficiency. It is shown here that a potential failure of biophysical models lies in neglecting any out-of-plane effects of nanopattern contact. To highlight this, stresses induced by a nanopattern were studied via an analytical model based on minimization of strain and adhesion energy. The in-plane (areal) and out-of-plane (contact pressure) stresses at equilibrium were derived, as well as a combined stress (von Mises), which comprises both. Contour plots were produced to illustrate which nanopatterns elicited the highest stresses over all combinations of tip radius between 0 and 100 nm and center spacing between 0 and 200 nm. Considering both the in-plane and out-of-plane stresses drastically transformed the contour plots from those when only in-plane stress was evaluated, clearly favoring small tipped, tightly packed nanopatterns. In addition, the effect of changes to radius and spacing in terms of the combined stress showed the best qualitative agreement with previous reported trends in killing efficiency. Together, the results affirm that the killing efficiency of a nanopattern can be maximized by simultaneous reduction in tip radius and increase in nanopattern packing ratio (i.e., radius/spacing). These findings provide a guide for the design of highly bactericidal nanopatterned surfaces.

Numerical simulation of intracellular drug delivery via rapid squeezing

Intracellular drug delivery by rapid squeezing is one of the most recent and simple cell membrane disruption-mediated drug encapsulation approaches. In this method, cell membranes are perforated in a microfluidic setup due to rapid cell deformation during squeezing through constricted channels. While squeezing-based drug loading has been successful in loading drug molecules into various cell types, such as immune cells, cancer cells, and other primary cells, there is so far no comprehensive understanding of the pore opening mechanism on the cell membrane and the systematic analysis on how different channel geometries and squeezing speed influence drug loading. This article aims to develop a three-dimensional computational model to study the intracellular delivery for compound cells squeezing through microfluidic channels. The Lattice Boltzmann method, as the flow solver, integrated with a spring-connected network via frictional coupling, is employed to capture compound capsule dynamics over fast squeezing. The pore size is proportional to the local areal strain of triangular patches on the compound cell through mathematical correlations derived from molecular dynamics and coarse-grained molecular dynamics simulations. We quantify the drug concentration inside the cell cytoplasm by introducing a new mathematical model for passive diffusion after squeezing. Compared to the existing models, the proposed model does not have any empirical parameters that depend on operating conditions and device geometry. Since the compound cell model is new, it is validated by simulating a nucleated cell under a simple shear flow at different capillary numbers and comparing the results with other numerical models reported in literature. The cell deformation during squeezing is also compared with the pattern found from our compound cell squeezing experiment. Afterward, compound cell squeezing is modeled for different cell squeezing velocities, constriction lengths, and constriction widths. We reported the instantaneous cell center velocity, variations of axial and vertical cell dimensions, cell porosity, and normalized drug concentration to shed light on the underlying physics in fast squeezing-based drug delivery. Consistent with experimental findings in the literature, the numerical results confirm that constriction width reduction, constriction length enlargement, and average cell velocity promote intracellular drug delivery. The results show that the existence of the nucleus increases cell porosity and loaded drug concentration after squeezing. Given geometrical parameters and cell average velocity, the maximum porosity is achieved at three different locations: constriction entrance, constriction middle part, and outside the constriction. Our numerical results provide reasonable justifications for experimental findings on the influences of constriction geometry and cell velocity on the performance of cell-squeezing delivery. We expect this model can help design and optimize squeezing-based cargo delivery.

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.

Mechanics of Bacterial Interaction and Death on Nanopatterned Surfaces

Nanopatterned surfaces are believed to kill bacteria through physical deformation, a mechanism that has immense potential against biochemical resistance. Because of its elusive nature, this mechanism is mostly understood through biophysical modeling. Problematically, accurate descriptions of the contact mechanics and various boundary conditions involved in the bacteria-nanopattern interaction remain to be seen. This may underpin conflicting predictions, found throughout the literature, regarding two important aspects of the mechanism-that is, its critical action site and relationship with geometry. Herein, a robust computational analysis of bacteria-nanopattern interaction is performed using a three-dimensional finite element modeling that incorporates relevant continuum mechanical properties, multilayered envelope structure, and adhesion interaction conditions. The model is applied to more accurately study the elusory mechanism and its enhancement via nanopattern geometry. Additionally, micrographs of bacteria adhered on a nanopatterned cicada wing are examined to further inform and verify the major modeling predictions. Together, the results indicate that nanopatterned surfaces do not kill bacteria predominantly by rupture in between protruding pillars as previously thought. Instead, nondevelopable deformation about pillar tips is more likely to create a critical site at the pillar apex, which delivers significant in-plane strains and may locally rupture and penetrate the cell. The computational analysis also demonstrates that envelope deformation is increased by adhesion to nanopatterns with smaller pillar radii and spacing. These results further progress understanding of the mechanism of nanopatterned surfaces and help guide their design for enhanced bactericidal efficiency.

Stabilizing Leaflet Asymmetry under Differential Stress in a Highly Coarse-Grained Lipid Membrane Model

We present a version of the coarse-grained Cooke lipid model, modified to simulate asymmetric lipid membranes. It is inspired by a method employed by Wang et al. [ Commun. Comput. Phys. 2013, 13, 1093-1106] for artificially penalizing lipid flip-flop but copes more robustly with differential stress, at the cost of one additional bead per lipid and the concomitant increase in computational overhead. Bilayer asymmetry ultimately breaks down beyond a system size dependent critical differential stress, which can be predicted from a simple analytical model. We remeasure many important material parameters for the new model and find it to be consistent with typical fluid lipid membranes. Maintaining a stable stress asymmetry has many applications, and we give two examples: (i) connecting monolayer stress to lipid number asymmetry in order to directly measure the monolayer area modulus and (ii) finding its strain-dependent higher-order correction by monitoring the equilibrium bilayer area.

Estimation of the parameters of the Smoluchowski equation describing the occurrence of pores in a bilayer lipid membrane under soft poration

The conductive lipid pores occurring in planar bilayer membranes are known to manifest themselves experimentally as current fluctuations. Reliable recording of such fluctuations during phase transitions, as well as in membranes with various additives (for example, SDS), allows one to determine the characteristics of hypothetical hydrophilic pores, namely, their number, sizes, lifetimes, and duration of time intervals between pores. Because, in contrast with electroporation, the emergence of pores in a membrane does not require high voltages, this process is called soft poration. Studying the characteristics of pores under soft poration allows us to estimate the parameters of the Smoluchowski equation and compare them with the corresponding parameters used to describe electroporation. In this work, the experimental characteristics of current fluctuations in the membrane with the addition of SDS to the bulk solution were used to estimate the parameters of the Smoluchowski equation: the pore edge tension, the energy of the hydrophobic pore/hydrophilic pore barrier, the coefficient of pore diffusion in the radius space, the initial distribution density of the number of pores, and the attempt rate density of the lipids in a membrane. The obtained estimates are close to the parameter values used in studies of electroporation.

Kelvin-Helmholtz-like instability of phospholipid bilayers under shear flow: System-size dependence

We performed a series of molecular dynamics (MD) simulations of phospholipid bilayers under shear flow to estimate the effect of the system size on Kelvin-Helmholtz (KH)-like instability of the bilayer at the molecular scale. To extend the estimation by the MD simulations to the microscale, we introduced linear stability analysis for the fluid-fluid interface consisting of a thin membrane. For both the MD simulations and theoretical model, the critical velocity difference across the bilayer, where instability occurs, decreased with increasing wavelength of the bilayer undulation λ, which corresponds to the system size. When λ was more than about ten times larger than the bilayer thickness, the critical velocity difference in the MD simulations was in quantitative agreement with that obtained by the theoretical model. This means that the theoretical model is applicable for the shear-induced KH-like instability of the bilayer for large λ. The theoretical model showed that the critical velocity difference for the KH-like instability was proportional to λ^{-3/2}. Based on these results, we discuss the implications of the shear-induced bilayer instability in the shear-induced cell damage observed in experiments.

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.

Prediction of mechanical hemolysis in medical devices via a Lagrangian strain-based multiscale model

This work introduces a new Lagrangian strain-based model to predict the shear-induced hemolysis in biomedical devices. Current computational models for device-induced hemolysis usually utilize empirical fitting of the released free hemoglobin (Hb) in plasma from damaged red blood cells (RBCs). These empirical correlations contain parameters that depend on specific device and operating conditions, thus cannot be used to predict hemolysis in a general device. The proposed algorithm does not have any empirical parameters, thus can presumably be used for hemolysis prediction in various blood-wetting medical devices. In contrast to empirical correlations in which the Hb release is related to the shear stress and exposure time without considering the physical processes, the proposed model links flow-induced deformation of the RBC membrane to membrane permeabilization and Hb release. In this approach, once the steady-state numerical solution of blood flow in the device is obtained under a prescribed operating condition, sample path lines are traced from the inlet of the device to the outlet to calculate the history of the shear stress tensor. In solving the fluid flow, it is assumed that RBCs do not have any influence on the flow pattern. Along each path line, shear stress tensor will be input into a coarse-grained (CG) RBC model to calculate the RBC deformation. Then the correlations obtained from molecular dynamics (MD) simulations are applied to relate the local areal RBC deformation to the perforated area on the RBC membrane. Finally, Hb released out of transient pores is calculated over each path line via a diffusion equation considering the effects of the steric hindrance and increased hydrodynamic drag due to the size of the Hb molecule. The total index of hemolysis (IH) is calculated by integration of released Hb over all the path lines in the computational domain. Hemolysis generated in the Food and Drug Administration (FDA) nozzle and two blood pumps, that is, a CentriMag blood pump (a centrifugal pump) and HeartMate II (an axial pump), for different flow regimes including the laminar and turbulent flows are calculated via the proposed algorithm. In all the simulations, the numerical predicted IH is close to the range of experimental data. The results promisingly indicate that this multiscale approach can be used as a tool for predicting hemolysis and optimizing the hematologic design of other types of blood-wetting devices.

Simulation Best Practices for Lipid Membranes [Article v1.0]

We establish a reliable and robust standardization of settings for practical molecular dynamics (MD) simulations of pure and mixed (single- and multi-component) lipid bilayer membranes. In lipid membranes research, particle-based molecular simulations are a powerful tool alongside continuum theory, lipidomics, and model, in vitro, and in vivo experiments. Molecular simulations can provide precise and reproducible spatiotemporal (atomic- and femtosecond-level) information about membrane structure, mechanics, thermodynamics, kinetics, and dynamics. Yet the simulation of lipid membranes can be a daunting task, given the uniqueness of lipid membranes relative to conventional liquid-liquid and solid-liquid interfaces, the immense and complex thermodynamic and statistical mechanical theory, the diversity of multiscale lipid models, limitations of modern computing power, the difficulty and ambiguity of simulation controls, finite size effects, competitive continuum simulation alternatives, and the desired application, including vesicle experiments and biological membranes. These issues can complicate an essential understanding of the field of lipid membranes, and create major bottlenecks to simulation advancement. In this article, we clarify these issues and present a consistent, thorough, and user-friendly framework for the design of state-of-the-art lipid membrane MD simulations. We hope to allow early-career researchers to quickly overcome common obstacles in the field of lipid membranes and reach maximal impact in their simulations.

Transmembrane domain dimerization induces cholesterol rafts in curved lipid bilayers

Are the dimerization of transmembrane (TM) domains and the reorganization of the lipid bilayer two independent events?

The role of scaffold reshaping and disassembly in dynamin driven membrane fission

The large GTPase dynamin catalyzes membrane fission in eukaryotic cells, but despite three decades of experimental work, competing and partially conflicting models persist regarding some of its most basic actions. Here we investigate the mechanical and functional consequences of dynamin scaffold shape changes and disassembly with the help of a geometrically and elastically realistic simulation model of helical dynamin-membrane complexes. Beyond changes of radius and pitch, we emphasize the crucial role of a third functional motion: an effective rotation of the filament around its longitudinal axis, which reflects alternate tilting of dynamin’s PH binding domains and creates a membrane torque. We also show that helix elongation impedes fission, hemifission is reached via a small transient pore, and coat disassembly assists fission. Our results have several testable structural consequences and help to reconcile mutual conflicting aspects between the two main present models of dynamin fission—the two-stage and the constrictase model.

When cells take up material from their surroundings, they must first transport this cargo across their outer membrane, a flexible sheet of tightly organized fat molecules that act as a barrier to the environment. Cells can achieve this by letting their membrane surround the object, pulling it inwards until it is contained in a pouch that bulges into the cell. This bag is then corded up so it splits off from the outer membrane. The ‘cord’ is a protein called dynamin, which is thought to form a tight spiral around the bag’s neck, closing it over and pinching it away. The structure of dynamin is fairly well known, and yet several theories compete to explain how it may snap the bag off the outer membrane.

Here, Pannuzzo et al. have created a computer simulation that faithfully replicates the geometry and the elasticity of the membrane and of dynamin, and used it to test different ways the protein could work. The first test featured simple constriction, where the dynamin spiral contracts around the membrane to pinch it; this only separated the bag from the membrane after implausibly tight constriction. The second test added elongation, with the spiral lengthening as well as reducing its diameter, but this further reduced the ability for the protein to snap off the membrane. The final test combined constriction and rotation, whereby dynamin ‘twirls’ as it presses on the neck of the bag: this succeeded in efficiently severing the membrane once the dynamin spiral disassembled. Indeed, the simulations suggested that dynamin might start to dismantle while it constricts, without compromising its role. In fact, getting rid of excess length as the protein contracts helps to dissolve any remnants of a membrane connection.

Defects in dynamin are associated with conditions such as centronuclear myopathy and Charcot‐Marie‐Tooth peripheral neuropathy. Recent research also indicates that the protein is involved in a much wider range of neurological disorders that include Alzheimer's, Parkinson's, Huntington's, and amyotrophic lateral sclerosis. The models created by Pannuzzo et al. are useful tools to understand how dynamin and similar proteins work and sometimes fail.

Nanoparticle-Engendered Rupture of Lipid Membranes

Tension-induced rupture of 1,2-dimyristoyl- sn-glycero-3-phosphocholine (DMPC) lipid membranes with encapsulated hydrophobic nanoparticles is elucidated using dissipative particle dynamics simulations. The dynamics of hole formation is studied, and a nanoparticle size-dependent relationship is established for the probability of membrane rupture within a given time as a function of the membrane tension. Two mechanisms of hole formation are explored: homogeneous nucleation and heterogeneous nucleation at the nanoparticle surface. While the kinetics of homogeneous nucleation in unloaded membranes complies with the predictions of the classical Deryagin-Gutop (DG) theory, the heterogeneous nucleation causes progressively lower lysis tensions as the particle size increases. The thermodynamics of heterogeneous nucleation is treated by introducing an effective contact angle at the three-phase, solvent-membrane-solid boundary into the DG theory. The proposed approach helps quantitatively interpret the simulation results and predict the membrane stability in real experiments with significantly larger (by many orders of magnitude) observation times and spatial scales.

Utilizing a Structural Mechanics Approach to Assess the Primary Effects of Injury Loads Onto the Axon and Its Components

Diffuse axonal injury (DAI) occurs as a result of the transmission of rapid dynamic loads from the head to the brain and specifically to its neurons. Despite being one of the most common and most deleterious types of traumatic brain injury (TBI), the inherent cell injury mechanism is yet to be understood. Experimental observations have led to the formulation of different hypotheses, such as mechanoporation of the axolemma and microtubules (MTs) breakage. With the goal of singling out the mechanical aspect of DAI and to resolve the ambiguity behind its injury mechanism, a composite finite element (FE) model of a representative volume of an axon was developed. Once calibrated and validated against published experimental data, the axonal model was used to simulate injury scenarios. The resulting strain distributions along its components were then studied in dependence of strain rate and of typical modeling choices such as the applied MT constraints and tau proteins failure. Results show that oversimplifying the MT bundle kinematic entails a systematic attenuation (cf = 2.33) of the computed maximum MT strain. Nevertheless, altogether, results support the hypothesis of axolemma mechanoporation as a cell-injury trigger. Moreover, for the first time the interconnection between the axolemma and the MT bundle is shown to play a role in damage localization. The proposed FE axonal model is a valuable tool to understand the axonal injury mechanism from a mechanical perspective and could be used in turn for the definition of well-informed injury criteria at the tissue and organ level.

Metastable Prepores in Tension-Free Lipid Bilayers

The formation and closure of aqueous pores in lipid bilayers is a key step in various biophysical processes. Large pores are well described by classical nucleation theory, but the free-energy landscape of small, biologically relevant pores has remained largely unexplored. The existence of small and metastable "prepores" was hypothesized decades ago from electroporation experiments, but resolving metastable prepores from theoretical models remained challenging. Using two complementary methods-atomistic simulations and self-consistent field theory of a minimal lipid model-we determine the parameters for which metastable prepores occur in lipid membranes. Both methods consistently suggest that pore metastability depends on the relative volume ratio between the lipid head group and lipid tails: lipids with a larger head-group volume fraction (or shorter saturated tails) form metastable prepores, whereas lipids with a smaller head-group volume fraction (or longer unsaturated tails) form unstable prepores.

Bending Lipid Bilayers: A Closed-Form Collective Variable for Effective Free-Energy Landscapes in Quantitative Biology

Curvature-related processes are of major importance during protein-membrane interactions. The illusive simplicity of membrane reshaping masks a complex molecular process crucial for a wide range of biological functions like fusion, endo- and exocytosis, cell division, cytokinesis, and autophagy. To date, no functional expression of a reaction coordinate capable of biasing molecular dynamics simulations to produce membrane curvature has been reported. This represents a major drawback given that the adequate identification of proper collective variables to enhance sampling is fundamental for restrained dynamics techniques. In this work, we present a closed-form equation of a collective variable that induces bending in lipid bilayers in a controlled manner, allowing for straightforward calculation of free energy landscapes of important curvature-related events, using standard methods such as umbrella sampling and metadynamics. As a direct application of the collective variable, we calculate the bending free energies of a ternary lipid bilayer in the presence and the absence of a Bin/Amphiphysin/Rvs domain with an N-terminal amphipathic helix (N-BAR), a well-known peripheral membrane protein that induces curvature.

Molecular dynamics simulations of heterogeneous cell membranes in response to uniaxial membrane stretches at high loading rates

The chemobiomechanical signatures of diseased cells are often distinctively different from that of healthy cells. This mainly arises from cellular structural/compositional alterations induced by disease development or therapeutic molecules. Therapeutic shock waves have the potential to mechanically destroy diseased cells and/or increase cell membrane permeability for drug delivery. However, the biomolecular mechanisms by which shock waves interact with diseased and healthy cellular components remain largely unknown. By integrating atomistic simulations with a novel multiscale numerical framework, this work provides new biomolecular mechanistic perspectives through which many mechanosensitive cellular processes could be quantitatively characterised. Here we examine the biomechanical responses of the chosen representative membrane complexes under rapid mechanical loadings pertinent to therapeutic shock wave conditions. We find that their rupture characteristics do not exhibit significant sensitivity to the applied strain rates. Furthermore, we show that the embedded rigid inclusions markedly facilitate stretch-induced membrane disruptions while mechanically stiffening the associated complexes under the applied membrane stretches. Our results suggest that the presence of rigid molecules in cellular membranes could serve as “mechanical catalysts” to promote the mechanical destructions of the associated complexes, which, in concert with other biochemical/medical considerations, should provide beneficial information for future biomechanical-mediated therapeutics.

Probing a Continuous Polar Defect: A Reaction Coordinate for Pore Formation in Lipid Membranes

Various biophysical processes involve the formation of aqueous pores over lipid membranes, including processes of membrane fusion, antimicrobial peptide activity, lipid flip-flop, and membrane permeation. Reliable and efficient free-energy calculations of pore formation using molecular dynamics simulations remained challenging due to the lack of good reaction coordinates (RCs) for pore formation. We present a new RC for pore formation that probes the formation and rupture of a continuous polar defect over the membrane. Potential of mean force (PMF) calculations along the new RC rapidly converge and exhibit no hysteresis between pore-opening and pore-closing pathways, in contrast to calculations based on previous RCs. We show that restraints along the new RC may restrain the system tightly to the transition state of pore formation, rationalizing the absence of hysteresis. We observe that the PMF of pore formation in a tension-free membrane of dimyristoylphosphatidylcholine (DMPC) reveals a free-energy barrier for pore nucleation, confirming a long-hypothesized metastable prepore state. We test the influence of the lipid force field, the cutoff distance used for Lennard-Jones interactions, and the lateral membrane size on the free energies of pore formation. In contrast to PMF calculations based on previous RCs, we find that such parameters have a relatively small influence on the free energies of pore nucleation. However, the metastability of the open pore in DMPC may depend on such parameters. The RC has been implemented into an extension of the GROMACS simulation software. The new RC allows for reliable and computationally efficient free-energy calculations of pore formation in lipid membranes.

A Cellular Model of Shear-Induced Hemolysis

A novel model is presented to study red blood cell (RBC) hemolysis at cellular level. Under high shear rates, pores form on RBC membranes through which hemoglobin (Hb) leaks out and increases free Hb content of plasma leading to hemolysis. By coupling lattice Boltzmann and spring connected network models through immersed boundary method, we estimate hemolysis of a single RBC under various shear rates. First, we use adaptive meshing to find local strain distribution and critical sites on RBC membranes, and then we apply underlying molecular dynamics simulations to evaluate damage. Our approach comprises three sub-models: defining criteria of pore formation, calculating pore size, and measuring Hb diffusive flux out of pores. Our damage model uses information of different scales to predict cellular level hemolysis. Results are compared with experimental studies and other models in literature. The developed cellular damage model can be used as a predictive tool for hydrodynamic and hematologic design optimization of blood-wetting medical devices.

Effect of Boundary Edge in DOPC/DPPC/Cholesterol Liposomes on Acceleration of l-Histidine Preferential Adsorption

In order to investigate the interaction of hydrophilic molecules with liposomal membranes, we employed 1-(4-(trimethylamino)phenyl)-6-phenyl-1,3,5-hexatriene and 1,2-dioleoyl-sn-glycero-3-phosphoethanolamine-N-(5-dimethylamino-1-naphthalenesulfonyl) as fluorescent probes to monitor the surface regions of the membrane, and the results for various liposomes were plotted in correlation diagrams. According to the formation of a variety of phase states, different tendencies of decreasing surface hydrophobicity were observed in the liposomes that were modified with high concentrations of cholesterol or in the liposomes that were composed of ternary components. These liposomes, with hydrophobic surfaces, also showed preferential adsorption of l-histidine (l-His), and the hydrophobicity of the liposomal membrane at the surface changed during l-His adsorption regardless of the initial liposomal properties. Furthermore, we revealed that accelerated adsorption of l-His and preferential binding was induced in ternary liposomes forming boundaries between two separate phases.

Shape deformation of lipid membranes by banana-shaped protein rods: Comparison with isotropic inclusions and membrane rupture

The assembly of curved protein rods on fluid membranes is studied using implicit-solvent meshless membrane simulations. As the rod curvature increases, the rods on a membrane tube assemble along the azimuthal direction first and subsequently along the longitudinal direction. Here, we show that both transition curvatures decrease with increasing rod stiffness. For comparison, curvature-inducing isotropic inclusions are also simulated. When the isotropic inclusions have the same bending rigidity as the other membrane regions, the inclusions are uniformly distributed on the membrane tubes and vesicles even for large spontaneous curvature of the inclusions. However, the isotropic inclusions with much larger bending rigidity induce shape deformation and are concentrated on the region of a preferred curvature. For high rod density, high rod stiffness, and/or low line tension of the membrane edge, the rod assembly induces vesicle rupture, resulting in the formation of a high-genus vesicle. A gradual change in the curvature suppresses this rupture. Hence, large stress, compared to the edge tension, induced by the rod assembly is the key factor determining rupture. For rod curvature with the opposite sign to the vesicle curvature, membrane rupture induces inversion of the membrane, leading to division into multiple vesicles as well as formation of a high-genus vesicle.

Membrane pore formation in atomistic and coarse-grained simulations

Biological cells and their organelles are protected by ultra thin membranes. These membranes accomplish a broad variety of important tasks like separating the cell content from the outer environment, they are the site for cell-cell interactions and many enzymatic reactions, and control the in- and efflux of metabolites. For certain physiological functions e.g. in the fusion of membranes and also in a number of biotechnological applications like gene transfection the membrane integrity needs to be compromised to allow for instance for the exchange of polar molecules across the membrane barrier. Mechanisms enabling the transport of molecules across the membrane involve membrane proteins that form specific pores or act as transporters, but also so-called lipid pores induced by external fields, stress, or peptides. Recent progress in the simulation field enabled to closely mimic pore formation as supposed to occur in vivo or in vitro. Here, we review different simulation-based approaches in the study of membrane pores with a focus on lipid pore properties such as their size and energetics, poration mechanisms based on the application of external fields, charge imbalances, or surface tension, and on pores that are induced by small molecules, peptides, and lipids. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Effects of Stretching Speed on Mechanical Rupture of Phospholipid/Cholesterol Bilayers: Molecular Dynamics Simulation

Rupture of biological cell membrane under mechanical stresses is critical for cell viability. It is triggered by local rearrangements of membrane molecules. We investigated the effects of stretching speed on mechanical rupture of phospholipid/cholesterol bilayers using unsteady molecular dynamics simulations. We focused on pore formation, the trigger of rupture, in a 40 mol% cholesterol-including bilayer. The unsteady stretching was modeled by proportional and temporal scaling of atom positions at stretching speeds from 0.025 to 30 m/s. The effects of the stretching speed on the critical areal strain, where the pore forms, is composed of two regimes. At low speeds (<1.0 m/s), the critical areal strain is insensitive to speed, whereas it significantly increases at higher speeds. Also, the strain is larger than that of a pure bilayer, regardless of the stretching speeds, which qualitatively agrees with available experimental data. Transient recovery of the cholesterol and phospholipid molecular orientations was evident at lower speeds, suggesting the formation of a stretch-induced interdigitated gel-like phase. However, this recovery was not confirmed at higher speeds or for the pure bilayer. The different responses of the molecular orientations may help explain the two regimes for the effect of stretching speed on pore formation.

On the edge energy of lipid membranes and the thermodynamic stability of pores

To perform its barrier function, the lipid bilayer membrane requires a robust resistance against pore formation. Using a self-consistent field (SCF) theory and a molecularly detailed model for membranes composed of charged or zwitterionic lipids, it is possible to predict structural, mechanical, and thermodynamical parameters for relevant lipid bilayer membranes. We argue that the edge energy in membranes is a function of the spontaneous lipid monolayer curvature, the mean bending modulus, and the membrane thickness. An analytical Helfrich-like model suggests that most bilayers should have a positive edge energy. This means that there is a natural resistance against pore formation. Edge energies evaluated explicitly in a two-gradient SCF model are consistent with this. Remarkably, the edge energy can become negative for phosphatidylglycerol (e.g., dioleoylphosphoglycerol) bilayers at a sufficiently low ionic strength. Such bilayers become unstable against the formation of pores or the formation of lipid disks. In the weakly curved limit, we study the curvature dependence of the edge energy and evaluate the preferred edge curvature and the edge bending modulus. The latter is always positive, and the former increases with increasing ionic strength. These results point to a small window of ionic strengths for which stable pores can form as too low ionic strengths give rise to lipid disks. Higher order curvature terms are necessary to accurately predict relevant pore sizes in bilayers. The electric double layer overlap across a small pore widens the window of ionic strengths for which pores are stable.

Morphological changes of amphiphilic molecular assemblies induced by chemical reactions

Shape transformations of amphiphilic molecular assemblies induced by chemical reactions are studied using coarse-grained molecular simulations. A binding reaction between hydrophilic and hydrophobic molecules is considered. It is found that the reaction induces transformation of an oil droplet to a tubular vesicle via bicelles and vesicles with discoidal arms. The discoidal arms close into vesicles, which are subsequently fused into the tubular vesicle. Under the chemical reaction, the bicelle-to-vesicle transition occurs at smaller sizes than in the absence of the hydrophobic molecules. It is revealed that the enhancement of this transition is due to embedded hydrophobic particles that reduce the membrane bending rigidity.

Free energy landscape of rim-pore expansion in membrane fusion

The productive fusion pore in membrane fusion is generally thought to be toroidally shaped. Theoretical studies and recent experiments suggest that its formation, in some scenarios, may be preceded by an initial pore formed near the rim of the extended hemifusion diaphragm (HD), a rim-pore. This rim-pore is characterized by a nontoroidal shape that changes with size. To determine this shape as well as the free energy along the pathway of rim-pore expansion, we derived a simple analytical free energy model. We argue that dilation of HD material via expansion of a rim-pore is favored over a regular, circular pore. Further, the expanding rim-pore faces a free energy barrier that linearly increases with HD size. In contrast, the tension required to expand the rim-pore decreases with HD size. Pore flickering, followed by sudden opening, occurs when the tension in the HD competes with the line energy of the rim-pore, and the rim-pore reaches its equilibrium size before reaching the critical pore size. The experimental observation of flickering and closing fusion pores (kiss-and-run) is very well explained by the observed behavior of rim-pores. Finally, the free energy landscape of rim-pore expansion/HD dilation may very well explain why some cellular fusion reactions, in their attempt to minimize energetic costs, progress via alternative formation and dilation of microscopic hemifusion intermediates.

The importance of membrane defects-lessons from simulations

The defects and pores within lipid membranes are scientifically interesting and have a number of biological applications. Although lipid bilayers are extremely thin hydrophobic barriers, just ∼3 nm thick, they include diverse chemistry and have complex structures. Bilayers are soft and dynamic, and as a result, they can bend and deform in response to different stimuli by means of structural changes in their component lipids. Though defects occur within these structures, their transience and small size have made it difficult to characterize them. However, with recent advances in computer power and computational modeling techniques, researchers can now use simulations as a powerful tool to probe the mechanism and energies of defect and pore formation in a number of situations. In this Account, we present results from our detailed molecular dynamics computer simulations of hydrophilic pores and related defects in lipid bilayers at an atomistic level. Electroporation can be used to increase the permeability of cellular membranes, with potential therapeutic applications. Atomistic simulations of electroporation have illustrated the molecular details of this process, including the importance of water dipole interactions at the water-membrane interface. Characterization of the lipid-protein interactions provides an important tool for understanding transmembrane protein structure and thermodynamic stability. Atomistic simulations give a detailed picture of the free energies of model peptides and side chains in lipid membranes; the energetic cost of defect formation strongly influences the energies of interactions between lipids and polar and charged residues. Many antimicrobial peptides form hydrophilic pores in lipid membranes, killing bacteria or cancer cells. On the basis of simulation data, at least some of these peptides form defects and pores near the center of the bilayer, with a common disordered structure where hydrated headgroups form an approximately toroidal shape. The localization and trafficking of lipids supports general membrane structure and a number of important signaling cascades, such as those involving ceramide, diacylglycerol, and cholesterol. Atomistic simulations have determined the rates and free energies of lipid flip-flop. During the flip-flop of most phosphatidylcholine lipids, a hydrophilic pore forms when the headgroup moves near the center of the bilayer. Simulations have provided novel insight into many features of defects and pores in lipid membranes. Simulation data from very different systems and models show how water penetration and defect formation can determine the free energies of many membrane processes. Bilayers can deform and allow transient defects and pores when exposed to a diverse range of stimuli. Future work will explore many aspects of membrane defects with increased resolution and scope, including the study of more complex lipid mixtures, membrane domains, and large-scale membrane remodeling. Such studies will examine processes including vesicle budding and fusion, non-bilayer lipid phases, and interactions between lipid bilayers and other biomolecules. Simulations provide information that complements experimental studies, allowing microscopic insight into experimental observations and suggesting novel hypotheses and experiments. These studies should enable a deeper understanding of the role of lipid bilayers in cellular biology and support the development of future lipid-based biotechnology.

Modulation of a small two-domain lipid vesicle by linactants

Linactants, molecules that preferentially localize at the boundary of lipid membrane domains, are attracting considerable attention in recent years due to the recognition that they might regulate lipid-phase separation and thereby modulate membrane morphology. Recent studies have also shown that clustering of some line active agents enhances their ability to modulate membrane curvature. However, the molecular origin of this phenomenon, and the degree to which it impacts biological membranes, remains poorly understood. In this work, we have investigated how linactants induce shape change in multidomain small unilamallar vesicles (SUVs) using extensive dissipative particle dynamics simulations. The linactant was modeled as a two-tailed hybrid lipid with the two tails differing in preference for different lipid domains. We found that addition of a small amount of linactants (∼1%) to a two-domain vesicle leads to substantial reduction in the line tension and neck curvature at the domain boundary. Using cross-linking as a surrogate for clustering, we further show that linactant clusters substantially enhance the boundary preference and therefore the reduction in neck curvature. Moreover, on the basis of analyses of the corresponding changes in the membrane energetics, we highlight how linactants might stabilize nanoscale domains. These results have important implications for the potential existence and physical explanations of nanosized domains in biological membranes.

Coupling of bending and stretching deformations in vesicle membranes

Biomimetic membranes are fluid and can undergo two different elastic deformations, bending and stretching. The bending of a membrane is primarily governed by two elastic parameters: its spontaneous (or preferred) curvature m and its bending rigidity κ. These two parameters define an intrinsic tension scale, the spontaneous tension 2 κm². Membrane stretching and compression, on the other hand, are determined by the mechanical tension acting within the membrane. For vesicle membranes, the two elastic deformations are coupled via the enclosed vesicle volume even in the absence of mechanical forces as shown here by minimizing the combined bending and stretching energy with respect to membrane area for fixed vesicle volume. As a consequence, the mechanical tension within a vesicle membrane depends on the spontaneous curvature and on the bending rigidity. This interdependence, which is difficult to grasp intuitively, is then illustrated for a variety of simple vesicle shapes. Depending on the vesicle morphology, the magnitude of the mechanical tension can be comparable to or can be much smaller than the spontaneous tension.

The free energy of nanopores in tense membranes

Membrane nanopores are central players for a range of important cellular membrane remodeling processes as well as membrane rupture. Understanding pore formation in tense membranes requires comprehension of the molecular mechanism of pore formation and the associated free energy change as a function of the membrane tension. Here we propose a scheme to calculate the free energy change associated with the formation of a nanometer sized pore in molecular dynamics simulations as a function of membrane tension, which requires the calculation of only one computationally expensive potential of mean force. We show that membrane elastic theory can be used to estimate the pore formation free energy at different tension values from the free energy change in a relaxed membrane and the area expansion curves of the membranes. We have computed the pore formation free energy for a dipalmitoyl-phosphatidylcholine (DPPC) membrane at two different lateral pressure values, 1 bar and -40 bar, by calculating the potential of mean force acting on the head group of a single lipid molecule. Unrestrained simulations of the closing process confirm that the intermediate states along this reaction coordinate are reasonable and show that hydrophilic indentations spanning half the bilayer connected by a hydrophobic pore segment represent the corresponding high energy transition state. A comparison of the stability of simulated membranes to experiment at high loading rates show that, contrary to expectation, pores form too easily in small simulated membrane patches. This discrepancy originates from a combination of the absence of ions in the simulations and the small membrane size.

Unique dynamical approach of fully wrapping dendrimer-like soft nanoparticles by lipid bilayer membrane

Wrapping dendrimer-like soft nanoparticles by cell membrane is an essential event in their endocytosis in drug and gene delivery, but this process remains poorly elucidated. Using computer simulations and theoretical analysis, we report the detailed dynamics of the process in which a lipid bilayer membrane fully wraps a dendrimer-like soft nanoparticle. By constructing a phase diagram, we firstly demonstrate that there exist three states in the interaction between a dendrimer and a lipid bilayer membrane, i.e., penetration, penetration and partial wrapping, and full wrapping states. The wrapping process of dendrimer-like nanoparticles is found to take a unique approach where the penetration of the dendrimer into the membrane plays a significant role. The analysis of various energies within the system provides a theoretical justification to the state transition observed from simulations. The findings also support recent experimental results and provide a theoretical explanation for them. We expect that these findings are of immediate interest to the study of the cellular uptake of dendrimer-like soft nanoparticles and can prompt the further application of this class of nanoparticles in nanomedicine.

Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model

We calculate the Gaussian curvature modulus kappa of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [Biophys. J., 2012, 102, 1403] to the MARTINI representation of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC). We find the value kappa/kappa = -1.04 +/- 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce kappa(m)/kappa(m) = -0.98 +/- 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K(0m). By also analyzing the lateral stress profile sigma0(z) of our system, two other lipid types and pertinent data from the literature, we show that determining K(0m) and kappa through the first and second moment of sigma0(z) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.

From permeation to pore nucleation in smectic stacks

The last stage of the spreading of a stratified droplet in the odd wetting case is the evolution from a trilayer to a monolayer, that is, vanishing of the last bilayer in the stack. We studied it in the case of 8CB smectic liquid crystal on a hydrophilic surface. Receding of the last bilayer is accompanied by formation of pores in it, which appear in the outer part of it. From analysis of real-time experimental observations of this phenomenon, we demonstrate that the dislocation loops which border these pores are not located at the same height in the trilayer stack as the dislocation lines that border the bilayer. Also, careful analysis of our results using a recently developed theoretical approach of smectic liquid nanodrop spreading strongly suggests that pore nucleation is triggered by differences in chemical potential between adjacent layers, which contrasts with the classical scheme where it is attributed to lateral tension along the layers.

Elastic properties and line tension of self-assembled bilayer membranes

The elastic properties of a self-assembled bilayer membrane are studied using the self-consistent field theory, applied to a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents. Examining the free energy of bilayer membranes with different geometries allows us to calculate their bending modulus, Gaussian modulus, two fourth-order membrane moduli, and the line tension. The dependence of these parameters on the microscopic characteristics of the amphiphilic chain, characterized by the volume fraction of the hydrophilic component, is systematically studied. The theoretical predictions are compared with the results from a simple monolayer model, which approximates a bilayer membrane by two monolayers. The region of validity of the linear elasticity theory is analyzed by examining the higher-order contributions.

Lipid nanotechnology

Nanotechnology is a multidisciplinary field that covers a vast and diverse array of devices and machines derived from engineering, physics, materials science, chemistry and biology. These devices have found applications in biomedical sciences, such as targeted drug delivery, bio-imaging, sensing and diagnosis of pathologies at early stages. In these applications, nano-devices typically interface with the plasma membrane of cells. On the other hand, naturally occurring nanostructures in biology have been a source of inspiration for new nanotechnological designs and hybrid nanostructures made of biological and non-biological, organic and inorganic building blocks. Lipids, with their amphiphilicity, diversity of head and tail chemistry, and antifouling properties that block nonspecific binding to lipid-coated surfaces, provide a powerful toolbox for nanotechnology. This review discusses the progress in the emerging field of lipid nanotechnology.

Engineering nanostructures with enhanced thermoplasmonic properties for biosensing and selective targeting applications

This paper connects the study of thermoplasmonic properties in nanoscale particles with areas of biophysics involving a cell membrane with or without conductive pores. Using a quasistatic finite element modeling of the heat transfer equation in three dimensions we simulate the stationary heat generation and temperature field around several types of gold-based nanostructures. Models were constructed that emphasized the importance of obtaining precise temperature fields that might subsequently be used for biosensing and selective targeting applications. By analyzing the observed temperature increase, effective complex permittivity, and electric field enhancement that result from plasmonic resonance, this theoretical framework provides insight into the role of the nanoparticle shape in heat generation. To illustrate the usefulness of this approach for biosensing applications, we consider how the positioning of the nanoantenna affects heating efficiency. Linear response calculations of the temperature increase reveal that symmetric gold nanosphere dimers are not only suitable for sensing applications, but can also play the role of heat sources which are more efficient than the case of a single nanosphere. We also predict that this specific type of nanoantenna allows us to detect the presence and size of a hole in the cell membrane. These results provide insight into the physics of the cell membrane and provide guidance for more detailed studies of the nanoscale control of temperature in biological materials.