We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: Direct interactions, lipid-induced depletion interactions, lipid bridging, lipid packing, and a smooth long-range contribution. The mechanisms leading to "hydrophobic mismatch" interactions are critically analyzed.
We present an experimental study of the pore formation processes of small amphipathic peptides in model phosphocholine lipid membranes. We used atomic force microscopy to characterize the spatial organization and structure of alamethicin- and melittin- induced defects in lipid bilayer membranes and the influence of the peptide on local membrane properties. Alamethicin induced holes in gel DPPC membranes were directly visualized at different peptide concentrations. We found that the thermodynamic state of lipids in gel membranes can be influenced by the presence of alamethicin such that nanosco…
For endocytosis and exocytosis, membranes transition between planar, budding, and vesicular topographies through nanoscale reorganization of lipids, proteins, and carbohydrates. However, prior attempts to understand the initial stages of nanoscale bending have been limited by experimental resolution. Through the implementation of polarized localization microscopy (PLM), this manuscript reports the inherent membrane bending capability of cholera toxin subunit B (CTxB) in quasi-one component supported lipid bilayers. Membrane buds were first detected with <50 nm radius, grew to >200 nm radius, a…
The biophysical consequences of nanoscale curvature have been challenging to resolve due to size-dependent membrane behavior and the experimental resolution limits imposed by optical diffraction. Recent advances in nanoengineering and super-resolution techniques have enabled new capabilities for creating and observing curvature. In particular, draping supported lipid bilayers over lithographically patterned substrates provides a model system for endocytic pits. The experiments and simulations presented below describe the possible detection of membrane curvature through fluorescence recovery af…
The collective motion of membrane lipids over hundred of nanometers and nanoseconds is essential for the formation of submicron complexes of lipids and proteins in the cell membrane. These dynamics are difficult to access experimentally and are currently poorly understood. One of the conclusions of the celebrated Saffman-Debrück (SD) theory is that lipid disturbances smaller than the Saffman length (microns) are not affected by the hydrodynamics of the embedding solvent. Using molecular dynamics and coarse-grained models with implicit hydrodynamics we show that this is not true. Hydrodynamic i…
Amyloid beta peptides (A\b{eta}), implicated in Alzheimers disease (AD), interact with the cellular membrane and induce amyloid toxicity. The composition of cellular membranes changes in aging and AD. We designed multi component lipid models to mimic healthy and diseased states of the neuronal membrane. Using atomic force microscopy (AFM), Kelvin probe force microscopy (KPFM) and black lipid membrane (BLM) techniques, we demonstrated that these model membranes differ in their nanoscale structure and physical properties, and interact differently with A\b{eta}. Based on our data, we propose a ne…
Contrary to existing theoretical models, experimental evidence points out that electroporation (membrane defect formation under external electric fields) starts to occur within the range of transmembrane voltages that cells may routinely experience, curiously, just above the range of transmembrane voltages involved in neural signal transmission. Understanding the underlying principles of electric fields-lipid membrane interactions seems to carry a great biological importance. An argument is presented toward understanding the theoretical aspects of electroporation by using the DLVO theory, whic…
Diffusion in biological membranes is seldom simply Brownian motion; instead, the rate of diffusion is dependent on the timescale of observation and so is often described as anomalous. In order to help better understand this phenomenon, model systems are needed where the anomalous subdiffusion of the lipid bilayer can be tuned and quantified. We recently demonstrated one such model by controlling the excluded area fraction in supported lipid bilayers (SLBs) through the incorporation of lipids derivatised with polyethylene glycol. Here we extend this work, using urea to induce anomalous subdiffu…
Diffusion in cell membranes is not just simple two-dimensional Brownian motion, but typically depends on the timescale of the observation. The physical origins of this anomalous sub-diffusion are unresolved, and model systems capable of quantitative and reproducible control of membrane diffusion have been recognised as a key experimental bottleneck. Here we control anomalous dif- fusion using supported lipids bilayers containing lipids derivatized with polyethylene glycol (PEG) headgroups. Bilayers with specific excluded area fractions are formed by control of PEG-lipid mole fraction. These bi…
Current fluctuations in pure lipid membranes have been shown to occur under the influence of transmembrane electric fields (electroporation) as well as a result from structural rearrangements of the lipid bilayer during phase transition (soft perforation). We demonstrate that the ion permeability during lipid phase transition exhibits the same qualitative temperature dependence as the macroscopic heat capacity of a D15PC/DOPC vesicle suspension. Microscopic current fluctuations show distinct characteristics for each individual phase state. While current fluctuations in the fluid phase show spi…
We investigate the permeability of lipid membranes for fluorescence dyes and ions. We find that permeability reaches a maximum close to the chain melting transition of the membranes. Close to transitions, fluctuations in area and compressibility are high, leading to an increased likelihood of spontaneous lipid pore formation. Fluorescence Correlation Spectroscopy (FCS) reveals the permeability for rhodamine dyes across 100 nm vesicles. Using FCS, we find that the permeability of vesicle membranes for fluorescence dyes is within error proportional to the excess heat capacity. To estimate defect…
At the neuromuscular junction (NMJ), the nicotinic acetylcholine receptor (nAChR) self-associates to give rise to rapid muscle movement. While lipid domains have maintained nAChR aggregates in-vitro, their specific roles in nAChR clustering are currently unknown. In the present study, we carried out coarse-grained molecular dynamics simulations (CG-MD) of 1-4 nAChR molecules in two membrane environments: One mixture containing domain-forming, homoacidic lipids, and a second mixture consisting of heteroacidic lipids. Spontaneous dimerization of nAChRs was up to ten times more likely in domain-f…
In this article we compare electrical conductance events from single channel recordings of three TRP channel proteins (TRPA1, TRPM2 and TRPM8) expressed in human embryonic kidney cells with channel events recorded on synthetic lipid membranes close to melting transitions. Ion channels from the TRP family are involved in a variety of sensory processes including thermo- and mechano-reception. Synthetic lipid membranes close to phase transitions display channel-like events that respond to stimuli related to changes in intensive thermodynamic variables such as pressure and temperature. TRP channel…
There is mounting evidence that lipid bilayers display conductive properties. However, when interpreting the electrical response of biological membranes to voltage changes, they are commonly considered as inert insulators. However, lipid bilayers under voltage-clamp conditions do not only display current traces with discrete conduction-steps indistinguishable from those attributed to the presence of protein channels. In current-voltage (I-V) plots they may also display outward rectification, i.e., voltage-gating. Surprisingly, this has even been observed in chemically symmetric lipid bilayers.…
We show that the activity of an ion channel is strictly related to the phase state of the lipid bilayer hosting the channel. By measuring unitary conductance, dwell times, and open probability of the K+ channel KcsA as a function of temperature in lipid bilayers composed of POPE and POPG in different relative proportions, we obtain that all those properties show a trend inversion when the bilayer is in the transition region between the liquid disordered and the solid ordered phase. These data suggest that the physical properties of the lipid bilayer influence ion channel activity likely via a …
Specific lipid environments are necessary for the establishment of protein signalling platforms in membranes, yet their origin has been highly debated. We present a continuum, exactly solvable model of protein induced local demixing of lipid membranes. The coupling between a local composition and a local thickness of the membrane induces lipid domains around inclusions with hydrophobic mismatch, even for temperatures above the miscibility critical point of the membrane. The model qualitatively explains the experimentally observed formation of lipid domains induced by anchoring of reconstituted…
Monolayer-protected gold nanoparticles (Au NPs) are promising biomedical tools with applications to diagnosis and therapy, thanks to their biocompatibility and versatility. Here we show how the NP surface functionalization can drive the mechanism of interaction with lipid membranes. In particular, we show that the spontaneous protonation of anionic carboxylic groups on the NP surface can make the NP-membrane interaction faster and less disruptive.
We use coarse grained molecular dynamics simulations to investigate diffusion properties of sheared lipid membranes with embedded transmembrane proteins. In membranes without proteins, we find normal in-plane diffusion of lipids in all flow conditions. Protein embedded membranes behave quite differently: by imposing a simple shear flow and sliding the monolayers of the membrane over each other, the motion of protein clusters becomes strongly superdiffusive in the shear direction. In such a circumstance, subdiffusion regime is predominant perpendicular to the flow. We show that superdiffusion i…
In this paper, phase field models are developed for multi-component vesicle membranes with different lipid compositions and membranes with free boundary. These models are used to simulate the deformation of membranes under the elastic bending energy and the line tension energy with prescribed volume and surface area constraints. By comparing our numerical simulations with recent experiments, it is demonstrated that the phase field models can capture the rich phenomena associated with the membrane transformation, thus it offers great functionality in the simulation and modeling of multicomponen…
Over recent decades, lipid membranes have become standard models for examining the biophysics and biochemistry of cell membranes. Interrogation of lipid domains within biomembranes is generally done with fluorescence microscopy via exogenous chemical probes. However, most fluorophores have limited partitioning tunability, with the majority segregating in the least biologically relevant domains (i.e., low-density liquid domains). Therefore, a molecular-level picture of the majority of non-labeled lipids forming the membrane is still elusive. Here, we present simple, label-free imaging of domain…
Lipid membranes are abundant in living organisms, where they constitute a surrounding shell for cells and their organelles. There are many circumstances in which the deformations of lipid membranes are involved in living cells: fusion and fission, membrane-mediated interaction between membrane inclusions, lipid-protein interaction, formation of pores, etc. In all of these cases, elastic parameters of lipid membranes are important for the description of membrane deformations, as these parameters determine energy barriers and characteristic times of membrane-involved phenomena. Since the develop…
The propagation of sound waves on lipid monolayers supported on water has been studied during the melting transition. Since changes in volume, area, and compressibility in lipid membranes have biological relevance, the observed sound propagation is of paramount importance. However, it is unknown what would occur on a lipid bilayer, which is a more approximate model of a cell membrane. With the aim to answer this relevant question, we built an experimental setup to assemble long artificial lipid membranes. We found that if these membranes are heated in order to force local melting, a thermo-mec…
A novel two-leaflet description of lipid membranes is proposed. Within its framework, phase separation phenomena in multicomponent biological membranes are analyzed. As we show, interactions between the leaflets tend to suppress macroscopic phase segregation (i.e., complete demixing of lipids) in such systems. Instead, microphase separation characterized by formation of equilibrium nanoscale domains can take place. The phase diagram is constructed and numerical simulations revealing nanostructures of different morphology are performed.
Simulating Curved Lipid Membranes Using Anchored Frozen Patches
Department of Materials Science and Engineering, Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格雷恩工程学院材料科学与工程系）
Lipid rafts are heterogeneous dynamic lipid domains of the cell membranes that are involved in several biological processes, like protein and lipids specific transport and signaling. Our understanding of lipid raft formation is still limited, due to the transient and elusive nature of these domains {\it in vivo}, in contrast to the stable phase-separated domains observed in artificial membranes. Inspired by experimental findings highlighting the relevance of transmembrane proteins for lipid rafts, we investigate lipid domain nucleation by coarse-grained molecular dynamics and Ising model simul…
By performing molecular dynamics simulations with up to 132 million coarse-grained particles in half-micron sized boxes, we show that hydrodynamics quantitatively explains the finite-size effects on diffusion of lipids, proteins, and carbon nanotubes in membranes. The resulting Oseen correction allows us to extract infinite-system diffusion coefficients and membrane surface viscosities from membrane simulations despite the logarithmic divergence of apparent diffusivities with increasing box width. The hydrodynamic theory of diffusion applies also to membranes with asymmetric leaflets and embed…
Water molecules on lipid membrane surfaces are known to contribute to membrane stability by connecting lipid molecules and acting as a water bridge. Although the number of water molecules near the membrane fluctuates dynamically, the hydration dynamics has been veiled. Here we investigate residence statistics of water molecules on the surface of a lipid membrane using all-atom molecular dynamics simulations. We show that hydration dynamics on the lipid membrane exhibit $1/f^β$ noise with two different power-law exponents, $β_l < 1$ and $β_h > 1$. By constructing a dichotomous process for the h…
A new model for the interaction of an electric pulse with a lipid membrane is proposed. Using this model we show that when a DC electric pulse is applied to an insulating lipid membrane separating fluids with different conductivities, the capacitive charging current through the membrane drives electrohydrodynamic flow that destabilizes the membrane. The instability is transient and decays as the membrane charges. The bulk conductivity mismatch plays an essential role in this instability because it results in a different rate of charge accumulation on the membrane's physical surfaces. Shearing …
By means of lattice-based Monte Carlo simulations, we address properties of two-component lipid membranes on the experimentally relevant spatial scales of order of a micrometer and time intervals of order of a second, using DMPC/DSPC lipid mixtures as a model system. Our large-scale simulations allowed us to obtain important results previously not reported in simulation studies of lipid membranes. We find that, within a certain range of lipid compositions, the phase transition from the fluid phase to the fluid-gel phase coexistence proceeds via near-critical fluctuations, while for other lipid…
Bilayer lipid membranes [BLMs] are an essential component of all biological systems, forming a functional barrier for cells and organelles from the surrounding environment. The lipid molecules that form membranes contain both permanent and induced dipoles, and an electric field can induce the formation of pores when the transverse field is sufficiently strong (electroporation). Here, a phenomenological free energy is constructed to model the response of a BLM to a transverse static electric field. The model contains a continuum description of the membrane dipoles and a coupling between the hea…
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic interactions and membrane curvature. Though the lateral diffusion rates of lipids on membrane of various compositions are measured and the electrostatic free energies of predetermined protein-membrane-lipid systems can be computed, the process of the aggregation and the evolution to the electrostatically favorable states remain undetermined. Here we propose an …
We study the indentation of a free-standing lipid membrane suspended over a nanopore on a hydrophobic substrate by means of molecular dynamics simulations. We find that in the course of indentation, the membrane bends at the point of contact, and the fringes of the membrane glide downward intermittently along the pore edges and stop gliding when the fringes reach the edge bottoms. The bending continues afterwards, and the large strain eventually induces a phase transition in the membrane, transformed from a bilayered structure to an interdigitated structure. The membrane is finally ruptured wh…
The impact of nanomaterials on lung fluids or on the plasma membrane of living cells has prompted researchers to examine the interactions between nanoparticles and lipid vesicles. Recent studies have shown that nanoparticle-lipid interaction leads to a broad range of structures including supported lipid bilayers (SLB), particles adsorbed at the surface or internalized inside vesicles, and mixed aggregates. Today, there is a need to have simple protocols that can readily assess the nature of structures obtained from particles and vesicles. Here we apply the method of continuous variation for me…
We reproduce the symmetric and asymmetric ``rippled'' $P_{β'}$ states of lipid membranes by Monte Carlo simulations of a coarse-grained molecular model for lipid-solvent mixtures. The structure and properties compare favorably with experiments. The asymmetric ripple state is characterized by a periodic array of fully interdigitated ``defect'' lines. The symmetric ripple state maintains a bilayer structure, but is otherwise structurally similar. The formation of both ripple states is driven by the propensity of lipid molecules with large head groups to exhibit splay.
In vivo and in vitro lipid bilayers are commonly supported by subcellular structures, particles, and artificial substrates. Deformation of the underlying structure can lead to large, localized deformations as the bilayer deforms to avoid stretching. In this work, we consider the effect of defects within the underlying substrate by simulating different bilayers supported by continuous and nanoporous substrates. We show that the bilayer behavior greatly depends on strain rate, and that substrate defects may contribute to the formation of nanotubes for compressed substrate.
We investigate how an externally imposed curvature influences lipid segregation on two-phase-coexistent membranes. We show that the bending-modulus contrast of the two phases and the curvature act together to yield a reduced effective line tension. On largely curved membranes, a state of multiple domains (or rafts) forms due to a mechanism analogous to that causing magnetic-vortex formation in type-II superconductors. We determine the criterion for such multi-domain state to occur; we then calculate respectively the size of the domains formed on cylindrically and spherically curved membranes.
With the aim of establishing a criterion for identifying when a lipid bilayer has reached steady state using the molecular dynamics simulation technique, lipid bilayers of different composition in their liquid crystalline phase were simulated in aqueous solution in presence of CaCl$_2$ as electrolyte, at different concentration levels. In this regard, we used two different lipid bilayer systems: one composed by 288 DPPC (DiPalmitoylPhosphatidylCholine) and another constituted by 288 DPPS (DiPalmitoylPhosphatidylSerine). In this sense, for both type of lipid bilayers, we have studied the tempor…
The theory of irreversible thermodynamics for arbitrarily curved lipid membranes is presented here. The coupling between elastic bending and irreversible processes such as intra-membrane lipid flow, intra-membrane phase transitions, and protein binding and diffusion is studied. The forms of the entropy production for the irreversible processes are obtained, and the corresponding thermodynamic forces and fluxes are identified. Employing the linear irreversible thermodynamic framework, the governing equations of motion along with appropriate boundary conditions are provided.
The activation kinetics of the ion channels formed by colicin Ia incorporated into a planar bilayer lipid membrane (BLM) was investigated by the voltage clamp technique using different step voltage stimuli. The temporal behaviour of ion channels put in evidence a gain or a loss of memory, revealed by a specific sequence of electrical pulses used for stimulation.
We describe a simple coarse-grained model which is suited to study lipid layers and their phase transitions. Lipids are modeled by short semiflexible chains of beads with a solvophilic head and a solvophobic tail component. They are forced to self-assemble into bilayers by a computationally cheap `phantom solvent' environment. The model reproduces the most important phases and phase transitions of monolayers and bilayers. Technical issues such as Monte Carlo parallelization schemes are briefly discussed.
We study the deformation of a lipid membrane in response to a local pH modification. Experimentally, a basic solution is microinjected close to a giant unilamellar vesicle. A local deformation appears in the zone of the membrane that is closest to the micropipette, and relaxes when the injection is stopped. A theoretical description of this phenomenon is provided. It takes fully into account the spatiotemporal evolution of the concentration of hydroxide ions during and after the microinjection, as well as the linear dynamics of the membrane. This description applies to a local injection of any…
As two-dimensional fluid shells, lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses. This property gives membranes the ability to adopt dramatic shape changes. In this paper, a finite element model is developed to study static equilibrium mechanics of membranes. In particular, a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers. The Augmented Lagrangian method is used to enforce global constraints on area and volume during membrane deformations. As a validation of…
Amphiphilic lipid bilayers modify the friction properties of the surfaces on top of which they are deposited. In particular, the measured sliding friction coefficient is significantly reduced compared with the native surface. We investigate in this work the friction properties of a numerical coarse-grained model of DSPC (1,2-distearoyl-sn-glycero-3-phosphocholine) lipid bilayer subject to longitudinal shear. The interleaflet friction coefficient is obtained from out-of-equilibrium pulling and relaxation simulations. In particular, we gain access to the transient viscoelastic response of a shea…
Animal cells are both encapsulated and subdivided by lipid bilayer membranes. Beyond just acting as boundaries, these membranes' shapes influence the function of cells and their compartments. Physically, membranes are two-dimensional fluids with complex elastic behavior, which makes it impossible, for all but a few simple cases, to predict membrane shapes analytically. Instead, the shape and behavior of biological membranes can be determined by simulations. However, the setup and use of such simulations require a significant programming background. The availability of open-source and user-frie…
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition of two-phase vesicles in the budding state; (iv) nonlocal theory of membrane elasticity; (v) relationship between symmetry and the magnitude of free energy.
In biological membranes, alpha-tocopherols (α-toc; vitamin E) protect polyunsaturated lipids from free radicals. Although the interactions of α-toc with non-oxidized lipid bilayers have been studied, their on oxidized bilayers remain unknown. In this study, atomistic molecular dynamics (MD) simulations of oxidized lipid bilayers were performed with varying concentrations of α-toc. Bilayers with 1-palmitoyl-2-lauroyl-sn-glycero-3-phosphocholine (PLPC) lipids and its aldehyde derivatives at 1:1 ratio were studied. Our simulations show that oxidized lipids self-assemble into aggregates with a wat…
Using Coarse-Grained Molecular Dynamics simulations, we study the relaxation of bilayer vesicles, uniaxially compressed by an Atomic Force Microscope (AFM) cantilever. The relaxation time exhibits a strong force-dependence. Force-compression curves are very similar to recent experiments wherein giant unilamellar vesicles were compressed in a nearly identical manner.
Combining extensive molecular dynamics simulations of lipid bilayer systems of varying chemical composition with single-trajectory analyses we systematically elucidate the stochastic nature of the lipid motion. We observe subdiffusion over more than four orders of magnitude in time, clearly stretching into the sub-microsecond domain. The lipid motion delicately depends on the lipid chemistry, the lipid phase, and especially on the presence of cholesterol. We demonstrate that fractional Langevin equation motion universally describes the lipid motion in all phases including the gel phase, and in…
BAR superfamily proteins have a banana-shaped domain that causes the local bending of lipid membranes. We study as to how such a local anisotropic curvature induces effective interaction between proteins and changes the global shape of vesicles and membrane tubes using meshless membrane simulations. The proteins are modeled as banana-shaped rods strongly adhered to the membrane. Our study reveals that the rods assemble via two continuous directional phase separations unlike a conventional two-dimensional phase separation. As the rod curvature increases, in the membrane tube the rods assemble a…
It is well known that at the gel-liquid phase transition temperature a lipid bilayer membrane exhibits an increased ion permeability. We analyze the quantized currents in which the increased permeability presents itself. The open time histogram shows a "-3/2" power law which implies an open-closed transition rate that decreases like $k(t) \propto t^{-1}$ as time evolves. We propose a "pore freezing" model to explain the observations. We discuss how this model also leads to the $1/f^α$ noise that is commonly observed in currents across biological and artificial membranes.
Understanding interactions between microparticles and lipid membranes is of increasing importance, especially for unraveling the influence of microplastics on our health and environment. Here, we study how a short-ranged adhesive force between microparticles and model lipid membranes causes membrane-mediated particle assembly. Using confocal microscopy, we observe the initial particle attachment to the membrane, then particle wrapping, and in rare cases spontaneous membrane tubulation. In the attached state, we measure that the particle mobility decreases by 26%. If multiple particles adhere t…
