Variation of lipid membrane composition caused by strong bending

Dynamic coupling between the morphology and molecular composition of cellular membranes is crucial for formation of the intracellular organelles and transport vesicles. Most of the membrane proteins and lipids discriminate membrane curvatures. However, it remains unclear whether the curvature alone is sufficient to support heterogeneous distribution of lipids. Here we demonstrate that the curvature-driven redistribution of phospholipids, such as dioleoylphosphatidylethanolamine (DOPE), requires strong membrane bending. We used cylindrical lipid nanotubes (NTs) pulled from planar lipid membranes with lateral tension of ∼1 dyn/cm. Such high tensions forced extreme curvatures of the NT membrane, with luminal radius approaching the thickness of the lipid bilayer, 5nm. When the NT contained lipid species with high spontaneous curvature (SC), such as DOPE, we observed slow reduction of its radius. This reduction indicated the redistribution of DOPE between the inner and outer monolayers of the NT. Accordingly, the SC of DOPE was recovered from the measured changes in the radii: the SC value, calculated under the assumption that the DOPE content is coupled to the monolayer curvature, was ∼0.4 nm⁻¹, consistent with the published data. Thus, redistribution of lipids should be taken into account in calculations of composition and material properties of strongly deformed membrane structures, such as intermediate structures arising in the processes of membrane fusion and fission.     

Calculation of line tension in various models of lipid bilayer pore edge

The line tension of the edge of the lipid bilayer pore is calculated on the basis of the elastic theory of continuous liquid-crystal medium. Three types of deformations of the membrane were taken into account: bending, lateral stretching/compression, and tilt of the lipidic tails. Various models of structure of the pore edge are considered: models of the cylindrical shape with given radius and optimum radius, “extrapolational” model, “two-coordinate” model, and model with a hydrophobic cavity (“void”). Models can be conventionally divided into two classes. The first class includes models in which membrane monolayers are in contact with each other everywhere. Models of the second class admit appearance of a hydrophobic cavity between monolayers. Models of the first class yield value of the line tension γ, strongly differing from that known from the literature (～10 pN). For example, the value of the line tension γ obtained in the cylindrical model equals to 21 pN; in the two-coordinate model, 19 pN, and in the extrapolational model, 62 pN. At the same time, the model with cavity gives the value of γ eqal ～10 pN, provided that surface tension at the boundary of the lipid tails is close to zero. This value is in a good agreement with the literature data.     

Mechanism of pore formation in stearoyl-oleoyl-phosphatidylcholine membranes subjected to lateral tension

Theoretical model of a through pore formation in lipid bilayer membrane under applied lateral tension was developed. In the framework of elastic theory of liquid crystals adapted to lipid membranes, we calculated a continuous trajectory from intact bilayer through a hydrophobic defect to a through pore. It was shown that the major energetic characteristic of membrane stability with respect to the pore formation, i. e., line tension, depends both on the pore radius and on the value of the applied lateral tension. This leads to a non-monotonous dependence of the average waiting time of the pore formation on the lateral tension: at low tensions the waiting time was large, then there was a local minimum, after which the average waiting time was increasing again. For membranes formed from stearoyl oleoyl phosphatidylcholine, the local minimum corresponded to the lateral tension of 7 mN/m; the calculated value of the edge line tension of a large pore was 16.5 pN. These results are consistent with available experimental data.     

Fission of membrane nanotube induced by osmotic pressure

The final stage of endocytosis is fission of a thin membrane neck, or nanotube (NT), connecting cell membrane with a forming vesicle. We studied this process using a model system consisting of NT pulled out from a flat bilayer lipid membrane. Fission of NT was induced by an increase of osmotic pressure created by local application of a concentrated salt solution in the vicinity of NT. Superfusion of NT with distilled water instead of the concentrated salt solution led to the NT expansion. This observation demonstrates the reversibility of the NT expansion-compression process under the osmotic pressure. The overall picture of fission is similar to that described earlier for the NT fission with participation of dynamin GTPase. In both cases, in order for fission to occur, it is necessary to compress the NT to a critical radius. The critical radius estimated for the osmotic pressure-induced fission exceeds the value obtained for the fission occurring in the presence of the protein. Fission under osmotic pressure, akin the dynamin-promoted fission, proceeds without leaky defects.     

Effect of membrane tension on the physical properties of DOPC lipid bilayer membrane

Molecular dynamics simulations of a dioleoylphosphocholine (DOPC) lipid bilayer were performed to explore its mechanosensitivity. Variations in the bilayer properties, such as area per lipid, volume, thickness, hydration depth (HD), hydration thickness (HT), lateral diffusion coefficient, and changes in lipid structural order were computed in the membrane tension range 0 to 15dyn/cm. We determined that an increase in membrane tension results in a decrease in the bilayer thickness and HD of ~5% and ~5.7% respectively, whereas area per lipid, volume, and HT/HD increased by 6.8%, 2.4%, and 5% respectively. The changes in lipid conformation and orientation were characterized using orientational (S(2)) and deuterium (S(CD)) order parameters. Upon increase of membrane tension both order parameters indicated an increase in lipid disorder by 10-20%, mostly in the tail end region of the hydrophobic chains. The effect of membrane tension on lipid lateral diffusion in the DOPC bilayer was analyzed on three different time scales corresponding to inertial motion, anomalous diffusion and normal diffusion. The results showed that lateral diffusion of lipid molecules is anomalous in nature due to the non-exponential distribution of waiting times. The anomalous and normal diffusion coefficients increased by 20% and 52% when the membrane tension changed from 0 to 15dyn/cm, respectively. In conclusion, our studies showed that membrane tension causes relatively significant changes in the area per lipid, volume, polarity, membrane thickness, and fluidity of the membrane suggesting multiple mechanisms by which mechanical perturbation of the membrane could trigger mechanosensitive response in cells.     

Energetic and spatial parameters for gating of the bacterial large conductance mechanosensitive channel, MscL

MscL is multimeric protein that forms a large conductance mechanosensitive channel in the inner membrane of Escherichia coli. Since MscL is gated by tension transmitted through the lipid bilayer, we have been able to measure its gating parameters as a function of absolute tension. Using purified MscL reconstituted in liposomes, we recorded single channel currents and varied the pressure gradient (P) to vary the tension (T). The tension was calculated from P and the radius of curvature was obtained using video microscopy of the patch. The probability of being open (Po) has a steep sigmoidal dependence on T, with a midpoint (T1/2) of 11.8 dyn/cm. The maximal slope sensitivity of Po/Pc was 0.63 dyn/cm per e-fold. Assuming a Boltzmann distribution, the energy difference between the closed and fully open states in the unstressed membrane was DeltaE = 18.6 kBT. If the mechanosensitivity arises from tension acting on a change of in-plane area (DeltaA), the free energy, TDeltaA, would correspond to DeltaA = 6.5 nm2. MscL is not a binary channel, but has four conducting states and a closed state. Most transition rates are independent of tension, but the rate-limiting step to opening is the transition between the closed state and the lowest conductance substate. This transition thus involves the greatest DeltaA. When summed over all transitions, the in-plane area change from closed to fully open was 6 nm2, agreeing with the value obtained in the two-state analysis. Assuming a cylindrical channel, the dimensions of the (fully open) pore were comparable to DeltaA. Thus, the tension dependence of channel gating is primarily one of increasing the external channel area to accommodate the pore of the smallest conducting state. The higher conducting states appear to involve conformational changes internal to the channel that don't involve changes in area.     

Fission of the bilayer lipid tube

The fusion of two black lipid membranes results in the formation of peculiar bilayer lipid tubes (‘cylindrical’) membranes (Neher, E. (1974) Biochim. Biophys. Acta 373, 328–336 and Melikyan, G.B., Abidor, L.G., Chernomordik, L.V. and Chailakhyan, L.M. (1983) Biochim. Biophys. Acta 730, 395–398). The mechanical stability of such tubes has been investigated experimentally and theoretically. With increasing hydrostatic pressure on the outside of the tube the radius of its middle part decreases. After this radius has reached a critical value, which constitutes 0.55 of the radius of the tube base, there occurs a collapse of the tube and its disintegration into two planar bilayers (fission). Expressions are obtained which relate the transmembrane difference of the hydrostatic pressure, causing the collapse, to the geometrical characteristics of the tube (its length and the radius of its base) and to the tension of the lipid bilayer. A method for measuring the membrane tension is proposed on the basis of the phenomenon considered.     

Hydrodynamic properties of a double-helical model for DNA.

The translational and rotational diffusion coefficients of very short DNA fragments have been calculated using a double-helical bead model in which each nucleotide is represented by one bead. The radius of the helix is regarded as an adjustable parameter. The translational coefficient and the perpendicular rotation coefficient agree very well with experimental values for oligonuclotides with 8, 12, and 20 base pairs, for a single value of the helical radius of about 10 A. We have also calculated a nuclear magnetic resonance relaxation time in which the coefficient for rotation about the main axis is involved. As found previously with cylindrical models, the results deviate from experimental values, indicating that the internal motion of the bases has a remarkable amplitude. An attempt to quantify the extent of internal motions is presented.     

Assessment of potential stimuli for mechano-dependent gating of MscL: effects of pressure, tension, and lipid headgroups

MscL is a mechanosensitive channel of large conductance that serves as an "emergency relief valve", protecting bacteria from acute hypoosmotic stress. Although it is well-accepted that the MscL protein and an adequate membrane matrix are necessary and sufficient for the function of this channel, the exact role of the membrane has yet to be elucidated. Here, we address the role of the membrane matrix through in vitro reconstitution of the MscL protein in defined lipid bilayers. We have applied Laplace's law to visualized membrane patches where we can measure patch curvature as described in previous studies. Here, by comparing patches with different curvatures, we demonstrate that the MscL channel senses tension within the membrane and that the pressure across it plays no detectable role as a stimulus. In addition, gating only occurs when the smallest radius of curvature is nearly achieved, suggesting that the lateral tension rather than membrane curvature is the important biophysical parameter. Finally, we have examined the contribution of specific headgroups by measuring their effect on the membrane tension required to gate the channel. We have found that the addition of neither anionic nor endogenous lipids to a non-native membrane effected a leftward shift in the activation curve. In fact, the major endogenous lipid of the Escherichia coli membrane, phosphatidylethanolamine, led to a channel activity at a higher tension threshold, suggesting that this lipid effects altered activity through changes in the biophysical properties of the membrane, rather than through an MscL-specific interaction.     

Computational investigation of pressure profiles in lipid bilayers with embedded proteins

The distribution of surface tension within a lipid bilayer, also referred to as the lateral pressure profile, has been the subject of theoretical scrutiny recently due to its potential to radically alter the function of biomedically important membrane proteins. Experimental measurements of the pressure profile are still hard to come by, leaving first-principles all-atom calculations of the profile as an important investigative tool. We describe and validate an efficient implementation of pressure profile calculations in the molecular dynamics package NAMD, capable of distinguishing between internal, bonded and nonbonded contributions as well as those of selected atom groups. The new implementation can also be used in conjunction with Ewald summation for long-range electrostatics, improving the accuracy and reproducibility of the calculated profiles. We then describe results of the calculation of a pressure profile for a simple protein–lipid system consisting of melittin embedded in a DMPC bilayer. While the lateral pressure in the protein–lipid system is nearly the same as that of the bilayer alone, partitioning of the lateral pressure by atom type revealed substantial perturbation of the pressure profile and surface tension in an asymmetric manner.     

Aqueous viscosity is the primary source of friction in lipidic pore dynamics

A new theory, to our knowledge, is developed that describes the dynamics of a lipidic pore in a liposome. The equations of the theory capture the experimentally observed three-stage functional form of pore radius over time—stage 1, rapid pore enlargement; stage 2, slow pore shrinkage; and stage 3, rapid pore closure. They also show that lipid flow is kinetically limited by the values of both membrane and aqueous viscosity; therefore, pore evolution is affected by both viscosities. The theory predicts that for a giant liposome, tens of microns in radius, water viscosity dominates over the effects of membrane viscosity. The edge tension of a lipidic pore is calculated by using the theory to quantitatively account for pore kinetics in stage 3, rapid pore closing. This value of edge tension agrees with the value as standardly calculated from the stage of slow pore closure, stage 2. For small, submicron liposomes, membrane viscosity affects pore kinetics, but only if the viscosity of the aqueous solution is comparable to that of distilled water. A first-principle fluid-mechanics calculation of the friction due to aqueous viscosity is in excellent agreement with the friction obtained by applying the new theory to data of previously published experimental results.     

Probing the mechanism of fusion in a two-dimensional computer simulation

A two-dimensional (2D) model of lipid bilayers was developed and used to investigate a possible role of membrane lateral tension in membrane fusion. We found that an increase of lateral tension in contacting monolayers of 2D analogs of liposomes and planar membranes could cause not only hemifusion, but also complete fusion when internal pressure is introduced in the model. With a certain set of model parameters it was possible to induce hemifusion-like structural changes by a tension increase in only one of the two contacting bilayers. The effect of lysolipids was modeled as an insertion of a small number of extra molecules into the cis or trans side of the interacting bilayers at different stages of simulation. It was found that cis insertion arrests fusion and trans insertion has no inhibitory effect on fusion. The possibility of protein participation in tension-driven fusion was tested in simulation, with one of two model liposomes containing a number of structures capable of reducing the area occupied by them in the outer monolayer. It was found that condensation of these structures was sufficient to produce membrane reorganization similar to that observed in simulations with "protein-free" bilayers. These data support the hypothesis that changes in membrane lateral tension may be responsible for fusion in both model phospholipid membranes and in biological protein-mediated fusion.     

Theoretical Analysis of Membrane Tension in Moving Cells

Lateral tension in cell plasma membranes plays an essential role in regulation of a number of membrane-related intracellular processes and cell motion. Understanding the physical factors generating the lateral tension and quantitative determination of the tension distribution along the cell membrane is an emerging topic of cell biophysics. Although experimental data are accumulating on membrane tension values in several cell types, the tension distribution along the membranes of moving cells remains largely unexplored. Here we suggest and analyze a theoretical model predicting the tension distribution along the membrane of a cell crawling on a flat substrate. We consider the tension to be generated by the force of actin network polymerization against the membrane at the cell leading edge. The three major factors determining the tension distribution are the membrane interaction with anchors connecting the actin network to the lipid bilayer, the membrane interaction with cell adhesions, and the force developing at the rear boundary due to the detachment of the remaining cell adhesion from the substrate in the course of cell crawling. Our model recovers the experimentally measured values of the tension in fish keratocytes and their dependence on the number of adhesions. The model predicts, quantitatively, the tension distribution between the leading and rear membrane edges as a function of the area fractions of the anchors and the adhesions.     

Theoretical Analysis of Membrane Tension in Moving Cells

Lateral tension in cell plasma membranes plays an essential role in regulation of a number of membrane-related intracellular processes and cell motion. Understanding the physical factors generating the lateral tension and quantitative determination of the tension distribution along the cell membrane is an emerging topic of cell biophysics. Although experimental data are accumulating on membrane tension values in several cell types, the tension distribution along the membranes of moving cells remains largely unexplored. Here we suggest and analyze a theoretical model predicting the tension distribution along the membrane of a cell crawling on a flat substrate. We consider the tension to be generated by the force of actin network polymerization against the membrane at the cell leading edge. The three major factors determining the tension distribution are the membrane interaction with anchors connecting the actin network to the lipid bilayer, the membrane interaction with cell adhesions, and the force developing at the rear boundary due to the detachment of the remaining cell adhesion from the substrate in the course of cell crawling. Our model recovers the experimentally measured values of the tension in fish keratocytes and their dependence on the number of adhesions. The model predicts, quantitatively, the tension distribution between the leading and rear membrane edges as a function of the area fractions of the anchors and the adhesions.     

Nonlinear material and ionic transport through membrane nanotubes

Membrane nanotubes (NTs) and their networks play an important role in intracellular membrane transport and intercellular communications. The transport characteristics of the NT lumen resemble those of conventional solid-state nanopores. However, unlike the rigid pores, the soft membrane wall of the NT can be deformed by forces driving the transport through the NT lumen. This intrinsic coupling between the NT geometry and transport properties remains poorly explored. Using synchronized fluorescence microscopy and conductance measurements, we revealed that the NT shape was changed by both electric and hydrostatic forces driving the ionic and solute fluxes through the NT lumen. Far from the shape instability, the strength of the force effect is determined by the lateral membrane tension and is scaled with membrane elasticity so that the NT can be operated as a linear elastic sensor. Near shape instabilities, the transport forces triggered large-scale shape transformations, both stochastic and periodic. The periodic oscillations were coupled to a vesicle passage along the NT axis, resembling peristaltic transport. The oscillations were parametrically controlled by the electric field, making NT a highly nonlinear nanofluidic circuitry element with biological and technological implications.     

Lipid bilayer pressure profiles and mechanosensitive channel gating

The function of membrane proteins often depends on the proteins' interaction with their lipid environment, spectacularly so in the case of mechanosensitive channels, which are gated through tension mediated by the surrounding lipids. Lipid bilayer tension is distributed quite inhomogeneously, but neither the scale at which relevant variation takes place nor the effect of varying lipid composition or tension has yet been investigated in atomic detail. We calculated lateral pressure profile distributions in lipid bilayers of various composition from all-atom molecular dynamics simulations totaling 110.5 ns in length. Reproducible pressure profile features at the 1 A length scale were determined. Lipids with phosphatidylcholine headgroups were found to shift the lateral pressure out of the hydrophobic core and into the headgroup region by an amount that is independent of area per lipid. POPE bilayers simulated at areas smaller than optimal exerted dramatically higher lateral pressure in a narrow region at the start of the aliphatic chain. Stretching of POPC bilayers increased tension predominantly in the same region. A simple geometric analysis for the gating of the mechanosensitive channel MscL suggests that pressure profiles affect its gating through the second moment of the profile in a tension-independent manner.     

Size distribution of barrel-stave aggregates of membrane peptides: influence of the bilayer lateral pressure profile

Some membrane peptides, such as Alamethicin, form barrel-stave aggregates with a broad probability distribution of size (number of peptides in the aggregate). This distribution has been shown to depend on the characteristics of the lipid bilayer. A mechanism for this influence is suggested, in analogy to earlier work on the effects of changes in bilayer composition on conformational equilibria in membrane proteins, that is based on coupling of shifts in the distribution of lateral pressures in the bilayer to depth-dependent changes in the lateral excluded area that accompanies the formation of an aggregate. Thermodynamic analysis is coupled with a simple geometric model of aggregates of kinked cylindrical peptides and with results of previously calculated lateral pressure distributions to predict the effects of changes in bilayer characteristics on aggregate size distributions, in qualitative agreement with experimental results.     

A finite element framework for studying the mechanical response of macromolecules: application to the gating of the mechanosensitive channel MscL

The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the membrane. Compared to popular all-atom-based techniques such as targeted or steered molecular-dynamics simulations, the finite element method-based continuum-mechanics framework offers a unique alternative to bridge detailed intermolecular interactions and biological processes occurring at large spatial scales and long timescales. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction.     

Lipid-glass adhesion in giga-sealed patch-clamped membranes.

Adhesion between patch-clamped lipid membranes and glass micropipettes is measured by high contrast video imaging of the mechanical response to the application of suction pressure across the patch. The free patch of membrane reversibly alters both its contact angle and radius of curvature on pressure changes. The assumption that an adhesive force between the membrane and the pipette can sustain normal tension up to a maximum Ta at the edge of the free patch accounts for the observed mechanical responses. When the normal component of the pressure-induced membrane tension exceeds Ta membrane at the contact point between the free patch and the lipid-glass interface is pulled away from the pipette wall, resulting in a decreased radius of curvature for the patch and an increased contact angle. Measurements of the membrane radius of curvature as a function of the suction pressure and pipette radius determine line adhesion tensions Ta which range from 0.5 to 4.0 dyn/cm. Similar behavior of patch-clamped cell membranes implies similar adhesion mechanics.