Minimum Membrane Bending Energies of Fusion Pores

Membranes fuse by forming highly curved intermediates, culminating in structures described as fusion pores. These hourglass-like figures that join two fusing membranes have high bending energies, which can be estimated using continuum elasticity models. Fusion pore bending energies depend strongly on shape, and the present study developed a method for determining the shape that minimizes bending energy. This was first applied to a fusion pore modeled as a single surface and then extended to a more realistic model treating a bilayer as two monolayers. For the two-monolayer model, fusion pores were found to have metastable states with energy minima at particular values of the pore diameter and bilayer separation. Fusion pore energies were relatively insensitive to membrane thickness but highly sensitive to spontaneous curvature and membrane asymmetry. With symmetrical bilayers and monolayer spontaneous curvatures of ?0.1 nm^?1 (a typical value) separated by 6 nm (closest distance determined by repulsive hydration forces), fusion pore formation required 43–65 kT. The pore radius of ~2.25 nm fell within the range estimated from conductance measurements. With bilayer separation >6 nm, fusion pore formation required less energy, suggesting that protein scaffolds can promote fusion by bending membranes toward one another. With nonzero spontaneous monolayer curvature, the shape that minimized the energy change during fusion pore formation differed from the shape that minimized its energy after it formed. Thus, a nascent fusion pore will relax spontaneously to a new shape, consistent with the experimentally observed expansion of nascent fusion pores during viral fusion.     

Curvature Generation and Pressure Profile Modulation in Membrane by Lysolipids: Insights from Coarse-Grained Simulations

Although many membrane additives are known to modulate the activities of membrane proteins via perturbing the properties of lipid membrane, the underlying mechanism is often not precisely understood. In this study, we investigate the impact of asymmetrically incorporating single-tailed lysophosphatidylcholine (LPC) into a membrane bilayer using coarse-grained molecular dynamics simulations. Using a simple computational protocol designed to approximately mimic a micropipette setting, we show that asymmetric incorporation of LPC can lead to significant curvature in a bilayer. Detailed analysis of geometrical and mechanical properties (pressure profile) of the resulting mound structure indicates that the degree of pressure profile perturbation is determined not by the local curvature per se but by the packing of lipid headgroups (i.e., area-per-lipid). The findings help provide a concrete basis for understanding the activation mechanism of mechanosensitive channels by asymmetric incorporation of LPC into membrane patches in patch-clamp experiments. The calculated local pressure profiles are valuable to the construction of realistic membrane models for the analysis of mechanosensation in a continuum mechanics framework.     

Magainin 2 and PGLa in bacterial membrane mimics IV: Membrane curvature and partitioning

We previously reported that the synergistically enhanced antimicrobial activity of magainin 2 (MG2a) and PGLa is related to membrane adhesion and fusion. Here, we demonstrate that equimolar mixtures of MG2a and L18W-PGLa induce positive monolayer curvature stress and sense, at the same time, positive mean and Gaussian bilayer curvatures already at low amounts of bound peptide. The combination of both abilities—membrane curvature sensing and inducing—is most likely the base for the synergistically enhanced peptide activity. In addition, our coarse-grained simulations suggest that fusion stalks are promoted by decreasing the free-energy barrier for their formation rather than by stabilizing their shape. We also interrogated peptide partitioning as a function of lipid and peptide concentration using tryptophan fluorescence spectroscopy and peptide-induced leakage of dyes from lipid vesicles. In agreement with a previous report, we find increased membrane partitioning of L18W-PGLa in the presence of MG2a. However, this effect does not prevail to lipid concentrations higher than 1 mM, above which all peptides associate with the lipid bilayers. This implies that synergistic effects of MG2a and L18W-PGLa in previously reported experiments with lipid concentrations >1 mM are due to peptide-induced membrane remodeling and not their specific membrane partitioning.     

Calculating Transition Energy Barriers and Characterizing Activation States for Steps of Fusion

We use continuum mechanics to calculate an entire least energy pathway of membrane fusion, from stalk formation, to pore creation, and through fusion pore enlargement. The model assumes that each structure in the pathway is axially symmetric. The static continuum stalk structure agrees quantitatively with experimental stalk architecture. Calculations show that in a stalk, the distal monolayer is stretched and the stored stretching energy is significantly less than the tilt energy of an unstretched distal monolayer. The string method is used to determine the energy of the transition barriers that separate intermediate states and the dynamics of two bilayers as they pass through them. Hemifusion requires a small amount of energy independently of lipid composition, while direct transition from a stalk to a fusion pore without a hemifusion intermediate is highly improbable. Hemifusion diaphragm expansion is spontaneous for distal monolayers containing at least two lipid components, given sufficiently negative diaphragm spontaneous curvature. Conversely, diaphragms formed from single-component distal monolayers do not expand without the continual injection of energy. We identify a diaphragm radius, below which central pore expansion is spontaneous. For larger diaphragms, prior studies have shown that pore expansion is not axisymmetric, and here our calculations supply an upper bound for the energy of the barrier against pore formation. The major energy-requiring deformations in the steps of fusion are: widening of a hydrophobic fissure in bilayers for stalk formation, splay within the expanding hemifusion diaphragm, and fissure widening initiating pore formation in a hemifusion diaphragm.     

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.     

Membrane Bending Energy and Fusion Pore Kinetics in Ca-Triggered Exocytosis

A fusion pore composed of lipid is an obligatory kinetic intermediate of membrane fusion, and its formation requires energy to bend membranes into highly curved shapes. The energetics of such deformations in viral fusion is well established, but the role of membrane bending in Ca²⁺-triggered exocytosis remains largely untested. Amperometry recording showed that during exocytosis in chromaffin and PC12 cells, fusion pores formed by smaller vesicles dilated more rapidly than fusion pores formed by larger vesicles. The logarithm of 1/(fusion pore lifetime) varied linearly with vesicle curvature. The vesicle size dependence of fusion pore lifetime quantitatively accounted for the nonexponential fusion pore lifetime distribution. Experimentally manipulating vesicle size failed to alter the size dependence of fusion pore lifetime. Manipulations of membrane spontaneous curvature altered this dependence, and applying the curvature perturbants to the opposite side of the membrane reversed their effects. These effects of curvature perturbants were opposite to those seen in viral fusion. These results indicate that during Ca²⁺-triggered exocytosis membrane bending opposes fusion pore dilation rather than fusion pore formation. Ca²⁺-triggered exocytosis begins with a proteinaceous fusion pore with less stressed membrane, and becomes lipidic as it dilates, bending membrane into a highly curved shape.     

Gating mechanism of mechanosensitive channel of large conductance: a coupled continuum mechanical-continuum solvation approach

Gating transition of the mechanosensitive channel of large conductance (MscL) represents a good example of important biological processes that are difficult to describe using atomistic simulations due to the large (submicron) length scale and long (millisecond) time scale. Here we develop a novel computational framework that tightly couples continuum mechanics with continuum solvation models to study the detailed gating behavior of E. coli-MscL. The components of protein molecules are modeled by continuum elements that properly describe their shape, material properties and physicochemical features (e.g., charge distribution). The lipid membrane is modeled as a three-layer material in which the lipid head group and tail regions are treated separately, taking into account the fact that fluidic lipid bilayers do not bear shear stress. Coupling between mechanical and chemical responses of the channel is realized by an iterative integration of continuum mechanics (CM) modeling and continuum solvation (CS) computation. Compared to previous continuum mechanics studies, the present model is capable of capturing the most essential features of the gating process in a much more realistic fashion: due mainly to the apolar solvation contribution, the membrane tension for full opening of MscL is reduced substantially to the experimental measured range. Moreover, the pore size stabilizes constantly during gating because of the intricate interactions of the multiple components of the system, implying the mechanism for sub-conducting states of MscL gating. A significant fraction (\(\sim \)2/3) of the gating membrane strain is required to reach the first sub-conducting state of our model, which is featured with a relative conductance of 0.115 to the fully opened state. These trends agree well with experimental observations. We anticipate that the coupled CM/CS modeling framework is uniquely suited for the analysis of many biomolecules and their assemblies under external mechanical stimuli.     

Modeling membrane shaping by proteins: Focus on EHD2 and N-BAR domains

Cellular membranes are highly dynamic, undergoing both persistent and dynamic shape changes driven by specialized proteins. The observed membrane shaping can be simple deformations of existing shapes or membrane remodeling involving fission or fusion. Here we describe several mechanistic principles by which membrane shaping proteins act. We especially consider models for membrane bending and fission by EHD2 proteins and membrane bending by N-BAR domains. There are major challenges ahead to understand the general principles by which diverse membrane bending proteins act and to understand how some proteins appear to span multiple modes of action from driving curvature to inducing membrane remodeling.     

Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape

Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes.     

Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape

Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes.     

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.     

Fusion pore stability of peptidergic vesicles

Abstract

It is believed that in regulated exocytosis the vesicle membrane fuses with the plasma membrane in response to a physiological stimulus. However, in the absence of stimulation, repetitive transient fusion events are also observed, reflecting a stable state. The mechanisms by which the initial fusion pore attains stability are poorly understood. We modelled energetic stability of the fusion pore by taking into account the anisotropic, intrinsic shape of the membrane constituents and their in-plane ordering in the local curvature of the membrane. We used cell-attached membrane capacitance techniques to monitor the appearance and conductance of single fusion pore events in cultured rat lactotrophs. The results revealed a bell-shaped distribution of the fusion pore conductance with a modal value of 25 pS. The experimentally observed increase of the fusion pore stability with decreasing fusion pore radius agrees well with the theoretical predictions. Moreover, the results revealed a correlation between the amplitude of transient capacitance increases and the fusion pore conductance, indicating that larger vesicles may attain a stable fusion pore with larger fusion pore diameters.     

Aggregation of model membrane proteins, modulated by hydrophobic mismatch, membrane curvature, and protein class

Aggregation of transmembrane proteins is important for many biological processes, such as protein sorting and cell signaling, and also for in vitro processes such as two-dimensional crystallization. We have used large-scale simulations to study the lateral organization and dynamics of lipid bilayers containing multiple inserted proteins. Using coarse-grained molecular dynamics simulations, we have studied model membranes comprising ∼7000 lipids and 16 identical copies of model cylindrical proteins of either α-helical or β-barrel types. Through variation of the lipid tail length and hence the degree of hydrophobic mismatch, our simulations display levels of protein aggregation ranging from negligible to extensive. The nature and extent of aggregation are shown to be influenced by membrane curvature and the shape or orientation of the protein. Interestingly, a model β-barrel protein aggregates to form one-dimensional strings within the bilayer plane, whereas a model α-helical bundle forms two-dimensional clusters. Overall, it is clear that the nature and extent of membrane protein aggregation is dependent on several aspects of the proteins and lipids, including hydrophobic mismatch, protein class and shape, and membrane curvature.     

Inner but Not Outer Membrane Leaflets Control the Transition from Glycosylphosphatidylinositol-anchored Influenza Hemagglutinin-induced Hemifusion to Full Fusion

Cells that express wild-type influenza hemagglutinin (HA) fully fuse to RBCs, while cells that express the HA-ectodomain anchored to membranes by glycosylphosphatidylinositol, rather than by a transmembrane domain, only hemifuse to RBCs. Amphipaths were inserted into inner and outer membrane leaflets to determine the contribution of each leaflet in the transition from hemifusion to fusion. When inserted into outer leaflets, amphipaths did not promote the transition, independent of whether the agent induces monolayers to bend outward (conferring positive spontaneous monolayer curvature) or inward (negative curvature). In contrast, when incorporated into inner leaflets, positive curvature agents led to full fusion. This suggests that fusion is completed when a lipidic fusion pore with net positive curvature is formed by the inner leaflets that compose a hemifusion diaphragm. Suboptimal fusion conditions were established for RBCs bound to cells expressing wild-type HA so that lipid but not aqueous dye spread was observed. While this is the same pattern of dye spread as in stable hemifusion, for this “stunted” fusion, lower concentrations of amphipaths in inner leaflets were required to promote transfer of aqueous dyes. Also, these amphipaths induced larger pores for stunted fusion than they generated within a stable hemifusion diaphragm. Therefore, spontaneous curvature of inner leaflets can affect formation and enlargement of fusion pores induced by HA. We propose that after the HA-ectodomain induces hemifusion, the transmembrane domain causes pore formation by conferring positive spontaneous curvature to leaflets of the hemifusion diaphragm.     

Imaging Plasma Membrane Deformations With pTIRFM

To gain novel insights into the dynamics of exocytosis, our group focuses on the changes in lipid bilayer shape that must be precisely regulated during the fusion of vesicle and plasma membranes. These rapid and localized changes are achieved by dynamic interactions between lipids and specialized proteins that control membrane curvature. The absence of such interactions would not only have devastating consequences for vesicle fusion, but a host of other cellular functions that involve control of membrane shape. In recent years, the identity of a number of proteins with membrane-shaping properties has been determined. What remains missing is a roadmap of when, where, and how they act as fusion and content release progress.Our understanding of the molecular events that enable membrane remodeling has historically been limited by a lack of analytical methods that are sensitive to membrane curvature or have the temporal resolution to track rapid changes. PTIRFM satisfies both of these criteria. We discuss how pTIRFM is implemented to visualize and interpret rapid, submicron changes in the orientation of chromaffin cell membranes during dense core vesicle (DCV) fusion. The chromaffin cells we use are isolated from bovine adrenal glands. The membrane is stained with a lipophilic carbocyanine dye,1,1''-dioctadecyl-3,3,3'',3''-tetramethylindodicarbocyanine, 4-chlorobenzenesulfonate, or diD. DiD intercalates in the membrane plane with a "fixed" orientation and is therefore sensitive to the polarization of the evanescent field. The diD-stained cell membrane is sequentially excited with orthogonal polarizations of a 561 nm laser (p-pol, s-pol). A 488 nm laser is used to visualize vesicle constituents and time the moment of fusion. Exocytosis is triggered by locally perfusing cells with a depolarizing KCl solution. Analysis is performed offline using custom-written software to understand how diD emission intensity changes relate to fusion pore dilation.     

Lipid flow through fusion pores connecting membranes of different tensions.

When two membranes fuse, their components mix; this is usually described as a purely diffusional process. However, if the membranes are under different tensions, the material will spread predominantly by convection. We use standard fluid mechanics to rigorously calculate the steady-state convective flux of lipids. A fusion pore is modeled as a toroid shape, connecting two planar membranes. Each of the membrane monolayers is considered separately as incompressible viscous media with the same shear viscosity, etas. The two monolayers interact by sliding past each other, described by an intermonolayer viscosity, etar. Combining a continuity equation with an equation that balances the work provided by the tension difference, Deltasigma, against the energy dissipated by flow in the viscous membrane, yields expressions for lipid velocity, upsilon, and area of lipid flux, Phi. These expressions for upsilon and Phi depend on Deltasigma, etas, etar, and geometrical aspects of a toroidal pore, but the general features of the theory hold for any fusion pore that has a roughly hourglass shape. These expressions are readily applicable to data from any experiments that monitor movement of lipid dye between fused membranes under different tensions. Lipid velocity increases nonlinearly from a small value for small pore radii, rp, to a saturating value at large rp. As a result of velocity saturation, the flux increases linearly with pore radius for large pores. The calculated lipid flux is in agreement with available experimental data for both large and transient fusion pores.     

Water under the BAR

Many cellular processes require the generation of highly curved regions of cell membranes by interfacial membrane proteins. A number of such proteins are now known, and several mechanisms of curvature generation have been suggested, but so far a quantitative understanding of the importance of the various potential mechanisms remains elusive. Following previous theoretical work, we consider the electrostatic attraction that underlies the scaffold mechanism of membrane bending in the context of the N-BAR domain of amphiphysin. Analysis of atomistic molecular dynamics simulations reveals considerable water between the membrane and the positively charged concave face of the BAR, even when it is tightly bound to highly curved membranes. This results in significant screening of electrostatic interactions, suggesting that electrostatic attraction is not the main driving force behind curvature sensing, supporting recent experimental work. These results also emphasize the need for care when building coarse-grained models of protein-membrane interactions. These results are emphasized by simulations of oligomerized amphiphysin N-BARs at the atomistic and coarse-grained level. In the coarse-grained simulations, we find a strong dependence of the induced curvature on the dielectric screening.     

Spontaneous local membrane curvature induced by transmembrane proteins

The (local) curvature of cellular membranes acts as a driving force for the targeting of membrane-associated proteins to specific membrane domains, as well as a sorting mechanism for transmembrane proteins, e.g., by accumulation in regions of matching spontaneous curvature. The latter measure was previously experimentally employed to study the curvature induced by the potassium channel KvAP and by aquaporin AQP0. However, the direction of the reported spontaneous curvature levels as well as the molecular driving forces governing the membrane curvature induced by these integral transmembrane proteins could not be addressed experimentally.Here, using both coarse-grained and atomistic molecular dynamics (MD) simulations, we report induced spontaneous curvature values for the homologous potassium channel Kv 1.2/2.1 Chimera (KvChim) and AQP0 embedded in unrestrained lipid bicelles that are in very good agreement with experiment. Importantly, the direction of curvature could be directly assessed from our simulations: KvChim induces a strong positive membrane curvature ($\approx 0.036$ nm^?1) whereas AQP0 causes a comparably small negative curvature ($\approx ?0.019$ nm^?1).Analyses of protein-lipid interactions within the bicelle revealed that the potassium channel shapes the surrounding membrane via structural determinants. Differences in shape of the protein-lipid interface of the voltage-gating domains between the extracellular and cytosolic membrane leaflets induce membrane stress and thereby promote a protein-proximal membrane curvature. In contrast, the water pore AQP0 displayed a high structural stability and an only faint effect on the surrounding membrane environment that is connected to its wedge-like shape.     

Changing Chromatin Fiber Conformation by Nucleosome Repositioning

Chromatin conformation is dynamic and heterogeneous with respect to nucleosome positions, which can be changed by chromatin remodeling complexes in the cell. These molecular machines hydrolyze ATP to translocate or evict nucleosomes, and establish loci with regularly and more irregularly spaced nucleosomes as well as nucleosome-depleted regions. The impact of nucleosome repositioning on the three-dimensional chromatin structure is only poorly understood. Here, we address this issue by using a coarse-grained computer model of arrays of 101 nucleosomes considering several chromatin fiber models with and without linker histones, respectively. We investigated the folding of the chain in dependence of the position of the central nucleosome by changing the length of the adjacent linker DNA in basepair steps. We found in our simulations that these translocations had a strong effect on the shape and properties of chromatin fibers: i), Fiber curvature and flexibility at the center were largely increased and long-range contacts between distant nucleosomes on the chain were promoted. ii), The highest destabilization of the fiber conformation occurred for a nucleosome shifted by two basepairs from regular spacing, whereas effects of linker DNA changes of ∼10 bp in phase with the helical twist of DNA were minimal. iii), A fiber conformation can stabilize a regular spacing of nucleosomes inasmuch as favorable stacking interactions between nucleosomes are facilitated. This can oppose nucleosome translocations and increase the energetic costs for chromatin remodeling. Our computational modeling framework makes it possible to describe the conformational heterogeneity of chromatin in terms of nucleosome positions, and thus advances theoretical models toward a better understanding of how genome compaction and access are regulated within the cell.