Simulated dynamic cholesterol redistribution favors membrane fusion pore constriction.

Endo- and exocytosis proceed through a highly strained membrane fusion pore topology regardless of the aiding protein machinery. The membrane's lipid components bias fusion pores toward expansion or closure, modifying the necessary work done by proteins. Cholesterol, a key component of plasma membranes, promotes both inverted lipid phases with concave leaflets (i.e., negative total curvature, which thins the leaflet) and flat bilayer phases with thick, ordered hydrophobic interiors. We demonstrate by theory and simulation that both leaflets of nascent catenoidal fusion pores have negative total curvature. Furthermore, the hydrophobic core of bilayers with strong negative Gaussian curvature is thinned. Therefore, it is an open question whether cholesterol will be enriched in these regions because of the negative total curvature or depleted because of the membrane thinning. Here, we compare all-atom molecular dynamics simulations (built using a procedure to create specific fusion pore geometries) and theory to understand the underlying reasons for lipid redistribution on fusion pores. Our all-atom molecular dynamics simulations resolve this question by showing that cholesterol is strongly excluded from the thinned neck of fusion and fission pores, revealing that thickness (and/or lipid order) influences cholesterol distributions more than curvature. The results imply that cholesterol exclusion can drive fusion pore closure by creating a small, cholesterol-depleted zone in the neck. This model agrees with literature evidence that membrane reshaping is connected to cholesterol-dependent lateral phase separation.

Physiological changes in bilayer thickness induced by cholesterol control GPCR rhodopsin function.

We monitored the effect on function of the G-protein-coupled receptor (GPCR) rhodopsin from small, stepwise changes in bilayer thickness induced by cholesterol. Over a range of phosphatidylcholine bilayers with hydrophobic thickness from ≈21 Å to 38 Å, the metarhodopsin-I (MI)/metarhodopsin-II (MII) equilibrium was monitored with UV-visible spectroscopy while ordering of hydrocarbon chains was probed by 2H-NMR. Addition of cholesterol shifted equilibrium toward MII for bilayers thinner than the average length of hydrophobic transmembrane helices (27 Å) and to MI for thicker bilayers, while small bilayer thickness changes within the range of the protein hydrophobic thickness drastically up- or downregulated MII formation. The cholesterol-induced shifts toward MII for thinner membranes correlated with the cholesterol-induced increase of bilayer hydrophobic thickness measured by NMR, consistent with continuum elastic modeling. The energetic penalty of adding cholesterol to thick bilayers caused rhodopsin oligomerization and a shift toward MI. In membranes of physiological thickness, changes in bilayer mechanical properties induced by cholesterol potentiated the interplay between bilayer and protein thickness resulting in large swings of the MI-MII equilibrium. In membrane containing cholesterol, elastic deformations near the protein are a dominant energetic contribution to the functional equilibrium of the model GPCR rhodopsin.

Large self-assembled clathrin lattices spontaneously disassemble without sufficient adaptor proteins.

Clathrin-coated structures must assemble on cell membranes to internalize receptors, with the clathrin protein only linked to the membrane via adaptor proteins. These structures can grow surprisingly large, containing over 20 clathrin, yet they often fail to form productive vesicles, instead aborting and disassembling. We show that clathrin structures of this size can both form and disassemble spontaneously when adaptor protein availability is low, despite high abundance of clathrin. Here, we combine recent in vitro kinetic measurements with microscopic reaction-diffusion simulations and theory to differentiate mechanisms of stable vs unstable clathrin assembly on membranes. While in vitro conditions drive assembly of robust, stable lattices, we show that concentrations, geometry, and dimensional reduction in physiologic-like conditions do not support nucleation if only the key adaptor AP-2 is included, due to its insufficient abundance. Nucleation requires a stoichiometry of adaptor to clathrin that exceeds 1:1, meaning additional adaptor types are necessary to form lattices successfully and efficiently. We show that the critical nucleus contains ~25 clathrin, remarkably similar to sizes of the transient and abortive structures observed in vivo. Lastly, we quantify the cost of bending the membrane under our curved clathrin lattices using a continuum membrane model. We find that the cost of bending the membrane could be largely offset by the energetic benefit of forming curved rather than flat structures, with numbers comparable to experiments. Our model predicts how adaptor density can tune clathrin-coated structures from the transient to the stable, showing that active energy consumption is therefore not required for lattice disassembly or remodeling during growth, which is a critical advance towards predicting productive vesicle formation.

Observed steric crowding at modest coverage requires a particular membrane-binding scheme or a complementary mechanism.

Membrane shape transitions, including fusion and fission, play an important role in many biological processes. It is therefore essential to understand mechanisms of "curvature generation," the mathematical quantification of membrane shape. Among the different mechanisms is the effect of steric pressure between proteins crowded on a surface. At a higher curvature, there is more space for the crowders and less steric pressure. Currently, the physical model of curvature induction by crowding views the proteins as being bound to the surface as a whole rather than to the underlying lipids. Here, we split the previously understood model into two pieces: first, the reduction in steric pressure due to reduced collisions between proteins, and second, the increased area available to the protein that is independent of other crowders. The cases are distinguished by how the crowder is attached to the membrane. When a protein is attached to a specific lipid, as is the case in a typical crowding experiment, one should not model its lateral entropy; this has already been accounted for by the underlying lipid. The Carnahan-Starling pressure includes this lateral entropy. The revised theory predicts that a purely entropic crowding mechanism is inconsistent with observations of reshaping at the lower range of surface coverage, suggesting that an additional mechanism is at play.

Molecular mechanisms of spontaneous curvature and softening in complex lipid bilayer mixtures.

Membrane reshaping is an essential biological process. The chemical composition of lipid membranes determines their mechanical properties and thus the energetics of their shape. Hundreds of distinct lipid species make up native bilayers, and this diversity complicates efforts to uncover what compositional factors drive membrane stability in cells. Simplifying assumptions, therefore, are used to generate quantitative predictions of bilayer dynamics based on lipid composition. One assumption commonly used is that "per lipid" mechanical properties are both additive and constant-that they are an intrinsic property of lipids independent of the surrounding composition. Related to this is the assumption that lipid bulkiness, or "shape," determines its curvature preference, independently of context. In this study, all-atom molecular dynamics simulations on three separate multilipid systems were used to explicitly test these assumptions, applying methodology recently developed to isolate properties of single lipids or nanometer-scale patches of lipids. The curvature preference experienced by populations of lipid conformations were inferred from their redistribution on a dynamically fluctuating bilayer. Representative populations were extracted by both structural similarity and semi-automated hidden Markov model analysis. The curvature preferences of lipid dimers were then determined and compared with an additive model that combines the monomer curvature preference of both the individual lipids. In all three systems, we identified conformational subpopulations of lipid dimers that showed non-additive curvature preference, in each case mediated by a special chemical interaction (e.g., hydrogen bonding). Our study highlights the importance of specific chemical interactions between lipids in multicomponent bilayers and the impact of interactions on bilayer stiffness. We identify two mechanisms of bilayer softening: diffusional softening, driven by the dynamic coupling between lipid distributions and membrane undulations, and conformational softening, driven by the inter-conversion between distinct dimeric conformations.

An implicit lipid model for efficient reaction-diffusion simulations of protein binding to surfaces of arbitrary topology.

Localization of proteins to a membrane is an essential step in a broad range of biological processes such as signaling, virion formation, and clathrin-mediated endocytosis. The strength and specificity of proteins binding to a membrane depend on the lipid composition. Single-particle reaction-diffusion methods offer a powerful tool for capturing lipid-specific binding to membrane surfaces by treating lipids explicitly as individual diffusible binding sites. However, modeling lipid particle populations is expensive. Here, we present an algorithm for reversible binding of proteins to continuum surfaces with implicit lipids, providing dramatic speed-ups to many body simulations. Our algorithm can be readily integrated into most reaction-diffusion software packages. We characterize changes to kinetics that emerge from explicit vs implicit lipids as well as surface adsorption models, showing excellent agreement between our method and the full explicit lipid model. Compared to models of surface adsorption, which couple together binding affinity and lipid concentration, our implicit lipid model decouples them to provide more flexibility for controlling surface binding properties and lipid inhomogeneity, thus reproducing binding kinetics and equilibria. Crucially, we demonstrate our method's application to membranes of arbitrary curvature and topology, modeled via a subdivision limit surface, again showing excellent agreement with explicit lipid simulations. Unlike adsorption models, our method retains the ability to bind lipids after proteins are localized to the surface (through, e.g., a protein-protein interaction), which can greatly increase the stability of multiprotein complexes on the surface. Our method will enable efficient cell-scale simulations involving proteins localizing to realistic membrane models, which is a critical step for predictive modeling and quantification of in vitro and in vivo dynamics.

Palmitoylation Contributes to Membrane Curvature in Influenza A Virus Assembly and Hemagglutinin-Mediated Membrane Fusion.

The highly conserved cytoplasmic tail of influenza virus glycoprotein hemagglutinin (HA) contains three cysteines, posttranslationally modified by covalently bound fatty acids. While viral HA acylation is crucial in virus replication, its physico-chemical role is unknown. We used virus-like particles (VLP) to study the effect of acylation on morphology, protein incorporation, lipid composition, and membrane fusion. Deacylation interrupted HA-M1 interactions since deacylated mutant HA failed to incorporate an M1 layer within spheroidal VLP, and filamentous particles incorporated increased numbers of neuraminidase (NA). While HA acylation did not influence VLP shape, lipid composition, or HA lateral spacing, acylation significantly affected envelope curvature. Compared to wild-type HA, deacylated HA is correlated with released particles with flat envelope curvature in the absence of the matrix (M1) protein layer. The spontaneous curvature of palmitate was calculated by molecular dynamic simulations and was found to be comparable to the curvature values derived from VLP size distributions. Cell-cell fusion assays show a strain-independent failure of fusion pore enlargement among H2 (A/Japan/305/57), H3 (A/Aichi/2/68), and H3 (A/Udorn/72) viruses. In contradistinction, acylation made no difference in the low-pH-dependent fusion of isolated VLPs to liposomes: fusion pores formed and expanded, as demonstrated by the presence of complete fusion products observed using cryo-electron tomography (cryo-ET). We propose that the primary mechanism of action of acylation is to control membrane curvature and to modify HA's interaction with M1 protein, while the stunting of fusion by deacylated HA acting in isolation may be balanced by other viral proteins which help lower the energetic barrier to pore expansion.IMPORTANCE Influenza A virus is an airborne pathogen causing seasonal epidemics and occasional pandemics. Hemagglutinin (HA), a glycoprotein abundant on the virion surface, is important in both influenza A virus assembly and entry. HA is modified by acylation whose removal abrogates viral replication. Here, we used cryo-electron tomography to obtain three-dimensional images to elucidate a role for HA acylation in VLP assembly. Our data indicate that HA acylation contributes to the capability of HA to bend membranes and to HA's interaction with the M1 scaffold protein during virus assembly. Furthermore, our data on VLP and, by hypothesis, virus suggests that HA acylation, while not critical to fusion pore formation, contributes to pore expansion in a target-dependent fashion.

Gramicidin A Channel Formation Induces Local Lipid Redistribution II: A 3D Continuum Elastic Model.

To change conformation, a protein must deform the surrounding bilayer. In this work, a three-dimensional continuum elastic model for gramicidin A in a lipid bilayer is shown to describe the sensitivity to thickness, curvature stress, and the mechanical properties of the lipid bilayer. A method is demonstrated to extract the gramicidin-lipid boundary condition from all-atom simulations that can be used in the three-dimensional continuum model. The boundary condition affects the deformation dramatically, potentially much more than typical variations in the material stiffness do as lipid composition is changed. Moreover, it directly controls the sensitivity to curvature stress. The curvature stress and hydrophobic surfaces of the all-atom and continuum models are found to be in excellent agreement. The continuum model is applied to estimate the enrichment of hydrophobically matched lipids near the channel in a mixture, and the results agree with single-channel experiments and extended molecular dynamics simulations from the companion article by Beaven et al. in this issue of Biophysical Journal.

Gramicidin A Channel Formation Induces Local Lipid Redistribution I: Experiment and Simulation.

Integral membrane protein function can be modulated by the host bilayer. Because biological membranes are diverse and nonuniform, we explore the consequences of lipid diversity using gramicidin A channels embedded in phosphatidylcholine (PC) bilayers composed of equimolar mixtures of di-oleoyl-PC and di-erucoyl-PC (dC18:1+dC22:1, respectively), di-palmitoleoyl-PC and di-nervonoyl-PC (dC16:1+dC24:1, respectively), and di-eicosenoyl-PC (pure dC20:1), all of which have the same average bilayer chain length. Single-channel lifetime experiments, molecular dynamics simulations, and a simple lipid compression model are used in tandem to gain insight into lipid redistribution around the channel, which partially alleviates the bilayer deformation energy associated with channel formation. The average single-channel lifetimes in the two-component bilayers (95 ± 10 ms for dC18:1+dC22:1 and 195 ± 20 ms for dC16:1+dC24:1) were increased relative to the single-component dC20:1 control bilayer (65 ± 10 ms), implying lipid redistribution. Using a theoretical treatment of thickness-dependent changes in channel lifetimes, the effective local enrichment of lipids around the channel was estimated to be 58 ± 4% dC18:1 and 66 ± 2% dC16:1 in the dC18:1+dC22:1 and dC16:1+dC24:1 bilayers, respectively. 3.5-µs molecular dynamics simulations show 66 ± 2% dC16:1 in the first lipid shell around the channel in the dC16:1+dC24:1 bilayer, but no significant redistribution (50 ± 4% dC18:1) in the dC18:1+dC22:1 bilayer; these simulated values are within the 95% confidence intervals of the experimental averages. The strong preference for the better matching lipid (dC16:1) near the channel in the dC16:1+dC24:1 mixture and lesser redistribution in the dC18:1+dC22:1 mixture can be explained by the energetic cost associated with compressing the lipids to match the channel's hydrophobic length.

Cation-Selective Channel Regulated by Anions According to Their Hofmeister Ranking.

Specificity of small ions, the Hofmeister ranking, is long-known and has many applications including medicine. Yet it evades consistent theoretical description. Here we study the effect of Hofmeister anions on gramicidin A channels in lipid membranes. Counterintuitively, we find that conductance of this perfectly cation-selective channel increases about two-fold in the H2 PO4-

Hexagonal Substructure and Hydrogen Bonding in Liquid-Ordered Phases Containing Palmitoyl Sphingomyelin.

All-atom simulation data are presented for ternary mixtures of palmitoyl sphingomyelin (PSM), cholesterol, and either palmitoyl oleoyl phosphatidyl choline or dioleoyl phosphatidyl choline (DOPC). For comparison, data for a mixture of dipalmitoyl phosphatidyl choline (DPPC), cholesterol, and DOPC are also presented. Compositions corresponding to the liquid-ordered phase, the liquid-disordered phase, and coexistence of the two phases are simulated for each mixture. Within the liquid-ordered phase, cholesterol is preferentially solvated by DOPC if it is available, but if DOPC is replaced by POPC, cholesterol is preferentially solvated by PSM. In the DPPC mixtures, cholesterol interacts preferentially with the saturated chains via its smooth face, whereas in the PSM mixtures, cholesterol interacts preferentially with PSM via its rough face. Interactions between cholesterol and PSM have a very particular character: hydrogen bonding between cholesterol and the amide of PSM rotates the tilt of the amide plane, which primes it for more robust hydrogen bonding with other PSM. Cholesterol-PSM hydrogen bonding also locally modifies the hexagonal packing of hydrocarbon chains in the liquid-ordered phase of PSM mixtures.

The Curvature Induction of Surface-Bound Antimicrobial Peptides Piscidin 1 and Piscidin 3 Varies with Lipid Chain Length.

The initial steps of membrane disruption by antimicrobial peptides (AMPs) involve binding to bacterial membranes in a surface-bound (S) orientation. To evaluate the effects of lipid composition on the S state, molecular dynamics simulations of the AMPs piscidin 1 (p1) and piscidin 3 (p3) were carried out in four different bilayers: 3:1 DMPC/DMPG, 3:1 POPC/POPG, 1:1 POPE/POPG, and 4:1 POPC/cholesterol. In all cases, the addition of 1:40 piscidin caused thinning of the bilayer, though thinning was least for DMPC/DMPG. The peptides also insert most deeply into DMPC/DMPG, spanning the region from the bilayer midplane to the headgroups, and thereby only mildly disrupting the acyl chains. In contrast, the peptides insert less deeply in the palmitoyl-oleoyl containing membranes, do not reach the midplane, and substantially disrupt the chains, i.e., the neighboring acyl chains bend under the peptide, forming a basket-like conformation. Curvature free energy derivatives calculated from the simulation pressure profiles reveal that the peptides generate positive curvature in membranes with palmitoyl and oleoyl chains but negative curvature in those with myristoyl chains. Curvature inductions predicted with a continuum elastic model follow the same trends, though the effect is weaker, and a small negative curvature induction is obtained in POPC/POPG. These results do not directly speak to the relative stability of the inserted (I) states or ease of pore formation, which requires the free energy pathway between the S and I states. Nevertheless, they do highlight the importance of lipid composition and acyl chain packing.

Multiple environment single system quantum mechanical/molecular mechanical (MESS-QM/MM) calculations. 1. Estimation of polarization energies.

In combined quantum mechanical/molecular mechanical (QM/MM) free energy calculations, it is often advantageous to have a frozen geometry for the quantum mechanical (QM) region. For such multiple-environment single-system (MESS) cases, two schemes are proposed here for estimating the polarization energy: the first scheme, termed MESS-E, involves a Roothaan step extrapolation of the self-consistent field (SCF) energy; whereas the other scheme, termed MESS-H, employs a Newton-Raphson correction using an approximate inverse electronic Hessian of the QM region (which is constructed only once). Both schemes are extremely efficient, because the expensive Fock updates and SCF iterations in standard QM/MM calculations are completely avoided at each configuration. They produce reasonably accurate QM/MM polarization energies: MESS-E can predict the polarization energy within 0.25 kcal/mol in terms of the mean signed error for two of our test cases, solvated methanol and solvated ß-alanine, using the M06-2X or ωB97X-D functionals; MESS-H can reproduce the polarization energy within 0.2 kcal/mol for these two cases and for the oxyluciferin-luciferase complex, if the approximate inverse electronic Hessians are constructed with sufficient accuracy.

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.

CHARMM all-atom additive force field for sphingomyelin: elucidation of hydrogen bonding and of positive curvature.

The C36 CHARMM lipid force field has been extended to include sphingolipids, via a combination of high-level quantum mechanical calculations on small molecule fragments, and validation by extensive molecular dynamics simulations on N-palmitoyl and N-stearoyl sphingomyelin. NMR data on these two molecules from several studies in bilayers and micelles played a strong role in the development and testing of the force field parameters. Most previous force fields for sphingomyelins were developed before the availability of the detailed NMR data and relied on x-ray diffraction of bilayers alone for the validation; these are shown to be too dense in the bilayer plane based on published chain order parameter data from simulations and experiments. The present simulations reveal O-H:::O-P intralipid hydrogen bonding occurs 99% of the time, and interlipid N-H:::O=C (26-29%, depending on the lipid) and N-H:::O-H (17-19%). The interlipid hydrogen bonds are long lived, showing decay times of 50 ns, and forming strings of lipids, and leading to reorientational correlation time of nearly 100 ns. The spontaneous radius of curvature for pure N-palmitoyl sphingomyelin bilayers is estimated to be 43-100 Å, depending on the assumptions made in assigning a bending constant; this unusual positive curvature for a two-tailed neutral lipid is likely associated with hydrogen bond networks involving the NH of the sphingosine group.

The molecular structure of the liquid-ordered phase of lipid bilayers.

Molecular dynamics simulations reveal substructures within the liquid-ordered phase of lipid bilayers. These substructures, identified in a 10 µs all-atom trajectory of liquid-ordered/liquid-disordered coexistence (L(o)/L(d)) are composed of saturated hydrocarbon chains packed with local hexagonal order and separated by interstitial regions enriched in cholesterol and unsaturated chains. Lipid hydrocarbon chain order parameters calculated from the L(o) phase are in excellent agreement with (2)H NMR measurements; the local hexagonal packing is also consistent with (1)H-MAS NMR spectra of the L(o) phase, NMR diffusion experiments, and small-angle X-ray and neutron scattering. The balance of cholesterol-rich to local hexagonal order is proposed to control the partitioning of membrane components into the L(o) regions. The latter have been frequently associated with formation of so-called rafts, platforms in the plasma membranes of cells that facilitate interaction between components of signaling pathways.

Computing the influence of lipids and lipid complexes on membrane mechanics.

Methodology for extracting the spontaneous curvature, bending modulus, and neutral surface of a lipid bilayer is described. The "SPEX" method is a robust technique for computing the bilayer bending modulus while allowing for resolution of the spontaneous curvature of specific interacting lipids and complexes, and the dependence of spontaneous curvature on wavelength. The method is described referring to the publicly available MembraneAnalysis.jl software package.

Softening in Two-Component Lipid Mixtures by Spontaneous Curvature Variance.

The bending modulus of a lipid bilayer quantifies its mechanical resistance to curvature. It is typically understood in terms of thickness; e.g., thicker bilayers are usually stiffer. Here, we describe an additional and powerful molecular determinant of stiffness─the variance in the distribution of curvature sensitivity of lipids and lipid conformations. Zwitterionic choline and ethanolamine headgroups of glycerophospholipids dynamically explore inter- and intraspecies interactions, leading to transient clustering. We demonstrate that these clusters couple strongly to negative curvature, exciting undulatory membrane modes and reducing the apparent bending modulus. Three force fields (Martini 2, Martini 3, and all-atom CHARMM C36) each show the effect to a different extent, with the coarse-grained Martini models showing the most clustering and thus the most softening. The theory is a guide to understanding the stiffness of biological membranes with their complex composition, as well as how choices of force field parameterization are translated into mechanical stiffness.