Molecular theory of lipid-protein interaction and the Lalpha-HII transition.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the HII lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor Lalpha phase coexists with a peptide-rich HII phase.     

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.     

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.     

Peptide Nanopores and Lipid Bilayers: Interactions by Coarse-Grained Molecular-Dynamics Simulations

A set of 49 protein nanopore-lipid bilayer systems was explored by means of coarse-grained molecular-dynamics simulations to study the interactions between nanopores and the lipid bilayers in which they are embedded. The seven nanopore species investigated represent the two main structural classes of membrane proteins (α-helical and β-barrel), and the seven different bilayer systems range in thickness from ∼28 to ∼43 Å. The study focuses on the local effects of hydrophobic mismatch between the nanopore and the lipid bilayer. The effects of nanopore insertion on lipid bilayer thickness, the dependence between hydrophobic thickness and the observed nanopore tilt angle, and the local distribution of lipid types around a nanopore in mixed-lipid bilayers are all analyzed. Different behavior for nanopores of similar hydrophobic length but different geometry is observed. The local lipid bilayer perturbation caused by the inserted nanopores suggests possible mechanisms for both lipid bilayer-induced protein sorting and protein-induced lipid sorting. A correlation between smaller lipid bilayer thickness (larger hydrophobic mismatch) and larger nanopore tilt angle is observed and, in the case of larger hydrophobic mismatches, the simulated tilt angle distribution seems to broaden. Furthermore, both nanopore size and key residue types (e.g., tryptophan) seem to influence the level of protein tilt, emphasizing the reciprocal nature of nanopore-lipid bilayer interactions.     

Atomistic-level study of the interactions between hIAPP protofibrils and membranes: Influence of pH and lipid composition

The pathology of type 2 diabetes mellitus is associated with the aggregation of human islet amyloid polypeptide (hIAPP) and aggregation-mediated membrane disruption. The interactions of hIAPP aggregates with lipid membrane, as well as the effects of pH and lipid composition at the atomic level, remain elusive. Herein, using molecular dynamics simulations, we investigate the interactions of hIAPP protofibrillar oligomers with lipids, and the membrane perturbation that they induce, when they are partially inserted in an anionic dipalmitoyl-phosphatidylglycerol (DPPG) membrane or a mixed dipalmitoyl-phosphatidylcholine (DPPC)/DPPG (7:3) lipid bilayer under acidic/neutral pH conditions. We observed that the tilt angles and insertion depths of the hIAPP protofibril are strongly correlated with the pH and lipid composition. At neutral pH, the tilt angle and insertion depth of hIAPP protofibrils at a DPPG bilayer reach ~52° and ~1.62 nm with respect to the membrane surface, while they become ~77° and ~1.75 nm at a mixed DPPC/DPPG membrane. The calculated tilt angle of hIAPP at DPPG membrane is consistent with a recent chiral sum frequency generation spectroscopic study. The acidic pH induces a smaller tilt angle of ~40° and a shallower insertion depth (~1.24 nm) of hIAPP at the DPPG membrane surface, mainly due to protonation of His18 near the turn region. These differences mainly result from a combination of distinct electrostatic, van der Waals, hydrogen bonding and salt-bridge interactions between hIAPP and lipid bilayers. The hIAPP-membrane interaction energy analysis reveals that besides charged residues K1, R11 and H18, aromatic residues Phe15 and Phe23 also exhibit strong interactions with lipid bilayers, revealing the crucial role of aromatic residues in stabilizing the membrane-bound hIAPP protofibrils. hIAPP-membrane interactions disturb the lipid ordering and the local bilayer thickness around the peptides. Our results provide atomic-level information of membrane interaction of hIAPP protofibrils, revealing pH-dependent and membrane-modulated hIAPP aggregation at the early stage.     

Two-component coarse-grained molecular-dynamics model for the human erythrocyte membrane

We present a two-component coarse-grained molecular-dynamics model for simulating the erythrocyte membrane. The proposed model possesses the key feature of combing the lipid bilayer and the erythrocyte cytoskeleton, thus showing both the fluidic behavior of the lipid bilayer and the elastic properties of the erythrocyte cytoskeleton. In this model, three types of coarse-grained particles are introduced to represent clusters of lipid molecules, actin junctions, and band-3 complexes, respectively. The proposed model facilitates simulations that span large length scales (approximately micrometers) and timescales (approximately milliseconds). By tuning the interaction potential parameters, we were able to control the diffusivity and bending rigidity of the membrane model. We studied the membrane under shearing and found that at a low shear strain rate, the developed shear stress was due mainly to the spectrin network, whereas the viscosity of the lipid bilayer contributed to the resulting shear stress at higher strain rates. In addition, we investigated the effects of a reduced spectrin network connectivity on the shear modulus of the membrane.     

Transmembrane helices of membrane proteins may flex to satisfy hydrophobic mismatch

A novel mechanism for membrane modulation of transmembrane protein structure, and consequently function, is suggested in which mismatch between the hydrophobic surface of the protein and the hydrophobic interior of the lipid bilayer induces a flexing or bending of a transmembrane segment of the protein. Studies on model hydrophobic transmembrane peptides predict that helices tilt to submerge the hydrophobic surface within the lipid bilayer to satisfy the hydrophobic effect if the helix length exceeds the bilayer width. The hydrophobic surface of transmembrane helix 1 (TM1) of lactose permease, LacY, is accessible to the bilayer, and too long to be accommodated in the hydrophobic portion of a typical lipid bilayer if oriented perpendicular to the membrane surface. Hence, nuclear magnetic resonance (NMR) data and molecular dynamics simulations show that TM1 from LacY may flex as well as tilt to satisfy the hydrophobic mismatch with the bilayer. In an analogous study of the hydrophobic mismatch of TM7 of bovine rhodopsin, similar flexing of the transmembrane segment near the conserved NPxxY sequence is observed. As a control, NMR data on TM5 of lacY, which is much shorter than TM1, show that TM5 is likely to tilt, but not flex, consistent with the close match between the extent of hydrophobic surface of the peptide and the hydrophobic thickness of the bilayer. These data suggest mechanisms by which the lipid bilayer in which the protein is embedded modulates conformation, and thus function, of integral membrane proteins through interactions with the hydrophobic transmembrane helices.     

Transmembrane helices of membrane proteins may flex to satisfy hydrophobic mismatch

A novel mechanism for membrane modulation of transmembrane protein structure, and consequently function, is suggested in which mismatch between the hydrophobic surface of the protein and the hydrophobic interior of the lipid bilayer induces a flexing or bending of a transmembrane segment of the protein. Studies on model hydrophobic transmembrane peptides predict that helices tilt to submerge the hydrophobic surface within the lipid bilayer to satisfy the hydrophobic effect if the helix length exceeds the bilayer width. The hydrophobic surface of transmembrane helix 1 (TM1) of lactose permease, LacY, is accessible to the bilayer, and too long to be accommodated in the hydrophobic portion of a typical lipid bilayer if oriented perpendicular to the membrane surface. Hence, nuclear magnetic resonance (NMR) data and molecular dynamics simulations show that TM1 from LacY may flex as well as tilt to satisfy the hydrophobic mismatch with the bilayer. In an analogous study of the hydrophobic mismatch of TM7 of bovine rhodopsin, similar flexing of the transmembrane segment near the conserved NPxxY sequence is observed. As a control, NMR data on TM5 of lacY, which is much shorter than TM1, show that TM5 is likely to tilt, but not flex, consistent with the close match between the extent of hydrophobic surface of the peptide and the hydrophobic thickness of the bilayer. These data suggest mechanisms by which the lipid bilayer in which the protein is embedded modulates conformation, and thus function, of integral membrane proteins through interactions with the hydrophobic transmembrane helices.     

A consistent model for thermal fluctuations and protein-induced deformations in lipid bilayers

We present an elastic Hamiltonian for membrane energetics that captures bilayer undulation and peristaltic deformations over all wavelengths, including the short wavelength protrusion regime. The model implies continuous functional forms for thermal undulation and peristaltic amplitudes as a function of wavelength and predicts previously overlooked relationships between these curves. Undulation and peristaltic spectra display excellent agreement with data from both atomistic and coarse-grained models over all simulated length scales. Additionally, the model accurately predicts the bilayer's response to a cylindrical protein inclusion as observed in coarse-grained simulation. This elastic response provides an explanation for gramicidin ion channel lifetime versus membrane thickness data that requires no fit constants. The physical parameters inherent to this picture may be expressed in terms of familiar material properties associated with lipid monolayers. Inclusion of a finite monolayer spontaneous curvature is essential to obtain fully consistent agreement between theory and the full range of available simulation/experimental data.     

Bending stiffness of lipid bilayers. I. Bilayer couple or single-layer bending?

To describe the resistance of a bilayer to changes in curvature two mechanisms are distinguished which are termed bilayer couple bending and single-layer bending. In bilayer couple bending, the resistance arises from the 2-D isotropic elasticity of the two layers and their fixed distance. Single-layer bending covers the intrinsic bending stiffness of each monolayer. The two mechanisms are not independent. Even so, the distinction is useful since bilayer couple bending can relax by a slip between the layers from the local to the global fashion. Therefore, the bending stiffness of a bilayer depends on the time scale and on the extent of the deformation imposed on the membrane. Based on experimental data, it is shown by order of magnitude estimates that (a) the bending stiffness determined from thermally induced shape fluctuations of almost spherical vesicles is dominated by single-layer bending; (b) in the tether experiment on lipid vesicles and on red cells, a contribution of local bilayer couple bending can not be excluded; and (c) at the sharp corners at the leading and the trailing edge of tanktreading red cells, local bilayer couple bending appears to be important.     

Revisiting Hydrophobic Mismatch with Free Energy Simulation Studies of Transmembrane Helix Tilt and Rotation

Protein-lipid interaction and bilayer regulation of membrane protein functions are largely controlled by the hydrophobic match between the transmembrane (TM) domain of membrane proteins and the surrounding lipid bilayer. To systematically characterize responses of a TM helix and lipid adaptations to a hydrophobic mismatch, we have performed a total of 5.8-μs umbrella sampling simulations and calculated the potentials of mean force (PMFs) as a function of TM helix tilt angle under various mismatch conditions. Single-pass TM peptides called WALPn (n = 16, 19, 23, and 27) were used in two lipid bilayers with different hydrophobic thicknesses to consider hydrophobic mismatch caused by either the TM length or the bilayer thickness. In addition, different flanking residues, such as alanine, lysine, and arginine, instead of tryptophan in WALP23 were used to examine their influence. The PMFs, their decomposition, and trajectory analysis demonstrate that 1), tilting of a single-pass TM helix is the major response to a hydrophobic mismatch; 2), TM helix tilting up to ∼10° is inherent due to the intrinsic entropic contribution arising from helix precession around the membrane normal even under a negative mismatch; 3), the favorable helix-lipid interaction provides additional driving forces for TM helix tilting under a positive mismatch; 4), the minimum-PMF tilt angle is generally located where there is the hydrophobic match and little lipid perturbation; 5), TM helix rotation is dependent on the specific helix-lipid interaction; and 6), anchoring residues at the hydrophilic/hydrophobic interface can be an important determinant of TM helix orientation.     

Effects of membrane reference state on shape memory of a red blood cell

By using a three-dimensional continuum model, we simulate the shape memory of a red blood cell after the remove of external forces. The purpose of this study is to illustrate the effect of membrane reference state on cell behavior during the recovery process. The reference state of an elastic element is the geometry with zero stress. Since the cell membrane is composed of cytoskeleton and lipid bilayer, both the reference states of cytoskeleton (RSC) and lipid bilayer (RSL) are considered. Results show that a non-spherical RSC can result in shape memory. The energy barrier due to non-spherical RSC is determined by the ratio of the equator length to the meridian length of the RSC. Thus different RSCs can have similar energy barrier and leading to identical recovery response. A series of simulations of more intermediate RSCs show that the recovery time scale is inversely proportional to the energy barrier. Comparing to spherical RSL, a spheroid RSL contributes to the energy barrier and recovery time. Furthermore, we observe a folding recovery due to the biconcave RSL which is different from the tank treading recovery. These results may motivate novel numerical and experimental studies to determine the exact RSC and RSL.     

On the nanoscale relaxation dynamics of a lipid bilayer

The Seifert–Langer theory of the relaxation dynamics of a one-component bilayer lipid membrane was extended to include a term that involves the gradient of the area per lipid molecule in the bilayer free energy per molecule. The extended theory is applicable over length scales comparable with the membrane thickness.     

Structure, topology, and tilt of cell-signaling peptides containing nuclear localization sequences in membrane bilayers determined by solid-state NMR and molecular dynamics simulation studies

Cell-signaling peptides have been extensively used to transport functional molecules across the plasma membrane into living cells. These peptides consist of a hydrophobic sequence and a cationic nuclear localization sequence (NLS). It has been assumed that the hydrophobic region penetrates the hydrophobic lipid bilayer and delivers the NLS inside the cell. To better understand the transport mechanism of these peptides, in this study, we investigated the structure, orientation, tilt of the peptide relative to the bilayer normal, and the membrane interaction of two cell-signaling peptides, SA and SKP. Results from CD and solid-state NMR experiments combined with molecular dynamics simulations suggest that the hydrophobic region is helical and has a transmembrane orientation with the helical axis tilted away from the bilayer normal. The influence of the hydrophobic mismatch, between the hydrophobic length of the peptide and the hydrophobic thickness of the bilayer, on the tilt angle of the peptides was investigated using thicker POPC and thinner DMPC bilayers. NMR experiments showed that the hydrophobic domain of each peptide has a tilt angle of 15 +/- 3 degrees in POPC, whereas in DMPC, 25 +/- 3 degree and 30 +/- 3 degree tilts were observed for SA and SKP peptides, respectively. These results are in good agreement with molecular dynamics simulations, which predict a tilt angle of 13.3 degrees (SA in POPC), 16.4 degrees (SKP in POPC), 22.3 degrees (SA in DMPC), and 31.7 degrees (SKP in DMPC). These results and simulations on the hydrophobic fragment of SA or SKP suggest that the tilt of helices increases with a decrease in bilayer thickness without changing the phase, order, and structure of the lipid bilayers.     

Energetics of inclusion-induced bilayer deformations.

The material properties of lipid bilayers can affect membrane protein function whenever conformational changes in the membrane-spanning proteins perturb the structure of the surrounding bilayer. This coupling between the protein and the bilayer arises from hydrophobic interactions between the protein and the bilayer. We analyze the free energy cost associated with a hydrophobic mismatch, i.e., a difference between the length of the protein's hydrophobic exterior surface and the average thickness of the bilayer's hydrophobic core, using a (liquid-crystal) elastic model of bilayer deformations. The free energy of the deformation is described as the sum of three contributions: compression-expansion, splay-distortion, and surface tension. When evaluating the interdependence among the energy components, one modulus renormalizes the other: e.g., a change in the compression-expansion modulus affects not only the compression-expansion energy but also the splay-distortion energy. The surface tension contribution always is negligible in thin solvent-free bilayers. When evaluating the energy per unit distance (away from the inclusion), the splay-distortion component dominates close to the bilayer/inclusion boundary, whereas the compression-expansion component is more prominent further away from the boundary. Despite this complexity, the bilayer deformation energy in many cases can be described by a linear spring formalism. The results show that, for a protein embedded in a membrane with an initial hydrophobic mismatch of only 1 A, an increase in hydrophobic mismatch to 1.3 A can increase the Boltzmann factor (the equilibrium distribution for protein conformation) 10-fold due to the elastic properties of the bilayer.     

Fluorescent quantification of size and lamellarity of membrane nanotubes

Membrane nanotubes, ubiquitous in cellular systems, adopt a spectrum of curvatures and shapes that are dictated by their intrinsic physical characteristics as well as their interactions with the local cellular environment. A high bending flexibility is needed in the crowded cytoplasm where tubes often need to bend significantly in the axial direction at sub-micron length scales. We find the stiffness of spontaneously formed membrane nanotubes by measuring the persistence length of reconstituted membrane nanotubes freely suspended in solution and imaged by fluorescence microscopy. By quantifying the tube diameter we demonstrate for the first time that the persistence length scales linearly with radius. Although most tubes are uni-lamellar, the predicted linear scaling between tube radius and persistence length allows us to identify tubes that spontaneously form as multilamellar structures upon hydration. We provide the first experimental evidence that illumination of lipid fluorophores can have a profound effect on the lipid bilayer which we sensitively detect as a continuous change in the tube persistence length with time. The novel assay and methodology here presented has potential for quantification of the structural reinforcement of membrane tubes by scaffolding proteins.     

E(z), a depth-dependent potential for assessing the energies of insertion of amino acid side-chains into membranes: derivation and applications to determining the orientation of transmembrane and interfacial helices

We have developed an empirical residue-based potential (E(z) potential) for protein insertion in lipid membranes. Propensities for occurrence as a function of depth in the bilayer were calculated for the individual amino acid types from their distribution in known structures of helical membrane proteins. The propensities were then fit to continuous curves and converted to a potential using a reverse-Boltzman relationship. The E(z) potential demonstrated a good correlation with experimental data such as amino acid transfer free energy scales (water to membrane center and water to interface), and it incorporates transmembrane helices of varying composition in the membrane with trends similar to those obtained with translocon-mediated insertion experiments. The potential has a variety of applications in the analysis of natural membrane proteins as well as in the design of new ones. It can help in calculating the propensity of single helices to insert in the bilayer and estimate their tilt angle with respect to the bilayer normal. It can be utilized to discriminate amphiphilic helices that assume a parallel orientation at the membrane interface, such as those of membrane-active peptides. In membrane protein design applications, the potential allows an environment-dependent selection of amino acid identities.     

Energy of dissociation of lipid bilayer from the membrane skeleton of red blood cells

The association between the lipid bilayer and the membrane skeleton is important to cell function. In red blood cells, defects in this association can lead to various forms of hemolytic anemia. Although proteins involved in this association have been well characterized biochemically, the physical strength of this association is only beginning to be studied. Formation of a small cylindrical strand of membrane material (tether) from the membrane involves separation of the lipid bilayer from the membrane skeleton. By measuring the force required to form a tether, and knowing the contribution to the force due to the deformation of a lipid bilayer, it is possible to calculate the additional contribution to the work of tether formation due to the separation of membrane skeleton from the lipid bilayer. In the present study, we measured the tethering force during tether formation using a microcantilever (a thin, flexible glass fiber) as a force transducer. Numerical calculations of the red cell contour were performed to examine how the shape of the contour affects the calculation of tether radius, and subsequently separation work per unit area W(sk) and bending stiffness k(c). At high aspiration pressure and small external force, the red cell contour can be accurately modeled as a sphere, but at low aspiration pressure and large external force, the contour deviates from a sphere and may affect the calculation. Based on an energy balance and numerical calculations of the cell contour, values of the membrane bending stiffness k(c) = 2.0 x 10(-19) Nm and the separation work per unit area W(sk) = 0.06 mJ/m2 were obtained.