Calculation of deformation energies and conformations in lipid membranes containing gramicidin channels

The gramicidin ion channel: A model membrane protein

The linear peptide gramicidin forms prototypical ion channels specific for monovalent cations and has been extensively used to study the organization, dynamics and function of membrane-spanning channels. In recent times, the availability of crystal structures of complex ion channels has challenged the role of gramicidin as a model membrane protein and ion channel. This review focuses on the suitability of gramicidin as a model membrane protein in general, and the information gained from gramicidin to understand lipid-protein interactions in particular. Special emphasis is given to the role and orientation of tryptophan residues in channel structure and function and recent spectroscopic approaches that have highlighted the organization and dynamics of the channel in membrane and membrane-mimetic media.

Bilayer thickness and membrane protein function: an energetic perspective

The lipid bilayer component of biological membranes is important for the distribution, organization, and function of bilayer-spanning proteins. This regulation is due to both specific lipid-protein interactions and general bilayer-protein interactions, which modulate the energetics and kinetics of protein conformational transitions, as well as the protein distribution between different membrane compartments. The bilayer regulation of membrane protein function arises from the hydrophobic coupling between the protein's hydrophobic domains and the bilayer hydrophobic core, which causes protein conformational changes that involve the protein/bilayer boundary to perturb the adjacent bilayer. Such bilayer perturbations, or deformations, incur an energetic cost, which for a given conformational change varies as a function of the bilayer material properties (bilayer thickness, intrinsic lipid curvature, and the elastic compression and bending moduli). Protein function therefore is regulated by changes in bilayer material properties, which determine the free-energy changes caused by the protein-induced bilayer deformation. The lipid bilayer thus becomes an allosteric regulator of membrane function.

Interaction of alamethicin pores in DMPC bilayers

We have investigated the x-ray scattering signal of highly aligned multilayers of the zwitterionic lipid 1,2-dimyristoyl-sn-glycero-3-phosphatidylcholine containing pores formed by the antimicrobial peptide alamethicin as a function of the peptide/lipid ratio. We are able to obtain information on the structure factor of the pore fluid, which then yields the interaction potential between pores in the plane of the bilayers. Aside from a hard core with a radius corresponding to the geometric radius of the pore, we find a repulsive lipid-mediated interaction with a range of approximately 30 A and a contact value of 2.4 k(B)T. This result is in qualitative agreement with recent theoretical models.

Elastic properties of biological membranes influenced by attached proteins

Positively charged proteins can attach themselves to the negatively charged outer surface of biological cell membranes and liposomes. In this work, the influence of the intrinsic shape of the membrane-attached proteins on the elastic properties of the membrane is considered theoretically. It is shown that attachment of anisotropic proteins to the outer surface of biological membranes may induce tubulation of the membrane. The attachment of semi-flexible rod-like proteins increases the local bending constant, while the attachment of semi-flexible plate-like anisotropic proteins may also reduce the local bending constant of the membrane. The role of the hydrophobic protrusion of the attached protein which is embedded in the outer membrane layer is also discussed.

Single-molecule methods for monitoring changes in bilayer elastic properties

Membrane-spanning proteins perturb the organization and dynamics of the adjacent bilayer lipids. For example, when the hydrophobic length (l) of a bilayer-spanning protein differs from the average thickness (d0) of the host bilayer, the bilayer thickness will vary locally in the vicinity of the protein in order to "match" the length of the protein's hydrophobic exterior to the thickness of the bilayer hydrophobic core. Such bilayer deformations incur an energetic cost, the bilayer deformation energy (DeltaG0def), which will vary as a function of the protein shape, the protein-bilayer hydrophobic mismatch (d0 - l), the lipid bilayer elastic properties, and the lipid intrinsic curvature (c0). Thus, if the membrane protein conformational changes underlying protein function involve the protein/bilayer interface, the ensuing changes in DeltaG0def (DeltaDeltaG0def) will contribute to the overall free-energy change of the conformational changes (DeltaG0tot)-meaning that the host lipid bilayer will modulate protein function. For a given protein, (DeltaDeltaG0def) varies as a function of the bilayer geometric properties (thickness and intrinsic curvature) and the elastic (bending and compression) moduli, which vary as a function of changes in lipid composition or with the adsorption of amphiphiles at the bilayer/solution interface. To understand how changes in bilayer properties modulate the function of bilayer-spanning proteins, single-molecule methods have been developed to probe changes in bilayer elastic properties using gramicidins as molecular force transducers. Different approaches to measuring the deformation energy are described: (1) measurements of changes in channel lifetimes and appearance rates as the lipid bilayer thickness or channel length are varied, (2) measurements of the equilibrium distribution among channels of different lengths, formed by homo- and heterodimers between gramicidin subunits of different lengths, and (3) measurements of the ratio of the appearance rates of heterodimer channels relative to parent homodimer channels formed by gramicidin subunits of different lengths.

Contributions of Gaussian curvature and nonconstant lipid volume to protein deformation of lipid bilayers

An elastic model for membrane deformations induced by integral membrane proteins is presented. An earlier theory is extended to account for nonvanishing saddle splay modulus within lipid monolayers and perturbations to lipid volume proximal to the protein. Analytical results are derived for the deformation profile surrounding a single cylindrical protein inclusion, which compare favorably to coarse-grained simulations over a range of protein sizes. Numerical results for multi-protein systems indicate that membrane-mediated interactions between inclusions are strongly affected by Gaussian curvature and display nonpairwise additivity. Implications for the aggregation of proteins are discussed.

Regulation of membrane protein function by lipid bilayer elasticity-a single molecule technology to measure the bilayer properties experienced by an embedded protein

Membrane protein function is generally regulated by the molecular composition of the host lipid bilayer. The underlying mechanisms have long remained enigmatic. Some cases involve specific molecular interactions, but very often lipids and other amphiphiles, which are adsorbed to lipid bilayers, regulate a number of structurally unrelated proteins in an apparently non-specific manner. It is well known that changes in the physical properties of a lipid bilayer (e.g., thickness or monolayer spontaneous curvature) can affect the function of an embedded protein. However, the role of such changes, in the general regulation of membrane protein function, is unclear. This is to a large extent due to lack of a generally accepted framework in which to understand the many observations. The present review summarizes studies which have demonstrated that the hydrophobic interactions between a membrane protein and the host lipid bilayer provide an energetic coupling, whereby protein function can be regulated by the bilayer elasticity. The feasibility of this 'hydrophobic coupling mechanism' has been demonstrated using the gramicidin channel, a model membrane protein, in planar lipid bilayers. Using voltage-dependent sodium channels, N-type calcium channels and GABA(A) receptors, it has been shown that membrane protein function in living cells can be regulated by amphiphile induced changes in bilayer elasticity. Using the gramicidin channel as a molecular force transducer, a nanotechnology to measure the elastic properties experienced by an embedded protein has been developed. A theoretical and technological framework, to study the regulation of membrane protein function by lipid bilayer elasticity, has been established.

Transbilayer Pores Induced by Thickness Fluctuations

Thermally-induced fluctuations of individual phospholipids in a bilayer lipid membrane (BLM) are converted into collective motions due to the intermolecular interactions. Here, we demonstrate that transbilayer stochastic pores can be generated via collective thermal movements (CTM). Using the elastic theory of continuous media applied to smectic-A liquid crystals, we estimate the pore radius and the energetic requirements for pore appearance. Three types of thermally-induced transbilayer pores could be formed through BLMs: open and stable, open and unstable, and closed. In most of the situations, two open and stable pores with different radii could be generated. Notably, the two pores have the same generation probability. Unstable pores are possible to appear across thin bilayers that contain phospholipids with a large polar headgroup. Closed pores are present throughout the cases that we have inspected. The effects of hydrophobic thickness, polar headgroup size of phospholipids, temperature, surface tension, and elastic compression on the pore formation and pore stability have been examined as well.

Energetics of rotational gating mechanisms of an ion channel induced by membrane deformation

We consider the gating mechanisms of an ion channel which has a conical structure for a closed state and a cylindrical or a bottleneck structure for an open state depending on the gating mechanisms. Applying the simplified continuum model of the membrane in the presence of a strong hydrophobic interaction between the channel proteins and the nearby lipid molecules of the membrane, we obtain energy differences between closed and open states for two known and one newly proposed rotational gating mechanism. We compare the energetics of three gating mechanisms and find out the most favorable mechanism under the given biological conditions such as hydrophobic mismatch, spontaneous curvature of a monolayer, and membrane moduli in our approach. Our results show that spontaneous curvature plays more important role in these gating mechanisms than surface tension does. Introducing spontaneous curvature to the inner or outer layer of the membrane affects the gating mechanism. We also discuss an effect of membrane thickness change due to the channel's conformational transition during gating.

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.

Implicit solvent simulation models for biomembranes

Fully atomic simulation strategies are infeasible for the study of many processes of interest to membrane biology, biophysics and biochemistry. We review various coarse-grained simulation methodologies with special emphasis on methods and models that do not require the explicit simulation of water. Examples from our own research demonstrate that such models have potential for simulating a variety of biologically relevant phenomena at the membrane surface.

Effects of hydrophobic mismatch and spontaneous curvature on ion channel gating with a hinge

We analyze the energetics of an ion-channel gating, focusing on effects of hydrophobic mismatch between the channel protein and the nearby lipid molecules, spontaneous curvature of monolayers, and thickness change of membranes. For the analysis we consider recently proposed open and closed conformations of a potassium channel which has a gating hinge, using the elastic continuum model of membranes. Gating energy, defined as the difference of deformation free energies for open and closed conformations, is quantitatively evaluated for various values of moduli related to the deformation of membranes and spontaneous curvature of monolayer imposing a strong hydrophobic boundary condition. We show that the gating mechanism with a hinge can work successfully even in a continuum model that considers hydrophobic mismatch and spontaneous curvature. When the energy cost for the thickness change of the membrane is neglected, the surface tension is not necessarily strong enough to open the channel. Otherwise, a relatively strong surface tension is required to open the channel.

Regulation of sodium channel function by bilayer elasticity: the importance of hydrophobic coupling. Effects of Micelle-forming amphiphiles and cholesterol

Membrane proteins are regulated by the lipid bilayer composition. Specific lipid–protein interactions rarely are involved, which suggests that the regulation is due to changes in some general bilayer property (or properties). The hydrophobic coupling between a membrane-spanning protein and the surrounding bilayer means that protein conformational changes may be associated with a reversible, local bilayer deformation. Lipid bilayers are elastic bodies, and the energetic cost of the bilayer deformation contributes to the total energetic cost of the protein conformational change. The energetics and kinetics of the protein conformational changes therefore will be regulated by the bilayer elasticity, which is determined by the lipid composition. This hydrophobic coupling mechanism has been studied extensively in gramicidin channels, where the channel–bilayer hydrophobic interactions link a “conformational” change (the monomer↔dimer transition) to an elastic bilayer deformation. Gramicidin channels thus are regulated by the lipid bilayer elastic properties (thickness, monolayer equilibrium curvature, and compression and bending moduli). To investigate whether this hydrophobic coupling mechanism could be a general mechanism regulating membrane protein function, we examined whether voltage-dependent skeletal-muscle sodium channels, expressed in HEK293 cells, are regulated by bilayer elasticity, as monitored using gramicidin A (gA) channels. Nonphysiological amphiphiles (β-octyl-glucoside, Genapol X-100, Triton X-100, and reduced Triton X-100) that make lipid bilayers less “stiff”, as measured using gA channels, shift the voltage dependence of sodium channel inactivation toward more hyperpolarized potentials. At low amphiphile concentration, the magnitude of the shift is linearly correlated to the change in gA channel lifetime. Cholesterol-depletion, which also reduces bilayer stiffness, causes a similar shift in sodium channel inactivation. These results provide strong support for the notion that bilayer–protein hydrophobic coupling allows the bilayer elastic properties to regulate membrane protein function.

Membrane-protein interactions in mechanosensitive channels

In this article, we examine the mechanical role of the lipid bilayer in ion channel conformation and function with specific reference to the case of the mechanosensitive channel of large conductance (MscL). In a recent article we argued that mechanotransduction very naturally arises from lipid-protein interactions by invoking a simple analytic model of the MscL channel and the surrounding lipid bilayer. In this article, we focus on improving and expanding this analytic framework for studying lipid-protein interactions with special attention to MscL. Our goal is to generate simple scaling relations which can be used to provide qualitative understanding of the role of membrane mechanics in protein function and to quantitatively interpret experimental results. For the MscL channel, we find that the free energies induced by lipid-protein interaction are of the same order as the measured free energy differences between conductance states. We therefore conclude that the mechanics of the bilayer plays an essential role in determining the conformation and function of the channel. Finally, we compare the predictions of our model to experimental results from the recent investigations of the MscL channel by a variety of investigators and suggest a suite of new experiments.

Interactions of hydrophobic peptides with lipid bilayers: Monte Carlo simulations with M2delta

We introduce here a novel Monte Carlo simulation method for studying the interactions of hydrophobic peptides with lipid membranes. Each of the peptide's amino acids is represented as two interaction sites: one corresponding to the backbone alpha-carbon and the other to the side chain, with the membrane represented as a hydrophobic profile. Peptide conformations and locations in the membrane and changes in the membrane width are sampled using the Metropolis criterion, taking into account the underlying energetics. Using this method we investigate the interactions between the hydrophobic peptide M2delta and a model membrane. The simulations show that starting from an extended conformation in the aqueous phase, the peptide first adsorbs onto the membrane surface, while acquiring an ordered helical structure. This is followed by formation of a helical-hairpin and insertion into the membrane. The observed path is in agreement with contemporary understanding of peptide insertion into biological membranes. Two stable orientations of membrane-associated M2delta were obtained: transmembrane (TM) and surface, and the value of the water-to-membrane transfer free energy of each of them is in agreement with calculations and measurements on similar cases. M2delta is most stable in the TM orientation, where it assumes a helical conformation with a tilt of 14 degrees between the helix principal axis and the membrane normal. The peptide conformation agrees well with the experimental data; average root-mean-square deviations of 2.1 A compared to nuclear magnetic resonance structures obtained in detergent micelles and supported lipid bilayers. The average orientation of the peptide in the membrane in the most stable configurations reported here, and in particular the value of the tilt angle, are in excellent agreement with the ones calculated using the continuum-solvent model and the ones observed in the nuclear magnetic resonance studies. This suggests that the method may be used to predict the three-dimensional structure of TM peptides.

Membrane inclusions as coupled harmonic oscillators: Effects due to anisotropic membrane slope relaxation

Membrane-mediated interaction between membrane-spanning peptides or protein segments plays an important role in their function and stability. Our rigorous "coupled harmonic oscillators" representation is extended to account for the complex boundary conditions permitting anisotropic relaxation of the membrane slope along the contours of the inclusions. Using this representation and applying a highly efficient finite-difference algorithm, we have analyzed the membrane-mediated interaction triggered by deformation of the hydrophobic tails of lipid molecules to match the lipophilic exterior of the inserted peptide. We establish that anisotropic relaxation crucially affects the interaction energy, leading to a short-range attraction between two inclusions, while conventional isotropic boundary conditions result in their strong repulsion. In a multi-inclusion cluster, this attraction is further enhanced and modified due to nonpairwise interactions. The results for dimyristoyl phosphatidylcholine and glyceryl monooleate membranes are compared, and the effects of the inclusion radius are considered. The possible role of slope relaxation in the reported stabilization of linked gramicidin channels and in proteins' functional cooperativity is outlined.

Genistein can modulate channel function by a phosphorylation-independent mechanism: importance of hydrophobic mismatch and bilayer mechanics

Genistein, a generic tyrosine kinase inhibitor, has been used extensively as a tool to investigate the possible regulation of membrane function by tyrosine phosphorylation. Genistein, in micromolar concentrations, alters the function of numerous ion channels and other membrane proteins, but only in few cases has it been demonstrated that the changes in membrane protein (ion channel) function are due to changes in a protein's phosphorylation status. The major common denominator characterizing proteins that are modulated by genistein seems to be that they are imbedded into, and span, the bilayer component of the plasma membrane. We therefore explored whether genistein could alter ion channel function by a bilayer-mediated mechanism and examined genistein's effect on gramicidin A (gA) channels in planar phospholipid bilayers. gA channels form by transmembrane dimerization of two nonconducting subunits, and genistein potentiates gA channel activity by increasing the appearance rate and prolonging the lifetime of bilayer-spanning gA dimers. That is, genistein shifts the equilibrium between nonconducting monomers and conducting dimers in favor of the bilayer-spanning dimers; the changes in channel activity therefore cannot be due to changes in bilayer fluidity. To obtain further insights into the mechanism underlying this modulation of gA channel function, we examined the effects of genistein on channels formed by gA analogues that differ in amino acid sequence. For a given channel length, the effects of genistein on gA dimerization do not depend on the specific sequence, or the chirality, of the channel-forming gA analogues. In contrast, when we change the channel length (by decreasing or increasing the number of amino acid residues in the sequence), or the bilayer thickness (by changing methylene groups in the acyl chains), the magnitude of genistein's effect increases with increasing hydrophobic mismatch between the channel length and the bilayer thickness. These results strongly suggest that genistein alters bilayer mechanical properties, which in turn modulates channel function. This bilayer-mediated mechanism is likely to apply to other pharmacological reagents and membrane proteins.

The effects of gramicidin on the structure of phospholipid assemblies

Gramicidin is an antibiotic peptide that can be incorporated into the monolayers of cell membranes. Dimerization through hydrogen bonding between gramicidin monomers in opposing leaflets of the membrane results in the formation of an iontophoretic channel. Surrounding phospholipids influence the gating properties of this channel. Conversely, gramicidin incorporation has been shown to affect the structure of spontaneously formed lipid assemblies. Using small-angle x-ray diffraction and model systems composed of phospholipids and gramicidin, the effects produced by gramicidin on lipid layers were measured. These measurements explore how peptides are able to modulate the spontaneous curvature properties of phospholipid assemblies. The reverse hexagonal, H(II), phase formed by dioleoylphosphatidylethanolamine (DOPE) monolayers decreased in lattice dimension with increasing incorporation of gramicidin. This indicated that gramicidin itself was adding negative curvature to the lipid layers. In this system, gramicidin was measured to have an apparent intrinsic radius of curvature, R0pgram, of -7.1 A. The addition of up to 4 mol% gramicidin in DOPE did not result in the monolayers becoming stiffer, as measured by the monolayer bending moduli. Dioleoylphosphatidylcholine (DOPC) alone forms the lamellar (L(alpha)) phase when hydrated, but undergoes a transition into the reverse hexagonal (H(II)) phase when mixed with gramicidin. The lattice dimension decreases systematically with increased gramicidin content. Again, this indicated that gramicidin was adding negative curvature to the lipid monolayers but the mixture behaved structurally much less consistently than DOPE/gramicidin. Only at 12 mol% gramicidin in dioleoylphosphatidylcholine could an apparent radius of intrinsic curvature of gramicidin (R0pgram) be estimated as -7.4 A. This mixture formed monolayers that were very resistant to bending, with a measured bending modulus of 115 kT.

Lateral heterogeneity of photosystems in thylakoid membranes studied by Brownian dynamics simulations

The aggregation and segregation of photosystems in higher plant thylakoid membranes as stromal cation-induced phenomena are studied by the Brownian dynamics method. A theoretical model of photosystems lateral movement within the membrane plane is developed, assuming their pairwise effective potential interaction in aqueous and lipid media and their diffusion. Along with the screened electrostatic repulsive interaction the model accounts for the van der Waals-type, elastic, and lipid-induced attractive forces between photosystems of different sizes and charges. Simulations with a priori estimated parameters demonstrate that all three studied repulsion-attraction alternatives might favor the local segregation of photosystems under physiologically reasonable conditions. However, only the lipid-induced potential combined with the size-corrected screened Coulomb interaction provides the segregated configurations with photosystems II localized in the central part of the grana-size simulation cell and photosystems I occupying its margins, as observed experimentally. Mapping of thermodynamic states reveals that the coexistence curves between isotropic and aggregated phases are the sigmoidlike functions regardless of the effective potential type. It correlates with measurements of the chlorophyll content of thylakoid fragments. Also the universality of the phase curves characterizes the aggregation and segregation of photosystems as order-disorder phase transitions with the Debye radius as a governing parameter.

Cholesterol-induced protein sorting: an analysis of energetic feasibility

The mechanism(s) underlying the sorting of integral membrane proteins between the Golgi complex and the plasma membrane remain uncertain because no specific Golgi retention signal has been found. Moreover one can alter a protein's eventual localization simply by altering the length of its transmembrane domain (TMD). M. S. Bretscher and S. Munro (SCIENCE: 261:1280-1281, 1993) therefore proposed a physical sorting mechanism based on the hydrophobic match between the proteins' TMD and the bilayer thickness, in which cholesterol would regulate protein sorting by increasing the lipid bilayer thickness. In this model, Golgi proteins with short TMDs would be excluded from cholesterol-enriched domains (lipid rafts) that are incorporated into transport vesicles destined for the plasma membrane. Although attractive, this model remains unproven. We therefore evaluated the energetic feasibility of a cholesterol-dependent sorting process using the theory of elastic liquid crystal deformations. We show that the distribution of proteins between cholesterol-enriched and cholesterol-poor bilayer domains can be regulated by cholesterol-induced changes in the bilayer physical properties. Changes in bilayer thickness per se, however, have only a modest effect on sorting; the major effect arises because cholesterol changes also the bilayer material properties, which augments the energetic penalty for incorporating short TMDs into cholesterol-enriched domains. We conclude that cholesterol-induced changes in the bilayer physical properties allow for effective and accurate sorting which will be important generally for protein partitioning between different membrane domains.

Proton transfer in gramicidin channels is modulated by the thickness of monoglyceride bilayers

The thickness of monoglyceride planar bilayers has significant effects on the transfer of protons in both native gramicidin A (gA) and in covalently linked SS- and RR-dioxolane-linked gA proteins. Planar bilayers with various thicknesses were formed from an appropriate combination of monoglyceride with various fatty acid lengths and solvent. Bilayer thicknesses ranged from 25 A (monoolein in squalene) to 54 A (monoeicosenoin in decane). Single-channel conductances to protons (g(H)) were measured in the concentration range of 10-5000 mM HCl. In native gA as well as in RR channels, the shape of the log(g(H))-log([H(+)]) relationships was nonlinear and remained basically unaltered in monoglyceride bilayers with various thicknesses. For both native gA and RR channels, g(H) values were systematically and significantly larger in thin than in thick bilayers. By contrast, the shape of the log(g(H))-log([H(+)]) relationships in the SS channel was linear (with a slope considerably smaller than 1) in thick (>37 A) bilayers. However, in thin (<37 A) bilayers these plots became nonlinear and g(H) values approached those obtained in native gA channels. The linearization of the log-log plots in the SS channel in thick bilayers is a consequence of a dramatic increase (instead of a decrease as in native gA and RR channels) of g(H) in these bilayers in [H(+)] <1 M. The gating characteristics of the various gA channels as a function of bilayer thickness followed the same pattern as described previously. It was noticed, however, that in the thickest monoglyceride bilayer used in this study, both the SS- and RR-dioxolane-linked channels opened in a mode of bursting activity instead of remaining in the open state as in thin bilayers. It is proposed that the thickness of monoglyceride bilayers modulates proton transfer in native gA channels by a combination of factors including the access resistances of channels to H(+), and fluctuations in both the structure of the lipid bilayer and in the distance between gA monomers. The differential effects of relatively thick monoglyceride bilayers on proton transfer in both dioxolane-linked gA channels must relate to distinct interactions between the bilayers and the SS and RR dioxolanes.

The effects of acyl chain length and saturation of diacylglycerols and phosphatidylcholines on membrane monolayer curvature

The second messenger, diacylglycerol (DAG), introduces negative curvature in phospholipid monolayers and strongly induces the lamellar (L(alpha)) to reverse hexagonal (H(II)) phase transition. The chain lengths and degree of unsaturation of symmetric DAGs influence this effect. Within dioleoylphosphatidylcholine (DOPC) monolayers, the apparent spontaneous radius of curvature (R(0)) of the short, saturated dicaprylglycerol (C10-DCG) itself was determined to be -13.3 A, compared with an R(0) value of -10.1 A for the long, di-monounsaturated dioleoylglycerol (C18-DOG). Such increased length and unsaturation of the DAG acyl chains produces this small change. Di-saturated phosphatidylcholines (PCs) with equal length chains (from C10-C18) with 25 mol % DOG do not form the H(II) phase, even under the unstressed conditions of excess water and alkane. Di-unsaturated PCs with equal chain length (from C14-C18) with 25 mol % DOG do form the H(II) phase. Asymmetric chained PCs (position 1 saturated with varying lengths, position 2 differentially unsaturated with varying lengths) all form the H(II) phase in the presence of 25 mol % DOG. As a general rule for PCs, their unsaturation is critical for the induction of the H(II) phase by DOG. The degree of curvature stress induced by the second messenger DOG in membranes, and any protein that might be affected by it, would appear to depend on chain unsaturation of neighboring PCs.

Stability of an ion channel in lipid bilayers: implicit solvent model calculations with gramicidin

Gramicidin is a helical peptide, 15 residues in length, which dimerizes to form ion-conducting channels in lipid bilayers. Here we report calculations of its free energy of transfer from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the desolvation free energy were calculated using implicit solvent models, in which gramicidin was described in atomic detail and the hydrocarbon region of the membrane was described as a slab of hydrophobic medium embedded in water. The free energy penalties from the lipid perturbation and membrane deformation effects, and the entropy loss associated with gramicidin immobilization in the bilayer, were estimated from a statistical thermodynamic model of the bilayer. The calculations were carried out using two classes of experimentally observed conformations: a head-to-head dimer of two single-stranded (SS) beta-helices and a double-stranded (DS) intertwined double helix. The calculations showed that gramicidin is likely to partition into the bilayer in all of these conformations. However, the SS conformation was found to be significantly more stable than the DS in the bilayer, in agreement with most of the experimental data. We tested numerous transmembrane and surface orientations of gramicidin in bilayers of various widths. Our calculations indicate that the most favorable orientation is transmembrane, which is indeed to be expected from a channel-forming peptide. The calculations demonstrate that gramicidin insertion into the membrane is likely to involve a significant deformation of the bilayer to match the hydrophobic width of the peptide (22 A), again in good agreement with experimental data. Interestingly, deformation of the bilayer was induced by all of the gramicidin conformations.

Gramicidin A channels switch between stretch activation and stretch inactivation depending on bilayer thickness

The patch clamp-liposome technique was used to examine the stretch sensitivity of a model membrane ion channel, gramicidin A, in membrane patches of different bilayer thickness. We found that small changes in phospholipid acyl chain length (i.e., PC-20 to PC-18) can switch gramicidin A from a stretch-activated to a stretch-inactivated channel. The demonstration that subnanometer changes in bilayer thickness can reverse the response polarity of a model channel has implications for other signaling proteins that may experience local changes in bilayer thickness as a consequence of dynamic targeting to lipid microdomains, electrocompression, or chemical modification of the bilayer.

On the origin of closing flickers in gramicidin channels: a new hypothesis

The submillisecond closing events (flickers) and the single channel conductances to protons (g(H)) were studied in native gramicidin A (gA) and in the SS and RR diastereoisomers of dioxolane-linked gA channels in planar bilayers. Bilayers were formed from glycerylmonooleate (GMO) in various solvents. In GMO/decane (thick) bilayers, the largest flicker frequency occurred in the SS channel (39 s(-1)), followed by the RR (4 s(-1)) and native gA channels (3 s(-1)). These frequencies were attenuated in GMO/squalene (thin) bilayers by 100-, 30-, and 70-fold in the SS, RR, and native gA channels, respectively. In thin bilayers, the average burst duration of native gA channels was 30-fold longer than in thick bilayers. The RR dioxolane-linked gA dimer "inactivated" in GMO/decane but not in squalene-containing bilayers. The mean closed time of flickers (approximately 0.12 ms) was essentially the same in various gA channels. In thin bilayers, g(H) values were larger by approximately 10% (SS), 30% (RR), and 20% (native gA) in relation to thick bilayers. It is concluded that flickers are not related to pre-dissociation or dissociation states of gA monomers, and do not seem to be caused by intrinsic conformational changes of channel proteins. It is proposed that flickers are caused by undulations of the bilayer that obliterate the openings of gA channels. Differences between flicker frequencies in various gA channels are likely to result from variations in channel geometries at the bilayer/channel interface. The smaller g(H) in thick bilayers suggests that the deformation of these bilayers around the gA channel creates a diffusional pathway next to the mouths of the channel that is longer and more restrictive than in thin GMO bilayers. A possible molecular interpretation for these effects is attempted.

Molecular basis of mechanotransduction in living cells

The simplest cell-like structure, the lipid bilayer vesicle, can respond to mechanical deformation by elastic membrane dilation/thinning and curvature changes. When a protein is inserted in the lipid bilayer, an energetic cost may arise because of hydrophobic mismatch between the protein and bilayer. Localized changes in bilayer thickness and curvature may compensate for this mismatch. The peptides alamethicin and gramicidin and the bacterial membrane protein MscL form mechanically gated (MG) channels when inserted in lipid bilayers. Their mechanosensitivity may arise because channel opening is associated with a change in the protein's membrane-occupied area, its hydrophobic mismatch with the bilayer, excluded water volume, or a combination of these effects. As a consequence, bilayer dilation/thinning or changes in local membrane curvature may shift the equilibrium between channel conformations. Recent evidence indicates that MG channels in specific animal cell types (e.g., Xenopus oocytes) are also gated directly by bilayer tension. However, animal cells lack the rigid cell wall that protects bacteria and plants cells from excessive expansion of their bilayer. Instead, a cortical cytoskeleton (CSK) provides a structural framework that allows the animal cell to maintain a stable excess membrane area (i.e., for its volume occupied by a sphere) in the form of membrane folds, ruffles, and microvilli. This excess membrane provides an immediate membrane reserve that may protect the bilayer from sudden changes in bilayer tension. Contractile elements within the CSK may locally slacken or tighten bilayer tension to regulate mechanosensitivity, whereas membrane blebbing and tight seal patch formation, by using up membrane reserves, may increase membrane mechanosensitivity. In specific cases, extracellular and/or CSK proteins (i.e., tethers) may transmit mechanical forces to the process (e.g., hair cell MG channels, MS intracellular Ca(2+) release, and transmitter release) without increasing tension in the lipid bilayer.

Inclusion-induced bilayer deformations: effects of monolayer equilibrium curvature

The energetics of protein-induced bilayer deformation in systems with finite monolayer equilibrium curvature were investigated using an elastic membrane model. In this model the bilayer deformation energy delta G(def) has two major components: a compression-expansion component and a splay-distortion component, which includes the consequences of a bilayer curvature frustration due to a monolayer equilibrium curvature, c(0), that is different from zero. For any choice of bilayer material constants, the value of delta G(def) depends on global bilayer properties, as described by the bilayer material constants, as well as the energetics of local lipid packing adjacent to the protein. We introduce this dependence on lipid packing through the contact slope, s, at the protein-bilayer boundary. When c(0) = 0, delta G(def) can be approximated as a biquadratic function of s and the monolayer deformation at the protein/bilayer boundary, u(0): delta G(def) = a(1)u(0)(2) + a(2)u(0)s + a(3)s(2), where a(1), a(2), and a(3) are functions of the bilayer thickness, the bilayer compression-expansion and splay-distortion moduli, and the inclusion radius (this expression becomes exact when the Gaussian curvature component of delta G(def) is negligible). When c(0) not equal 0, the curvature frustration contribution is determined by the choice of boundary conditions at the protein-lipid boundary (by the value of s), and delta G(def) is the sum of the energy for c(0) = 0 plus the curvature frustration-dependent contribution. When the energetic penalty for the local lipid packing can be ignored, delta G(def) will be determined only by the global bilayer properties, and a c(0) > 0 will tend to promote a local inclusion-induced bilayer thinning. When the energetic penalty for local lipid packing is large, s will be constrained by the value of c(0). In a limiting case, where s is determined only by geometric constraints imposed by c(0), a c(0) > 0 will impede such local bilayer thinning. One cannot predict curvature effects without addressing the proper choice of boundary conditions at the protein-bilayer contact surface.

Membrane cholesterol content modulates activation of volume-regulated anion current in bovine endothelial cells

Activation of volume-regulated anion current (VRAC) plays a key role in the maintenance of cellular volume homeostasis. The mechanisms, however, that regulate VRAC activity are not fully understood. We have examined whether VRAC activation is modulated by the cholesterol content of the membrane bilayer. The cholesterol content of bovine aortic endothelial cells was increased by two independent methods: (a) exposure to a methyl-beta-cyclodextrin saturated with cholesterol, or (b) exposure to cholesterol-enriched lipid dispersions. Enrichment of bovine aortic endothelial cells with cholesterol resulted in a suppression of VRAC activation in response to a mild osmotic gradient, but not to a strong osmotic gradient. Depletion of membrane cholesterol by exposing the cells to methyl-beta-cyclodextrin not complexed with cholesterol resulted in an enhancement of VRAC activation when the cells were challenged with a mild osmotic gradient. VRAC activity in cells challenged with a strong osmotic gradient were unaffected by depletion of membrane cholesterol. These observations show that changes in membrane cholesterol content shift VRAC sensitivity to osmotic gradients. Changes in VRAC activation were not accompanied by changes in anion permeability ratios, indicating that channel selectivity was not affected by the changes in membrane cholesterol. This suggests that membrane cholesterol content affects the equilibrium between the closed and open states of VRAC channel rather than the basic pore properties of the channel. We hypothesize that changes in membrane cholesterol modulate VRAC activity by affecting the membrane deformation energy associated with channel opening.

Common structural features in gramicidin and other ion channels

This review compares and contrasts the structures of several different types of ion channels with known three-dimensional structures, including gramicidin and the family of peptaibol channels, as well as the Streptomyces lividans potassium channel, to reveal common features in their structures that relate to their functional roles in ion binding and transport across membranes. Specifically, the locations of aromatic amino acids, the dimensions of the molecules, the multimeric nature of the channels and the roles of hydrogen bonds in stabilising such structures, the means by which the channels open and close, and the chemical nature of the groups which make up the channel lumen are discussed. The emphasis is on the commonality of features found in model channels, which may ultimately be found in other biological channel structures.

Continuum solvent model calculations of alamethicin-membrane interactions: thermodynamic aspects

Alamethicin is a 20-amino acid antibiotic peptide that forms voltage-gated ion channels in lipid bilayers. Here we report calculations of its association free energy with membranes. The calculations take into account the various free-energy terms that contribute to the transfer of the peptide from the aqueous phase into bilayers of different widths. The electrostatic and nonpolar contributions to the solvation free energy are calculated using continuum solvent models. The contributions from the lipid perturbation and membrane deformation effects and the entropy loss associated with peptide immobilization in the bilayer are estimated from a statistical thermodynamic model. The calculations were carried out using two classes of experimentally observed conformations, both of which are helical: the NMR and the x-ray crystal structures. Our calculations show that alamethicin is unlikely to partition into bilayers in any of the NMR conformations because they have uncompensated backbone hydrogen bonds and their association with the membrane involves a large electrostatic solvation free energy penalty. In contrast, the x-ray conformations provide enough backbone hydrogen bonds for the peptide to associate with bilayers. We tested numerous transmembrane and surface orientations of the peptide in bilayers, and our calculations indicate that the most favorable orientation is transmembrane, where the peptide protrudes approximately 4 A into the water-membrane interface, in very good agreement with electron paramagnetic resonance and oriented circular dichroism measurements. The calculations were carried out using two alamethicin isoforms: one with glutamine and the other with glutamate in the 18th position. The calculations indicate that the two isoforms have similar membrane orientations and that their insertion into the membrane is likely to involve a 2-A deformation of the bilayer, again, in good agreement with experimental data. The implications of the results for the biological function of alamethicin and its capacity to oligomerize and form ion channels are discussed.

Theoretical analysis of hydrophobic matching and membrane-mediated interactions in lipid bilayers containing gramicidin

We present a quantitative analysis of the effects of hydrophobic matching and membrane-mediated protein-protein interactions exhibited by gramicidin embedded in dimyristoylphosphatidylcholine (DMPC) and dilauroylphosphatidylcholine (DLPC) bilayers (Harroun et al., 1999. Biophys. J. 76:937-945). Incorporating gramicidin, at 1:10 peptide/lipid molar ratio, decreases the phosphate-to-phosphate (PtP) peak separation in the DMPC bilayer from 35.3 A without gramicidin to 32.7 A. In contrast, the same molar ratio of gramicidin in DLPC increases the PtP from 30.8 A to 32.1 A. Concurrently, x-ray in-plane scattering showed that the most probable nearest-neighbor separation between gramicidin channels was 26.8 A in DLPC, but reduced to 23.3 A in DMPC. In this paper we review the idea of hydrophobic matching in which the lipid bilayer deforms to match the hydrophobic surface of the embedded proteins. We use a simple elasticity theory, including thickness compression, tension, and splay terms to describe the membrane deformation. The energy of membrane deformation is compared with the energy cost of hydrophobic mismatch. We discuss the boundary conditions between a gramicidin channel and the lipid bilayer. We used a numerical method to solve the problem of membrane deformation profile in the presence of a high density of gramicidin channels and ran computer simulations of 81 gramicidin channels to find the equilibrium distributions of the channels in the plane of the bilayer. The simulations contain four parameters: bilayer thickness compressibility 1/B, bilayer bending rigidity Kc, the channel-bilayer mismatch Do, and the slope of the interface at the lipid-protein boundary s. B, Kc, and Do were experimentally measured; the only free parameter is s. The value of s is determined by the requirement that the theory produces the experimental values of bilayer thinning by gramicidin and the shift in the peak position of the in-plane scattering due to membrane-mediated channel-channel interactions. We show that both hydrophobic matching and membrane-mediated interactions can be understood by the simple elasticity theory.

Simulation study of a gramicidin/lipid bilayer system in excess water and lipid. I. Structure of the molecular complex

This paper reports on a simulation of a gramicidin channel inserted into a fluid phase DMPC bilayer with 100 lipid molecules. Two lipid molecules per leaflet were removed to insert the gramicidin, so the resulting preparation had 96 lipid molecules and 3209 water molecules. Constant surface tension boundary conditions were employed. Like previous simulations with a lower lipid/gramicidin ratio (Woolf, T. B., and B. Roux. 1996. Proteins: Struct., Funct., Genet. 24:92-114), it is found that tryptophan-water hydrogen bonds are more common than tryptophan-phospholipid hydrogen bonds. However, one of the tryptophan NH groups entered into an unusually long-lived hydrogen bonding pattern with two glycerol oxygens of one of the phospholipid molecules. Comparisons were made between the behavior of the lipids adjacent to the channel with those farther away. It was found that hydrocarbon chains of lipids adjacent to the channel had higher-order parameters than those farther away. The thickness of the lipid bilayer immediately adjacent to the channel was greater than it was farther away. In general, the lipids adjacent to the membrane had similar orientations to those seen by Woolf and Roux, while those farther away had similar orientations to those pertaining before the insertion of the gramicidin. A corollary to this observation is that the thickness of the hydrocarbon region adjacent to the gramicidin was much thicker than what other studies have identified as the "hydrophobic length" of the gramicidin channel.

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.

Spring constants for channel-induced lipid bilayer deformations. Estimates using gramicidin channels

Hydrophobic interactions between a bilayer and its embedded membrane proteins couple protein conformational changes to changes in the packing of the surrounding lipids. The energetic cost of a protein conformational change therefore includes a contribution from the associated bilayer deformation energy (DeltaGdef0), which provides a mechanism for how membrane protein function depends on the bilayer material properties. Theoretical studies based on an elastic liquid-crystal model of the bilayer deformation show that DeltaGdef0 should be quantifiable by a phenomenological linear spring model, in which the bilayer mechanical characteristics are lumped into a single spring constant. The spring constant scales with the protein radius, meaning that one can use suitable reporter proteins for in situ measurements of the spring constant and thereby evaluate quantitatively the DeltaGdef0 associated with protein conformational changes. Gramicidin channels can be used as such reporter proteins because the channels form by the transmembrane assembly of two nonconducting monomers. The monomerleft arrow over right arrow dimer reaction thus constitutes a well characterized conformational transition, and it should be possible to determine the phenomenological spring constant describing the channel-induced bilayer deformation by examining how DeltaGdef0 varies as a function of a mismatch between the hydrophobic channel length and the unperturbed bilayer thickness. We show this is possible by analyzing experimental studies on the relation between bilayer thickness and gramicidin channel duration. The spring constant in nominally hydrocarbon-free bilayers agrees well with estimates based on a continuum analysis of inclusion-induced bilayer deformations using independently measured material constants.

Electron-spin resonance study of aggregation of gramicidin in dipalmitoylphosphatidylcholine bilayers and hydrophobic mismatch

The effect of aggregation of gramicidin A' (GA) on the phase structure of dipalmitoylphosphatidylcholine (DPPC) multilamellar vesicles was studied by cw-ESR using a chain-labeled lipid (16PC) at temperatures between 30 degrees and 45 degreesC that span the main phase transition of DPPC. Boundary lipids were observed only in dispersions with GA/DPPC molar ratios >1:15, where GA aggregates. Detailed fits by nonlinear least squares (NLLS) methods are consistent with the boundary lipid being characterized by a large negative order parameter ( approximately -0.4), indicative of a dynamic bending of the end of the acyl chain, and a substantially reduced motion, about an order of magnitude slower than that of the bulk lipid. The NLLS analysis compares favorably with a recent two-dimensional Fourier transform ESR study on DPPC/GA vesicles, which accurately discerned the bulk lipid. The detailed ESR observables are discussed in terms of the ordering effect of GA at low concentration of GA, the dissociation of the GA channel and the dynamic bending of the end chain segment of boundary lipid at high concentration of GA, and of HII phase formation induced by GA. It is suggested that these phenomena can be interpreted in terms of the combined effects of partial dehydration of the lipid headgroup by the GA and of the hydrophobic mismatch between GA and DPPC molecules. Substantial hysteresis is observed for heating versus cooling cycles, but only for a GA/DPPC molar ratio >1:15. This is consistent with the aggregation of GA molecules at high concentrations.

Theoretical analysis of protein organization in lipid membranes

The fundamental physical principles of the lateral organization of trans-membrane proteins and peptides as well as peripheral membrane proteins and enzymes are considered from the point of view of the lipid-bilayer membrane, its structure, dynamics, and cooperative phenomena. Based on a variety of theoretical considerations and model calculations, the nature of lipid-protein interactions is considered both for a single protein and an assembly of proteins that can lead to aggregation and protein crystallization in the plane of the membrane. Phenomena discussed include lipid sorting and selectivity at protein surfaces, protein-lipid phase equilibria, lipid-mediated protein-protein interactions, wetting and capillary condensation as means of protein organization, mechanisms of two-dimensional protein crystallization, as well as non-equilibrium organization of active proteins in membranes. The theoretical findings are compared with a variety of experimental data.

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.

Gramicidin channel kinetics under tension

We have measured the effect of tension on dimerization kinetics of the channel-forming peptide gramicidin A. By aspirating large unilamellar vesicles into a micropipette electrode, we are able to simultaneously monitor membrane tension and electrical activity. We find that the dimer formation rate increases by a factor of 5 as tension ranges from 0 to 4 dyn/cm. The dimer lifetime also increases with tension. This behavior is well described by a phenomenological model of membrane elasticity in which tension modulates the mismatch in thickness between the gramicidin dimer and membrane.

Gramicidin channels in phospholipid bilayers with unsaturated acyl chains

In organic solvents gramicidin A (gA) occurs as a mixture of slowly interconverting double-stranded dimers. Membrane-spanning gA channels, in contrast, are almost exclusively single-stranded beta(6,3)-helical dimers. Based on spectroscopic evidence, it has previously been concluded that the conformational preference of gA in phospholipid bilayers varies as a function of the degree of unsaturation of the acyl chains. Double-stranded pi pi(5,6)-helical dimers predominate (over single-stranded beta(6,3)-helical dimers) in lipid bilayer membranes with polyunsaturated acyl chains. We therefore examined the characteristics of channels formed by gA in 1-palmitoyl-2-oleoylphosphatidylcholine/n-decane, 1,2-dioleoylphosphatidylcholine/n-decane, and 1,2-dilinoleoylphosphatidylcholine/n-decane bilayers. We did not observe long-lived channels that could be conducting double-stranded pi pi(5,6)-helical dimers in any of these different membrane environments. We conclude that the single-stranded beta(6,3)-helical dimer is the only conducting species in these bilayers. Somewhat surprisingly, the average channel duration and channel-forming potency of gA are increased in dilinoleoylphosphatidylcholine/n-decane bilayers compared to 1-palmitoyl-2-oleoylphosphatidylcholine/n-decane and dioleoylphosphatidylcholine/n-decane bilayers. To test for specific interactions between the aromatic side chains of gA and the acyl chains of the bilayer, we examined the properties of channels formed by gramicidin analogues in which the four tryptophan residues were replaced with naphthylalanine (gN), tyrosine (gT), and phenylalanine (gM). The results show that all of these analogue channels experience the same relative stabilization when going from dioleoylphosphatidylcholine to dilinoleoylphosphatidylcholine bilayers.

Interaction between inclusions embedded in membranes

We calculate the membrane-induced interaction between inclusions, in terms of the membrane stretching and bending moduli and the spontaneous curvature. We find that the membrane-induced interaction between inclusions varies nonmonotonically as a function of the inclusion spacing. The location of the energy minimum depends on the spontaneous curvature and the membrane perturbation decay length, where the latter is set by the membrane moduli. The membrane perturbation energy increases with the inclusion radius. The Ornstein-Zernike theory, with the Percus-Yevick closure, is used to calculate the radial distribution function of inclusions. We find that when the spontaneous curvature is zero, the interaction between inclusions due to the membrane deformation is qualitatively similar to the hard-core interaction. However, in the case of finite spontaneous curvature, the effective interaction is dramatically modified.

Gramicidin channel-induced lipid membrane deformation energy: influence of chain length and boundary conditions

The influence of boundary conditions on the deformation energy of a lipid membrane containing a gramicidin A channel was evaluated numerically. A liquid crystal model was used to calculate the relative contributions of compression, splay and surface tension. It is proposed that the nearest neighbor lipid molecules are displaced from the channel end in a direction perpendicular to the bilayer and it is concluded that surface tension is the major component of the deformation free energy for monoolein (gmo)/n-alkane membranes. This unexpected result supports the validity of the liquid crystal models of membrane deformation since gramicidin lifetime has been shown to correlate with surface tension for gmo membranes. The theory accurately predicts the experimentally measured relative lifetimes without the use of adjustable parameters. For conditions where splay may be neglected surface tension is always the major component of the deformation energy, irrespective of the magnitude of the compression coefficient. The deformation may extend for hundreds of angstroms from the peptide. The results obtained here are expected to be important for the characterization of protein-membrane interactions in general.

Incorporation of surface tension into molecular dynamics simulation of an interface: a fluid phase lipid bilayer membrane

In this paper we report on the molecular dynamics simulation of a fluid phase hydrated dimyristoylphosphatidylcholine bilayer. The initial configuration of the lipid was the x-ray crystal structure. A distinctive feature of this simulation is that, upon heating the system, the fluid phase emerged from parameters, initial conditions, and boundary conditions determined independently of the collective properties of the fluid phase. The initial conditions did not include chain disorder characteristic of the fluid phase. The partial charges on the lipids were determined by ab initio self-consistent field calculations and required no adjustment to produce a fluid phase. The boundary conditions were constant pressure and temperature. Thus the membrane was not explicitly required to assume an area/phospholipid molecule thought to be characteristic of the fluid phase, as is the case in constant volume simulations. Normal to the membrane plane, the pressure was 1 atmosphere, corresponding to the normal laboratory situation. Parallel to the membrane plane a negative pressure of -100 atmospheres was applied, derived from the measured surface tension of a monolayer at an air-water interface. The measured features of the computed membrane are generally in close agreement with experiment. Our results confirm the concept that, for appropriately matched temperature and surface pressure, a monolayer is a close approximation to one-half of a bilayer. Our results suggest that the surface area per phospholipid molecule for fluid phosphatidylcholine bilayer membranes is smaller than has generally been assumed in computational studies at constant volume. Our results confirm that the basis of the measured dipole potential is primarily water orientations and also suggest the presence of potential barriers for the movement of positive charges across the water-headgroup interfacial region of the phospholipid.