Entropic part of the boundary energy in a lipid membrane

Two-phase lipid membrane is modeled with lipids of different bending rigidity of hydrophobic tails: domains consist of “rigid” lipid liquid condensed phase and are surrounded by the “flexible” lipid liquid expanded phase. Within the framework of the earlier proposed model of flexible strings, entropic contribution not including mismatch energy is calculated analytically. “Entropic” line tension is found to be weakly dependent on the domain radius. According to the model, it is shown that merely “entropic mismatch” is not enough for the domain formation. In the paper it is assumed that lipids at the boundary, on the average, have larger area than the ones in the volume. This leads to an increase of energy of boundary lipids. Cases of lipids with nearly the same bending rigidities and with strongly different ones are considered. Free energy is calculated using Taylor expansion on the difference of area of lipids at the domain’s boundary and in the volume. Based on the calculated boundary energy domain stability in the finite system is estimated.     

A theoretical model for the association of amphiphilic transmembrane peptides in lipid bilayers

A theoretical model is proposed for the association of trans-bilayer peptides in lipid bilayers. The model is based on a lattice model for the pure lipid bilayer, which accounts accurately for the most important conformational states of the lipids and their mutual interactions and statistics. Within the lattice formulation the bilayer is formed by two independent monolayers, each represented by a triangular lattice, on which sites the lipid chains are arrayed. The peptides are represented by regular objects, with no internal flexibility, and with a projected area on the bilayer plane corresponding to a hexagon with seven lattice sites. In addition, it is assumed that each peptide surface at the interface with the lipid chains is partially hydrophilic, and therefore interacts with the surrounding lipid matrix via selective anisotropic forces. The peptides would therefore assemble in order to shield their hydrophilic residues from the hydrophobic surroundings. The model describes the self-association of peptides in lipid bilayers via lateral and rotational diffusion, anisotropic lipid-peptide interactions, and peptide-peptide interactions involving the peptide hydrophilic regions. The intent of this model study is to analyse the conditions under which the association of trans-bilayer and partially hydrophilic peptides (or their dispersion in the lipid matrix) is lipid-mediated, and to what extent it is induced by direct interactions between the hydrophilic regions of the peptides. The model properties are calculated by a Monte Carlo computer simulation technique within the canonical ensemble. The results from the model study indicate that direct interactions between the hydrophilic regions of the peptides are necessary to induce peptide association in the lipid bilayer in the fluid phase. Furthermore, peptides within each aggregate are oriented in such a way as to shield their hydrophilic regions from the hydrophobic environment. The average number of peptides present in the aggregates formed depends on the degree of mismatch between the peptide hydrophobic length and the lipid bilayer hydrophobic thickness: The lower the degree of mismatch is the higher this number is. Received: 30 December 1996 / Accepted: 9 May 1997     

Cooperative elastic stresses, the hydrophobic effect, and lipid tilt in membrane remodeling

One of the fundamental properties of biological membranes is the high lateral integrity provided by the lipid bilayer, the structural core and the foundation of their barrier function. This tensile strength is due to the intrinsic properties of amphiphilic lipid molecules, which spontaneously self-assemble into a stable bilayer structure due to the hydrophobic effect. In the highly dynamic life of cellular membranes systems, however, this integrity has to be regularly compromised. One of the emerging puzzles is the mechanism of localized rupture of lipid monolayer, the formation of tiny hydrophobic patches and flipping of lipid tails between closely apposed monolayers. The energy cost of such processes is prohibitively high, unless cooperative deformations in a small membrane patch are carefully organized. Here we review the latest experimental and theoretical data on how such deformations can be conducted, specifically describing how elastic stresses yield tilting of lipids leading to cooperative restructuring of lipid monolayers. Proteins specializing in membrane remodeling assemble into closely packed circular complexes to arrange these deformations in time and space.     

Thylakoid membrane landscape in the sixties: a tribute to Andrew Benson

Prior to the 1960s, the model for the molecular structure of cell membranes consisted of a lipid bilayer held in place by a thin film of electrostatically-associated protein stretched over the bilayer surface: (the Danielli–Davson–Robertson “unit membrane” model). Andrew Benson, an expert in the lipids of chloroplast thylakoid membranes, questioned the relevance of the unit membrane model for biological membranes, especially for thylakoid membranes, instead of emphasizing evidence in favour of hydrophobic interactions of membrane lipids within complementary hydrophobic regions of membrane-spanning proteins. With Elliot Weier, Benson postulated a remarkable subunit lipoprotein monolayer model for thylakoids. Following the advent of freeze fracture microscopy and the fluid lipid-protein mosaic model by Singer and Nicolson, the subunits, membrane-spanning integral proteins, span a dynamic lipid bilayer. Now that high resolution X-ray structures of photosystems I and II are being revealed, the seminal contribution of Andrew Benson can be appreciated.     

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

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

Effect of hydrophobic mismatch and interdigitation on sterol/sphingomyelin interaction in ternary bilayer membranes

Sphingomyelin (SM) is a major phospholipid in most cell membranes. SMs are composed of a long-chain base (often sphingosine, 18:1(Δ4t)), and N-linked acyl chains (often 16:0, 18:0 or 24:1(Δ15c)). Cholesterol interacts with SM in cell membranes, but the acyl chain preference of this interaction is not fully elucidated. In this study we have examined the effects of hydrophobic mismatch and interdigitation on cholesterol/sphingomyelin interaction in complex bilayer membranes. We measured the capacity of cholestatrienol (CTL) and cholesterol to form sterol-enriched ordered domains with saturated SM species having different chain lengths (14 to 24 carbons) in ternary bilayer membranes. We also determined the equilibrium bilayer partitioning coefficient of CTL with 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membranes containing 20mol% of saturated SM analogs. Ours results show that while CTL and cholesterol formed sterol-enriched domains with both short and long-chain SM species, the sterols preferred interaction with 16:0-SM over any other saturated chain length SM analog. When CTL membrane partitioning was determined with fluid POPC bilayers containing 20mol% of a saturated chain length SM analog, the highest affinity was seen with 16:0-SM (both at 23 and 37°C). These results indicate that hydrophobic mismatch and/or interdigitation attenuate sterol/SM association and thus affect lateral distribution of sterols in the bilayer membrane.     

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.     

A molecular model for lipid-protein interaction in membranes: the role of hydrophobic mismatch.

The interaction free energy between a hydrophobic, transmembrane, protein and the surrounding lipid environment is calculated based on a microscopic model for lipid organization. The protein is treated as a rigid hydrophobic solute of thickness dP, embedded in a lipid bilayer of unperturbed thickness doL. The lipid chains in the immediate vicinity of the protein are assumed to adjust their length to that of the protein (e.g., they are stretched when dP > doL) in order to bridge over the lipid-protein hydrophobic mismatch (dP-doL). The bilayer's hydrophobic thickness is assumed to decay exponentially to its asymptotic, unperturbed, value. The lipid deformation free energy is represented as a sum of chain (hydrophobic core) and interfacial (head-group region) contributions. The chain contribution is calculated using a detailed molecular theory of chain packing statistics, which allows the calculation of conformational properties and thermodynamic functions (in a mean-field approximation) of the lipid tails. The tails are treated as single chain amphiphiles, modeled using the rotational isometric state scheme. The interfacial free energy is represented by a phenomenological expression, accounting for the opposing effects of head-group repulsions and hydrocarbon-water surface tension. The lipid deformation free energy delta F is calculated as a function of dP-doL. Most calculations are for C14 amphiphiles which, in the absence of a protein, pack at an average area per head-group ao approximately equal to 32 A2 (doL approximately 24.5 A), corresponding to the fluid state of the membrane. When dP = doL, delta F > 0 and is due entirely to the loss of conformational entropy experienced by the chains around the protein. When dP > doL, the interaction free energy is further increased due to the enhanced stretching of the tails. When dP < doL, chain flexibility (entropy) increases, but this contribution to delta F is overcounted by the increase in the interfacial free energy. Thus, delta F obtains a minimum at dP-doL approximately 0. These qualitative interpretations are supported by detailed numerical calculations of the various contributions to the interaction free energy, and of chain conformational properties. The range of the perturbation of lipid order extends typically over few molecular diameters. A rather detailed comparison of our approach to other models is provided in the discussion.     

Nonpolar interactions between trans-membrane helical EGF peptide and phosphatidylcholines, sphingomyelins and cholesterol. Molecular dynamics simulation studies.

A molecular dynamics simulation study of four lipid bilayers with inserted trans-membrane helical fragment of epithelial growth factor (EGF) receptor (EGF peptide) was performed. The lipid bilayers differ in their lipid composition and consist of (i) unsaturated phosphatidylcholine (palmitoyloleoylphosphatidylcholine, POPC), (ii) POPC and 20 mol% of cholesterol (Chol), (iii) sphingomyelin (SM) and 20 mol% of Chol, and (iv) SM and 50 mol% of Chol. Only 1 out of 26 residues in the EGF-peptide sequence is polar (Thr). The hydrophobic thickness of each bilayer is different but shorter than the length of the peptide and so, due to hydrophobic mismatch, the inserted peptide is tilted in each bilayer. Additionally, in the POPC bilayer, which is the thinnest, the peptide loses its helical structure in a short three-amino acid fragment. This facilitates bending of the peptide and burying all hydrophobic amino acids inside the membrane core (Figure 1(b)). Bilayer lipid composition affects interactions between the peptide and lipids in the membrane core. Chol increases packing of atoms relative to the peptide side chains, and thus increases van der Waals interactions. On average, the packing around the peptide is higher in SM-based bilayers than POPC-based bilayers but for certain amino acids, packing depends on their position relative to the bilayer center. In the bilayer center, packing is higher in POPC-based bilayers, while in regions closer to the interface packing is higher in SM-based bilayers. In general, amino acids with larger side chains interact strongly with lipids, and thus the peptide sequence is important for the pattern of interactions at different membrane depths. This pattern closely resembles the shape of recently published lateral pressure profiles [Ollila et alJ. Struct. Biol. DOI:10.1016/j.jsb.2007.01.012].     

The determinants of hydrophobic mismatch response for transmembrane helices

Hydrophobic mismatch arises from a difference in the hydrophobic thickness of a lipid membrane and a transmembrane protein segment, and is thought to play an important role in the folding, stability and function of membrane proteins. We have investigated the possible adaptations that lipid bilayers and transmembrane α-helices undergo in response to mismatch, using fully-atomistic molecular dynamics simulations totaling 1.4 μs. We have created 25 different tryptophan-alanine-leucine transmembrane α-helical peptide systems, each composed of a hydrophobic alanine–leucine stretch, flanked by 1–4 tryptophan side chains, as well as the β-helical peptide dimer, gramicidin A. Membrane responses to mismatch include changes in local bilayer thickness and lipid order, varying systematically with peptide length. Adding more flanking tryptophan side chains led to an increase in bilayer thinning for negatively mismatched peptides, though it was also associated with a spreading of the bilayer interface. Peptide tilting, bending and stretching were systematic, with tilting dominating the responses, with values of up to ~ 45° for the most positively mismatched peptides. Peptide responses were modulated by the number of tryptophan side chains due to their anchoring roles and distributions around the helices. Potential of mean force calculations for local membrane thickness changes, helix tilting, bending and stretching revealed that membrane deformation is the least energetically costly of all mismatch responses, except for positively mismatched peptides where helix tilting also contributes substantially. This comparison of energetic driving forces of mismatch responses allows for deeper insight into protein stability and conformational changes in lipid membranes.     

Chain ordering in liquid crystals: II. Structure of bilayer membranes

The ordering of the hydrocarbon chain interior of bilayer membranes has been calculated using the molecular field approximation developed in previous work on liquid crystals. Different statistical averages are evaluated by exact summation over all conformations of a single chain in the field due to neighboring molecules. The internal energy of each conformation, as well as contributions arising from interaction with the molecular field and from a lateral pressure on the chain have been included.The results describe properties of both lipid monolayers and bilayers. For monolayers, the calculated pressure-area relationships are in good agreement with experimental observations. The order parameter for hydrocarbon chains in bilayers (or monolayers) as a function of temperature, lateral pressure and position along the chain, is shown and compared with the available NMR data. Combining the results of calculation and NMR measurements we obtain the value for intrinsic lateral pressure within bilayer membranes, in excellent agreement with direct measurements on surface monolayers.The calculation also gives average length of hydrocarbon chains, thermal expansion coefficient and fraction of bonds in gauche conformations. The effect of cholesterol and proteins within the bilayer is qualitatively described, and the contribution of the bilayer interior to membrane elasticity is determined.     

Sensitivity of Prestin-Based Membrane Motor to Membrane Thickness

Prestin is the membrane protein in outer hair cells that harnesses electrical energy by changing its membrane area in response to changes in the membrane potential. To examine the effect of membrane thickness on this protein, phosphatidylcholine (PC) with various acyl-chain lengths were incorporated into the plasma membrane by using γ-cyclodextrin. Incorporation of short chain PCs increased the linear capacitance and positively shifted the voltage dependence of prestin, up to 120 mV, in cultured cells. PCs with long acyl chains had the opposite effects. Because the linear capacitance is inversely related to the membrane thickness, these voltage shifts are attributable to membrane thickness. The corresponding voltage shifts of electromotility were observed in outer hair cells. These results demonstrate that electromotility is extremely sensitive to the thickness of the plasma membrane, presumably involving hydrophobic mismatch. These observations indicate that the extended state of the motor molecule, which is associated with the elongation of outer hair cells, has a conformation with a shorter hydrophobic height in the lipid bilayer.     

A mean-field model of the alkane-saturated lipid bilayer above its phase transition. I. Development of the model

A statistical mechanical model of a bilayer of dipalmitoyl-3-sn-phosphatidylcholine molecules in equilibrium with an aqueous phase saturated with an n-alkane is presented. A mean-field approach developed in previous work on a solventless bilayer (Gruen, Biochim. Biophys. Acta. 595:161--183, 1980) is extended to allow alkane chains to exist in the hydrophobic core of the membrane. As the alkane chains are chemically similar to the lipid chains, much of the analysis follows directly from the solventless model. Novel features of the present model are the inclusion of (a) a term which models the free energy cost of creating space for alkane conformations, (b) a term which constrains the chains to pack evenly in the hydrophobic region of the membrane, and (c) a term which estimates the free energy of mixing of the lipid and alkane molecules in the plane of the bilayer. On uptake of alkane, the dimensions of the bilayer increase. Allowance is made for an increase in thickness and/or an increase in area per lipid. A thermodynamic framework is established which allows evaluation of the free energy of a bilayer of arbitrary dimensions with a view to predicting the equilibrium structure.     

Regulation of channel function due to physical energetic coupling with a lipid bilayer

Regulation of membrane protein functions due to hydrophobic coupling with a lipid bilayer has been investigated. An energy formula describing interactions between lipid bilayer and integral ion channels with different structures, which is based on the screened Coulomb interaction approximation, has been developed. Here the interaction energy is represented as being due to charge-based interactions between channel and lipid bilayer. The hydrophobic bilayer thickness channel length mismatch is found to induce channel destabilization exponentially while negative lipid curvature linearly. Experimental parameters related to channel dynamics are consistent with theoretical predictions. To measure comparable energy parameters directly in the system and to elucidate the mechanism at an atomistic level we performed molecular dynamics (MD) simulations of the ion channel forming peptide–lipid complexes. MD simulations indicate that peptides and lipids experience electrostatic and van der Waals interactions for short period of time when found within each other’s proximity. The energies from these two interactions are found to be similar to the energies derived theoretically using the screened Coulomb and the van der Waals interactions between peptides (in ion channel) and lipids (in lipid bilayer) due to mainly their charge properties. The results of in silico MD studies taken together with experimental observable parameters and theoretical energetic predictions suggest that the peptides induce ion channels inside lipid membranes due to peptide–lipid physical interactions. This study provides a new insight helping better understand of the underlying mechanisms of membrane protein functions in cell membrane leading to important biological implications.     

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.     

Penetration of Lysozyme and Cytochrome C in Lipid Bilayer: Fluorescent Study

Lysozyme and cytochrome c (CytC) are well-investigated proteins. Their specific interactions with lipid membranes, however, keep surprising secrets. Lysozyme destroys bacterial membrane; CytC binds hydrophobically to alkyl chains of the membrane lipid tails, indicating that both proteins are able to interact directly with the inner membrane components, especially with the fatty acyl chains of membrane lipids. The degrees of integration, depth of localization in the hydrophobic interior of different types of model membranes, and the type of interaction of lysozyme and CytC with surrounding lipids were investigated by fluorescent spectroscopy. Three different fluorescent markers, located at approximately 6.5, 9, and 18 Å into the lipid bilayer, were used. In addition, liposomes were designed as electrically neutral or positively or negatively charged to unravel the importance of the net electrical charge for lipid/protein interaction. CytC penetrates deeper into the lipid bilayer in comparison with lysozyme, and data are discussed in the terms of Stern–Volmer quenching of fluorescence.     

The Mechanism of a Nuclear Pore Assembly: A Molecular Biophysics View

The basic problem of nuclear pore assembly is the big perinuclear space that must be overcome for nuclear membrane fusion and pore creation. Our investigations of ternary complexes: DNA–PC liposomes–Mg²⁺, and modern conceptions of nuclear pore structure allowed us to introduce a new mechanism of nuclear pore assembly. DNA-induced fusion of liposomes (membrane vesicles) with a single-lipid bilayer or two closely located nuclear membranes is considered. After such fusion on the lipid bilayer surface, traces of a complex of ssDNA with lipids were revealed. At fusion of two identical small liposomes (membrane vesicles) <100 nm in diameter, a “big” liposome (vesicle) with ssDNA on the vesicle equator is formed. ssDNA occurrence on liposome surface gives a biphasic character to the fusion kinetics. The “big” membrane vesicle surrounded by ssDNA is the base of nuclear pore assembly. Its contact with the nuclear envelope leads to fast fusion of half of the vesicles with one nuclear membrane; then ensues a fusion delay when ssDNA reaches the membrane. The next step is to turn inside out the second vesicle half and its fusion to other nuclear membrane. A hole is formed between the two membranes, and nucleoporins begin pore complex assembly around the ssDNA. The surface tension of vesicles and nuclear membranes along with the kinetic energy of a liquid inside a vesicle play the main roles in this process. Special cases of nuclear pore formation are considered: pore formation on both nuclear envelope sides, the difference of pores formed in various cell-cycle phases and linear nuclear pore clusters.     

Line tension and structure of raft boundary calculated from bending,tilt, and lateral compression/stretching

Bilayer thickness in membrane domains enriched with sphingomielin and cholesterol (known as “rafts”) is bigger than thickness of neighboring membrane. Monolayers need to deform to compensate the thicknesses difference in the vicinity of the raft boundary. Line tension of the boundary of rafts associated with elastic deformations originating from the compensation of the thickness mismatch is calculated in the frame-work of the elasticity theory. In the calculations deformations of splay, tilt and lateral stretching/compression are considered. It is assumed that raft consists of two monolayer domains situated in the different membrane monolayers; it is also assumed that the boundaries of domains can shift in the lateral direction with respect to relative to each other. Dependence of the boundary energy of raft on the value of the relative shift of the boundaries is calculated. It is shown that the boundary energy is minimal when shift is equal to 4.5 nm. Dependence of the optimal shift on the mismatch of the monolayer thicknesses of raft and surrounding membrane as well as membrane shape in the vicinity of boundary are calculated. The calculated values of line tension are in a good agreement with available experimental data. Taking into account deformation of stretching/compression increases the accuracy of calculations by 30%; this exceeds the uncertainty of the line tension measurements by modern techniques.     

Protein shape change has a major effect on the gating energy of a mechanosensitive channel

Increasing experimental evidence has shown that membrane protein functionality depends on molecular composition of cell membranes. However, the origin of this dependence is not fully understood. It is reasonable to assume that specific lipid-protein interactions are important, yet more generic effects due to mechanical properties of lipid bilayers likely play a significant role too. Previously it has been demonstrated using models for elastic properties of membranes and lateral pressure profiles of lipid bilayers that the mechanical properties of a lipid bilayer can contribute as much as ∼10 k_BT to the free energy difference associated with a change in protein conformational state. Here, we extend those previous approaches to a more realistic model for a large mechanosensitive channel (MscL). We use molecular dynamics together with the MARTINI model to simulate the open and closed states of MscL embedded in a DOPC bilayer. We introduce a procedure to calculate the mechanical energy change in the channel gating using a three-dimensional pressure distribution inside a membrane, computed from the molecular dynamics simulations. We decompose the mechanical energy to terms associated with area dilation and shape contribution. Our results highlight that the lateral pressure profile of a lipid bilayer together with the shape change in gating can induce a contribution of ∼30 k_BT on the gating energy of MscL. This contribution arises largely from the interfacial tension between hydrophobic and hydrophilic regions in a lipid bilayer.