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

Interaction of anionic Fe3O4 nanoparticles with lipid vesicles: a review on deformation and poration under various conditions

This review focuses on the deformation and poration of lipid vesicles caused by the interaction of anionic magnetite nanoparticles (MNPs). Effects of various factors, such as surface charge density, salt and sugar concentrations in buffer, membrane cholesterol content, polymer-grafted phospholipid, and membrane potential have been discussed for the interaction of MNPs with lipid vesicles. To quantify these effects on the vesicles, compactness, fraction of deformation and poration, dynamics of membrane permeation, and kinetics of membrane permeation have been critically evaluated. The review explores the potential advancements as well as future directions of the research field in the biomedical application of MNPs.

Effects of membrane potentials on the electroporation of giant unilamellar vesicles

Living organisms maintain a resting membrane potential, which plays an important role in various biophysical and biological processes. In the context of medical applications, irreversible electroporation (IRE) is a non-thermal and minimally invasive technique that utilizes precisely controlled electric field pulses of micro- to millisecond durations to effectively ablate cancer and tumor cells. Previous studies on IRE-induced rupture of cell-mimetic giant unilamellar vesicles (GUVs) have primarily been conducted in the absence of membrane potentials. In this study, we investigated the electroporation of GUVs, including parameters such as the rate constant of rupture and the probability of rupture, in the presence of various negative membrane potentials. The membranes of GUVs were prepared using lipids and channel forming proteins. As the membrane potential increased from 0 to -90 mV, the rate constant of rupture showed a significant increase from (7.5 ± 1.6)×10-3 to (35.6 ± 5.5)×10-3 s-1. The corresponding probability of rupture also exhibited a notable increase from 0.40 ± 0.05 to 0.68 ± 0.05. To estimate the pore edge tension, the electric tension-dependent logarithm of the rate constant was fitted with the Arrhenius equation for different membrane potentials. The presence of membrane potential did not lead to any significant changes in the pore edge tension. The increase in electroporation is reasonably explained by the decrease in the prepore free energy barrier. The choice of buffer used in GUVs can significantly influence the kinetics of electroporation. This study provides valuable insights that can contribute to the application of electroporation techniques in the biomedical field.

Increase in anionic Fe3O4 nanoparticle-induced membrane poration and vesicle deformation due to membrane potential - an experimental study

The membrane potential plays a significant role in various cellular processes while interacting with membrane active agents. So far, all the investigations of the interaction of nanoparticles (NPs) with lipid vesicles have been performed in the absence of membrane potential. In this study, the anionic magnetite NP-induced poration along with deformation of cell-mimetic giant unilamellar vesicles (GUVs) has been studied in the presence of various membrane potentials. Lipids 1,2-dioleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) (DOPG), 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC), and channel forming protein gramicidin A (GrA) are used to synthesize the DOPG/DOPC/GrA-GUVs. The static and dynamic nature of GUVs is investigated using phase contrast fluorescent microscopy. The presence of GrA in the membrane decreases the leakage constant of the encapsulating fluorescent probe (calcein) in the absence of membrane potential. With the increase of negative membrane potential, the leakage shifts from a single exponential to two exponential functions, obtaining two leakage constants. The leakage became faster at the initial stage, and at the final stage, it became slower with the increase in negative membrane potential. Both the fraction of poration and deformation increase with the increase of negative membrane potential. These results suggested that the membrane potential enhances the NP-induced poration along with the deformation of DOPG/DOPC/GrA-GUVs. The increase of the binding constant in the NPs with membrane potential is one of the important factors for increasing membrane permeation and vesicle deformation.

Dependence of protein-induced lipid bilayer deformations on protein shape

Membrane proteins typically deform the surrounding lipid bilayer membrane, which can play an important role in the function, regulation, and organization of membrane proteins. Membrane elasticity theory provides a beautiful description of protein-induced lipid bilayer deformations, in which all physical parameters can be directly determined from experiments. While analytic solutions of protein-induced elastic bilayer deformations are most easily developed for proteins with approximately circular cross sections, structural biology has shown that membrane proteins come in a variety of distinct shapes, with often considerable deviations from a circular cross section. We develop here a boundary value method (BVM) that permits the construction of analytic solutions of protein-induced elastic bilayer deformations for protein shapes with arbitrarily large deviations from a circular cross section, for constant as well as variable boundary conditions along the bilayer-protein interface. We apply this BVM to protein-induced lipid bilayer thickness deformations. Our BVM reproduces available analytic solutions for proteins with circular cross section and yields, for proteins with noncircular cross section, excellent agreement with numerical, finite element solutions. On this basis, we formulate a simple analytic approximation of the bilayer thickness deformation energy associated with general protein shapes and show that, for modest deviations from rotational symmetry, this analytic approximation is in good agreement with BVM solutions. Using the BVM, we survey the dependence of protein-induced elastic bilayer thickness deformations on protein shape, and thus explore how the coupling of protein shape and bilayer thickness deformations affects protein oligomerization and transitions in protein conformational state.

Regulation of Gramicidin Channel Function Solely by Changes in Lipid Intrinsic Curvature

Membrane protein function is regulated by the lipid bilayer composition. In many cases the changes in function correlate with changes in the lipid intrinsic curvature (c 0), and c 0 is considered a determinant of protein function. Yet, water-soluble amphiphiles that cause either negative or positive changes in curvature have similar effects on membrane protein function, showing that changes in lipid bilayer properties other than c 0 are important-and may be dominant. To further investigate the mechanisms underlying the bilayer regulation of protein function, we examined how maneuvers that alter phospholipid head groups effective "size"-and thereby c 0-alter gramicidin (gA) channel function. Using dioleoylphospholipids and planar bilayers, we varied the head groups' physical volume and the electrostatic repulsion among head groups (and thus their effective size). When 1,2-dioleyol-sn-glycero-3-phosphocholine (DOPC), was replaced by 1,2-dioleyol-sn-glycero-3-phosphoethanolamine (DOPE) with a smaller head group (causing a more negative c 0), the channel lifetime (τ) is decreased. When the pH of the solution bathing a 1,2-dioleyol-sn-glycero-3-phosphoserine (DOPS) bilayer is decreased from 7 to 3 (causing decreased head group repulsion and a more negative c 0), τ is decreased. When some DOPS head groups are replaced by zwitterionic head groups, τ is similarly decreased. These effects do not depend on the sign of the change in surface charge. In DOPE:DOPC (3:1) bilayers, pH changes from 5→9 to 5→0 (both increasing head group electrostatic repulsion, thereby causing a less negative c 0) both increase τ. Nor do the effects depend on the use of planar, hydrocarbon-containing bilayers, as similar changes were observed in hydrocarbon-free lipid vesicles. Altering the interactions among phospholipid head groups may alter also other bilayer properties such as thickness or elastic moduli. Such changes could be excluded using capacitance measurements and single channel measurements on gA channels of different lengths. We conclude that changes gA channel function caused by changes in head group effective size can be predicted from the expected changes in c 0.

Characterizing Residue-Bilayer Interactions Using Gramicidin A as a Scaffold and Tryptophan Substitutions as Probes

Previous experiments have shown that the lifetime of a gramicidin A dimer channel (which forms from two nonconducting monomers) in a lipid bilayer is modulated by mutations of the tryptophan (Trp) residues at the bilayer-water interface. We explore this further using extensive molecular dynamics simulations of various gA dimer and monomer mutants at the Trp positions in phosphatidylcholine bilayers with different tail lengths. gA interactions with the surrounding bilayer are strongly modulated by mutating these Trp residues. There are three principal effects: eliminating residue hydrogen bonding ability (i.e., reducing the channel-monolayer coupling strength) reduces the extent of the bilayer deformation caused by the assembled dimeric channel; a residue's size and geometry affects its orientation, leading to different hydrogen bonding partners; and increasing a residue's hydrophobicity increases the depth of gA monomer insertion relative to the bilayer center, thereby increasing the lipid bending frustration.

New Continuum Approaches for Determining Protein-Induced Membrane Deformations

The influence of the membrane on transmembrane proteins is central to a number of biological phenomena, notably the gating of stretch activated ion channels. Conversely, membrane proteins can influence the bilayer, leading to the stabilization of particular membrane shapes, topological changes that occur during vesicle fission and fusion, and shape-dependent protein aggregation. Continuum elastic models of the membrane have been widely used to study protein-membrane interactions. These mathematical approaches produce physically interpretable membrane shapes, energy estimates for the cost of deformation, and a snapshot of the equilibrium configuration. Moreover, elastic models are much less computationally demanding than fully atomistic and coarse-grained simulation methodologies; however, it has been argued that continuum models cannot reproduce the distortions observed in fully atomistic molecular dynamics simulations. We suggest that this failure can be overcome by using chemically and geometrically accurate representations of the protein. Here, we present a fast and reliable hybrid continuum-atomistic model that couples the protein to the membrane. We show that the model is in excellent agreement with fully atomistic simulations of the ion channel gramicidin embedded in a POPC membrane. Our continuum calculations not only reproduce the membrane distortions produced by the channel but also accurately determine the channel's orientation. Finally, we use our method to investigate the role of membrane bending around the charged voltage sensors of the transient receptor potential cation channel TRPV1. We find that membrane deformation significantly stabilizes the energy of insertion of TRPV1 by exposing charged residues on the S4 segment to solution.

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

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

Continuum descriptions of membranes and their interaction with proteins: Towards chemically accurate models

Biological membranes deform in response to resident proteins leading to a coupling between membrane shape and protein localization. Additionally, the membrane influences the function of membrane proteins. Here we review contributions to this field from continuum elastic membrane models focusing on the class of models that couple the protein to the membrane. While it has been argued that continuum models cannot reproduce the distortions observed in fully-atomistic molecular dynamics simulations, we suggest that this failure can be overcome by using chemically accurate representations of the protein. We outline our recent advances along these lines with our hybrid continuum-atomistic model, and we show the model is in excellent agreement with fully-atomistic simulations of the nhTMEM16 lipid scramblase. We believe that the speed and accuracy of continuum-atomistic methodologies will make it possible to simulate large scale, slow biological processes, such as membrane morphological changes, that are currently beyond the scope of other computational approaches. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Molecular modeling of proteinlike inclusions in lipid bilayers: lipid-mediated interactions

We investigated the insertion of transmembrane structures in a lipid bilayer and their interactions using self-consistent field theory. The lipids are coarse-grained on a united-atom level and consist of a phosphatidylcholinelike headgroup and two hydrophobic tails. The inclusions, acting as simple models for proteins that span biological membranes, are rigid rods (radius R ) with a hydrophobic surface and hydrophilic end caps. The insertion free energy Omega of an individual rod is strongly regulated by the affinity between its hydrophobic surface and the lipid tails. This affinity also controls the best match of the hydrophobic length of the rod with that of the bilayer. The line tension tau(=Omega/2piR) is practically independent of R . The perturbations in the bilayer as a function of distance from the inclusion, have the shape of a damped oscillation. The wavelength and decay length are related to the elastic properties of the bilayer and do not depend on R . These results are used to analyze how the lipid matrix affects the interaction between transmembrane objects, for computational reasons considering the limit of R-->infinity . Contributions on different length scales can be distinguished: (i) a long-range elastic interaction, which is an exponentially decaying oscillation; (ii) an exponentially decaying repulsion on an intermediate length scale, resulting from the loss of conformational entropy of the lipid tails; and (iii) a short-range interaction due to the finite compressibility of the lipid tails, which manifests either as a depletion attraction if there is no affinity between the tails and the inclusions' surface or, otherwise, as an oscillatory structural force.

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.

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.

Gating gramicidin channels in lipid bilayers: reaction coordinates and the mechanism of dissociation

The dissociation of gramicidin A (gA) channels into monomers is the simplest example of a channel gating process. The initial steps in this process are studied via a computational model that simulates the reaction coordinate for dimer-monomer dissociation. The nonbonded interaction energy between the monomers is determined, allowing for their free relative translational and rotational motion. Lowest energy pathways and reaction coordinates of the gating process are determined. Partial rupture of the six hydrogen bonds (6HB) at the dimer junction takes place by coupling monomer rotation and lateral displacement. Coupling rotation with axial separation is far more expensive energetically. The transition state for channel dissociation occurs when monomers are displaced laterally by approximately 4-6 A, separated by approximately 1.6-2 A, and rotated by approximately 120 degrees, breaking two hydrogen bonds. In membranes with significant hydrophobic mismatch there is a much greater likelihood of forming 4HB and possibly even 2HB states. In the 4HB state the pore remains fully open and conductive. However, transitions from the 6HB to 4HB and 4HB to 2HB states take place via intermediates in which the gA pore is closed and nonconductive. These lateral monomer displacements give rise to transitory pore occlusion at the dimer junction, which provides a rationale for fast closure events (flickers). Local dynamics of gA monomers also leads to lateral and rotational diffusion of the whole gA dimer, giving rise to diffusional rotation of the dimer about the channel axis.

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.

Voltage-dependent formation of gramicidin channels in lipid bilayers

The formation kinetics of gramicidin A channels in lipid bilayer membranes has been characterized as a function of voltage for different solution conditions and membrane composition. The frequency of channel events was measured during the application of voltage ramps and counted in given intervals, a procedure that eliminated the effects of drift in gramicidin concentration. The formation rate was found to increase strongly with voltages up to approximately 50 mV and then to level off slightly. The shape of the voltage dependence was independent of lipid solvent and ramp speed but differed for different ions and different solution concentrations. This suggested an ion occupancy effect on the formation rate that was further supported by the fact that the minimum of the formation rate was shifted toward the equilibrium potential in asymmetric solution concentrations. The effects are explained in terms of a model that contains two contributions to the voltage dependence, a voltage-dependent ion binding to the monomers and a polarization of monomers by the applied electric field and by the occupied ions. The theory is found to give a good fit to experimental data.

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.

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.

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.

Effect of the dipole potential of a bilayer lipid membrane on gramicidin channel dissociation kinetics

A technique of measuring of the light-induced transients of the gramicidin-mediated electric current across a membrane in the presence of a photosensitizer has been applied for the study of the effect of agents modifying the dipole potential of a bilayer lipid membrane (phloretin, 6-ketocholestanol, and RH421) on the processes of the gramicidin channel dissociation and formation. It is shown that phloretin, known to lower the dipole potential, decelerates the flash-induced decrease in the current, whereas 6-ketocholestanol and RH421, known to raise the dipole potential, accelerate the current decrease. It is revealed that the addition of phloretin leads to a decrease in the dissociation rate constant, whereas addition of either 6-ketocholestanol or RH421 causes an increase in this constant. Single-channel data show that phloretin brings about an increase in the lifetime of the gramicidin channels, whereas RH421 produces a more complicated effect. It is conclude that the dipole potential affects the process of channel dissociation, presumably via the influence on the movement of the dipoles of gramicidin molecules through the layer of the dipole potential drop near the membrane-water interface.