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

Neutron scattering studies on dynamics of lipid membranes

Neutron scattering methods are powerful tools for the study of the structure and dynamics of lipid bilayers in length scales from sub Å to tens to hundreds nm and the time scales from sub ps to μs. These techniques also are nondestructive and, perhaps most importantly, require no additives to label samples. Because the neutron scattering intensities are very different for hydrogen- and deuterium-containing molecules, one can replace the hydrogen atoms in a molecule with deuterium to prepare on demand neutron scattering contrast without significantly altering the physical properties of the samples. Moreover, recent advances in neutron scattering techniques, membrane dynamics theories, analysis tools, and sample preparation technologies allow researchers to study various aspects of lipid bilayer dynamics. In this review, we focus on the dynamics of individual lipids and collective membrane dynamics as well as the dynamics of hydration water.

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.

Determining Spatial Variability of Elastic Properties for Biological Samples Using AFM

Measuring the mechanical properties (i.e., elasticity in terms of Young's modulus) of biological samples using Atomic Force Microscopy (AFM) indentation at the nanoscale has opened new horizons in studying and detecting various pathological conditions at early stages, including cancer and osteoarthritis. It is expected that AFM techniques will play a key role in the future in disease diagnosis and modeling using rigorous mathematical criteria (i.e., automated user-independent diagnosis). In this review, AFM techniques and mathematical models for determining the spatial variability of elastic properties of biological materials at the nanoscale are presented and discussed. Significant issues concerning the rationality of the elastic half-space assumption, the possibility of monitoring the depth-dependent mechanical properties, and the construction of 3D Young's modulus maps are also presented.

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.

Endothelial Cell Plasma Membrane Biomechanics Mediates Effects of Pro-Inflammatory Factors on Endothelial Mechanosensors: Vicious Circle Formation in Atherogenic Inflammation

Chronic low-grade vascular inflammation and endothelial dysfunction significantly contribute to the pathogenesis of cardiovascular diseases. In endothelial cells (ECs), anti-inflammatory or pro-inflammatory signaling can be induced by different patterns of the fluid shear stress (SS) exerted by blood flow on ECs. Laminar blood flow with high magnitude is anti-inflammatory, while disturbed flow and laminar flow with low magnitude is pro-inflammatory. Endothelial mechanosensors are the key upstream signaling proteins in SS-induced pro- and anti-inflammatory responses. Being transmembrane proteins, mechanosensors, not only experience fluid SS but also become regulated by the biomechanical properties of the lipid bilayer and the cytoskeleton. We review the apparent effects of pro-inflammatory factors (hypoxia, oxidative stress, hypercholesterolemia, and cytokines) on the biomechanics of the lipid bilayer and the cytoskeleton. An analysis of the available data suggests that the formation of a vicious circle may occur, in which pro-inflammatory cytokines enhance and attenuate SS-induced pro-inflammatory and anti-inflammatory signaling, respectively.

A Note of Caution: Gramicidin Affects Signaling Pathways Independently of Its Effects on Plasma Membrane Conductance

Gramicidin is a thoroughly studied cation ionophore widely used to experimentally manipulate the plasma membrane potential (PMP). In addition, it has been established that the drug, due to its hydrophobic nature, is capable of affecting the organization of membrane lipids. We have previously shown that modifications in the plasma membrane potential of epithelial cells in culture determine reorganizations of the cytoskeleton. To elucidate the molecular mechanisms involved, we explored the effects of PMP depolarization on some putative signaling intermediates. In the course of these studies, we came across some results that could not be interpreted in terms of the properties of gramicidin as an ionic channel. The purpose of the present work is to communicate these results and, in general, to draw attention to the fact that gramicidin effects can be misleadingly attributed to its ionic or electrical properties. In addition, this work also contributes with some novel findings of the modifications provoked on the signaling intermediates by PMP depolarization and hyperpolarization.

Collective dynamics in lipid membranes containing transmembrane peptides

Biological membranes are composed of complex mixtures of lipids and proteins that influence each other's structure and function. The biological activities of many channel-forming peptides and proteins are known to depend on the material properties of the surrounding lipid bilayer. However, less is known about how membrane-spanning channels affect the lipid bilayer properties, and in particular, their collective fluctuation dynamics. Here we use neutron spin echo spectroscopy (NSE) to measure the collective bending and thickness fluctuation dynamics in dimyristoylphosphatidylcholine (di 14 : 0 PC, DMPC) lipid membranes containing two different antimicrobial peptides, alamethicin (Ala) and gramicidin (gD). Ala and gD are both well-studied antimicrobial peptides that form oligomeric membrane-spanning channels with different structures. At low concentrations, the peptides did not have a measurable effect on the average bilayer structure, yet significantly changed the collective membrane dynamics. Despite both peptides forming transmembrane channels, they had opposite effects on the relaxation time of the collective bending fluctuations and associated effective bending modulus, where gD addition stiffened the membrane while Ala addition softened the membrane. Meanwhile, the lowest gD concentrations enhanced the collective thickness fluctuation dynamics, while the higher gD concentrations and all studied Ala concentrations dampened these dynamics. The results highlight the synergy between lipids and proteins in determining the collective membrane dynamics and that not all peptides can be universally treated as rigid bodies when considering their effects on the lipid bilayer fluctuations.

Molecular Mechanism for Gramicidin Dimerization and Dissociation in Bilayers of Different Thickness

Membrane protein functions can be altered by subtle changes in the host lipid bilayer physical properties. Gramicidin channels have emerged as a powerful system for elucidating the underlying mechanisms of membrane protein function regulation through changes in bilayer properties, which are reflected in the thermodynamic equilibrium distribution between nonconducting gramicidin monomers and conducting bilayer-spanning dimers. To improve our understanding of how subtle changes in bilayer thickness alter the gramicidin monomer and dimer distributions, we performed extensive atomistic molecular dynamics simulations and fluorescence-quenching experiments on gramicidin A (gA). The free-energy calculations predicted a nonlinear coupling between the bilayer thickness and channel formation. The energetic barrier inhibiting gA channel formation was sharply increased in the thickest bilayer (1,2-dierucoyl-sn-glycero-3-phosphocholine). This prediction was corroborated by experimental results on gramicidin channel activity in bilayers of different thickness. To further explore the mechanism of channel formation, we performed extensive unbiased molecular dynamics simulations, which allowed us to observe spontaneous gA dimer formation in lipid bilayers. The simulations revealed structural rearrangements in the gA subunits and changes in lipid packing, as well as water reorganization, that occur during the dimerization process. Together, the simulations and experiments provide new, to our knowledge, insights into the process and mechanism of gramicidin channel formation, as a prototypical example of the bilayer regulation of membrane protein function.

Quantitative Characterization of Protein-Lipid Interactions by Free Energy Simulation between Binary Bilayers

Using a recently developed binary bilayer system (BBS) consisting of two patches of laterally contacting bilayers, umbrella sampling molecular dynamics (MD) simulations were performed for quantitative characterization of protein-lipid interactions. The BBS is composed of 1,2-dilauroyl-sn-glycero-3-phosphocholine (DLPC) and 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) with an embedded model membrane protein, a gramicidin A (gA) channel. The calculated free energy difference for the transfer of a gA channel from DLPC (hydrophobic thickness ≈ 21.5 Å) to DMPC (hydrophobic thickness ≈ 25.5 Å) bilayers, ΔG(DLPC → DMPC), is -2.2 ± 0.7 kcal/mol. This value appears at odds with the traditional view that the hydrophobic length of the gA channel is ∼22 Å. To understand this discrepancy, we first note that recent MD simulations by different groups have shown that lipid bilayer thickness profiles in the vicinity of a gA channel differ qualitatively from the deformation profile predicted from continuum elastic bilayer models. Our MD simulations at low and high gA:lipid molar ratios and different membrane compositions indicate that the gA channel's effective hydrophobic length is ∼26 Å. Using this effective hydrophobic length, ΔG(DLPC → DMPC) determined here is in excellent agreement with predictions based on continuum elastic models (-3.0 to -2.2 kcal/mol) where the bilayer deformation energy is approximated as a harmonic function of the mismatch between the channel's effective hydrophobic length and the hydrophobic thickness of the bilayer. The free energy profile for gA in the BBS includes a barrier at the interface between the two bilayers which can be attributed to the line tension at the interface between two bilayers with different hydrophobic thicknesses. This observation implies that translation of a peptide between two different regions of a cell membrane (such as between the liquid ordered and disordered phases) may include effects of a barrier at the interface in addition to the relative free energies of the species far from the interface. The BBS allows for direct transfer free energy calculations between bilayers without a need of a reference medium, such as bulk water, and thus provides an efficient simulation protocol for the quantitative characterization of protein-lipid interactions at all-atom resolution.

Incubation of human sperm with micelles made from glycerophospholipid mixtures increases sperm motility and resistance to oxidative stress

Membrane integrity is essential in maintaining sperm viability, signaling, and motility, which are essential for fertilization. Sperm are highly susceptible to oxidative stress, as they are rich in sensitive polyunsaturated fatty acids (PUFA), and are unable to synthesize and repair many essential membrane constituents. Because of this, sperm cellular membranes are important targets of this process. Membrane Lipid Replacement (MLR) with glycerophospholipid mixtures (GPL) has been shown to ameliorate oxidative stress in cells, restore their cellular membranes, and prevent loss of function. Therefore, we tested the effects of MLR on sperm by tracking and monitoring GPL incorporation into their membrane systems and studying their effects on sperm motility and viability under different experimental conditions. Incubation of sperm with mixtures of exogenous, unoxidized GPL results in their incorporation into sperm membranes, as shown by the use of fluorescent dyes attached to GPL. The percent overall (total) sperm motility was increased from 52±2.5% to 68±1.34% after adding GPL to the incubation media, and overall sperm motility was recovered from 7±2% after H2O2 treatment to 58±2.5%)(n = 8, p<0.01) by the incorporation of GPL into sperm membranes. When sperm were exposed to H2O2, the mitochondrial inner membrane potential (MIMP), monitored using the MIMP tracker dye JC-1 in flow cytometry, diminished, whereas the addition of GPL prevented the decrease in MIMP. Confocal microscopy with Rhodamine-123 and JC-1 confirmed the mitochondrial localization of the dyes. We conclude that incubation of human sperm with glycerolphospholipids into the membranes of sperm improves sperm viability, motility, and resistance to oxidizing agents like H2O2. This suggests that human sperm might be useful to test innovative new treatments like MLR, since such treatments could improve fertility when it is adversely affected by increased oxidative stress.

Coupling between Inclusions and Membranes at the Nanoscale

The activity of cell membrane inclusions (such as ion channels) is influenced by the host lipid membrane, to which they are elastically coupled. This coupling concerns the hydrophobic thickness of the bilayer (imposed by the length of the channel, as per the hydrophobic matching principle) but also its slope at the boundary of the inclusion. However, this parameter has never been measured so far. We combine small-angle x-ray scattering data and a complete elastic model to measure the slope for the model gramicidin channel and show that it is surprisingly steep in two membrane systems with very different elastic properties. This conclusion is confirmed and generalized by the comparison with recent results in the simulation literature and with conductivity measurements.

Integrated microfluidic biosensing platform for simultaneous confocal microscopy and electrophysiological measurements on bilayer lipid membranes and ion channels

Combining high-resolution imaging and electrophysiological recordings is key for various types of experimentation on lipid bilayers and ion channels. Here, we propose an integrated biosensing platform consisting of a microfluidic cartridge and a dedicated chip-holder to conduct such dual measurements on suspended lipid bilayers, in a user-friendly manner. To illustrate the potential of the integrated platform, we characterize lipid bilayers in terms of thickness and fluidity while simultaneously monitoring single ion channel currents. For that purpose, POPC lipid bilayers are supplemented with a fluorescently-tagged phospholipid (NBD-PE, 1% mol) for Fluorescence Recovery After Photobleaching (FRAP) measurements and a model ion channel (gramicidin, 1 nM). These combined measurements reveal that NBD-PE has no effect on the lipid bilayer thickness while gramicidin induces thinning of the membrane. Furthermore, the presence of gramicidin does not alter the lipid bilayer fluidity. Surprisingly, in lipid bilayers supplemented with both probes, a reduction in gramicidin open probability and lifetime is observed compared to lipid bilayers with gramicidin only, suggesting an influence of NBD-PE on the gramicidin ion function. Altogether, our proposed microfluidic biosensing platform in combination with the herein presented multi-parametric measurement scheme paves the way to explore the interdependent relationship between lipid bilayer properties and ion channel function.

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.

Divergent effects of anesthetics on lipid bilayer properties and sodium channel function

General anesthetics revolutionized medicine by allowing surgeons to perform more complex and much longer procedures. This widely used class of drugs is essential to patient care, yet their exact molecular mechanism(s) are incompletely understood. One early hypothesis over a century ago proposed that nonspecific interactions of anesthetics with the lipid bilayer lead to changes in neuronal function via effects on membrane properties. This model was supported by the Meyer-Overton correlation between anesthetic potency and lipid solubility and despite more recent evidence for specific protein targets, in particular ion-channels, lipid bilayer-mediated effects of anesthetics is still under debate. We therefore tested a wide range of chemically diverse general anesthetics on lipid bilayer properties using a sensitive and functional gramicidin-based assay. None of the tested anesthetics altered lipid bilayer properties at clinically relevant concentrations. Some anesthetics did affect the bilayer, though only at high supratherapeutic concentrations, which are unlikely relevant for clinical anesthesia. These results suggest that anesthetics directly interact with membrane proteins without altering lipid bilayer properties at clinically relevant concentrations. Voltage-gated Na⁺ channels are potential anesthetic targets and various isoforms are inhibited by a wide range of volatile anesthetics. They inhibit channel function by reducing peak Na⁺ current and shifting steady-state inactivation toward more hyperpolarized potentials. Recent advances in crystallography of prokaryotic Na⁺ channels, which are sensitive to volatile anesthetics, together with molecular dynamics simulations and electrophysiological studies will help identify potential anesthetic interaction sites within the channel protein itself.

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

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

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

Integral membrane protein function can be modulated by the host bilayer. Because biological membranes are diverse and nonuniform, we explore the consequences of lipid diversity using gramicidin A channels embedded in phosphatidylcholine (PC) bilayers composed of equimolar mixtures of di-oleoyl-PC and di-erucoyl-PC (dC_18:1+dC_22:1, respectively), di-palmitoleoyl-PC and di-nervonoyl-PC (dC_16:1+dC_24:1, respectively), and di-eicosenoyl-PC (pure dC_20:1), all of which have the same average bilayer chain length. Single-channel lifetime experiments, molecular dynamics simulations, and a simple lipid compression model are used in tandem to gain insight into lipid redistribution around the channel, which partially alleviates the bilayer deformation energy associated with channel formation. The average single-channel lifetimes in the two-component bilayers (95 ± 10 ms for dC_18:1+dC_22:1 and 195 ± 20 ms for dC_16:1+dC_24:1) were increased relative to the single-component dC_20:1 control bilayer (65 ± 10 ms), implying lipid redistribution. Using a theoretical treatment of thickness-dependent changes in channel lifetimes, the effective local enrichment of lipids around the channel was estimated to be 58 ± 4% dC_18:1 and 66 ± 2% dC_16:1 in the dC_18:1+dC_22:1 and dC_16:1+dC_24:1 bilayers, respectively. 3.5-μs molecular dynamics simulations show 66 ± 2% dC_16:1 in the first lipid shell around the channel in the dC_16:1+dC_24:1 bilayer, but no significant redistribution (50 ± 4% dC_18:1) in the dC_18:1+dC_22:1 bilayer; these simulated values are within the 95% confidence intervals of the experimental averages. The strong preference for the better matching lipid (dC_16:1) near the channel in the dC_16:1+dC_24:1 mixture and lesser redistribution in the dC_18:1+dC_22:1 mixture can be explained by the energetic cost associated with compressing the lipids to match the channel's hydrophobic length.

Membrane-mediated action of the endocannabinoid anandamide on membrane proteins: implications for understanding the receptor-independent mechanism

Endocannabinoids are amphiphilic molecules that play crucial neurophysiological functions acting as lipid messengers. Antagonists and knockdown of the classical CB1 and CB2 cannabinoid receptors do not completely abolish many endocannabinoid activities, supporting the idea of a mechanism independent of receptors whose mode of action remains unclear. Here we combine gramicidin A (gA) single channel recordings and membrane capacitance measurements to investigate the lipid bilayer-modifying activity of endocannabinoids. Single channel recordings show that the incorporation of endocannabinoids into lipid bilayers reduces the free energy necessary for gramicidin channels to transit from the monomeric to the dimeric conformation. Membrane capacitance demonstrates that the endocannabinoid anandamide has limited effects on the overall structure of the lipid bilayers. Our results associated with the theory of membrane elastic deformation reveal that the action of endocannabinoids on membrane proteins can involve local adjustments of the lipid/protein hydrophobic interface. The current findings shed new light on the receptor-independent mode of action of endocannabinoids on membrane proteins, with important implications towards their neurobiological function.

Shared mechanisms in physiological and pathological nucleoplasmic reticulum formation

The mammalian nuclear envelope (NE) can develop complex dynamic membrane-bounded invaginations in response to both physiological and pathological stimuli. Since the formation of these nucleoplasmic reticulum (NR) structures can occur during interphase, without mitotic NE breakdown and reassembly, some other mechanism must drive their development. Here we consider models for deformation of the interphase NE, together with the evidence for their potential roles in NR formation.

Membrane curvature in cell biology: An integration of molecular mechanisms

Curving biological membranes establishes the complex architecture of the cell and mediates membrane traffic to control flux through subcellular compartments. Common molecular mechanisms for bending membranes are evident in different cell biological contexts across eukaryotic phyla. These mechanisms can be intrinsic to the membrane bilayer (either the lipid or protein components) or can be brought about by extrinsic factors, including the cytoskeleton. Here, we review examples of membrane curvature generation in animals, fungi, and plants. We showcase the molecular mechanisms involved and how they collaborate and go on to highlight contexts of curvature that are exciting areas of future research. Lessons from how membranes are bent in yeast and mammals give hints as to the molecular mechanisms we expect to see used by plants and protists.

Role of the Membrane for Mechanosensing by Tethered Channels

Biologically important membrane channels are gated by force at attached tethers. Here, we generically characterize the nontrivial interplay of force, membrane tension, and channel deformations that can affect gating. A central finding is that minute conical channel deformation under force leads to significant energy release during opening. We also calculate channel-channel interactions and show that they can amplify the force sensitivity of tethered channels.

Bilayer-thickness-mediated interactions between integral membrane proteins

Hydrophobic thickness mismatch between integral membrane proteins and the surrounding lipid bilayer can produce lipid bilayer thickness deformations. Experiment and theory have shown that protein-induced lipid bilayer thickness deformations can yield energetically favorable bilayer-mediated interactions between integral membrane proteins, and large-scale organization of integral membrane proteins into protein clusters in cell membranes. Within the continuum elasticity theory of membranes, the energy cost of protein-induced bilayer thickness deformations can be captured by considering compression and expansion of the bilayer hydrophobic core, membrane tension, and bilayer bending, resulting in biharmonic equilibrium equations describing the shape of lipid bilayers for a given set of bilayer-protein boundary conditions. Here we develop a combined analytic and numerical methodology for the solution of the equilibrium elastic equations associated with protein-induced lipid bilayer deformations. Our methodology allows accurate prediction of thickness-mediated protein interactions for arbitrary protein symmetries at arbitrary protein separations and relative orientations. We provide exact analytic solutions for cylindrical integral membrane proteins with constant and varying hydrophobic thickness, and develop perturbative analytic solutions for noncylindrical protein shapes. We complement these analytic solutions, and assess their accuracy, by developing both finite element and finite difference numerical solution schemes. We provide error estimates of our numerical solution schemes and systematically assess their convergence properties. Taken together, the work presented here puts into place an analytic and numerical framework which allows calculation of bilayer-mediated elastic interactions between integral membrane proteins for the complicated protein shapes suggested by structural biology and at the small protein separations most relevant for the crowded membrane environments provided by living cells.

Biomimetic Nanotubes Based on Cyclodextrins for Ion-Channel Applications

Biomimetic membrane channels offer a great potential for fundamental studies and applications. Here, we report the fabrication and characterization of short cyclodextrin nanotubes, their insertion into membranes, and cytotoxicity assay. Mass spectrometry and high-resolution transmission electron microscopy were used to confirm the synthesis pathway leading to the formation of short nanotubes and to describe their structural parameters in terms of length, diameter, and number of cyclodextrins. Our results show the control of the number of cyclodextrins threaded on the polyrotaxane leading to nanotube synthesis. Structural parameters obtained by electron microscopy are consistent with the distribution of the number of cyclodextrins evaluated by mass spectrometry from the initial polymer distribution. An electrophysiological study at single molecule level demonstrates the ion channel formation into lipid bilayers, and the energy penalty for the entry of ions into the confined nanotube. In the presence of nanotubes, the cell physiology is not altered.

Volatile anesthetics inhibit sodium channels without altering bulk lipid bilayer properties

Although general anesthetics are clinically important and widely used, their molecular mechanisms of action remain poorly understood. Volatile anesthetics such as isoflurane (ISO) are thought to alter neuronal function by depressing excitatory and facilitating inhibitory neurotransmission through direct interactions with specific protein targets, including voltage-gated sodium channels (Na(v)). Many anesthetics alter lipid bilayer properties, suggesting that ion channel function might also be altered indirectly through effects on the lipid bilayer. We compared the effects of ISO and of a series of fluorobenzene (FB) model volatile anesthetics on Na(v) function and lipid bilayer properties. We examined the effects of these agents on Na(v) in neuronal cells using whole-cell electrophysiology, and on lipid bilayer properties using a gramicidin-based fluorescence assay, which is a functional assay for detecting changes in lipid bilayer properties sensed by a bilayer-spanning ion channel. At clinically relevant concentrations (defined by the minimum alveolar concentration), both the FBs and ISO produced prepulse-dependent inhibition of Na(v) and shifted the voltage dependence of inactivation toward more hyperpolarized potentials without affecting lipid bilayer properties, as sensed by gramicidin channels. Only at supra-anesthetic (toxic) concentrations did ISO alter lipid bilayer properties. These results suggest that clinically relevant concentrations of volatile anesthetics alter Na(v) function through direct interactions with the channel protein with little, if any, contribution from changes in bulk lipid bilayer properties. Our findings further suggest that changes in lipid bilayer properties are not involved in clinical anesthesia.

Channel-forming bacterial toxins in biosensing and macromolecule delivery

To intoxicate cells, pore-forming bacterial toxins are evolved to allow for the transmembrane traffic of different substrates, ranging from small inorganic ions to cell-specific polypeptides. Recent developments in single-channel electrical recordings, X-ray crystallography, protein engineering, and computational methods have generated a large body of knowledge about the basic principles of channel-mediated molecular transport. These discoveries provide a robust framework for expansion of the described principles and methods toward use of biological nanopores in the growing field of nanobiotechnology. This article, written for a special volume on "Intracellular Traffic and Transport of Bacterial Protein Toxins", reviews the current state of applications of pore-forming bacterial toxins in small- and macromolecule-sensing, targeted cancer therapy, and drug delivery. We discuss the electrophysiological studies that explore molecular details of channel-facilitated protein and polymer transport across cellular membranes using both natural and foreign substrates. The review focuses on the structurally and functionally different bacterial toxins: gramicidin A of Bacillus brevis, α-hemolysin of Staphylococcus aureus, and binary toxin of Bacillus anthracis, which have found their "second life" in a variety of developing medical and technological applications.

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.

Phosphoinositides alter lipid bilayer properties

Phosphatidylinositol-4,5-bisphosphate (PIP₂), which constitutes ∼1% of the plasma membrane phospholipid, plays a key role in membrane-delimited signaling. PIP₂ regulates structurally and functionally diverse membrane proteins, including voltage- and ligand-gated ion channels, inwardly rectifying ion channels, transporters, and receptors. In some cases, the regulation is known to involve specific lipid–protein interactions, but the mechanisms by which PIP₂ regulates many of its various targets remain to be fully elucidated. Because many PIP₂ targets are membrane-spanning proteins, we explored whether the phosphoinositides might alter bilayer physical properties such as curvature and elasticity, which would alter the equilibrium between membrane protein conformational states—and thereby protein function. Taking advantage of the gramicidin A (gA) channels’ sensitivity to changes in lipid bilayer properties, we used gA-based fluorescence quenching and single-channel assays to examine the effects of long-chain PIP₂s (brain PIP₂, which is predominantly 1-stearyl-2-arachidonyl-PIP₂, and dioleoyl-PIP₂) on bilayer properties. When premixed with dioleoyl-phosphocholine at 2 mol %, both long-chain PIP₂s produced similar changes in gA channel function (bilayer properties); when applied through the aqueous solution, however, brain PIP₂ was a more potent modifier than dioleoyl-PIP₂. Given the widespread use of short-chain dioctanoyl-phosphoinositides, we also examined the effects of diC₈-phosphoinositol (PI), PI(4,5)P₂, PI(3,5)P₂, PI(3,4)P₂, and PI(3,4,5)P₃. The diC₈ phosphoinositides, except for PI(3,5)P₂, altered bilayer properties with potencies that decreased with increasing head group charge. Nonphosphoinositide diC₈ phospholipids generally were more potent bilayer modifiers than the polyphosphoinositides. These results show that physiological increases or decreases in plasma membrane PIP₂ levels, as a result of activation of PI kinases or phosphatases, are likely to alter lipid bilayer properties, in addition to any other effects they may have. The results further show that exogenous PIP₂, as well as structural analogues that differ in acyl chain length or phosphorylation state, alters lipid bilayer properties at the concentrations used in many cell physiological experiments.

Dynamic Heterogeneous Dielectric Generalized Born (DHDGB): An implicit membrane model with a dynamically varying bilayer thickness

An extension to the heterogeneous dielectric generalized Born (HDGB) implicit membrane formalism is presented to allow dynamic membrane deformations in response to membrane-inserted biomolecules during molecular dynamic simulations. The flexible membrane is implemented through additional degrees of freedom that represent the membrane deformation at the contact points of a membrane-inserted solute with the membrane. The extra degrees of freedom determine the dielectric and non-polar solvation free energy profiles that are used to obtain the solvation free energy in the presence of the membrane and are used to calculate membrane deformation free energies according to an elastic membrane model. With the dynamic HDGB (DHDGB) model the membrane is able to deform in response to the insertion of charged molecules thereby avoiding the overestimation of insertion free energies with static membrane models. The DHDGB model also allows the membrane to respond to the insertion of membrane-spanning solutes with hydrophobic mismatch. The model is tested with the membrane insertion of amino acid side chain analogs, arginine-containing helices, the WALP23 peptide, and the gramicidin A channel.

Assessing smectic liquid-crystal continuum models for elastic bilayer deformations

For four decades, since W. Helfrich's pioneering study of smectic A liquid crystals in 1973, continuum elastic models (CEMs) have been employed as tools to understand the energetics of protein-induced lipid bilayer deformations. Among the assumptions underlying this use is that all relevant protein-lipid interactions can be included in the continuum representation of the protein-bilayer interactions through the physical parameters determined for protein-free bilayers and the choice of boundary conditions at the protein/bilayer interface. To better understand this assumption, we review the general structure of CEMs, examine how different choices of boundary conditions and physical moduli profiles alter the predicted bilayer thickness profiles around gramicidin A (gA) and mitochondrial voltage-dependent anion channels (VDAC), respectively, and compare these profiles with those obtained from all-atom molecular dynamics simulations. We find that the profiles differ qualitatively in the first lipid shell around the channels, indicating that the CEMs do not capture accurately the consequences of the protein-induced local changes in lipid bilayer dynamics. Therefore, one needs to be careful when interpreting the results of CEM-based analyses of lipid bilayer-membrane protein interactions.

Surface electrostatics of lipid bilayers by EPR of a pH-sensitive spin-labeled lipid

Many biophysical processes such as insertion of proteins into membranes and membrane fusion are governed by bilayer electrostatic potential. At the time of this writing, the arsenal of biophysical methods for such measurements is limited to a few techniques. Here we describe a, to our knowledge, new spin-probe electron paramagnetic resonance (EPR) approach for assessing the electrostatic surface potential of lipid bilayers that is based on a recently synthesized EPR probe (IMTSL-PTE) containing a reversibly ionizable nitroxide tag attached to the lipids' polar headgroup. EPR spectra of the probe directly report on its ionization state and, therefore, on electrostatic potential through changes in nitroxide magnetic parameters and the degree of rotational averaging. Further, the lipid nature of the probe provides its full integration into lipid bilayers. Tethering the nitroxide moiety directly to the lipid polar headgroup defines the location of the measured potential with respect to the lipid bilayer interface. Electrostatic surface potentials measured by EPR of IMTSL-PTE show a remarkable (within ±2%) agreement with the Gouy-Chapman theory for anionic DMPG bilayers in fluid (48°C) phase at low electrolyte concentration (50 mM) and in gel (17°C) phase at 150-mM electrolyte concentration. This agreement begins to diminish for DMPG vesicles in gel phase (17°C) upon varying electrolyte concentration and fluid phase bilayers formed from DMPG/DMPC and POPG/POPC mixtures. Possible reasons for such deviations, as well as the proper choice of an electrostatically neutral reference interface, have been discussed. Described EPR method is expected to be fully applicable to more-complex models of cellular membranes.

Three-dimensional stress field around a membrane protein: atomistic and coarse-grained simulation analysis of gramicidin A

Using both atomistic and coarse-grained (CG) models, we compute the three-dimensional stress field around a gramicidin A (gA) dimer in lipid bilayers that feature different degrees of negative hydrophobic mismatch. The general trends in the computed stress field are similar at the atomistic and CG levels, supporting the use of the CG model for analyzing the mechanical features of protein/lipid/water interfaces. The calculations reveal that the stress field near the protein-lipid interface exhibits a layered structure with both significant repulsive and attractive regions, with the magnitude of the stress reaching 1000 bar in certain regions. Analysis of density profiles and stress field distributions helps highlight the Trp residues at the protein/membrane/water interface as mechanical anchors, suggesting that similar analysis is useful for identifying tension sensors in other membrane proteins, especially membrane proteins involved in mechanosensation. This work fosters a connection between microscopic and continuum mechanics models for proteins in complex environments and makes it possible to test the validity of assumptions commonly made in continuum mechanics models for membrane mediated processes. For example, using the calculated stress field, we estimate the free energy of membrane deformation induced by the hydrophobic mismatch, and the results for regions beyond the annular lipids are in general consistent with relevant experimental data and previous theoretical estimates using elasticity theory. On the other hand, the assumptions of homogeneous material properties for the membrane and a bilayer thickness at the protein/lipid interface being independent of lipid type (e.g., tail length) appear to be oversimplified, highlighting the importance of annular lipids of membrane proteins. Finally, the stress field analysis makes it clear that the effect of even rather severe hydrophobic mismatch propagates to only about two to three lipid layers, thus putting a limit on the range of cooperativity between membrane proteins in crowded cellular membranes.

Bilayer elasticity at the nanoscale: the need for new terms

Continuum elastic models that account for membrane thickness variations are especially useful in the description of nanoscale deformations due to the presence of membrane proteins with hydrophobic mismatch. We show that terms involving the gradient and the Laplacian of the area per lipid are significant and must be retained in the effective Hamiltonian of the membrane. We reanalyze recent numerical data, as well as experimental data on gramicidin channels, in light of our model. This analysis yields consistent results for the term stemming from the gradient of the area per molecule. The order of magnitude we find for the associated amplitude, namely 13-60 mN/m, is in good agreement with the 25 mN/m contribution of the interfacial tension between water and the hydrophobic part of the membrane. The presence of this term explains a systematic variation in previously published numerical data.

Formation of tubules by p-tert-butylphenylamide derivatives of chenodeoxycholic and ursodeoxycholic acids in aqueous solution

The formation of tubules by p-tert-butylphenylamide derivatives of chenodeoxycholic and ursodeoxycholic acids in aqueous solution is investigated. The critical aggregation concentrations of the new surfactants are much lower than those of ursodeoxycholate and chenodeoxycholate, indicating the enhanced surfactant properties resulting by the presence of the hydrophobic p-tert-butylphenyl group. The molecular areas at the air-water interface suggest the formation of monolayer films with molecules upright oriented. The shape of the aggregates was investigated by TEM. The main structure present in solution corresponds to tubules. The estimated value for the wall thickness of tubules suggests that a bilayer structure is formed. Host of positively charged latex beads by tubules suggests that their inner and outer surfaces are negatively charged. The acid form of the chenodeoxycholate derivative was recrystallized from toluene and its crystal structure analyzed.

Influence of hydrophobic mismatch on structures and dynamics of gramicidin a and lipid bilayers

Gramicidin A (gA) is a 15-amino-acid antibiotic peptide with an alternating L-D sequence, which forms (dimeric) bilayer-spanning, monovalent cation channels in biological membranes and synthetic bilayers. We performed molecular dynamics simulations of gA dimers and monomers in all-atom, explicit dilauroylphosphatidylcholine (DLPC), dimyristoylphosphatidylcholine (DMPC), dioleoylphosphatidylcholine (DOPC), and 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayers. The variation in acyl chain length among these different phospholipids provides a way to alter gA-bilayer interactions by varying the bilayer hydrophobic thickness, and to determine the influence of hydrophobic mismatch on the structure and dynamics of both gA channels (and monomeric subunits) and the host bilayers. The simulations show that the channel structure varied little with changes in hydrophobic mismatch, and that the lipid bilayer adapts to the bilayer-spanning channel to minimize the exposure of hydrophobic residues. The bilayer thickness, however, did not vary monotonically as a function of radial distance from the channel. In all simulations, there was an initial decrease in thickness within 4-5 Å from the channel, which was followed by an increase in DOPC and POPC or a further decrease in DLPC and DMPC bilayers. The bilayer thickness varied little in the monomer simulations-except one of three independent simulations for DMPC and all three DLPC simulations, where the bilayer thinned to allow a single subunit to form a bilayer-spanning water-permeable pore. The radial dependence of local lipid area and bilayer compressibility is also nonmonotonic in the first shell around gA dimers due to gA-phospholipid interactions and the hydrophobic mismatch. Order parameters, acyl chain dynamics, and diffusion constants also differ between the lipids in the first shell and the bulk. The lipid behaviors in the first shell around gA dimers are more complex than predicted from a simple mismatch model, which has implications for understanding the energetics of membrane protein-lipid interactions.

Thiazolidinedione insulin sensitizers alter lipid bilayer properties and voltage-dependent sodium channel function: implications for drug discovery

The thiazolidinediones (TZDs) are used in the treatment of diabetes mellitus type 2. Their canonical effects are mediated by activation of the peroxisome proliferator–activated receptor γ (PPARγ) transcription factor. In addition to effects mediated by gene activation, the TZDs cause acute, transcription-independent changes in various membrane transport processes, including glucose transport, and they alter the function of a diverse group of membrane proteins, including ion channels. The basis for these off-target effects is unknown, but the TZDs are hydrophobic/amphiphilic and adsorb to the bilayer–water interface, which will alter bilayer properties, meaning that the TZDs may alter membrane protein function by bilayer-mediated mechanisms. We therefore explored whether the TZDs alter lipid bilayer properties sufficiently to be sensed by bilayer-spanning proteins, using gramicidin A (gA) channels as probes. The TZDs altered bilayer elastic properties with potencies that did not correlate with their affinity for PPARγ. At concentrations where they altered gA channel function, they also altered the function of voltage-dependent sodium channels, producing a prepulse-dependent current inhibition and hyperpolarizing shift in the steady-state inactivation curve. The shifts in the inactivation curve produced by the TZDs and other amphiphiles can be superimposed by plotting them as a function of the changes in gA channel lifetimes. The TZDs’ partition coefficients into lipid bilayers were measured using isothermal titration calorimetry. The most potent bilayer modifier, troglitazone, alters bilayer properties at clinically relevant free concentrations; the least potent bilayer modifiers, pioglitazone and rosiglitazone, do not. Unlike other TZDs tested, ciglitazone behaves like a hydrophobic anion and alters the gA monomer–dimer equilibrium by more than one mechanism. Our results provide a possible mechanism for some off-target effects of an important group of drugs, and underscore the importance of exploring bilayer effects of candidate drugs early in drug development.

Linear rate-equilibrium relations arising from ion channel-bilayer energetic coupling

Linear rate-equilibrium (RE) relations, also known as linear free energy relations, are widely observed in chemical reactions, including protein folding, enzymatic catalysis, and channel gating. Despite the widespread occurrence of linear RE relations, the principles underlying the linear relation between changes in activation and equilibrium energy in macromolecular reactions remain enigmatic. When examining amphiphile regulation of gramicidin channel gating in lipid bilayers, we noted that the gating process could be described by a linear RE relation with a simple geometric interpretation. This description is possible because the gating process provides a well-understood reaction, in which structural changes in a bilayer-embedded model protein can be studied at the single-molecule level. It is thus possible to obtain quantitative information about the energetics of the reaction transition state and its position on a spatial coordinate. It turns out that the linear RE relation for the gramicidin monomer-dimer reaction can be understood, and the quantitative relation between changes in activation energy and equilibrium energy can be interpreted, by considering the effects of amphiphiles on the changes in bilayer elastic energy associated with channel gating. We are not aware that a similar simple mechanistic explanation of a linear RE relation has been provided for a chemical reaction in a macromolecule. RE relations generally should be useful for examining how amphiphile-induced changes in bilayer properties modulate membrane protein folding and function, and for distinguishing between direct (e.g., due to binding) and indirect (bilayer-mediated) effects.

Continuum simulations of biomembrane dynamics and the importance of hydrodynamic effects

Traditional particle-based simulation strategies are impractical for the study of lipid bilayers and biological membranes over the longest length and time scales (microns, seconds and longer) relevant to cellular biology. Continuum-based models developed within the frameworks of elasticity theory, fluid dynamics and statistical mechanics provide a framework for studying membrane biophysics over a range of mesoscopic to macroscopic length and time regimes, but the application of such ideas to simulation studies has occurred only relatively recently. We review some of our efforts in this direction with emphasis on the dynamics in model membrane systems. Several examples are presented that highlight the prominent role of hydrodynamics in membrane dynamics and we argue that careful consideration of fluid dynamics is key to understanding membrane biophysics at the cellular scale.

A one-dimensional continuum elastic model for membrane-embedded gramicidin dimer dissociation

Membrane elastic properties, which are subject to alteration by compounds such as cholesterol, lipid metabolites and other amphiphiles, as well as pharmaceuticals, can have important effects on membrane proteins. A useful tool for measuring some of these effects is the gramicidin A channels, which are formed by transmembrane dimerization of non-conducting subunits that reside in each bilayer leaflet. The length of the conducting channels is less than the bilayer thickness, meaning that channel formation is associated with a local bilayer deformation. Electrophysiological studies have shown that the dimer becomes increasingly destabilized as the hydrophobic mismatch between the channel and the host bilayer increases. That is, the bilayer imposes a disjoining force on the channel, which grows larger with increasing hydrophobic mismatch. The energetic analysis of the channel-bilayer coupling is usually pursued assuming that each subunit, as well as the subunit-subunit interface, is rigid. Here we relax the latter assumption and explore how the bilayer junction responds to changes in this disjoining force using a simple one-dimensional energetic model, which reproduces key features of the bilayer regulation of gramicidin channel lifetimes.

Electroelastic coupling between membrane surface fluctuations and membrane-embedded charges: continuum multidielectric treatment

The coupling of electric fields and charges with membrane-water interfacial fluctuations affects membrane electroporation, ionic conductance, and voltage gating. A modified continuum model is introduced to study charge interaction with membrane-water interfacial fluctuations in multidielectric environments. By surrounding a point charge with a low dielectric sphere, the linear Poisson-Boltzmann equation is directly solved by calculating the reaction field potential via a method that eliminates singularity contributions. This allows treatment of charges located at dielectric boundaries. Two complementary mechanisms governing charge-fluctuation interactions are considered: (1) electroelastic deformation (EED), treating the membrane as an elastic slab (smectic bilayer model), and (2) electrohydrophobic solvation (EHS), accounting for water penetration into the membrane's hydrophobic core. EED often leads to large membrane thickness perturbations, far larger than those consistent with elastic model descriptions [M. B. Partenskii, G. V. Miloshevsky, and P. C. Jordan, Isr. J. Chem. 47, 385 (2007)]. We argue that a switch from EED to EHS can be energetically advantageous at intermediate perturbation amplitudes. Both perturbation mechanisms are simulated by introducing adjustable shapes optimized by the kinetic Monte Carlo reaction path following approach [G. V. Miloshevsky and P. C. Jordan, J. Chem. Phys. 122, 214901 (2005)]. The resulting energy profiles agree with those of recent atomistic molecular dynamics studies on translating a charged residue across a lipid bilayer [S. Dorairaj and T. W. Allen, Proc. Natl. Acad. Sci. U.S.A. 104, 4943 (2007)].

Nonlinearities in tilt and layer displacements of planar lipid bilayers

A novel continuum model is proposed to describe the deformations of a planar lipid bilayer suspended across a circular pore. The model is derived within a new theoretical framework for smectic A liquid crystals in which the usual director n, which defines the average orientation of the molecules, is not constrained to be normal to the layers. The free energy is defined by considering the elastic splay of the director, the bending and compression of the lipid bilayer, the cost of tilting the director with respect to the layer normal, the surface tension, and the weak anchoring of the director. Variational methods are used to derive the equilibrium equations and boundary conditions. The resulting boundary value problem is then solved numerically to compute the fully nonlinear displacement of the layers and tilt of the lipid molecules. A parametric study shows that an increase in surface tension produces a decrease in the deformation of the lipid bilayers while an opposite effect is obtained when increasing the anchoring strength.

Gramicidin channels are internally gated

Gramicidin channels are archetypal molecular subjects for solid-state NMR studies and investigations of single-channel or cation conductance. Until now, the transitions between on and off conductance states have been thought, based on multichannel studies, to represent monomer <--> dimer reactions. Here we use a single-molecule deposition method (vesicle fusion to a planar bilayer) to show that gramicidin dimer channels do not normally dissociate when conductance terminates. Furthermore, the observation of two 13C peaks in solid-state NMR indicates very stable dichotomous conformations for both the first and second peptide bonds in the monomers, and a two-dimensional chemical exchange spectrum with a 12-s mixing time demonstrates that the Val1 carbonyl conformations exchange slowly, with lifetimes of several seconds. It is proposed that gramicidin channels are gated by small conformational changes in the channel near the permeation pathway. These studies demonstrate how regulation of conformations governing closed <--> open transitions may be achieved and studied at the molecular level.

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.

Lipid bilayer regulation of membrane protein function: gramicidin channels as molecular force probes

Membrane protein function is regulated by the host lipid bilayer composition. This regulation may depend on specific chemical interactions between proteins and individual molecules in the bilayer, as well as on non-specific interactions between proteins and the bilayer behaving as a physical entity with collective physical properties (e.g. thickness, intrinsic monolayer curvature or elastic moduli). Studies in physico-chemical model systems have demonstrated that changes in bilayer physical properties can regulate membrane protein function by altering the energetic cost of the bilayer deformation associated with a protein conformational change. This type of regulation is well characterized, and its mechanistic elucidation is an interdisciplinary field bordering on physics, chemistry and biology. Changes in lipid composition that alter bilayer physical properties (including cholesterol, polyunsaturated fatty acids, other lipid metabolites and amphiphiles) regulate a wide range of membrane proteins in a seemingly non-specific manner. The commonality of the changes in protein function suggests an underlying physical mechanism, and recent studies show that at least some of the changes are caused by altered bilayer physical properties. This advance is because of the introduction of new tools for studying lipid bilayer regulation of protein function. The present review provides an introduction to the regulation of membrane protein function by the bilayer physical properties. We further describe the use of gramicidin channels as molecular force probes for studying this mechanism, with a unique ability to discriminate between consequences of changes in monolayer curvature and bilayer elastic moduli.

Application of the fuzzy-oil-drop model to membrane protein simulation

The analysis of structural properties and biological activity of membrane proteins requires long lasting simulation of molecular dynamics. The large number of atoms present in protein molecule, membrane (phospholipids), and water environment makes the simulation of large scale. The implementation of simplified model representing the natural environment for membrane proteins is presented and compared with the vacuum simulation and simulation in the presence of water molecules and membrane phospholipids presented explicite. The comparative structural analysis and computational times for these three models makes the simplified model promising.

Membrane-protein interactions in a generic coarse-grained model for lipid bilayers

We study membrane-protein interactions and membrane-mediated protein-protein interactions by Monte Carlo simulations of a generic coarse-grained model for lipid bilayers with cylindrical hydrophobic inclusions. The strength of the hydrophobic force and the hydrophobic thickness of the proteins are systematically varied. The results are compared with analytical predictions of two popular analytical theories: The Landau-de Gennes theory and the elastic theory. The elastic theory provides an excellent description of the fluctuation spectra of pure membranes and successfully reproduces the deformation profiles of membranes around single proteins. However, its prediction for the potential of mean force between proteins is not compatible with the simulation data for large distances. The simulations show that the lipid-mediated interactions are governed by five competing factors: direct interactions; lipid-induced depletion interactions; lipid bridging; lipid packing; and a smooth long-range contribution. The mechanisms leading to hydrophobic mismatch interactions are critically analyzed.