A continuum method for determining membrane protein insertion energies and the problem of charged residues

Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how they interact with binding partners. However, it is unclear whether continuum methods can be used to quantitatively understand the energetics of membrane protein insertion and stability. Recent translation experiments suggest that the energy required to insert charged peptides into membranes is much smaller than predicted by present continuum theories. Atomistic simulations have pointed to bilayer inhomogeneity and membrane deformation around buried charged groups as two critical features that are neglected in simpler models. Here, we develop a fully continuum method that circumvents both of these shortcomings by using elasticity theory to determine the shape of the deformed membrane and then subsequently uses this shape to carry out continuum electrostatics calculations. Our method does an excellent job of quantitatively matching results from detailed molecular dynamics simulations at a tiny fraction of the computational cost. We expect that this method will be ideal for studying large membrane protein complexes.     

Lipid bilayer deformation and the free energy of interaction of a Kv channel gating-modifier toxin

A number of membrane proteins act via binding at the water/lipid bilayer interface. An important example of such proteins is provided by the gating-modifier toxins that act on voltage-gated potassium (Kv) channels. They are thought to partition to the headgroup region of lipid bilayers, and so provide a good system for probing the nature of interactions of a protein with the water/bilayer interface. We used coarse-grained molecular dynamics simulations to compute the one-dimensional potential of mean force (i.e., free energy) profile that governs the interaction between a Kv channel gating-modifier toxin (VSTx1) and model phospholipid bilayers. The reaction coordinate sampled corresponds to the position of the toxin along the bilayer normal. The course-grained representation of the protein and lipids enabled us to explore extended time periods, revealing aspects of toxin/bilayer dynamics and energetics that would be difficult to observe on the timescales currently afforded by atomistic molecular dynamics simulations. In particular, we show for this model system that the bilayer deforms as it interacts with the toxin, and that such deformations perturb the free energy profile. Bilayer deformation therefore adds an additional layer of complexity to be addressed in investigations of membrane/protein systems. In particular, one should allow for local deformations that may arise due to the spatial array of charged and hydrophobic elements of an interfacially located membrane protein.     

Anchoring of a monotopic membrane protein: the binding of prostaglandin H2 synthase-1 to the surface of a phospholipid bilayer

Prostaglandin H₂ synthases (PGHS-1 and -2) are monotopic peripheral membrane proteins that catalyse the synthesis of prostaglandins in the arachidonate cascade. Picot et al. (1994) proposed that the enzyme is anchored to one leaflet of the bilayer by a membrane anchoring domain consisting of a right-handed spiral of amphipathic helices (residues 73–116) forming a planar motif. Two different computational approaches are used to examine the association of the PGHS-1 membrane anchoring domain with a membrane via the proposed mechanism. The electrostatic contribution to the free energy of solvation is obtained by solving numerically the finite-difference Poisson equation for the protein attached to a membrane represented as a planar slab of low dielectric. The nonpolar cavity formation and van der Waals contributions to the solvation free energy are assumed to be proportional to the water accessible surface area. Based on the optimum position determined from the continuum solvent model, two atomic models of the PGHS-1 anchoring domain associated with an explicit dimyristoylphosphatidylcholine (DMPC) bilayer differing by the thickness of the membrane bilayer were constructed. A total of 2 ns molecular dynamics simulation were performed to study the details of lipid- protein interactions at the microscopic level. In the simulations the lipid hydrocarbon chains interacting with the anchoring domain assume various shapes, suggesting that the plasticity of the membrane is significant. The hydrophobic residues in the membrane side of the helices interact with the hydrophobic membrane core, while the positively charged residues interact with the lipid polar headgroups to stabilize the anchoring of the membrane domain to the upper half of the bilayer. The phosphate headgroup of one DMPC molecule disposed at the center of the spiral formed by helices A, B, C and D interacts strongly with Arg120, a residue on helix D that has previously been identified as being important in the activity of PGHS-1. In the full enzyme structure, this position corresponds to the entrance of a long hydrophobic channel leading to the cyclooxygenase active site. These observations provide insights into the association of the arachidonic acid substrate to the cyclooxygenase active site of PGHS-1. Received: 20 December 1999 / Revised version: 26 March 2000 / Accepted: 26 March 2000     

Life at the border: Adaptation of proteins to anisotropic membrane environment

This review discusses main features of transmembrane (TM) proteins which distinguish them from water‐soluble proteins and allow their adaptation to the anisotropic membrane environment. We overview the structural limitations on membrane protein architecture, spatial arrangement of proteins in membranes and their intrinsic hydrophobic thickness, co‐translational and post‐translational folding and insertion into lipid bilayers, topogenesis, high propensity to form oligomers, and large‐scale conformational transitions during membrane insertion and transport function. Special attention is paid to the polarity of TM protein surfaces described by profiles of dipolarity/polarizability and hydrogen‐bonding capacity parameters that match polarity of the lipid environment. Analysis of distributions of Trp resides on surfaces of TM proteins from different biological membranes indicates that interfacial membrane regions with preferential accumulation of Trp indole rings correspond to the outer part of the lipid acyl chain region—between double bonds and carbonyl groups of lipids. These “midpolar” regions are not always symmetric in proteins from natural membranes. We also examined the hydrophobic effect that drives insertion of proteins into lipid bilayer and different free energy contributions to TM protein stability, including attractive van der Waals forces and hydrogen bonds, side‐chain conformational entropy, the hydrophobic mismatch, membrane deformations, and specific protein–lipid binding.     

Membrane insertion of a voltage sensor helix

Most membrane proteins contain a transmembrane (TM) domain made up of a bundle of lipid-bilayer-spanning α-helices. TM α-helices are generally composed of a core of largely hydrophobic amino acids, with basic and aromatic amino acids at each end of the helix forming interactions with the lipid headgroups and water. In contrast, the S4 helix of ion channel voltage sensor (VS) domains contains four or five basic (largely arginine) side chains along its length and yet adopts a TM orientation as part of an independently stable VS domain. Multiscale molecular dynamics simulations are used to explore how a charged TM S4 α-helix may be stabilized in a lipid bilayer, which is of relevance in the context of mechanisms of translocon-mediated insertion of S4. Free-energy profiles for insertion of the S4 helix into a phospholipid bilayer suggest that it is thermodynamically favorable for S4 to insert from water to the center of the membrane, where the helix adopts a TM orientation. This is consistent with crystal structures of Kv channels, biophysical studies of isolated VS domains in lipid bilayers, and studies of translocon-mediated S4 helix insertion. Decomposition of the free-energy profiles reveals the underlying physical basis for TM stability, whereby the preference of the hydrophobic residues of S4 to enter the bilayer dominates over the free-energy penalty for inserting charged residues, accompanied by local distortion of the bilayer and penetration of waters. We show that the unique combination of charged and hydrophobic residues in S4 allows it to insert stably into the membrane.     

The spontaneous insertion of proteins into and across membranes: The helical hairpin hypothesis

We propose that the initial event in the secretion of proteins across membranes and their insertion into membranes is the spontaneous penetration of the hydrophobic portion of the bilayer by a helical hairpin. Energetic considerations of polypeptide structures in a nonpolar, lipid environment compared with an aqueous environment suggest that only α and 3₁₀ helices will be observed in the hydrophobic interior of membranes. Insertion of a polypeptide is accomplished by a hairpin structure composed of two helices, which will partition into membranes if the free energy arising from burying hydrophobic helical surfaces exceeds the free energy “cost” of burying potentially charged and hydrogen-bonding groups. We suggest, for example, that the hydrophobic leader peptide found in secreted proteins and in many membrane proteins forms one of these helices and is oriented in the membrane with its N terminus inside. In secreted proteins, the leader functions by pulling polar portions of a protein into the membrane as the second helix of the hairpin. The occurrence of all categories of membrane proteins can be rationalized by the hydrophobic or hydrophilic character of the two helices of the inserted hairpin and, for some integral membrane proteins, by events in which a single terminal helix is inserted. We propose that, because of the distribution of polar and nonpolar sequences in the polypeptide sequence, secretion and the insertion of membrane proteins are spontaneous processes that do not require the participation of additional specific membrane receptors or transport proteins.     

Continuum Approaches to Understanding Ion and Peptide Interactions with the Membrane

Experimental and computational studies have shown that cellular membranes deform to stabilize the inclusion of transmembrane (TM) proteins harboring charge. Recent analysis suggests that membrane bending helps to expose charged and polar residues to the aqueous environment and polar head groups. We previously used elasticity theory to identify membrane distortions that minimize the insertion of charged TM peptides into the membrane. Here, we extend our work by showing that it also provides a novel, computationally efficient method for exploring the energetics of ion and small peptide penetration into membranes. First, we show that the continuum method accurately reproduces energy profiles and membrane shapes generated from molecular simulations of bare ion permeation at a fraction of the computational cost. Next, we demonstrate that the dependence of the ion insertion energy on the membrane thickness arises primarily from the elastic properties of the membrane. Moreover, the continuum model readily provides a free energy decomposition into components not easily determined from molecular dynamics. Finally, we show that the energetics of membrane deformation strongly depend on membrane patch size both for ions and peptides. This dependence is particularly strong for peptides based on simulations of a known amphipathic, membrane binding peptide from the human pathogen Toxoplasma gondii. In total, we address shortcomings and advantages that arise from using a variety of computational methods in distinct biological contexts.     

Membrane topography of ColE1 gene products: the hydrophobic anchor of the colicin E1 channel is a helical hairpin.

The paucity of crystallographic data on the structure of intrinsic membrane proteins necessitates the development of additional techniques to probe their structures. The colicin E1 ion channel domain contains one prominent hydrophobic region near its COOH terminus that has been proposed to be an anchor for the assembly of the channel. Saturation site-directed mutagenesis of the hydrophobic anchor region of the colicin E1 ion channel was used to probe whether it spanned the bilayer once or twice. A nonpolar amino acid was replaced by a charged residue in 29 mutations made at 26 positions in the channel domain. Substitution of the charged amino acid at all positions except those in the center of the hydrophobic region and the periphery of the hydrophobic region caused a large decrease in the cytotoxicity of the purified mutant colicin E1 protein. This result implies that the hydrophobic domain spans the membrane bilayer twice in a helical hairpin loop, with the center of this domain residing in an aqueous or polar phase. The lengths of the trans-membrane helices appear to be approximately 18 and 16 residues. The absence of significant changes in ion selectivity in five of nine mutants indicated that these mutations did not cause a large change in the channel structure. The ion selectivity changes in four mutants and those previously documented for the flanking Lys residues imply that the hydrophobic hairpin is part of the channel lumen. Water may "abhor" the hydrophobic side of the channel, explaining the small effects of residue charge changes on ion selectivity.     

Interactions of cholesterol with lipid bilayers: the preferred configuration and fluctuations.

The free energy difference associated with the transfer of a single cholesterol molecule from the aqueous phase into a lipid bilayer depends on its final location, namely on its insertion depth and orientation within the bilayer. We calculated desolvation and lipid bilayer perturbation contributions to the water-to-membrane transfer free energy, thus allowing us to determine the most favorable location of cholesterol in the membrane and the extent of fluctuations around it. The electrostatic and nonpolar contributions to the solvation free energy were calculated using continuum solvent models. Lipid layer perturbations, resulting from both conformational restrictions of the lipid chains in the vicinity of the (rigid) cholesterol backbone and from cholesterol-induced elastic deformations, were calculated using a simple director model and elasticity theory, respectively. As expected from the amphipathic nature of cholesterol and in agreement with the available experimental data, our results show that at the energetically favorable state, cholesterol's hydrophobic core is buried within the hydrocarbon region of the bilayer. At this state, cholesterol spans approximately one leaflet of the membrane, with its OH group protruding into the polar (headgroup) region of the bilayer, thus avoiding an electrostatic desolvation penalty. We found that the transfer of cholesterol into a membrane is mainly driven by the favorable nonpolar contributions to the solvation free energy, whereas only a small opposing contribution is caused by conformational restrictions of the lipid chains. Our calculations also predict a strong tendency of the lipid layer to elastically respond to (thermally excited) vertical fluctuations of cholesterol so as to fully match the hydrophobic height of the solute. However, orientational fluctuations of cholesterol were found to be accompanied by both an elastic adjustment of the surrounding lipids and by a partial exposure of the hydrophobic cholesterol backbone to the polar (headgroup) environment. Our calculations of the molecular order parameter, which reflects the extent of orientational fluctuations of cholesterol in the membrane, are in good agreement with available experimental data.     

Quantitative modeling of membrane deformations by multihelical membrane proteins: application to G-protein coupled receptors

The interpretation of experimental observations of the dependence of membrane protein function on the properties of the lipid membrane environment calls for a consideration of the energy cost of protein-bilayer interactions, including the protein-bilayer hydrophobic mismatch. We present a novel (to our knowledge) multiscale computational approach for quantifying the hydrophobic mismatch-driven remodeling of membrane bilayers by multihelical membrane proteins. The method accounts for both the membrane remodeling energy and the energy contribution from any partial (incomplete) alleviation of the hydrophobic mismatch by membrane remodeling. Overcoming previous limitations, it allows for radially asymmetric bilayer deformations produced by multihelical proteins, and takes into account the irregular membrane-protein boundaries. The approach is illustrated by application to two G-protein coupled receptors: rhodopsin in bilayers of different thickness, and the serotonin 5-HT_2A receptor bound to pharmacologically different ligands. Analysis of the results identifies the residual exposure that is not alleviated by bilayer adaptation, and its quantification at specific transmembrane segments is shown to predict favorable contact interfaces in oligomeric arrays. In addition, our results suggest how distinct ligand-induced conformations of G-protein coupled receptors may elicit different functional responses through differential effects on the membrane environment.     

Not Just an Oil Slick: How the Energetics of Protein-Membrane Interactions Impacts the Function and Organization of Transmembrane Proteins

The membrane environment, its composition, dynamics, and remodeling, have been shown to participate in the function and organization of a wide variety of transmembrane (TM) proteins, making it necessary to study the molecular mechanisms of such proteins in the context of their membrane settings. We review some recent conceptual advances enabling such studies, and corresponding computational models and tools designed to facilitate the concerted experimental and computational investigation of protein-membrane interactions. To connect productively with the high resolution achieved by cognate experimental approaches, the computational methods must offer quantitative data at an atomistically detailed level. We show how such a quantitative method illuminated the mechanistic importance of a structural characteristic of multihelical TM proteins, that is, the likely presence of adjacent polar and hydrophobic residues at the protein-membrane interface. Such adjacency can preclude the complete alleviation of the well-known hydrophobic mismatch between TM proteins and the surrounding membrane, giving rise to an energy cost of residual hydrophobic mismatch. The energy cost and biophysical formulation of hydrophobic mismatch and residual hydrophobic mismatch are reviewed in the context of their mechanistic role in the function of prototypical members of multihelical TM protein families: 1), LeuT, a bacterial homolog of mammalian neurotransmitter sodium symporters; and 2), rhodopsin and the β1- and β2-adrenergic receptors from the G-protein coupled receptor family. The type of computational analysis provided by these examples is poised to translate the rapidly growing structural data for the many TM protein families that are of great importance to cell function into ever more incisive insights into mechanisms driven by protein-ligand and protein-protein interactions in the membrane environment.     

Not Just an Oil Slick: How the Energetics of Protein-Membrane Interactions Impacts the Function and Organization of Transmembrane Proteins

The membrane environment, its composition, dynamics, and remodeling, have been shown to participate in the function and organization of a wide variety of transmembrane (TM) proteins, making it necessary to study the molecular mechanisms of such proteins in the context of their membrane settings. We review some recent conceptual advances enabling such studies, and corresponding computational models and tools designed to facilitate the concerted experimental and computational investigation of protein-membrane interactions. To connect productively with the high resolution achieved by cognate experimental approaches, the computational methods must offer quantitative data at an atomistically detailed level. We show how such a quantitative method illuminated the mechanistic importance of a structural characteristic of multihelical TM proteins, that is, the likely presence of adjacent polar and hydrophobic residues at the protein-membrane interface. Such adjacency can preclude the complete alleviation of the well-known hydrophobic mismatch between TM proteins and the surrounding membrane, giving rise to an energy cost of residual hydrophobic mismatch. The energy cost and biophysical formulation of hydrophobic mismatch and residual hydrophobic mismatch are reviewed in the context of their mechanistic role in the function of prototypical members of multihelical TM protein families: 1), LeuT, a bacterial homolog of mammalian neurotransmitter sodium symporters; and 2), rhodopsin and the β1- and β2-adrenergic receptors from the G-protein coupled receptor family. The type of computational analysis provided by these examples is poised to translate the rapidly growing structural data for the many TM protein families that are of great importance to cell function into ever more incisive insights into mechanisms driven by protein-ligand and protein-protein interactions in the membrane environment.     

Transmembrane helices of membrane proteins may flex to satisfy hydrophobic mismatch

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

Hydrophobic organization of α-helix membrane bundle in bacteriorhodopsin

The hydrophobic organization of the intramembraneα-helical bundle in bacteriorhodopsin (BRh) was assessed based on a new approach to characterization of spatial hydrophobic properties of transmembrane (TM)α-helical peptides. The method employs two independent techniques: Monte Carlo simulations of nonpolar solvent around TM peptides and analysis of molecular hydrophobicity potential on their surfaces. The results obtained by the two methods agree with each other and permit precise hydrophobicity mapping of TM peptides. Superimposition of such data on the experimentally derived spatial model of the membrane moiety together with 2D maps of hydrophobic hydrophilic contacts provide considerable insight into the hydrophobic organization of BRh. The helix bundle is stabilized to a large extent by hydrophobic interactions between helices—neighbors in the sequence of BRh, by long-range interactions in helix pairs C-E, C-F, and C-G, and by nonpolar contracts between retinal and helices C, D, E, F. Unlike globular proteins, no polar contacts between residues distantly separated in the sequence of BRh were found in the bundle. One of the most striking results of this study is the finding that the hydrophobic organization of BRh is significantly different from those in bacterial photoreaction centers. Thus, TMα-helices in BRh expose their most nonpolar sides to the bilayer as well as to the neighboring helices and to the interior of the bundle. Some of them contact lipids with their relatively hydrophilic surfaces. No correlation was found between disposition of the most hydrophobic and the most variable sides of the TM helices.     

Transmembrane helices of membrane proteins may flex to satisfy hydrophobic mismatch

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

On Calculation of the Electrostatic Potential of a Phosphatidylinositol Phosphate-Containing Phosphatidylcholine Lipid Membrane Accounting for Membrane Dynamics

Many signaling events require the binding of cytoplasmic proteins to cell membranes by recognition of specific charged lipids, such as phosphoinositol-phosphates. As a model for a protein-membrane binding site, we consider one charged phosphoinositol phosphate (PtdIns(3)P) embedded in a phosphatidylcholine bilayer. As the protein-membrane binding is driven by electrostatic interactions, continuum solvent models require an accurate representation of the electrostatic potential of the phosphoinositol phosphate-containing membrane. We computed and analyzed the electrostatic potentials of snapshots taken at regular intervals from molecular dynamics simulations of the bilayer. We observe considerable variation in the electrostatic potential of the bilayer both along a single simulation and between simulations performed with the GAFF or CHARMM c36 force fields. However, we find that the choice of GAFF or CHARMM c36 parameters has little effect on the electrostatic potential of a given configuration of the bilayer with a PtdIns(3)P embedded in it. From our results, we propose a remedian averaging method for calculating the electrostatic potential of a membrane system that is suitable for simulations of protein-membrane binding with a continuum solvent model.     

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

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

Lipid demixing and protein-protein interactions in the adsorption of charged proteins on mixed membranes

The adsorption free energy of charged proteins on mixed membranes, containing varying amounts of (oppositely) charged lipids, is calculated based on a mean-field free energy expression that accounts explicitly for the ability of the lipids to demix locally, and for lateral interactions between the adsorbed proteins. Minimization of this free energy functional yields the familiar nonlinear Poisson-Boltzmann equation and the boundary condition at the membrane surface that allows for lipid charge rearrangement. These two self-consistent equations are solved simultaneously. The proteins are modeled as uniformly charged spheres and the (bare) membrane as an ideal two-dimensional binary mixture of charged and neutral lipids. Substantial variations in the lipid charge density profiles are found when highly charged proteins adsorb on weakly charged membranes; the lipids, at a certain demixing entropy penalty, adjust their concentration in the vicinity of the adsorbed protein to achieve optimal charge matching. Lateral repulsive interactions between the adsorbed proteins affect the lipid modulation profile and, at high densities, result in substantial lowering of the binding energy. Adsorption isotherms demonstrating the importance of lipid mobility and protein-protein interactions are calculated using an adsorption equation with a coverage-dependent binding constant. Typically, at bulk-surface equilibrium (i.e., when the membrane surface is "saturated" by adsorbed proteins), the membrane charges are "overcompensated" by the protein charges, because only about half of the protein charges (those on the hemispheres facing the membrane) are involved in charge neutralization. Finally, it is argued that the formation of lipid-protein domains may be enhanced by electrostatic adsorption of proteins, but its origin (e.g., elastic deformations associated with lipid demixing) is not purely electrostatic.     

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.