Towards Molecular Understanding of the pH Dependence Characterizing NhaA of Which Structural Fold is Shared by Other Transporters.

Na+/H+ antiporters comprise a super-family (CPA) of membrane proteins that are found in all kingdoms of life and are essential in cellular homeostasis of pH, Na+ and volume. Their activity is strictly dependent on pH, a property that underpins their role in pH homeostasis. While several human homologues have long been drug targets, NhaA of Escherichia coli has become the paradigm for this class of secondary active transporters as NhaA crystal structure provided insight into the architecture of this molecular machine. However, the mechanism of the strict pH dependence of NhaA is missing. Here, as a follow up of a recent evolutionary analysis that identified a 'CPA motif', we rationally designed three E. coli NhaA mutants: D133S, I134T, and the double mutant D133S-I134T. Exploring growth phenotype, transport activity and Li+-binding of the mutants, we revealed that Asp133 does not participate directly in proton binding, nor does it directly dictate the pH-dependent transport of NhaA. Strikingly, the variant I134T lost some of the pH control, and the D133S-Il134T double mutant retained Li+ binding in a pH independent fashion. Concurrent to loss of pH control, these mutants bound Li+ more strongly than the WT. Both positions are in close vicinity to the ion-binding site of the antiporter, attributing the results to electrostatic interaction between these residues and Asp164 of the ion-binding site. This is consistent with pH sensing resulting from direct coupling between cation binding and deprotonation in Asp164, which applies also to other CPA antiporters that are involved in human diseases.

Hijacking the Fusion Complex of Human Parainfluenza Virus as an Antiviral Strategy.

The receptor binding protein of parainfluenza virus, hemagglutinin-neuraminidase (HN), is responsible for actively triggering the viral fusion protein (F) to undergo a conformational change leading to insertion into the target cell and fusion of the virus with the target cell membrane. For proper viral entry to occur, this process must occur when HN is engaged with host cell receptors at the cell surface. It is possible to interfere with this process through premature activation of the F protein, distant from the target cell receptor. Conformational changes in the F protein and adoption of the postfusion form of the protein prior to receptor engagement of HN at the host cell membrane inactivate the virus. We previously identified small molecules that interact with HN and induce it to activate F in an untimely fashion, validating a new antiviral strategy. To obtain highly active pretriggering candidate molecules we carried out a virtual modeling screen for molecules that interact with sialic acid binding site II on HN, which we propose to be the site responsible for activating F. To directly assess the mechanism of action of one such highly effective new premature activating compound, PAC-3066, we use cryo-electron tomography on authentic intact viral particles for the first time to examine the effects of PAC-3066 treatment on the conformation of the viral F protein. We present the first direct observation of the conformational rearrangement induced in the viral F protein.IMPORTANCE Paramyxoviruses, including human parainfluenza virus type 3, are internalized into host cells by fusion between viral and target cell membranes. The receptor binding protein, hemagglutinin-neuraminidase (HN), upon binding to its cell receptor, triggers conformational changes in the fusion protein (F). This action of HN activates F to reach its fusion-competent state. Using small molecules that interact with HN, we can induce the premature activation of F and inactivate the virus. To obtain highly active pretriggering compounds, we carried out a virtual modeling screen for molecules that interact with a sialic acid binding site on HN that we propose to be the site involved in activating F. We use cryo-electron tomography of authentic intact viral particles for the first time to directly assess the mechanism of action of this treatment on the conformation of the viral F protein and present the first direct observation of the induced conformational rearrangement in the viral F protein.

Multi-stage regulation, a key to reliable adaptive biochemical pathways.

A general "multi-stage" regulation model, based on linearly connected regulatory units, is formulated to demonstrate how biochemical pathways may achieve high levels of accuracy. The general mechanism, which is robust to changes in biochemical parameters, such as protein concentration and kinetic rate constants, is incorporated into a mathematical model of the bacterial chemotaxis network and provides a new framework for explaining regulation and adaptiveness in this extensively studied system. Although conventional theories suggest that methylation feedback pathways are responsible for chemotactic regulation, the model, which is deduced from known experimental data, indicates that protein interactions downstream of the bacterial receptor complex, such as CheAs and CheZ, may play a crucial and complementary role.

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.

Continuum solvent model studies of the interactions of an anticonvulsant drug with a lipid bilayer.

Valproic acid (VPA) is a short, branched fatty acid with broad-spectrum anticonvulsant activity. It has been suggested that VPA acts directly on the plasma membrane. We calculated the free energy of interaction of VPA with a model lipid bilayer using simulated annealing and the continuum solvent model. Our calculations indicate that VPA is likely to partition into the bilayer both in its neutral and charged forms, as expected from such an amphipathic molecule. The calculations also show that VPA may migrate (flip-flop) across the membrane; according to our (theoretical) study, the most likely flip-flop path at neutral pH involves protonation of VPA pending its insertion into the lipid bilayer and deprotonation upon departure from the other side of the bilayer. Recently, the flip-flop of long fatty acids across lipid bilayers was studied using fluorescence and NMR spectroscopies. However, the measured value of the flip-flop rate appears to depend on the method used in these studies. Our calculated value of the flip-flop rate constant, 20/s, agrees with some of these studies. The limitations of the model and the implications of the study for VPA and other fatty acids are discussed.

Residue frequencies and pairing preferences at protein-protein interfaces.

We used a nonredundant set of 621 protein-protein interfaces of known high-resolution structure to derive residue composition and residue-residue contact preferences. The residue composition at the interfaces, in entire proteins and in whole genomes correlates well, indicating the statistical strength of the data set. Differences between amino acid distributions were observed for interfaces with buried surface area of less than 1,000 A(2) versus interfaces with area of more than 5,000 A(2). Hydrophobic residues were abundant in large interfaces while polar residues were more abundant in small interfaces. The largest residue-residue preferences at the interface were recorded for interactions between pairs of large hydrophobic residues, such as Trp and Leu, and the smallest preferences for pairs of small residues, such as Gly and Ala. On average, contacts between pairs of hydrophobic and polar residues were unfavorable, and the charged residues tended to pair subject to charge complementarity, in agreement with previous reports. A bootstrap procedure, lacking from previous studies, was used for error estimation. It showed that the statistical errors in the set of pairing preferences are generally small; the average standard error is approximately 0.2, i.e., about 8% of the average value of the pairwise index (2.9). However, for a few pairs (e.g., Ser-Ser and Glu-Asp) the standard error is larger in magnitude than the pairing index, which makes it impossible to tell whether contact formation is favorable or unfavorable. The results are interpreted using physicochemical factors and their implications for the energetics of complex formation and for protein docking are discussed. Proteins 2001;43:89-102.

ConSurf: an algorithmic tool for the identification of functional regions in proteins by surface mapping of phylogenetic information.

Experimental approaches for the identification of functionally important regions on the surface of a protein involve mutagenesis, in which exposed residues are replaced one after another while the change in binding to other proteins or changes in activity are recorded. However, practical considerations limit the use of these methods to small-scale studies, precluding a full mapping of all the functionally important residues on the surface of a protein. We present here an alternative approach involving the use of evolutionary data in the form of multiple-sequence alignment for a protein family to identify hot spots and surface patches that are likely to be in contact with other proteins, domains, peptides, DNA, RNA or ligands. The underlying assumption in this approach is that key residues that are important for binding should be conserved throughout evolution, just like residues that are crucial for maintaining the protein fold, i.e. buried residues. A main limitation in the implementation of this approach is that the sequence space of a protein family may be unevenly sampled, e.g. mammals may be overly represented. Thus, a seemingly conserved position in the alignment may reflect a taxonomically uneven sampling, rather than being indicative of structural or functional importance. To avoid this problem, we present here a novel methodology based on evolutionary relations among proteins as revealed by inferred phylogenetic trees, and demonstrate its capabilities for mapping binding sites in SH2 and PTB signaling domains. A computer program that implements these ideas is available freely at: http://ashtoret.tau.ac.il/ approximately rony

Implicit solvent model studies of the interactions of the influenza hemagglutinin fusion peptide with lipid bilayers.

The "fusion peptide," a segment of approximately 20 residues of the influenza hemagglutinin (HA), is necessary and sufficient for HA-induced membrane fusion. We used mean-field calculations of the free energy of peptide-membrane association (DeltaG(tot)) to deduce the most probable orientation of the fusion peptide in the membrane. The main contributions to DeltaG(tot) are probably from the electrostatic (DeltaG(el)) and nonpolar (DeltaG(np)) components of the solvation free energy; these were calculated using continuum solvent models. The peptide was described in atomic detail and was modeled as an alpha-helix based on spectroscopic data. The membrane's hydrocarbon region was described as a structureless slab of nonpolar medium embedded in water. All the helix-membrane configurations, which were lower in DeltaG(tot) than the isolated helix in the aqueous phase, were in the same (wide) basin in configurational space. In each, the helix was horizontally adsorbed at the water-bilayer interface with its principal axis parallel to the membrane plane, its hydrophobic face dissolved in the bilayer, and its polar face in the water. The associated DeltaG(tot) value was approximately -8 to -10 kcal/mol (depending on the rotameric state of one of the phenylalanine residues). In contrast, the DeltaG(tot) values associated with experimentally observed oblique orientations were found to be near zero, suggesting they are marginally stable at best. The theoretical model did not take into account the interactions of the polar headgroups with the peptide and peptide-induced membrane deformation effects. Either or both may overcompensate for the DeltaG(tot) difference between the horizontal and oblique orientations.

Calculations suggest a pathway for the transverse diffusion of a hydrophobic peptide across a lipid bilayer.

Alamethicin is a hydrophobic antibiotic peptide 20 amino acids in length. It is predominantly helical and partitions into lipid bilayers mostly in transmembrane orientations. The rate of the peptide transverse diffusion (flip-flop) in palmitoyl-oleyl-phosphatidylcholine vesicles has been measured recently and the results suggest that it involves an energy barrier, presumably due to the free energy of transfer of the peptide termini across the bilayer. We used continuum-solvent model calculations, the known x-ray crystal structure of alamethicin and a simplified representation of the lipid bilayer as a slab of low dielectric constant to calculate the flip-flop rate. We assumed that the lipids adjust rapidly to each configuration of alamethicin in the bilayer because their motions are significantly faster than the average peptide flip-flop time. Thus, we considered the process as a sequence of discrete peptide-membrane configurations, representing critical steps in the diffusion, and estimated the transmembrane flip-flop rate from the calculated free energy of the system in each configuration. Our calculations indicate that the simplest possible pathway, i.e., the rotation of the helix around the bilayer midplane, involving the simultaneous burial of the two termini in the membrane, is energetically unfavorable. The most plausible alternative is a two-step process, comprised of a rotation of alamethicin around its C-terminus residue from the initial transmembrane orientation to a surface orientation, followed by a rotation around the N-terminus residue from the surface to the final reversed transmembrane orientation. This process involves the burial of one terminus at a time and is much more likely than the rotation of the helix around the bilayer midplane. Our calculations give flip-flop rates of approximately 10(-7)/s for this pathway, in accord with the measured value of 1.7 x 10(-6)/s.

Association entropy in adsorption processes.

The association of two species to form a bound complex, e.g., the binding of a ligand to a protein or the adsorption of a peptide on a lipid membrane, involves an entropy loss, reflecting the conversion of free translational and rotational degrees of freedom into bound motions. Previous theoretical estimates of the standard entropy change in bimolecular binding processes, DeltaS(o), have been derived from the root-mean-square fluctuations in protein crystals, suggesting DeltaS(o) approximately -50 e.u., i.e., TDeltaS degrees approximately -25 kT = -15 kcal/mol. In this work we focus on adsorption, rather than binding processes. We first present a simple statistical-thermodynamic scheme for calculating the adsorption entropy, including its resolution into translational and rotational contributions, using the known distance-orientation dependent binding (adsorption) potential. We then utilize this scheme to calculate the free energy of interaction and entropy of pentalysine adsorption onto a lipid membrane, obtaining TDeltaS(o) approximately -1.7 kT approximately -1.3 kcal/mol. Most of this entropy change is due to the conversion of one free translation into a bound motion, the rest arising from the confinement of two rotational degrees of freedom. The smaller entropy loss in adsorption compared to binding processes arises partly because a smaller number of degrees of freedom become restricted, but mainly due to the fact that the binding potential is much "softer."

Theoretical calculations of the permeability of monensin-cation complexes in model bio-membranes.

Monensin is one of the best-characterized ionophores; it functions in the electroneutral exchange of cations between the extracellular and cytoplasmic sides of cell membranes. The X-ray crystal structures of monensin in free acid form and in complex with Na(+), K(+) and Ag(+) are known and we have recently measured the diffusion rates of monensin in free acid form (Mo-H) and in complex with Na(+) (Mo-Na) and with K(+) (Mo-K) using laser pulse techniques. The results have shown that Mo-H diffuses across the membrane one order of magnitude faster than Mo-Na and two orders of magnitude faster than Mo-K. Here, we report calculations of the translocation free energy of these complexes across the membrane along the most favorable path, i.e. the lowest free energy path. The calculations show that the most favorable orientation of monensin is with its hydrophobic furanyl and pyranyl moieties in the hydrocarbon region of the membrane and the carboxyl group and the cation at the water-membrane interface. Further, the calculations show that Mo-H is likely to be inserted deeper than Mo-Na into the bilayer, and that the free energy barrier for transfer of Mo-H across the membrane is approximately 1 kcal/mol lower than for Mo-Na, in good agreement with our measurements. Our results show that the Mo-K complex is unlikely to diffuse across lipid bilayers in its X-ray crystal structure, in contrast to the Mo-H and Mo-Na complexes. Apparently, when diffusing across the membrane, the Mo-K complex assumes a different conformation and/or thinning defects in the bilayer lower significantly the free energy barrier for the process. The suitability of the model for treating the membrane association of small molecules is discussed in view of the successes and failures observed for the monensin system.

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

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

Electrostatic properties of membranes containing acidic lipids and adsorbed basic peptides: theory and experiment.

The interaction of heptalysine with vesicles formed from mixtures of the acidic lipid phosphatidylserine (PS) and the zwitterionic lipid phosphatidylcholine (PC) was examined experimentally and theoretically. Three types of experiments showed that smeared charge theories (e.g., Gouy-Chapman-Stern) underestimate the membrane association when the peptide concentration is high. First, the zeta potential of PC/PS vesicles in 100 mM KCl solution increased more rapidly with heptalysine concentration (14.5 mV per decade) than predicted by a smeared charge theory (6.0 mV per decade). Second, changing the net surface charge density of vesicles by the same amount in two distinct ways produced dramatically different effects: the molar partition coefficient decreased 1000-fold when the mole percentage of PS was decreased from 17% to 4%, but decreased only 10-fold when the peptide concentration was increased to 1 microM. Third, high concentrations of basic peptides reversed the charge on PS and PC/PS vesicles. Calculations based on finite difference solutions to the Poisson-Boltzmann equation applied to atomic models of heptalysine and PC/PS membranes provide a molecular explanation for the observations: a peptide adsorbing to the membrane in the presence of other surface-adsorbed peptides senses a local potential more negative than the average potential. The biological implications of these "discreteness-of-charge" effects are discussed.

kPROT: a knowledge-based scale for the propensity of residue orientation in transmembrane segments. Application to membrane protein structure prediction.

Modeling of integral membrane proteins and the prediction of their functional sites requires the identification of transmembrane (TM) segments and the determination of their angular orientations. Hydrophobicity scales predict accurately the location of TM helices, but are less accurate in computing angular disposition. Estimating lipid-exposure propensities of the residues from statistics of solved membrane protein structures has the disadvantage of relying on relatively few proteins. As an alternative, we propose here a scale of knowledge-based Propensities for Residue Orientation in Transmembrane segments (kPROT), derived from the analysis of more than 5000 non-redundant protein sequences. We assume that residues that tend to be exposed to the membrane are more frequent in TM segments of single-span proteins, while residues that prefer to be buried in the transmembrane bundle interior are present mainly in multi-span TMs. The kPROT value for each residue is thus defined as the logarithm of the ratio of its proportions in single and multiple TM spans. The scale is refined further by defining it for three discrete sections of the TM segment; namely, extracellular, central, and intracellular. The capacity of the kPROT scale to predict angular helical orientation was compared to that of alternative methods in a benchmark test, using a diversity of multi-span alpha-helical transmembrane proteins with a solved 3D structure. kPROT yielded an average angular error of 41 degrees, significantly lower than that of alternative scales (62 degrees -68 degrees ). The new scale thus provides a useful general tool for modeling and prediction of functional residues in membrane proteins. A WWW server (http://bioinfo.weizmann.ac.il/kPROT) is available for automatic helix orientation prediction with kPROT.

Electrostatics and the membrane association of Src: theory and experiment.

The binding of Src to phospholipid membranes requires both hydrophobic insertion of its myristate into the hydrocarbon interior of the membrane and nonspecific electrostatic interaction of its N-terminal cluster of basic residues with acidic phospholipids. We provide a theoretical description of the electrostatic partitioning of Src onto phospholipid membranes. Specifically, we use molecular models to represent a nonmyristoylated peptide corresponding to residues 2-19 of Src [nonmyr-Src(2-19); GSSKSKPKDPSQRRRSLE-NH2] and a phospholipid bilayer, calculate the electrostatic interaction by solving the nonlinear Poisson-Boltzmann equation, and predict the molar partition coefficient using statistical thermodynamics. The theoretical predictions agree with experimental data obtained by measuring the partitioning of nonmyr-Src(2-19) onto phospholipid vesicles: membrane binding increases as the mole percent of acidic lipid in the vesicles is increased, the ionic strength of the solution is decreased, or the net positive charge of the peptide is increased. The theoretical model also correctly predicts the measured partitioning of the myristoylated peptide, myr-Src(2-19); for example, adding 33% acidic lipid to electrically neutral vesicles increases the partitioning of myr-Src(2-19) 100-fold. Phosphorylating either serine 12 (by protein kinase C) or serine 17 (by cAMP-dependent protein kinase) decreases the partitioning of myr-Src(2-19) onto vesicles containing acidic lipid 10-fold. We investigated the effect of phosphorylation on the localization of Src to biological membranes by expressing fusion constructs of Src's N terminus with a soluble carrier protein in COS-1 cells; phosphorylation produces a small shift in the distribution of the Src chimeras from the plasma membrane to the cytosol.

Electrostatic binding of proteins to membranes. Theoretical predictions and experimental results with charybdotoxin and phospholipid vesicles.

We previously applied the Poisson-Boltzmann equation to atomic models of phospholipid bilayers and basic peptides to calculate their electrostatic interactions from first principles (Ben-Tal, N., B. Honig, R. M. Peitzsch, G. Denisov, and S. McLaughlan. 1996. Binding of small basic peptides to membranes containing acidic lipids. Theoretical models and experimental results. Biophys. J. 71:561-575). Specifically, we calculated the molar partition coefficient, K (the reciprocal of the lipid concentration at which 1/2 the peptide is bound), of simple basic peptides (e.g., pentalysine) with phospholipid vesicles. The theoretical predictions agreed well with experimental measurements of the binding, but the agreement could have been fortuitous because the structure(s) of these flexible peptides is not known. Here we use the same theoretical approach to calculate the membrane binding of two small proteins of known structure: charybdotoxin (CTx) and iberiotoxin (IbTx); we also measure the binding of these proteins to phospholipid vesicles. The theoretical model describes accurately the dependence of K on the ionic strength and mol % acidic lipid in the membrane for both CTx (net charge +4) and IbTx (net charge +2). For example, the theory correctly predicts that the value of K for the binding of CTx to a membrane containing 33% acidic lipid should decrease by a factor of 10(5) when the salt concentration increases from 10 to 200 mM. We discuss the limitations of the theoretical approach and also consider a simple extension of the theory that incorporates nonpolar interactions.

Electrostatic interaction of myristoylated proteins with membranes: simple physics, complicated biology.

Cell membrane association by several important peripheral proteins, such as Src, MARCKS, HIV-1 Gag, and K-Ras, requires nonspecific electrostatic interactions between a cluster of basic residues on the protein and acidic phospholipids in the plasma membrane. A simple theoretical model based on the nonlinear Poisson-Boltzmann equation describes well the experimentally measured electrostatic association between such proteins and the cell membrane.

Helix-helix interactions in lipid bilayers.

Using a continuum model, we calculated the electrostatic interaction free energy between two alpha-helices in three environments: the aqueous phase, a low dielectric alkane phase, and a simple representation of a lipid bilayer. As was found in previous work, helix-helix interactions in the aqueous phase are quite weak, because of solvent screening, and slightly repulsive, because of desolvation effects that accompany helix assembly. In contrast, the interactions can be quite strong in a hypothetical alkane phase because desolvation effects are essentially nonexistent and because helix-helix interactions are not well screened. In this type of environment, the antiparallel helix orientation is strongly favored over the parallel orientation. In previous work we found that the free energy penalty associated with burying helix termini in a bilayer is quite high, which is why the termini tend to protrude into the solvent. Under these conditions the electrostatic interaction is strongly screened by solvent; indeed, it is sufficient for the termini to protrude a few angstroms from the two surfaces of the bilayer for their interaction to diminish almost completely. The effect is consistent with the classical model of the helix dipole in which the dipole moment is represented by point charges located at either terminus. Our results suggest, in agreement with previous models, that there is no significant nonspecific driving force for helix aggregation and, hence, that membrane protein folding must be driven by specific interactions such as close packing and salt-bridge and hydrogen bond formation.

Binding of small basic peptides to membranes containing acidic lipids: theoretical models and experimental results.

We measured directly the binding of Lys3, Lys5, and Lys7 to vesicles containing acidic phospholipids. When the vesicles contain 33% acidic lipids and the aqueous solution contains 100 mM monovalent salt, the standard Gibbs free energy for the binding of these peptides is 3, 5, and 7 kcal/mol, respectively. The binding energies decrease as the mol% of acidic lipids in the membrane decreases and/or as the salt concentration increases. Several lines of evidence suggest that these hydrophilic peptides do not penetrate the polar headgroup region of the membrane and that the binding is mainly due to electrostatic interactions. To calculate the binding energies from classical electrostatics, we applied the nonlinear Poisson-Boltzmann equation to atomic models of the phospholipid bilayers and the basic peptides in aqueous solution. The electrostatic free energy of interaction, which arises from both a long-range coulombic attraction between the positively charged peptide and the negatively charged lipid bilayer, and a short-range Born or image charge repulsion, is a minimum when approximately 2.5 A (i.e., one layer of water) exists between the van der Waals surfaces of the peptide and the lipid bilayer. The calculated molar association constants, K, agree well with the measured values: K is typically about 10-fold smaller than the experimental value (i.e., a difference of about 1.5 kcal/mol in the free energy of binding). The predicted dependence of K (or the binding free energies) on the ionic strength of the solution, the mol% of acidic lipids in the membrane, and the number of basic residues in the peptide agree very well with the experimental measurements. These calculations are relevant to the membrane binding of a number of important proteins that contain clusters of basic residues.

Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes.

A statistical thermodynamic approach is used to analyze the various contributions to the free energy change associated with the insertion of proteins and protein fragments into lipid bilayers. The partition coefficient that determines the equilibrium distribution of proteins between the membrane and the solution is expressed as the ratio between the partition functions of the protein in the two phases. It is shown that when all of the relevant degrees of freedom (i.e., those that change their character upon insertion into the membrane) can be treated classically, the partition coefficient is fully determined by the ratio of the configurational integrals and thus does not involve any mass-dependent factors, a conclusion that is also valid for related processes such as protein adsorption on a membrane surface or substrate binding to proteins. The partition coefficient, and hence the transfer free energy, depend only on the potential energy of the protein in the membrane. Expressing this potential as a sum of a "static" term, corresponding to the equilibrium (minimal free energy) configuration of the protein in the membrane, and a "dynamical" term representing fluctuations around the equilibrium configuration, we show that the static term contains the "solvation" and "lipid perturbation" contributions to the transfer free energy. The dynamical term is responsible for the "immobilization" free energy, reflecting the loss of translational and rotational entropy of the protein upon incorporation into the membrane. Based on a recent molecular theory of lipid-protein interactions, the lipid perturbation and immobilization contributions are then expressed in terms of the elastic deformation free energy resulting from the perturbation of the lipid environment by the foreign (protein) inclusion. The model is formulated for cylindrically shaped proteins, and numerical estimates are given for the insertion of an alpha-helical peptide into a lipid bilayer. The immobilization free energy is shown to be considerably smaller than in previous estimates of this quantity, and the origin of the difference is discussed in detail.