An implicit membrane generalized born theory for the study of structure, stability, and interactions of membrane proteins

Exploiting recent developments in generalized Born (GB) electrostatics theory, we have reformulated the calculation of the self-electrostatic solvation energy to account for the influence of biological membranes. Consistent with continuum Poisson-Boltzmann (PB) electrostatics, the membrane is approximated as an solvent-inaccessible infinite planar low-dielectric slab. The present membrane GB model closely reproduces the PB electrostatic solvation energy profile across the membrane. The nonpolar contribution to the solvation energy is taken to be proportional to the solvent-exposed surface area (SA) with a phenomenological surface tension coefficient. The proposed membrane GB/SA model requires minor modifications of the pre-existing GB model and appears to be quite efficient. By combining this implicit model for the solvent/bilayer environment with advanced computational sampling methods, like replica-exchange molecular dynamics, we are able to fold and assemble helical membrane peptides. We examine the reliability of this model and approach by applications to three membrane peptides: melittin from bee venom, the transmembrane domain of the M2 protein from Influenza A (M2-TMP), and the transmembrane domain of glycophorin A (GpA). In the context of these proteins, we explore the role of biological membranes (represented as a low-dielectric medium) in affecting the conformational changes in melittin, the tilt of transmembrane peptides with respect to the membrane normal (M2-TMP), helix-to-helix interactions in membranes (GpA), and the prediction of the configuration of transmembrane helical bundles (GpA). The present method is found to perform well in each of these cases and is anticipated to be useful in the study of folding and assembly of membrane proteins as well as in structure refinement and modeling of membrane proteins where a limited number of experimental observables are available.     

Orientation and dynamics of transmembrane peptides: the power of simple models

In this review we discuss recent insights obtained from well-characterized model systems into the factors that determine the orientation and tilt angles of transmembrane peptides in lipid bilayers. We will compare tilt angles of synthetic peptides with those of natural peptides and proteins, and we will discuss how tilt can be modulated by hydrophobic mismatch between the thickness of the bilayer and the length of the membrane spanning part of the peptide or protein. In particular, we will focus on results obtained on tryptophan-flanked model peptides (WALP peptides) as a case study to illustrate possible consequences of hydrophobic mismatch in molecular detail and to highlight the importance of peptide dynamics for the experimental determination of tilt angles. We will conclude with discussing some future prospects and challenges concerning the use of simple peptide/lipid model systems as a tool to understand membrane structure and function.     

Configuration of influenza hemagglutinin fusion peptide monomers and oligomers in membranes

The 20 N-terminal residues of the HA2 subunit of influenza hemagglutinin (HA), known as the fusion peptide, play a crucial role in membrane fusion. Molecular dynamics simulations with implicit solvation are employed here to study the structure and orientation of the fusion peptide in membranes. As a monomer the α-helical peptide adopts a shallow, slightly tilted orientation along the lipid tail-head group interface. The average angle of the peptide with respect to membrane plane is 12.4 °. We find that the kinked structure proposed on the basis of NMR data is not stable in our model because of the high energy cost related to the membrane insertion of polar groups. Because hemagglutinin-mediated membrane fusion is promoted by low pH, we examined the effect of protonation of the Glu and Asp residues. The configurations of the protonated peptides were slightly deeper in the membrane but at similar angles. Finally, because HA is a trimer, we modeled helical fusion peptide trimers. We find that oligomerization affects the insertion depth of the peptide and its orientation with respect to the membrane: a trimer exhibits equally favorable configurations in which some or all of the helices in the bundle insert obliquely deep into the membrane.     

Configuration of influenza hemagglutinin fusion peptide monomers and oligomers in membranes

The 20 N-terminal residues of the HA2 subunit of influenza hemagglutinin (HA), known as the fusion peptide, play a crucial role in membrane fusion. Molecular dynamics simulations with implicit solvation are employed here to study the structure and orientation of the fusion peptide in membranes. As a monomer the alpha-helical peptide adopts a shallow, slightly tilted orientation along the lipid tail-head group interface. The average angle of the peptide with respect to membrane plane is 12.4 degrees . We find that the kinked structure proposed on the basis of NMR data is not stable in our model because of the high energy cost related to the membrane insertion of polar groups. Because hemagglutinin-mediated membrane fusion is promoted by low pH, we examined the effect of protonation of the Glu and Asp residues. The configurations of the protonated peptides were slightly deeper in the membrane but at similar angles. Finally, because HA is a trimer, we modeled helical fusion peptide trimers. We find that oligomerization affects the insertion depth of the peptide and its orientation with respect to the membrane: a trimer exhibits equally favorable configurations in which some or all of the helices in the bundle insert obliquely deep into the membrane.     

Interpretation of H-NMR Experiments on the Orientation of the Transmembrane Helix WALP23 by Computer Simulations

Orientation, dynamics, and packing of transmembrane helical peptides are important determinants of membrane protein structure, dynamics, and function. Because it is difficult to investigate these aspects by studying real membrane proteins, model transmembrane helical peptides are widely used. NMR experiments provide information on both orientation and dynamics of peptides, but they require that motional models be interpreted. Different motional models yield different interpretations of quadrupolar splittings (QS) in terms of helix orientation and dynamics. Here, we use coarse-grained (CG) molecular dynamics (MD) simulations to investigate the behavior of a well-known model transmembrane peptide, WALP23, under different hydrophobic matching/mismatching conditions. We compare experimental ²H-NMR QS (directly measured in experiments), as well as helix tilt angle and azimuthal rotation (not directly measured), with CG MD simulation results. For QS, the agreement is significantly better than previously obtained with atomistic simulations, indicating that equilibrium sampling is more important than atomistic details for reproducing experimental QS. Calculations of helix orientation confirm that the interpretation of QS depends on the motional model used. Our simulations suggest that WALP23 can form dimers, which are more stable in an antiparallel arrangement. The origin of the preference for the antiparallel orientation lies not only in electrostatic interactions but also in better surface complementarity. In most cases, a mixture of monomers and antiparallel dimers provides better agreement with NMR data compared to the monomer and the parallel dimer. CG MD simulations allow predictions of helix orientation and dynamics and interpretation of QS data without requiring any assumption about the motional model.     

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.     

Dipole lattice membrane model for protein calculations

A dipole lattice model for lipid membranes and their interactions with peptides is presented. It uses the Langevin dipole method to calculate electrostatic interactions in the heterogeneous membrane environment. A series of test cases are presented, including spherical charges, dipoles, side chain analogs, and helical peptides. The model consistently produces qualitatively correct results.     

Structure, topology, and tilt of cell-signaling peptides containing nuclear localization sequences in membrane bilayers determined by solid-state NMR and molecular dynamics simulation studies

Cell-signaling peptides have been extensively used to transport functional molecules across the plasma membrane into living cells. These peptides consist of a hydrophobic sequence and a cationic nuclear localization sequence (NLS). It has been assumed that the hydrophobic region penetrates the hydrophobic lipid bilayer and delivers the NLS inside the cell. To better understand the transport mechanism of these peptides, in this study, we investigated the structure, orientation, tilt of the peptide relative to the bilayer normal, and the membrane interaction of two cell-signaling peptides, SA and SKP. Results from CD and solid-state NMR experiments combined with molecular dynamics simulations suggest that the hydrophobic region is helical and has a transmembrane orientation with the helical axis tilted away from the bilayer normal. The influence of the hydrophobic mismatch, between the hydrophobic length of the peptide and the hydrophobic thickness of the bilayer, on the tilt angle of the peptides was investigated using thicker POPC and thinner DMPC bilayers. NMR experiments showed that the hydrophobic domain of each peptide has a tilt angle of 15 +/- 3 degrees in POPC, whereas in DMPC, 25 +/- 3 degree and 30 +/- 3 degree tilts were observed for SA and SKP peptides, respectively. These results are in good agreement with molecular dynamics simulations, which predict a tilt angle of 13.3 degrees (SA in POPC), 16.4 degrees (SKP in POPC), 22.3 degrees (SA in DMPC), and 31.7 degrees (SKP in DMPC). These results and simulations on the hydrophobic fragment of SA or SKP suggest that the tilt of helices increases with a decrease in bilayer thickness without changing the phase, order, and structure of the lipid bilayers.     

Interactions of hydrophobic peptides with lipid bilayers: Monte Carlo simulations with M2delta

We introduce here a novel Monte Carlo simulation method for studying the interactions of hydrophobic peptides with lipid membranes. Each of the peptide's amino acids is represented as two interaction sites: one corresponding to the backbone alpha-carbon and the other to the side chain, with the membrane represented as a hydrophobic profile. Peptide conformations and locations in the membrane and changes in the membrane width are sampled using the Metropolis criterion, taking into account the underlying energetics. Using this method we investigate the interactions between the hydrophobic peptide M2delta and a model membrane. The simulations show that starting from an extended conformation in the aqueous phase, the peptide first adsorbs onto the membrane surface, while acquiring an ordered helical structure. This is followed by formation of a helical-hairpin and insertion into the membrane. The observed path is in agreement with contemporary understanding of peptide insertion into biological membranes. Two stable orientations of membrane-associated M2delta were obtained: transmembrane (TM) and surface, and the value of the water-to-membrane transfer free energy of each of them is in agreement with calculations and measurements on similar cases. M2delta is most stable in the TM orientation, where it assumes a helical conformation with a tilt of 14 degrees between the helix principal axis and the membrane normal. The peptide conformation agrees well with the experimental data; average root-mean-square deviations of 2.1 A compared to nuclear magnetic resonance structures obtained in detergent micelles and supported lipid bilayers. The average orientation of the peptide in the membrane in the most stable configurations reported here, and in particular the value of the tilt angle, are in excellent agreement with the ones calculated using the continuum-solvent model and the ones observed in the nuclear magnetic resonance studies. This suggests that the method may be used to predict the three-dimensional structure of TM peptides.     

Membrane adsorption, folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Membrane adsorption,folding, insertion and translocation of synthetic trans-membrane peptides

Spontaneous membrane adsorption, folding and insertion of the synthetic WALP16 and KALP16 peptides was studied by computer simulations starting from completely extended conformations. The peptides were simulated using an unmodified all-atom force field in combination with an efficient Monte Carlo sampling algorithm. The membrane is represented implicitly as a hydrophobic zone inside a continuum solvent modelled using the generalized Born theory of solvation. The method was previously parameterized to match insertion energies of hydrophobic side chain analogs into cyclohexane and no parameters were optimized for the present simulations. Both peptides rapidly precipitate out of bulk solution and adsorb to the membrane surface. Interfacial folding into a helical conformation is followed by membrane insertion. Both the peptide conformations and their location in the membrane are strongly temperature dependent. The temperature dependent behaviour can be summarized by fitting to a four-state model, separating the system into folded and unfolded conformers, which are either inserted into the membrane or located at the interfaces. As the temperature is lowered the dominant peptide conformation of the system changes from unfolded surface bound configurations to folded surface bound states. Folded trans-membrane conformers represent the dominant configuration at low temperatures. The analysis allows direct estimates of the free energies of peptide folding and membrane insertion. In the case of WALP the quality of the fit is excellent and the thermodynamic behaviour is in good agreement with expected theoretical consideration. For KALP the fit is more problematic due to the large solvation energies of the charged lysine residues.     

Modeling of Peptides in Implicit Membrane-Mimetic Media

Abstract

Lipid bilayer plays a crucial role in folding of membrane peptides and their stabilization in the membrane-bound state. Correct treatment of the media effects is thus essential for realistic simulations of peptides in bilayers. Previously (Volynsky et al., 1999), we proposed an efficient solvation model which mimics heterogeneous membrane-water system. The model is based on combined employment of atomic solvation parameters for water and hydrocarbon, which approximate hydrated headgroups and acyl chains of lipids, respectively. In this study, the model is employed in non-restrained Monte Carlo simulations of several peptides: totally apolar 20-residue poly-L-Leu, hydrophobic peptide with polar edges, and strongly amphiphilic pep-tide. The principal goals are: to explore energy landscape of these peptides in membrane; to characterize the structures of low-energy states and their orientations with respect to the bilayer. Simulations were performed starting from different structures (unordered or helical) and orientations. It was found that the membrane environment significantly promotes an α-helical conformation for all the peptides, while their energetically favourable orientations are quite different. Thus, poly-Leu was immobilized inside the membrane, the hydrophobic peptide with polar termini adapted transbilayer orientation, whereas the amphiphilic peptide stayed on the lipid-water interface in peripherial orientation. Energy barriers between different states were characterized. The computational results were compared with the experimental structural data.     

Peptide insertion, positioning, and stabilization in a membrane: insight from an all-atom molecular dynamics simulation

Peptide insertion, positioning, and stabilization in a model membrane are probed via an all-atom molecular dynamics (MD) simulation. One peptide (WL5) is simulated in each leaflet of a solvated dimyristoylglycero-3-phosphate (DMPC) membrane. Within the first 5 ns, the peptides spontaneously insert into the membrane and then stabilize during the remaining 70 ns of simulation time. In both leaflets, the peptides localize to the membrane interface, and this localization is attributed to the formation of peptide-lipid hydrogen bonds. We show that the single tryptophan residue in each peptide contributes significantly to these hydrogen bonds; specifically, the nitrogen heteroatom of the indole ring plays a critical role. The tilt angles of the indole rings relative to the membrane normal in the upper and lower leaflets are approximately 26 degrees and 54 degrees , respectively. The tilt angles of the entire peptide chain are 62 degrees and 74 degrees . The membrane induces conformations of the peptide that are characteristic of beta-sheets, and the peptide enhances the lipid ordering in the membrane. Finally, the diffusion rate of the peptides in the membrane plane is calculated (based on experimental peptide concentrations) to be approximately 6 A(2)/ns, thus suggesting a 500 ns time scale for intermolecular interactions.     

A Comparative Study on the Ability of Two Implicit Solvent Lipid Models to Predict Transmembrane Helix Tilt Angles

Free-energy profiles describing the relative orientation of membrane proteins along predefined coordinates can be efficiently calculated by means of umbrella simulations. Such simulations generate reliable orientational distributions but are difficult to converge because of the very long equilibration times of the solvent and the lipid bilayer in explicit representation. Two implicit lipid membrane models are here applied in combination with the umbrella sampling strategy to the simulation of the transmembrane (TM) helical segment from virus protein U (Vpu). The models are used to study both orientation and energetics of this α-helical peptide as a function of hydrophobic mismatch. We observe that increasing the degree of positive hydrophobic mismatch increased the tilt angle of Vpu. These findings agree well with experimental data and as such validate the solvation models used in this study.     

Energetics of the native and non-native states of the glycophorin transmembrane helix dimer

Using an implicit membrane model (IMM1), we examine whether the structure of the transmembrane domain of Glycophorin A (GpA) could be predicted based on energetic considerations alone. The energetics of native GpA shows that van der Waals interactions make the largest contribution to stability. Although specific electrostatic interactions are stabilizing, the overall electrostatic contribution is close to zero. The GXXXG motif contributes significantly to stability, but residues outside this motif contribute almost twice as much. To generate non-native states a global conformational search was done on two segments of GpA: an 18-residue peptide (GpA74-91) that is embedded in the membrane and a 29-residue peptide (GpA70-98) that has additional polar residues flanking the transmembrane region. Simulated annealing was done on a large number of conformations generated from parallel, antiparallel, left- and right-handed starting structures by rotating each helix at 20 degrees intervals around its helical axis. Several crossing points along the helix dimer were considered. For 18-residue parallel topology, an ensemble of native-like structures was found at the lowest effective energy region; the effective energy is lowest for a right-handed structure with an RMSD of 1.0 A from the solid-state NMR structure with correct orientation of the helices. For the 29-residue peptide, the effective energies of several left-handed structures were lower than that of the native, right-handed structure. This could be due to deficiencies in modeling the interactions between charged sidechains and/or omission of the sidechain entropy contribution to the free energy. For 18-residue antiparallel topology, both IMM1 and a Generalized Born model give effective energies that are lower than that of the native structure. In contrast, the Poisson-Boltzmann solvation model gives lower effective energy for the parallel topology, largely because the electrostatic solvation energy is more favorable for the parallel structure. IMM1 seems to underestimate the solvation free energy advantage when the CO and NH dipoles just outside the membrane are parallel. This highlights the importance of electrostatic interactions even when these are not obvious by looking at the structures.     

Method of oriented circular dichroism.

We present a new method for determining the orientation of alpha-helical sections of proteins or peptides in membrane. To apply this method, membranes containing proteins must be prepared in a multilayer array. Circular dichroism (CD) spectra of the multilayer sample are then measured at the normal as well as oblique incident angles with respect to the bilayer planes; we call such spectra oriented circular dichroism (OCD). The procedure of OCD measurement, particularly the ways to avoid the spectral artifacts due to the effects of dielectric interfaces, linear dichroism and birefringence, and the method of data analysis are described in detail. To illustrate the method, we analyze the OCD of alamethicin in diphytanoylphosphatidylcholine multilayers. We conclude unambiguously that the helical section of alamethicin is parallel to the membrane normal when the sample is in the full-hydration state, but the helical section rotates to the plane of membrane when the sample is in a low-hydration state. We also obtained the parallel and perpendicular CD spectra of alpha-helix, and found them to be in agreement with previous theoretical calculations based on the exciton theory. These spectra are useful for analyzing protein orientations in future experiments.     

Tilt and Rotation Angles of a Transmembrane Model Peptide as Studied by Fluorescence Spectroscopy

In this study the membrane orientation of a tryptophan-flanked model peptide, WALP23, was determined by using peptides that were labeled at different positions along the sequence with the environmentally sensitive fluorescent label BADAN. The fluorescence properties, reflecting the local polarity, were used to determine the tilt and rotation angles of the peptide based on an ideal α-helix model. For WALP23 inserted in dioleoylphosphatidylcholine (DOPC), an estimated tilt angle of the helix with respect to the bilayer normal of 24° ± 5° was obtained. When the peptides were inserted into bilayers with different acyl chain lengths or containing different concentrations of cholesterol, small changes in tilt angle were observed as response to hydrophobic mismatch, whereas the rotation angle appeared to be independent of lipid composition. In all cases, the tilt angles were significantly larger than those previously determined from ²H NMR experiments, supporting recent suggestions that the relatively long timescale of ²H NMR measurements may result in an underestimation of tilt angles due to partial motional averaging. It is concluded that although the fluorescence technique has a rather low resolution and limited accuracy, it can be used to resolve the discrepancies observed between previous ²H NMR experiments and molecular-dynamics simulations.     

Structures and mode of membrane interaction of a short alpha helical lytic peptide and its diastereomer determined by NMR, FTIR, and fluorescence spectroscopy.

The interaction of many lytic cationic antimicrobial peptides with their target cells involves electrostatic interactions, hydrophobic effects, and the formation of amphipathic secondary structures, such as alpha helices or beta sheets. We have shown in previous studies that incorporating approximately 30%d-amino acids into a short alpha helical lytic peptide composed of leucine and lysine preserved the antimicrobial activity of the parent peptide, while the hemolytic activity was abolished. However, the mechanisms underlying the unique structural features induced by incorporating d-amino acids that enable short diastereomeric antimicrobial peptides to preserve membrane binding and lytic capabilities remain unknown. In this study, we analyze in detail the structures of a model amphipathic alpha helical cytolytic peptide KLLLKWLL KLLK-NH2 and its diastereomeric analog and their interactions with zwitterionic and negatively charged membranes. Calculations based on high-resolution NMR experiments in dodecylphosphocholine (DPCho) and sodium dodecyl sulfate (SDS) micelles yield three-dimensional structures of both peptides. Structural analysis reveals that the peptides have an amphipathic organization within both membranes. Specifically, the alpha helical structure of the L-type peptide causes orientation of the hydrophobic and polar amino acids onto separate surfaces, allowing interactions with both the hydrophobic core of the membrane and the polar head group region. Significantly, despite the absence of helical structures, the diastereomer peptide analog exhibits similar segregation between the polar and hydrophobic surfaces. Further insight into the membrane-binding properties of the peptides and their depth of penetration into the lipid bilayer has been obtained through tryptophan quenching experiments using brominated phospholipids and the recently developed lipid/polydiacetylene (PDA) colorimetric assay. The combined NMR, FTIR, fluorescence, and colorimetric studies shed light on the importance of segregation between the positive charges and the hydrophobic moieties on opposite surfaces within the peptides for facilitating membrane binding and disruption, compared to the formation of alpha helical or beta sheet structures.     

Modeling of peptides and proteins in a membrane environment: I. A solvation model mimicking a lipid bilayer

A theoretical solvation model of peptides and proteins that mimics the heterogeneous membrane-water system was proposed. Our approach is based on the combined use of atomic parameters of solvation for water and hydrocarbons, which approximates the hydrated polar groups and acyl chains of lipids, respectively. This model was tested in simulations of several peptides: a nonpolar 20-mer polyleucine, a hydrophobic peptide with terminal polar groups, and a strongly amphiphilic peptide. The conformational space of the peptides in the presence of the membrane was studied by the Monte Carlo method. Unlike a polar solvent and vacuum, the membrane-like environment was shown to stabilize the α-helical conformation: low-energy structures have a helicity index of 100% in all cases. At the same time, the energetically most favorable orientations of the peptides relative to the membrane depend on their hydrophobic properties: nonpolar polyleucine is entirely immersed in the bilayer and the hydrophobic peptide with polar groups at the termini adopts a transbilayer orientation, whereas the amphiphilic peptide lies at the interface parallel to the membrane plane. The results of the simulations agree well with the available experimental data for these systems. In the following communications of this series, we plan to describe applications of the solvation model to membrane-bound proteins and peptides with biologically important functional activities.