Membrane bending is critical for the stability of voltage sensor segments in the membrane

The interaction between membrane proteins and the surrounding membrane is becoming increasingly appreciated for its role in regulating protein function, protein localization, and membrane morphology. In particular, recent studies have suggested that membrane deformation is needed to stably accommodate proteins harboring charged amino acids in their transmembrane (TM) region, as it is energetically prohibitive to bury charge in the hydrophobic core of the bilayer. Unfortunately, current computational methods are poorly equipped for describing such deformations, as atomistic simulations are often too short to observe large-scale membrane reorganization and most continuum approaches assume a flat membrane. Previously, we developed a method that overcomes these shortcomings by using elasticity theory to characterize equilibrium membrane distortions in the presence of a TM protein, while using traditional continuum electrostatic and nonpolar energy models to determine the energy of the protein in the membrane. Here, we linked the elastostatics, electrostatics, and nonpolar numeric solvers to permit the calculation of energies for nontrivial membrane deformations. We then coupled this procedure to a robust search algorithm that identifies optimal membrane shapes for a TM protein of arbitrary chemical composition. This advance now permits us to explore a host of biological phenomena that were beyond the scope of our original method. We show that the energy required to embed charged residues in the membrane can be highly nonadditive, and our model provides a simple mechanical explanation for this nonadditivity. Our results also predict that isolated voltage sensor segments do not insert into rigid membranes, but membrane bending dramatically stabilizes these proteins in the bilayer despite their high charge content. Additionally, we use the model to explore hydrophobic mismatch with regard to nonpolar peptides and mechanosensitive channels. Our method is in quantitative agreement with molecular dynamics simulations at a tiny fraction of the computational cost.     

Imaging the electrostatic potential of transmembrane channels: atomic probe microscopy of OmpF porin

The atomic force microscope (AFM) was used to image native OmpF porin and to detect the electrostatic potential generated by the protein. To this end the OmpF porin trimers from Escherichia coli was reproducibly imaged at a lateral resolution of approximately 0.5 nm and a vertical resolution of approximately 0.1 nm at variable electrolyte concentrations of the buffer solution. At low electrolyte concentrations the charged AFM probe not only contoured structural details of the membrane protein surface but also interacted with local electrostatic potentials. Differences measured between topographs recorded at variable ionic strength allowed mapping of the electrostatic potential of OmpF porin. The potential map acquired by AFM showed qualitative agreement with continuum electrostatic calculations based on the atomic OmpF porin embedded in a lipid bilayer at the same electrolyte concentrations. Numerical simulations of the experimental conditions showed the measurements to be reproduced quantitatively when the AFM probe was included in the calculations. This method opens a novel avenue to determine the electrostatic potential of native protein surfaces at a lateral resolution better than 1 nm and a vertical resolution of approximately 0.1 nm.     

Exploring the binding dynamics of BAR proteins

We used a continuum model based on the Helfrich free energy to investigate the binding dynamics of a lipid bilayer to a BAR domain surface of a crescent-like shape of positive (e.g. I-BAR shape) or negative (e.g. F-BAR shape) intrinsic curvature. According to structural data, it has been suggested that negatively charged membrane lipids are bound to positively charged amino acids at the binding interface of BAR proteins, contributing a negative binding energy to the system free energy. In addition, the cone-like shape of negatively charged lipids on the inner side of a cell membrane might contribute a positive intrinsic curvature, facilitating the initial bending towards the crescent-like shape of the BAR domain. In the present study, we hypothesize that in the limit of a rigid BAR domain shape, the negative binding energy and the coupling between the intrinsic curvature of negatively charged lipids and the membrane curvature drive the bending of the membrane. To estimate the binding energy, the electric potential at the charged surface of a BAR domain was calculated using the Langevin-Bikerman equation. Results of numerical simulations reveal that the binding energy is important for the initial instability (i.e. bending of a membrane), while the coupling between the intrinsic shapes of lipids and membrane curvature could be crucial for the curvature-dependent aggregation of negatively charged lipids near the surface of the BAR domain. In the discussion, we suggest novel experiments using patch clamp techniques to analyze the binding dynamics of BAR proteins, as well as the possible role of BAR proteins in the fusion pore stability of exovesicles.     

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.     

Protocol for MM/PBSA molecular dynamics simulations of proteins

Continuum solvent models have been employed in past years for understanding processes such as protein folding or biomolecular association. In the last decade, several attempts have been made to merge atomic detail molecular dynamics simulations with solvent continuum models. Among continuum models, the Poisson-Boltzmann solvent accessible surface area model is one of the oldest and most fundamental. Notwithstanding its wide usage for simulation of biomolecular electrostatic potential, the Poisson-Boltzmann equation has been very seldom used to obtain solvation forces for molecular dynamics simulation. We propose here a fast and reliable methodology to implement continuum forces in standard molecular mechanics and dynamics algorithms. Results for a totally unrestrained 1 ns molecular dynamics simulation of a small protein are quantitatively similar to results obtained by explicit solvent molecular dynamics simulations.     

Molecular dynamics simulation of Pf1 coat protein.

The results of molecular dynamics simulations of Pf1 coat protein are described and compared to experimental NMR data on both the membrane bound and structural forms of this viral coat protein. Molecular dynamics simulations of the 46 residue coat protein and related model sequences were performed according to a simple protocol. The simulations were initiated with the polypeptides in a completely uniform alpha helical conformation in a dielectric continuum (epsilon = 2) and the motions of individual residues were followed as a function of time by monitoring the angular fluctuations of amide NH bond vectors. The simulations of Pf1 coat protein were able to identify the same mobile and structured segments found in experimental NMR studies of the membrane bound form of the protein (Shon, K.-J., Y. Kim, L. A. Colnago, and S. J. Opella. 1991. Science (Wash. DC). 252:1303-1305). Significantly, in addition to mobile amino and carboxyl terminal regions, a mobile internal loop was found that connects the rigid hydrophobic and amphipathic helices in the protein. NMR experiments show that this mobile loop is present in both the viral and membrane bound forms of the protein and that it plays a role in viral assembly (Nambudripad, R., W. Stark, S. J. Opella, and L. Makowski. 1991. Science (Wash. DC) 252:1305-1308). The results of simulations of several alanine based 46 residue polypeptides with some of the charged residues present in the Pf1 coat protein sequence suggest that interactions between the Asp 14 and Asp 18 sidechains and the peptide backbone are responsible for the formation of the mobile loop.(ABSTRACT TRUNCATED AT 250 WORDS)     

Simulations of (an)isotropic diffusion on curved biological surfaces

We present a computational particle method for the simulation of isotropic and anisotropic diffusion on curved biological surfaces that have been reconstructed from image data. The method is capable of handling surfaces of high curvature and complex shape, which are often encountered in biology. The method is validated on simple benchmark problems and is shown to be second-order accurate in space and time and of high parallel efficiency. It is applied to simulations of diffusion on the membrane of endoplasmic reticula (ER) in live cells. Diffusion simulations are conducted on geometries reconstructed from real ER samples and are compared to fluorescence recovery after photobleaching experiments in the same ER samples using the transmembrane protein tsO45-VSV-G, C-terminally tagged with green fluorescent protein. Such comparisons allow derivation of geometry-corrected molecular diffusion constants for membrane components from fluorescence recovery after photobleaching data. The results of the simulations indicate that the diffusion behavior of molecules in the ER membrane differs significantly from the volumetric diffusion of soluble molecules in the lumen of the same ER. The apparent speed of recovery differs by a factor of approximately 4, even when the molecular diffusion constants of the two molecules are identical. In addition, the specific shape of the membrane affects the recovery half-time, which is found to vary by a factor of approximately 2 in different ER samples.     

Protein diffusion on charged membranes: a dynamic mean-field model describes time evolution and lipid reorganization

As charged macromolecules adsorb and diffuse on cell membranes in a large variety of cell signaling processes, they can attract or repel oppositely charged lipids. This results in lateral membrane rearrangement and affects the dynamics of protein function. To address such processes quantitatively we introduce a dynamic mean-field scheme that allows self-consistent calculations of the equilibrium state of membrane-protein complexes after such lateral reorganization of the membrane components, and serves to probe kinetic details of the process. Applicable to membranes with heterogeneous compositions containing several types of lipids, this comprehensive method accounts for mobile salt ions and charged macromolecules in three dimensions, as well as for lateral demixing of charged and net-neutral lipids in the membrane plane. In our model, the mobility of membrane components is governed by the diffusion-like Cahn-Hilliard equation, while the local electrochemical potential is based on nonlinear Poisson-Boltzmann theory. We illustrate the method by applying it to the adsorption of the anionic polypeptide poly-Lysine on negatively charged lipid membranes composed of binary mixtures of neutral and monovalent lipids, or onto ternary mixtures of neutral, monovalent, and multivalent lipids. Consistent with previous calculations and experiments, our results show that at steady-state multivalent lipids (such as PIP₂), but not monovalent lipid (such as phosphatidylserine), will segregate near the adsorbing macromolecules. To address the corresponding diffusion of the adsorbing protein in the membrane plane, we couple lipid mobility with the propagation of the adsorbing protein through a dynamic Monte Carlo scheme. We find that due to their higher mobility dictated by the electrochemical potential, multivalent lipids such as PIP₂ more quickly segregate near oppositely charged proteins than do monovalent lipids, even though their diffusion constants may be similar. The segregation, in turn, slows protein diffusion, as lipids introduce an effective drag on the motion of the adsorbate. In contrast, monovalent lipids such as phosphatidylserine only weakly segregate, and the diffusions of protein and lipid remain largely uncorrelated.     

Membrane-Mediated Protein-Protein Interactions and Connection to Elastic Models: A Coarse-Grained Simulation Analysis of Gramicidin A Association

To further foster the connection between particle based and continuum mechanics models for membrane mediated biological processes, we carried out coarse-grained (CG) simulations of gramicidin A (gA) dimer association and analyzed the results based on the combination of potential of mean force (PMF) and stress field calculations. Similar to previous studies, we observe that the association of gA dimers depends critically on the degree of hydrophobic mismatch, with the estimated binding free energy of >10 kcal/mol in a distearoylphosphatidylcholine bilayer. Qualitative trends in the computed PMF can be understood based on the stress field distributions near a single gA dimer and between a pair of gA dimers. For example, the small PMF barrier, which is ∼1 kcal/mol independent of lipid type, can be captured nearly quantitatively by considering membrane deformation energy associated with the region confined by two gA dimers. However, the PMF well depth is reproduced poorly by a simple continuum model that only considers membrane deformation energy beyond the annular lipids. Analysis of lipid orientation, configuration entropy, and stress distribution suggests that the annular lipids make a significant contribution to the association of two gA dimers. These results highlight the importance of explicitly considering contributions from annular lipids when constructing approximate models to study processes that involve a significant reorganization of lipids near proteins, such as protein-protein association and protein insertion into biomembranes. Finally, large-scale CG simulations indicate that multiple gA dimers also form clusters, although the preferred topology depends on the protein concentration. Even at high protein concentrations, every gA dimer requires contact to lipid hydrocarbons to some degree, and at most three to four proteins are in contact with each gA dimer; this observation highlights another aspect of the importance of interactions between proteins and annular lipids.     

Factors influencing local membrane curvature induction by N-BAR domains as revealed by molecular dynamics simulations

N-BAR domains are protein modules that bind to and induce curvature in membranes via a charged concave surface and N-terminal amphipathic helices. Recently, molecular dynamics simulations have demonstrated that the N-BAR domain can induce a strong local curvature that matches the curvature of the BAR domain surface facing the bilayer. Here we present further molecular dynamics simulations that examine in greater detail the roles of the concave surface and amphipathic helices in driving local membrane curvature. We find that the strong curvature induction observed in our previous simulations requires the stable presentation of the charged concave surface to the membrane and is not driven by the membrane-embedded amphipathic helices. Nevertheless, without these amphipathic helices embedded in the membrane, the N-BAR domain does not maintain a close association with the bilayer, and fails to drive membrane curvature. Increasing the membrane negative charge through the addition of PIP₂ facilitates closer association with the membrane in the absence of embedded helices. At sufficiently high concentrations, amphipathic helices embedded in the membrane drive membrane curvature independently of the BAR domain.     

Ion-binding properties of calbindin D9k: a Monte Carlo simulation study

Monte Carlo simulations are used to calculate the binding constant of two Ca2+ ions to the protein bovine calbindin D9k. The change in binding constant with respect to mutation of charged amino acids, presence of various electrolytes, protein concentration, solution pH, and competitive binding of monovalent ions is investigated. Each of these factors may have a large influence on the binding constant. The simulations are performed in a dielectric continuum model, the so-called primitive model of electrolyte theory, with a fixed protein structure and a uniform dielectric permittivity. The calculated binding constants are in excellent agreement with experimental data and describe changes in the binding constant over six orders of magnitude.     

Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape

Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes.     

Molecular Modeling of Lipid Membrane Curvature Induction by a Peptide: More than Simply Shape

Molecular dynamics simulations of an amphipathic helix embedded in a lipid bilayer indicate that it will induce substantial positive curvature (e.g., a tube of diameter 20 nm at 16% surface coverage). The induction is twice that of a continuum model prediction that only considers the shape of the inclusion. The discrepancy is explained in terms of the additional presence of specific interactions described only by the molecular model. The conclusion that molecular shape alone is insufficient to quantitatively model curvature is supported by contrasting molecular and continuum models of lipids with large and small headgroups (choline and ethanolamine, respectively), and of the removal of a lipid tail (modeling a lyso-lipid). For the molecular model, curvature propensity is analyzed by computing the derivative of the free energy with respect to bending. The continuum model predicts that the inclusion will soften the bilayer near the headgroup region, an effect that may weaken curvature induction. The all-atom predictions are consistent with experimental observations of the degree of tubulation by amphipathic helices and variation of the free energy of binding to liposomes.     

H-bonding in protein hydration revisited

H-bonding between protein surface polar/charged groups and water is one of the key factors of protein hydration. Here, we introduce an Accessible Surface Area (ASA) model for computationally efficient estimation of a free energy of water-protein H-bonding at any given protein conformation. The free energy of water-protein H-bonds is estimated using empirical formulas describing probabilities of hydrogen bond formation that were derived from molecular dynamics simulations of water molecules at the surface of a small protein, Crambin, from the Abyssinian cabbage (Crambe abyssinica) seed. The results suggest that atomic solvation parameters (ASP) widely used in continuum hydration models might be dependent on ASA for polar/charged atoms under consideration. The predictions of the model are found to be in qualitative agreement with the available experimental data on model compounds. This model combines the computational speed of ASA potential, with the high resolution of more sophisticated solvation methods.     

Helical integrity and microsolvation of transmembrane domains from Flaviviridae envelope glycoproteins

Charged and polar amino acids in the transmembrane domains of integral membrane proteins can be crucial for protein function and also promote helix-helix association or protein oligomerization. Yet, our current understanding is still limited on how these hydrophilic amino acids are efficiently translocated from the Sec61/SecY translocon into the cell membrane during the biogenesis of membrane proteins. In hepatitis C virus, the putative transmembrane segments of envelope glycoproteins E1 and E2 were suggested to heterodimerize via a Lys-Asp ion-pair in the host endoplasmic reticulum. Therefore in this work, we carried out molecular dynamic simulations in explicit lipid bilayer and solvent environment to explore the stability of all possible bridging ion-pairs using the model of H-segment helix dimers. We observed that, frequently, several water molecules penetrated from the interface into the membrane core to stabilize the charged and polar pairs. The hydration time and amount of water molecules in the membrane core depended on the position of the charged residues as well as on the type of ion-pairs. Similar microsolvation events were observed in simulations of the putative E1-E2 transmembrane helix dimers. Simulations of helix monomers from other members of the Flaviviridae family suggest that these systems show similar behaviors. Thus this study illustrates the important contribution of water microsolvation to overcome the unfavorable energetic cost of burying charged and polar amino acids in membrane lipid bilayers. Also, it emphasizes the novel role of bridging charged or polar interactions stabilized by water molecules in the hydrophobic lipid bilayer core that has an important biological function for helix dimerization in several envelope glycoproteins from the family of Flaviviridae viruses.     

On the charge regulation of proteins

It is known that the overall charge of a protein can change as the molecule approaches a charged object like another protein or a cell membrane. We have formalized this mechanism using a statistical mechanical framework and show how this rather overlooked interaction increases the attraction between protein molecules. From the theory, we can identify a unique property, the protein charge capacitance, that contains all information needed to describe the charge regulation mechanism. The capacitance can be obtained from experiment or theory and is a function of pH, salt concentration, and the number of titrating residues. For a range of different protein molecules, we calculate the capacitance and demonstrate how it can be used to quantify the charge regulation interaction. With minimal effort, the derived formulas can be used to improve existing models by including a charge regulation term. Good agreement is found between theory, simulations, and experimental data.     

Aggregation of model membrane proteins, modulated by hydrophobic mismatch, membrane curvature, and protein class

Aggregation of transmembrane proteins is important for many biological processes, such as protein sorting and cell signaling, and also for in vitro processes such as two-dimensional crystallization. We have used large-scale simulations to study the lateral organization and dynamics of lipid bilayers containing multiple inserted proteins. Using coarse-grained molecular dynamics simulations, we have studied model membranes comprising ∼7000 lipids and 16 identical copies of model cylindrical proteins of either α-helical or β-barrel types. Through variation of the lipid tail length and hence the degree of hydrophobic mismatch, our simulations display levels of protein aggregation ranging from negligible to extensive. The nature and extent of aggregation are shown to be influenced by membrane curvature and the shape or orientation of the protein. Interestingly, a model β-barrel protein aggregates to form one-dimensional strings within the bilayer plane, whereas a model α-helical bundle forms two-dimensional clusters. Overall, it is clear that the nature and extent of membrane protein aggregation is dependent on several aspects of the proteins and lipids, including hydrophobic mismatch, protein class and shape, and membrane curvature.