Electrostatics of deformable lipid membranes

The Membrane Dipole Potential and the Roles of Interfacial Water and Lipid Hydrocarbon Chains

Understanding membrane charge transport processes, including the actions of ion channels, pumps, carriers, and membrane-active peptides, requires a description of the electrostatics of the lipid bilayer. We have simulated a library of different lipid chemistries to reveal the impact of the headgroup, glycerol backbone, and hydrocarbon chains on the membrane dipole potential. We found a strong dependence of the potential on lipid packing, but this was not caused by the packing of lipid polar components, due to cancellation of their electric fields by electrolyte. In contrast, lipid tail contributions were determined by area per lipid, arising from two countering effects. Increased area per lipid leads to chain tilting that increases methylene dipole projections to strengthen the electric field within the bilayer, while at the same time decreasing the electric field from terminal methyl groups. Moreover, electric fields from some nonterminal groups and the terminal methyl group can extend beyond the bilayer center and be canceled by the opposing leaflet. This interleaflet field annulment explains the experimental reduction in dipole potential for unsaturated and branched lipid bilayers, by as much as ∼200 mV, as well as experiments that substitute chain carbons with sulfur. Replacing ester with ether groups (eliminating two carbonyl groups) causes a significant reduction in potential, also by ∼200 mV, in agreement with experiment. We show that the effect can be largely attributed to the loss of aligned water molecules in the glycerol backbone region, lowering the potential inside the bilayer core. When only one of the two carbonyls is removed (using a hybrid ester-ether lipid or a single-chain lipid), most of this reduction in potential was lost, with the single carbonyl group able to maintain full hydration in the interfacial region. While headgroup chemistry can have a major effect (by as much as ±100 mV relative to phosphatidylcholine), anionic headgroups either decrease or increase the dipole potential, with the variation involving perturbation in hydrogen-bonded water molecules and changes in packing of lipid tails. Overall, these results suggest that membrane electrostatics are dominated by aligned water molecules at the polar-hydrocarbon interface and, surprisingly, by the charge distribution of the nonpolar lipid tails, and not the packing of headgroup and glycerol carbonyl dipoles.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Implicit model to capture electrostatic features of membrane environment

Membrane protein structure prediction and design are challenging due to the complexity of capturing the interactions in the lipid layer, such as those arising from electrostatics. Accurately capturing electrostatic energies in the low-dielectric membrane often requires expensive Poisson-Boltzmann calculations that are not scalable for membrane protein structure prediction and design. In this work, we have developed a fast-to-compute implicit energy function that considers the realistic characteristics of different lipid bilayers, making design calculations tractable. This method captures the impact of the lipid head group using a mean-field-based approach and uses a depth-dependent dielectric constant to characterize the membrane environment. This energy function Franklin2023 (F23) is built upon Franklin2019 (F19), which is based on experimentally derived hydrophobicity scales in the membrane bilayer. We evaluated the performance of F23 on five different tests probing (1) protein orientation in the bilayer, (2) stability, and (3) sequence recovery. Relative to F19, F23 has improved the calculation of the tilt angle of membrane proteins for 90% of WALP peptides, 15% of TM-peptides, and 25% of the adsorbed peptides. The performances for stability and design tests were equivalent for F19 and F23. The speed and calibration of the implicit model will help F23 access biophysical phenomena at long time and length scales and accelerate the membrane protein design pipeline.

Design of Peptides for Membrane Insertion: The Critical Role of Charge Separation

A physical understanding of membrane permeation and translocation by small, positively charged molecules can illuminate cell penetrating peptide mechanisms of entry and inform drug design. We have previously investigated the permeation of the doubly charged peptide WKW and proposed a defect-assisted permeation mechanism where a small molecule with +2 charge can achieve a metastable state spanning the bilayer by forming a membrane defect with charges stabilized by phospholipid phosphate groups. Here, we investigate the membrane permeation of two doubly charged peptides, WWK and WWWK, with charges separated by different lengths. Through complementary experiments and molecular dynamics simulations, we show that membrane permeation was an order of magnitude more favorable when charges were separated by an ∼2-3 Å greater distance on WWWK compared to WWK. These results agree with the previously proposed defect-assisted permeation mechanism, where a greater distance between positive charges would require a less extreme membrane defect to stabilize the membrane-spanning metastable state. We discuss the implications of these results in understanding the membrane permeation of cell-penetrating peptides and other small, positively charged membrane permeants.

Amphiphilic Gold Nanoparticles: A Biomimetic Tool to Gain Mechanistic Insights into Peptide-Lipid Interactions

Functional peptides are now widely used in a myriad of biomedical and clinical contexts, from cancer therapy and tumor targeting to the treatment of bacterial and viral infections. Underlying this diverse range of applications are the non-specific interactions that can occur between peptides and cell membranes, which, in many contexts, result in spontaneous internalization of the peptide within cells by avoiding energy-driven endocytosis. For this to occur, the amphipathicity and surface structural flexibility of the peptides play a crucial role and can be regulated by the presence of specific molecular residues that give rise to precise molecular events. Nevertheless, most of the mechanistic details regulating the encounter between peptides and the membranes of bacterial or animal cells are still poorly understood, thus greatly limiting the biomimetic potential of these therapeutic molecules. In this arena, finely engineered nanomaterials-such as small amphiphilic gold nanoparticles (AuNPs) protected by a mixed thiol monolayer-can provide a powerful tool for mimicking and investigating the physicochemical processes underlying peptide-lipid interactions. Within this perspective, we present here a critical review of membrane effects induced by both amphiphilic AuNPs and well-known amphiphilic peptide families, such as cell-penetrating peptides and antimicrobial peptides. Our discussion is focused particularly on the effects provoked on widely studied model cell membranes, such as supported lipid bilayers and lipid vesicles. Remarkable similarities in the peptide or nanoparticle membrane behavior are critically analyzed. Overall, our work provides an overview of the use of amphiphilic AuNPs as a highly promising tailor-made model to decipher the molecular events behind non-specific peptide-lipid interactions and highlights the main affinities observed both theoretically and experimentally. The knowledge resulting from this biomimetic approach could pave the way for the design of synthetic peptides with tailored functionalities for next-generation biomedical applications, such as highly efficient intracellular delivery systems.

Experimental Investigations on the Conductance of Lipid Membranes under Differential Hydrostatic Pressure

The unassisted transport of inorganic ions through lipid membranes has become increasingly relevant to an expansive range of biological phenomena. Recent simulations indicate a strong influence of a lipid membrane's curvature on its permeability, which may be part of the overall cell sensitivity to mechanical stimulation. However, most ionic permeability experiments employ a flat, uncurved lipid membrane, which disregards the physiological relevance of curvature on such investigations. To fill this gap in our knowledge, we adapted a traditional experimental system consisting of a planar lipid membrane, which we exposed to a controlled, differential hydrostatic pressure. Our electrophysiology experiments indicate a strong correlation between the changes in membrane geometry elicited by the application of pressure, as inferred from capacitance measurements, and the resulting conductance. Our experiments also confirmed the well-established influence of cholesterol addition to lipid membranes in adjusting their mechanical properties and overall permeability. Therefore, the proposed experimental system may prove useful for a better understanding of the intricate connections between membrane mechanics and adjustments of cellular functionalities upon mechanical stimulation, as well as for confirmation of predictions made by simulations and theoretical modeling.

Ion permeation, selectivity, and electronic polarization in fluoride channels

Fluoride channels (Flucs) export toxic F^- from the cytoplasm. Crystallography and mutagenesis have identified several conserved residues crucial for fluoride transport, but the permeation mechanism at the molecular level has remained elusive. Herein, we have applied constant-pH molecular dynamics and free-energy-sampling methods to investigate fluoride permeation through a Fluc protein from Escherichia coli. We find that fluoride is facile to permeate in its charged form, i.e., F^-, by traversing through a non-bonded network. The extraordinary F^- selectivity is gained by the hydrogen-bonding capability of the central binding site and the Coulombic filter at the channel entrance. The F^- permeation rate calculated using an electronically polarizable force field is significantly more accurate compared with the experimental value than that calculated using a more standard additive force field, suggesting an essential role for electronic polarization in the F^--Fluc interactions.

Molecular Dynamics Simulations Based on Polarizable Models Show that Ion Permeation Interconverts between Different Mechanisms as a Function of Membrane Thickness

Different mechanisms have been proposed to explain the permeation of charged compounds through lipid membranes. Overall, it is expected that an ion-induced defect permeation mechanism, where substantial membrane deformations accompany ion movement, should be dominant in thin membranes but that a solubility-diffusion mechanism, where ions partition into the membrane core with large associated dehydration energy costs, becomes dominant in thicker membranes. However, while this physical picture is intuitively reasonable, capturing the interconversion between these two permeation mechanisms in molecular dynamics (MD) simulations based on atomic models is challenging. In particular, simulations relying on nonpolarizable force fields are artificially unfavorable to the solubility-diffusion mechanism, as induced polarization of the nonpolar hydrocarbon is ignored, causing overestimated free energy costs for charged molecules to enter into this region of the membrane. In this study, all-atom MD simulations based on nonpolarizable and polarizable force fields are used to quantitatively characterize the permeation process for the arginine side chain analog methyl-guanidinium through bilayer membranes of mono-unsaturated phosphatidylcholine lipids with and without cholesterol, resulting in thicknesses spanning from ∼24 to ∼42 Å. With simulations based on a nonpolarizable force field, ion translocation can take place solely through an ion-induced defect mechanism, with free energy barriers increasing linearly from 14 to 40 kcal/mol, depending on the thickness. However, with simulations based on a polarizable force field, ion translocation is predominantly dominated by an ion-induced defect mechanism in thin membranes, which progressively converts to a solubility-diffusion mechanism as the membranes get thicker. The transition between the two mechanisms occurs at a thickness of ∼29 Å, with lipid tails of 22 or more carbon atoms. This situation appears to represent the upper limit for ion-induced defect permeation within the current polarizable models. Beyond this thickness, it becomes energetically preferable for the ion to dehydrate and partition into the membrane core-a phenomenon that cannot be captured using the nonpolarizable models. Induced electronic polarizability therefore leads not just to a shift in permeation energetics but to an interconversion between two strikingly different physical mechanisms. The result highlights the importance of induced polarizability in modeling lipid membranes.

Challenges and advances in atomistic simulations of potassium and sodium ion channel gating and permeation

Ion channels are implicated in many essential physiological events such as electrical signal propagation and cellular communication. The advent of K⁺ and Na⁺ ion channel structure determination has facilitated numerous investigations of molecular determinants of their behaviour. At the same time, rapid development of computer hardware and molecular simulation methodologies has made computational studies of large biological molecules in all-atom representation tractable. The concurrent evolution of experimental structural biology with biomolecular computer modelling has yielded mechanistic details of fundamental processes unavailable through experiments alone, such as ion conduction and ion channel gating. This review is a short survey of the atomistic computational investigations of K⁺ and Na⁺ ion channels, focusing on KcsA and several voltage-gated channels from the K_V and Na_V families, which have garnered many successes and engendered several long-standing controversies regarding the nature of their structure-function relationship. We review the latest advancements and challenges facing the field of molecular modelling and simulation regarding the structural and energetic determinants of ion channel function and their agreement with experimental observations.

Extracellular Surface Potential Mapping by Scanning Ion Conductance Microscopy Revealed Transient Transmembrane Pore Formation Induced by Conjugated Polymer Nanoparticles

In-depth understanding of the biophysicochemical interactions at the nano-bio interface is important for basic cell biology and applications in nanomedicine and nanobiosensors. Here, the extracellular surface potential and topography changes of live cell membranes interacting with polymeric nanomaterials using a scanning ion conductance microscopy-based potential imaging technique are investigated. Two structurally similar amphiphilic conjugated polymer nanoparticles (CPNs) containing different functional groups (i.e., primary amine versus guanidine) are used to study incubation time and functional group-dependent extracellular surface potential and topographic changes. Transmembrane pores, which induce significant changes in potential, only appear transiently in the live cell membranes during the initial interactions. The cells are able to self-repair the damaged membrane and become resilient to prolonged CPN exposure. This study provides an important observation on how the cells interact with and respond to extracellular polymeric nanomaterials at the early stage. This study also demonstrates that extracellular surface potential imaging can provide a new insight to help understand the complicated interactions at the nano-bio interface and the following cellular responses.

In situ examination of a charged amino acid-induced structural change in lipid bilayers by sum frequency generation vibrational spectroscopy

The interactions between amino acids (AAs) and membranes represent various short-range and long-range interactions for biological phenomena; however, they are still poorly understood. In this study, we used cationic lysine and arginine as AA models, and systematically investigated the interactions between charged AAs and lipid bilayers using sum frequency generation vibrational spectroscopy (SFG-VS) in situ and in real time. The AA-induced dynamic structural changes of the lipid bilayer were experimentally monitored using the spectral features of CD₂, CD₃, the lipid head phosphate, and carbonyl groups in real time. Time-dependent SFG changes in the structure of the lipid bilayer provide direct evidence for the different interactions of lysine and arginine with the membrane. It was found that the discrepancy between lysine and arginine in binding with the lipid bilayer is due to the nature of the terminal functional groups. Arginine exhibits a more drastic impact on the membrane than lysine. SFG responses of the acyl chains, phosphate groups, and carbonyl groups provide evidence that the interaction between AAs and the membrane most likely follows an electrostatics and hydrogen bond-induced defect model. This work presents an exemplary method for comprehensive investigations of interactions between membranes and other functionally significant substances.

Digging into Lipid Membrane Permeation for Cardiac Ion Channel Blocker d-Sotalol with All-Atom Simulations

Interactions of drug molecules with lipid membranes play crucial role in their accessibility of cellular targets and can be an important predictor of their therapeutic and safety profiles. Very little is known about spatial localization of various drugs in the lipid bilayers, their active form (ionization state) or translocation rates and therefore potency to bind to different sites in membrane proteins. All-atom molecular simulations may help to map drug partitioning kinetics and thermodynamics, thus providing in-depth assessment of drug lipophilicity. As a proof of principle, we evaluated extensively lipid membrane partitioning of d-sotalol, well-known blocker of a cardiac potassium channel K_v11.1 encoded by the hERG gene, with reported substantial proclivity for arrhythmogenesis. We developed the positively charged (cationic) and neutral d-sotalol models, compatible with the biomolecular CHARMM force field, and subjected them to all-atom molecular dynamics (MD) simulations of drug partitioning through hydrated lipid membranes, aiming to elucidate thermodynamics and kinetics of their translocation and thus putative propensities for hydrophobic and aqueous hERG access. We found that only a neutral form of d-sotalol accumulates in the membrane interior and can move across the bilayer within millisecond time scale, and can be relevant to a lipophilic channel access. The computed water-membrane partitioning coefficient for this form is in good agreement with experiment. There is a large energetic barrier for a cationic form of the drug, dominant in water, to cross the membrane, resulting in slow membrane translocation kinetics. However, this form of the drug can be important for an aqueous access pathway through the intracellular gate of hERG. This route will likely occur after a neutral form of a drug crosses the membrane and subsequently re-protonates. Our study serves to demonstrate a first step toward a framework for multi-scale in silico safety pharmacology, and identifies some of the challenges that lie therein.

A Polarizable Atomic Multipole-Based Force Field for Molecular Dynamics Simulations of Anionic Lipids

In all of the classical force fields, electrostatic interaction is simply treated and explicit electronic polarizability is neglected. The condensed-phase polarization, relative to the gas-phase charge distributions, is commonly accounted for in an average way by increasing the atomic charges, which remain fixed throughout simulations. Based on the lipid polarizable force field DMPC and following the same framework as Atomic Multipole Optimized Energetics for BiomoleculAr (AMOEBA) simulation, the present effort expands the force field to new anionic lipid models, in which the new lipids contain DMPG and POPS. The parameters are compatible with the AMOEBA force field, which includes water, ions, proteins, etc. The charge distribution of each atom is represented by the permanent atomic monopole, dipole and quadrupole moments, which are derived from the ab initio gas phase calculations. Many-body polarization including the inter- and intramolecular polarization is modeled in a consistent manner with distributed atomic polarizabilities. Molecular dynamics simulations of the two aqueous DMPG and POPS membrane bilayer systems, consisting of 72 lipids with water molecules, were then carried out to validate the force field parameters. Membrane width, area per lipid, volume per lipid, deuterium order parameters, electron density profile, electrostatic potential difference between the center of the bilayer and water are all calculated, and compared with limited experimental data.

Insight into the interactions, residue snorkeling, and membrane disordering potency of a single antimicrobial peptide into different lipid bilayers

Pardaxin, with a bend-helix-bend-helix structure, is a membrane-active antimicrobial peptide that its membrane activity depends on the lipid bilayer composition. Herein, all-atom molecular dynamics (MD) simulations were performed to provide further molecular insight into the interactions, structural dynamics, orientation behavior, and cationic residues snorkeling of pardaxin in the DMPC, DPPC, POPC, POPG, POPG/POPE (3:1), and POPG/POPE (1:3) lipid bilayers. The results showed that the C-terminal helix of the peptide was maintained in all six types of the model-bilayers and pardaxin was tilted into the DMPC, DPPC, and POPG/POPE mixed bilayers more than the POPC and POPG bilayers. As well as, the structure of zwitterionic membranes was more affected by the peptide than the anionic bilayers. Taken together, the study demonstrated that the cationic residues of pardaxin snorkeled toward the interface of lipid bilayers and all phenylalanine residues of the peptide played important roles in the peptide-membrane interactions. We hope that this work will provide a better understanding of the interactions of antimicrobial peptides with the membranes.

Passive Transmembrane Permeation Mechanisms of Monovalent Ions Explored by Molecular Dynamics Simulations

Passive or unassisted ion permeation through lipid bilayers involves a type of rare events by which cells regulate their salt concentrations and pH. It is important to understand its mechanism in order to develop technologies of, for example, delivering or maintaining small drug-like molecules inside cells. In earlier simulations of passive ion permeations, the commonly used sampling methods usually define the positions of ions relative to the membrane as a measure of permeation, i.e., the collective variable, ignoring the active participations of other particles. Newly defined collective variables involving the movements of ions, lipids, and water molecules allow us to identify the transition paths on the free energy landscape using the 2D umbrella sampling techniques. In this work, this technique was used to study the permeation processes of some well-known ions, sodium, potassium, and chloride. It is found permeations of sodium and potassium are assisted by important lipid bilayer deformations and massive water solvation, while chloride may not. Chloride may have two different possible pathways, in which the energetic favorable one is similar to the solubility-diffusion model. The free energy barriers for the permeation of these ions are in semiquantitative agreement with experiments. Further analyses on the distributions of oxygens and interaction energies suggest the electrostatic interactions between ions and polar headgroups of lipids may greatly influence membrane deformation as well as the water wire and furthermore the free energy barriers of waterwire mediated pathways. For chloride, the nonwaterwire pathway may be energetically favorable.

Estimation of activation energy for electroporation and pore growth rate in liquid crystalline and gel phases of lipid bilayers using molecular dynamics simulations

Molecular dynamics simulations of electroporation in POPC and DPPC lipid bilayers have been carried out at different temperatures ranging from 230 K to 350 K for varying electric fields. The dynamics of pore formation, including threshold field, pore initiation time, pore growth rate, and pore closure rate after the field is switched off, was studied in both the gel and liquid crystalline (Lα) phases of the bilayers. Using an Arrhenius model of pore initiation kinetics, the activation energy for pore opening was estimated to be 25.6 kJ mol(-1) and 32.6 kJ mol(-1) in the Lα phase of POPC and DPPC lipids respectively at a field strength of 0.32 V nm(-1). The activation energy decreases to 24.2 kJ mol(-1) and 23.7 kJ mol(-1) respectively at a higher field strength of 1.1 V nm(-1). At temperatures below the melting point, the activation energy in the gel phase of POPC and DPPC increases to 28.8 kJ mol(-1) and 34.4 kJ mol(-1) respectively at the same field of 1.1 V nm(-1). The pore closing time was found to be higher in the gel than in the Lα phase. The pore growth rate increases linearly with temperature and quadratically with field, consistent with viscosity limited growth models.

Surfactant functionalization induces robust, differential adhesion of tumor cells and blood cells to charged nanotube-coated biomaterials under flow

The metastatic spread of cancer cells from the primary tumor to distant sites leads to a poor prognosis in cancers originating from multiple organs. Increasing evidence has linked selectin-based adhesion between circulating tumor cells (CTCs) and endothelial cells of the microvasculature to metastatic dissemination, in a manner similar to leukocyte adhesion during inflammation. Functionalized biomaterial surfaces hold promise as a diagnostic tool to separate CTCs and potentially treat metastasis, utilizing antibody and selectin-mediated interactions for cell capture under flow. However, capture at high purity levels is challenged by the fact that CTCs and leukocytes both possess selectin ligands. Here, a straightforward technique to functionalize and alter the charge of naturally occurring halloysite nanotubes using surfactants is reported to induce robust, differential adhesion of tumor cells and blood cells to nanotube-coated surfaces under flow. Negatively charged sodium dodecanoate-functionalized nanotubes simultaneously enhanced tumor cell capture while negating leukocyte adhesion, both in the presence and absence of adhesion proteins, and can be utilized to isolate circulating tumor cells regardless of biomarker expression. Conversely, diminishing nanotube charge via functionalization with decyltrimethylammonium bromide both abolished tumor cell capture while promoting leukocyte adhesion.

Membrane permeation of a peptide: it is better to be positive

A joint experimental and computational study investigates the translocation of a tryptophan molecule through a phospholipid membrane. Time dependent spectroscopy of the tryptophan side chain determines the rate of permeation into 150 nm phospholipid vesicles. Atomically detailed simulations are conducted to calculate the free energy profiles and the permeation coefficient. Different charging conditions of the peptide (positive, negative, or zwitterion) are considered. Both experiment and simulation reproduce the qualitative trend and suggest that the fastest permeation is when the tryptophan is positively charged. The permeation mechanism, which is revealed by molecular dynamics simulations, is of a translocation assisted by a local defect. The influence of long-range electrostatic interactions, such as the membrane dipole potential on the permeation process, is not significant.

Electrostatics-driven shape transitions in soft shells

Manipulating the shape of nanoscale objects in a controllable fashion is at the heart of designing materials that act as building blocks for self-assembly or serve as targeted drug delivery carriers. Inducing shape deformations by controlling external parameters is also an important way of designing biomimetic membranes. In this paper, we demonstrate that electrostatics can be used as a tool to manipulate the shape of soft, closed membranes by tuning environmental conditions such as the electrolyte concentration in the medium. Using a molecular dynamics-based simulated annealing procedure, we investigate charged elastic shells that do not exchange material with their environment, such as elastic membranes formed in emulsions or synthetic nanocontainers. We find that by decreasing the salt concentration or increasing the total charge on the shell's surface, the spherical symmetry is broken, leading to the formation of ellipsoids, discs, and bowls. Shape changes are accompanied by a significant lowering of the electrostatic energy and a rise in the surface area of the shell. To substantiate our simulation findings, we show analytically that a uniformly charged disc has a lower Coulomb energy than a sphere of the same volume. Further, we test the robustness of our results by including the effects of charge renormalization in the analysis of the shape transitions and find the latter to be feasible for a wide range of shell volume fractions.

Continuum approaches to understanding ion and peptide interactions with the membrane

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

The free energy of nanopores in tense membranes

Membrane nanopores are central players for a range of important cellular membrane remodeling processes as well as membrane rupture. Understanding pore formation in tense membranes requires comprehension of the molecular mechanism of pore formation and the associated free energy change as a function of the membrane tension. Here we propose a scheme to calculate the free energy change associated with the formation of a nanometer sized pore in molecular dynamics simulations as a function of membrane tension, which requires the calculation of only one computationally expensive potential of mean force. We show that membrane elastic theory can be used to estimate the pore formation free energy at different tension values from the free energy change in a relaxed membrane and the area expansion curves of the membranes. We have computed the pore formation free energy for a dipalmitoyl-phosphatidylcholine (DPPC) membrane at two different lateral pressure values, 1 bar and -40 bar, by calculating the potential of mean force acting on the head group of a single lipid molecule. Unrestrained simulations of the closing process confirm that the intermediate states along this reaction coordinate are reasonable and show that hydrophilic indentations spanning half the bilayer connected by a hydrophobic pore segment represent the corresponding high energy transition state. A comparison of the stability of simulated membranes to experiment at high loading rates show that, contrary to expectation, pores form too easily in small simulated membrane patches. This discrepancy originates from a combination of the absence of ions in the simulations and the small membrane size.

Ion-induced defect permeation of lipid membranes

We have explored the mechanisms of uncatalyzed membrane ion permeation using atomistic simulations and electrophysiological recordings. The solubility-diffusion mechanism of membrane charge transport has prevailed since the 1960s, despite inconsistencies in experimental observations and its lack of consideration for the flexible response of lipid bilayers. We show that direct lipid bilayer translocation of alkali metal cations, Cl(-), and a charged arginine side chain analog occurs via an ion-induced defect mechanism. Contrary to some previous suggestions, the arginine analog experiences a large free-energy barrier, very similar to those for Na(+), K(+), and Cl(-). Our simulations reveal that membrane perturbations, due to the movement of an ion, are central for explaining the permeation process, leading to both free-energy and diffusion-coefficient profiles that show little dependence on ion chemistry and charge, despite wide-ranging hydration energies and the membrane's dipole potential. The results yield membrane permeabilities that are in semiquantitative agreement with experiments in terms of both magnitude and selectivity. We conclude that ion-induced defect-mediated permeation may compete with transient pores as the dominant mechanism of uncatalyzed ion permeation, providing new understanding for the actions of a range of membrane-active peptides and proteins.

The different interactions of lysine and arginine side chains with lipid membranes

The basic amino acids lysine (Lys) and arginine (Arg) play important roles in membrane protein activity, the sensing of membrane voltages, and the actions of antimicrobial, toxin, and cell-penetrating peptides. These roles are thought to stem from the strong interactions and disruptive influences of these amino acids on lipid membranes. In this study, we employ fully atomistic molecular dynamics simulations to observe, quantify, and compare the interactions of Lys and Arg with saturated phosphatidylcholine membranes of different thickness. We make use of both charged (methylammonium and methylguanidinium) and neutral (methylamine and methylguanidine) analogue molecules, as well as Lys and Arg side chains on transmembrane helix models. We find that the free energy barrier experienced by a charged Lys crossing the membrane is strikingly similar to that of a charged Arg (to within 2 kcal/mol), despite the two having different chemistries, H-bonding capability, and hydration free energies that differ by ∼10 kcal/mol. In comparison, the barrier for neutral Arg is higher than that for neutral Lys by around 5 kcal/mol, being more selective than that for the charged species. This can be explained by the different transport mechanisms for charged or neutral amino acid side chains in the membrane, involving membrane deformations or simple dehydration, respectively. As a consequence, we demonstrate that Lys would be deprotonated in the membrane, whereas Arg would maintain its charge. Our simulations also reveal that Arg attracts more phosphate and water in the membrane, and can form extensive H-bonding with its five H-bond donors to stabilize Arg-phosphate clusters. This leads to enhanced interfacial binding and membrane perturbations, including the appearance of a trans-membrane pore in a thinner membrane. These results highlight the special role played by Arg as an amino acid to bind to, disrupt, and permeabilize lipid membranes, as well as to sense voltages for a range of peptide and protein activities in nature and in engineered bionanodevices.

Free energetics of arginine permeation into model DMPC lipid bilayers: coupling of effective counterion concentration and lateral bilayer dimensions

Mechanisms and underlying thermodynamic determinants of translocation of charged cationic peptides such as cell-penetrating peptides across the cellular membrane continue to receive much attention. Two widely held views include endocytotic and non-endocytotic (diffusive) processes of permeant transfer across the bilayer. Considering a purely diffusive process, we consider the free energetics of translocation of a monoarginine peptide mimic across a model DMPC bilayer. We compute potentials of mean force for the transfer of a charged monoarginine peptide unit from water to the center of a 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) model lipid bilayer. We use fully atomistic molecular dynamics simulations coupled with the adaptive biasing force (ABF) method for free energy estimation. The estimated potential of mean force difference from bulk to bilayer center is 6.94 ± 0.28 kcal/mol. The order of magnitude of this prediction is consistent with past experimental estimates of arginine partitioning into physiological bilayers in the context of translocon-based experiments, though the correlation between the bench and computer experiments is not unambiguous. Moreover, the present value is roughly one-half of previous estimates based on all-atom molecular dynamics free energy calculations. We trace the differences between the present and earlier calculations to system sizes used in the simulations and the dependence of the contributions to the free energy from various system components (water, lipids, ions, peptide) on overall system size. By varying the bilayer lateral dimensions in simulations using only sufficient numbers of counterions to maintain overall system charge neutrality, we find the possibility of an inherent convergent transfer free energy value.

Simulations of anionic lipid membranes: development of interaction-specific ion parameters and validation using NMR data

Overbinding of ions to lipid head groups is a potentially serious artifact in simulations of charged lipid bilayers. In this study, the Lennard-Jones radii in the CHARMM force field for interactions of Na(+) and lipid oxygen atoms of carboxyl, phosphate, and ester groups were revised to match osmotic pressure data on sodium acetate and electrophoresis data on palmitoyloleoyl phosphatidylcholine (POPC) vesicles. The new parameters were then validated by successfully reproducing previously published experimental NMR deuterium order parameters for dimyristoyl phosphatidylglycerol (DMPG) and newly obtained values for palmitoyloleoyl phosphatidylserine (POPS). Although the increases in Lennard-Jones diameters are only 0.02-0.12 Å, they are sufficient to reduce Na+ binding, and thereby increase surface areas per lipid by 5-10% compared with the unmodified parameters.

A polarizable force field of dipalmitoylphosphatidylcholine based on the classical Drude model for molecular dynamics simulations of lipids

A polarizable force field of saturated phosphatidylcholine-containing lipids based on the classical Drude oscillator model is optimized and used in molecular dynamics simulations of bilayer and monolayer membranes. The hierarchical parametrization strategy involves the optimization of parameters for small molecules representative of lipid functional groups, followed by their application in larger model compounds and full lipids. The polar headgroup is based on molecular ions tetramethyl ammonium and dimethyl phosphate, the esterified glycerol backbone is based on methyl acetate, and the aliphatic lipid hydrocarbon tails are based on linear alkanes. Parameters, optimized to best represent a collection of gas and liquid properties for these compounds, are assembled into a complete model of dipalmitoylphosphatidylcholine (DPPC) lipids that is tested against the experimental properties of bilayer and monolayer membranes. The polarizable model yields average structural properties that are in broad accord with experimental data. The area per lipid of the model is 60 Å(2), slightly smaller than the experimental value of 63 Å(2). The order parameters from nuclear magnetic resonance deuterium quadrupolar splitting measures, the electron density profile, and the monolayer dipole potential are in reasonable agreement with experimental data, and with the nonpolarizable CHARMM C36 lipid force field.

Free energetics and the role of water in the permeation of methyl guanidinium across the bilayer-water interface: insights from molecular dynamics simulations using charge equilibration potentials

Combining umbrella sampling molecular dynamics (MD) simulations, the weighted histogram analysis method (WHAM) for unbiasing probabilities, and polarizable charge equilibration force fields, we compute the potential of mean force for the reversible transfer of methyl guanidinium from bulk solution to the center of a model DPPC bilayer. A 5 kcal/mol minimum in the potential of mean force profile for membrane permeation suggests that the analogue will preferentially reside in the headgroup region of the lipid, qualitatively in agreement with previously published results. We find the potential of mean force for permeation to be approximately 28 kcal/mol (relative to the minimum in the headgroups), within the range of values reported for similar types of simulations using fixed-charge force fields. From analysis of the lipid structure, we find that the lipid deformation leads to a substantial destabilizing contribution to the free energy of the methyl guanidinium as it resides in the bilayer center, though this deformation allows more efficient stabilization by water defects and transient pores. Water in the bilayer core stabilizes the charged residue. The role of water in stabilizing or destabilizing the solute as it crosses the bilayer depends on bulk electrolyte concentration. In 1 M KCl solution, the water contribution to the potential of mean force is stabilizing over the entire range of the permeation coordinate, with the sole destabilizing force originating from the anionic species in solution. Conversely, methyl guanidinium experiences net destabilization from water in the absence of electrolyte. The difference in solvent contributions to permeation free energy is traced to a local effect arising from differences in water density in the bilayer-water solution interface, thus leading to starkly opposite net forces on the permeant. The origin of the local water density differential rests with the penetration of hydrated chloride anions into the solution-bilayer interface. Finally, water permeation into the bilayer is required for the deformation of individual lipid molecules and permeation of ions into the membrane. From simulations where water is first excluded from the bilayer center where methyl guanidinium is restrained and then, after equilibration, allowed to enter the bilayer, we find that in the absence of any water defects/permeation into the bilayer, the lipid headgroups do not follow the methyl guanidinium. Only when water enters the bilayer do we see deformation of individual lipid molecules to associate with the amino acid analogue at bilayer center.

Polarizable force fields

This chapter provides an overview of the most common methods for including an explicit description of electronic polarization in molecular mechanics force fields: the induced point dipole, shell, and fluctuating charge models. The importance of including polarization effects in biomolecular simulations is discussed, and some of the most important achievements in the development of polarizable biomolecular force fields to date are highlighted.

The determinants of hydrophobic mismatch response for transmembrane helices

Hydrophobic mismatch arises from a difference in the hydrophobic thickness of a lipid membrane and a transmembrane protein segment, and is thought to play an important role in the folding, stability and function of membrane proteins. We have investigated the possible adaptations that lipid bilayers and transmembrane α-helices undergo in response to mismatch, using fully-atomistic molecular dynamics simulations totaling 1.4 μs. We have created 25 different tryptophan-alanine-leucine transmembrane α-helical peptide systems, each composed of a hydrophobic alanine-leucine stretch, flanked by 1-4 tryptophan side chains, as well as the β-helical peptide dimer, gramicidin A. Membrane responses to mismatch include changes in local bilayer thickness and lipid order, varying systematically with peptide length. Adding more flanking tryptophan side chains led to an increase in bilayer thinning for negatively mismatched peptides, though it was also associated with a spreading of the bilayer interface. Peptide tilting, bending and stretching were systematic, with tilting dominating the responses, with values of up to ~45° for the most positively mismatched peptides. Peptide responses were modulated by the number of tryptophan side chains due to their anchoring roles and distributions around the helices. Potential of mean force calculations for local membrane thickness changes, helix tilting, bending and stretching revealed that membrane deformation is the least energetically costly of all mismatch responses, except for positively mismatched peptides where helix tilting also contributes substantially. This comparison of energetic driving forces of mismatch responses allows for deeper insight into protein stability and conformational changes in lipid membranes.

The Role of Atomic Polarization in the Thermodynamics of Chloroform Partitioning to Lipid Bilayers

In spite of extensive research and use in medical practice, the precise molecular mechanism of volatile anesthetic action remains unknown. The distribution of anesthetics within lipid bilayers and potential targeting to membrane proteins is thought to be central to therapeutic function. Therefore, obtaining a molecular level understanding of volatile anesthetic partitioning into lipid bilayers is of vital importance to modern pharmacology. In this study we investigate the partitioning of the prototypical anesthetic, chloroform, into lipid bilayers and different organic solvents using molecular dynamics simulations with potential models ranging from simplified coarse-grained MARTINI to additive and polarizable CHARMM all-atom force fields. Many volatile anesthetics display significant inducible dipole moments, which correlate with their potency, yet the exact role of molecular polarizability in their stabilization within lipid bilayers remains unknown. We observe that explicit treatment of atomic polarizability makes it possible to accurately reproduce solvation free energies in solvents with different polarities, allowing for quantitative studies in heterogeneous molecular distributions, such as lipid bilayers. We calculate the free energy profiles for chloroform crossing lipid bilayers to reveal a role of polarizability in modulating chloroform partitioning thermodynamics via the chloroform-induced dipole moment and highlight competitive binding to the membrane core and toward the glycerol backbone that may have significant implications for understanding anesthetic action.

Influence of the membrane dipole potential on peptide binding to lipid bilayers

The implicit membrane model IMM1 is extended to include the membrane dipole potential and applied to molecular dynamics simulations of the helical peptides alamethicin, WALP23, influenza hemagglutinin fusion peptide, HIV fusion peptide, magainin, and the pre-sequence of cytochrome c oxidase subunit IV (p25). The results show that the orientation of the peptides in the membrane can be influenced by the dipole potential. The binding affinity of all peptides except for the hemagglutinin fusion peptide decreases upon increase of the dipole potential. The changes in both orientation and binding affinity are explained by the interaction of the dipole potential with the helix backbone dipole and ionic side-chains. In general, peptides that tend to insert the N-terminus in the membrane and/or have positively charged side chains will lose binding affinity upon increase of the dipole potential.

The role of membrane thickness in charged protein-lipid interactions

Charged amino acids are known to be important in controlling the actions of integral and peripheral membrane proteins and cell disrupting peptides. Atomistic molecular dynamics studies have shed much light on the mechanisms of membrane binding and translocation of charged protein groups, yet the impact of the full diversity of membrane physico-chemical properties and topologies has yet to be explored. Here we have performed a systematic study of an arginine (Arg) side chain analog moving across saturated phosphatidylcholine (PC) bilayers of variable hydrocarbon tail length from 10 to 18 carbons. For all bilayers we observe similar ion-induced defects, where Arg draws water molecules and lipid head groups into the bilayers to avoid large dehydration energy costs. The free energy profiles all exhibit sharp climbs with increasing penetration into the hydrocarbon core, with predictable shifts between bilayers of different thickness, leading to barrier reduction from 26 kcal/mol for 18 carbons to 6 kcal/mol for 10 carbons. For lipids of 10 and 12 carbons we observe narrow transmembrane pores and corresponding plateaus in the free energy profiles. Allowing for movements of the protein and side chain snorkeling, we argue that the energetic cost for burying Arg inside a thin bilayer will be small, consistent with recent experiments, also leading to a dramatic reduction in pK(a) shifts for Arg. We provide evidence that Arg translocation occurs via an ion-induced defect mechanism, except in thick bilayers (of at least 18 carbons) where solubility-diffusion becomes energetically favored. Our findings shed light on the mechanisms of ion movement through membranes of varying composition, with implications for a range of charged protein-lipid interactions and the actions of cell-perturbing peptides. This article is part of a Special Issue entitled: Membrane protein structure and function.

Transfer of arginine into lipid bilayers is nonadditive

Computer simulations suggest that the translocation of arginine through the hydrocarbon core of a lipid membrane proceeds by the formation of a water-filled defect that keeps the arginine molecule hydrated even at the center of the bilayer. We show here that adding additional arginine molecules into one of these water defects causes only a small change in free energy. The barrier for transferring multiple arginines through the membrane is approximately the same as for a single arginine and may even be lower depending on the exact geometry of the system. We discuss these results in the context of arginine-rich peptides such as antimicrobial and cell-penetrating peptides.

Hydrophobicity scales: a thermodynamic looking glass into lipid-protein interactions

The partitioning of amino acid sidechains into the membrane is a key aspect of membrane protein folding. However, lipid bilayers exhibit rapidly changing physicochemical properties over their nanometer-scale thickness, which complicates understanding the thermodynamics and microscopic details of membrane partitioning. Recent data from diverse approaches, including protein insertion by the Sec translocon, folding of a small beta-barrel membrane protein and computer simulations of the exact distribution of a variety of small molecules and peptides, have joined older hydrophobicity scales for membrane protein prediction. We examine the correlations among the scales and find that they are remarkably correlated even though there are large differences in magnitude. We discuss the implications of these scales for understanding membrane protein structure and function.

An NMR database for simulations of membrane dynamics

Computational methods are powerful in capturing the results of experimental studies in terms of force fields that both explain and predict biological structures. Validation of molecular simulations requires comparison with experimental data to test and confirm computational predictions. Here we report a comprehensive database of NMR results for membrane phospholipids with interpretations intended to be accessible by non-NMR specialists. Experimental ¹³C-¹H and ²H NMR segmental order parameters (S(CH) or S(CD)) and spin-lattice (Zeeman) relaxation times (T(1Z)) are summarized in convenient tabular form for various saturated, unsaturated, and biological membrane phospholipids. Segmental order parameters give direct information about bilayer structural properties, including the area per lipid and volumetric hydrocarbon thickness. In addition, relaxation rates provide complementary information about molecular dynamics. Particular attention is paid to the magnetic field dependence (frequency dispersion) of the NMR relaxation rates in terms of various simplified power laws. Model-free reduction of the T(1Z) studies in terms of a power-law formalism shows that the relaxation rates for saturated phosphatidylcholines follow a single frequency-dispersive trend within the MHz regime. We show how analytical models can guide the continued development of atomistic and coarse-grained force fields. Our interpretation suggests that lipid diffusion and collective order fluctuations are implicitly governed by the viscoelastic nature of the liquid-crystalline ensemble. Collective bilayer excitations are emergent over mesoscopic length scales that fall between the molecular and bilayer dimensions, and are important for lipid organization and lipid-protein interactions. Future conceptual advances and theoretical reductions will foster understanding of biomembrane structural dynamics through a synergy of NMR measurements and molecular simulations.

Arginine in membranes: the connection between molecular dynamics simulations and translocon-mediated insertion experiments

Several laboratories have carried out molecular dynamics (MD) simulations of arginine interactions with lipid bilayers and found that the energetic cost of placing arginine in lipid bilayers is an order of magnitude greater than observed in molecular biology experiments in which Arg-containing transmembrane helices are inserted across the endoplasmic reticulum membrane by the Sec61 translocon. We attempt here to reconcile the results of the two approaches. We first present MD simulations of guanidinium groups alone in lipid bilayers, and then, to mimic the molecular biology experiments, we present simulations of hydrophobic helices containing single Arg residues at different positions along the helix. We discuss the simulation results in the context of molecular biology results and show that the energetic discrepancy is reduced, but not eliminated, by considering free energy differences between Arg at the interface and at the center of the model helices. The reduction occurs because Arg snorkeling to the interface prevents Arg from residing in the bilayer center where the energetic cost of desolvation is highest. We then show that the problem with MD simulations is that they measure water-to-bilayer free energies, whereas the molecular biology experiments measure the energetics of partitioning from translocon to bilayer, which raises the fundamental question of the relationship between water-to-bilayer and water-to-translocon partitioning. We present two thermodynamic scenarios as a foundation for reconciliation of the simulation and molecular biology results. The simplest scenario is that translocon-to-bilayer partitioning is independent of water-to-bilayer partitioning; there is no thermodynamic cycle connecting the two paths.

Determining peptide partitioning properties via computer simulation

The transfer of polypeptide segments into lipid bilayers to form transmembrane helices represents the crucial first step in cellular membrane protein folding and assembly. This process is driven by complex and poorly understood atomic interactions of peptides with the lipid bilayer environment. The lack of suitable experimental techniques that can resolve these processes both at atomic resolution and nanosecond timescales has spurred the development of computational techniques. In this review, we summarize the significant progress achieved in the last few years in elucidating the partitioning of peptides into lipid bilayer membranes using atomic detail molecular dynamics simulations. Indeed, partitioning simulations can now provide a wealth of structural and dynamic information. Furthermore, we show that peptide-induced bilayer distortions, insertion pathways, transfer free energies, and kinetic insertion barriers are now accurate enough to complement experiments. Further advances in simulation methods and force field parameter accuracy promise to turn molecular dynamics simulations into a powerful tool for investigating a wide range of membrane active peptide phenomena.

On the role of anionic lipids in charged protein interactions with membranes

We investigate the role of anionic lipids in the binding to, and subsequent movement of charged protein groups in lipid membranes, to help understand the role of membrane composition in all membrane-active protein sequences. We demonstrate a small effect of phosphatidylglycerol (PG) lipids on the ability of an arginine (Arg) side chain to bind to, and cross a lipid membrane, despite possessing a neutralizing charge. We observe similar membrane deformations in lipid bilayers composed of phosphatidylcholine (PC) and PC/PG mixtures, with comparable numbers of water and lipid head groups pulled into the bilayer hydrocarbon core, and prohibitively large ~20 kcal/mol barriers for Arg transfer across each bilayer, dropping by just 2-3 kcal/mol due to the binding of PG lipids. We explore the causes of this small effect of introducing PG lipids and offer an explanation in terms of the limited membrane interaction for the choline groups of PC lipids bound to the translocating ion. Our calculations reveal a surprising lack of preference for Arg binding to PG lipids themselves, but a small increase in interfacial binding affinity for lipid bilayers containing PG lipids. These results help to explain the nature of competitive lipid binding to charged protein sequences, with implications for a wide range of membrane binding domains and cell perturbing peptides.