Accelerating Convergence in Molecular Dynamics Simulations of Solutes in Lipid Membranes by Conducting a Random Walk along the Bilayer Normal

A molecular dynamics study of cell-penetrating peptide transportan-10 (TP10): Binding, folding and insertion to transmembrane state in zwitterionic membrane

Transportan 10 (TP10) is a 21-residue, cationic, α-helical cell-penetrating peptide that can be used as a delivery vector for various bioactive molecules. Based on recent confocal microscopy studies, it is believed that TP10 can translocate across neutral lipid membrane passively, possibly as a monomer, without the formation of permanent pore. Here, we performed extensive molecular dynamics (MD) simulations of TP10W (Y3W variant of TP10) to find the microscopic details of binding, folding and insertion of TP10W to transmembrane state in POPC bilayer. Binding study with CHARMM36 force field showed that TP10W initially binds to the membrane surface in unstructured configuration, but it spontaneously folds into α-helical conformation under the lipid head groups. Further insertion of TP10W, changing from a surface bound state to a vertically oriented transmembrane state, was investigated via umbrella simulations. The resulting free energy profile shows a relatively small barrier between two states, suggesting a possible translocation pathway as a monomer. In fact, unbiased simulation of transmembrane TP10W revealed how a charged Lys side chain can move from one leaflet to the other without a significant free energy cost. Finally, we compared the results of TP10W simulations with those of point mutated variants (TP10W-K12A18 and TP10W-K19L) to understand the effect of charge distribution on the peptide. It was observed that such a conservative mutation can cause noticeable changes in the conformations of both surface bound and transmembrane states. The results of present study will be discussed in relation to the experimentally observed activities of TP10W against neutral membrane.

Combining SILCS and Artificial Intelligence for High-Throughput Prediction of the Passive Permeability of Drug Molecules

Membrane permeability of drug molecules plays a significant role in the development of new therapeutic agents. Accordingly, methods to predict the passive permeability of drug candidates during a medicinal chemistry campaign offer the potential to accelerate the drug design process. In this work, we combine the physics-based site identification by ligand competitive saturation (SILCS) method and data-driven artificial intelligence (AI) to create a high-throughput predictive model for the passive permeability of druglike molecules. In this study, we present a comparative analysis of four regression models to predict membrane permeabilities of small druglike molecules; of the tested models, Random Forest was the most predictive yielding an R2 of 0.81 for the independent data set. The input feature vector used to train the developed prediction model includes absolute free energy profiles of ligands through a POPC-cholesterol bilayer based on ligand grid free energy (LGFE) profiles obtained from the SILCS approach. The use of the membrane free energy profiles from SILCS offers information on the physical forces contributing to ligand permeability, while the use of AI yields a more predictive model trained on experimental PAMPA permeability data for a collection of 229 molecules. This combination allows for rapid estimations of ligand permeability at a level of accuracy beyond currently available predictive models while offering insights into the contributions of the functional groups in the ligands to the permeability barrier, thereby offering quantitative information to facilitate rational ligand design.

Permeation of a Homologous Series of NBD-Labeled Fatty Amines through Lipid Bilayers: A Molecular Dynamics Study

Permeation through biomembranes is ubiquitous for drugs to reach their active sites. Asymmetry of the cell plasma membrane (PM) has been described as having an important role in this process. Here we describe the interaction of a homologous series of 7-nitrobenz-2-oxa-1,3-diazol-4-yl (NBD)-labeled amphiphiles (NBD-Cn, n = 4 to 16) with lipid bilayers of different compositions (1-palmitoyl, 2-oleoyl-sn-glycero-3-phosphocholine (POPC):cholesterol (1:1) and palmitoylated sphingomyelin (SpM):cholesterol (6:4)), including an asymmetric bilayer. Both unrestrained and umbrella sampling (US) simulations (at varying distances to the bilayer center) were carried out. The free energy profile of NBD-Cn at different depths in the membrane was obtained from the US simulations. The behavior of the amphiphiles during the permeation process was described regarding their orientation, chain elongation, and H-bonding to lipid and water molecules. Permeability coefficients were also calculated for the different amphiphiles of the series, using the inhomogeneous solubility-diffusion model (ISDM). Quantitative agreement with values obtained from kinetic modeling of the permeation process could not be obtained. However, for the longer, and more hydrophobic amphiphiles, the variation trend along the homologous series was qualitatively better matched by the ISDM when the equilibrium location of each amphiphile was taken as reference (ΔG = 0), compared to the usual choice of bulk water.

Coarse-grained molecular simulation of extracellular vesicle squeezing for drug loading

In recent years, extracellular vesicles have become promising carriers as next-generation drug delivery platforms. Effective loading of exogenous cargos without compromising the extracellular vesicle membrane is a major challenge. Rapid squeezing through nanofluidic channels is a widely used approach to load exogenous cargoes into the EV through the nanopores generated temporarily on the membrane. However, the exact mechanism and dynamics of nanopore opening, as well as cargo loading through nanopores during the squeezing process remains unknown and it is impossible to visualize or quantify it experimentally due to the small size of the EV and the fast transient process. This paper developed a systemic algorithm to simulate nanopore formation and predict drug loading during extracellular vesicle (EV) squeezing by leveraging the power of coarse-grain (CG) molecular dynamics simulations with fluid dynamics. The EV CG beads are coupled with implicit the fluctuating lattice Boltzmann solvent. The effects of EV properties and various squeezing test parameters, such as EV size, flow velocity, channel width, and length, on pore formation and drug loading efficiency are analyzed. Based on the simulation results, a phase diagram is provided as a design guide for nanochannel geometry and squeezing velocity to generate pores on the membrane without damaging the EV. This method can be utilized to optimize the nanofluidic device configuration and flow setup to obtain desired drug loading into EVs.

Simulated Tempering-Enhanced Umbrella Sampling Improves Convergence of Free Energy Calculations of Drug Membrane Permeation

Molecular dynamics simulations have been widely used to study solute permeation across biological membranes. The potential of mean force (PMF) for solute permeation is typically computed using enhanced sampling techniques such as umbrella sampling (US). For bulky drug-like permeants, however, obtaining converged PMFs remains challenging and often requires long simulation times, resulting in an unacceptable computational cost. Here, we augmented US with simulated tempering (ST), an extended-ensemble technique that consists in varying the temperature of the system along a pre-defined temperature ladder. Simulated tempering-enhanced US (STeUS) was employed to improve the convergence of PMF calculations for the permeation of methanol and three common drug molecules. To obtain sufficient sampling of the umbrella histograms, which were computed only from the ground temperature, we modified the simulation time fraction spent at the ground temperature between 1/K and 50%, where K is the number of ST temperature states. We found that STeUS accelerates convergence, when compared to standard US, and that the benefit of STeUS is system-dependent. For bulky molecules, for which standard US poorly converged, the application of ST was highly successful, leading to a more than fivefold accelerated convergence of the PMFs. For the small methanol solute, for which conventional US converges moderately, the application of ST is only beneficial if 50% of the STeUS simulation time is spent at the ground temperature. This study establishes STeUS as an efficient and simple method for PMF calculations, thereby strongly reducing the computational cost of routine high-throughput studies of drug permeability.

Design of a protein-targeted DNA aptamer using atomistic simulation

The concentrations of specific macromolecular species can be quantified using diagnostic tools that rely on molecular recognition by nucleic acid aptamers. One such approach involves the formation of osmium tetroxide 2,2'-bipyridine protein adducts, followed by electrochemical detection of analytes that bind specifically to electrode-tethered aptamers. In conjunction with a 27-mer DNA aptamer that binds specifically to exosite II on human alpha thrombin, this technique permits, in theory, a highly sensitive diagnostic tool for the quantification of serum thrombin levels. However, thrombin's aptamer binding site is lined by two tryptophan residues and the conjugation of bulky osmium groups to these residues weakens aptamer binding by an estimated 4 to 12 kcal/mol, undermining detection sensitivity. Therefore, we have rationally modified this DNA aptamer to strengthen its thrombin binding in the presence of conjugated osmium. Specifically, aptamers carrying long hydrophobic thymine derivatives in place of guanine 21 have binding affinities for osmium-conjugated thrombin that are enhanced by 10 to 15 kcal/mol, suggesting that these modified aptamers may be effective in a highly sensitive electrochemical sensor for the quantification of low concentrations of thrombin. Our approach of using molecular simulation to subtly re-engineer a DNA aptamer may be generally applicable for the optimization of other macromolecular binding interfaces.Communicated by Ramaswamy H. Sarma.

De Novo Transmembrane Aggregation of Aβ10-40 Peptides in an Anionic Lipid Bilayer

Using the all-atom model and 10 μs serial replica-exchange molecular dynamics (SREMD), we investigated the binding of Alzheimer's Aβ10-40 peptides to the anionic dimyristoylphosphatidylcholine/dimyristoylphosphatidylglycerol (DMPC/DMPG) lipid bilayer. Our objective was to probe de novo transmembrane Aβ10-40 aggregation and to test the utility of SREMD. Our results are threefold. First, upon binding, Aβ10-40 adopts a helical structure in the C-terminus and deeply inserts into the bilayer. Binding is primarily controlled by electrostatic interactions of the peptides with water, ions, and lipids, particularly, anionic DMPG. Second, Aβ-bilayer interactions reorganize lipids in the proximity of the bound peptides, causing an influx of DMPG lipids into the Aβ binding footprint. Third and most important, computed free energy landscapes reveal that Aβ10-40 peptides partition into monomeric and dimeric species. The dimers result from transmembrane aggregation of the peptides and induce a striking lipid density void throughout both leaflets in the bilayer. There are multiple factors stabilizing transmembrane dimers, including van der Waals and steric interactions, electrostatic interactions, and hydrogen bonding, hydration, and entropic gains originating from dimer conformations and lipid disorder. We argue that helix dipole-dipole interactions underestimated in the all-atom force field must be a contributing factor to stabilizing antiparallel transmembrane dimers. We propose that transmembrane aggregates serve as mechanistic links between the populations of extra- and intracellular Aβ peptides. From the computational perspective, SREMD is found to be a viable alternative to traditional replica-exchange simulations.

Calculation of the permeability coefficients of small molecules through lipid bilayers by free-energy reaction network analysis following the explicit treatment of the internal conformation of the solute

Biomembrane permeation represents a major barrier to pharmacokinetics. During preclinical drug discovery, the coefficients of the permeation of molecules through lipid bilayers account for a valuable property of such molecules. Therefore, the control of the permeation of molecules through lipid bilayers is an essential factor in drug design, and the estimation of the permeation phenomena is a crucial study in pharmacy. Thus, there are many published studies on the theoretical estimations of permeation coefficients. Here, we propose a molecular dynamics (MD) simulation method for estimating the permeation of small molecules through lipid bilayers based on the free-energy reaction network (FERN) analysis. In this method, the collective variables (CVs) of the free energy calculations explicitly include the conformational changes in the rotational bonds of the solute molecules. The advantages of the present method over the other method are that it is possible to estimate reaction pathways and their reaction rates, i.e., permeation coefficients or passage times, in multidimensional space spanned by CVs though conventional methods such as the umbrella sampling method and target MDs often dealt with a few degrees of freedom. To demonstrate the efficacy of our method, we calculate the coefficients of the permeation of three small aromatic peptides, namely N-acetylphenylalanineamide (Ac-Phe-NH2 or NAFA), N-acetyltyrosineamide (Ac-Tyr-NH2 or NAYA), and N-acetyltryptophanamide (Ac-Trp-NH2 or NATA), through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer. In these cases we adopted one CV for the permeation direction and four CVs for the internal rotational coordinates. The results reveal that the permeation coefficients of NAFA, NAYA, and NATA are 1.7 × 10^-2, 0.51 × 10^-4, and 5.7 × 10^-4 cm s^-1, respectively. Compared with the experimental data, our simulation results followed the same trend, i.e., NAFA > NATA > NAYA. By analyzing the structures of metastable points of the solute molecules, our simulation result reveals that the aforementioned trend is caused by the differences in stability among their rotamers. Furthermore, we evaluate the statistical fluctuation of the rotamers, and the time scale of flipping the side chain reveals that the structures rigidify as the ligand moves deeper into the membrane.

Lipid Composition Is Critical for Accurate Membrane Permeability Prediction of Cyclic Peptides by Molecular Dynamics Simulations

Cyclic peptides have attracted attention as a promising pharmaceutical modality due to their potential to selectively inhibit previously undruggable targets, such as intracellular protein-protein interactions. Poor membrane permeability is the biggest bottleneck hindering successful drug discovery based on cyclic peptides. Therefore, the development of computational methods that can predict membrane permeability and support elucidation of the membrane permeation mechanism of drug candidate peptides is much sought after. In this study, we developed a protocol to simulate the behavior in membrane permeation steps and estimate the membrane permeability of large cyclic peptides with more than or equal to 10 residues. This protocol requires the use of a more realistic membrane model than a single-lipid phospholipid bilayer. To select a membrane model, we first analyzed the effect of cholesterol concentration in the model membrane on the potential of mean force and hydrogen bonding networks along the direction perpendicular to the membrane surface as predicted by molecular dynamics simulations using cyclosporine A. These results suggest that a membrane model with 40 or 50 mol % cholesterol was suitable for predicting the permeation process. Subsequently, two types of membrane models containing 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine and 40 and 50 mol % cholesterol were used. To validate the efficiency of our protocol, the membrane permeability of 18 ten-residue peptides was predicted. Correlation coefficients of R > 0.8 between the experimental and calculated permeability values were obtained with both model membranes. The results of this study demonstrate that the lipid membrane is not just a medium but also among the main factors determining the membrane permeability of molecules. The computational protocol proposed in this study and the findings obtained on the effect of membrane model composition will contribute to building a schematic view of the membrane permeation process. Furthermore, the results of this study will eventually aid the elucidation of design rules for peptide drugs with high membrane permeability.

Improving the accuracy and convergence of drug permeation simulations via machine-learned collective variables

Understanding the permeation of biomolecules through cellular membranes is critical for many biotechnological applications, including targeted drug delivery, pathogen detection, and the development of new antibiotics. To this end, computer simulations are routinely used to probe the underlying mechanisms of membrane permeation. Despite great progress and continued development, permeation simulations of realistic systems (e.g., more complex drug molecules or biologics through heterogeneous membranes) remain extremely challenging if not intractable. In this work, we combine molecular dynamics simulations with transition-tempered metadynamics and techniques from the variational approach to conformational dynamics to study the permeation mechanism of a drug molecule, trimethoprim, through a multicomponent membrane. We show that collective variables (CVs) obtained from an unsupervised machine learning algorithm called time-structure based Independent Component Analysis (tICA) improve performance and substantially accelerate convergence of permeation potential of mean force (PMF) calculations. The addition of cholesterol to the lipid bilayer is shown to increase both the width and height of the free energy barrier due to a condensing effect (lower area per lipid) and increase bilayer thickness. Additionally, the tICA CVs reveal a subtle effect of cholesterol increasing the resistance to permeation in the lipid head group region, which is not observed when canonical CVs are used. We conclude that the use of tICA CVs can enable more efficient PMF calculations with additional insight into the permeation mechanism.

Analysis of Charged Peptide Loop-Flipping across a Lipid Bilayer Using the String Method with Swarms of Trajectories

The hydrophobic core of the lipid bilayer is conventionally considered a barrier to the translocation of charged species such that the translocation of even single ions occurs on long time scales. In contrast, experiments have revealed that some materials, including peptides, proteins, and nanoparticles, can translocate multiple charged moieties across the bilayer on experimentally relevant time scales. Understanding the molecular mechanisms underlying this behavior is challenging because resolving corresponding free-energy landscapes with molecular simulation techniques is computationally expensive. To address this challenge, we use atomistic molecular dynamics simulations with the swarms-of-trajectories (SOT) string method to analyze charge translocation pathways across single-component lipid bilayers as a function of multiple collective variables. We first demonstrate that the SOT string method can reproduce the free-energy barrier for the translocation of a charged lysine amino acid analogue in good agreement with the literature. We then obtain minimum free-energy pathways for the translocation, or flipping, of charged peptide loops across the lipid bilayer by utilizing trajectories from prior temperature-accelerated molecular dynamics (TAMD) simulations as initial configurations. The corresponding potential of mean force calculations reveal that the protonation of a central membrane-exposed aspartate residue substantially reduces the free-energy barrier for flipping charged loops by modulating the water content of the bilayer. These results provide new insight into the thermodynamics underlying loop-flipping processes and highlight how the combination of TAMD and the SOT string method can be used to understand complex charge translocation mechanisms.

Rational design of antimicrobial peptides targeting Gram-negative bacteria

Membrane-targeting host antimicrobial peptides (AMPs) can kill or inhibit the growth of Gram-negative bacteria. However, the evolution of resistance among microbes poses a substantial barrier to the long-term utility of the host AMPs. Combining experiment and molecular dynamics simulations, we show that terminal carboxyl capping enhances both membrane insertion and antibacterial activity of an AMP called P1. Furthermore, we show that a bacterial strain with evolved resistance to this peptide becomes susceptible to P1 variants with either backbone capping or lysine-to-arginine substitutions. Our results suggest that cocktails of closely related AMPs may be useful in overcoming evolved resistance.

Selecting Collective Variables and Free-Energy Methods for Peptide Translocation across Membranes

The selective permeability of cellular membranes is a crucial property for controlled transport into and out of cells. Molecules that can bypass the cellular machinery and spontaneously translocate across membranes could be used as therapeutics or drug carriers. Peptides are a prominent class of such molecules, which include natural and man-developed antimicrobial and cell-penetrating peptides. However, the necessary peptide properties for translocation remain elusive. Computer simulations could uncover these properties once we have a good collective variable (CV) that accurately describes the translocation process. Here, we developed a new CV, which includes a description of peptide insertion, local membrane deformation, and peptide internal degrees of freedom related to its charged groups. By comparison of CVs, we demonstrated that all these components are necessary for an accurate description of peptide translocation. Moreover, the advantages and disadvantages of three common methods for free-energy calculations with our CV were evaluated using the MARTINI coarse-grained model: umbrella sampling, umbrella sampling with replica exchange, and metadynamics. The developed CV leads to the reliable and effective calculation of the free energy of peptide translocation, and thus, it could be useful in the design of spontaneously translocating peptides.

Effects of fluidity and charge density on the morphology of a bicellar mixture - A SANS study

The spontaneously formed structures of physiologically relevant lipid model membranes made of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, 1-palmitoyl-2-oleoyl-sn-glycero-3-phospho-(1'-rac-glycerol) and 1,2-hexanoyl-sn-glycero-3-phosphocholine have been evaluated in depth using small angle neutron scattering. Although a common molar ratio of long- to short- chain phospholipids (~4) as reported in many bicellar mixtures was used, discoidal bicelles were not found as the major phase throughout the range of lipid concentration and temperature studied, indicating that the required condition for the formation of bicelle is the immiscibility between the long- and short- chain lipids, which were in the gel and L_α phases, respectively, in previous reports. In this study, all lipids are in the L_α phase. The characterization outcome suggests that the spontaneous structures tie strongly with the physical parameters of the system such as melting transition temperature of the long-chain lipid, total lipid concentration and charge density of the system. Multilamellar vesicles, unilamellar vesicles, ribbons and perforated lamellae can be obtained based on the analysis of the small angle neutron scattering results, leading to the construction of structural diagrams. This report provides the important map to choose suitable lipid systems for the structural study of membrane-associated proteins, design of theranostic nanocarriers or other related research fields.

Effect of Protein Flexibility from Coarse-Grained Elastic Network Parameterizations on the Calculation of Free Energy Profiles of Ligand Binding

The characterization of the affinity and binding mechanism of specific molecules to a protein active site is scientifically and industrially relevant for many applications. In principle, this information can be obtained using molecular dynamics (MD) simulations by calculating the free energy profile of the process. However, this is a computationally demanding calculation. Currently, coarse-grained (CG) force fields are very well implemented for MD simulations of biomolecular systems. These computationally efficient force fields are a major advantage to the study of large model systems and/or those requiring long simulation times. The Martini model is currently one of the most popular CG force fields for these systems. For the specific case of protein simulations, to correctly maintain the macromolecular three-dimensional structure, the Martini model needs to include an elastic network (EN). In this work, the effect of protein flexibility, as induced by three EN models compatible with the Martini force field, was tested on the calculation of free energy profiles for protein-ligand binding. The EN models used were ElNeDyn, GoMartini, and GEN. The binding of triolein (TOG) and triacetin (TAG) to a lipase protein (thermomyces lanuginosa lipase-TLL) was used as a case study. The results show that inclusion of greater flexibility in the CG parameterization of proteins is of high importance in the calculation of the free energy profiles of protein-ligand systems. However, care must be taken in order to avoid unjustified large protein deformations. In addition, due to molecular flexibility there may be no absolute need for the center of the ligand to reach the center of the protein-binding site. The calculation of the energy profile to a distance of about 0.5 nm from the active site center can be sufficient to differentiate the affinity of different ligands to a protein.

Molecular Dynamics Simulation of Small Molecules Interacting with Biological Membranes

Cell membranes protect and compartmentalise cells and their organelles. The semi-permeable nature of these membranes controls the exchange of solutes across their structure. Characterising the interaction of small molecules with biological membranes is critical to understanding of physiological processes, drug action and permeation, and many biotechnological applications. This review provides an overview of how molecular simulations are used to study the interaction of small molecules with biological membranes, with a particular focus on the interactions of water, organic compounds, drugs and short peptides with models of plasma cell membrane and stratum corneum lipid bilayers. This review will not delve on other types of membranes which might have different composition and arrangement, such as thylakoid or mitochondrial membranes. The application of unbiased molecular dynamics simulations and enhanced sampling methods such as umbrella sampling, metadynamics and replica exchange are described using key examples. This review demonstrates how state-of-the-art molecular simulations have been used successfully to describe the mechanism of binding and permeation of small molecules with biological membranes, as well as associated changes to the structure and dynamics of these membranes. The review concludes with an outlook on future directions in this field.

Interplay of hydrophobic and hydrophilic interactions in sequence-dependent cell penetration of spontaneous membrane-translocating peptides revealed by bias-exchange metadynamics simulations

Spontaneous Membrane Translocating Peptides (SMTPs) can translocate silently across the bilayer and, thus, have the best potential to improve the delivery of therapeutic molecules to cells without toxicity. However, how their translocation mechanisms are affected by a specific peptide sequence remains poorly understood. Here, bias-exchange metadynamics simulations were employed to investigate the translocation mechanisms of five SMTPs with the same composition of amino acids (LLRLR, LRLLR, LLLRR, RLLLR, and LRLRL). Simulation results yield sequence-dependent free energy barrier using the FESs along the z-directional distance. An in-depth analysis of sequence-dependent interactions in different regions of the bilayers indicates that the free-energy barrier height of a specific sequence is resulted from the accessibility balance of isolated or clustered hydrophobic residues (L) and hydrophilic residues (R) that leads to different levels of resistance for moving of a peptide into the hydrophobic center of the membrane. At the maximal of the free-energy barrier, all peptides have a conformation parallel to the membrane surface with the barrier height determined by their affinity to the hydrophobic region. The appropriate bilayer perturbation and GDM⁺ pairing are beneficial for peptide translocation. These results provide an improved microscopic understanding of how peptide sequence influences the translocation efficiency and mechanism.

Modelling lipid systems in fluid with Lattice Boltzmann Molecular Dynamics simulations and hydrodynamics

In this work we present the coupling between Dry Martini, an efficient implicit solvent coarse-grained model for lipids, and the Lattice Boltzmann Molecular Dynamics (LBMD) simulation technique in order to include naturally hydrodynamic interactions in implicit solvent simulations of lipid systems. After validating the implementation of the model, we explored several systems where the action of a perturbing fluid plays an important role. Namely, we investigated the role of an external shear flow on the dynamics of a vesicle, the dynamics of substrate release under shear, and inquired the dynamics of proteins and substrates confined inside the core of a vesicle. Our methodology enables future exploration of a large variety of biological entities and processes involving lipid systems at the mesoscopic scale where hydrodynamics plays an essential role, e.g. by modulating the migration of proteins in the proximity of membranes, the dynamics of vesicle-based drug delivery systems, or, more generally, the behaviour of proteins in cellular compartments.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Different effects of cholesterol on membrane permeation of arginine and tryptophan revealed by bias-exchange metadynamics simulations

Experiments have shown that cholesterol influences the membrane permeability of small molecules, amino acids, and cell-penetrating peptides. However, their exact translocation mechanisms under the influence of cholesterol remain poorly understood. Given the practical importance of cell-penetrating peptides and the existence of varied cholesterol contents in different cell types, it is necessary to examine the permeation of amino acids in cholesterol-containing membranes at atomic level of details. Here, bias-exchange metadynamics simulations were employed to investigate the molecular mechanism of the membrane permeation of two amino acids Arg and Trp important for cell-penetrating peptides in the presence of different concentrations of cholesterol. We found that the free energy barrier of Arg+ (the protonated form) permeation increased linearly as the cholesterol concentration increased, whereas the barrier of Trp permeation had a rapid increase from 0 mol. % to 20 mol. % cholesterol-containing membranes and nearly unchanged from 20 mol. % to 40 mol. % cholesterol-containing membranes. Arg0 becomes slightly more stable than Arg+ at the center of the dipalmitoylphosphatidylcholine (DPPC) membrane with 40 mol. % cholesterol concentrations. As a result, Arg+ has a similar permeability as Trp at 0 mol. % and 20 mol. % cholesterol, but a significantly lower permeability than Trp at 40 mol. % cholesterol. This difference is caused by the gradual reduction of water defects for Arg+ as the cholesterol concentration increases but lack of water defects for Trp in cholesterol-containing membranes. Strong but different orientation dependence between Arg+ and Trp permeations is observed. These results provide an improved microscopic understanding of amino-acid permeation through cholesterol-containing DPPC membrane systems.

Characterizing the Molecular Mechanisms for Flipping Charged Peptide Flanking Loops across a Lipid Bilayer

The cell membrane largely prevents the passive diffusion of charged molecules due to the large free energy barrier associated with translocating charged groups across the hydrophobic lipid bilayer core. Despite this barrier, some peptides can interconvert between transmembrane and surface-adsorbed states by "flipping" charged flanking loops across the bilayer on a surprisingly rapid second-minute time scale. The transmembrane helices of some multispanning membrane proteins undergo similar reorientation processes, suggesting that loop-flipping may be a mechanism for regulating membrane protein topology; however, the molecular mechanisms underlying this behavior remain unknown. In this work, we study the loop-flipping behavior exhibited by a peptide with a hydrophobic transmembrane helix, charged flanking loops, and a central, membrane-exposed aspartate residue of varying protonation state. We utilize all-atom temperature accelerated molecular dynamics simulations to predict the likelihood of loop-flipping without predefining specific loop-flipping pathways. We demonstrate that this approach can identify multiple possible flipping pathways, with the prevalence of each pathway depending on the protonation state of the central residue. In particular, we find that a charged central residue facilitates loop-flipping by stabilizing membrane water defects, enabling the "self-catalysis" of charge translocation. These findings provide detailed molecular-level insights into charged loop-flipping pathways that may generalize to other charge translocation processes, such as lipid flip-flop or the large-scale conformational rearrangements of multispanning membrane proteins.

Vitamin E Has Reduced Affinity for a Polyunsaturated Phospholipid: An Umbrella Sampling Molecular Dynamics Simulations Study

Vitamin E is an essential micronutrient. The primary function of this lipid-soluble antioxidant is to protect membrane phospholipids from oxidation. Whether vitamin E preferentially interacts with polyunsaturated phospholipids to optimize protection of the lipid species most vulnerable to oxidative attack has been an unanswered question for a long time. In this work, we compared the binding of α-tocopherol (αtoc), the form of vitamin E retained by the human body, in bilayers composed of polyunsaturated 1-stearoyl-2-docosahexaenoylphosphatidylcholine (SDPC, 18:0-22:6PC) and, as a control, monounsaturated 1-stearoyl-2-oleoylphosphatidylcholine (SOPC, 18:0-18:1PC) by umbrella sampling molecular dynamics simulations. From the potential of mean force as a function depth within the bilayer, we find that the binding energy of αtoc is less in SDPC (Δ G_bind = 16.7 ± 0.3 kcal/mol) than that in SOPC (Δ G_bind = 18.3 ± 0.4 kcal/mol). The lower value in SDPC is ascribed to the high disorder of polyunsaturated fatty acids that produces a less tightly packed arrangement. Deformation of the bilayer is observed during desorption, indicating that phosphatidylcholine (PC)-PC and αtoc-PC interactions contribute to the binding energy. Our results do not support the proposal that vitamin E interacts more favorably with polyunsaturated phospholipids.

Perturbations of Native Membrane Protein Structure in Alkyl Phosphocholine Detergents: A Critical Assessment of NMR and Biophysical Studies

Membrane proteins perform a host of vital cellular functions. Deciphering the molecular mechanisms whereby they fulfill these functions requires detailed biophysical and structural investigations. Detergents have proven pivotal to extract the protein from its native surroundings. Yet, they provide a milieu that departs significantly from that of the biological membrane, to the extent that the structure, the dynamics, and the interactions of membrane proteins in detergents may considerably vary, as compared to the native environment. Understanding the impact of detergents on membrane proteins is, therefore, crucial to assess the biological relevance of results obtained in detergents. Here, we review the strengths and weaknesses of alkyl phosphocholines (or foscholines), the most widely used detergent in solution-NMR studies of membrane proteins. While this class of detergents is often successful for membrane protein solubilization, a growing list of examples points to destabilizing and denaturing properties, in particular for α-helical membrane proteins. Our comprehensive analysis stresses the importance of stringent controls when working with this class of detergents and when analyzing the structure and dynamics of membrane proteins in alkyl phosphocholine detergents.

Dimer Interface of the Human Serotonin Transporter and Effect of the Membrane Composition

The oligomeric state of membrane proteins has recently emerged in many cases as having an effect on their function. However, the intrinsic dynamics of their spatial organization in cells and model systems makes it challenging to characterize. Here we use molecular dynamics (MD) simulations at multiple resolutions to determine the dimer conformation of the human serotonin transporter (hSERT). From self-assembly simulations we predict dimer candidates and subsequently quantify their relative strength. We use umbrella sampling (US) replica exchange MD simulations for which we present extensive analysis of their efficiency and improved sampling compared to regular US MD simulations. The data shows that the most stable hSERT dimer interface is symmetrical and involves transmembrane helix 12 (TM12), similar to the crystal structure of the bacterial homologue LeuT, but with a slightly different orientation. We also describe the supramolecular organization of hSERT from a 250 μs self-assembly simulation. Finally, the effects of the presence of phosphatidylinositol bisphosphate or cholesterol in the membrane model has been quantified for the TM12-TM12 predicted interface. Collectively, the presented data bring new insight to the area of protein and lipid interplay in biological membranes.

Composition Dependence of Water Permeation Across Multicomponent Gel-Phase Bilayers

The permeability of multicomponent phospholipid bilayers in the gel phase is investigated via molecular dynamics simulation. The physical role of the different molecules is probed by comparing multiple mixed-component bilayers containing distearylphosphatidylcholine (DSPC) with varying amounts of either the emollient isostearyl isostearate or long-chain alcohol (dodecanol, octadecanol, or tetracosanol) molecules. Permeability is found to depend on both the tail packing density and hydrogen bonding between lipid headgroups and water. Whereas the addition of emollient or alcohol molecules to a gel-phase DSPC bilayer can increase the tail packing density, it also disturbed the hydrogen-bonding network, which in turn can increase interfacial water dynamics. These phenomena have opposing effects on bilayer permeability, which is found to depend on the balance between enhanced tail packing and decreased hydrogen bonding.

Free Energy Calculations of Membrane Permeation: Challenges Due to Strong Headgroup-Solute Interactions

Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solute's permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased molecular dynamics computer simulations to calculate and compare the free energy profiles of translocation of several small molecules across 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step toward determining the most efficient method for free energy calculations. We study the translocation of arginine, a sodium ion, alanine, and a single water molecule using the metadynamics, umbrella sampling, and replica exchange umbrella sampling techniques. Within the fixed lengths of our simulations, we find that all methods produce similar results for charge-neutral permeants, but not for polar or positively charged molecules. We identify the long relaxation time scale of electrostatic interactions between lipid headgroups and the solute to be the principal cause of this difference and show that this slow process can lead to an erroneous dependence of computed free energy profiles on the initial system configuration. We demonstrate the use of committor analysis to validate the proper sampling of the presumed transition state, which in our simulations is achieved only in replica exchange calculations. On the basis of these results we provide some useful guidance to perform and evaluate free energy calculations of membrane permeation.

Molecular recognition and packing frustration in a helical protein

Biomolecular recognition entails attractive forces for the functional native states and discrimination against potential nonnative interactions that favor alternate stable configurations. The challenge posed by the competition of nonnative stabilization against native-centric forces is conceptualized as frustration. Experiment indicates that frustration is often minimal in evolved biological systems although nonnative possibilities are intuitively abundant. Much of the physical basis of minimal frustration in protein folding thus remains to be elucidated. Here we make progress by studying the colicin immunity protein Im9. To assess the energetic favorability of nonnative versus native interactions, we compute free energies of association of various combinations of the four helices in Im9 (referred to as H1, H2, H3, and H4) by extensive explicit-water molecular dynamics simulations (total simulated time > 300 μs), focusing primarily on the pairs with the largest native contact surfaces, H1-H2 and H1-H4. Frustration is detected in H1-H2 packing in that a nonnative packing orientation is significantly stabilized relative to native, whereas such a prominent nonnative effect is not observed for H1-H4 packing. However, in contrast to the favored nonnative H1-H2 packing in isolation, the native H1-H2 packing orientation is stabilized by H3 and loop residues surrounding H4. Taken together, these results showcase the contextual nature of molecular recognition, and suggest further that nonnative effects in H1-H2 packing may be largely avoided by the experimentally inferred Im9 folding transition state with native packing most developed at the H1-H4 rather than the H1-H2 interface.

Biomolecules need to recognize one another with high specificity: promoting “native” functional intermolecular binding events while avoiding detrimental “nonnative” bound configurations; i.e., “frustration”—the tendency for nonnative interactions—has to be minimized. Folding of globular proteins entails a similar discrimination. To gain physical insight, we computed the binding affinities of helical structures of the protein Im9 in various native or nonnative configurations by atomic simulations, discovering that partial packing of the Im9 core is frustrated. This frustration is overcome when the entire core of the protein is assembled, consistent with experiment indicating no significant kinetic trapping in Im9 folding. Our systematic analysis thus reveals a subtle, contextual aspect of biomolecular recognition and provides a general approach to characterize folding frustration.

Efficient potential of mean force calculation from multiscale simulations: Solute insertion in a lipid membrane

The determination of potentials of mean force for solute insertion in a lipid membrane by means of all-atom molecular dynamics simulations is often hampered by sampling issues. Recently, a multiscale method has been proposed to leverage the conformational ensemble of a lower-resolution model as starting point for higher resolution simulations. In this work, we analyze the efficiency of this method by comparing its predictions for propanol insertion into a lipid membrane against conventional atomistic umbrella sampling simulation results. The multiscale approach is confirmed to provide accurate results with a gain of one order of magnitude in computational time. We then investigate the role of the coarse-grained representation. We find that the accuracy of the results is tightly connected to the presence of a good configurational overlap between the coarse-grained and atomistic models-a general requirement when developing multiscale simulation methods.

Probing a Continuous Polar Defect: A Reaction Coordinate for Pore Formation in Lipid Membranes

Various biophysical processes involve the formation of aqueous pores over lipid membranes, including processes of membrane fusion, antimicrobial peptide activity, lipid flip-flop, and membrane permeation. Reliable and efficient free-energy calculations of pore formation using molecular dynamics simulations remained challenging due to the lack of good reaction coordinates (RCs) for pore formation. We present a new RC for pore formation that probes the formation and rupture of a continuous polar defect over the membrane. Potential of mean force (PMF) calculations along the new RC rapidly converge and exhibit no hysteresis between pore-opening and pore-closing pathways, in contrast to calculations based on previous RCs. We show that restraints along the new RC may restrain the system tightly to the transition state of pore formation, rationalizing the absence of hysteresis. We observe that the PMF of pore formation in a tension-free membrane of dimyristoylphosphatidylcholine (DMPC) reveals a free-energy barrier for pore nucleation, confirming a long-hypothesized metastable prepore state. We test the influence of the lipid force field, the cutoff distance used for Lennard-Jones interactions, and the lateral membrane size on the free energies of pore formation. In contrast to PMF calculations based on previous RCs, we find that such parameters have a relatively small influence on the free energies of pore nucleation. However, the metastability of the open pore in DMPC may depend on such parameters. The RC has been implemented into an extension of the GROMACS simulation software. The new RC allows for reliable and computationally efficient free-energy calculations of pore formation in lipid membranes.

Thermodynamics of Protein Folding Studied by Umbrella Sampling along a Reaction Coordinate of Native Contacts

Spontaneous transitions between the native and non-native protein conformations are normally rare events that hardly take place in typical unbiased molecular dynamics simulations. It was recently demonstrated that such transitions can be well described by a reaction coordinate, Q, that represents the collective fraction of the native contacts between the protein atoms. Here we attempt to use this reaction coordinate to enhance the conformational sampling. We perform umbrella sampling simulations with biasing potentials on Q for two model proteins, Trp-Cage and BBA, using the CHARMM force field. Hamiltonian replica exchange is implemented in these simulations to further facilitate the sampling. The simulations appear to have reached satisfactory convergence, resulting in unbiased free energies as a function of Q. In addition to the native structure, multiple folded conformations are identified in the reconstructed equilibrium ensemble. Some conformations without any native contacts nonetheless have rather compact geometries and are stabilized by hydrogen bonds not present in the native structure. Whereas the enhanced sampling along Q reasonably reproduces the equilibrium conformational space, we also find that the folding of an α-helix in Trp-Cage is a slow degree of freedom orthogonal to Q and therefore cannot be accelerated by biasing the reaction coordinate. Overall, we conclude that whereas Q is an excellent parameter to analyze the simulations, it is not necessarily a perfect reaction coordinate for enhanced sampling, and better incorporation of other slow degrees of freedom may further improve this reaction coordinate.

Grafting Charged Species to Membrane-Embedded Scaffolds Dramatically Increases the Rate of Bilayer Flipping

The cell membrane is a barrier to the passive diffusion of charged molecules due to the chemical properties of the lipid bilayer. Surprisingly, recent experiments have identified processes in which synthetic and biological charged species directly transfer across lipid bilayers on biologically relevant time scales. In particular, amphiphilic nanoparticles have been shown to insert into lipid bilayers, requiring the transport of charged species across the bilayer. The molecular factors facilitating this rapid insertion process remain unknown. In this work, we use atomistic molecular dynamics simulations to calculate the free energy barrier associated with "flipping" charged species across a lipid bilayer for species that are grafted to a membrane-embedded scaffold, such as a membrane-embedded nanoparticle. We find that the free energy barrier for flipping a grafted ligand can be over 7 kcal/mol lower than the barrier for translocating an isolated, equivalent ion, yielding a 5 order of magnitude decrease in the corresponding flipping time scale. Similar results are found for flipping charged species grafted to either nanoparticle or protein scaffolds. These results reveal new mechanistic insight into the flipping of charged macromolecular components that might play an important, yet overlooked, role in signaling and charge transport in biological settings. Furthermore, our results suggest guidelines for the design of synthetic materials capable of rapidly flipping charged moieties across the cell membrane.

Finite Temperature String Method with Umbrella Sampling: Application on a Side Chain Flipping in Mhp1 Transporter

Protein conformational change is of central importance in molecular biology. Here we demonstrate a computational approach to characterize the transition between two metastable conformations in all-atom simulations. Our approach is based on the finite temperature string method, and the implementation is essentially a generalization of umbrella sampling simulations with Hamiltonian replica exchange. We represent the transition pathway by a curve in the conformational space, with the curve parameter taken as the reaction coordinate. Our approach can efficiently refine a transition pathway and compute a one-dimensional free energy as a function of the reaction coordinate. A diffusion model can then be used to calculate the forward and backward transition rates, the major kinetic quantities for the transition. We applied the approach on a local transition in the ligand-free Mhp1 transporter, between its outward-facing conformation and an intermediate conformation with the side chain of Phe305 flipped to the outside of the protein. Our simulations predict that the flipped-out position of this side chain has a free energy 6.5 kcal/mol higher than the original position in the crystal structure, and that the forward and backward transition rates are in the millisecond and submicrosecond time scales, respectively.

Generalized Langevin Methods for Calculating Transmembrane Diffusivity

The membrane permeability coefficient of a solute can be estimated using the solubility-diffusion model. This model requires the diffusivity profile (D(z)) of the solute as it moves along the transmembrane axis, z. The generalized Langevin equation provides one strategy for calculating position-dependent diffusivity from straightforward molecular dynamics simulations where the solute is restrained to a series of positions on the z-coordinate by a harmonic potential. The diffusivity of the solute is calculated from its correlation functions, which are related to the friction experienced by the solute. Roux and Hummer have derived expressions for the diffusion coefficient from the velocity autocorrelation function (VACF) and position autocorrelation function (PACF), respectively. In this work, these methods are validated by calculating the diffusivity of H₂O and O₂ in homogeneous liquids. These methods are then used to calculate transmembrane diffusivity profiles. The VACF method is less sensitive to thermostat forces and has incrementally lower errors but is more sensitive to the spring constant of the harmonic restraint. For the permeation of a solute through a lipid bilayer, the diffusion coefficients calculated using these methods provided significantly different results. Long-lived correlations of the restrained solute due to inhomogeneities in the bilayer can result in spuriously low diffusivity when using the PACF method. The method based on the VACF does not have this issue and predicts higher rates of diffusion inside the bilayer.

Estimation of Liposome Penetration Barriers of Drug Molecules with All-Atom and Coarse-Grained Models

Liposomes are common carriers of drug molecules, providing enhanced delivery and accumulation of hydrophilic agents or larger biomolecules. Molecular simulations can be used to estimate key features of the drug molecules upon interaction with the liposomes, such as penetration barriers and localization. Herein, we investigate several aspects of the computational estimation of penetration barriers, viz. the potential of mean force (PMFs) along a vector spanning the membrane. First, we provide an evaluation of the all-atom (AA) and coarse-grained (CG) parametrization of 5-aminolevulinic acid (5-ALA) and two of its alkyl esters by computing n-octanol/water partition coefficients. We find that the CG parametrization of the esters performs significantly better than the CG model of 5-ALA, highlighting the difficulty to coarse-grain small, polar molecules. However, the expected trend in partition coefficients is reproduced also with the CG models. Second, we compare PMFs in a small membrane slab described with either the AA or CG models. Here, we are able to reproduce the all-atom PMF of 5-ALA with CG. However, for the alkyl esters it is unfortunately not possible to correctly reproduce both the depth and the penetration barrier of the PMF seen in the AA simulations with any of the tested CG models. We argue that it is more important to choose a CG parametrization that reproduces the depth of the PMF. Third, we compare, using the CG model, PMFs in the membrane slab with PMFs in a large, realistic liposome. We find similar depths but slightly different penetration barriers most likely due to differences in the lipid density along the membrane axis. Finally, we compute PMFs in liposomes with three different lipid compositions. Unfortunately, differences in the PMFs could not be quantified, and it remains to be investigated to what extent liposome simulations can fully reproduce experimental findings.

Can Specific Protein-Lipid Interactions Stabilize an Active State of the Beta 2 Adrenergic Receptor?

G-protein-coupled receptors are eukaryotic membrane proteins with broad biological and pharmacological relevance. Like all membrane-embedded proteins, their location and orientation are influenced by lipids, which can also impact protein function via specific interactions. Extensive simulations totaling 0.25 ms reveal a process in which phospholipids from the membrane's cytosolic leaflet enter the empty G-protein binding site of an activated β2 adrenergic receptor and form salt-bridge interactions that inhibit ionic lock formation and prolong active-state residency. Simulations of the receptor embedded in an anionic membrane show increased lipid binding, providing a molecular mechanism for the experimental observation that anionic lipids can enhance receptor activity. Conservation of the arginine component of the ionic lock among Rhodopsin-like G-protein-coupled receptors suggests that intracellular lipid ingression between receptor helices H6 and H7 may be a general mechanism for active-state stabilization.

Simulation-Based Approaches for Determining Membrane Permeability of Small Compounds

Predicting the rate of nonfacilitated permeation of solutes across lipid bilayers is important to drug design, toxicology, and signaling. These rates can be estimated using molecular dynamics simulations combined with the inhomogeneous solubility-diffusion model, which requires calculation of the potential of mean force and position-dependent diffusivity of the solute along the transmembrane axis. In this paper, we assess the efficiency and accuracy of several methods for the calculation of the permeability of a model DMPC bilayer to urea, benzoic acid, and codeine. We compare umbrella sampling, replica exchange umbrella sampling, adaptive biasing force, and multiple-walker adaptive biasing force for the calculation of the transmembrane PMF. No definitive advantage for any of these methods in their ability to predict the membrane permeability coefficient Pm was found, provided that a sufficiently long equilibration is performed. For diffusivities, a Bayesian inference method was compared to a generalized Langevin method, both being sensitive to chosen parameters and the slow relaxation of membrane defects. Agreement within 1.5 log units of the computed Pm with experiment is found for all permeants and methods. Remaining discrepancies can likely be attributed to limitations of the force field as well as slowly relaxing collective movements within the lipid environment. Numerical calculations based on model profiles show that Pm can be reliably estimated from only a few data points, leading to recommendations for calculating Pm from simulations.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Sampling errors in free energy simulations of small molecules in lipid bilayers

Free energy simulations are a powerful tool for evaluating the interactions of molecular solutes with lipid bilayers as mimetics of cellular membranes. However, these simulations are frequently hindered by systematic sampling errors. This review highlights recent progress in computing free energy profiles for inserting molecular solutes into lipid bilayers. Particular emphasis is placed on a systematic analysis of the free energy profiles, identifying the sources of sampling errors that reduce computational efficiency, and highlighting methodological advances that may alleviate sampling deficiencies. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.