Exploring the Free Energy Landscape of Solutes Embedded in Lipid Bilayers

Computational Methods for Modeling Lipid-Mediated Active Pharmaceutical Ingredient Delivery

Lipid-mediated delivery of active pharmaceutical ingredients (API) opened new possibilities in advanced therapies. By encapsulating an API into a lipid nanocarrier (LNC), one can safely deliver APIs not soluble in water, those with otherwise strong adverse effects, or very fragile ones such as nucleic acids. However, for the rational design of LNCs, a detailed understanding of the composition-structure-function relationships is missing. This review presents currently available computational methods for LNC investigation, screening, and design. The state-of-the-art physics-based approaches are described, with the focus on molecular dynamics simulations in all-atom and coarse-grained resolution. Their strengths and weaknesses are discussed, highlighting the aspects necessary for obtaining reliable results in the simulations. Furthermore, a machine learning, i.e., data-based learning, approach to the design of lipid-mediated API delivery is introduced. The data produced by the experimental and theoretical approaches provide valuable insights. Processing these data can help optimize the design of LNCs for better performance. In the final section of this Review, state-of-the-art of computer simulations of LNCs are reviewed, specifically addressing the compatibility of experimental and computational insights.

Split Membrane: A New Model to Accelerate All-Atom MD Simulation of Phospholipid Bilayers

All-atom molecular dynamics simulations are powerful tools for studying cell membranes and their interactions with proteins and other molecules. However, these processes occur on time scales determined by the diffusion rate of phospholipids, which are challenging to achieve in all-atom models. Here, we present a new all-atom model that accelerates lipid diffusion by splitting phospholipid molecules into head and tail groups. The bilayer structure is maintained by using external lateral potentials, which compensate for the lipid split. This split model enhances lateral lipid diffusion more than ten times, allowing faster and cheaper equilibration of large systems with different phospholipid types. The current model has been tested on membranes containing PSM, POPC, POPS, POPE, POPA, and cholesterol. We have also evaluated the interaction of the split model membranes with the Disheveled DEP domain and amphiphilic helix motif of the transcriptional repressor Opi1 as representative of peripheral proteins as well as the dimeric fragment of the epidermal growth factor receptor transmembrane domain and the Human A2A Adenosine of G protein-coupled receptors as representative of transmembrane proteins. The split model can predict the interaction sites of proteins and their preferred phospholipid type. Thus, the model could be used to identify lipid binding sites and equilibrate large membranes at an affordable computational cost.

Fatty Alcohol Membrane Model for Quantifying and Predicting Amphiphilicity

Amphiphilicity is an important property for drug development and self-assembly. This paper introduces a general approach based on a simple fatty alcohol (dodecanol) membrane model that can be used to quantify the amphiphilicity of small molecules that are in good agreement with experimental surface tension data. By applying the model to a systematic series of compounds, it was possible to elucidate the effect of different motifs on amphiphilicity. The results further indicate that amphiphilicity correlates strongly with water-octanol partition coefficients (logP) for the 29 organic molecules examined in the 0 < logP < 4 range. Importantly, the simulation of the model membrane is an order of magnitude faster than a phospholipid membrane (e.g., 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) simulation and offers a simple atomistic approach for quantifying and predicting amphiphilicity of small drug-like molecules that could be used in quantitative structure-activity relationship studies.

Atomic-level mechanisms of abnormal activation in NRAS oncogenes from two-dimensional free energy landscapes

The NRAS-mutant subset of melanoma is one of the most aggressive and lethal types associated with poor overall survival. Unfortunately, a low understanding of the NRAS-mutant dynamic behavior has led to the lack of clinically approved therapeutic agents able to directly target NRAS oncogenes. In this work, accurate local structures of NRAS and its mutants have been fully explored through the corresponding free energy surfaces obtained by microsecond scale well-tempered metadynamics simulations. Free energy calculations are crucial to reveal the precise mechanisms of Q61 mutations at the atomic level. Considering specific atom-atom distances d and angles ϕ as appropriate reaction coordinates we have obtained free energy surfaces revealing local and global minima together with their main transition states, unveiling the mechanisms of abnormal NRAS activation from the atomic-level and quantitatively analyzing the corresponding stable states. This will help in advancing our understanding of the basic mechanisms of NRAS mutations, offering new opportunities for the design of potential inhibitors.

Employing Metadynamics to Predict the Membrane Partitioning of Carboxy-2H-Azirine Natural Products

Natural products containing the carboxy-2H-azirine moiety are an exciting target for investigation due to their broad-spectrum antimicrobial activity and new chemical space they afford for novel therapeutic development. The carboxy-2H-azirine moiety, including those appended to well-characterized chemical scaffolds, is understudied, which creates a challenge for understanding potential modes of inhibition. In particular, some known natural product carboxy-2H-azirines have long hydrophobic tails, which could implicate them in membrane-associated processes. In this study, we examined a small set of carboxy-2H-azirine natural products with varied structural features that could alter membrane partitioning. We compared the predicted membrane partitioning and alignment of these compounds to those of established membrane embedders with similar chemical scaffolds. To accomplish this, we developed parameters within the framework of the CHARMM36 force field for the 2H-azirine functional group and performed metadynamics simulations of the partitioning into a model bacterial membrane from aqueous solution. We determined that the carboxy-2H-azirine functional group is strongly hydrophilic, imbuing the long-chain natural products with amphipathicity similar to the known membrane-embedding molecules to which they were compared. For the long-chain analogs, the carboxy-2H-azirine head group stays within 1 nm of the phosphate layer, while the hydrophobic tail sits within the membrane. The carboxy-2H-azirine lacking the long alkyl chain instead partitions completely into aqueous solution.

Permeability of TB drugs through the mycolic acid monolayer: a tale of two force fields

Tuberculosis (TB) treatment becomes challenging due to the unique cell wall structure of Mycobacterium tuberculosis (M. tb). Among various components of the M.tb cell wall, mycolic acid (MA) is of particular interest because it is speculated to exhibit extremely low permeability for most of the drug molecules, thus helping M.tb to survive against medical treatment. However, no quantitative assessment of the thermodynamic barrier encountered by various well-known TB drugs in the mycolic acid monolayer has been performed so far using computational tools. On this premise, our present work aims to probe the permeability of some first and second line TB drugs, namely ethambutol, ethionamide, and isoniazid, through the modelled mycolic acid monolayer, using molecular dynamics (MD) simulation with two sets of force field (FF) parameters, namely GROMOS 54A7-ATB (GROMOS) and CHARMM36 (CHARMM) FFs. Our findings indicate that both FFs provide consistent results in terms of the mode of drug-monolayer interactions but significantly differ in the drug permeability through the monolayer. The mycolic acid monolayer generally exhibited a higher free energy barrier of crossing with CHARMM FF, while with GROMOS FF, better stability of drug molecules on the monolayer surface was observed, which can be attributed to the greater electrostatic potential at the monolayer-water interface, found for the later. Although both the FF parameters predicted the highest resistance against ethambutol (permeability values of 8.40 × 10-34 cm s-1 and 9.61 × 10-31 cm s-1 for the CHARMM FF and the GROMOS FF, respectively), results obtained using GROMOS were found to be consistent with the water solubility of drugs, suggesting it to be a slightly better FF for modelling drug-mycolic acid interactions. Therefore, this study enhances our understanding of TB drug permeability and highlights the potential of the GROMOS FF in simulating drug-mycolic acid interactions.

Collective Variable-Based Enhanced Sampling: From Human Learning to Machine Learning

Enhanced-sampling algorithms relying on collective variables (CVs) are extensively employed to study complex (bio)chemical processes that are not amenable to brute-force molecular simulations. The selection of appropriate CVs characterizing the slow movement modes is of paramount importance for reliable and efficient enhanced-sampling simulations. In this Perspective, we first review the application and limitations of CVs obtained from chemical and geometrical intuition. We also introduce path-sampling algorithms, which can identify path-like CVs in a high-dimensional free-energy space. Machine-learning algorithms offer a viable approach to finding suitable CVs by analyzing trajectories from preliminary simulations. We discuss both the performance of machine-learning-derived CVs in enhanced-sampling simulations of experimental models and the challenges involved in applying these CVs to realistic, complex molecular assemblies. Moreover, we provide a prospective view of the potential advancements of machine-learning algorithms for the development of CVs in the field of enhanced-sampling simulations.

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.

Computational Insights into the Adsorption of Ligands on Gold Nanosurfaces

We study the adsorption process of model peptides, nucleobases, and selected standard ligands on gold through the development of a computational protocol based on fully atomistic classical molecular dynamics (MD) simulations combined with umbrella sampling techniques. The specific features of the interface components, namely, the molecule, the metallic substrate, and the solvent, are taken into account through different combinations of force fields (FFs), which are found to strongly affect the results, especially changing absolute and relative adsorption free energies and trends. Overall, noncovalent interactions drive the process along the adsorption pathways. Our findings also show that a suitable choice of the FF combinations can shed light on the affinity, position, orientation, and dynamic fluctuations of the target molecule with respect to the surface. The proposed protocol may help the understanding of the adsorption process at the microscopic level and may drive the in-silico design of biosensors for detection purposes.

Localization of the ibuprofen molecule in model lipid membranes revealed by spin-label-enhanced NMR relaxation

Non-steroidal anti-inflammatory drugs (NSAIDs) have antipyretic, anti-inflammatory and analgesic effects, and can be used in the treatment of various diseases. These drugs have also a number of side effects, which may be related to their interaction with lipid membranes. In this study, we use the spin-labeled NSAID ibuprofen (ibuprofen-SL) as a relaxation enhancer to study its interaction with model lipid membranes employing liquid-state 1H NMR at 500 MHz. The high magnetic moment of unpaired electron in the spin label made it possible to reduce the concentration of the studied drug in the membrane to tenths of a mole percent. As model membranes, unilamellar POPC liposomes and bicelles consisting of a 2:1 mixture of DHPC:DMPC or DHPC:POPC lipids were used. An increase in the rate of proton spin-lattice relaxation, T1-1, selectively detected for protons at different positions in the lipid molecule, showed that ibuprofen-SL is localized in the hydrophobic part of the lipid bilayer. As the concentration of ibuprofen-SL increases to 0.5 mol%, the distribution of positions of ibuprofen-SL across the bilayer becomes wider. In the presence of 20 mol% of cholesterol, ibuprofen-SL is displaced from the core of the membrane to a region closer to the head group of the bilayer. This displacement was also confirmed by the NMR NOESY experiment conducted with unlabeled ibuprofen. For bilayers containing unsaturated POPC lipids, the distribution of ibuprofen positions across the bilayer becomes narrower compared to the presence of saturated DMPC lipids.

Path sampling with memory reduction and replica exchange to reach long permeation timescales

Assessing kinetics in biological processes with molecular dynamics simulations remains a computational and conceptual challenge, given the large time and length scales involved. For kinetic transport of biochemical compounds or drug molecules, the permeability through the phospholipid membranes is a key kinetic property, but long timescales are hindering the accurate computation. Technological advances in high-performance computing therefore need to be accompanied by theoretical and methodological developments. In this contribution, the replica exchange transition interface sampling (RETIS) methodology is shown to give perspective toward observing longer permeation pathways. It is first reviewed how RETIS, a path-sampling methodology that gives in principle exact kinetics, can be used to compute membrane permeability. Next, recent and current developments in three RETIS aspects are discussed: several new Monte Carlo moves in the path-sampling algorithm, memory reduction by reducing pathlengths, and exploitation of parallel computing with CPU-imbalanced replicas. Finally, the memory reduction presenting a new replica exchange implementation, coined REPPTIS, is showcased with a permeant needing to pass a membrane with two permeation channels, either representing an entropic or energetic barrier. The REPPTIS results showed clearly that inclusion of some memory and enhancing ergodic sampling via replica exchange moves are both necessary to obtain correct permeability estimates. In an additional example, ibuprofen permeation through a dipalmitoylphosphatidylcholine membrane was modeled. REPPTIS succeeded in estimating the permeability of this amphiphilic drug molecule with metastable states along the permeation pathway. In conclusion, the presented methodological advances allow for deeper insight into membrane biophysics even if the pathways are slow, as RETIS and REPPTIS push the permeability calculations to longer timescales.

Ionizable lipids penetrate phospholipid bilayers with high phase transition temperatures: perspectives from free energy calculations

The efficacies of modern gene-therapies strongly depend on their contents. At the same time the most potent formulations might not contain the best compounds. In this work we investigated the effect of phospholipids and their saturation on the binding ability of (6Z,9Z,28Z,31Z)-heptatriacont-6,9,28,31-tetraene-19-yl 4-(dimethylamino) butanoate (DLin-MC3-DMA) to model membranes at the neutral pH. We discovered that DLin-MC3-DMA has affinity to the most saturated monocomponent lipid bilayer 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and an aversion to the unsaturated one 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC). The preference to a certain membrane was also well-correlated to the phase transition temperatures of phospholipid bilayers, and to their structural and dynamical properties. Additionally, in the case of the presence of DLin-MC3-DMA in the membrane with DOPC the ionizable lipid penetrated it, which indicates possible synergistic effects. Comparisons with other ionizable lipids were performed using a model lipid bilayer of 1-palmitoyl-2-oleoyl-glycero-3-phosphocholine (POPC). Particularly, the lipids heptadecan-9-yl 8-[2-hydroxyethyl-(6-oxo-6-undecoxyhexyl)amino]octanoate (SM-102) and [(4-Hydroxybutyl) azanediyl] di(hexane-6,1-diyl) bis(2-hexyldecanoate) (ALC-0315) from modern mRNA-vaccines against COVID-19 were investigated and force fields parameters were derived for those new lipids. It was discovered that ALC-0315 binds strongest to the membrane, while DLin-MC3-DMA is not able to reside in the bilayer center. The ability to penetrate the membrane POPC by SM-102 and ALC-0315 can be related to their saturation, comparing to DLin-MC3-DMA.

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.

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.

Ibuprofen in a Lipid Bilayer: Nanoscale Spatial Arrangement

Ibuprofen is a non-steroidal anti-inflammatory drug (NSAID) with analgesic and antipyretic effects. Understanding the molecular mechanisms of drug interaction with cell membranes is important to improving drug delivery, uptake by cells, possible side effects, etc. Double electron-electron resonance spectroscopy (DEER, also known as PELDOR) provides information on the nanoscale spatial arrangement of spin-labeled molecules. Here, DEER was applied to study (mono-)spin-labeled ibuprofen (ibuprofen-SL) in a bilayer of palmitoyl-oleoyl-sn-glycerophosphocholine (POPC). The results obtained show that the ibuprofen-SL molecules are located within a plane in each bilayer leaflet. At their low molar concentration in the bilayer χ, the found surface concentration of ibuprofen-SL is two times higher than χ, which can be explained by alternative assembling in the two leaflets of the bilayer. When χ > 2 mol%, these assemblies merge. The findings shed new light on the nanoscale spatial arrangement of ibuprofen in biological membranes.

Modeling the Effect of Hydrophobicity on the Passive Permeation of Solutes across a Bacterial Model Membrane

Passive diffusion across biomembranes is an important mechanism of permeation for multiple drugs, including antibiotics. However, this process is frequently neglected while studying drug uptake and, in our view, warrants further investigation. Here, we apply molecular dynamics simulations to investigate the impact of changes in molecular hydrophobicity on the permeability of a series of inhibitors of the quorum sensing of Pseudomonas aeruginosa, previously discovered by us, across a membrane model. Overall, we show that permeation across this membrane model does not correlate with the molecule's hydrophobicity. We demonstrate that using a simple model for permeation, based on the difference between the maximum and minimum of the free energy profile, outperforms the inhomogeneous solubility-diffusion model, yielding a permeability ranking that better agrees with the experimental results, especially for hydrophobic permeants. The calculated differences in permeability could not explain differences in in bacterio activity. Nevertheless, substantial differences in molecular orientation along the permeation pathway correlate with the in bacterio activity, emphasizing the importance of analyzing, at an atomistic level, the permeation pathway of these solutes.

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.

Synthesis of Spin-Labeled Ibuprofen and Its Interaction with Lipid Membranes

Ibuprofen is a non-steroidal anti-inflammatory drug possessing analgesic and antipyretic activity. Electron paramagnetic resonance (EPR) spectroscopy could be applied to study its interaction with biological membranes and proteins if its spin-labeled analogs were synthesized. Here, a simple sequence of ibuprofen transformations—nitration, esterification, reduction, Sandmeyer reaction, Sonogashira cross-coupling, oxidation and saponification—was developed to attain this goal. The synthesis resulted in spin-labeled ibuprofen (ibuprofen-SL) in which the spin label TEMPOL is attached to the benzene ring. EPR spectra confirmed interaction of ibuprofen-SL with 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. Using ²H electron spin echo envelope modulation (ESEEM) spectroscopy, ibuprofen-SL was found to be embedded into the hydrophobic bilayer interior.

Predicting the conformational variability of oncogenic GTP-bound G12D mutated KRas-4B proteins at zwitterionic model cell membranes

KRas proteins are the largest family of mutated Ras isoforms, participating in a wide variety of cancers. Due to their importance, large effort is being carried out on drug development by small-molecule inhibitors. However, understanding protein conformational variability remains a challenge in drug discovery. In the case of the Ras family, their multiple conformational states can affect the binding of potential drug inhibitors. To overcome this challenge, we propose a computational framework based on combined all-atom Molecular Dynamics and Metadynamics simulations in order to accurately access conformational variants of the target protein. We tested the methodology using a G12D mutated GTP bound oncogenic KRas-4B protein located at the interface of a DOPC/DOPS/cholesterol model anionic cell membrane. Two main orientations of KRas-4B at the anionic membrane have been determined. The corresponding torsional angles are taken as reliable reaction coordinates so that free-energy landscapes are obtained by well-tempered metadynamics simulations, revealing local and global minima of the free-energy hypersurface and unveiling reactive paths of the system between the two preferential orientations. We have observed that GTP-binding to KRas-4B has huge influence on the stabilisation of the protein and it can potentially help to open Switch I/II druggable pockets, lowering energy barriers between stable states and resulting in cumulative conformers of KRas-4B. This may highlight new opportunities for targeting the unique meta-stable states through the design of new efficient drugs.

Polarization Switching Method for Effective Free Energy Calculation of Membrane Translocation on the Nano-scale

Free-energy calculations are crucial for investigating biomolecular interactions on the Nano-scale level. However, in theoretical studies, the neglect of electronic polarization can jeopardize their accuracy and correct predictive capabilities, specifically...

Mechanistic Understanding from Molecular Dynamics in Pharmaceutical Research 2: Lipid Membrane in Drug Design

We review the use of molecular dynamics (MD) simulation as a drug design tool in the context of the role that the lipid membrane can play in drug action, i.e., the interaction between candidate drug molecules and lipid membranes. In the standard "lock and key" paradigm, only the interaction between the drug and a specific active site of a specific protein is considered; the environment in which the drug acts is, from a biophysical perspective, far more complex than this. The possible mechanisms though which a drug can be designed to tinker with physiological processes are significantly broader than merely fitting to a single active site of a single protein. In this paper, we focus on the role of the lipid membrane, arguably the most important element outside the proteins themselves, as a case study. We discuss work that has been carried out, using MD simulation, concerning the transfection of drugs through membranes that act as biological barriers in the path of the drugs, the behavior of drug molecules within membranes, how their collective behavior can affect the structure and properties of the membrane and, finally, the role lipid membranes, to which the vast majority of drug target proteins are associated, can play in mediating the interaction between drug and target protein. This review paper is the second in a two-part series covering MD simulation as a tool in pharmaceutical research; both are designed as pedagogical review papers aimed at both pharmaceutical scientists interested in exploring how the tool of MD simulation can be applied to their research and computational scientists interested in exploring the possibility of a pharmaceutical context for their research.

Large-Scale Membrane Permeability Prediction of Cyclic Peptides Crossing a Lipid Bilayer Based on Enhanced Sampling Molecular Dynamics Simulations

Membrane permeability is a significant obstacle facing the development of cyclic peptide drugs. However, membrane permeation mechanisms are poorly understood. To investigate common features of permeable (and nonpermeable) designs, it is necessary to reproduce the membrane permeation process of cyclic peptides through the lipid bilayer. We simulated the membrane permeation process of 100 six-residue cyclic peptides across the lipid bilayer based on steered molecular dynamics (MD) and replica-exchange umbrella sampling simulations and predicted membrane permeability using the inhomogeneous solubility-diffusion model and a modified version of it. Furthermore, we confirmed the effectiveness of this protocol by predicting the membrane permeability of 56 eight-residue cyclic peptides with diverse chemical structures, including some confidential designs from a pharmaceutical company. As a result, a reasonable correlation between experimentally assessed and calculated membrane permeability of cyclic peptides was observed for the peptide libraries, except for strongly hydrophobic peptides. Our analysis of the MD trajectory demonstrated that most peptides were stabilized in the boundary region between bulk water and membrane and that for most peptides, the process of crossing the center of the membrane is the main obstacle to membrane permeation. The height of this barrier is well correlated with the electrostatic interaction between the peptide and the surrounding media. The structural and energetic features of the representative peptide at each vertical position within the membrane were also analyzed, revealing that peptides permeate the membrane by changing their orientation and conformation according to the surrounding environment.

Combining Well-Tempered Metadynamics Simulation and SPR Assays to Characterize the Binding Mechanism of the Universal T-Lymphocyte Tetanus Toxin Epitope TT830-843

Peptide TT830-843 from the tetanus toxin is a universal T-cell epitope. It helps in vaccination and induces T-cell activation. However, the fine molecular interaction between this antigen and the major histocompatibility complex (MHC) remains unknown. Molecular analysis of its interaction with murine MHC (H-2) was proposed to explore its immune response efficiency. Molecular dynamics simulations are important mechanisms for understanding the basis of protein-ligand interactions, and metadynamics is a useful technique for enhancing sampling in molecular dynamics. SPR (surface plasmon resonance) assays were used to validate whether the metadynamics results are in accordance with the experimental results. The peptide TT830-843 unbinding process was simulated, and the free energy surface reconstruction revealed a detailed conformational landscape. The simulation described the exiting path as a stepwise mechanism between progressive detachment states. We pointed out how the terminus regions act as anchors for binding and how the detachment mechanism includes the opening of α-helices to permit the peptide's central region dissociation. The results indicated the peptide/H-2 receptor encounter occurs within a distance lesser than 27.5 Å, and the encounter can evolve to form a stable complex. SPR assays confirmed the complex peptide/H-2 as a thermodynamically stable system, exhibiting enough free energy to interact with TCR on the antigen-presenting cell surface. Therefore, combining in silico and in vitro assays provided significant evidence to support the peptide/H-2 complex formation.

Microscopic Interactions of Melatonin, Serotonin and Tryptophan with Zwitterionic Phospholipid Membranes

The interactions at the atomic level between small molecules and the main components of cellular plasma membranes are crucial for elucidating the mechanisms allowing for the entrance of such small species inside the cell. We have performed molecular dynamics and metadynamics simulations of tryptophan, serotonin, and melatonin at the interface of zwitterionic phospholipid bilayers. In this work, we will review recent computer simulation developments and report microscopic properties, such as the area per lipid and thickness of the membranes, atomic radial distribution functions, angular orientations, and free energy landscapes of small molecule binding to the membrane. Cholesterol affects the behaviour of the small molecules, which are mainly buried in the interfacial regions. We have observed a competition between the binding of small molecules to phospholipids and cholesterol through lipidic hydrogen-bonds. Free energy barriers that are associated to translational and orientational changes of melatonin have been found to be between 10-20 kJ/mol for distances of 1 nm between melatonin and the center of the membrane. Corresponding barriers for tryptophan and serotonin that are obtained from reversible work methods are of the order of 10 kJ/mol and reveal strong hydrogen bonding between such species and specific phospholipid sites. The diffusion of tryptophan and melatonin is of the order of 10-7 cm2/s for the cholesterol-free and cholesterol-rich setups.

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.

Long-lasting Salt Bridges Provide the Anchoring Mechanism of Oncogenic Kirsten Rat Sarcoma Proteins at Cell Membranes

RAS proteins work as GDP-GTP binary switches and regulate cytoplasmic signaling networks that are able to control several cellular processes, playing an essential role in signal transduction pathways involved in cell growth, differentiation, and survival, so that overacting RAS signaling can lead to cancer. One of the hardest challenges to face is the design of mutation-selective therapeutic strategies. In this work, a G12D-mutated farnesylated GTP-bound Kirsten RAt sarcoma (KRAS) protein has been simulated at the interface of a DOPC/DOPS/cholesterol model anionic cell membrane. A specific long-lasting salt bridge connection between farnesyl and the hypervariable region of the protein has been identified as the main mechanism responsible for the binding of oncogenic farnesylated KRAS-4B to the cell membrane. Free-energy landscapes allowed us to characterize local and global minima of KRAS-4B binding to the cell membrane, revealing the main pathways between anchored and released states.

Unassisted N-acetyl-phenylalanine-amide transport across membrane with varying lipid size and composition: kinetic measurements and atomistic molecular dynamics simulation

Biological membranes are essential to preserve structural integrity and regulate functional properties through the permeability of nutrients, pharmaceutical drugs, and neurotransmitters of a living cell. The movement of acetylated and amidated phenylalanine (NAFA) across 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) membrane bilayers is investigated to probe physical transport. The rate of transport is measured experimentally applying parallel artificial membrane permeation assay (PAMPA). At the physiological temperature, 310 K, the measured time constants in the neutral pH were ∼6 h in DOPC and ∼3 h in POPC, while in a more acidic condition, at a pH 4.8, the time constants were ∼8 h in both lipids. Computationally, we have expanded our transport study of three aromatic dipeptides across a bilayer composed of DOPC¹⁸. In this study, we have examined the effects of lipid composition and bilayer size on the passive transport of NAFA by simulating the dipeptide in three different bilayers, with 50 DOPC lipids, 50 POPC lipids, and 40 POPC molecules. Specifically, atomistic molecular dynamics simulations with umbrella sampling were used to calculate the potential of mean force for the passive permeation of NAFA across the bilayers. Diffusion constants were then calculated by numerically solving the Smoluchowski equation. Permeability coefficients and mean first passage times were then calculated. Structural properties - Ramachandran plots, sidechain torsions, peptide insertion angles, radial distribution functions, and proximal peptide water molecules - were also examined to determine the effect of system size and lipid type. In terms of systems size, we observed a small decrease in the highest barrier of the potential of mean force and fewer sampled sidechain dihedral angle conformations with 40 versus 50 POPC lipids due to weaker membrane deformations within a smaller lipid bilayer. In terms of lipid type, DOPC contains two monounsaturated acyl chains compared to only one such acyl chain in POPC; therefore, DOPC bilayers are less ordered and more easily deformed, as seen by a much broader potential of mean force profile. The NAFA in DOPC lipid also transitioned to an internally hydrogen-bonded backbone conformation at lower membrane depths than in POPC. Similarly, as for other aromatic dipeptides, NAFA tends to insert into the membrane sidechain-first, remains mostly desolvated in the membrane center, and exhibits slow reorientations within the bilayer in both DOPC and POPC. With a joint experimental and computational study we have gained a new insight into the rate of transport and the underlying microscopic mechanism in different lipid bilayer conditions of the simplest hydrophobic aromatic dipeptide.Communicated by Ramaswamy H. Sarma.

Permeation of Biopolymers Across the Cell Membrane: A Computational Comparative Study on Polylactic Acid and Polyhydroxyalkanoate

Polymeric nanoparticles, which by virtue of their size (1-1000 nm) are able to penetrate even into cells, are attracting increasing interest in the emerging field of nanomedicine, as devices for, e.g., drugs or vaccines delivery. Because of the involved dimensional scale in the nanoparticle/cell membrane interactions, modeling approaches at molecular level are the natural choice in order to understand the impact of nanoparticle formulation on cellular uptake mechanisms. In this work, the passive permeation across cell membrane of oligomers made of two employed polymers in the biomedical field [poly-D,L-lactic acid (PDLA) and poly(3-hydroxydecanoate) (P3HD)] is investigated at fundamental atomic scale through molecular dynamics simulations. The free energy profile related to membrane crossing is computed adopting umbrella sampling. Passive permeation is also investigated using a coarse-grained model with MARTINI force field, adopting well-tempered metadynamics. Simulation results showed that P3HD permeation is favored with respect to PDLA by virtue of its higher hydrophobicity. The free energy profiles obtained at full atomistic and coarse-grained scale are in good agreement each for P3HD, while only a qualitative agreement was obtained for PDLA. Results suggest that a reparameterization of non-bonded interactions of the adopted MARTINI beads for the oligomer is needed in order to obtain a better agreement with more accurate simulations at atomic scale.

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.

Cellular absorption of small molecules: free energy landscapes of melatonin binding at phospholipid membranes

Free energy calculations are essential to unveil mechanisms at the atomic scale such as binding of small solutes and their translocation across cell membranes, eventually producing cellular absorption. Melatonin regulates biological rhythms and is directly related to carcinogenesis and neurodegenerative disorders. Free energy landscapes obtained from well-tempered metadynamics simulations precisely describe the characteristics of melatonin binding to specific sites in the membrane and reveal the role of cholesterol in free energy barrier crossing. A specific molecular torsional angle and the distance between melatonin and the center of the membrane along the normal to the membrane Z-axis have been considered as suitable reaction coordinates. Free energy barriers between two particular orientations of the molecular structure (folded and extended) have been found to be of about 18 kJ/mol for z-distances of about 1–2 nm. The ability of cholesterol to expel melatonin out of the internal regions of the membrane towards the interface and the external solvent is explained from a free energy perspective. The calculations reported here offer detailed free energy landscapes of melatonin embedded in model cell membranes and reveal microscopic information on its transition between free energy minima, including the location of relevant transition states, and provide clues on the role of cholesterol in the cellular absorption of small molecules.

Interaction of Camptothecin with Model Cellular Membranes

Accurate and efficient prediction of drug partitioning in model membranes is of significant interest to the pharmaceutical industry. Herein, we utilize advanced sampling methods, specifically, the adaptive biasing force methodology to calculate the potential of mean force for a model hydrophobic anticancer drug, camptothecin (CPT), across three model interfaces. We consider an octanol bilayer, a thick octanol/water interface, and a model 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/water interface. We characterize the enthalpic and entropic contributions of the drug to the potential of mean force. We show that the rotational entropy of the drug is inversely related to the probability of hydrogen bond formation of the drug with the POPC membrane. In addition, in long-time microsecond simulations of a high concentration of CPT above the POPC membrane, we show that strong drug-drug aromatic interactions shift the spatial orientation of the drug with the membrane. Stacks of hydrophobic drugs form, allowing penetration of the drug just under the POPC head groups. These results imply that inhomogeneous membrane models need to take into account the effect of drug aggregation on the membrane environment.

Computer simulations of protein-membrane systems

The interactions between proteins and membranes play critical roles in signal transduction, cell motility, and transport, and they are involved in many types of diseases. Molecular dynamics (MD) simulations have greatly contributed to our understanding of protein-membrane interactions, promoted by a dramatic development of MD-related software, increasingly accurate force fields, and available computer power. In this chapter, we present available methods for studying protein-membrane systems with MD simulations, including an overview about the various all-atom and coarse-grained force fields for lipids, and useful software for membrane simulation setup and analysis. A large set of case studies is discussed.

Improved Sampling in Ab Initio Free Energy Calculations of Biomolecules at Solid–Liquid Interfaces: Tight-Binding Assessment of Charged Amino Acids on TiO2 Anatase (101)

Atomistic simulations can complement the scarce experimental data on free energies of molecules at bio-inorganic interfaces. In molecular simulations, adsorption free energy landscapes are efficiently explored with advanced sampling methods, but classical dynamics is unable to capture charge transfer and polarization at the solid–liquid interface. Ab initio simulations do not suffer from this flaw, but only at the expense of an overwhelming computational cost. Here, we introduce a protocol for adsorption free energy calculations that improves sampling on the timescales relevant to ab initio simulations. As a case study, we calculate adsorption free energies of the charged amino acids Lysine and Aspartate on the fully hydrated anatase (101) TiO2 surface using tight-binding forces. We find that the first-principle description of the system significantly contributes to the adsorption free energies, which is overlooked by calculations with previous methods.

Modelling of interactions between Aβ(25-35) peptide and phospholipid bilayers: effects of cholesterol and lipid saturation

Aggregation of amyloid beta (Aβ) peptides in neuronal membranes is a known promoter of Alzheimer’s disease. To gain insight into the molecular details of Aβ peptide aggregation and its effect on model neuronal membranes, we carried out molecular dynamics simulations of the Aβ(25–35) fragment of the amyloid precursor protein in phospholipid bilayers composed of either fully saturated or highly unsaturated lipids, in the presence or absence of cholesterol. It was found that the peptide does not penetrate through any of the considered membranes, but can reside in the headgroup region and upper part of the lipid tails showing a clear preference to a polyunsaturated cholesterol-free membrane. Due to the ordering and condensing effect upon addition of cholesterol, membranes become more rigid facilitating peptide aggregation on the surface. Except for the case of the cholesterol-free saturated lipid bilayer, the peptides have a small effect on the membrane structure and ordering. It was also found that the most “active” amino-acid for peptide–lipid and peptide–cholesterol interaction is methionine-35, followed by asparagine-27 and serine-26, which form hydrogen bonds between peptides and polar atoms of lipid headgroups. These amino acids are also primarily responsible for peptide aggregation. This work will be relevant for designing strategies to develop drugs to combat Alzheimer’s disease.

Molecular dynamics simulations of Aβ(25–35) peptides in phospholipid bilayers are carried out to investigate the effect of polyunsaturated lipids and cholesterol on aggregation of the peptides.

Does the Lipid Bilayer Orchestrate Access and Binding of Ligands to Transmembrane Orthosteric/Allosteric Sites of G Protein-Coupled Receptors?

The ligand-binding sites of many G protein-coupled receptors (GPCRs) are situated around and deeply embedded within the central pocket formed by their seven transmembrane-spanning α-helical domains. Generally, these binding sites are assumed accessible to endogenous ligands from the aqueous phase. Recent advances in the structural biology of GPCRs, along with biophysical and computational studies, suggest that amphiphilic and lipophilic molecules may gain access to these receptors by first partitioning into the membrane and then reaching the binding site via lateral diffusion through the lipid bilayer. In addition, several crystal structures of class A and class B GPCRs bound to their ligands offer unprecedented details on the existence of lipid-facing allosteric binding sites outside the transmembrane helices that can only be reached via lipid pathways. The highly organized structure of the lipid bilayer may direct lipophilic or amphiphilic drugs to a specific depth within the bilayer, changing local concentration of the drug near the binding site and affecting its binding kinetics. Additionally, the constraints of the lipid bilayer, including its composition and biophysical properties, may play a critical role in "pre-organizing" ligand molecules in an optimal orientation and conformation to facilitate receptor binding. Despite its clear involvement in molecular recognition processes, the critical role of the membrane in binding ligands to lipid-exposed transmembrane binding sites remains poorly understood and warrants comprehensive investigation. Understanding the mechanistic basis of the structure-membrane interaction relationship of drugs will not only provide useful insights about receptor binding kinetics but will also enhance our ability to take advantage of the apparent membrane contributions when designing drugs that target transmembrane proteins with improved efficacy and safety. In this minireview, we summarize recent structural and computational studies on membrane contributions to binding processes, elucidating both lipid pathways of ligand access and binding mechanisms for several orthosteric and allosteric ligands of class A and class B GPCRs.

Reactive Oxygen and Nitrogen Species at Phospholipid Bilayers: Peroxynitrous Acid and Its Homolysis Products

Peroxynitrite is a powerful and long-lived oxidant generated in vivo. Peroxynitrous acid (ONOOH), its protonated form, may penetrate into phospholipid bilayers and undergo homolytic cleavage to nitrogen dioxide (·NO₂) and hydroxyl radicals (·OH), causing severe nitro-oxidative damage. The membrane environment is thought to influence ONOOH reactions, but the mechanisms remain speculative. Most experimental techniques lack the level of resolution required to keep track of the motion of very reactive species and their interactions with the membrane. Here, we performed molecular dynamics simulations of the permeation, interactions, and dynamics of ONOOH and its homolysis products in the phospholipid membrane environment. We started by developing an ONOOH model that successfully accounted for its conformational equilibria and solvation energies. Membrane permeation of ONOOH was accompanied by conformational changes. ONOOH exhibited a strong tendency to bind to and accumulate at the membrane headgroup region. There, ONOOH homolysis led to ·NO₂ radicals, which in turn partitioned to the membrane interior. About one-third of the ·OH radicals readily escaped to the aqueous phase within 1 ns. However, a significant number of ·OH radicals became trapped at the lipid headgroup region for a longer period. The possible implications for membrane-based nitration and oxidation processes were discussed.

Local low dose curcumin treatment improves functional recovery and remyelination in a rat model of sciatic nerve crush through inhibition of oxidative stress

Traumatic injuries to peripheral nerves are frequent, however, specific pharmacological treatments are currently lacking. Curcumin has antioxidant, anti-inflammatory and neuroprotective properties but high oral doses are required for therapeutic use, particularly due to its low bioavailability. The aim of the present study was to investigate the effects of local and continuous treatment using low curcumin doses on functional recovery and nerve regeneration after rat sciatic nerve crush (SNC). Curcumin was administered by osmotic pumps with a catheter delivering the drug at the injury site (0.2 mg/day for 4 weeks). Functionally, early improvements in mechanical sensitivity, finger spacing of the injured paw, skilful walking and grip strength were observed in curcumin-treated animals. The curcumin treatment increased expression of compact myelin proteins (MPZ and PMP22), myelin sheath thickness and, correspondingly, increased motor and sensitive nerve conduction velocity. Microscopic analysis of gastrocnemius muscle indicated a curcumin-induced decrease in neurogenic lesions. Curcumin treatment reduced the production of reactive oxygen species (ROS) (which were notably produced by macrophages), lipid peroxidation and increased expression of transcription factor Nrf2. In silico analyses indicated that curcumin combines all the characteristics required to be an efficient lipid peroxidation inhibitor at the heart of biological membranes, hence protecting their degradation due to ROS. This antioxidant capacity is likely to contribute to the beneficial effects of curcumin after SNC injury. These results demonstrate that, when administrated locally, low doses of curcumin represent a promising therapy for peripheral nerve regeneration.

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.

Bias-Exchange Metadynamics Simulation of Membrane Permeation of 20 Amino Acids

Thermodynamics of the permeation of amino acids from water to lipid bilayers is an important first step for understanding the mechanism of cell-permeating peptides and the thermodynamics of membrane protein structure and stability. In this work, we employed bias-exchange metadynamics simulations to simulate the membrane permeation of all 20 amino acids from water to the center of a dipalmitoylphosphatidylcholine (DPPC) membrane (consists of 256 lipids) by using both directional and torsion angles for conformational sampling. The overall accuracy for the free energy profiles obtained is supported by significant correlation coefficients (correlation coefficient at 0.5-0.6) between our results and previous experimental or computational studies. The free energy profiles indicated that (1) polar amino acids have larger free energy barriers than nonpolar amino acids; (2) negatively charged amino acids are the most difficult to enter into the membrane; and (3) conformational transitions for many amino acids during membrane crossing is the key for reduced free energy barriers. These results represent the first set of simulated free energy profiles of membrane crossing for all 20 amino acids.