A novel approach to the investigation of passive molecular permeation through lipid bilayers from atomistic simulations

Application of Generative Artificial Intelligence in Predicting Membrane Partitioning of Drugs: Combining Denoising Diffusion Probabilistic Models and MD Simulations Reduces the Computational Cost to One-Third

The optimal interaction of drugs with plasma membranes and membranes of subcellular organelles is a prerequisite for desirable pharmacology. Importantly, for drugs targeting the transmembrane lipid-facing sites of integral membrane proteins, the relative affinity of a drug to the bilayer lipids compared to the surrounding aqueous phase affects the partitioning, access, and binding of the drug to the target site. Molecular dynamics (MD) simulations, including enhanced sampling techniques such as steered MD, umbrella sampling (US), and metadynamics, offer valuable insights into the interactions of drugs with the membrane lipids and water in atomistic detail. However, these methods are computationally prohibitive for the high-throughput screening of drug candidates. This study shows that applying denoising diffusion probabilistic models (DDPMs), a generative AI method, to US simulation data reduces the computational cost significantly. Specifically, the models used only partial (one-third) data from the US simulations and reproduced the complete potential of mean force (PMF) profiles for three FDA-approved drugs (β2-adrenergic agonists) and ∼20 biologically relevant chemicals with known experimentally characterized bilayer locations. Intriguingly, the model can predict the solvation-free energies for partitioning and crossing the bilayer, preferred bilayer locations (low-energy well), and orientations of the ligands with high accuracy. The results indicate that DDPMs can be used to characterize the complete membrane partitioning profile of drug molecules using fewer umbrella sampling simulations at select positions along the bilayer normal (z-axis), irrespective of their amphiphilic-lipophilic-cephalophilic characteristics.

A methodology of quantifying membrane permeability based on returning probability theory and molecular dynamics simulation

We propose a theoretical approach to estimate the permeability coefficients of substrates (permeants) for crossing membranes from donor (D) phase to acceptor (A) phase by means of molecular dynamics (MD) simulation. A fundamental aspect of our approach involves reformulating the returning probability (RP) theory, a rigorous bimolecular reaction theory, to describe permeation phenomena. This reformulation relies on the parallelism between permeation and bimolecular reaction processes. In the present method, the permeability coefficient is represented in terms of the thermodynamic and kinetic quantities for the reactive (R) phase that exists within the inner region of a membrane. One can evaluate these quantities using multiple MD trajectories starting from phase R. We apply the RP theory to the permeation of ethanol and methylamine at different concentrations (infinitely dilute and 1 mol % conditions of permeants). Under the 1 mol% condition, the present method yields a larger permeability coefficient for ethanol (0.12 ± 0.01 cm s-1) than for methylamine (0.069 ± 0.006 cm s-1), while the values of the permeability coefficient are satisfactorily close to those obtained from the brute-force MD simulations (0.18 ± 0.03 and 0.052 ± 0.005 cm s-1 for ethanol and methylamine, respectively). Moreover, upon analyzing the thermodynamic and kinetic contributions to the permeability, we clarify that a higher concentration dependency of permeability for ethanol, as compared to methylamine, arises from the sensitive nature of ethanol's free-energy barrier within the inner region of the membrane against ethanol concentration.

tICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation

Molecular simulations are commonly used to understand the mechanism of membrane permeation of small molecules, particularly for biomedical and pharmaceutical applications. However, despite significant advances in computing power and algorithms, calculating an accurate permeation free energy profile remains elusive for many drug molecules because it can require identifying the rate-limiting degrees of freedom (i.e., appropriate reaction coordinates). To resolve this issue, researchers have developed machine learning approaches to identify slow system dynamics. In this work, we apply time-lagged independent component analysis (tICA), an unsupervised dimensionality reduction algorithm, to molecular dynamics simulations with well-tempered metadynamics to find the slowest collective degrees of freedom of the permeation process of trimethoprim through a multicomponent membrane. We show that tICA-metadynamics yields translational and orientational collective variables (CVs) that increase convergence efficiency ∼1.5 times. However, crossing the periodic boundary is shown to introduce artifacts in the translational CV that can be corrected by taking absolute values of molecular features. Additionally, we find that the convergence of the tICA CVs is reached with approximately five membrane crossings and that data reweighting is required to avoid deviations in the translational CV.

A least-squares-fitting procedure for an efficient preclinical ranking of passive transport across the blood-brain barrier endothelium

The treatment of various disorders of the central nervous system (CNS) is often impeded by the limited brain exposure of drugs, which is regulated by the human blood-brain barrier (BBB). The screening of lead compounds for CNS penetration is challenging due to the biochemical complexity of the BBB, while experimental determination of permeability is not feasible for all types of compounds. Here we present a novel method for rapid preclinical screening of libraries of compounds by utilizing advancements in computing hardware, with its foundation in transition-based counting of the flux. This method has been experimentally validated for in vitro permeabilities and provides atomic-level insights into transport mechanisms. Our approach only requires a single high-temperature simulation to rank a compound relative to a library, with a typical simulation time converging within 24 to 72 h. The method offers unbiased thermodynamic and kinetic information to interpret the passive transport of small-molecule drugs across the BBB.

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.

tICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation

Molecular simulations are commonly used to understand the mechanism of membrane permeation of small molecules, particularly for biomedical and pharmaceutical applications. However, despite significant advances in computing power and algorithms, calculating an accurate permeation free energy profile remains elusive for many drug molecules because it can require identifying the rate-limiting degrees of freedom (i.e., appropriate reaction coordinates). To resolve this issue, researchers have developed machine learning approaches to identify slow system dynamics. In this work, we apply time-lagged independent component analysis (tICA), an unsupervised dimensionality reduction algorithm, to molecular dynamics simulations with well-tempered metadynamics to find the slowest collective degrees of freedom of the permeation process of trimethoprim through a multicomponent membrane. We show that tICA-metadynamics yields translational and orientational collective variables (CVs) that increase convergence efficiency ∼1.5 times. However, crossing the periodic boundary is shown to introduce artefacts in the translational CV that can be corrected by taking absolute values of molecular features. Additionally, we find that the convergence of the tICA CVs is reached with approximately five membrane crossings, and that data reweighting is required to avoid deviations in the translational CV.

Predictions from First-Principles of Membrane Permeability to Small Molecules: How Useful Are They in Practice?

Predicting from first-principles the rate of passive permeation of small molecules across the biological membrane represents a promising strategy for screening lead compounds upstream in the drug-discovery and development pipeline. One popular avenue for the estimation of permeation rates rests on computer simulations in conjunction with the inhomogeneous solubility-diffusion model, which requires the determination of the free-energy change and position-dependent diffusivity of the substrate along the translocation pathway through the lipid bilayer. In this Perspective, we will clarify the physical meaning of the membrane permeability inferred from such computer simulations, and how theoretical predictions actually relate to what is commonly measured experimentally. We will also examine why these calculations remain both technically challenging and overly computationally expensive, which has hitherto precluded their routine use in nonacademic settings. We finally synopsize possible research directions to meet these challenges, increase the predictive power of physics-based rates of passive permeation, and, by ricochet, improve their practical usefulness.

MemCross: Accelerated Weight Histogram method to assess membrane permeability

Passive permeation events across biological membranes are determining steps in the pharmacokinetics of xenobiotics. To reach an accurate and rapid prediction of membrane permeation coefficients of drugs is a complex challenge, which can efficiently support drug discovery. Such predictions are indeed highly valuable as they may guide the selection of potential leads with optimum bioavailabilities prior to synthesis. Theoretical models exist to predict these coefficients. Many of them are based on molecular dynamics (MD) simulations, which allow calculation of permeation coefficients through the evaluation of both the potential of mean force (PMF) and the diffusivity profiles. However, these simulations still require intensive computational efforts, and novel methodologies should be developed and benchmarked. Free energy perturbation (FEP) method was recently shown to estimate PMF with a significantly reduced computational cost compared to the adaptive biasing force method. This benchmarking was achieved with small molecules, namely short-chain alcohols. Here, we show that to estimate the PMF of bulkier, drug-like xenobiotics, conformational sampling is a critical issue. To reach a sufficient sampling with FEP calculations requires a relatively long time-scale, which can lower the benefits related to the computational gain. In the present work, the Accelerated Weight Histogram (AWH) method was employed for the first time in all-atom membrane models. The AWH-based protocol, named MemCross, appears affordable to estimate PMF profiles of a series of drug-like xenobiotics, compared to other enhanced sampling methods. The continuous exploration of the crossing pathway by MemCross also allows modeling subdiffusion by computing fractional diffusivity profiles. The method is also versatile as its input parameters are largely insensitive to the molecule properties. It also ensures a detailed description of the molecule orientations along the permeation pathway, picturing all intermolecular interactions at an atomic resolution. Here, MemCross was applied on a series of 12 xenobiotics, including four weak acids, and a coherent structure-activity relationship was established.

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.

Atomistic Model of Solute Transport across the Blood-Brain Barrier

The blood-brain barrier remains a major roadblock to the delivery of drugs to the brain. While in vitro and in vivo measurements of permeability are widely used to predict brain penetration, very little is known about the mechanisms of passive transport. Detailed insight into interactions between solutes and cell membranes could provide new insight into drug design and screening. Here, we perform unbiased atomistic MD simulations to visualize translocation of a library of 24 solutes across a lipid bilayer representative of brain microvascular endothelial cells. A temperature bias is used to achieve steady state of all solutes, including those with low permeability. Based on free-energy surface profiles, we show that the solutes can be classified into three groups that describe distinct mechanisms of transport across the bilayer. Simulations down to 310 K for solutes with fast permeability were used to justify the extrapolation of values at 310 K from higher temperatures. Comparison of permeabilities at 310 K to experimental values obtained from in vitro transwell measurements and in situ brain perfusion revealed that permeabilities obtained from simulations vary from close to the experimental values to more than 3 orders of magnitude faster. The magnitude of the difference was dependent on the group defined by free-energy surface profiles. Overall, these results show that MD simulations can provide new insight into the mechanistic details of brain penetration and provide a new approach for drug discovery.

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.

Molecular dynamics simulations of ethanol permeation through single and double-lipid bilayers

Permeation of small molecules through membranes is a fundamental biological process, and molecular dynamics simulations have proven to be a promising tool for studying the permeability of membranes by providing a precise characterization of the free energy and diffusivity. In this study, permeation of ethanol through three different membranes of 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylserine (POPS), PO-phosphatidylethanolamine (POPE), and PO-phosphatidylcholine (POPC) is studied. Permeabilities are calculated and compared with two different approaches based on Fick's first law and the inhomogeneous solubility-diffusion model. Microsecond simulation of double bilayers of these membranes provided a direct measurement of permeability by a flux-based counting method. These simulations show that a membrane of POPC has the highest permeability, followed by POPE and POPS. Due to the membrane-modulating properties of ethanol, the permeability increases as functions of concentration and saturation of the inner leaflet in a double bilayer setting, as opposed to the customary definition as a proportionality constant. This concentration dependence is confirmed by single bilayer simulations at different ethanol concentrations ranging from 1% to 18%, where permeability estimates are available from transition-based counting and the inhomogeneous solubility-diffusion model. We show that the free energy and diffusion profiles for ethanol lack accuracy at higher permeant concentrations due to non-Markovian kinetics caused by collective behavior. In contrast, the counting method provides unbiased estimates. Finally, the permeabilities obtained from single bilayer simulations are combined to represent natural gradients felt by a cellular membrane, which accurately models the non-equilibrium effects on ethanol permeability from single bilayer simulations in equilibrium.

Recent Experimental Developments in Studying Passive Membrane Transport of Drug Molecules

The ability to measure the passive membrane permeation of drug-like molecules is of fundamental biological and pharmaceutical importance. Of significance, passive diffusion across the cellular membranes plays an effective role in the delivery of many pharmaceutical agents to intracellular targets. Hence, approaches for quantitative measurement of membrane permeability have been the topics of research for decades, resulting in sophisticated biomimetic systems coupled with advanced techniques. In this review, recent developments in experimental approaches along with theoretical models for quantitative and real-time analysis of membrane transport of drug-like molecules through mimetic and living cell membranes are discussed. The focus is on time-resolved fluorescence-based, surface plasmon resonance, and second-harmonic light scattering approaches. The current understanding of how properties of the membrane and permeant affect the permeation process is discussed.

Comparison of Different Chitosan Lipid Nanoparticles for Improved Ophthalmic Tetrandrine Delivery: Formulation, Characterization, Pharmacokinetic and Molecular Dynamics Simulation

In this study, three different chitosan, namely carboxymethyl chitosan (CMC), hydroxypropyl chitosan (HPC) and trimethyl chitosan (TMC) were used as cationic materials to prepare tetrandrine lipid nanoparticles (TET-LNPs) for the treatment of glaucoma. In vitro drug release and pre-corneal retention were used to select the optimal chitosan. In vitro drug release curves of three kinds of LNPs showed a sustained release and TMC-TET-LNPs were the slowest. Moreover, compared with CMC-TET-LNPs and HPC-TET-LNPs, TMC-TET-LNPs had longer corneal retention time. Afterwards, the characteristics of TMC-TET-LNPs were investigated. The ocular irritation study revealed no sign of irritation in rabbit eyes. The pharmacokinetic studies showed that the area under the curve of TMC-TET-LNPs was increased by 2.03 times than TET solution (p < 0.01). Furthermore, the drug biofilm interactions were evaluated by molecular dynamics (MD) simulation. In MD simulation, the strong hydrophobic group of TET interacted with the tail of POPC, making it hard to enter the hydrophobic region of the membrane, thereby restricting TET ocular bioavailability. The experiments and MD simulation indicated that TMC-TET-LNPs had great potential for ocular administration and MD simulation could predict transmembrane transport of drugs.

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.

Trimethyl chitosan nanoparticles for ocular baicalein delivery: Preparation, optimization, in vitro evaluation, in vivo pharmacokinetic study and molecular dynamics simulation

To improve ocular bioavailability of baicalein (BAI), trimethyl chitosan coated lipid nanoparticles of baicalein (TMC-BAI-LNPs) were prepared, optimized and characterized. The properties of TMC-BAI-LNPs such as morphology, particle size, zeta potential and fourier transform infrared spectroscopy were investigated. Additionally, molecular dynamics simulation was applied as a new method to evaluate drug-biological membrane interactions. Transmission electron microscopy showed that the LNPs were approximately spherical in shape with a smooth surface. TMC-BAI-LNPs had a particle size of 162.8 nm, a positive surface charge with a zeta potential of 26.6 mV. The entrapment efficiency and drug loading values of BAI in the formulation were 90.65% and 2.04%, respectively. Moreover, in vitro drug release revealed that TMC-BAI-LNPs had a sustained release effect. In vivo studies indicated TMC-BAI-LNPs had no ocular irritation and the AUC of TMC-BAI-LNPs was 3.17-fold than that of the control (p < 0.01). Molecular dynamics simulation data showed that BAI had a poor membrane permeability, which limited the ocular bioavailability. The results indicated that TMC-BAI-LNPs might open up a new avenue for ocular administration. Furthermore, molecular dynamics simulation could predict permeability of drugs.

How Computational Chemistry and Drug Delivery Techniques Can Support the Development of New Anticancer Drugs

The early and late development of new anticancer drugs, small molecules or peptides can be slowed down by some issues such as poor selectivity for the target or poor ADME properties. Computer-aided drug design (CADD) and target drug delivery (TDD) techniques, although apparently far from each other, are two research fields that can give a significant contribution to overcome these problems. Their combination may provide mechanistic understanding resulting in a synergy that makes possible the rational design of novel anticancer based therapies. Herein, we aim to discuss selected applications, some also from our research experience, in the fields of anticancer small organic drugs and peptides.

Modulation of membrane permeability by carbon dioxide

Promoting drug delivery across the biological membrane is a common strategy to improve bioavailability. Inspired by the observation that carbonated alcoholic beverages can increase the absorption rate of ethanol, we speculate that carbon dioxide (CO₂ ) molecules could also enhance membrane permeability to drugs. In the present work, we have investigated the effect of CO₂ on the permeability of a model membrane formed by 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine lipids to three drug-like molecules, namely, ethanol, 2',3'-dideoxyadenosine, and trimethoprim. The free-energy and fractional-diffusivity profiles underlying membrane translocation were obtained from μs-timescale simulations and combined in the framework of the fractional solubility-diffusion model. We find that addition of CO₂ in the lipid environment results in an increase of the membrane permeability to the three substrates. Further analysis of the permeation events reveals that CO₂ expands and loosens the membrane, which, in turn, facilitates permeation of the drug-like molecules. © 2019 Wiley Periodicals, Inc.

Physics-Based Method for Modeling Passive Membrane Permeability and Translocation Pathways of Bioactive Molecules

Assessment of permeability is a critical step in the drug development process for selection of drug candidates with favorable ADME properties. We have developed a novel physics-based method for fast computational modeling of passive permeation of diverse classes of molecules across lipid membranes. The method is based on heterogeneous solubility-diffusion theory and operates with all-atom 3D structures of solutes and the anisotropic solvent model of the lipid bilayer characterized by transbilayer profiles of dielectric and hydrogen bonding capacity parameters. The optimal translocation pathway of a solute is determined by moving an ensemble of representative conformations of the molecule through the dioleoyl-phosphatidylcholine (DOPC) bilayer and optimizing their rotational orientations in every point of the transmembrane trajectory. The method calculates (1) the membrane-bound state of the solute molecule; (2) free energy profile of the solute along the permeation pathway; and (3) the permeability coefficient obtained by integration over the transbilayer energy profile and assuming a constant size-dependent diffusivity along the membrane normal. The accuracy of the predictions was evaluated against experimental permeability coefficients measured in pure lipid membranes (for 78 compounds, R² was 0.88 and rmse was 1.15 log units), PAMPA-DS (for 280 compounds, R² was 0.75 and rmse was 1.59 log units), BBB (for 182 compounds, R² was 0.69 and rmse was 0.87 log units), and Caco-2/MDCK assays (for 165 compounds, R² was 0.52 and rmse was 0.89 log units).

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.

Effects of lipid composition on membrane permeation

Passive permeation through lipid membranes is an essential process in biology. In vivo membranes typically consist of mixtures of lamellar and nonlamellar lipids. Lamellar lipids are characterized by their tendency to form lamellar sheet-like structures, which are predominant in nature. Nonlamellar lipids, when isolated, instead form more geometrically complex nonlamellar phases. While mixed lamellar/nonlamellar lipid membranes tend to adopt the ubiquitous lamellar bilayer structure, the presence of nonlamellar lipids is known to have profound effects on key membrane properties, such as internal distributions of stress and elastic properties, which in turn may alter related biological processes. This work focuses on one such process, i.e., permeation, by utilising atomistic molecular dynamics simulations in order to obtain transfer free energy profiles, diffusion profiles and permeation coefficients for a series of thirteen small molecules and drugs. Each permeant is tested on two bilayer membranes of different lipid composition, i.e., purely lamellar and mixed lamellar/nonlamellar. Our results indicate that the presence of nonlamellar lipids reduces permeation for smaller molecules (molecular weight < 100) but facilitates it for the largest ones (molecular weight > 100). This work represents an advancement towards the development of more realistic in silico permeability assays, which may have a substantial future impact in the area of rational drug design.

Molecular transport through membranes: Accurate permeability coefficients from multidimensional potentials of mean force and local diffusion constants

Estimating the permeability coefficient of small molecules through lipid bilayer membranes plays an important role in the development of effective drug candidates. In silico simulations can produce acceptable relative permeability coefficients for a series of small molecules; however, the absolute permeability coefficients from simulations are usually off by orders of magnitude. In addition to differences between the lipid bilayers used in vitro and in silico, the poor convergence of permeation free energy profiles and over-simplified diffusion models have contributed to these discrepancies. In this paper, we present a multidimensional inhomogeneous solubility-diffusion model to study the permeability of a small molecule drug (trimethoprim) passing through a POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) lipid bilayer. Our approach improves the permeation model in three ways: First, the free energy profile (potential of mean force, PMF) is two-dimensional in two key coordinates rather than simply one-dimensional along the direction normal to the bilayer. Second, the 2-D PMF calculation has improved convergence due to application of the recently developed transition-tempered metadynamics with randomly initialized replicas, while third, the local diffusivity coefficient was calculated along the direction of the minimum free energy path on the two-dimensional PMF. The permeability is then calculated as a line integral along the minimum free energy path of the PMF. With this approach, we report a considerably more accurate permeability coefficient (only 2-5 times larger than the experimental value). We also compare our approach with the common practice of computing permeability coefficients based only on the translation of the center of mass of the drug molecule. Our paper concludes with a discussion of approaches for minimizing the computational cost for the purpose of more rapidly screening a large number of drug candidate molecules.

Link between Membrane Composition and Permeability to Drugs

Prediction of membrane permeability to small molecules represents an important aspect of drug discovery. First-principles calculations of this quantity require an accurate description of both the thermodynamics and kinetics that underlie translocation of the permeant across the lipid bilayer. In this contribution, the membrane permeability to three drugs, or drug-like molecules, namely, 9-anthroic acid (ANA), 2',3'-dideoxyadenosine (DDA), and hydrocortisone (HYL), are estimated in a pure 1-palmitoyl-2-oleoylphosphatidylcholine (POPC) and in a POPC:cholesterol (2:1) mixture. On the basis of independent 2-5-μs free-energy calculations combined with a time-fractional Smoluchowski determination of the diffusivity, the estimated membrane permeabilities to these chemically diverse permeants fall within an order of magnitude from the experimental values obtained in egg-lecithin bilayers, with the exception of HYL in pure POPC. This exception is particularly interesting because the calculated permeability of the sterol-rich bilayer to HYL, in close agreement with the experimental value, is about 600 times lower than that of the pure POPC bilayer to HYL. In contrast, the permeabilities to ANA and DDA differ by less than a factor of 10 between the pure POPC and POPC:cholesterol bilayers. The unusual behavior of HYL, a large, amphiphilic compound, may be linked with the longer range perturbation of the lipid bilayer it induces, compared to ANA and DDA, suggestive of a possibly different translocation mechanism. We find that the tendency of lower permeabilities of the POPC:cholesterol bilayer relative to those of the pure POPC one is a consequence of increased free-energy barriers. Beyond reporting accurate estimates of the membrane permeability, the present contribution also demonstrates that rigorous free-energy calculations and a fractional-diffusion model are key in revealing the molecular phenomena linking the composition of a membrane to its permeability to drugs.

Cooperative Modes of Action of Antimicrobial Peptides Characterized with Atomistic Simulations: A Study on Cecropin B

Antimicrobial peptides (AMPs) are widely occurring host defense agents of interest as one route for addressing the growing problem of multidrug-resistant pathogens. Understanding the mechanisms behind their antipathogen activity is instrumental in designing new AMPs. Herein, we present an all-atom molecular dynamics and free energy study on cecropin B (CB) and its constituent domains. We find a cooperative mechanism in which CB inserts into an anionic model membrane with its amphipathic N-terminal segment, supported by the hydrophobic C-terminal segment of a second peptide. The two peptides interact via a Glu···Lys salt bridge and together sustain a pore in the membrane. Using a modified membrane composition, we demonstrate that when the lower leaflet is overall neutral, insertion of the cationic segment is retarded and thus this mode of action is membrane specific. The observed mode of action utilizes a flexible hinge, a common structural motif among AMPs, which allows CB to insert into the membrane using either or both termini. Data from both unbiased trajectories and enhanced sampling simulations indicate that a requirement for CB to be an effective AMP is the interaction of its hydrophobic C-terminal segment with the membrane. Simulations of these segments in isolation reveal their aggregation in the membrane and a different mechanism of supporting pore formation. Together, our results show the complex interaction of different structural motifs of AMPs and, in particular, a potential role for electronegative side chains in an overall cationic AMP.

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.

Effects of hydration on the protonation state of a lysine analog crossing a phospholipid bilayer – insights from molecular dynamics and free-energy calculations

Protonation states of amino acids crossing lipid bilayers from multidimensional free energy surfaces.

Permeability of a Fluid Lipid Bilayer to Short-Chain Alcohols from First Principles

Computational prediction of membrane permeability to small molecules requires accurate description of both the thermodynamics and kinetics underlying translocation across the lipid bilayer. In this contribution, well-converged, microsecond-long free-energy calculations are combined with a recently developed subdiffusive kinetics framework to describe the membrane permeation of a homologous series of short-tail alcohols, from methanol to 1-butanol, with unprecedented fidelity to the underlying molecular models. While the free-energy profiles exhibit barriers for passage through the center of the bilayer in all cases, the height of these barriers decreases with the length of the aliphatic chain of the alcohol, in quantitative agreement with experimentally determined differential solvation free energies in water and oil. A unique aspect of the subdiffusive model employed herein, which was developed in a previous article, is the determination of a position-dependent fractional order which quantifies the degree to which the motion of the alcohol deviates from classical diffusion along the thickness of the membrane. In the aqueous medium far from the bilayer, this quantity approaches 1.0, the asymptotic limit for purely classical diffusion, whereas it dips below 0.75 near the center of the membrane irrespective of the permeant. Remarkably, the fractional diffusivity near the center of membrane, where its influence on the permeability is the greatest, is similar among the four permeants despite the large difference in molecular weight and lipophilicity between methanol and 1-butanol. The relative permeabilities, which are estimated from the free-energy and fractional diffusivity profiles, are therefore determined predominantly by differences in the former rather than the latter. The predicted relative permeabilities are highly correlated with existing experimental results, albeit they do not agree quantitatively with them. On the other hand, quite unexpectedly, the reported experimental values for the short-tail alcohols are nearly three orders of magnitude lower than the available experimental measurement for water. Plausible explanations for this apparent disagreement between theory and experiment are considered in detail.

Subdiffusion in Membrane Permeation of Small Molecules

Within the solubility-diffusion model of passive membrane permeation of small molecules, translocation of the permeant across the biological membrane is traditionally assumed to obey the Smoluchowski diffusion equation, which is germane for classical diffusion on an inhomogeneous free-energy and diffusivity landscape. This equation, however, cannot accommodate subdiffusive regimes, which have long been recognized in lipid bilayer dynamics, notably in the lateral diffusion of individual lipids. Through extensive biased and unbiased molecular dynamics simulations, we show that one-dimensional translocation of methanol across a pure lipid membrane remains subdiffusive on timescales approaching typical permeation times. Analysis of permeant motion within the lipid bilayer reveals that, in the absence of a net force, the mean squared displacement depends on time as t0.7, in stark contrast with the conventional model, which assumes a strictly linear dependence. We further show that an alternate model using a fractional-derivative generalization of the Smoluchowski equation provides a rigorous framework for describing the motion of the permeant molecule on the pico- to nanosecond timescale. The observed subdiffusive behavior appears to emerge from a crossover between small-scale rattling of the permeant around its present position in the membrane and larger-scale displacements precipitated by the formation of transient voids.

Transition-Tempered Metadynamics Is a Promising Tool for Studying the Permeation of Drug-like Molecules through Membranes

Metadynamics is an important enhanced sampling technique in molecular dynamics simulation to efficiently explore potential energy surfaces. The recently developed transition-tempered metadynamics (TTMetaD) has been proven to converge asymptotically without sacrificing exploration of the collective variable space in the early stages of simulations, unlike other convergent metadynamics (MetaD) methods. We have applied TTMetaD to study the permeation of drug-like molecules through a lipid bilayer to further investigate the usefulness of this method as applied to problems of relevance to medicinal chemistry. First, ethanol permeation through a lipid bilayer was studied to compare TTMetaD with nontempered metadynamics and well-tempered metadynamics. The bias energies computed from various metadynamics simulations were compared to the potential of mean force calculated from umbrella sampling. Though all of the MetaD simulations agree with one another asymptotically, TTMetaD is able to predict the most accurate and reliable estimate of the potential of mean force for permeation in the early stages of the simulations and is robust to the choice of required additional parameters. We also show that using multiple randomly initialized replicas allows convergence analysis and also provides an efficient means to converge the simulations in shorter wall times and, more unexpectedly, in shorter CPU times; splitting the CPU time between multiple replicas appears to lead to less overall error. After validating the method, we studied the permeation of a more complicated drug-like molecule, trimethoprim. Three sets of TTMetaD simulations with different choices of collective variables were carried out, and all converged within feasible simulation time. The minimum free energy paths showed that TTMetaD was able to predict almost identical permeation mechanisms in each case despite significantly different definitions of collective variables.

In silico pharmacology: Drug membrane partitioning and crossing

Over the past decade, molecular dynamics (MD) simulations have become particularly powerful to rationalize drug insertion and partitioning in lipid bilayers. MD simulations efficiently support experimental evidences, with a comprehensive understanding of molecular interactions driving insertion and crossing. Prediction of drug partitioning is discussed with respect to drug families (anesthetics; β-blockers; non-steroidal anti-inflammatory drugs; antioxidants; antiviral drugs; antimicrobial peptides). To accurately evaluate passive permeation coefficients turned out to be a complex theoretical challenge; however the recent methodological developments based on biased MD simulations are particularly promising. Particular attention is paid to membrane composition (e.g., presence of cholesterol), which influences drug partitioning and permeation. Recent studies concerning in silico models of membrane proteins involved in drug transport (influx and efflux) are also reported here. These studies have allowed gaining insight in drug efflux by, e.g., ABC transporters at an atomic resolution, explicitly accounting for the mandatory forces induced by the surrounded lipid bilayer. Large-scale conformational changes were thoroughly analyzed.

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.

Calculation of Lipid-Bilayer Permeabilities Using an Average Force

Calculations of lipid bilayer permeabilities from first principles, using molecular simulations, would be valuable to rapidly assess the bioavailability of drug candidates, as well as to decipher, at the atomic level, the mechanisms that underlie the translocation of permeants. The most common theoretical approach, the solubility-diffusion model, requires determination of the free energy and the diffusivity as functions of the position of the permeant. Quantitative predictions of permeability have, however, been stymied by acute difficulties in calculating the diffusivity, inadequate sampling, and, most insidiously, systematic biases due to imperfections in the force field, simulation parameters, and the inherent limitations of the diffusive model. In the present work, we combine importance-sampling simulations employing an adaptive biasing force with a Bayesian-inference algorithm to determine the free energy and diffusivity with noteworthy precision and spatial resolution. In multimicrosecond simulations, we probe the sensitivity of the permeability estimates to different aspects of the methodology, including the truncation of short-range interactions, the thermostat, the force-field parameters of the permeant, the time scale over which the diffusivity is estimated, and the size of the simulated system. The force-field parameters and time scale dependence of the diffusivities impose the greatest uncertainties on the permeability estimates. Our simulations highlight the importance of membrane distortion due to the presence of the permeant, which may be partially suppressed if the bilayer patch is not large enough. We suggest that improvements to force fields and more robust kinetic models may be needed to reduce systematic errors below a factor of two.

Diffusive Models of Membrane Permeation with Explicit Orientational Freedom

Accurate calculation of permeabilities from first-principles has been a long-standing challenge for computer simulations, notably in the context of drug discovery, as a route to predict the propensity of small, organic molecules to spontaneously translocate biological membranes. Of equal importance is the understanding of the permeation process and the pathway followed by the permeant from the aqueous medium to the interior of the lipid bilayer, and back out again. A convenient framework for the computation of permeabilities is provided by the solubility-diffusion model, which requires knowledge of the underlying free-energy and diffusivity landscapes. Here, we develop a formalism that includes an explicit description of the orientational motion of the solute as it diffuses across the membrane. Toward this end, we have generalized a recently proposed method that reconciles thermodynamics and kinetics in importance-sampling simulations by means of a Bayesian-inference scheme to reverse-solve the underlying Smoluchowski equation. Performance of the proposed formalism is examined in the model cases of a water and an ethanol molecule crossing a fully hydrated lipid bilayer. Our analysis reveals a conspicuous dependence of the free-energy and rotational diffusivity on the orientation of ethanol when it lies within the headgroup region of the bilayer. Specifically, orientations for which the hydroxyl group lies among the polar lipid head groups, while the ethyl group recedes toward the hydrophobic interior are associated with free-energy minima ∼2kBT deep, as well as significantly slower orientational kinetics compared to the bulk solution or the core of the bilayer. The conspicuous orientational anisotropy of ethanol at the aqueous interface is suggestive of a complete rotation of the permeant as it crosses the hydrophobic interior of the membrane.

Molecular simulation of nonfacilitated membrane permeation

This is a review. Non-electrolytic compounds typically cross cell membranes by passive diffusion. The rate of permeation is dependent on the chemical properties of the solute and the composition of the lipid bilayer membrane. Predicting the permeability coefficient of a solute is important in pharmaceutical chemistry and toxicology. Molecular simulation has proven to be a valuable tool for modeling permeation of solutes through a lipid bilayer. In particular, the solubility-diffusion model has allowed for the quantitative calculation of permeability coefficients. The underlying theory and computational methods used to calculate membrane permeability are reviewed. We also discuss applications of these methods to examine the permeability of solutes and the effect of membrane composition on permeability. The application of coarse grain and polarizable models is discussed. This article is part of a Special Issue entitled: Membrane Proteins edited by J.C. Gumbart and Sergei Noskov.

Partition, orientation and mobility of ubiquinones in a lipid bilayer

Ubiquinone is the universal mobile charge carrier involved in biological electron transfer processes. Its redox properties and biological function depend on the molecular partition and lateral diffusion over biological membranes. However, ubiquinone localization and dynamics within lipid bilayers are long debated and still uncertain. Here we present molecular dynamics simulations of several ubiquinone homologs with variable isoprenoid tail lengths complexed to phosphatidylcholine bilayers. Initially, a new force-field parametrization for ubiquinone is derived from and compared to high level quantum chemical data. Free energy profiles for ubiquinone insertion in the lipid bilayer are obtained with the new force-field. The profiles allow for the determination of the equilibrium location of ubiquinone in the membrane as well as for the validation of the simulation model by direct comparison with experimental partition coefficients. A detailed analysis of structural properties and interactions shows that the ubiquinone polar head group is localized at the water-bilayer interface at the same depth of the lipid glycerol groups and oriented normal to the membrane plane. Both the localization and orientation of ubiquinone head groups do not change significantly when increasing the number of isoprenoid units. The isoprenoid tail is extended and packed with the lipid acyl chains. For ubiquinones with long tails, the terminal isoprenoid units have high flexibility. Calculated ubiquinone diffusion coefficients are similar to that found for the phosphatidylcholine lipid. These results may have further implications for the mechanisms of ubiquinone transport and binding to respiratory and photosynthetic protein complexes.

A Permeability Study of O2 and the Trace Amine p-Tyramine through Model Phosphatidylcholine Bilayers

We study here the permeability of the hydrophobic O2 molecule through a model DPPC bilayer at 323K and 350K, and of the trace amine p-tyramine through PC bilayers at 310K. The tyramine results are compared to previous experimental work at 298K. Nonequilibrium work methods were used in conjunction to simultaneously obtain both the potential of mean force (PMF) and the position dependent transmembrane diffusion coefficient, D(z), from the simulations. These in turn were used to calculate the permeability coefficient, P, through the inhomogeneous solubility-diffusion model. The results for O2 are consistent with previous simulations, and agree with experimentally measured P values for PC bilayers. A temperature dependence in the permeability of O2 through DPPC was obtained, with P decreasing at higher temperatures. Two relevant species of p-tyramine were simulated, from which the PMF and D(z) were calculated. The charged species had a large energetic barrier to crossing the bilayer of ~ 21 kcal/mol, while the uncharged, deprotonated species had a much lower barrier of ~ 7 kcal/mol. The effective in silico permeability for p-tyramine was calculated by applying three approximations, all of which gave nearly identical results (presented here as a function of the pKa). As the permeability value calculated from simulation was highly dependent on the pKa of the amine group, a further pKa study was performed that also varied the fraction of the uncharged and zwitterionic p-tyramine species. Using the experimental P value together with the simulated results, we were able to label the phenolic group as responsible for the pKa1 and the amine for the pKa2, that together represent all of the experimentally measured pKa values for p-tyramine. This agrees with older experimental results, in contrast to more recent work that has suggested there is a strong ambiguity in the pKa values.

Modeling kinetics and equilibrium of membranes with fields: milestoning analysis and implication to permeation

Coarse graining of membrane simulations by translating atomistic dynamics to densities and fields with Milestoning is discussed. The space of the membrane system is divided into cells and the different cells are characterized by order parameters presenting the number densities. The dynamics of the order parameters are probed with Milestoning. The methodology is illustrated here for a phospholipid membrane system (a hydrated bilayer of DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) lipid molecules). Significant inhomogeneity in membrane internal number density leads to complex free energy landscape and local maps of transition times. Dynamics and distributions of cavities within the membrane assist the permeation of nonpolar solutes such as xenon atoms. It is illustrated that quantitative and detailed dynamics of water transport through DOPC membrane can be analyzed using Milestoning with fields. The reaction space for water transport includes at least two slow variables: the normal to the membrane plane, and the water density.