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

Membrane Composition Allows the Optimization of Berberine Encapsulation in Liposomes

Berberine (BBR) is a natural molecule with noteworthy pharmacological properties, including the prevention of antibiotic resistance in Gram-negative bacteria. However, its oral bioavailability is poor, thus resulting in an impaired absorption and efficacy in humans. In combination with other drugs, liposomes have been shown to enhance the availability of the drug, representing a smart delivery system to target tissues and reduce negative side effects. To date, there is a lack of studies on BBR and liposomes that enable the rationalization and molecular-based design of such formulations for future use in humans. In this work, the encapsulation of BBR into liposomes is proposed to overcome current limitations using a combination of experimental and computational assays to rationalize the membrane composition of liposomes that maximizes BBR encapsulation. First, the encapsulation efficiency was measured for several membrane compositions, revealing that it is enhanced by cholesteryl hemisuccinate and, to a lesser extent, by cholesterol. The physical basis of the BBR encapsulation efficiency and permeability was clarified using molecular dynamics simulation: using the lipid composition, one can tune the capability of membranes to attract, i.e., to adsorb, the molecules onto their surface. Overall, these findings suggest a rational strategy to maximize the encapsulation efficiency of liposomes by using negatively charged lipids, thus representing the basis for designing delivery systems for BBR, useful to treat, e.g., antibiotic resistance.

Interaction between Permeation Enhancers and Lipid Bilayers

Permeation enhancers (PEs) are a class of molecules that interact with the epithelial membrane and transiently increase its transcellular permeability. Although there have been few clinical trials of PE coformulated drugs, the mechanism of action of PEs remains elusive. In this paper, the interaction between two archetypes of PEs [salcaprozate sodium (SNAC) and sodium caprate (C10)] and membranes is investigated with extensive all-atom molecular dynamics simulations. The simulations show that (1) the association between the neutral PEs and membranes is favored in free energy, (2) the propensity of neutral PE aggregation is larger in aqueous solution than in lipid bilayers, (3) the equilibrium distribution of neutral PEs in membranes is fast, e.g., accessible with unbiased MD simulations, and (4) the micelle of neutral PEs formed in aqueous solution does not rupture the membranes (e.g., not forming pores or breaking up the membrane) under simulation conditions. All results combined, this study indicates that PEs insert into the membranes in an equilibrium or near equilibrium process. This study lays the foundation for future investigations of how PEs impact the free energy of permeation for small molecules.

How is Membrane Permeation of Small Ionizable Molecules Affected by Protonation Kinetics?

According to the pH-partition hypothesis, the aqueous solution adjacent to a membrane is a mixture of the ionization states of the permeating molecule at fixed Henderson-Hasselbalch concentrations, such that each state passes through the membrane in parallel with its own specific permeability. An alternative view, based on the assumption that the rate of switching ionization states is instantaneous, represents the permeation of ionizable molecules via an effective Boltzmann-weighted average potential (BWAP). Such an assumption is used in constant-pH molecular dynamics simulations. The inhomogeneous solubility-diffusion framework can be used to compute the pH-dependent membrane permeability for each of these two limiting treatments. With biased WTM-eABF molecular dynamics simulations, we computed the potential of mean force and diffusivity of each ionization state of two weakly basic small molecules: nicotine, an addictive drug, and varenicline, a therapeutic for treating nicotine addiction. At pH = 7, the BWAP effective permeability is greater than that determined by pH-partitioning by a factor of 2.5 for nicotine and 5 for varenicline. To assess the importance of ionization kinetics, we present a Smoluchowski master equation that includes explicitly the protonation and deprotonation processes coupled with the diffusive motion across the membrane. At pH = 7, the increase in permeability due to the explicit ionization kinetics is negligible for both nicotine and varenicline. This finding is reaffirmed by combined Brownian dynamics and Markov state model simulations for estimating the permeability of nicotine while allowing changes in its ionization state. We conclude that for these molecules the pH-partition hypothesis correctly captures the physics of the permeation process. The small free energy barriers for the permeation of nicotine and varenicline in their deprotonated neutral forms play a crucial role in establishing the validity of the pH-partitioning mechanism. Essentially, BWAP fails because ionization kinetics are too slow on the time scale of membrane crossing to affect the permeation of small ionizable molecules such as nicotine and varenicline. For the singly protonated state of nicotine, the computational results agree well with experimental measurements (P1 = 1.29 × 10-7 cm/s), but the agreement for neutral (P0 = 6.12 cm/s) and doubly protonated nicotine (P2 = 3.70 × 10-13 cm/s) is slightly worse, likely due to factors associated with the aqueous boundary layer (neutral form) or leaks through paracellular pathways (doubly protonated form).

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.

Physical Chemistry of Chloroquine Permeation through the Cell Membrane with Atomistic Detail

We provide a molecular-level description of the thermodynamics and mechanistic aspects of drug permeation through the cell membrane. As a case study, we considered the antimalaria FDA approved drug chloroquine. Molecular dynamics simulations of the molecule (in its neutral and protonated form) were performed in the presence of different lipid bilayers, with the aim of uncovering key aspects of the permeation process, a fundamental step for the drug's action. Free energy values obtained by well-tempered metadynamics simulations suggest that the neutral form is the only permeating protomer, consistent with experimental data. H-bond interactions of the drug with water molecules and membrane headgroups play a crucial role for permeation. The presence of the transmembrane potential, investigated here for the first time in a drug permeation study, does not qualitatively affect these conclusions.

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.

Structure-based identification of novel scaffolds as potential HIV-1 entry inhibitors involving CCR5

C-C chemokine receptor 5 (CCR5), which is part of the chemokine receptor family, is a member of the G protein-coupled receptor superfamily. The interactions of CCR5 with HIV-1 during viral entry position it as an effective therapeutic target for designing potent antiviral therapies. The small-molecule Maraviroc was approved by the FDA as a CCR5 drug in 2007, while clinical trials failure has characterised many of the other CCR5 inhibitors. Thus, the continual identification of potential CCR5 inhibitors is, therefore, warranted. In this study, a structure-based discovery approach has been utilised to screen and retrieved novel potential CCR5 inhibitors from the Asinex antiviral compound (∼ 8,722) database. Explicit lipid-bilayer molecular dynamics simulation, in silico physicochemical and pharmacokinetic analyses, were further performed for the top compounds. A total of 23 structurally diverse compounds with binding scores higher than Maraviroc were selected. Subsequent molecular dynamics (MD) simulations analysis of the top four compounds LAS 51495192, BDB 26405401, BDB 26419079, and LAS 34154543, maintained stability at the CCR5 binding site. Furthermore, these compounds made pertinent interactions with CCR5 residues critical for the HIV-1 gp120-V3 loop binding such as Trp86, Tyr89, Phe109, Tyr108, Glu283 and Tyr251. Additionally, the predicted in silico physicochemical and pharmacokinetic descriptors of the selected compounds were within the acceptable range for drug-likeness. The results suggest positive indications that the identified molecules may represent promising CCR5 entry inhibitors. Further structural optimisations and biochemical testing of the proposed compounds may assist in the discovery of effective HIV-1 therapy.Communicated by Ramaswamy H. Sarma.

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.

Membrane thickness, lipid phase and sterol type are determining factors in the permeability of membranes to small solutes

Cell membranes provide a selective semi-permeable barrier to the passive transport of molecules. This property differs greatly between organisms. While the cytoplasmic membrane of bacterial cells is highly permeable for weak acids and glycerol, yeasts can maintain large concentration gradients. Here we show that such differences can arise from the physical state of the plasma membrane. By combining stopped-flow kinetic measurements with molecular dynamics simulations, we performed a systematic analysis of the permeability of a variety of small molecules through synthetic membranes of different lipid composition to obtain detailed molecular insight into the permeation mechanisms. While membrane thickness is an important parameter for the permeability through fluid membranes, the largest differences occur when the membranes transit from the liquid-disordered to liquid-ordered and/or to gel state, which is in agreement with previous work on passive diffusion of water. By comparing our results with in vivo measurements from yeast, we conclude that the yeast membrane exists in a highly ordered and rigid state, which is comparable to synthetic saturated DPPC-sterol membranes.

Membrane permeability of small molecules depends on the composition of the lipid bilayer. Here, authors compare permeability measured on membranes in different physical states and conclude that the yeast membrane exists in a highly ordered phase.

Calculation of Permeability Coefficients from Solute Equilibration Dynamics: An Assessment of Various Methods

Predicting the rate at which substances permeate membrane barriers in vivo is crucial for drug development. Permeability coefficients obtained from in vitro studies are valuable for this goal. These are normally determined by following the dynamics of solute equilibration between two membrane-separated compartments. However, the correct calculation of permeability coefficients from such data is not always straightforward. To address these problems, here we develop a kinetic model for solute permeation through lipid membrane barriers that includes the two membrane leaflets as compartments in a four-compartment model. Accounting for solute association with the membrane allows assessing various methods in a wide variety of conditions. The results showed that the often-used expression Papp= β × r/3 is inapplicable to very large or very small vesicles, to moderately or highly lipophilic solutes, or when the development of a significant pH gradient opposes the solute’s flux. We establish useful relationships that overcome these limitations and allow predicting permeability in compartmentalised in vitro or in vivo systems with specific properties. Finally, from the parameters for the interaction of the solute with the membrane barrier, we defined an intrinsic permeability coefficient that facilitates quantitative comparisons between solutes.

Conformational Change from U- to I-Shape of Ion Transporters Facilitates K+ Transport across Lipid Bilayers

We have investigated, at the atomic level, the ion-fishing mechanism underlying the ion transport across membranes mediated by an artificial ion transporter composed of a hydroxyl-rich cholesterol group, a flexible alkyl chain, and a crown ether. Our results show that the transporter can spontaneously insert into the membrane and switch between the folded (U-shaped) and extended (I-shaped) conformations. The free-energy profile associated with the conformational transition indicates that compared with the U-shaped conformation of the transporter, the I-shaped one is thermodynamically more favorable. Furthermore, the free-energy profiles describing the ion translocation reveal that the transporter capturing the ion in U-shape on one side of the membrane and releasing it in I-shape on the other side constitutes a key way for the highly efficient transport of K⁺ ions. We present herewith a rigorous and rational framework to decipher the detailed ion-fishing mechanism of transmembrane ion transport with exceptionally high activity.

Assessing the Intestinal Permeability of Small Molecule Drugs via Diffusion Motion on a Multidimensional Free Energy Surface

A protocol that accurately assesses the intestinal permeability of small molecule compounds plays an essential role in decreasing the cost and time in inventing a new drug. This manuscript presents a novel computational method to study the passive permeation of small molecule drugs based on the inhomogeneous solubility-diffusion model. The multidimensional free energy surface of the drug transiting through a lipid bilayer is computed with transition-tempered metadynamics that accurately captures the mechanisms of passive permeation. The permeability is computed by following the diffusion motion of the drug molecules along the minimal free energy path found on the multidimensional free energy surface. This computational method is assessed by studying the permeability of five small molecule drugs (ketoprofen, naproxen, metoprolol, propranolol, and salicylic acid). The results demonstrate a remarkable agreement between the computed permeabilities and those measured with the intestinal assay. The in silico method reported in this manuscript also reproduces the permeability measured from the intestinal assay (in vivo) better than the cell-based assays (e.g., PAMPA and Caco-2) do. In addition, the multidimensional free energy surface reveals the interplay between the structure of the small molecule and its permeability, shedding light on strategies of drug optimization.

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.

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.

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.

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.

Tuning the permeability of regular polymeric networks by the cross-link ratio

The amount of cross-linking in the design of polymer materials is a key parameter for the modification of numerous physical properties, importantly, the permeability to molecular solutes. We consider networks with a diamond-like architecture and different cross-link ratios, concurring with a wide range of the polymer volume fraction. We particularly focus on the effect and the competition of two independent component-specific solute-polymer interactions, i.e., we distinguish between chain-monomers and cross-linkers, which individually act on the solutes and are altered to cover attractive and repulsive regimes. For this purpose, we employ coarse-grained, Langevin computer simulations to study how the cross-link ratio of polymer networks controls the solute partitioning, diffusion, and permeability. We observe different qualitative behaviors as a function of the cross-link ratio and interaction strengths. The permeability can be tuned ranging over two orders of magnitude relative to the reference bulk permeability. Finally, we provide scaling theories for the partitioning and diffusion that explicitly account for the component-specific interactions as well as the cross-link ratio and the polymer volume fraction. These are in overall good agreement with the simulation results and grant insight into the underlying physics, rationalizing how the cross-link ratio can be exploited to tune the solute permeability of polymeric networks.

Membrane permeability of small molecules from unbiased molecular dynamics simulations

Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé-Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé-Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations.

Computational Study of the Ion and Water Permeation and Transport Mechanisms of the SARS-CoV-2 Pentameric E Protein Channel

Coronavirus disease 2019 (COVID-19) is caused by a novel coronavirus (SARS-CoV-2) and represents the causative agent of a potentially fatal disease that is a public health emergency of international concern. Coronaviruses, including SARS-CoV-2, encode an envelope (E) protein, which is a small, hydrophobic membrane protein; the E protein of SARS-CoV-2 shares a high level of homology with severe acute respiratory syndrome coronavirus (SARS-CoV). In this study, we provide insights into the function of the SARS-CoV-2 E protein channel and the ion and water permeation mechanisms using a combination of in silico methods. Based on our results, the pentameric E protein promotes the penetration of cation ions through the channel. An analysis of the potential mean force (PMF), pore radius and diffusion coefficient reveals that Leu10 and Phe19 are the hydrophobic gates of the channel. In addition, the pore exhibits a clear wetting/dewetting transition with cation selectivity under transmembrane voltage, indicating that it is a hydrophobic voltage-dependent channel. Overall, these results provide structure-based insights and molecular dynamic information that are needed to understand the regulatory mechanisms of ion permeability in the pentameric SARS-CoV-2 E protein channel.

Water-ion permselectivity of narrow-diameter carbon nanotubes

Carbon nanotube (CNT) pores, which mimic the structure of the aquaporin channels, support extremely high water transport rates that make them strong candidates for building artificial water channels and high-performance membranes. Here, we measure water and ion permeation through 0.8-nm-diameter CNT porins (CNTPs)-short CNT segments embedded in lipid membranes-under optimized experimental conditions. Measured activation energy of water transport through the CNTPs agrees with the barrier values typical for single-file water transport. Well-tempered metadynamics simulations of water transport in CNTPs also report similar activation energy values and provide molecular-scale details of the mechanism for water entry into these channels. CNTPs strongly reject chloride ions and show water-salt permselectivity values comparable to those of commercial desalination membranes.

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.

What Coordinate Best Describes the Affinity of the Hydrated Excess Proton for the Air-Water Interface?

Molecular dynamics simulations and free energy sampling are employed in this work to investigate the surface affinity of the hydrated excess proton with two definitions of the interface: The Gibbs dividing interface (GDI) and the Willard-Chandler interface (WCI). Both the multistate empirical valence bond (MS-EVB) reactive molecular dynamics method and the density functional theory-based ab initio molecular dynamics (AIMD) were used to describe the hydrated excess proton species, including "vehicular" (standard diffusion) transport and (Grotthuss) proton hopping transport and associated structures of the hydrated excess proton net positive charge defect. The excess proton is found to exhibit a similar trend and quantitative free energy behavior in terms of its surface affinity as a function of the GDI or WCI. Importantly, the definitions of the two interfaces in terms of the excess proton charge defect are highly correlated and far from independent of one another, thus undermining the argument that one interface is superior to the other when describing the proton interface affinity. Moreover, the hydrated excess proton and its solvation shell significantly influence the location and local curvature of the WCI, making it difficult to disentangle the interfacial thermodynamics of the excess proton from the influence of that species on the instantaneous surface curvature.

Molecular dynamics trajectories for 630 coarse-grained drug-membrane permeations

The permeation of small-molecule drugs across a phospholipid membrane bears much interest both in the pharmaceutical sciences and in physical chemistry. Connecting the chemistry of the drug and the lipids to the resulting thermodynamic properties remains of immediate importance. Here we report molecular dynamics (MD) simulation trajectories using the coarse-grained (CG) Martini force field. A wide, representative coverage of chemistry is provided: across solutes-exhaustively enumerating all 105 CG dimers-and across six phospholipids. For each combination, umbrella-sampling simulations provide detailed structural information of the solute at all depths from the bilayer midplane to bulk water, allowing a precise reconstruction of the potential of mean force. Overall, the present database contains trajectories from 15,120 MD simulations. This database may serve the further identification of structure-property relationships between compound chemistry and drug permeability.

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.

Dynamic Protonation Dramatically Affects the Membrane Permeability of Drug-like Molecules

Permeability (P_m) across biological membranes is of fundamental importance and a key factor in drug absorption, distribution, and development. Although the majority of drugs will be charged at some point during oral delivery, our understanding of membrane permeation by charged species is limited. The canonical model assumes that only neutral molecules partition into and passively permeate across membranes, but there is mounting evidence that these processes are also facile for certain charged species. However, it is unknown whether such ionizable permeants dynamically neutralize at the membrane surface or permeate in their charged form. To probe protonation-coupled permeation in atomic detail, we herein apply continuous constant-pH molecular dynamics along with free energy sampling to study the permeation of a weak base propranolol (PPL), and evaluate the impact of including dynamic protonation on P_m. The simulations reveal that PPL dynamically neutralizes at the lipid-tail interface, which dramatically influences the permeation free energy landscape and explains why the conventional model overestimates the assigned intrinsic permeability. We demonstrate how fixed-charge-state simulations can account for this effect, and propose a revised model that better describes pH-coupled partitioning and permeation. Our results demonstrate how dynamic changes in protonation state may play a critical role in the permeation of ionizable molecules, including pharmaceuticals and drug-like molecules, thus requiring a revision of the standard picture.

Mycolactone Toxin Membrane Permeation: Atomistic versus Coarse-Grained MARTINI Simulations

Mycolactone, a cytotoxic and immunosuppressive macrolide produced by Mycobacterium ulcerans, is the central virulent factor in the skin disease Buruli ulcer. This multifunctional cytotoxin affects fundamental cellular processes such as cell adhesion, immune response, and cell death by targeting various cellular structures. Developing effective diagnostics that target mycolactone has been challenging, potentially because of suspected interactions with lipophilic architectures, including membranes. To better understand the pathogenesis of Buruli ulcer disease, aid in the development of diagnostics, and learn how amphiphiles in general use lipid trafficking to navigate the host environment, we seek to understand the nature of mycolactone-membrane interactions. Herein, we characterize how the two dominant isomers of mycolactone (A and B) interact with and permeate DPPC membranes with all-atom molecular dynamics simulations employing transition-tempered metadynamics and compare these results to those obtained by MARTINI coarse-grained simulations. Our all-atom simulations reveal that both isomers have a strong preference to associate with the membrane, although their mechanisms and energetics of membrane permeation differ slightly. Water molecules are found to play an important role in the permeation process. Although the MARTINI coarse-grained simulations give the correct free energy of membrane association, they fail to capture the mechanism of permeation and role of water during permeation as seen in all-atom simulations.

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).

In Silico Prediction of PAMPA Effective Permeability Using a Two-QSAR Approach

Oral administration is the preferred and predominant route of choice for medication. As such, drug absorption is one of critical drug metabolism and pharmacokinetics (DM/PK) parameters that should be taken into consideration in the process of drug discovery and development. The cell-free in vitro parallel artificial membrane permeability assay (PAMPA) has been adopted as the primary screening to assess the passive diffusion of compounds in the practical applications. A classical quantitative structure–activity relationship (QSAR) model and a machine learning (ML)-based QSAR model were derived using the partial least square (PLS) scheme and hierarchical support vector regression (HSVR) scheme to elucidate the underlying passive diffusion mechanism and to predict the PAMPA effective permeability, respectively, in this study. It was observed that HSVR executed better than PLS as manifested by the predictions of the samples in the training set, test set, and outlier set as well as various statistical assessments. When applied to the mock test, which was designated to mimic real challenges, HSVR also showed better predictive performance. PLS, conversely, cannot cover some mechanistically interpretable relationships between descriptors and permeability. Accordingly, the synergy of predictive HSVR and interpretable PLS models can be greatly useful in facilitating drug discovery and development by predicting passive diffusion.

Molecular Dynamics Simulations of Membrane Permeability

This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.

Does Size Really Matter? Probing the Efficacy of Structural Reduction in the Optimization of Bioderived Compounds - A Computational "Proof-of-Concept"

Over the years, numerous synthetic approaches have been utilized in drug design to improve the pharmacological properties of naturally derived compounds and most importantly, minimize toxic effects associated with their transition to drugs. The reduction of complex bioderived compounds to simpler bioactive fragments has been identified as a viable strategy to develop lead compounds with improved activities and minimal toxicities. Although this ‘reductive’ strategy has been widely exemplified, underlying biological events remain unresolved, hence the unanswered question remains how does the fragmentation of a natural compound improve its bioactivity and reduce toxicities? Herein, using a combinatorial approach, we initialize a computational “proof-of- concept” to expound the differential pharmacological and antagonistic activities of a natural compound, Anguinomycin D, and its synthetic fragment, SB640 towards Exportin Chromosome Region Maintenance 1 (CRM1). Interestingly, our findings revealed that in comparison with the parent compound, SB640 exhibited improved pharmacological attributes, while toxicities and off-target activities were relatively minimal. Moreover, we observed that the reduced size of SB640 allowed ‘deep access’ at the Nuclear Export Signals (NES) binding groove of CRM1, which favored optimal and proximal positioning towards crucial residues while the presence of the long polyketide tail in Anguinomycin D constrained its burial at the hydrophobic groove. Furthermore, with regards to their antagonistic functions, structural inactivation (rigidity) was more pronounced in CRM1 when bound by SB640 as compared to Anguinomycin D. These findings provide essential insights that portray synthetic fragmentation of natural compounds as a feasible approach towards the discovery of potential leads in disease treatment.