Molecular simulation of nonfacilitated membrane permeation

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.

Generating Concentration Gradients across Membranes for Molecular Dynamics Simulations of Periodic Systems

The plasma membrane forms the boundary between a living entity and its environment and acts as a barrier to permeation and flow of substances. Several computational means of calculating permeability have been implemented for molecular dynamics (MD) simulations-based approaches. Except for double bilayer systems, most permeability studies have been performed under equilibrium conditions, in large part due to the challenges associated with creating concentration gradients in simulations utilizing periodic boundary conditions. To enhance the scientific understanding of permeation and complement the existing computational means of characterizing membrane permeability, we developed a non-equilibrium method that enables the generation and maintenance of steady-state gradients in MD simulations. We utilize PBCs advantageously by imposing a directional bias to the motion of permeants so that their crossing of the boundary replenishes the gradient, like a previous study on ions. Under these conditions, a net flow of permeants across membranes may be observed to determine bulk permeability by a direct application of J=PΔc. In the present study, we explore the results of its application to an exemplary O2 and POPC bilayer system, demonstrating accurate and precise permeability measurements. In addition, we illustrate the impact of permeant concentration and the choice of thermostat on the permeability. Moreover, we demonstrate that energetics of permeation can be closely examined by the dissipation of the gradient across the membrane to gain nuanced insights into the thermodynamics of permeability.

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.

Exploring Giant Unilamellar Vesicle Production for Artificial Cells - Current Challenges and Future Directions

Creating an artificial cell from the bottom up is a long-standing challenge and, while significant progress has been made, the full realization of this goal remains elusive. Arguably, one of the biggest hurdles that researchers are facing now is the assembly of different modules of cell function inside a single container. Giant unilamellar vesicles (GUVs) have emerged as a suitable container with many methods available for their production. Well-studied swelling-based methods offer a wide range of lipid compositions but at the expense of limited encapsulation efficiency. Emulsion-based methods, on the other hand, excel at encapsulation but are only effective with a limited set of membrane compositions and may entrap residual additives in the lipid bilayer. Since the ultimate artificial cell will need to comply with both specific membrane and encapsulation requirements, there is still no one-method-fits-all solution for GUV formation available today. This review discusses the state of the art in different GUV production methods and their compatibility with GUV requirements and operational requirements such as reproducibility and ease of use. It concludes by identifying the most pressing issues and proposes potential avenues for future research to bring us one step closer to turning artificial cells into a reality.

How a few help all: cooperative crossing of lipid membranes by COSAN anions

Experimental results show that the presence of a concentration gradient of certain nano-ions (most notably cobaltabisdicarbollide ([o-COSAN]- anions), induce a current across intact artificial phospholipid bilayers in spite of the high Born free energy estimated for these ions. The mechanism underlying this observed translocation of nano-anions across membranes has yet to be determined. Here we show, using molecular dynamics simulations, that the permeation of [o-COSAN]- anions across a lipid bilayer proceeds in a cooperative manner. Single nano-ions can enter the bilayer but permeation is hampered by a free energy barrier of about 8kBT. The interaction between these nano-ions inside a leaflet induces a flip-flop translocation mechanism with the formation of transient, elongated structure inside the membrane. This cooperative flip-flop allows an efficient distribution of [o-COSAN]- anions in both leaflets of the bilayer. These results suggest the existence of a new mechanism for permeation of nano-ions across lipid membranes, relevant for those that have the appropriate self-assembly character.

Translocation Processes of Pt(II)-Based Drugs through Human Breast Cancer Cell Membrane: In Silico Experiments

Breast cancer is one of the most frequent modalities of cancer worldwide, with notable mortality. The medication based on platinum drugs (cisplatin (cddp), carboplatin (cpx), and oxaliplatin (oxa)) is a conventional chemotherapy despite severe side effects and the development of drug resistance. In order to provide a deeper molecular description of the influx and efflux processes of platinum drugs through breast cancer tissues, this study focuses on molecular dynamics (MD) simulations of the passive translocation process through a realistic plasma membrane prototype of human breast cancer cell (c_memb). The results showed that the permeation events were mainly mediated by neutral lipids (DOPC, DOPE, and cholesterol), producing a low and temporary membrane deformation. The drug insertion in the region of polar heads was the most favorable stage of the translocation mechanism, especially for cddp and oxa with potential wells of -8.6 and -9.8 kcal mol-1, respectively. However, the potentials of mean force (PMF) revealed unfavorable kinetics for the permeation of these drugs through lipid tails, with energy barriers of 28.3 (cddp), 32.2 (cpx), and 30.4 kcal mol-1 (oxa). The low permeability coefficients (P) of cpx and oxa, which were 3 and 1 orders of magnitude inferior than for cddp, resulted from the high energy barriers for their traslocation processes through the membrane. The obtained results provide a more accurate picture of the permeation of Pt(II)-based drugs through breast cancer cells, which may be relevant for the design and evaluation of new platinum complexes.

Hydrophobin Bilayer as Water Impermeable Protein Membrane

One of the most important properties of membranes is their permeability to water and other small molecules. A targeted change in permeability allows the passage of molecules to be controlled. Vesicles made of membranes with low water permeability are preferable for drug delivery, for example, because they are more stable and maintain the drug concentration inside. This study reports on the very low water permeability of pure protein membranes composed of a bilayer of the amphiphilic protein hydrophobin HFBI. Using a droplet interface bilayer setup, we demonstrate that HFBI bilayers are essentially impermeable to water. HFBI bilayers withstand far larger osmotic pressures than lipid membranes. Only by disturbing the packing of the proteins in the HFBI bilayer is a measurable water permeability induced. To investigate possible molecular mechanisms causing the near-zero permeability, we used all-atom molecular dynamics simulations of various HFBI bilayer models. The simulations suggest that the experimental HFBI bilayer permeability is compatible neither with a lateral honeycomb structure, as found for HFBI monolayers, nor with a residual oil layer within the bilayer or with a disordered lateral packing similar to the packing in lipid bilayers. These results suggest that the low permeabilities of HFBI and lipid bilayers rely on different mechanisms. With their extremely low but adaptable permeability and high stability, HFBI membranes could be used as an osmotic pressure-insensitive barrier in situations where lipid membranes fail such as desalination membranes.

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.

Targeted Protein Degradation: Advances, Challenges, and Prospects for Computational Methods

The therapeutic approach of targeted protein degradation (TPD) is gaining momentum due to its potentially superior effects compared with protein inhibition. Recent advancements in the biotech and pharmaceutical sectors have led to the development of compounds that are currently in human trials, with some showing promising clinical results. However, the use of computational tools in TPD is still limited, as it has distinct characteristics compared with traditional computational drug design methods. TPD involves creating a ternary structure (protein-degrader-ligase) responsible for the biological function, such as ubiquitination and subsequent proteasomal degradation, which depends on the spatial orientation of the protein of interest (POI) relative to E2-loaded ubiquitin. Modeling this structure necessitates a unique blend of tools initially developed for small molecules (e.g., docking) and biologics (e.g., protein-protein interaction modeling). Additionally, degrader molecules, particularly heterobifunctional degraders, are generally larger than conventional small molecule drugs, leading to challenges in determining drug-like properties like solubility and permeability. Furthermore, the catalytic nature of TPD makes occupancy-based modeling insufficient. TPD consists of multiple interconnected yet distinct steps, such as POI binding, E3 ligase binding, ternary structure interactions, ubiquitination, and degradation, along with traditional small molecule properties. A comprehensive set of tools is needed to address the dynamic nature of the induced proximity ternary complex and its implications for ubiquitination. In this Perspective, we discuss the current state of computational tools for TPD. We start by describing the series of steps involved in the degradation process and the experimental methods used to characterize them. Then, we delve into a detailed analysis of the computational tools employed in TPD. We also present an integrative approach that has proven successful for degrader design and its impact on project decisions. Finally, we examine the future prospects of computational methods in TPD and the areas with the greatest potential for impact.

Converging PMF Calculations of Antibiotic Permeation across an Outer Membrane Porin with Subkilocalorie per Mole Accuracy

The emergence of multidrug-resistant pathogens led to a critical need for new antibiotics. A key property of effective antibiotics against Gram-negative bacteria is their ability to permeate through the bacterial outer membrane via transmembrane porin proteins. Molecular dynamics (MD) simulations are, in principle, capable of modeling antibiotic permeation across outer membrane porins (OMPs). However, owing to sampling problems, it has remained challenging to obtain converged potentials of mean force (PMFs) for antibiotic permeation across OMPs. Here, we investigated the convergence of PMFs along a single collective variable aimed at quantifying the permeation of the antibiotic fosmidomycin across the OprO porin. We compared standard umbrella sampling (US) with three advanced flavors of the US technique: (i) Hamiltonian replica exchange with solute tempering in combination with US, (ii) simulated tempering-enhanced US, and (iii) replica-exchange US. To quantify the PMF convergence and to reveal hysteresis problems, we computed several independent sets of US simulations starting from pulling simulations in the outward and inward permeation directions. We find that replica-exchange US in combination with well-chosen restraints is highly successful for obtaining converged PMFs of fosmidomycin permeation through OprO, reaching PMFs converged to subkilocalorie per mole accuracy.

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.

Molecular Dynamics Simulation Study of the Protonation State Dependence of Glutamic Acid Transport through a Cyclic Peptide Nanotube

The effect of the protonation state of glutamic acid on its translocation through cyclic peptide nanotubes (CPNs) was assessed by using molecular dynamics (MD) simulations. Anionic (GLU-), neutral zwitterionic (GLU0), and cationic (GLU+) forms of glutamic acid were selected as three different protonation states for an analysis of energetics and diffusivity for acid transport across a cyclic decapeptide nanotube. Based on the solubility-diffusion model, permeability coefficients for the three protonation states of the acid were calculated and compared with experimental results for CPN-mediated glutamate transport through CPNs. Potential of mean force (PMF) calculations reveal that, due to the cation-selective nature of the lumen of CPNs, GLU-, so-called glutamate, shows significantly high free energy barriers, while GLU+ displays deep energy wells and GLU0 has mild free energy barriers and wells inside the CPN. The considerable energy barriers for GLU- inside CPNs are mainly attributed to unfavorable interactions with DMPC bilayers and CPNs and are reduced by favorable interactions with channel water molecules through attractive electrostatic interactions and hydrogen bonding. Unlike the distinct PMF curves, position-dependent diffusion coefficient profiles exhibit comparable frictional behaviors regardless of the charge status of three protonation states due to similar confined environments imposed by the lumen of the CPN. The calculated permeability coefficients for the three protonation states clearly demonstrate that glutamic acid has a strong protonation state dependence for its transport through CPNs, as determined by the energetics rather than the diffusivity of the protonation state. In addition, the permeability coefficients also imply that GLU- is unlikely to pass through a CPN due to the high energy barriers inside the CPN, which is in disagreement with experimental measurements, where a considerable amount of glutamate permeating through the CPN was detected. To resolve the discrepancy between this work and the experimental observations, several possibilities are proposed, including a large concentration gradient of glutamate between the inside and outside of lipid vesicles and bilayers in the experiments, the glutamate activity difference between our MD simulations and experiments, an overestimation of energy barriers due to the artifacts imposed in MD simulations, and/or finally a transformation of the protonation state from GLU- to GLU0 to reduce the energy barriers. Overall, our study demonstrates that the protonation state of glutamic acid has a strong effect on the transport of the acid and suggests a possible protonation state change for glutamate permeating through CPNs.

Sucrose Osmotic Self-Oscillation Drives Membrane Permeability

Molecular permeation through phospholipid membranes is a fundamental biological process for small molecules. Sucrose is one of the most widely used sweeteners and a key factor in the pathogenesis of obesity and diabetes, yet a detailed understanding of its mechanism involved in permeability into phospholipid membranes is still lacking. Here, using giant unimolecular vesicles (GUVs) reconstituting membrane properties, we compared the osmotic behavior of sucrose in GUVs and HepG2 cells to explore the effect of sucrose on membrane stability in the absence of protein enhancers. The results suggested that the particle size and potential of GUVs and the cellular membrane potential changed significantly with increasing the sucrose concentration (p < 0.05). In microscopic images of cells containing GUVs and sucrose, the fluorescence intensity of vesicles was 537 ± 17.69 after 15 min, and the value was significantly higher than that of microscopic images of cells without sucrose addition (p < 0.05). These changes suggested that the permeability of the phospholipid membrane became larger under a sucrose environment. This study provides a theoretical basis for better insight on the role of sucrose in the physiological environment.

Interaction of Uperin Peptides with Model Membranes: Molecular Dynamics Study

The interaction of antimicrobial and amyloid peptides with cell membranes is a critical step in their activities. Peptides of the uperin family obtained from the skin secretion of Australian amphibians demonstrate antimicrobial and amyloidogenic properties. All-atomic molecular dynamics and an umbrella sampling approach were used to study the interaction of uperins with model bacterial membrane. Two stable configurations of peptides were found. In the bound state, the peptides in helical form were located right under the head group region in parallel orientation with respect to the bilayer surface. Stable transmembrane configuration was observed for wild-type uperin and its alanine mutant in both alpha-helical and extended unstructured forms. The potential of mean force characterized the process of peptide binding from water to the lipid bilayer and its insertion into the membrane, and revealed that the transition of uperins from the bound state to the transmembrane position was accompanied by the rotation of peptides and passes through the energy barrier of 4-5 kcal/mol. Uperins have a weak effect on membrane properties.

Computational Prodrug Design Methodology for Liposome Formulability Enhancement of Small-Molecule APIs

Encapsulation into liposomes is a formulation strategy that can improve efficacy and reduce side effects of active pharmaceutical ingredients (APIs) that exhibit poor biodistribution or pharmacokinetics when administered alone. However, many APIs are unsuitable for liposomal formulations intended for parenteral administration due to their inherent physicochemical properties─lipid bilayer permeability and water-lipid equilibrium partitioning coefficient. Too high permeability results in premature leakage from liposomes, while too low permeability means the API is not able to pass across biological barriers. There are several options for solving this issue: (i) change of the lipid bilayer composition, (ii) addition of a permeability enhancer, or (iii) modification of the chemical structure of the API to design a prodrug. The latter approach was taken in the present work, and the effect of small changes in the molecular structure of the API on its permeation rate across a lipidic bilayer was systematically explored utilizing computer simulations. An in silico methodology for prodrug design based on the COSMOperm approach has been proposed and applied to four APIs (abiraterone, cytarabine, 5-fluorouracil, and paliperidone). It is shown that the addition of aliphatic hydrocarbon chains via ester or amide bonds can render the molecule more lipophilic and increase its permeability by approximately 1 order of magnitude for each 2 carbon atoms added, while the formation of fructose adducts can provide a more hydrophilic character to the molecule and reduce its lipid partitioning. While partitioning was found to depend only on the size and type of the added group, permeability was found to depend also on the added group location. Overall, it has been shown that both permeability and lipid partitioning coefficient can be systematically shifted into the desired liposome formulability window by appropriate group contributions to the parental drug. This can significantly increase the portfolio of APIs for which liposome or lipid nanoparticle formulations become feasible.

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.

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

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

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

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

Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux

Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.

Simulations reveal that antimicrobial BP100 induces local membrane thinning, slows lipid dynamics and favors water penetration

MD simulations reveal that BP100 peptide induces local membrane thinning and negative curvature, slows lipid dynamics and increases the water life time in the lipid hydrophobic core and transmembrane water transport in the direction of the peptide.

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

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

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.

Momentum removal to obtain the position-dependent diffusion constant in constrained molecular dynamics simulation

The position-dependent diffusion coefficient along with free energy profile are important parameters needed to study mass transport in heterogeneous systems such as biological and polymer membranes, and molecular dynamics (MD) calculation is a popular tool to obtain them. Among many methodologies, the Marrink-Berendsen (MB) method is often employed to calculate the position-dependent diffusion coefficient, in which the autocorrelation function of the force on a fixed molecule is related to the friction on the molecule. However, the diffusion coefficient is shown to be affected by the period of the removal of the center-of-mass velocity, τ v 0 , which is necessary when performing MD calculations using the Ewald method for Coulombic interaction. We have clarified theoretically in this study how this operation affects the diffusion coefficient calculated by the MB method, and the theoretical predictions are proven by MD calculations. Therefore, we succeeded in providing guidance on how to select an appropriate τ v 0 value in estimating the position-dependent diffusion coefficient by the MB method. This guideline is applicable also to the Woolf-Roux method.

The future of biomolecular simulation in the pharmaceutical industry: what we can learn from aerodynamics modelling and weather prediction. Part 1. understanding the physical and computational complexity of in silico drug design

The predictive power of simulation has become embedded in the infrastructure of modern economies. Computer-aided design is ubiquitous throughout industry. In aeronautical engineering, built infrastructure and materials manufacturing, simulations are routinely used to compute the performance of potential designs before construction. The ability to predict the behaviour of products is a driver of innovation by reducing the cost barrier to new designs, but also because radically novel ideas can be piloted with relatively little risk. Accurate weather forecasting is essential to guide domestic and military flight paths, and therefore the underpinning simulations are critical enough to have implications for national security. However, in the pharmaceutical and biotechnological industries, the application of computer simulations remains limited by the capabilities of the technology with respect to the complexity of molecular biology and human physiology. Over the last 30 years, molecular-modelling tools have gradually gained a degree of acceptance in the pharmaceutical industry. Drug discovery has begun to benefit from physics-based simulations. While such simulations have great potential for improved molecular design, much scepticism remains about their value. The motivations for such reservations in industry and areas where simulations show promise for efficiency gains in preclinical research are discussed. In this, the first of two complementary papers, the scientific and technical progress that needs to be made to improve the predictive power of biomolecular simulations, and how this might be achieved, is firstly discussed (Part 1). In Part 2, the status of computer simulations in pharma is contrasted with aerodynamics modelling and weather forecasting, and comments are made on the cultural changes needed for equivalent computational technologies to become integrated into life-science industries.

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.

Role of Permeability on the Biopredictive Dissolution of Amorphous Solid Dispersions

An ideal dissolution test for amorphous solid dispersions (ASDs) should reflect physicochemical, physiological, and hydrodynamic conditions which accurately represent in vivo dissolution. However, this is confounded by the evolution of different molecular and colloidal species during dissolution, generating a supersaturated state of the drug. The supersaturated state of a drug is thermodynamically unstable which drives the process of precipitation resulting in a loss of solubility advantage. Maintaining a supersaturated state of the drug with the help of precipitation inhibiting excipients is a key component in the design of ASDs. Therefore, a biopredictive dissolution test is critical for proper risk assessment during the development of an optimal ASD formulation. One of the overlooked components of biopredictive dissolution is the role of drug permeability. The kinetic changes in the phase behavior of a drug during dissolution of ASDs are influenced by drug permeability across a membrane. Conventionally, drug dissolution and permeation are analyzed separately although they occur simultaneously in vivo. The kinetic phase changes occurring during dissolution of ASDs can influence the thermodynamic activity and membrane flux of a drug. The present review evaluates the feasibility, predictability, and practicability of permeability/dissolution for the optimal development and risk assessment of ASD formulations.

Molecular dynamics simulation for membrane separation and porous materials: A current state of art review

Computational frameworks have been under specific attention within the last two decades. Molecular Dynamics (MD) simulations, identical to the other computational approaches, try to address the unknown question, lighten the dark areas of unanswered questions, to achieve probable explanations and solutions. Owing to their complex microporous structure on one side and the intricate biochemical nature of various materials used in the structure, separative membrane materials possess peculiar degrees of complications. More notably, as nanocomposite materials are often integrated into separative membranes, thin-film nanocomposites and porous separative nanocomposite materials could possess an additional level of complexity with regard to the nanoscale interactions brought to the structure. This critical review intends to cover the recent methods used to assess membranes and membrane materials. Incorporation of MD in membrane technology-related fields such as desalination, fuel cell-based energy production, blood purification through hemodialysis, etc., were briefly covered. Accordingly, this review could be used to understand the current extent of MD applications for separative membranes. The review could also be used as a guideline to use the proper MD implementation within the related fields.

Effect of paracellular permeation enhancers on intestinal permeability of two peptide drugs, enalaprilat and hexarelin, in rats

Transcellular permeation enhancers are known to increase the intestinal permeability of enalaprilat, a 349 Da peptide, but not hexarelin (887 Da). The primary aim of this paper was to investigate if paracellular permeability enhancers affected the intestinal permeation of the two peptides. This was investigated using the rat single-pass intestinal perfusion model with concomitant blood sampling. These luminal compositions included two paracellular permeation enhancers, chitosan (5 mg/mL) and ethylenediaminetetraacetate (EDTA, 1 and 5 mg/mL), as well as low luminal tonicity (100 mOsm) with or without lidocaine. Effects were evaluated by the change in lumen-to-blood permeability of hexarelin and enalaprilat, and the blood-to-lumen clearance of 51chromium-labeled EDTA (CLCr-EDTA), a clinical marker for mucosal barrier integrity. The two paracellular permeation enhancers increased the mucosal permeability of both peptide drugs to a similar extent. The data in this study suggests that the potential for paracellular permeability enhancers to increase intestinal absorption of hydrophilic peptides with low molecular mass is greater than for those with transcellular mechanism-of-action. Further, the mucosal blood-to-lumen flux of 51Cr-EDTA was increased by the two paracellular permeation enhancers and by luminal hypotonicity. In contrast, luminal hypotonicity did not affect the lumen-to-blood transport of enalaprilat and hexarelin. This suggests that hypotonicity affects paracellular solute transport primarily in the mucosal crypt region, as this area is protected from luminal contents by a constant water flow from the crypts.

The Whole Is Bigger than the Sum of Its Parts: Drug Transport in the Context of Two Membranes with Active Efflux

Cell envelope plays a dual role in the life of bacteria by simultaneously protecting it from a hostile environment and facilitating access to beneficial molecules. At the heart of this ability lie the restrictive properties of the cellular membrane augmented by efflux transporters, which preclude intracellular penetration of most molecules except with the help of specialized uptake mediators. Recently, kinetic properties of the cell envelope came into focus driven on one hand by the urgent need in new antibiotics and, on the other hand, by experimental and theoretical advances in studies of transmembrane transport. A notable result from these studies is the development of a kinetic formalism that integrates the Michaelis-Menten behavior of individual transporters with transmembrane diffusion and offers a quantitative basis for the analysis of intracellular penetration of bioactive compounds. This review surveys key experimental and computational approaches to the investigation of transport by individual translocators and in whole cells, summarizes key findings from these studies and outlines implications for antibiotic discovery. Special emphasis is placed on Gram-negative bacteria, whose envelope contains two separate membranes. This feature sets these organisms apart from Gram-positive bacteria and eukaryotic cells by providing them with full benefits of the synergy between slow transmembrane diffusion and active efflux.

Functional Group Distributions, Partition Coefficients, and Resistance Factors in Lipid Bilayers Using Site Identification by Ligand Competitive Saturation

Small molecules such as metabolites and drugs must pass through the membrane of the cell, a barrier primarily comprising phospholipid bilayers and embedded proteins. To better understand the process of passive diffusion, knowledge of the ability of various functional groups to partition across bilayers and the associated energetics would be of utility. In the present study, the site identification by ligand competitive saturation (SILCS) methodology has been applied to sample the distributions of a diverse set of chemical solutes representing the functional groups of small molecules across phospholipid bilayers composed of 0.9:0.1 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine/cholesterol and a mixture of 0.52:0.18:0.3 1,2-dioleoyl-sn-glycero-3-phospho-l-serine/1,2-dioleoyl-sn-glycero-3-phosphocholine/cholesterol used in parallel artificial membrane permeability assay experiments. A combination of oscillating chemical potential grand canonical Monte Carlo and molecular dynamics in the SILCS simulations was applied to achieve solute sampling through the bilayers and surrounding aqueous environment from which the distribution of solutes and the functional groups they represent were obtained. Results show differential distribution of aliphatic versus aromatic groups with the former having increased sampling in the center of the bilayers versus in the region of the glycerol linker for the latter. Variations in the distribution of different polar groups are evident, with large differences between negative acetate and positive methylammonium with accumulation of the polar-neutral and acetate solutes above the bilayer head groups. Conversion of the distributions to absolute free energies allows for a detailed understanding of energetics of functional groups in different regions of the bilayers and for calculation of absolute free-energy profiles of multifunctional drug-like molecules across the bilayers from which partition coefficients and resistance factors suitable for insertion into the homogenous solubility-diffusion equation for calculation of permeability were obtained. Comparisons of the calculated bilayer/solution partition coefficients with 1-octanol/water experimental data for both drug-like molecules and the solutes show overall good agreement, validating the calculated distributions and associated absolute free-energy profiles.

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.

Boundary conditions at a thin membrane for the normal diffusion equation which generate subdiffusion

We consider a particle transport process in a one-dimensional system with a thin membrane, described by the normal diffusion equation. We consider two boundary conditions at the membrane that are linear combinations of integral operators, with time-dependent kernels, which act on the functions and their spatial derivatives defined on both membrane surfaces. We show how boundary conditions at the membrane change the temporal evolution of the first and second moments of particle position distribution (the Green's function) which is a solution to the normal diffusion equation. As these moments define the kind of diffusion, an appropriate choice of boundary conditions generates the moments characteristic for subdiffusion. The interpretation of the process is based on a particle random walk model in which the subdiffusion effect is caused by anomalously long stays of the particle in the membrane.

Molecular Study of Ultrasound-Triggered Release of Fluorescein from Liposomes

Several investigations have suggested that ultrasound triggers the release of drugs encapsulated into liposomes at acoustic pressures low enough to avoid cavitation or high hyperthermia. However, the mechanism leading to this triggered release as well as the adequate composition of the liposome membrane remains unknown. Here, we investigate the ultrasound-triggered release of fluorescein disodium salt encapsulated into liposomes made of 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) or 1,2-distearoylphosphatidyl-ethanolamine (DSPC) lipids with various concentrations of cholesterol (from 0 to 44 mol %). The passive release of encapsulated fluorescein was first characterized. It was observed to be higher when the membrane is in a fluid phase and increased with temperature but decreased upon addition of cholesterol. Next, the release of fluorescein was measured at different acoustic frequencies (0.8, 1.1, and 3.3 MHz) and peak-to-peak pressures (0, 2, 2.5, 5, and 8 MPa). Measurements were performed at temperatures where DOPC and DSPC liposomes were, respectively, in the fluid or gel phase. We found that the release rate did not depend on the ultrasound frequency. For DOPC liposomes, the ultrasound-triggered release of fluorescein decreased with increasing concentration of cholesterol in liposomes, while the behavior was more complex for DSPC liposomes. Overall, the triggered release from DSPC liposomes was up to ten times less than DOPC liposomes. Molecular dynamics simulations performed on a pure DOPC membrane showed that a membrane experiences, under a directional pressure of ±2.4 MPa, various changes in properties such as the area per lipid (APL). An increase in the APL was notably observed when the simulation box was laterally stretched or perpendicularly compressed, which was accompanied by an increase in the number of water molecules crossing the membrane. This suggests that ultrasound most probably enhances the diffusion of encapsulated molecules at small acoustic pressures by increasing the distance between lipids.

Molecular simulations of lipid membrane partitioning and translocation by bacterial quorum sensing modulators

Quorum sensing (QS) is a bacterial communication process mediated by both native and non-native small-molecule quorum sensing modulators (QSMs), many of which have been synthesized to disrupt QS pathways. While structure-activity relationships have been developed to relate QSM structure to the activation or inhibition of QS receptors, less is known about the transport mechanisms that enable QSMs to cross the lipid membrane and access intracellular receptors. In this study, we used atomistic MD simulations and an implicit solvent model, called COSMOmic, to analyze the partitioning and translocation of QSMs across lipid bilayers. We performed umbrella sampling at atomistic resolution to calculate partitioning and translocation free energies for a set of naturally occurring QSMs, then used COSMOmic to screen the water-membrane partition and translocation free energies for 50 native and non-native QSMs that target LasR, one of the LuxR family of quorum-sensing receptors. This screening procedure revealed the influence of systematic changes to head and tail group structures on membrane partitioning and translocation free energies at a significantly reduced computational cost compared to atomistic MD simulations. Comparisons with previously determined QSM activities suggest that QSMs that are least likely to partition into the bilayer are also less active. This work thus demonstrates the ability of the computational protocol to interrogate QSM-bilayer interactions which may help guide the design of new QSMs with engineered membrane interactions.

Comparison of umbrella sampling and steered molecular dynamics methods for computing free energy profiles of aromatic substrates through phospholipid bilayers

Understanding the permeation of molecules through lipid membranes is fundamental for predicting the cellular uptake of solutes and drug delivery mechanisms. In molecular simulations, the usual approach is to compute the free energy (FE) profile of a molecule across a model lipid bilayer, which can then be used to estimate the permeability of the molecule. Umbrella Sampling (US), which involves carrying out a series of biased simulations along a defined reaction coordinate (usually the bilayer normal direction), is a popular method for the computation of such FE profiles. However, US can be challenging to implement because the results are dependent on the strength of the biasing potential and the spacing of windows along the reaction coordinate, which, in practice, are usually optimized by an inefficient trial and error approach. The Steered Molecular Dynamics implementation of the Jarzynski Equality (JE-SMD) has been identified as an alternative to equilibrium sampling methods for measuring the FE change across a reaction coordinate. In the JE-SMD approach, equilibrium FE values are evaluated from the average of rapid non-equilibrium trajectories, thus avoiding the practical issues that come with US. Here, we use three different corrections of the JE-SMD method to calculate the FE change for the translocation of two aromatic substrates, phenylalanine and toluene, across a lipid bilayer and compare the accuracy and computational efficiency of these approaches to the results obtained using US. We show evidence that when computing the free energy profile, the JE-SMD approach suffers from insufficient sampling convergence of the bilayer environment and is dependent on the characteristic of the aromatic substrate itself. We deduce that, despite its drawbacks, US remains the more viable approach of the two for computing the FE profile.

In Silico Prediction of Permeability Coefficients

In silico simulations of biological systems are of the significant importance to obtain insights on specific processes that experimental protocols have difficulty to elucidate. More particularly, and to ensure that a given molecule is able to reach its cellular target, the development of computational methods able to quickly estimate the cellular permeabilities for small molecules can become an important tool in the early stages of drug development. Herein, a computational protocol for predicting permeability coefficients, concerning both membranes and proteins, is presented and discussed.

Molecular Dynamics Simulations in Drug Discovery and Pharmaceutical Development

Molecular dynamics (MD) simulations have become increasingly useful in the modern drug development process. In this review, we give a broad overview of the current application possibilities of MD in drug discovery and pharmaceutical development. Starting from the target validation step of the drug development process, we give several examples of how MD studies can give important insights into the dynamics and function of identified drug targets such as sirtuins, RAS proteins, or intrinsically disordered proteins. The role of MD in antibody design is also reviewed. In the lead discovery and lead optimization phases, MD facilitates the evaluation of the binding energetics and kinetics of the ligand-receptor interactions, therefore guiding the choice of the best candidate molecules for further development. The importance of considering the biological lipid bilayer environment in the MD simulations of membrane proteins is also discussed, using G-protein coupled receptors and ion channels as well as the drug-metabolizing cytochrome P450 enzymes as relevant examples. Lastly, we discuss the emerging role of MD simulations in facilitating the pharmaceutical formulation development of drugs and candidate drugs. Specifically, we look at how MD can be used in studying the crystalline and amorphous solids, the stability of amorphous drug or drug-polymer formulations, and drug solubility. Moreover, since nanoparticle drug formulations are of great interest in the field of drug delivery research, different applications of nano-particle simulations are also briefly summarized using multiple recent studies as examples. In the future, the role of MD simulations in facilitating the drug development process is likely to grow substantially with the increasing computer power and advancements in the development of force fields and enhanced MD methodologies.

Thermodynamics and Mechanism of the Membrane Permeation of Hv1 Channel Blockers

The voltage-gated proton channel Hv1 mediates efflux of protons from the cell. Hv1 integrally contributes to various physiological processes including pH homeostasis and the respiratory burst of phagocytes. Inhibition of Hv1 may provide therapeutic avenues for the treatment of inflammatory diseases, breast cancer, and ischemic brain damage. In this work, we investigate two prototypical Hv1 inhibitors, 2-guanidinobenzimidazole (2GBI), and 5-chloro-2-guanidinobenzimidazole (GBIC), from an experimentally screened class of guanidine derivatives. Both compounds block proton conduction by binding the same site located on the intracellular side of the channel. However, when added to the extracellular medium, the compounds strongly differ in their ability to inhibit proton conduction, suggesting substantial differences in membrane permeability. Here, we compute the potential of mean force for each compound to permeate through the membrane using atomistic molecular dynamics simulations with the adaptive biasing force method. Our results rationalize the putative distinction between these two blockers with respect to their abilities to permeate the cellular membrane.

Anesthetics significantly increase the amount of intramembrane water in lipid membranes

The potency of anesthesia was directly linked to the partitioning of the drug molecules in cell membranes by Meyer and Overton. Many molecules interact with lipid bilayers and lead to structural and functional changes. It remains an open question which change in membrane properties is responsible for a potential anesthetic effect or if anesthetics act by binding to direct targets. We studied the effect of ethanol, diethyl ether and isoflurane on the water distribution in lipid bilayers by combining all-atom molecular dynamics simulations and neutron diffraction experiments. The simulations show strong membrane-drug interactions with partitioning coefficients of 38%, 92% and 100% for ethanol, diethyl ether and isoflurane, respectively, and provide evidence for an increased water partitioning in the membrane core. The amount of intramembrane water molecules was experimentally determined by selectively deuterium labeling lipids, anesthetic drug and water molecules in neutron diffraction experiments. Four additional water molecules per lipid were observed in the presence of ethanol. Diethyl ether and isoflurane were found to significantly increase the amount of intramembrane water by 25% (8 water molecules). This increase in intramembrane water may contribute to the non-specific interactions between anesthetics and lipid membranes.

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

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

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.

Update of the CHARMM36 United Atom Chain Model for Hydrocarbons and Phospholipids

Accurate lipid force field (FF) parameters used in molecular dynamics (MD) simulations are crucial for understanding the properties of lipid-containing systems and biological processes related to lipids. The last update of the CHARMM36 united atom chain model (C36UA) was in 2013 [Lee, S. J. Phys. Chem. B 2014, 118, 547 556]; it utilized CHARMM36 (C36) lipid FF parameters for headgroups and OPLS-UA Lennard-Jones (LJ) parameters for tails. Simulations with the FF were able to reproduce many experimental observables of lipid bilayers accurately, but to be more applicable for a wide range of lipids, additional FF parameter optimization was needed. In this work, we present an update of the model, named C36UAr. The parameterization included the LJ parameters for hydrocarbons and related dihedrals. Bulk liquid properties (density, heat of vaporization, isothermal compressibility, and diffusion constant) of model compounds were used as targets for the LJ parameter fitting, and dihedrals were fit to either quantum mechanical (QM) or potential of mean force (PMF) calculations using C36. Thermodynamic reweighting was used to further improve the parameters. Bilayer simulations of various lipid headgroups (phosphatidylcholine, phosphatidylethanolamine, and phosphatidylglycerol) and tails (saturated, monounsaturated, and polyunsaturated) were performed to validate the model, and significant improvements were seen in bilayer properties, including surface area, membrane thicknesses, NMR deuterium order parameters, and density profiles. C36UAr was also compared to the hydrogen mass repartitioning (HMR) method. The high accuracy and competitive efficiency shown in this study make C36UAr one of the best choices for studies of membrane structure and membrane-associated proteins.

New Molecular-Mechanics Model for Simulations of Hydrogen Fluoride in Chemistry and Biology

Hydrogen fluoride (HF) is the most polar diatomic molecule and one of the simplest molecules capable of hydrogen-bonding. HF deviates from ideality both in the gas phase and in solution and is thus of great interest from a fundamental standpoint. Pure and aqueous HF solutions are broadly used in chemical and industrial processes, despite their high toxicity. HF is a stable species also in some biological conditions, because it does not readily dissociate in water unlike other hydrogen halides; yet, little is known about how HF interacts with biomolecules. Here, we set out to develop a molecular-mechanics model to enable computer simulations of HF in chemical and biological applications. This model is based on a comprehensive high-level ab initio quantum chemical investigation of the structure and energetics of the HF monomer and dimer; (HF)_n clusters, for n = 3-7; various clusters of HF and H₂O; and complexes of HF with analogs of all 20 amino acids and of several commonly occurring lipids, both neutral and ionized. This systematic analysis explains the unique properties of this molecule: for example, that interacting HF molecules favor nonlinear geometries despite being diatomic and that HF is a strong H-bond donor but a poor acceptor. The ab initio data also enables us to calibrate a three-site molecular-mechanics model, with which we investigate the structure and thermodynamic properties of gaseous, liquid, and supercritical HF in a wide range of temperatures and pressures; the solvation structure of HF in water and of H₂O in liquid HF; and the free diffusion of HF across a lipid bilayer, a key process underlying the high cytotoxicity of HF. Despite its inherent simplifications, the model presented significantly improves upon previous efforts to capture the properties of pure and aqueous HF fluids by molecular-mechanics methods and to our knowledge constitutes the first parameter set calibrated for biomolecular simulations.

Model-Informed Drug Discovery and Development Strategy for the Rapid Development of Anti-Tuberculosis Drug Combinations

The increasing emergence of drug-resistant tuberculosis requires new effective and safe drug regimens. However, drug discovery and development are challenging, lengthy and costly. The framework of model-informed drug discovery and development (MID3) is proposed to be applied throughout the preclinical to clinical phases to provide an informative prediction of drug exposure and efficacy in humans in order to select novel anti-tuberculosis drug combinations. The MID3 includes pharmacokinetic-pharmacodynamic and quantitative systems pharmacology models, machine learning and artificial intelligence, which integrates all the available knowledge related to disease and the compounds. A translational in vitro-in vivo link throughout modeling and simulation is crucial to optimize the selection of regimens with the highest probability of receiving approval from regulatory authorities. In vitro-in vivo correlation (IVIVC) and physiologically-based pharmacokinetic modeling provide powerful tools to predict pharmacokinetic drug-drug interactions based on preclinical information. Mechanistic or semi-mechanistic pharmacokinetic-pharmacodynamic models have been successfully applied to predict the clinical exposure-response profile for anti-tuberculosis drugs using preclinical data. Potential pharmacodynamic drug-drug interactions can be predicted from in vitro data through IVIVC and pharmacokinetic-pharmacodynamic modeling accounting for translational factors. It is essential for academic and industrial drug developers to collaborate across disciplines to realize the huge potential of MID3.

Liposomal membrane permeability assessment by fluorescence techniques: Main permeabilizing agents, applications and challenges

Liposomes are lipid vesicles made of one or multiple lipid bilayers surrounding an internal aqueous core. They are broadly employed as models to study membrane structure and properties. Among these properties, liposome membrane permeability is crucial and widely assessed by fluorescence techniques. The first part of this review is devoted to describe the various techniques used for membrane permeability assessment. Attention is paid to fluorescence techniques based on vesicle leakage of self-quenching probes, dye/quencher pair or cation/ligand pair. Secondly, the membrane-active agents inducing membrane permeabilization is presented and details on their mechanisms of action are given. Emphasis is also laid on the intrinsic and extrinsic factors that can modulate the membrane permeability. Hence, a suitable liposomal membrane should be formulated according to the aim of the study and its application.

The In Vivo Effect of Transcellular Permeation Enhancers on the Intestinal Permeability of Two Peptide Drugs Enalaprilat and Hexarelin

Permeation enhancers like sodium dodecyl sulfate (SDS) and caprate increase the intestinal permeability of small model peptide compounds, such as enalaprilat (349 Da). However, their effects remain to be investigated for larger low-permeability peptide drugs, such as hexarelin (887 Da). The objective of this single-pass perfusion study in rat was to investigate the effect of SDS at 5 mg/mL and of caprate administered at different luminal concentrations (5, 10, and 20 mg/mL) and pH (6.5 and 7.4). The small intestinal permeability of enalaprilat increased by 8- and 9-fold with SDS at 5 mg/mL and with caprate at 10 and 20 mg/mL but only at pH 7.4, where the free dissolved caprate concentration is higher than at pH 6.5 (5 vs. 2 mg/mL). Neither SDS nor caprate at any of the investigated luminal concentrations enhanced absorption of the larger peptide hexarelin. These results show that caprate requires doses above its saturation concentration (a reservoir suspension) to enhance absorption, most likely because dissolved caprate itself is rapidly absorbed. The absent effect on hexarelin may partly explain why the use of permeation enhancers for enabling oral peptide delivery has largely failed to evolve from in vitro evaluations into approved oral products. It is obvious that more innovative and effective drug delivery strategies are needed for this class of drugs.

Translocation of a hydroxyl functionalized carbon dot across a lipid bilayer: an all-atom molecular dynamics simulation study

Passive permeation of CD across lipid bilayer is almost impossible. Forced permeation results membrane rupture.