Predicting solute partitioning in lipid bilayers: Free energies and partition coefficients from molecular dynamics simulations and COSMOmic

Explicit Configurational Entropy of Mixing in Molecular Dynamics Simulations

The entropy of mixing of a multicomponent system of particles is a simple expression of the molar fractions for the equilibrium state, but its intermediate values for transient (nonequilibrium) states can not be calculated directly from the particle coordinates so far. We propose a simple expression for the configurational entropy of mixing based solely on the set of instantaneous coordinates, which is suitable for the on-the-fly determination of the degree of mixing along a molecular dynamics trajectory. We illustrate the applicability of our scheme with the example of several molecular mixtures that exhibit fast and slow mixing and demixing processes within a molecular dynamics simulation.

Protonation State of a Bioactive Compound Regulates Its Release from Lamellar Gel-Phase Bilayers

Lamellar gel networks (LGNs) in personal care or pharmaceutical lotions and creams provide an opaque cream appearance and a creamy texture to these products. Within the LGNs, the lamellar gel (Lβ) phase composed of regularly spaced bilayers of surfactants and long-chain fatty alcohols is predominately responsible for the unique rheological properties of the LGNs. To extend the shelf life of LGN-containing products, bioactive compounds with antimicrobial properties are often incorporated into the formulation. However, how the protonation state of the bioactive compounds regulates their release from the Lβ-phase bilayers is currently unknown. Using molecular dynamics simulations, we found that the protonated (neutral) form of cinnamic acid, a common antimicrobial food additive, has a retention ratio higher than that of its deprotonated (charged) counterpart in the Lβ-phase bilayer. From free energy calculations, we determined that not only is the protonated molecule more stable in the hydrophobic interior of the bilayer but also the formation of hydrogen-bonded dimers significantly enhances its stability within the bilayer. Thus, the protonation state has a profound impact on bioavailability of the compounds. Our results also highlight the importance of considering possible oligomeric states of molecules when performing calculations to estimate the permeability of molecules within various bilayers.

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.

Partitioning into phosphatidylcholine-cholesterol membranes: liposome measurements, coarse-grained simulations, and implications for bioaccumulation

Membrane-water partitioning is an important physical property for the assessment of bioaccumulation and environmental impact. Here, we advance simulation methodology for predicting the partitioning of small molecules into lipid membranes and compare the computational predictions to experimental measurements in liposomes. As a step towards high-throughput screening, we present an automated mapping and parametrization procedure to produce coarse-grained models compatible with the Martini 3 force field. The methodology is general and can also be used for other applications where coarse-grained simulations are appropriate. This article addresses the effect on membrane-water partitioning of adding cholesterol to POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine) membranes. Nine contrasting neutral, zwitterionic and charged solutes are tested. Agreement between experiment and simulation is generally good, with the most challenging cases being permanently charged solutes. For all solutes, partitioning is found to be insensitive to membrane cholesterol concentration up to 25% mole fraction. Hence, for assessment of bioaccumulation into a range of membranes (such as those found in fish), partitioning data measured in pure lipid membranes are still informative.

Partitioning of Antioxidants in Edible Oil-Water Binary Systems and in Oil-in-Water Emulsions

In recent years, partitioning of antioxidants in oil-water two-phase systems has received great interest because of their potential in the downstream processing of biomolecules, their benefits in health, and because partition constant values between water and model organic solvents are closely related to important biological and pharmaceutical properties such as bioavailability, passive transport, membrane permeability, and metabolism. Partitioning is also of general interest in the oil industry. Edible oils such as olive oil contain a variety of bioactive components that, depending on their partition constants, end up in an aqueous phase when extracted from olive fruits. Frequently, waste waters are subsequently discarded, but their recovery would allow for obtaining extracts with antioxidant and/or biological activities, adding commercial value to the wastes and, at the same time, would allow for minimizing environmental risks. Thus, given the importance of partitioning antioxidants, in this manuscript, we review the background theory necessary to derive the relevant equations necessary to describe, quantitatively, the partitioning of antioxidants (and, in general, other drugs) and the common methods for determining their partition constants in both binary (PWOIL) and multiphasic systems composed with edible oils. We also include some discussion on the usefulness (or not) of extrapolating the widely employed octanol-water partition constant (PWOCT) values to predict PWOIL values as well as on the effects of acidity and temperature on their distributions. Finally, there is a brief section discussing the importance of partitioning in lipidic oil-in-water emulsions, where two partition constants, that between the oil-interfacial, POI, and that between aqueous-interfacial, PwI, regions, which are needed to describe the partitioning of antioxidants, and whose values cannot be predicted from the PWOIL or the PWOCT ones.

Using membrane-water partition coefficients in a critical membrane burden approach to aid the identification of neutral and ionizable chemicals that induce acute toxicity below narcosis levels

The risk assessment of thousands of chemicals used in our society benefits from adequate grouping of chemicals based on the mode and mechanism of toxic action (MoA). We measure the phospholipid membrane-water distribution ratio (D_MLW) using a chromatographic assay (IAM-HPLC) for 121 neutral and ionized organic chemicals and screen other methods to derive D_MLW. We use IAM-HPLC based D_MLW as a chemical property to distinguish between baseline narcosis and specific MoA, for reported acute toxicity endpoints on two separate sets of chemicals. The first set comprised 94 chemicals of US EPA's acute fish toxicity database: 47 categorized as narcosis MoA, 27 with specific MoA, and 20 predominantly ionic chemicals with mostly unknown MoA. The narcosis MoA chemicals clustered around the median narcosis critical membrane burden (CMB_narc) of 140 mmol kg^-1 lipid, with a lower limit of 14 mmol kg^-1 lipid, including all chemicals labelled Narcosis_I and Narcosis_II. This maximum 'toxic ratio' (TR) between CMB_narc and the lower limit narcosis endpoint is thus 10. For 23/28 specific MoA chemicals a TR >10 was derived, indicative of a specific adverse effect pathway related to acute toxicity. For 10/12 cations categorized as "unsure amines", the TR <10 suggests that these affect fish via narcosis MoA. The second set comprised 29 herbicides, including 17 dissociated acids, and evaluated the TR for acute toxic effect concentrations to likely sensitive aquatic plant species (green algae and macrophytes Lemna and Myriophyllum), and non-target animal species (invertebrates and fish). For 21/29 herbicides, a TR >10 indicated a specific toxic mode of action other than narcosis for at least one of these aquatic primary producers. Fish and invertebrate TRs were mostly <10, particularly for neutral herbicides, but for acidic herbicides a TR >10 indicated specific adverse effects in non-target animals. The established critical membrane approach to derive the TR provides for useful contribution to the weight of evidence to bin a chemical as having a narcosis MoA or less likely to have acute toxicity caused by a more specific adverse effect pathway. After proper calibration, the chromatographic assay provides consistent and efficient experimental input for both neutral and ionizable chemicals to this approach.

In Silico Prediction of Stratum Corneum Partition Coefficients via COSMOmic and Molecular Dynamics Simulations

Stratum corneum (SC) is the main barrier of human skin where the inter-corneocytes lipids provide the main pathway for transdermal permeation of functional actives of skin care and health. Molecular dynamics (MD) has been increasingly used to simulate the SC lipid bilayer structure so that the barrier property and its affecting factors can be elucidated. Among reported MD simulation studies, solute partition in the SC lipids, an important parameter affecting SC permeability, has received limited attention. In this work, we combine MD simulation with COSMOmic to predict the partition coefficients of dermatologically relevant solutes in SC lipid bilayer. Firstly, we run MD simulations to obtain equilibrated SC lipid bilayers with different lipid types, compositions, and structures. Then, the simulated SC lipid bilayer structures are fed to COSMOmic to calculate the partition coefficients of the solutes. The results show that lipid types and bilayer geometries play a minor role in the predicted partition coefficients. For the more lipophilic solutes, the predicted results of solute partition in SC lipid bilayers agree well with reported experimental values of solute partition in extracted SC lipids. For the more hydrophilic molecules, there is a systematical underprediction. Nevertheless, the MD/COSMOmic approach correctly reproduces the phenomenological correlation between the SC lipid/water partition coefficients and the octanol/water partition coefficients. Overall, the results show that the MD/COSMOmic approach is a fast and valid method for predicting solute partitioning into SC lipids and hence supporting the assessment of percutaneous absorption of skin care ingredients, dermatological drugs as well as environmental pollutants.

Partition of the Reactive Species of the Suzuki-Miyaura Reaction between Aqueous and Micellar Environments

The Suzuki-Miyaura reaction between the aryl halide (1) and the phenyl boronic acid (2), in the presence of the palladium(0) complex (3) as catalyst, gives the cross-coupling product (4) in quantitative yield when performed in basic aqueous solution of the nonionic surfactant Kolliphor-EL (K-EL). The partition between the aqueous and micellar environments of the species of this reaction has been investigated by means of Molecular Dynamics (MD) simulations. Starting from the K-EL molecules dispersed in water, a micelle model has been generated by MD simulations, adopting the 2016H66 force field. Reagent and product species have been described with the same force field, once the reliability of this force field has been tested comparing the n-octanol/water partition free energies calculated from the MD and Free Energy Perturbation (FEP) method with those obtained from the quantum-mechanical SMD method. The potential of mean force for the transfer process between water and the micellar phase of the different species has been calculated by the MD simulations and the Umbrella Sampling (US) method. The overall picture that emerges from these results confirms that the molecular species involved in this reaction prefers the micellar environment and concentrates in different but close zones of the micelle. This supports the experimental evidence that the use of suitable surfactant agents promotes reactivity, allowing micelles to behave as nanoreactors in which reactive species are solubilized and enhance their local concentration.

Charged Small Molecule Binding to Membranes in MD Simulations Evaluated against NMR Experiments

Interactions of charged molecules with biomembranes regulate many of their biological activities, but their binding affinities to lipid bilayers are difficult to measure experimentally and model theoretically. Classical molecular dynamics (MD) simulations have the potential to capture the complex interactions determining how charged biomolecules interact with membranes, but systematic overbinding of sodium and calcium cations in standard MD simulations raises the question of how accurately force fields capture the interactions between lipid membranes and charged biomolecules. Here, we evaluate the binding of positively charged small molecules, etidocaine, and tetraphenylphosphonium to a phosphatidylcholine (POPC) lipid bilayer using the changes in lipid head-group order parameters. We observed that these molecules behave oppositely to calcium and sodium ions when binding to membranes: (i) their binding affinities are not overestimated by standard force field parameters, (ii) implicit inclusion of electronic polarizability increases their binding affinity, and (iii) they penetrate into the hydrophobic membrane core. Our results can be explained by distinct binding mechanisms of charged small molecules with hydrophobic moieties and monoatomic ions. The binding of the former is driven by hydrophobic effects, while the latter has direct electrostatic interactions with lipids. In addition to elucidating how different kinds of charged biomolecules bind to membranes, we deliver tools for further development of MD simulation parameters and methodology.

Advances in the control of lipid peroxidation in oil-in-water emulsions: kinetic approaches†

Large efforts have been, and still are, devoted to minimize the harmful effects of lipid peroxidation. Much of the early work focused in understanding both the lipid oxidation mechanisms and the action of antioxidants in bulk solution. However, food-grade oils are mostly present in the form of oil-in-water emulsions, bringing up an increasing complexity because of the three-dimensional interfacial region. This review presents an overview of the kinetic approaches employed in controlling the oxidative stability of edible oil-in-water emulsions and of the main outcomes, with particular emphasis on the role of antioxidants and on the kinetics of the inhibition reaction. Application of physical-organic chemistry methods, such as the pseudophase models to investigate antioxidant partitioning, constitute a remarkable example on how kinetic methodologies contribute to model chemical reactivity in multiphasic systems and to rationalize the role of interfaces, opening new opportunities for designing novel antioxidants with tailored properties and new prospects for modulating environmental conditions in attempting to optimize their efficiency. Here we will summarize the main kinetic features of the inhibition reaction and will discuss on the main factors affecting its rate, including the determination of antioxidant efficiencies from kinetic profiles, structure-reactivity relationships, partitioning of antioxidants and concentration effects.

The effects of molecular weight and orientation on the membrane permeation and partitioning of polycyclic aromatic hydrocarbons: a computational study

Membrane permeation and the partitioning of polycyclic aromatic hydrocarbons (PAHs) are crucial aspects affecting their carcinogenicity and mutagenicity. However, a clear understanding of these processes is still rare due to the difficulty of determining the details experimentally. Here, the interactions between PAHs and lipid bilayers were studied by molecular simulations, mainly to check the influence of molecular weight and orientation. The liposome-water partition coefficient (K_LW), transmembrane time (τ), and permeability coefficient (P) of the PAHs were calculated by integrating free energy profiles from umbrella sampling. For selected PAHs, the membrane adsorption is a spontaneous process. The preferred location is near the CC bond and the orientation is related to the molecular structure. The P values of all the PAHs are basically the same order of magnitude, which means that the molecular weight contributes little to the process. As for K_LW and τ, they show obvious increases with different molecular weights. Unconstrained simulations showed that a flat orientation on the membrane surface would prevent PAHs from being transported through the membrane. Highly hydrophobic driving forces are not always good for the absorption of PAHs, especially the formation of aggregates. In addition, the orientations and energetic barriers of PAHs near the midplane of the lipid bilayer explain the different transitions of high- and low-weight PAHs. This work provides molecular level details relating to the interactions of PAHs with lipid membranes, with significance for understanding the health effects of PAHs.

Concentration of Antioxidant Compounds from Calendula officinalis through Sustainable Supercritical Technologies, and Computational Study of Their Permeability in Skin for Cosmetic Use

The growing interest in the cosmetic industry in using compounds of natural and sustainable origin that are safe for humans is encouraging the development of processes that can satisfy these needs. Chlorogenic acid (CHA), caffeic acid (CAF) and ferulic acid (FA) are three compounds widely used within the cosmetic industry due to their functionalities as antioxidants, collagen modifiers or even as radiation protectors. In this work, two advanced separation techniques with supercritical CO2 are used to obtain these three compounds from Calendula officinalis, and these are then evaluated using a computational skin permeability model. This model is encompassed by the COSMO-RS model, the calculations of which make it possible to study the behaviour of the compounds in the epidermis. The results show that both CAF and FA are retained in the stratum corneum, while CHA manages to penetrate to the stratum spinosum. These compounds were concentrated by antisolvent fractionation with super-critical CO2 using a Response Surface Methodology to study the effect of pressure and CO2 flow rate. CHA, CAF and FA were completely retained in the precipitation vessel, with concentrations between 40% and 70% greater than in the original extract. The conditions predicted that the optimal overall yield and enrichment achieved would be 153 bar and 42 g/min.

Molecular Dynamics Simulations and Experimental Results Provide Insight into Clinical Performance Differences between Sandimmune® and Neoral® Lipid-Based Formulations

OBJECTIVE

Molecular dynamics (MD) simulations provide an in silico method to study the structure of lipid-based formulations (LBFs) and the incorporation of poorly water-soluble drugs within such formulations. In order to validate the ability of MD to effectively model the properties of LBFs, this work investigates the well-known cyclosporine A formulations, Sandimmune® and Neoral®. Sandimmune® exhibits poor dispersibility and its absorption from the gastrointestinal tract is enhanced when administered after food, whereas Neoral® disperses comparatively well and shows no food effect.

METHODS

MD simulations were performed of both LBFs to investigate the differences observed in fasted and fed conditions. These conditions were also tested using an in vitro experimental model of dispersion and digestion.

RESULTS

These MD simulations were able to show that the food effect observed for Sandimmune® can be explained by large changes in drug solubilization on addition of bile. In contrast, Neoral® is well dispersed in water or in simulated fasted conditions, and this dispersion is relatively unchanged on moving to fed conditions. These differences were confirmed using dispersion and digestion in vitro experimental model.

CONCLUSIONS

The current data suggests that MD simulations are a potential method to model the fate of LBFs in the gastrointestinal tract, predict their dispersion and digestion, investigate behaviour of APIs within the formulations, and provide insights into the clinical performance of LBFs.

Automated Coarse-Grained Mapping Algorithm for the Martini Force Field and Benchmarks for Membrane-Water Partitioning

With a view to high-throughput simulations, we present an automated system for mapping and parameterizing organic molecules for use with the coarse-grained Martini force field. The method scales to larger molecules and a broader chemical space than existing schemes. The core of the mapping process is a graph-based analysis of the molecule's bonding network, which has the advantages of being fast, general, and preserving symmetry. The parameterization process pays special attention to coarse-grained beads in aromatic rings. It also includes a method for building efficient and stable frameworks of constraints for molecules with structural rigidity. The performance of the method is tested on a diverse set of 87 neutral organic molecules and the ability of the resulting models to capture octanol-water and membrane-water partition coefficients. In the latter case, we introduce an adaptive method for extracting partition coefficients from free-energy profiles to take into account the interfacial region of the membrane. We also use the models to probe the response of membrane-water partitioning to the cholesterol content of the membrane.

Interface-Mediated Mechanism of Action-The Root of the Cytoprotective Effect of Immediate-Release Omeprazole

Omeprazole is usually administered under an enteric coating. However, there is a Food and Drug Administration-approved strategy that enables its release in the stomach. When locally absorbed, omeprazole shows a higher efficacy and a cytoprotective effect, whose mechanism was still unknown. Therefore, we aimed to assess the effect of the absorption route on the gastric mucosa. 2D and 3D models of dipalmitoylphosphatidylcholine (DPPC) at different pH values (5.0 and 7.4) were used to mimic different absorption conditions. Several experimental techniques, namely, fluorescence studies, X-ray scattering methodologies, and Langmuir monolayers coupled with microscopy, X-ray diffraction, and infrared spectroscopy techniques, were combined with molecular dynamics simulations. The results showed that electrostatic and hydrophobic interactions between omeprazole and DPPC rearranged the conformational state of DPPC. Omeprazole intercalates among DPPC molecules, promoting domain formation with untilted phospholipids. Hence, the local release of omeprazole enables its action as a phospholipid-like drug, which can reinforce and protect the gastric mucosa.

A novel approach to calculate protein adsorption isotherms by molecular dynamics simulations

Protein adsorption plays a role in many fields, where in some it is desirable to maximize the amount adsorbed, in others it is important to avoid protein adsorption altogether. Therefore, theoretical methods are needed for a better understanding of the underlying processes and for the prediction of adsorption quantities. In this study, we present a proof-of-concept that the calculation of protein adsorption isotherms by molecular dynamics (MD) simulations is possible using the steric mass action (SMA) theory. Here we are investigating the adsorption of bovine/human serum albumin (BSA/HSA) and hemoglobin (bHb) on Q Sepharose FF. Protein adsorption isotherms were experimentally determined and modeled. Free energy profiles of protein adsorption were calculated by MD simulations to determine the Henry isotherms as a first step. Although each simulation contained only one protein, notably the calculated isotherms are in reasonably good agreement with the experimental isotherms. Hence, we could show that MD data can lead to protein adsorption data in good agreement with experimental data. The results were critically discussed and requirements for future applications are identified.

Predicting Partition Coefficients of Neutral and Charged Solutes in the Mixed SLES-Fatty Acid Micellar System

Sodium laureth sulfate (SLES) and fatty acids are common ingredients in many cosmetic products. Understanding how neutral and charged fatty acid compounds partition between micellar and water phases is crucial to achieve the optimal design of the product formulation. In this paper, we first study the formation of mixed SLES and fatty acid micelles using molecular dynamics (MD) simulations. Micelle/water partition coefficients of neutral and charged fatty acids are then calculated using COSMOmic as well as a MD approach based on the potential of mean force (PMF) calculations performed using umbrella sampling (US). The combined US/PMF approach was performed with both the additive, non-polarizable CHARMM general force field (CGenFF) and the classical Drude polarizable force field. The partition coefficients for the neutral solutes are shown to be accurately calculated with the COSMOmic and additive CGenFF US/PMF approaches, while only the US/PMF approach with the Drude polarizable force field accurately calculated the experimental partition coefficient of the charged solute. These results indicate the utility of the Drude polarizable force field as a tool for the rational development of mixed micelles.

A relationship between membrane permeation and partitioning of nitroaromatic explosives and their functional groups. A computational study

Nitroaromatic explosives, such as 2,4,6-trinitrotoluene, are representative aromatic compounds, which are generally highly toxic.

Permeability of membranes in the liquid ordered and liquid disordered phases

The functional significance of ordered nanodomains (or rafts) in cholesterol rich eukaryotic cell membranes has only begun to be explored. This study exploits the correspondence of cellular rafts and liquid ordered (Lo) phases of three-component lipid bilayers to examine permeability. Molecular dynamics simulations of Lo phase dipalmitoylphosphatidylcholine (DPPC), dioleoylphosphatidylcholine (DOPC), and cholesterol show that oxygen and water transit a leaflet through the DOPC and cholesterol rich boundaries of hexagonally packed DPPC microdomains, freely diffuse along the bilayer midplane, and escape the membrane along the boundary regions. Electron paramagnetic resonance experiments provide critical validation: the measured ratio of oxygen concentrations near the midplanes of liquid disordered (Ld) and Lo bilayers of DPPC/DOPC/cholesterol is 1.75 ± 0.35, in very good agreement with 1.3 ± 0.3 obtained from simulation. The results show how cellular rafts can be structurally rigid signaling platforms while remaining nearly as permeable to small molecules as the Ld phase.

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).

Molecular simulation as a computational pharmaceutics tool to predict drug solubility, solubilization processes and partitioning

In this review we will discuss how computational methods, and in particular classical molecular dynamics simulations, can be used to calculate solubility of pharmaceutically relevant molecules and systems. To the extent possible, we focus on the non-technical details of these calculations, and try to show also the added value of a more thorough and detailed understanding of the solubilization process obtained by using computational simulations. Although the main focus is on classical molecular dynamics simulations, we also provide the reader with some insights into other computational techniques, such as the COSMO-method, and also discuss Flory-Huggins theory and solubility parameters. We hope that this review will serve as a valuable starting point for any pharmaceutical researcher, who has not yet fully explored the possibilities offered by computational approaches to solubility calculations.

COSMOplex: self-consistent simulation of self-organizing inhomogeneous systems based on COSMO-RS

During the past 20 years, the efficient combination of quantum chemical calculations with statistical thermodynamics by the COSMO-RS method has become an important alternative to force-field based simulations for the accurate prediction of free energies of molecules in liquid systems. While it was originally restricted to homogeneous liquids, it later has been extended to the prediction of the free energy of molecules in inhomogeneous systems such as micelles, biomembranes, or liquid interfaces, but these calculations were based on external input about the structure of the inhomogeneous system. Here we report the rigorous extension of COSMO-RS to a self-consistent prediction of the structure and the free energies of molecules in self-organizing inhomogeneous systems. This extends the application range to many new areas, such as the prediction of micellar structures and critical micelle concentrations, finite loading effects in micelles and biomembranes, the free energies and structure of liquid interfaces, microemulsions, and many more related topics, which often are of great practical importance.

Coarse-grained model of titrating peptides interacting with lipid bilayers

Molecular-level computer simulations of peptide aggregation, translocation, and protonation at and in biomembranes are impeded by the large time and length scales involved. We present a computationally efficient, coarse-grained, and solvent-free model for the interaction between lipid bilayers and peptides. The model combines an accurate description of mechanical membrane properties with a new granular representation of the dielectric mismatch between lipids and the aqueous phase. All-atom force fields can be easily mapped onto the coarse-grained model, and parameters for coarse-grained monopeptides accurately extrapolate to membrane permeation free energies for the corresponding dipeptides and tripeptides. Acid-base equilibria of titratable amino acid residues are further studied using a constant-pH ensemble, capturing protonation state changes upon membrane translocation. Important differences between histidine, lysine, and arginine are observed, which are in good agreement with experimental observations.

In silico screening of drug-membrane thermodynamics reveals linear relations between bulk partitioning and the potential of mean force

The partitioning of small molecules in cell membranes-a key parameter for pharmaceutical applications-typically relies on experimentally available bulk partitioning coefficients. Computer simulations provide a structural resolution of the insertion thermodynamics via the potential of mean force but require significant sampling at the atomistic level. Here, we introduce high-throughput coarse-grained molecular dynamics simulations to screen thermodynamic properties. This application of physics-based models in a large-scale study of small molecules establishes linear relationships between partitioning coefficients and key features of the potential of mean force. This allows us to predict the structure of the insertion from bulk experimental measurements for more than 400 000 compounds. The potential of mean force hereby becomes an easily accessible quantity-already recognized for its high predictability of certain properties, e.g., passive permeation. Further, we demonstrate how coarse graining helps reduce the size of chemical space, enabling a hierarchical approach to screening small molecules.

Metronidazole within phosphatidylcholine lipid membranes: New insights to improve the design of imidazole derivatives

Metronidazole is a imidazole derivative with antibacterial and antiprotozoal activity. Despite its therapeutic efficacy, several studies have been developing new imidazole derivatives with lower toxicity. Considering that drug-membrane interactions are key factors for drugs pharmacokinetic and pharmacodynamic properties, the aim of this work is to provide new insights into the structure-toxicity relationship of metronidazole within phosphatidylcholine membranes. For that purpose, lipid membrane models (liposomes and monolayers) composed of dipalmitoylphosphatidylcholine were used. Experimental techniques (determination of partition coefficients and Langmuir isotherm measurements) were combined with molecular dynamics simulations. Different pHs and lipid phases were evaluated to enable a better extrapolation for in vivo conditions. The partition of metronidazole depends on the pH and on the biphasic system (octanol/water or DPPC/water system). At pH 1.2, metronidazole is hydrophilic. At pH 7.4, metronidazole disturbs the order and the packing of phospholipids. For this toxic effect, the hydroxyl group of the side chain of metronidazole is crucial by interacting with the water embedded in the membrane and with the phosphate group and the apolar chains of phospholipids.

Accessing lipophilicity of drugs with biomimetic models: A comparative study using liposomes and micelles

Lipophilicity is a physicochemical property of crucial importance in drug discovery and drug design. Biomimetic models, such as liposomes and micelles, constitute a valuable tool for the assessment of lipophilicity through the determination of partition coefficients (log K_p). However, the lack of standardization hampers the judgment about which model or method has the best and broadest passive drug permeation predictive capacity. This work provides a comparative analysis between the methodologies based on biomimetic models to determine the partition coefficient (log K_p). For that purpose, a set of reference substances preconized by the Organization for Economic Cooperation and Development (OECD) guidelines was used. The biomimetic models employed were liposomes and micelles composed by 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC) and hexadecylphosphocholine (HePC), respectively. Both lipids were used as representative phospholipids of natural membranes. The partition coefficients between biomimetic models and aqueous phases were determined by derivative spectroscopy at physiological conditions (37 °C and pH 7.4). The partition coefficients obtained using biomimetic models are quite different and more reliable than the ones obtained using an octanol/water system. Comparing the performance of the two biomimetic models, micelles revealed to be suitable only for substances with high molar absorption coefficient and log K_p > 3, but in general liposomes are the best model for accessing lipophilicity of drugs. Furthermore, a comparison between experimental data and the partition coefficients determined by the computational method COSMOmic is also provided and discussed. As a final summarizing result, a decision tree is provided in order to guide the selection of a tool for assessing the lipophilicity of drugs.

Diffusion of energetic compounds through biological membrane: Application of classical MD and COSMOmic approximations

Computational studies of the potential biological impact of several energetic compounds were performed. The most commonly used explosives were considered in the present studies: trinitrotoluene (TNT), 2,4-dinitrotoluene (2,4-DNT), 2,4-dinitroanisole (DNAN), and 5-Nitro-2,4-dihydro-3H-1,2,4-triazol-3-one (NTO). The effect of such factors as ionic strength and presence of DMSO in the water solution on the structure of the membrane were considered using the POPC lipid bilayer as an example. Molecular dynamics (MD) simulations revealed that, even on a short-time scale, the influence of those additives is noticeable, and therefore those factors should always be taken into account. The MD and the COSMOmic approaches were used to elucidate the ability of the energetic compounds to penetrate the living cell. Calculated free energy profiles and partitioning coefficients revealed distributions of the compounds in the lipid bilayer as well as an overall ability to enter the cell. MD in this case provides a better representation of the free energy profile, while the COSMOmic approach works better to predict log(K_lipw) values. The effect of the functional group was observed for the profiles that were obtained using the MD method.

Micellization and Partition Equilibria in Mixed Nonionic/Ionic Micellar Systems: Predictions with Molecular Models

In practical applications, surfactant solutions are mostly used in mixtures of nonionic and ionic surfactants because they have improved characteristics compared to those of single surfactant solutions. By adjusting the composition of the micelles and the pH value, the solubilization of solutes can be enhanced. Nevertheless, the partitioning of solutes between nonionic/ionic mixed micelles and the aqueous phase is studied to a much lesser extent than for single surfactant solutions. Theoretical methods to predict partition equilibria in mixed micelles are of interest for screening studies. For those, the composition of the mixed micelle has to be known. Here we investigate mixtures of TX-114 (Triton X-114), Brij35 (C12E23), SDS (sodium dodecyl sulfate), and CTAB (cetyltrimethylammonium bromide). First, to investigate the surfactant compositions in the micelles, molecular dynamics (MD) self-assembly simulations were applied. Thereafter, the predictive COSMO-RS model, which applies the pseudophase approach, and its extension to anisotropic systems termed COSMOmic were compared for the prediction of partition equilibria in mixed micelles, where various molar ratios of the surfactants were considered. It could be demonstrated that both methods are applicable and lead to reasonable predictions for neutral molecules. However, taking into account the three-dimensional structure of the micelle is beneficial because the calculations with COSMOmic are in better agreement with experimental results. Because the partitioning behavior of ionizable molecules in mixed micelles is of particular interest, the partitioning of ionized isovanillin in mixed Brij35/CTAB micelles at different micelle compositions was calculated with COSMOmic. Using a thermodynamic cycle, the position-dependent pK_a of isovanillin within the micelle is calculated on the basis of COSMOmic free energy profiles. As a result, the protolytic equilibrium of isovanillin within the micelles can be taken into account, which is crucial for the reliable prediction of partition coefficients.

Contributions of the membrane dipole potential to the function of voltage-gated cation channels and modulation by small molecule potentiators

The membrane dipole potential (Ψ_d) constitutes one of three electrical potentials generated by cell membranes. Ψ_d arises from the unfavorable parallel alignment of phospholipid and water dipoles, and varies in magnitude both longitudinally and laterally across the bilayer according to membrane composition and phospholipid packing density. In this work, we propose that dynamic counter-balancing between Ψ_d and the transmembrane potential (ΔΨ_m) governs the conformational state transitions of voltage-gated ion channels. Ψ_d consists of 1) static outer, and dynamic inner leaflet components (Ψ_d(extra) and Ψ_d(intra), respectively); and 2) a transmembrane component (ΔΨ_{d(inner-outer)}), ariing from differences in intra- and extracellular leaflet composition. Ψ_d(intra), which transitions between high and low energy states (Ψ_{d(intra, high)} and Ψ_{d(intra, low)}) as a function of channel conformation, is transduced by the pore domain. ΔΨ_{d(inner-outer)} is transduced by the voltage-sensing (VS) domain in summation with ΔΨ_m. Potentiation of voltage-gated ion channels is of interest for the treatment of cardiac, neuronal, and other disorders arising from inherited/acquired ion channel dysfunction. Potentiators are widely believed to alter the rates and voltage-dependencies of channel gating transitions by binding to pockets in the membrane-facing and other regions of ion channel targets. Here, we propose that potentiators alter Ψ_d(intra) and/or Ψ_d(extra), thereby increasing or decreasing the energy barriers governing channel gating transitions. We used quantum mechanical and molecular dynamics (MD) simulations to predict the overall Ψ_d-modulating effects of a series of published positive hERG potentiators partitioned into model DOPC bilayers. Our findings suggest a strong correlation between the magnitude of Ψ_d-lowering and positive hERG potentiation across the series.

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

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

Comparison of different models predicting the phospholipid-membrane water partition coefficients of charged compounds

A large fraction of commercially used chemicals is ionizable. This results in the need for mechanistic models to describe the physicochemical properties of ions, like the membrane-water partition coefficient (K(mw)), which is related to toxicity and bioaccumulation. In this work we compare 3 different and already existing modelling approaches to describe the liposome-water partition coefficient (K(lipw)) of organic ions, including 36 cations, 56 anions, 2 divalent cations and 2 zwitterions (plus 207 neutral compounds for ensuring model consistency). 1) The empirical correlation with the octanol-water partition coefficient of the corresponding neutral species yielded better results for the prediction of anions (RMSE = 0.79) than for cations (RMSE = 1.14). Though describing most anions reasonably well, the lack of mechanistic basis and the poor performance for cations constrain the usage of this model. 2) The polyparameter linear free energy relationship (pp-LFER) model performs worse (RMSE = 1.26/1.12 for anions/cations). The different physicochemical environments, due to different sorption depths into the membrane of the different species, cannot be described with a single pp-LFER model. 3) COSMOmic is based on quantum chemistry and fluid phase thermodynamics and has the widest applicability domain. It was the only model applicable for multiply charged ions and gave the best results for anions (RMSE = 0.66) and cations (RMSE = 0.71). We expect COSMOmic to contribute to a better estimation of the environmental risk of ionizable emerging pollutants.

Automated parametrization of the coarse-grained Martini force field for small organic molecules

The systematic exploration of chemical compound space holds many promises toward structure-function relationships and material design. In the context of computer simulations, progress is hampered by both the sheer number of compounds and the efforts associated with parametrizing a force field for every new molecule. A coarse-grained (CG) representation provides not only a reduced phase space but also a smaller number of compounds, due to the redundancy of CG representations mapping to the same structure. Though many CG models require the explicit force-field parametrization of a molecule with all others, others assume transferability by means of mixing rules, such as the Martini force field. To alleviate the burden associated with tedious parametrizations for each new compound, the present work aims at automating the mapping and parametrization of common small organic molecules for Martini. We test the method by analyzing the water/octanol partitioning of more than 650 neutral molecules, the hydration free energy of 354 others, and the free energies of hydration and solvation in octanol of another 69 compounds. Last, we compare with all-atom simulations the thermodynamics of insertion of four individual solute molecules in a phospholipid membrane. The protocol demonstrates the feasibility of an automated parametrization scheme for Martini and provides prospects for high-throughput simulation methodologies.

Molecular dynamics of dibenz[a,h]anthracene and its metabolite interacting with lung surfactant phospholipid bilayers

Dibenz[a,h]anthracene and its metabolite may form aggregates, which have implications in the clearance process of the lung surfactant phospholipid bilayers.