Molecular simulation of nonfacilitated membrane permeation

Regulation of Membrane Calcium Transport Proteins by the Surrounding Lipid Environment

Calcium ions (Ca2+) are major messengers in cell signaling, impacting nearly every aspect of cellular life. Those signals are generated within a wide spatial and temporal range through a large variety of Ca2+ channels, pumps, and exchangers. More and more evidences suggest that Ca2+ exchanges are regulated by their surrounding lipid environment. In this review, we point out the technical challenges that are currently being overcome and those that still need to be defeated to analyze the Ca2+ transport protein-lipid interactions. We then provide evidences for the modulation of Ca2+ transport proteins by lipids, including cholesterol, acidic phospholipids, sphingolipids, and their metabolites. We also integrate documented mechanisms involved in the regulation of Ca2+ transport proteins by the lipid environment. Those include: (i) Direct interaction inside the protein with non-annular lipids; (ii) close interaction with the first shell of annular lipids; (iii) regulation of membrane biophysical properties (e.g., membrane lipid packing, thickness, and curvature) directly around the protein through annular lipids; and (iv) gathering and downstream signaling of several proteins inside lipid domains. We finally discuss recent reports supporting the related alteration of Ca2+ and lipids in different pathophysiological events and the possibility to target lipids in Ca2+-related diseases.

Effect of Liposomal Encapsulation on the Chemical Exchange Properties of Diamagnetic CEST Agents

Exogenous chemical exchange saturation transfer (CEST) contrast agents such as glucose or 2-deoxy-d-glucose (2-DG) have shown high sensitivities and significant potential for monitoring glucose uptake in tumors with MRI. Here, we show that liposome encapsulation of such agents can be exploited to enhance the CEST signal by reducing the overall apparent exchange rate. We have developed a concise analytical model to describe the liposomal contrast dependence on several parameters such as pH, temperature, irradiation amplitude, and intraliposomal water content. This is the first study in which a model has been constructed to measure the exchange properties of diamagnetic CEST agents encapsulated inside liposomes. Experimentally measured exchange rates of glucose and 2-DG in the liposomal system were found to be reduced due to the intermembrane exchange between the intra- and extraliposomal compartments because of restrictions in water transfer imposed by the lipid membrane. These new theoretical and experimental findings will benefit applications of diamagnetic liposomes to image biological processes. In addition, combining this analytical model with measurements of the CEST signal enhancement using liposomes as a model membrane system is an important new general technique for studying membrane permeability.

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

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

Intestinal Permeability and Drug Absorption: Predictive Experimental, Computational and In Vivo Approaches

The main objective of this review is to discuss recent advancements in the overall investigation and in vivo prediction of drug absorption. The intestinal permeability of an orally administered drug (given the value P_eff) has been widely used to determine the rate and extent of the drug’s intestinal absorption (F_abs) in humans. Preclinical gastrointestinal (GI) absorption models are currently in demand for the pharmaceutical development of novel dosage forms and new drug products. However, there is a strong need to improve our understanding of the interplay between pharmaceutical, biopharmaceutical, biochemical, and physiological factors when predicting F_abs and bioavailability. Currently, our knowledge of GI secretion, GI motility, and regional intestinal permeability, in both healthy subjects and patients with GI diseases, is limited by the relative inaccessibility of some intestinal segments of the human GI tract. In particular, our understanding of the complex and highly dynamic physiology of the region from the mid-jejunum to the sigmoid colon could be significantly improved. One approach to the assessment of intestinal permeability is to use animal models that allow these intestinal regions to be investigated in detail and then to compare the results with those from simple human permeability models such as cell cultures. Investigation of intestinal drug permeation processes is a crucial biopharmaceutical step in the development of oral pharmaceutical products. The determination of the intestinal P_eff for a specific drug is dependent on the technique, model, and conditions applied, and is influenced by multiple interactions between the drug molecule and the biological membranes.

Effects of absorption-modifying excipients on jejunal drug absorption in simulated fasted and fed luminal conditions

Oral administration of drug products is the preferred administration route. In recent decades there has been an increase in drug candidates with low solubility and/or low permeability. To increase the possibility of oral administration for the poorly permeating drugs, the use of absorption modifying excipients (AMEs) has been proposed. These types of AMEs may also affect the regulatory assessment of a novel drug delivery system if they affect the absorption of a drug from any of the four BCS classes. The effects of AMEs have previously been investigated in various animal models, including the single-pass intestinal perfusion (SPIP) in rats. To further improve the biorelevance and the in vivo predictiveness of the SPIP model, four compounds (atenolol, enalaprilat, ketoprofen, metoprolol) were perfused in fasted or fed state simulated intestinal fluid (FaSSIF or FeSSIF) together with the AMEs N-acetyl-cysteine, caprate, or sodium dodecyl sulfate. For the highly soluble and poorly permeating compounds enalaprilat and atenolol (BCS class III), the flux was increased the most by the addition of SDS in both FaSSIF and FeSSIF. For ketoprofen (BCS class II), the flux decreased in the presence of all AMEs in at least one of the perfusion media. The flux of metoprolol (BCS class I) was not affected by any of the excipients in none of simulated prandial states. The changes in magnitude in the absorption of the compounds were in general smaller in FeSSIF than in FaSSIF. This may be explained by a reduced free concentration AMEs in FeSSIF. Further, the results in FeSSIF were similar to those from intrajejunal bolus administration in rat in a previous study. This suggests that the biorelevance of the SPIP method may be increased when investigating the effects of AMEs, by the addition of intraluminal constituents representative to fasted and/or fed state to the inlet perfusate.

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).

A DFT mechanistic and kinetic study on the reaction of phloroglucinol with •OH in different media: Hydrogen atom transfer versus oxidation

A theoretical study on the reaction of phloroglucinol with •OH has been performed with the aim of elucidating the geometric, energetic and kinetic properties of the reaction as well as identifying the preferred reaction pathway. Three reaction mechanisms have been considered, namely, direct hydrogen atom abstraction, addition–elimination mechanism in the absence and in the presence of a base catalyst and oxidation mechanism in the absence and in the presence of O2. The study has been performed using the DFT/M06[Formula: see text]2X, DFT/BHHLYP and DFT/MPW1K methods in conjunction with either the 6-31++G(d,p) or the 6-311++G(3df,2p) basis set. The energetic parameters are influenced by the type of function utilized and the media in which the calculation is done. The direct hydrogen abstraction mechanism provides the smallest branching ratio with respect to the •OH addition mechanisms. The PG + •OH reaction under atmospheric conditions saturated with O2 would predominantly form tetrahydroxybenzene; the predominant product within the biological system would largely depend on physiological conditions; under pH [Formula: see text] 7 and with oxygen dissolved within the biological system, the preferred product would be tetrahydroxybenzene; however, if the reaction takes place in some part of the biological system where the pH [Formula: see text] 7, the preferred product would be the phenoxyl radical.

Permeabilities of CO2, H2S and CH4 through Choline-Based Ionic Liquids: Atomistic-Scale Simulations

Molecular dynamics simulations are used to study the transport of CO2, H2S and CH4 molecules across environmentally friendly choline-benzoate and choline-lactate ionic liquids (ILs). The permeability coefficients of the considered molecules are calculated using the free energy and diffusion rate profiles. Both systems show the largest resistance to CH4, whereas more than 5 orders of magnitude larger permeability coefficients are obtained for the other two gas molecules. The CO2/CH4 and H2S/CH4 selectivity was estimated to be more than 104 and 105, respectively. These results indicate the great potential of the considered ILs for greenhouse gas control.

Molecular Dynamics Simulations of Membrane Permeability

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

An experimentally validated approach to calculate the blood-brain barrier permeability of small molecules

Drug development for the treatment of central nervous system (CNS) diseases is extremely challenging, in large part due to the difficulty in crossing the blood-brain barrier (BBB). Here we develop and experimentally validate a new in silico method to predict quantitatively the BBB permeability for small-molecule drugs. We show accurate prediction of solute permeabilities at physiological temperature using high-temperature unbiased atomic detail molecular dynamics simulations of spontaneous drug diffusion across BBB bilayers. These simulations provide atomic detail insights into the transport mechanisms, as well as converged kinetics and thermodynamics. The method is validated computationally against physiological temperature simulations for fast-diffusing compounds, as well as experimentally by direct determination of the compound permeabilities using a transwell assay as an in vitro BBB model. The overall agreement of the predicted values with both direct simulations at physiological temperatures and experimental data is excellent. This new tool has the potential to replace current semi-empirical in silico screening and in vitro permeability measurements in CNS drug discovery.

The asymmetry of plasma membranes and their cholesterol content influence the uptake of cisplatin

The composition of the plasma membrane of malignant cells is thought to influence the cellular uptake of cisplatin and to take part in developing resistance to this widespread anti-cancer drug. In this work we study the permeation of cisplatin through the model membranes of normal and cancer cells using molecular dynamics simulations. A special attention is paid to lipid asymmetry and cholesterol content of the membranes. The loss of lipid asymmetry, which is common for cancer cells, leads to a decrease in their permeability to cisplatin by one order of magnitude in comparison to the membranes of normal cells. The change in the cholesterol molar ratio from 0% to 33% also decreases the permeability of the membrane by approximately one order of magnitude. The permeability of pure DOPC membrane is 5-6 orders of magnitude higher than one of the membranes with realistic lipid composition, which makes it as an inadequate model for the studies of drug permeability.

Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance

Biological membranes are tricky to investigate. They are complex in terms of molecular composition and structure, functional over a wide range of time scales, and characterized by nonequilibrium conditions. Because of all of these features, simulations are a great technique to study biomembrane behavior. A significant part of the functional processes in biological membranes takes place at the molecular level; thus computer simulations are the method of choice to explore how their properties emerge from specific molecular features and how the interplay among the numerous molecules gives rise to function over spatial and time scales larger than the molecular ones. In this review, we focus on this broad theme. We discuss the current state-of-the-art of biomembrane simulations that, until now, have largely focused on a rather narrow picture of the complexity of the membranes. Given this, we also discuss the challenges that we should unravel in the foreseeable future. Numerous features such as the actin-cytoskeleton network, the glycocalyx network, and nonequilibrium transport under ATP-driven conditions have so far received very little attention; however, the potential of simulations to solve them would be exceptionally high. A major milestone for this research would be that one day we could say that computer simulations genuinely research biological membranes, not just lipid bilayers.

Thermodynamics and kinetics of joint action of antiviral agent tilorone and DMSO on model lipid membranes

Individual and joint action of two water-soluble drugs, DMSO and tilorone, on model l-α-dipalmitoylphosphatidylcholine (DPPC) membranes were studied in equilibrium and kinetic regimes by differential scanning calorimetry (DSC). For equilibrium experiments, the drugs were introduced during preparation of the model membrane. In kinetic studies, one of the drugs was added to the DPPC membrane already containing the other drug, and the effects of drug-membrane interactions were monitored in real-time regime. It was found that tilorone and DMSO had opposite effects on the membrane melting temperature, which were non-additive under joint introduction of these drugs. Analysis of kinetics of DSC profiles under drugs introduction allowed us to discriminate two processes in drug-membrane interactions with different characteristic times, i.e., drug sorption onto the membrane (minutes) and drug diffusion through stacks of lipid bilayers (hours). It was established that 0.1 mol% DMSO effectively enhanced membrane penetration for tilorone with the rate of tilorone diffusion being dependent upon the scheme of drugs administration. A model was proposed describing how sorption of a dopant onto lipid membrane could affect the membrane permeability for other dopants. Conditions were determined for enhancement of membrane permeability, as it was observed for DPPC/DMSO/tilorone system.

Effects of lipid composition on membrane permeation

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

Simulations of lipid bilayers using the CHARMM36 force field with the TIP3P-FB and TIP4P-FB water models

The CHARMM36 force field for lipids is widely used in simulations of lipid bilayers. The CHARMM family of force fields were developed for use with the mTIP3P water model. This water model has an anomalously high dielectric constant and low viscosity, which limits its accuracy in the calculation of quantities like permeability coefficients. The TIP3P-FB and TIP4P-FB water models are more accurate in terms of the dielectric constant and transport properties, which could allow more accurate simulations of systems containing water and lipids. To test whether the CHARMM36 lipid force field is compatible with the TIP3P-FB and TIP4P-FB water models, we have performed simulations of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine and 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayers. The calculated headgroup area, compressibility, order parameters, and X-ray form factors are in good agreement with the experimental values, indicating that these improved water models can be used with the CHARMM36 lipid force field without modification when calculating membrane physical properties. The water permeability predicted by these models is significantly different; the mTIP3P-model diffusion in solution and at the lipid-water interface is anomalously fast due to the spuriously low viscosity of mTIP3P-model water, but the potential of mean force of permeation is higher for the TIP3P-FB and TIP4P-FB models due to their high excess chemical potentials. As a result, the rates of water permeation calculated the FB water models are slower than the experimental value by a factor of 15-17, while simulations with the mTIP3P model only underestimate the water permeability by a factor of 3.

Composition Dependence of Water Permeation Across Multicomponent Gel-Phase Bilayers

The permeability of multicomponent phospholipid bilayers in the gel phase is investigated via molecular dynamics simulation. The physical role of the different molecules is probed by comparing multiple mixed-component bilayers containing distearylphosphatidylcholine (DSPC) with varying amounts of either the emollient isostearyl isostearate or long-chain alcohol (dodecanol, octadecanol, or tetracosanol) molecules. Permeability is found to depend on both the tail packing density and hydrogen bonding between lipid headgroups and water. Whereas the addition of emollient or alcohol molecules to a gel-phase DSPC bilayer can increase the tail packing density, it also disturbed the hydrogen-bonding network, which in turn can increase interfacial water dynamics. These phenomena have opposing effects on bilayer permeability, which is found to depend on the balance between enhanced tail packing and decreased hydrogen bonding.

Free Energy Calculations of Membrane Permeation: Challenges Due to Strong Headgroup-Solute Interactions

Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solute's permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased molecular dynamics computer simulations to calculate and compare the free energy profiles of translocation of several small molecules across 1,2-dioleoyl- sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step toward determining the most efficient method for free energy calculations. We study the translocation of arginine, a sodium ion, alanine, and a single water molecule using the metadynamics, umbrella sampling, and replica exchange umbrella sampling techniques. Within the fixed lengths of our simulations, we find that all methods produce similar results for charge-neutral permeants, but not for polar or positively charged molecules. We identify the long relaxation time scale of electrostatic interactions between lipid headgroups and the solute to be the principal cause of this difference and show that this slow process can lead to an erroneous dependence of computed free energy profiles on the initial system configuration. We demonstrate the use of committor analysis to validate the proper sampling of the presumed transition state, which in our simulations is achieved only in replica exchange calculations. On the basis of these results we provide some useful guidance to perform and evaluate free energy calculations of membrane permeation.

Computational modeling in glioblastoma: from the prediction of blood-brain barrier permeability to the simulation of tumor behavior

The integrated in silico-in vitro-in vivo approaches have fostered the development of new treatment strategies for glioblastoma patients and improved diagnosis, establishing the bridge between biochemical research and clinical practice. These approaches have provided new insights on the identification of bioactive compounds and on the complex mechanisms underlying the interactions among glioblastoma cells, and the tumor microenvironment. This review focuses on the key advances pertaining to computational modeling in glioblastoma, including predictive data on drug permeability across the blood-brain barrier, tumor growth and treatment responses. Structure- and ligand-based methods have been widely adopted, enabling the study of dynamic and evolutionary aspects of glioblastoma. Their potential applications as predictive tools and the advantages over other well-known methodologies are outlined. Challenges regarding in silico approaches for predicting tumor properties are also discussed.

Is the cholesterol bilayer domain a barrier to oxygen transport into the eye lens?

In the eye lens, the oxygen partial pressure is very low and the cholesterol (Chol) content in cell membranes is very high. Disturbance of these quantities results in cataract development. In human lens membranes, both bulk phospholipid-Chol domains and the pure Chol bilayer domains (CBDs) were experimentally detected. It is hypothesized that the CBD constitutes a significant barrier to oxygen transport into the lens. Transmembrane profiles of the oxygen diffusion-concentration product, obtained with electron paramagnetic resonance spin-labeling methods, allow evaluation of the oxygen permeability (P_M) of phospholipid membranes but not the CBD. Molecular dynamics simulation can independently provide components of the product across any bilayer domain, thus allowing evaluation of the P_M across the CBD. Therefore, to test the hypothesis, MD simulation was used. Three bilayers containing palmitoyl-oleoyl-phosphorylcholine (POPC) and Chol were built. The pure Chol bilayer modeled the CBD, the 1:1 POPC-Chol bilayer modeled the bulk membrane in which the CBD is embedded, and the POPC bilayer was a reference. To each model, 200 oxygen molecules were added. After equilibration, the oxygen concentration and diffusion profiles were calculated for each model and multiplied by each other. From the respective product profiles, the P_M of each bilayer was calculated. Favorable comparison with experimental data available only for the POPC and POPC-Chol bilayers validated these bilayer models and allowed the conclusion that oxygen permeation across the CBD is ~10 smaller than across the bulk membrane, supporting the hypothesis that the CBD is a barrier to oxygen transport into the eye lens.

Modeling of the Passive Permeation of Mercury and Methylmercury Complexes Through a Bacterial Cytoplasmic Membrane

Cellular uptake and export are important steps in the biotransformation of mercury (Hg) by microorganisms. However, the mechanisms of transport across biological membranes remain unclear. Membrane-bound transporters are known to be relevant, but passive permeation may also be involved. Inorganic Hg^II and methylmercury ([CH₃Hg^II]⁺) are commonly complexed with thiolate ligands. Here, we have performed extensive molecular dynamics simulations of the passive permeation of Hg^II and [CH₃Hg^II]⁺ complexes with thiolate ligands through a model bacterial cytoplasmic membrane. We find that the differences in free energy between the individual complexes in bulk water and at their most favorable position within the membrane are ∼2 kcal mol^-1. We provide a detailed description of the molecular interactions that drive the membrane crossing process. Favorable interactions with carbonyl and tail groups of phospholipids stabilize Hg-containing solutes in the tail-head interface region of the membrane. The calculated permeability coefficients for the neutral compounds CH₃S-Hg^II-SCH₃ and CH₃Hg^II-SCH₃ are on the order of 10^-5 cm s^-1. We conclude that small, nonionized Hg-containing species can permeate readily through cytoplasmic membranes.

Influence of Cholesterol on the Oxygen Permeability of Membranes: Insight from Atomistic Simulations

Cholesterol is widely known to alter the physical properties and permeability of membranes. Several prior works have implicated cell membrane cholesterol as a barrier to tissue oxygenation, yet a good deal remains to be explained with regard to the mechanism and magnitude of the effect. We use molecular dynamics simulations to provide atomic-resolution insight into the influence of cholesterol on oxygen diffusion across and within the membrane. Our simulations show strong overall agreement with published experimental data, reproducing the shapes of experimental oximetry curves with high accuracy. We calculate the upper-limit transmembrane oxygen permeability of a 1-palmitoyl,2-oleoylphosphatidylcholine phospholipid bilayer to be 52 ± 2 cm/s, close to the permeability of a water layer of the same thickness. With addition of cholesterol, the permeability decreases somewhat, reaching 40 ± 2 cm/s at the near-saturating level of 62.5 mol % cholesterol and 10 ± 2 cm/s in a 100% cholesterol mimic of the experimentally observed noncrystalline cholesterol bilayer domain. These reductions in permeability can only be biologically consequential in contexts where the diffusional path of oxygen is not water dominated. In our simulations, cholesterol reduces the overall solubility of oxygen within the membrane but enhances the oxygen transport parameter (solubility-diffusion product) near the membrane center. Given relatively low barriers to passing from membrane to membrane, our findings support hydrophobic channeling within membranes as a means of cellular and tissue-level oxygen transport. In such a membrane-dominated diffusional scheme, the influence of cholesterol on oxygen permeability is large enough to warrant further attention.

Asymmetric osmotic water permeation through a vesicle membrane

Understanding the water permeation through a cell membrane is of primary importance for biological activities and a key step to capture its shape transformation in salt solution. In this work, we reveal the dynamical behaviors of osmotically driven transport of water molecules across a vesicle membrane by molecular dynamics simulations. Of particular interest is that the water transport in and out of vesicles is highly distinguishable given the osmotic force are the same, suggesting an asymmetric osmotic transportation. This asymmetric phenomenon exists in a broad range of parameter space such as the salt concentration, temperature, and vesicle size and can be ascribed to the similar asymmetric potential energy of lipid-ion, lipid-water, lipid-solution, lipid-lipid, and the lipid-lipid energy fluctuation. Specifically, the water flux has a linear increase with the salt concentration, similar to the prediction by Nernst-Planck equation or Fick's first law. Furthermore, due to the Arrhenius relation between the membrane permeability and temperature, the water flux also exhibits excellent Arrhenius dependence on the temperature. Meanwhile, the water flux shows a linear increase with the vesicle surface area since the flux amount across a unit membrane area should be a constant. Finally, we also present the anonymous diffusion behaviors for the vesicle itself, where transitions from normal diffusion at short times to subdiffusion at long times are identified. Our results provide significant new physical insights for the osmotic water permeation through a vesicle membrane and are helpful for future experimental studies.

Position-Dependent Diffusion Tensors in Anisotropic Media from Simulation: Oxygen Transport in and through Membranes

A Bayesian-based methodology is developed to estimate diffusion tensors from molecular dynamics simulations of permeants in anisotropic media, and is applied to oxygen in lipid bilayers. By a separation of variables in the Smoluchowski diffusion equation, the multidimensional diffusion is reduced to coupled one-dimensional diffusion problems that are treated by discretization. The resulting diffusivity profiles characterize the membrane transport dynamics as a function of the position across the membrane, discriminating between diffusion normal and parallel to the membrane. The methodology is first validated with neat water, neat hexadecane, and a hexadecane slab surrounded by water, the latter being a simple model for a lipid membrane. Next, a bilayer consisting of pure 1-palmitoyl 2-oleoylphosphatidylcholine (POPC), and a bilayer mimicking the lipid composition of the inner mitochondrial membrane, including cardiolipin, are investigated. We analyze the detailed time evolution of oxygen molecules, in terms of both normal diffusion through and radial diffusion inside the membrane. Diffusion is fast in the more loosely packed interleaflet region, and anisotropic, with oxygen spreading more rapidly in the membrane plane than normal to it. Visualization of the propagator shows that oxygen enters the membrane rapidly, reaching its thermodynamically favored center in about 1 ns, despite the free energy barrier at the headgroup region. Oxygen transport is quantified by computing the oxygen permeability of the membranes and the average radial diffusivity, which confirm the anisotropy of the diffusion. The position-dependent diffusion constants and free energies are used to construct compartmental models and test assumptions used in estimating permeability, including Overton's rule. In particular, a hexadecane slab surrounded by water is found to be a poor model of oxygen transport in membranes because the relevant energy barriers differ substantially.

Modeling covalent-modifier drugs

In this review, we present a summary of how computer modeling has been used in the development of covalent-modifier drugs. Covalent-modifier drugs bind by forming a chemical bond with their target. This covalent binding can improve the selectivity of the drug for a target with complementary reactivity and result in increased binding affinities due to the strength of the covalent bond formed. In some cases, this results in irreversible inhibition of the target, but some targeted covalent inhibitor (TCI) drugs bind covalently but reversibly. Computer modeling is widely used in drug discovery, but different computational methods must be used to model covalent modifiers because of the chemical bonds formed. Structural and bioinformatic analysis has identified sites of modification that could yield selectivity for a chosen target. Docking methods, which are used to rank binding poses of large sets of inhibitors, have been augmented to support the formation of protein-ligand bonds and are now capable of predicting the binding pose of covalent modifiers accurately. The pK_a's of amino acids can be calculated in order to assess their reactivity towards electrophiles. QM/MM methods have been used to model the reaction mechanisms of covalent modification. The continued development of these tools will allow computation to aid in the development of new covalent-modifier drugs. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Computational Models of the Gastrointestinal Environment. 2. Phase Behavior and Drug Solubilization Capacity of a Type I Lipid-Based Drug Formulation after Digestion

Lipid-based drug formulations can greatly enhance the bioavailability of poorly water-soluble drugs. Following the oral administration of formulations containing tri- or diglycerides, the digestive processes occurring within the gastrointestinal (GI) tract hydrolyze the glycerides to mixtures of free fatty acids and monoglycerides that are, in turn, solubilized by bile. The behavior of drugs within the resulting colloidal mixtures is currently not well characterized. This work presents matched in vitro experimental and molecular dynamics (MD) theoretical models of the GI microenvironment containing a digested triglyceride-based (Type I) drug formulation. Both the experimental and theoretical models consist of molecular species representing bile (glycodeoxycholic acid), digested triglyceride (1:2 glyceryl-1-monooleate and oleic acid), and water. We have characterized the phase behavior of the physical system using nephelometry, dynamic light scattering, and polarizing light microscopy and compared these measurements to phase behavior observed in multiple MD simulations. Using this model microenvironment, we have investigated the dissolution of the poorly water-soluble drug danazol experimentally using LC-MS and theoretically by MD simulation. The results show how the formulation lipids alter the environment of the GI tract and improve the solubility of danazol. The MD simulations successfully reproduce the experimental results showing the utility of MD in modeling the fate of drugs after digestion of lipid-based formulations within the intestinal lumen.

On Atomistic Models for Molecular Oxygen

Molecular oxygen (O₂) is key to all life on earth, as it is constantly cycled via photosynthesis and cellular respiration. Substantial scientific effort has been devoted to understanding every part of this cycle. Classical molecular dynamics (MD) simulations have been used to study some of the key processes involved in cellular respiration: O₂ permeation through alveolar monolayers and cellular membranes, its binding to hemoglobin during transport in the bloodstream, as well as its transport along optimal pathways toward its reduction sites in proteins. Moreover, MD simulations can help interpret the results of several imaging techniques in which O₂ is used because of its paramagnetic nature. However, despite the widespread use of computational models for the O₂ molecule, their performances have never been systematically evaluated. In this paper, we assess the performances of 14 different models of O₂ available in the literature by calculating four thermodynamic properties: density, heat of vaporization, free energy of hydration, and free energy of solvation in hexadecane. For each property, reliable experimental data are available. Most models perform reasonably well in predicting the correct trends, but they fail to reproduce the experimental data quantitatively. We then develop new models for O₂, with and without a quadrupole moment, and compare their behavior with the behavior of previously published models. The new models show significant improvement in terms of density, heat of vaporization, and free energy of hydration. However, quantitative agreement with water-oil partitioning is not reached due to discrepancies between the calculated and measured free energies of solvation in hexadecane. We suggest that classical pairwise-additive models may be inadequate to properly describe the thermodynamics of solvation of apolar species, such as O₂, in apolar solvents.

How Do Short Chain Nonionic Detergents Destabilize G-Protein-Coupled Receptors?

Stability of detergent-solubilized G-protein-coupled receptors (GPCRs) is crucial for their purification in a biologically relevant state, and it is well-known that short chain detergents such as octylglucoside are more denaturing than long chain detergents such as dodecylmaltoside. However, the molecular basis for this phenomenon is poorly understood. To gain insights into the mechanism of detergent destabilization of GPCRs, we used atomistic molecular dynamics simulations of thermostabilized adenosine receptor (A2AR) mutants embedded in either a lipid bilayer or detergent micelles of alkylmaltosides and alkylglucosides. A2AR mutants in dodecylmaltoside or phospholipid showed low flexibility and good interhelical packing. In contrast, A2AR mutants in either octylglucoside or nonylglucoside showed decreased α-helicity in transmembrane regions, decreased α-helical packing, and the interpenetration of detergent molecules between transmembrane α-helices. This was not observed in octylglucoside containing phospholipid. Cholesteryl hemisuccinate in dodecylmaltoside increased the energetic stability of the receptor by wedging into crevices on the hydrophobic surface of A2AR, increasing packing interactions within the receptor and stiffening the detergent micelle. The data suggest a three-stage process for the initial events in the destabilization of GPCRs by octylglucoside: (i) highly mobile detergent molecules form small micelles around the receptor; (ii) loss of α-helicity and decreased interhelical packing interactions in transmembrane regions are promoted by increased receptor thermal motion; (iii) transient separation of transmembrane helices allowed penetration of detergent molecules into the core of the receptor. The relative hydration of the headgroup and alkyl chain correlates with detergent harshness and suggests new avenues to develop milder versions of octylglucoside for receptor crystallization.

Subdiffusion in Membrane Permeation of Small Molecules

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

Generalized Langevin Methods for Calculating Transmembrane Diffusivity

The membrane permeability coefficient of a solute can be estimated using the solubility-diffusion model. This model requires the diffusivity profile (D(z)) of the solute as it moves along the transmembrane axis, z. The generalized Langevin equation provides one strategy for calculating position-dependent diffusivity from straightforward molecular dynamics simulations where the solute is restrained to a series of positions on the z-coordinate by a harmonic potential. The diffusivity of the solute is calculated from its correlation functions, which are related to the friction experienced by the solute. Roux and Hummer have derived expressions for the diffusion coefficient from the velocity autocorrelation function (VACF) and position autocorrelation function (PACF), respectively. In this work, these methods are validated by calculating the diffusivity of H₂O and O₂ in homogeneous liquids. These methods are then used to calculate transmembrane diffusivity profiles. The VACF method is less sensitive to thermostat forces and has incrementally lower errors but is more sensitive to the spring constant of the harmonic restraint. For the permeation of a solute through a lipid bilayer, the diffusion coefficients calculated using these methods provided significantly different results. Long-lived correlations of the restrained solute due to inhomogeneities in the bilayer can result in spuriously low diffusivity when using the PACF method. The method based on the VACF does not have this issue and predicts higher rates of diffusion inside the bilayer.

Two Relations to Estimate Membrane Permeability Using Milestoning

Prediction of passive permeation rates of solutes across lipid bilayers is important to drug design, toxicology, and other biological processes such as signaling. The inhomogeneous solubility-diffusion (ISD) equation is traditionally used to relate the position-dependent potential of mean force and diffusivity to the permeability coefficient. The ISD equation is derived via the Smoluchowski equation and assumes overdamped system dynamics. It has been suggested that the complex membrane environment may exhibit more complicated damping conditions. Here we derive a variant of the inhomogeneous solubility diffusion equation as a function of the mean first passage time (MFPT) and show how milestoning, a method that can estimate kinetic quantities of interest, can be used to estimate the MFPT of membrane crossing and, by extension, the permeability coefficient. We further describe a second scheme, agnostic to the damping condition, to estimate the permeability coefficient from milestoning results or other methods that compute a probability of membrane crossing. The derived relationships are tested using a one-dimensional Langevin dynamics toy system confirming that the presented theoretical methods can be used to estimate permeabilities given simulation and milestoning results.

Study of procaine and tetracaine in the lipid bilayer using molecular dynamics simulation

Despite available experimental results, the molecular mechanism of action of local anesthetics upon the nervous system and contribution of the cell membrane to the process are still controversial. In this work, molecular dynamics simulations were performed to investigate the effect of two clinically used local anesthetics, procaine and tetracaine, on the structure and dynamics of a fully hydrated dimyristoylphosphatidylcholine lipid bilayer. We focused on comparing the main effects of uncharged and charged drugs on various properties of the lipid membrane: mass density distribution, diffusion coefficient, order parameter, radial distribution function, hydrogen bonding, electrostatic potential, headgroup angle, and water dipole orientation. To compare the diffusive nature of anesthetic through the lipid membrane quantitatively, we investigated the hexadecane/water partition coefficient using expanded ensemble simulation. We predicted the permeability coefficient of anesthetics in the following order: uncharged tetracaine > uncharged procaine > charged tetracaine > charged procaine. We also shown that the charged forms of drugs are more potent in hydrogen bonding, disturbing the lipid headgroups, changing the orientation of water dipoles, and increasing the headgroup electrostatic potential more than uncharged drugs, while the uncharged drugs make the lipid diffusion faster and increase the tail order parameter. The results of these simulation studies suggest that the different forms of anesthetics induce different structural modifications in the lipid bilayer, which provides new insights into their molecular mechanism.

Lipid bilayer permeation of aliphatic amine and carboxylic acid drugs: rates of insertion, translocation and dissociation from MD simulations

The overabundance of drugs containing aliphatic amine and carboxylic acid groups is rationalized in terms of their membrane permeability.