Molecular Dynamics Study on the Effects of Chain Branching on the Physical Properties of Lipid Bilayers: 2. Permeability

Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook

Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Besides discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.

Non-Polar Lipids as Regulators of Membrane Properties in Archaeal Lipid Bilayer Mimics

The modification of archaeal lipid bilayer properties by the insertion of apolar molecules in the lipid bilayer midplane has been proposed to support cell membrane adaptation to extreme environmental conditions of temperature and hydrostatic pressure. In this work, we characterize the insertion effects of the apolar polyisoprenoid squalane on the permeability and fluidity of archaeal model membrane bilayers, composed of lipid analogues. We have monitored large molecule and proton permeability and Laurdan generalized polarization from lipid vesicles as a function of temperature and hydrostatic pressure. Even at low concentration, squalane (1 mol%) is able to enhance solute permeation by increasing membrane fluidity, but at the same time, to decrease proton permeability of the lipid bilayer. The squalane physicochemical impact on membrane properties are congruent with a possible role of apolar intercalants on the adaptation of Archaea to extreme conditions. In addition, such intercalant might be used to cheaply create or modify chemically resistant liposomes (archeaosomes) for drug delivery.

Mechanical properties of ester- and ether-DPhPC bilayers: A molecular dynamics study

In addition to its biological importance, DPhPC lipid bilayers are widely used in droplet bilayers, study of integral membrane proteins, drug delivery systems as well as patch-clamp electrophysiology of ion channels, yet their mechanical properties are not fully measured. Herein, we examined the effect of the ether linkage on the mechanical properties of ester- and ether-DPhPC lipid bilayers using all-atom molecular dynamics simulation. The values of area per lipid, thickness, intrinsic lateral pressure profile, order parameter, and elasticity moduli were estimated using various computational frameworks and were compared with available experimental values. Overall, a good agreement was observed between the two. The global properties of the two lipid bilayers are vastly different, with ether bilayer being stiffer, less ordered, and thicker than ester bilayer. Moreover, ether linkage decreased the area per lipid in the ether lipid bilayer. Our computational framework and output demonstrate how ether modification changes the mechano-chemical properties of DPhPC bilayers.

Conformation and Orientation of Branched Acyl Chains Responsible for the Physical Stability of Diphytanoylphosphatidylcholine

Diphytanoylphosphatidylcholine (DPhPC) is a synthetic phospholipid in which two methyl-branched acyl chains are introduced into the glycerol moiety, mimicking phospholipids of eukaryotic and eubacterial origins. The lipid bilayers of DPhPC reproduce the outstanding physical properties of methyl-branched lipids that occur in archaeal membranes. DPhPC is commonly used as the base lipid in biophysical experiments, particularly for recording ion-channel currents. However, the dynamics of lipid molecules that induces their useful physical properties is still unclear. In this study, we examined the conformation and orientation of the methyl-branched acyl chain of DPhPC in a membrane using ²H nuclear magnetic resonance (NMR) measurements of the synthetic lipid with a high stereochemical purity and molecular dynamics (MD) simulations. Deuterium-labeled 3',3'-CD₃,D-DPhPC (2) and 7',7'-CD₃,D-DPhPC (3) showed the characteristic quadrupole splitting width in the ²H NMR spectra, which corresponded to the bent orientation reported for the archaeal lipid PGP-Me [Yamagami, M., et al. (2019) Biochemistry 58, 3869-3879]. However, MD simulations, which reproduced the ²H NMR results well, unveiled the unknown features of DPhPC in the membrane; DPhPC has a chain-specific average orientation, where two bent orientations with upward and downward methyl groups occur at positions C3 and C7 of the sn-1 and sn-2 chains of DPhPC, respectively. These MD and NMR results reveal that these two bent orientations define the average orientation of DPhPC for the shallow part of the acyl chains, which is considered to be an important factor in the stability of DPhPC membranes.

Lipid Phase Separation Induced by the Apolar Polyisoprenoid Squalane Demonstrates Its Role in Membrane Domain Formation in Archaeal Membranes

Archaea synthesize methyl-branched, ether phospholipids, which confer the archaeal membrane exceptional physicochemical properties. A novel membrane organization was proposed recently to explain the thermal and high pressure tolerance of the polyextremophilic archaeon Thermococcus barophilus. According to this theoretical model, apolar molecules could populate the midplane of the bilayer and could alter the physicochemical properties of the membrane, among which is the possibility to form membrane domains. We tested this hypothesis using neutron diffraction on a model archaeal membrane composed of two archaeal diether lipids with phosphocholine and phosphoethanolamine headgroups in the presence of the apolar polyisoprenoid squalane. We show that squalane is inserted in the midplane at a maximal concentration between 5 and 10 mol % and that squalane can modify the lateral organization of the membrane and induces the coexistence of separate phases. The lateral reorganization is temperature- and squalane concentration-dependent and could be due to the release of lipid chain frustration and the induction of a negative curvature in the lipids.

Model lipid systems and their use to evaluate the phase state of biomembranes, their mechanical properties and the effect of non-conventional antibiotics: the case of daptomycin

The lipid bilayer is the basis of the structure and function of the cell membrane. The study of the molecular phenomena that affect biological membranes has a great impact on the understanding of cellular physiology. To understand these phenomena, it has become increasingly necessary to develop simple synthetic models that allow the most basic details of such processes to be reproduced. In this short communication, we took advantage of the properties of two well-established lipid model systems, GUVs and SLBs, with compositions mimicking the cell membrane present in mammals and bacteria, to study the thermotropic phase behavior of lipids as well as the effect of daptomycin, a cyclic lipopeptide used as an antibiotic. The study of mechanical and thermodynamical properties of these model systems could contribute to establish a theoretical framework to develop more efficient strategies for biological control.

Structural Characterization of an Archaeal Lipid Bilayer as a Function of Hydration and Temperature

Archaea, the most extremophilic domain of life, contain ether and branched lipids which provide extraordinary bilayer properties. We determined the structural characteristics of diether archaeal-like phospholipids as functions of hydration and temperature by neutron diffraction. Hydration and temperature are both crucial parameters for the self-assembly and physicochemical properties of lipid bilayers. In this study, we detected non-lamellar phases of archaeal-like lipids at low hydration levels, and lamellar phases at levels of 90% relative humidity or more exclusively. Moreover, at 90% relative humidity, a phase transition between two lamellar phases was discernible. At full hydration, lamellar phases were present up to 70ᵒC and no phase transition was observed within the temperature range studied (from 25 °C to 70 °C). In addition, we determined the neutron scattering length density and the bilayer's structural parameters from different hydration and temperature conditions. At the highest levels of hydration, the system exhibited rearrangements on its corresponding hydrophobic region. Furthermore, the water uptake of the lipids examined was remarkably high. We discuss the effect of ether linkages and branched lipids on the exceptional characteristics of archaeal phospholipids.

Induction of non-lamellar phases in archaeal lipids at high temperature and high hydrostatic pressure by apolar polyisoprenoids

It is now well established that cell membranes are much more than a barrier that separate the cytoplasm from the outside world. Regarding membrane's lipids and their self-assembling, the system is highly complex, for example, the cell membrane needs to adopt different curvatures to be functional. This is possible thanks to the presence of non-lamellar-forming lipids, which tend to curve the membrane. Here, we present the effect of squalane, an apolar isoprenoid molecule, on an archaea-like lipid membrane. The presence of this molecule provokes negative membrane curvature and forces lipids to self-assemble under inverted cubic and inverted hexagonal phases. Such non-lamellar phases are highly stable under a broad range of external extreme conditions, e.g. temperatures and high hydrostatic pressures, confirming that such apolar lipids could be included in the architecture of membranes arising from cells living under extreme environments.

Double-sides sticking mechanism of vinblastine interacting with α,β-tubulin to get activity against cancer cells

Vinblastine (VLB) and its derivatives have been used for clinical first-line drugs to treat various cancers. Due to the resistance and serious side effects from using VLB and its derivatives, there is a need to discover and develop novel VLB derivatives with high activity against cancer cells. In order to better discover and develop new VLB derivatives, we need to study the structural basis of VLB's anti-cancer cytotoxicity and the mechanism of its interaction with α,β-tubulins. Based on the crystal structure of α,β-microtubule complex protein, the molecular dynamics method including the sampling PMF method was used to study the variation of dissociation free energy (ΔG) of α,β-tubulins under different system conditions, and then from which to study the mechanism of the interaction between VLB and α,β-tubulins. The obtained results show that the dissociation of pure α,β-tubulins requires 197.8 kJ·mol^-1 for ΔG. When the VLB molecule exists between the interface of α,β-tubulins, the dissociation ΔG of α,β-tubulins reaches 220.5 kJ·mol^-1, which is greater than that of pure α,β-tubulin. The VLB molecule is formed by connecting a vindoline moiety (VM) molecule with a catharanthine moiety (CM) molecule through a carbon-carbon bond, which is a larger molecule. When the CM molecule exists in the middle of α,β-tubulin interface, the dissociation ΔG of α,β-tubulins is 46.2 kJ·mol^-1, during which the CM moves with β-tubulin. When the VM molecule exists between the middle of α,β-tubulin interface, the dissociation ΔG of α,β-tubulins is 86.7 kJ·mol^-1, during which it moves with α-tubulin. Therefore, the VLB molecule is like a double-sides tape to stick α-tubulin and β-tubulin together. The VLB molecule intervenes the dynamic equilibrium between dissociation and aggregation of α-tubulin and β-tubulin by a double-sides sticking mechanism to exert high activity with toxicity against cancer cell. Besides, our results demonstrate that VLB has its structural basis for anticancer cytotoxicity due to its two compositions composed of a CM molecule and a VM molecule although they have little toxicity against cancer cell alone.

Membrane Permeability: Characteristic Times and Lengths for Oxygen and a Simulation-Based Test of the Inhomogeneous Solubility-Diffusion Model

The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.

Molecular Mechanism and Dynamics of S-Deoxyephedrine Moving through Molecular Channels within D3R

In this article, the trajectories of S-deoxyephedrine (SBD) along molecular channels within the complex protein structure of third dopamine receptor (D₃R) are analyzed via molecular dynamic techniques, including potential mean force calculations of umbrella samplings from the 4.5 version of the GROMACS program. Changes in free energy due to the movement of SBD within D₃R are determined, and the molecular dynamic mechanisms of SBD transmitting along molecular channels are probed. Molecular simulated results show that the change in free energy is calculated as 171.7 kJ·mol^-1 for the transmission of SBD toward the outside of the cell along the y+ axis functional molecular channel and is 275.0 kJ·mol^-1 for movement toward the intracellular structure along the y- axis. Within the internal structure of D₃R, the changes in free energy are determined to be 103.6, 242.1, 459.7, and 127.8 kJ·mol^-1 for transmission of SBD along the x+, x-, z+, and z- axes, respectively, toward the cell bilayer membrane, which indicates that SBD leaves much more easily along the x+ axis through the gap between the TM5 (the fifth transmembrane helix) and TM6 (the sixth transmembrane helix) from the internal structure of D₃R. The values of free-energy changes indicate that SBD molecules can clear the protective channel within D₃R, which helps dopamine molecules to leave the D₃R internal structure along the x+ axis and to prevent them for exerting excessive neurotransmitter function. Therefore, our results suggest that SBD is effective for development as a drug for treating schizophrenia and its pharmacology is closely related to its dynamics and mechanisms within the molecular pathway of dopamine receptors.

Membrane Permeability of Fatty Acyl Compounds Studied via Molecular Simulation

Interest in fatty acid-derived products as fuel and chemical precursors has grown substantially. Microbes can be genetically engineered to produce fatty acid-derived products that are able to cross host membranes and can be extracted into an applied organic overlay. This process is thought to be passive, with a rate dependent on the chemistry of the crossing compound. The relationship between the chemical composition and the energetics and kinetics of product accumulation within the overlay is not well understood. Through biased and unbiased molecular simulation, we compute the membrane permeability coefficients from production to extraction for different fatty acyl products, including fatty acids, fatty alcohols, fatty aldehydes, alkanes, and alkenes. These simulations identify specific interactions that accelerate the transit of aldehydes across the membrane bilayer relative to other oxidized products, specifically the lack of hydrogen bonds to the surrounding membrane environment. However, since extraction from the outer membrane leaflet into the organic phase is found to be rate limiting for the entire process, we find that fatty alcohols and fatty aldehydes would both manifest similar fluxes into a dodecane overlay under equivalent conditions, outpacing the accumulation of acids or alkanes into the organic phase. Since aldehydes are known to be highly reactive as well as toxic in high quantities, the findings suggest that indeed fatty alcohols are the optimal long-tail fatty acyl product for extraction.

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.

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.

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.

Molecular dynamics simulation of d-Benzedrine transmitting through molecular channels within D3R

Dex-Benzedrine (known as d-Benzedrine or SAT) acts in dopamine receptors of central nerve cell system. In clinic, SAT is used to treat a variety of diseases; meanwhile, it has dependence and addiction. In order to investigate the pharmacology and addiction mechanisms of SAT as a medicine, in this paper, we have studied the structure of D₃R complex protein with SAT, and based on which, using potential mean force with umbrella samplings and the simulated phospholipid bilayer membrane (or POPC bilayer membrane), the molecular dynamics simulation was performed to obtain free energy changes upon the trajectories for SAT moving along the molecular channels within D₃R. The free energy change for SAT transmitting toward the outside of cell along the functional molecular channel within D₃R is 83.5 kJ mol^-1. The change of free energy for SAT to permeate into the POPC bilayer membrane along the protective molecular channel within D₃R is 87.7 kJ mol^-1. Our previous work gave that the free energy for Levo-Benzedrine (RAT) transmitting toward the outside of cell along the functional molecular channel within D₃R is 91.4 kJ mol^-1, while it is 117.7 kJ mol^-1 for RAT to permeate into the POPC bilayer membrane along the protective molecular channel within D₃R. The values of free energy suggest that SAT relatively prefers likely to pass through the functional molecular channel within D₃R for increasing the release of dopamine molecules resulting in a variety of functional effects for SAT. The obtained results show that the pharmacology and addiction mechanisms of SAT as a drug are closely related to the molecular dynamics and mechanism for SAT transmitting along molecular channels within D₃R.

Effects of Lipid Tethering in Extremophile-Inspired Membranes on H(+)/OH(-) Flux at Room Temperature

This work explores the proton/hydroxide permeability (PH+/OH-) of membranes that were made of synthetic extremophile-inspired phospholipids with systematically varied structural elements. A fluorescence-based permeability assay was optimized to determine the effects on the PH+/OH- through liposome membranes with variations in the following lipid attributes: transmembrane tethering, tether length, and the presence of isoprenoid methyl groups on one or both lipid tails. All permeability assays were performed in the presence of a low concentration of valinomycin (10 nM) to prevent buildup of a membrane potential without artificially increasing the measured PH+/OH-. Surprisingly, the presence of a transmembrane tether did not impact PH+/OH- at room temperature. Among tethered lipid monolayers, PH+/OH- increased with increasing tether length if the number of carbons in the untethered acyl tail was constant. Untethered lipids with two isoprenoid methyl tails led to lower PH+/OH- values than lipids with only one or no isoprenoid tails. Molecular dynamics simulations revealed a strong positive correlation between the probability of observing water molecules in the hydrophobic core of these lipid membranes and their proton permeability. We propose that water penetration as revealed by molecular dynamics may provide a general strategy for predicting proton permeability through various lipid membranes without the need for experimentation.

Permeability across lipid membranes

Molecular permeation through lipid membranes is a fundamental biological process that is important for small neutral molecules and drug molecules. Precise characterization of free energy surface and diffusion coefficients along the permeation pathway is required in order to predict molecular permeability and elucidate the molecular mechanisms of permeation. Several recent technical developments, including improved molecular models and efficient sampling schemes, are illustrated in this review. For larger penetrants, explicit consideration of multiple collective variables, including orientational, conformational degrees of freedom, are required to be considered in addition to the distance from the membrane center along the membrane normal. Although computationally demanding, this method can provide significant insights into the molecular mechanisms of permeation for molecules of medical and pharmaceutical importance. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

Dependence of norfloxacin diffusion across bilayers on lipid composition

Antibiotic resistance is a growing concern in medicine and raises the need to develop and design new drug molecules that can efficiently inhibit bacterial replication. Spurring the passive uptake of the drug molecules is an obvious solution. However our limited understanding of drug-membrane interactions due to the presence of an overwhelming variety of lipids constituting cellular membranes and the lack of facile tools to probe the bio-physical interactions between drugs and lipids imposes a major challenge towards developing new drug molecules that can enter the cell via passive diffusion. Here, we used a label-free micro-fluidic platform combined with giant unilamellar lipid vesicles to investigate the permeability of membranes containing mixtures of DOPE and DOPG in DOPC, leading to a label-free measurement of passive membrane-permeability of autofluorescent antibiotics. A fluoroquinolone drug, norfloxacin was used as a case study. Our results indicate that the diffusion of norfloxacin is strongly dependent on the lipid composition which is not expected from the traditional octanol-lipid partition co-efficient assay. The anionic lipid, DOPG, slows the diffusion process whereas the diffusion across liposomes containing DOPE increases with higher DOPE concentration. Our findings emphasise the need to investigate drug-membrane interactions with focus on the specificity of drugs to lipids for efficient drug delivery, drug encapsulation and targeted drug-delivery.

Molecular simulation of nonfacilitated membrane permeation

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

Water Permeability across Symmetric and Asymmetric Droplet Interface Bilayers: Interaction of Cholesterol Sulfate with DPhPC

Cellular membranes employ a variety of strategies for controlling the flow of small molecules into the cytoplasmic space, including incorporation of sterols for modulation of permeability and maintenance of lipid asymmetry to provide both sides of the membrane with differing biophysical properties. The specific case of cholesterol asymmetry, especially, is known to have profound effects in neurological cellular systems. Synthetic membrane models that can readily determine valuable physical parameters, such as water transport rates, for sterol-containing membranes of defined lipid composition remain in demand. We report the use of the droplet interface bilayer (DIB), composed of adherent aqueous droplets surrounded by a lipid monolayer and immersed in a hydrophobic medium, for measurement of water permeability across the membrane, with rapid visualization and ease of experimental setup. We studied droplet bilayer membranes composed of the prototypical synthetic membrane lipid (i.e., the archaeal lipid DPhPC) as well as of symmetric and asymmetric DIBs formed by DPhPC and sodium cholesterol sulfate (S-Chol). The presence of S-Chol in DPhPC in symmetric DIB reduced the passive water permeability rate (P(f)) at all concentrations and increased the activation energy (E(a)) to 17-18 kcal/mol. When only one side of the DIB contains S-Chol (asymmetric DIB), an E(a) of 14-15 kcal/mol was obtained, a value intermediate that of pure lipid and symmetrical DIB containing lipid and S-Chol. Our data are consistent with a capability for regulation of water transport by one leaflet independent of the other. The engineering of our various systems is believed to have implications for garnering detailed knowledge regarding the transport of small moieties across bilayers in a wide variety of lipid systems.

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

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

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

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

Molecular Simulation of the Transport of Drugs across Model Membranes

This Perspective describes recent progress in the area of the molecular simulation of the interactions of hydrophobic and hydrophilic solutes with membranes. The ability to predict drug solubility prior to synthesis is an extremely desirable goal for pharmaceutical research. A major advantage of molecular dynamics is the ability to computationally probe both the drug solubility as well as the pathway for the transport of drugs across membranes. Computational methods to predict the interaction free energy of solutes with membranes have advanced significantly in recent years and can characterize the intra- and intermolecular state of the drug as well as perturbations of the drug to the membrane environment itself. In addition to a brief review on computational methods to characterize the transport of drugs across membranes, we will highlight recent discoveries and discuss the challenges and opportunities in the field.

Ion-induced defect permeation of lipid membranes

We have explored the mechanisms of uncatalyzed membrane ion permeation using atomistic simulations and electrophysiological recordings. The solubility-diffusion mechanism of membrane charge transport has prevailed since the 1960s, despite inconsistencies in experimental observations and its lack of consideration for the flexible response of lipid bilayers. We show that direct lipid bilayer translocation of alkali metal cations, Cl(-), and a charged arginine side chain analog occurs via an ion-induced defect mechanism. Contrary to some previous suggestions, the arginine analog experiences a large free-energy barrier, very similar to those for Na(+), K(+), and Cl(-). Our simulations reveal that membrane perturbations, due to the movement of an ion, are central for explaining the permeation process, leading to both free-energy and diffusion-coefficient profiles that show little dependence on ion chemistry and charge, despite wide-ranging hydration energies and the membrane's dipole potential. The results yield membrane permeabilities that are in semiquantitative agreement with experiments in terms of both magnitude and selectivity. We conclude that ion-induced defect-mediated permeation may compete with transient pores as the dominant mechanism of uncatalyzed ion permeation, providing new understanding for the actions of a range of membrane-active peptides and proteins.

Water channel formation and ion transport in linear and branched lipid bilayers

The lipid bilayer stability and water channel morphologies are affected by the presence of methyl branches on lipid tails.

Calculation of the intrinsic solvation free energy profile of an ionic penetrant across a liquid-liquid interface with computer simulations

We introduce the novel concept of an intrinsic free energy profile, allowing one to remove the artificial smearing caused by thermal capillary waves, which renders difficulties for the calculation of free energy profiles across fluid interfaces in computer simulations. We apply this concept to the problem of a chloride ion crossing the interface between water and 1,2-dichloroethane and show that the present approach is able to reveal several important features of the free energy profile which are not detected with the usual, nonintrinsic calculations. Thus, in contrast to the nonintrinsic profile, a free energy barrier is found at the aqueous side of the (intrinsic) interface, which is attributed to the formation of a water "finger" the ion pulls with itself upon approaching the organic phase. Further, by the presence of a nonsampled region, the intrinsic free energy profile clearly indicates the coextraction of the first hydration shell water molecules of the ion when entering the organic phase.

Nontrivial behavior of water in the vicinity and inside lipid bilayers as probed by molecular dynamics simulations

The atomic-scale diffusion of water in the presence of several lipid bilayers mimicking biomembranes is characterized via unconstrained molecular dynamics (MD) simulations. Although the overall water dynamics corresponds well to literature data, namely, the efficient braking near polar head groups of lipids, a number of interesting and biologically relevant details observed in this work have not been sufficiently discussed so far; for instance, the fact that waters "sense" the membrane unexpectedly early, before water density begins to decrease. In this "transitional zone" the velocity distributions of water and their H-bonding patterns deviate from those in the bulk solution. The boundaries of this zone are well preserved even despite the local (<1 nm size) perturbation of the lipid bilayer, thus indicating a decoupling of the surface and bulk dynamics of water. This is in excellent agreement with recent experimental data. Near the membrane surface, water movement becomes anisotropic, that is, solvent molecules preferentially move outward the bilayer. Deep in the membrane interior, the velocities can even exceed those in the bulk solvent and undergo large-scale fluctuations. The analysis of MD trajectories of individual waters in the middle part of the acyl chain region of lipids reveals a number of interesting rare phenomena, such as the fast (ca. 50 ps) breakthrough across the membrane or long-time (up to 750 ps) "roaming" between lipid leaflets. The analysis of these events was accomplished to delineate the mechanisms of spontaneous water permeation inside the hydrophobic membrane core. It was shown that such nontrivial dynamics of water in an "alien" environment is driven by the dynamic heterogeneities of the local bilayer structure and the formation of transient atomic-scale "defects" in it. The picture observed in lipid bilayers is drastically different from that in a primitive membrane mimic, a hydrated cyclohexane slab. The possible biological impact of such phenomena in equilibrated lipid bilayers is discussed.

On the electroporation thresholds of lipid bilayers: molecular dynamics simulation investigations

Electroporation relates to the cascade of events that follows the application of high electric fields and that leads to cell membrane permeabilization. Despite a wide range of applications, little is known about the electroporation threshold, which varies with membrane lipid composition. Here, using molecular dynamics simulations, we studied the response of dipalmitoyl-phosphatidylcholine, diphytanoyl-phosphocholine-ester and diphytanoyl-phosphocholine-ether lipid bilayers to an applied electric field. Comparing between lipids with acyl chains and methyl branched chains and between lipids with ether and ester linkages, which change drastically the membrane dipole potential, we found that in both cases the electroporation threshold differed substantially. We show, for the first time, that the electroporation threshold of a lipid bilayer depends not only on the "electrical" properties of the membrane, i.e., its dipole potential, but also on the properties of its component hydrophobic tails.

Prediction of micelle/water and liposome/water partition coefficients based on molecular dynamics simulations, COSMO-RS, and COSMOmic

Liposomes and micelles find various applications as potential solubilizers in extraction processes or in drug delivery systems. Thermodynamic and transport processes governing the interactions of different kinds of solutes in liposomes or micelles can be analyzed regarding the free energy profiles of the solutes in the system. However, free energy profiles in heterogeneous systems such as micelles are experimentally almost not accessible. Therefore, the development of predictive methods is desirable. Molecular dynamics (MD) simulations reliably simulate the structure and dynamics of lipid membranes and micelles, whereas COSMO-RS accurately reproduces solvation free energies in different solvents. For the first time, free energy profiles in micellar systems, as well as mixed lipid bilayers, are investigated, taking advantage of both methods: MD simulations and COSMO-RS, referred to as COSMOmic (Klamt, A.; Huniar, U.; Spycher, S.; Keldenich, J. COSMOmic: A Mechanistic Approach to the Calculation of Membrane-Water Partition Coefficients and Internal Distributions within Membranes and Micelles. J. Phys. Chem. B 2008, 112, 12148-12157). All-atom molecular dynamics simulations of the system SDS/water and CTAB/water have been applied in order to retrieve representative micelle structures for further analysis with COSMOmic. For the system CTAB/water, different surfactant concentrations were considered, which results in different micelle sizes. Free energy profiles of more than 200 solutes were predicted and validated by means of experimental partition coefficients. To our knowledge, these are the first quantitative predictions of micelle/water partition coefficients, which are based on whole free energy profiles from molecular methods. Further, the partitioning in lipid bilayer systems containing different hydrophobic tail groups (DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine), SOPC (stearoyl-oleoylphosphatidylcholine), DMPC (1,2-dimyristoyl-sn-glycero-3-phosphocholine), and POPC (1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine)) as well as mixed bilayers was calculated. Experimental partition coefficients (log P) were reproduced with a root-mean-square error (RMSE) of 0.62. To determine the influence of cholesterol as an important component of cellular membranes, free energy profiles in the presence of cholesterol were calculated and shown to be in good agreement with experimental data.

Molecular insight into affinities of drugs and their metabolites to lipid bilayers

The penetration properties of drug-like molecules on human cell membranes are crucial for understanding the metabolism of xenobiotics and overall drug distribution in the human body. Here, we analyze partitioning of substrates of cytochrome P450s (caffeine, chlorzoxazone, coumarin, ibuprofen, and debrisoquine) and their metabolites (paraxanthine, 6-hydroxychlorzoxazone, 7-hydroxycoumarin, 3-hydroxyibuprofen, and 4-hydroxydebrisoquine) on two model membranes: dioleoylphosphatidylcholine (DOPC) and palmitoyloleoylphophatidylglycerol (POPG). We calculated the free energy profiles of these molecules and the distribution coefficients on the model membranes. The drugs were usually located deeper in the membrane than the corresponding metabolites and also had a higher affinity to the membranes. Moreover, the behavior of the molecules on the membranes differed, as they seemed to have a higher affinity to the DOPC membrane than to POPG, implying they have different modes of action in human (mostly PC) and bacterial (mostly PG) cells. As the xenobiotics need to pass through lipid membranes on their way through the body and the effect of some drugs might depend on their accumulation on membranes, we believe that detailed information of penetration phenomenon is important for understanding the overall metabolism of xenobiotics.

Fatty acids regulate stress resistance and virulence factor production for Listeria monocytogenes

Fatty acids (FAs) are the major structural component of cellular membranes, which provide a physical and chemical barrier that insulates intracellular reactions from environmental fluctuations. The native composition of membrane FAs establishes the topological and chemical parameters for membrane-associated functions and is therefore modulated diligently by microorganisms especially in response to environmental stresses. However, the consequences of altered FA composition during host-pathogen interactions are poorly understood. The food-borne pathogen Listeria monocytogenes contains mostly saturated branched-chain FAs (BCFAs), which support growth at low pH and low temperature. In this study, we show that anteiso-BCFAs enhance bacterial resistance against phagosomal killing in macrophages. Specifically, BCFAs protect against antimicrobial peptides and peptidoglycan hydrolases, two classes of phagosome antimicrobial defense mechanisms. In addition, the production of the critical virulence factor, listeriolysin O, was compromised by FA modulation, suggesting that FAs play a key role in virulence regulation. In summary, our results emphasize the significance of FA metabolism, not only in bacterial virulence regulation but also in membrane barrier function by providing resistance against host antimicrobial stress.