Lipids out of equilibrium: energetics of desorption and pore mediated flip-flop

The potential of mean force (PMF) of a phospholipid in a bilayer is a key thermodynamic property that describes the energetic cost of localized lipid defects. We have calculated the PMF by umbrella sampling using molecular dynamics simulations. The profile has a deep minimum at the equilibrium position in the bilayer and steeply rises for displacements both deeper into the bilayer and moving away from the bilayer. As the lipid loses contact with the bilayer, the profile abruptly flattens without a significant barrier. The calculated free energy difference of 80 kJ/mol between the minimum of the PMF and the value in water agrees well with the free energy difference calculated from the experimentally measured critical micelle concentration. Significant water/lipid defects form when a lipid is forced into the bilayer interior, in the form of a small water pore that spans the membrane. The energy required to form such a water pore is also found to be 80 kJ/mol. On the basis of this energy, we estimate the lipid flip-flop rate and permeability rate of sodium ions. The resulting rates are in good agreement with experimental measurements, suggesting lipid flip-flop and basal permeability of ions are pore mediated.     

Flip-flop in adsorbed bilayers

There is very rapid exchange between molecules between an adsorbed (supported) bilayer and solution. Complete exchange of a bilayer occurs within seconds; the actual exchange process may be faster but is limited by the resolution of our technique. The exchange process was monitored by infrared spectroscopy, which can independently monitor deuterium-labeled and unlabeled surfactants, and surface selectivity was achieved by using an internal reflection configuration. Total exchange requires exchange of both the inner and outer layer. We demonstrate that the desorption of a monolayer into water is extremely slow, yet exchange of the inner layer into surfactant solution is extremely fast when a bilayer is present. This shows that flip-flop for an adsorbed bilayer is very fast. Rapid flip-flop at interfaces is in sharp contrast to the extremely slow rate of flip-flop in vesicles. We hypothesize that the rapid rate of flip-flop in adsorbed layers is a consequence of surface-induced defects; in free vesicles, the defects are closed by the film pressure.     

Convergence of Free Energy Profile of Coumarin in Lipid Bilayer

Atomistic molecular dynamics (MD) simulations of druglike molecules embedded in lipid bilayers are of considerable interest as models for drug penetration and positioning in biological membranes. Here we analyze partitioning of coumarin in dioleoylphosphatidylcholine (DOPC) bilayer, based on both multiple, unbiased 3 μs MD simulations (total length) and free energy profiles along the bilayer normal calculated by biased MD simulations (～7 μs in total). The convergences in time of free energy profiles calculated by both umbrella sampling and z-constraint techniques are thoroughly analyzed. Two sets of starting structures are also considered, one from unbiased MD simulation and the other from "pulling" coumarin along the bilayer normal. The structures obtained by pulling simulation contain water defects on the lipid bilayer surface, while those acquired from unbiased simulation have no membrane defects. The free energy profiles converge more rapidly when starting frames from unbiased simulations are used. In addition, z-constraint simulation leads to more rapid convergence than umbrella sampling, due to quicker relaxation of membrane defects. Furthermore, we show that the choice of RESP, PRODRG, or Mulliken charges considerably affects the resulting free energy profile of our model drug along the bilayer normal. We recommend using z-constraint biased MD simulations based on starting geometries acquired from unbiased MD simulations for efficient calculation of convergent free energy profiles of druglike molecules along bilayer normals. The calculation of free energy profile should start with an unbiased simulation, though the polar molecules might need a slow pulling afterward. Results obtained with the recommended simulation protocol agree well with available experimental data for two coumarin derivatives.     

A molecular dynamics simulation study of C60 fullerenes inside a dimyristoylphosphatidylcholine lipid bilayer

We have carried out atomistic molecular dynamics simulations of C60 fullerenes inside a dimyristoylphosphatidylcholine lipid bilayer and an alkane melt. Simulations reveal that the preferred position of a single C60 fullerene is about 6-7 A off of the center plane, allowing the fullerene to take advantage of strong dispersion interactions with denser regions of the bilayer. Further displacement (>8 A) of the fullerene away from the center plane results in a rapid increase in free energy likely due to distortion of the lipid head group layer. The effective interaction between fullerenes (direct interaction plus environment (bilayer)-induced interaction), measured as the potential of mean force (POMF) between two fullerenes as a function of their separation, was found to be significantly less attractive in the lipid bilayer than in an alkane melt of the same molecular weight as the lipid tails. Only part of this difference can be accounted for by the more favorable interaction of the fullerene with the relatively denser bilayer. Additionally, our POMF studies indicate that the bilayer is less able to accommodate the larger aggregated fullerene pair than isolated single fullerenes, again likely due to distortion of the bilayer structure. The implications of these effects on aggregation of fullerenes within lipid bilayer are considered.     

Solvent-free coarse-grained lipid model for large-scale simulations

A coarse-grained molecular model, which consists of a spherical particle and an orientation vector, is proposed to simulate lipid membrane on a large length scale. The solvent is implicitly represented by an effective attractive interaction between particles. A bilayer structure is formed by orientation-dependent (tilt and bending) potentials. In this model, the membrane properties (bending rigidity, line tension of membrane edge, area compression modulus, lateral diffusion coefficient, and flip-flop rate) can be varied over broad ranges. The stability of the bilayer membrane is investigated via droplet-vesicle transition. The rupture of the bilayer and worm-like micelle formation can be induced by an increase in the spontaneous curvature of the monolayer membrane.     

Comparative molecular dynamics study of ether- and ester-linked phospholipid bilayers

The lipid membranes found in archaea have high bilayer stability and low permeability. The molecular structure of their constituent lipids is characterized by ether-linked, branched hydrophobic chains, whereas the conventional lipids obtained from eukaryotic or eubacterial sources have ester linked straight chains. In order to elucidate the influence of the ether linkage, instead of an ester one, on the physical properties of the lipid bilayers, we have carried out comparative 10 ns molecular dynamics simulations of diphytanyl phosphatidylcholine (ether-DPhPC) and diphytanoyl phosphatidylcholine (ester-DPhPC) bilayers in water, respectively. We analyze bilayer structures, hydration of the lipids, membrane dipole potentials, and free energy profiles of water and oxygen across the bilayers. We observe that the membrane dipole potential for the ether-DPhPC bilayer, which arises mainly from the ether linkage, is about half of that of the ester-DPhPC. The calculated free energy barrier for a water molecule in the ether-DPhPC bilayer system is slightly higher than that in the ester-DPhPC counterpart, which is in accord with experimental data.     

Thermodynamic study of benzocaine insertion into different lipid bilayers

Despite the general consensus concerning the role played by sodium channels in the molecular mechanism of local anesthetics, the potency of anaesthetic drugs also seems to be related with their solubility in lipid bilayers. In this respect, this work represents a thermodynamic study of benzocaine insertion into lipid bilayers of different compositions by means of molecular dynamics simulation. Thus, the free energy profiles associated with benzocaine insertion into symmetric lipid bilayers composed of different proportions of dipalmitoylphosphatidylcholine and dipalmitoylphosphatidylserine were studied. From the simulation results, a maximum in the free energy (ΔG) profile was measured in the region of the lipid/solution interface. This free energy barrier appears to be very much dependent on the lipid composition of the membrane. On the other hand, the minimum free energy (ΔG) within the bilayer remained almost independent of the lipid composition of the bilayer. By repeating the study at different temperatures, it was seen how the spontaneity of benzocaine insertion into the lipid bilayer is due to an increase in the entropy associated with the process.     

甲基多巴透过POPC磷脂双层膜过程的分子动力学模拟

采用分子动力学模拟研究甲基多巴分子透过磷脂双层膜的动力学机制.研究所采用的磷脂双层膜是一种卵磷脂脂质分子双层膜,即1-棕榈酰-2-油酰-卵磷脂(POPC)双层膜,分子动力学模拟基于Gromacs程序.通过分子动力学模拟获得甲基多巴透过POPC双层膜的自由能垒是99.9 kJ·mol-1(310 K),显示甲基多巴分子可以透过细胞生物膜.模拟获得甲基多巴在POPC双层膜中间层扩散运动的自由能垒是16.9-27.7 kJ·mol-1(310 K),证明甲基多巴分子在细胞膜中间层容易扩散.研究工作加深了对甲基多巴治疗高血压病机制的理解,促进研发治疗高血压病的新药物.     

Energy dependent decay rates of Lennard-Jones clusters for use in nucleation theory

Decay rates of small clusters (containing between 10 and 40 Lennard-Jones atoms) are determined by molecular dynamics simulations. The cluster is defined by the condition that the atoms must lie within a specified distance of their center of mass, and initial isothermal states are generated using a Metropolis Monte Carlo method. Plots of the logarithm of the survival fraction against time are found to be nonlinear, indicating that the decay of constant temperature clusters is non-Markovian and depends on the collision rate with a thermalizing gas. However, when the clusters are banded according to their energies, exponential decay is seen. The energy dependent decay rates from simulations agree to within a factor of 2 with those estimated from equilibrium considerations (using free energies from thermodynamic integration and assuming a Gaussian energy distribution), indicating that clusters defined in this way can be used in Markovian rate equations. During nucleation, the cluster energy distribution is shifted from its equilibrium value, leading to a reduction in the nucleation rate by a temperature dependent factor of 100 or more, in the absence of a thermalizing carrier gas.     

Stearic acid spin labels in lipid bilayers: insight through atomistic simulations

Spin-labeled stearic acid species are commonly used for electron paramagnetic resonance (EPR) studies of cell membranes to investigate phase transitions, fluidity, and other physical properties. In this paper, we use large-scale molecular dynamics simulations to investigate the position and behavior of nitroxide spin labels attached to stearic acid molecules in dipalmitoylphosphatidylcholine (DPPC) bilayers. The results of these studies are potentially very important for the interpretation of EPR spectra, which rely on assumptions about the position of the label in the membrane. Additionally, we investigate the effect of chirality and ionization of the carboxyl group of the label. For a non-ionized species, we observe that spin-label molecules are even able to make flip-flop transitions between the leaflets of the bilayer. Such transitions have been previously observed only in very rare cases in molecular simulations.     

甲基多巴透过POPC磷脂双层膜过程的分子动力学模拟

采用分子动力学模拟研究甲基多巴分子透过磷脂双层膜的动力学机制. 研究所采用的磷脂双层膜是一种卵磷脂脂质分子双层膜,即1-棕榈酰-2-油酰-卵磷脂（POPC）双层膜,分子动力学模拟基于Gromacs程序. 通过分子动力学模拟获得甲基多巴透过POPC双层膜的自由能垒是99.9 kJ·mol^-1（310 K）,显示甲基多巴分子可以透过细胞生物膜. 模拟获得甲基多巴在POPC双层膜中间层扩散运动的自由能垒是16.9-27.7 kJ·mol^-1（310 K）,证明甲基多巴分子在细胞膜中间层容易扩散. 研究工作加深了对甲基多巴治疗高血压病机制的理解,促进研发治疗高血压病的新药物.     

Enhanced hydrophobicity of fluorinated lipid bilayer: a molecular dynamics study

A molecular dynamics simulation of a partially fluorinated phospholipid bilayer has been carried out to understand the effects of fluorination of the hydrophobic chains on the structure and water permeability across the membrane. Fluorocarbon chains typically have an all-trans conformation, showing a highly ordered structure in the membrane core compared to ordinary hydrocarbon chains. The free energy profiles of water across the bilayers were successfully estimated by a revised cavity insertion Widom method. The fluorinated bilayer showed a higher free energy barrier than an ordinary nonfluorinated lipid bilayer by about 1.2 kcal/mol, suggesting a lower water permeability of the fluorinated bilayer membrane. A cavity distribution analysis elucidated the reduced free volume in the fluorinated membrane due to the neatly packed chains, which should account for the higher free energy barrier.     

Equilibrium distributions of dipalmitoyl phosphatidylcholine and dilauroyl phosphatidylcholine in a mixed lipid bilayer: atomistic semigrand canonical ensemble simulations

Conventional molecular dynamics (MD) simulations are seriously limited by the slow rate of diffusive mixing in their ability to predict lateral distributions of different lipid types within mixed-lipid bilayers using atomistic models. A method to overcome this limitation, using configuration-bias Monte Carlo (MC) "mutation" moves to transform lipids from one type to another in dynamic equilibrium, is demonstrated in binary fluid-phase mixtures of lipids whose tails differ in length by four carbons. The hybrid MC-MD method operates within a semigrand canonical ensemble, so that an equilibrium composition of the mixture is determined by a constant difference in chemical potential (Delta(mu)) chosen for the components. Within several nanoseconds, bilayer structures initiated as pure dipalmitoyl phosphatidylcholine (DPPC) or pure dilauroyl phosphatidylcholine (DLPC) converge to a common composition and structure in independent simulations conducted at the same Delta(mu). Trends in bilayer thickness, area per lipid, density distributions across the bilayer, and order parameters have been investigated at three mixture compositions and compared with results from the pure bilayers at 323 K. The mixtures showed a moderate increase in DPPC acyl tail sites crossing the bilayer midplane relative to pure DPPC. Correlations between lateral positions of the two lipid types within or across the bilayer were found to be weak or absent. While the lateral distribution is consistent with nearly ideal mixing, the dependence of composition on Delta(mu) indicates a positive excess free energy of mixing.     

SHORT-RANGE MOLECULAR INTERACTIONS AND STABILITY OF AMPHIPHILE BILAYER

A new approach is proposed for the study of short-range molecular interactions between first neighboring molecules in amphiphile bilayers by means of experimentally determined dependencies of the bilayer mean lifetime on the surfactant concentration and of the critical concentration for bilayer formation on the temperature. Short-range molecular interactions are demonstrated by the parameters binding energy Q of an amphiphile molecule in the bilayer and specific line energy γ of the nucleus hole. These parameters are calculated from the experimental dependencies by using the hole-nucleation theory [D. Kashchiev and D. Exerowa, J. Colloid Interface Sci., 77, 501 (1980)] describing the stability of amphiphile bilayers. It is shown the decisive role of the short-range molecular interactions for the bilayer stability and the occurrence of first-order phase transition in phospholipid foam bilayers. The values of Q and γ are calculated for various amphiphile bilayers: anionic and nonionic surfactants, phospholipids and their natural mixtures.     

左苯丙胺在多巴胺第三受体分子通道中传输分子动力学模拟

左旋苯丙胺(又称左苯丙胺, RAT)在临床上被用于治疗多种病症,作用在中枢神经细胞多巴胺受体上,同时它具有依赖性和成瘾性。为了探讨RAT被用作药物的药理和成瘾机制,本文用分子模拟获得RAT与多巴胺第三受体(D₃R)复合蛋白优化结构,并且采用伞形样本平均力势(PMF)方法和卵磷脂脂质分子模拟生物膜,采用分子动力学模拟获得RAT在D₃R结构中分子通道运动轨迹和自由能变化。RAT通过D₃R结构中的功能分子通道,朝细胞外方向传输运动的自由能变化为91.4 kJ·mol^-1。RAT通过D₃R结构中的保护分子通道,朝细胞双层膜方向传输运动的自由能变化为117.7 kJ·mol^-1。自由能数值表明RAT分子更容易通过D₃R结构中的功能分子通道,发挥其功能作用,增大功能多巴胺分子的释放,导致包括依赖性和成瘾性多种功能效果。研究结果证明RAT被用作药物的药理和成瘾机制与它在多巴胺受体中的分子通道上传输动力学和机制有密切关联。     

Langmuir-Blodgett film characteristics and phospholipid membrane ion conduction : Part 1. Modification by Cholesterol and Oxidized Derivatives

The energy barrier to inorganic ion conduction through bilayer lipid membranes (BLM) is investigated as a function of molecular packing and dipolar potential characteristics. Arrhenius energy barrier information is derived from temperature-dependent electrochemical experiments with phosphatidyl choline/steroid BLM. The steroids studied at 0.65 mole fraction in phospholipid were 5-cholesten-3β-ol, 5,7-cholestadien-3β-ol, 5-cholesten-3β,7α-diol, 5α-cholestan-3β,5α,6β-triol, 5α-cholestan-5α,6α-epoxy-3β-ol, 5-cholesten-3β-ol-7-one and 5α-cholestan-3-one. Correlation of the barrier magnitude with molecular packing characteristics, obtained by collecting monolayer data from a Langmuir-Blodgett trough, indicates that the BLM ion current is almost completely controlled by molecular density. The sensitivity of the energy barrier as a function of molecular packing is as great as 0.1 eV for a 0.01-nm² adjustment.     

Molecular mechanism for lipid flip-flops

Transmembrane lipid translocation (flip-flop) processes are involved in a variety of properties and functions of cell membranes, such as membrane asymmetry and programmed cell death. Yet, flip-flops are one of the least understood dynamical processes in membranes. In this work, we elucidate the molecular mechanism of pore-mediated transmembrane lipid translocation (flip-flop) acquired from extensive atomistic molecular dynamics simulations. On the basis of 50 successful flip-flop events resolved in atomic detail, we demonstrate that lipid flip-flops may spontaneously occur in protein-free phospholipid membranes under physiological conditions through transient water pores on a time scale of tens of nanoseconds. While the formation of a water pore is induced here by a transmembrane ion density gradient, the particular way by which the pore is formed is irrelevant for the reported flip-flop mechanism: the appearance of a transient pore (defect) in the membrane inevitably leads to diffusive translocation of lipids through the pore, which is driven by thermal fluctuations. Our findings strongly support the idea that the formation of membrane defects in terms of water pores is the rate-limiting step in the process of transmembrane lipid flip-flop, which, on average, requires several hours. The findings are consistent with available experimental and computational data and provide a view to interpret experimental observations. For example, the simulation results provide a molecular-level explanation in terms of pores for the experimentally observed fact that the exposure of lipid membranes to electric field pulses considerably reduces the time required for lipid flip-flops.     

Determination of liposome permeability of ionizable carbamates of zidovudine by steady state fluorescence spectroscopy

In the present paper the relative permeabilities of AZT-Pyp and AZT-Ethy across a phospholipid bilayer were estimated by the means of fluorescence spectroscopy.

The center of spectral mass of both non-encapsulated AZT-derivatives (AZT-der) emission spectra increased as a function of the illumination time inside the spectrofluorimeter cell. This phenomenon was even more evident when drugs were incubated under an UV mercury lamp, suggesting its photolytic origin. AZT-der were protected from photolysis inside liposomes and decomposed upon irradiation when they were free in the aqueous phase. The time-dependent decrease in the fluorescence intensity at a constant wavelength was fitted to a two-exponential equation and the values of rate constants for permeability and photolysis were calculated. It was concluded that AZT-Pyp but not AZT-Ethy diffused across the bilayer. This behavior correlated with the molecular volumes of AZT-Pyp (379.6 Å³) and AZT-Ethy (450.5 Å³), determined from the minimum energy conformations but not with previously reported log P values. These results reinforce the concept that not only lipophilicity but also membrane structure and AZT-der molecular size had a critical influence in passive diffusion across bilayers and may help in future refinements of other AZT-der molecular design.     

Heterogeneous and anomalous diffusion inside lipid tubules

Self-assembled lipid tubules with crystalline bilayer walls are promising candidates for controlled drug delivery vehicles on the basis of their ability to release preloaded biological molecules in a sustained manner. While a previous study has shown that the release rate of protein molecules from lipid tubules depends on the associated molecular mass, suggesting that the pertinent diffusion follows the well-known Stokes-Einstein relationship, only a few attempts have been made toward investigating the details of molecular diffusion in the tubule interior. Herein, we have characterized the diffusion rates of several molecules encapsulated in lipid tubules formed by 1,2-bis(10,12-tricosadiynoyl)-sn-glycero-3-phosphocholine (DC8,9PC) using the techniques of fluorescence recovery after photobleaching (FRAP) and fluorescence correlation spectroscopy (FCS). Our results show that the mobility of these molecules depends not only on their positions in the DC8,9PC tubules but also on their respective concentrations. While the former indicates that the interior of the DC8,9PC tubules is heterogeneous in terms of diffusion, the latter further highlights the possibility of engineering specific conditions for achieving sustained release of a "drug molecule" over a targeted period of time. In addition, our FCS results indicate that the molecular diffusions inside the crystalline bilayer walls of the DC8,9PC tubules strongly deviate from the normal, stochastic processes, with features characterizing not only anomalous subdiffusions but also motions that are superdiffusive in nature.     

New fluorescent probes reveal that flippase-mediated flip-flop of phosphatidylinositol across the endoplasmic reticulum membrane does not depend on the stereochemistry of the lipid

Glycerophospholipid flip-flop across biogenic membranes such as the endoplasmic reticulum (ER) is a fundamental feature of membrane biogenesis. Flip-flop requires the activity of specific membrane proteins called flippases. These proteins have yet to be identified in biogenic membranes and the molecular basis of their action is unknown. It is generally believed that flippase-facilitated glycerophospholipid flip-flop across the ER is governed by the stereochemistry of the glycerolipid, but this important issue has not been resolved. Here we investigate whether the ER flippase stereochemically recognizes the glycerophospholipids that it transports. To address this question we selected phosphatidylinositol (PI), a biologically important molecule with chiral centres in both its myo-inositol headgroup and its glycerol-lipid tail. The flip-flop of PI across the ER has not been previously reported. We synthesized fluorescence-labeled forms of all four diastereoisomers of PI and evaluated their flipping in rat liver ER vesicles, as well as in flippase-containing proteoliposomes reconstituted from a detergent extract of ER. Our results show that the flippase is able to translocate all four PI isomers and that both glycerol isomers of PI flip-flop across the ER membrane at rates similar to that measured for fluorescence-labeled phosphatidylcholine. Our data have important implications for recent hypotheses concerning the evolution of distinct homochiral glycerophospholipid membranes during the speciation of archaea and bacteria/eukarya from a common cellular ancestor.