Linear free energy relationship for osmotic water flow through a membrane

A linear free-energy relationship has been found for the osmotic water flux through membranes in a broad variety of systems including electrolytes, organic compounds, intact biological cells and industrial scale filtration. In all cases, broad concentration ranges were found in which the equation In v = In m + β (v. flux (in kg cm⁻² min⁻¹: m. molarity)) was valid. The parameters and β were interpreted in terms of molecular weight, mean ionic radius, enthalpy of solvation. electronic structure and H-bonding propensity. The equation is independent of the membrane material and of the presence of other solutes and precipitates, as long as the latter are incompressible. Its parameters are only slightly dependent upon the temperature. The contributions from different solutes to the osmotic flux are at appreciable concentrations even additive. The relationship permits the prediction of the osmotic water flux and of the rate of filtration of systems of known composition. For simple systems it permits determination of the molecular weight, mean ionic radius, degree of hydration and enthalpy of solvalion. It is suggested that osmosis is primarily due to the shift of hydration equilibria and that guanidine hydrochloride. in a realistic concentration range, forms practically infinite clathrates with water. The properties of the urea and Gdn.HCl systems indicate that these solutes either reversibly change the membrane structure and/or display intrinsic hysteresis.     

Protein-induced membrane disorder: a molecular dynamics study of melittin in a dipalmitoylphosphatidylcholine bilayer

A molecular dynamics simulation of melittin in a hydrated dipalmitoylphosphatidylcholine (DPPC) bilayer was performed. The 19, 000-atom system included a 72-DPPC phospholipid bilayer, a 26-amino acid peptide, and more than 3000 water molecules. The N-terminus of the peptide was protonated and embedded in the membrane in a transbilayer orientation perpendicular to the surface. The simulation results show that the peptide affects the lower (intracellular) layer of the bilayer more strongly than the upper (extracellular) layer. The simulation results can be interpreted as indicating an increased level of disorder and structural deformation for lower-layer phospholipids in the immediate vicinity of the peptide. This conclusion is supported by the calculated deuterium order parameters, the observed deformation at the intracellular interface, and an increase in fractional free volume. The upper layer was less affected by the embedded peptide, except for an acquired tilt relative to the bilayer normal. The effect of melittin on the surrounding membrane is localized to its immediate vicinity, and its asymmetry with respect to the two layers may result from the fact that it is not fully transmembranal. Melittin's hydrophilic C-terminus anchors it at the extracellular interface, leaving the N-terminus "loose" in the lower layer of the membrane. In general, the simulation supports a role for local deformation and water penetration in melittin-induced lysis. As for the peptide, like other membrane-embedded polypeptides, melittin adopts a significant 25 degree tilt relative to the membrane normal. This tilt is correlated with a comparable tilt of the lipids in the upper membrane layer. The peptide itself retains an overall helical structure throughout the simulation (with the exception of the three N-terminal residues), adopting a 30 degree intrahelical bend angle.     

Molecular dynamics simulation of dipalmitoylphosphatidylcholine membrane with cholesterol sulfate

Using the molecular dynamics simulation technique, we studied the changes occurring in a dipalmitoylphosphatidylcholine (DPPC):cholesterol (CH) membrane at 50 mol% sterol when cholesterol is replaced with cholesterol sulfate (CS). Our simulations were performed at constant pressure and temperature on a nanosecond time scale. We found that 1) the area per DPPC:CS heterodimer is greater than the area of the DPPC:CH heterodimer; 2) CS increases ordering of DPPC acyl chains, but to a lesser extent than CH; 3) the number of hydrogen bonds between DPPC and water is decreased in a CS-containing membrane, but CS forms more water hydrogen bonds than CH; and 4) the membrane dipole potential reverses its sign for a DPPC-CS membrane compared to a DPPC-CH bilayer. We also studied the changes occurring in lipid headgroup conformations and determined the location of CS molecules in the membrane. Our results are in good agreement with the data available from experiments.     

Changes in apparent free energy of helix-helix dimerization in a biological membrane due to point mutations

We present an implementation of the TOXCAT membrane protein self-association assay that measures the change in apparent free energy of transmembrane helix dimerization caused by point mutations. Quantifying the reporter gene expression from cells carrying wild-type and mutant constructs shows that single point mutations that disrupt dimerization of the transmembrane domain of glycophorin A reproducibly lower the TOXCAT signal more than 100-fold. Replicate cultures can show up to threefold changes in the level of expression of the membrane bound fusion construct, and correcting for these variations improves the precision of the calculated apparent free energy change. The remarkably good agreement between our TOXCAT apparent free energy scale and free energy differences from sedimentation equilibrium studies for point mutants of the glycophorin A transmembrane domain dimer indicate that sequence changes usually affect membrane helix-helix interactions quite similarly in these two very different environments. However, the effects of point mutations at threonine 87 suggest that intermonomer polar contacts by this side-chain contribute significantly to dimer stability in membranes but not in detergents. Our findings demonstrate that a comparison of quantitative measurements of helix-helix interactions in biological membranes and genuine thermodynamic data from biophysical measurements on purified proteins can elucidate how changes in the lipidic environment modulate membrane protein stability.     

Molecular dynamics simulation of dipalmitoylphosphatidylcholine modified with a MTSL nitroxide spin label in a lipid membrane

We investigate the interaction between dipalmitoylphosphatidylcholine (DPPC) and a nitroxide spin label in order to understand its influences on lipid structure and dynamics using molecular dynamics simulations. The system was modified by covalently attaching nitroxide spin labels to the headgroups of two DPPC molecules. (S-(2,2,5,5-tetramethyl-2,5-dihydro-1H-pyrrol-3-yl)methyl methanesulfonothioate) (MTSL) was used as the spin label. The label position and dynamics were analyzed as was the impact of the modified DPPC on the structure of the surrounding lipids. The modified DPPC molecules locate closer to the center of the membrane than unmodified DPPC molecules. The rotation of the spin label is unrestricted, but there are favored orientations. MTSL depresses the deuterium order parameters of the carbon atoms close to the headgroup in surrounding DPPC molecules. The spin label has no impact on order parameters of carbon atoms at the end of the lipid tails. The lateral diffusion constant of the modified DPPC is indistinguishable from unmodified DPPC molecules. These novel computational results suggest an experimental validation.     

Molecular dynamics simulation of Bombolitin II in the dipalmitoylphosphatidylcholine membrane bilayer

The orientation behavior of Bombolitin II (BLT2) in the dipalmitoylphosphatidylcholine membrane bilayer was investigated by using molecular-dynamics simulation. During the 20-ns simulation, the BLT2 began to tilt and finally reached the angle of 51° from the membrane-normal. The structure of the peptide formed the amphipathic α-helical structure during the entire simulation time. The peptide tilts with its hydrophobic side faced to the hydrophobic core of the bilayer. We analyzed the mechanism of the tilting behavior of the peptide associated with the membrane in detail. The analysis showed that the hydrogen-bond interaction and the electrostatic interaction were found to exist between Lys¹² and a lipid molecule. These interactions are considered to work as an important factor in tilting the peptide to the membrane-normal.     

Electrostatic free energy and spontaneous curvature of spherical charged layered membrane

A biophysical model for the equilibrium curvature of a composite membrane element is derived taking into account the mechanical bilayer properties and the adjacent charged protein layers. The minimum of the total free energy density with respect to the curvature of such a membrane curved was estimated from the sum of the electrostatic free energy density of the charges of the membrane and the elastic surface energy density due to bending the lipid bilayer membrane. It was shown that the equilibrium curvature, i.e. the spontaneous curvature, of such a charged composite sandwich-like membrane depends inversely on the bending stiffness of the lipid membrane itself and directly on the charge amount inside and outside the membrane to the second power. Furthermore the geometric and electrostatic structure of the protein layers and the physico-chemical environment conditions are involved. Corresponding to the model developed a "standard RBC" membrane element has a negative spontaneous curvature, accounting for a discocyte RBC shape. The shape change from a discocyte to a more stomatocytic shape (increase in the negative spontaneous curvature) after reducing the charges in the glycocalyx is also explained within this model.     

Simulating the free energy of passive membrane permeation for small molecules

Abstract

Computer simulations of passive membrane permeation provide important microscopic insights into the molecular mechanism of this important biological process that are complementary to experimental data. Our review focuses on the main approaches for calculating the free energy, or potential of mean force, for permeation of small molecules through lipid bilayers. The theoretical background for most currently used methods for potential of mean force calculation is described, including particle insertion, thermodynamic integration, umbrella sampling, metadynamics, adaptive biasing force and milestoning. A brief comparison of strengths and weaknesses of the competing approaches is presented. This is followed by a survey of results obtained by the different methods, with special attention to describing the mechanistic insights generated by modelling and illustrating capabilities of the different techniques. We conclude with a discussion of recent advances and future directions in modelling membrane permeation, including latest methodological enhancements, consideration of multiple slow variables and memory effects.     

Nonselective squeeze-out of dioleoylphosphatidylcholine and dioleoylphosphatidylglycerol from binary mixed monolayers with dipalmitoylphosphatidylcholine

In order to enable the possible use of dipalmitoylphosphatidylcholine as an artificial lung surfactant, the addition of dioleoylphosphatidylcholine or dioleoylphosphatidylglycerol has been suggested. A preferential loss of molecules of the second component during compression of the interfacial layer was proposed. In this study two types of measurement were carried out in order to verify such a preferential squeeze-out. In the first type, electron micrographs of a pure dipalmitoylphosphatidylcholine monolayer and of mixed monolayers of dipalmitoylphosphatidylcholine and egg phosphatidylglycerol were taken in order to study the nature of the structures formed during compression of the monolayer. The electron microscopy photos show horizontally stacked layers in the collapse phase of dipalmitoylphosphatidylcholine, and long vertical ridges in the mixed monolayers up to 20% second component. At higher concentrations of the second component no such structures can be detected. The second type involved monolayer studies with binary mixtures of dipalmitoylphosphatidylcholine and dioleoylphosphatidylcholine or dioleoylphosphatidylglycerol, one of the pair being always radioactively labelled. Counting the radioactivities in bulk phase and monolayer after compression revealed nonselective squeeze-out of either component.     

Association of daunomycin to membrane domains studied by fluorescence resonance energy transfer

1,6-Diphenyl-1,3,5-hexatriene and 1-(4-trimethylammoniumphenyl)-6-phenyl-1,3,5-hexatriene are fluorophores used to explore different hydrophobic domains of membrane bilayers (Andrich, M.P. and Vanderkooi, J.M. (1976) Biochemistry 15, 1257-1265; Prendergast, F.G., Haugland, R.P. and Callahan, P.J. (1981) Biochemistry 20, 7333-7338). Fluorescence resonance energy transfer between these fluorophores, acting as energy donors, and the anthracycline, daunomycin, as the acceptor, was used to analyze the interaction of the drug with natural membranes, and its relative location within the membrane bilayer. The transfer process was demonstrated by: (1) emission fluorescence of the acceptor when the samples were excited at the excitation maximum of the donor (360 nm); and (2) progressive quenching of the energy donor (at 428 nm) when in the presence of increasing acceptor concentration. Also, the disruption of the energy transfer by solubilization of the membrane with Triton X-100 evidences a role for the membrane in providing the appropriate site(s) for energy transfer to occur. At moderately low daunomycin/membrane lipid ratios, the different efficiencies of resonance energy transfer between the two donors and daunomycin predicts a preferential, but not exclusive, location of the drug at membrane 'surface' domains, i.e., those regions of the bilayer explored by the 1-(4-trimethylammoniumphenyl)-6-phenyl-1,3,5-hexatriene probe. In support of this observation, a large fraction (approx. 75%) of membrane-associated daunomycin was rapidly sequestered away from the membrane upon addition of excess DNA, which forms high-affinity complexes with daunomycin (Chaires, J.B., Dattagupta, n. and Crothers, D.M. (1982) Biochemistry 21, 3927-3932), thus acting as a drug 'sink'. Also, a large fraction of drug was accessible to fluorescence quenching by iodide, a collisional water-soluble quencher. On the other hand, a smaller population of the membrane-associated daunomycin was characterized by slow sequestering by the added DNA and inaccessibility to quenching by iodide. We conclude that the daunomycin, which is only slowly sequestered, is located deep within the hydrophobic domains of the bilayer, likely to be those probed by 1,6-diphenyl-1,3,5-hexatriene.     

Influence of the membrane potential on the free energy of an intrinsic protein

A modified Poisson-Boltzmann equation is developed from statistical mechanical considerations to describe the influence of the transmembrane potential on macromolecular systems. Using a Green's function formalism, the electrostatic free energy of a protein associated with the membrane is expressed as the sum of three terms: a contribution from the energy required to charge the system's capacitance, a contribution corresponding to the interaction of the protein charges with the membrane potential, and a contribution corresponding to a voltage-independent reaction field free energy. The membrane potential, which is due to the polarization interface, is calculated in the absence of the protein charges, whereas the reaction field is calculated in the absence of transmembrane potential. Variations in the capacitive energy associated with typical molecular processes are negligible under physiological conditions. The formulation of the theory is closely related to standard algorithms used to solve the Poisson-Boltzmann equation and only small modifications to current source codes are required for its implementation. The theory is illustrated by examining the voltage-dependent membrane insertion of a simple polyalanine alpha-helix and by computing the electrostatic potential across a 60-A-diameter sphere meant to represent a large intrinsic protein.     

Interaction of surfactants with vesicle membrane of dipalmitoylphosphatidylcholine: fluorescence depolarization study

The effect of surfactants on the "fluidity" of dipalmitoylphosphatidylcholine (DPPC) vesicle membrane was studied by means of the fluorescence depolarization technique with fatty acid fluorescent probes, in which the anthroyloxy group is introduced at different positions along the acyl chain. Three types of surfactants were examined; anionic sodium alkylsulfates, cationic alkyltrimethylammonium chlorides, and non-ionic alkanoyl-N-methylglucamides (MEGA-n). Perturbing effects of the surfactants depended on both the alkyl chain-length and the type of head group. Sodium alkylsulfates with octyl- and decyl-chain and alkyltrimethylammonium chlorides with octyl-, decyl- and dodecyl-chain did not affect the membrane fluidity when incorporated in the membrane, whereas sodium dodecylsulfate and tetradecyltrimethylammonium chloride decreased the membrane fluidity at both gel and liquid crystalline states of the membrane. All the MEGA series surfactants decreased the membrane fluidity, whose perturbing potency was in the order of MEGA-8 less than MEGA-9 approximately equal to MEGA-10. The perturbation at different depths in the membrane by sodium dodecylsulfate and MEGA-9 was also examined. No significant change in the fluidity gradient across the membrane was induced by the addition of these surfactants.     

Prediction of the mutation-induced change in thermodynamic stabilities of membrane proteins from free energy simulations

Comparative protein structure modeling and free energy perturbation simulation have been applied in a consecutive manner to investigate the mutation-induced stabilization of membrane proteins (MPs) in aqueous solution without knowledge of their three-dimensional structures. The calculated difference in protein solvation free energy between the wild type and a mutant compares well with their relative thermodynamic stabilities in solution. For monomeric MPs, a mutant reveals a higher stability than the wild type if the calculated solvation free energy indicates a favorable change. On the contrary, for oligomeric MPs the stability of a mutant increases as the solvation free energy of a mutated monomer becomes less favorable, indicating that the oligomeric MP mutant would be stabilized in solution due to the reduced desolvation cost for oligomerization. The present computational strategy is expected to find its way as a useful tool for assessing the relative stability of a mutant MP with respect to its wild type in solution.     

Role of a reaction coordinate in free energy calculations

Abstract

The free energy calculation method emerges as a viable technique for ‘in-silico’ calorimetry. Efficient sampling techniques and the good choice of a reaction path connecting the reactant and the product state enable accurate computations of the free energy differences. We argue that in many cases the thermodynamic integration technique has the lowest variance when the transformation between the reactant and the product state proceeds along the natural path of the studied chemical reaction. We provide examples of free energy calculations for the fragmentation of the charged clusters and the swapping reaction of oligomer formation in proteins that follow a tentative reaction mechanism.     

Raman spectroscopic studies of the packing properties of mixed dihexadecyl- and dipalmitoylphosphatidylcholine bilayer dispersions

X-ray diffraction studies suggest the existence of two separate gel phases for mixed dihexadecylphosphatidylcholine (DHPC)/dipalmitoylphosphatidylcholine (DPPC) bilayers [Kim, J. T., Mattai, J., & Shipley, G. G. (1987) Biochemistry 26, 6599-6603; Lohner, K., Schuster, A., Degovics, G., Müller, K., & Laggner, P. (1987) Chem. Phys. Lipids 44, 61-70]. In one gel phase the lipid chains are interdigitated, while the other gel phase exhibits the conventional bilayer form. We use Raman spectroscopy to provide a detailed molecular analysis of the intermolecular and intramolecular interactions of the DHPC and DPPC molecules within these mixed bilayers. Observation of the methylene chain C-H stretching modes of DHPC and the methylene chain C-D stretching modes of DPPC-d62 for various mixed DHPC/DPPC-d62 bilayers enables the packing characteristics and conformational order of each lipid to be monitored separately. The spectral data indicate that the packing properties of DPPC-d62 in the mixed-lipid bilayers remain relatively unchanged, while the intramolecular and intermolecular properties of DHPC change dramatically as a function of the composition of the DHPC/DPPC-d62 mixed bilayer. This is consistent with a model based upon the existence of three characteristic lipid types for the mixed-lipid system, namely, domains of pure DPPC-d62 and pure DHPC species with interface lipids or boundary regions between the bulk domains.     

Molecular dynamics simulation of neuropeptide B and neuropeptide W in the dipalmitoylphosphatidylcholine membrane bilayer

GPR7 and GPR8 are recently deorphanized G-protein-coupled receptors that are implicated in the regulation of neuroendocrine function, feeding behavior, and energy homeostasis. Neuropeptide B (NPB) and neuropeptide W (NPW) are two membrane-bound hypothalamic peptides, which specifically antagonize GPR7 and GPR8. Despite years of research, an accurate estimation of structure and molecular recognition of these neuropeptide systems still remains elusive. Herein, we investigated the structure, orientation, and interaction of NPB and NPW in a dipalmitoylphosphatidylcholine bilayer using long-range molecular dynamics (MD) simulation. During 30-ns simulation, membrane-embedded helical axes of NPB and NPW tilted 30 and 15°, respectively, from the membrane normal in order to overcome possible hydrophobic mismatch with the lipid bilayer. The calculation of various structural parameters indicated that NPW is more rigid and compact as compared to NPB. Qualitatively, the peptides exhibited flexible N-terminal (residues 1–12) and rigid C-terminal α-helical parts (residues 13–21), confirming previous NMR data. A strong electrostatic attraction between C-termini and headgroup atoms caused translocation of the peptides towards lower leaflet of the bilayer. The stabilizing hydrogen bonds (H-bonds) between phosphate groups and Trp1, Lys3, and Arg15 of the peptides played important roles for membrane anchoring. MD simulations of Alanine (Ala) mutants revealed that WYK->Ala variant of NPB/NPW lacked crucial H-bond interactions with phospholipid headgroups and also caused severe misfolding in NPB. Altogether, the knowledge of preferred structural fold and interaction of neuropeptides within the membrane bilayer will be useful to develop synthetic agonist or antagonist peptides for GPR7 and GPR8.     

Deformation free energy of bilayer membrane and its effect on gramicidin channel lifetime.

The deformation free energy of a lipid bilayer is presented based on the principle of a continuum theory. For small deformations, the free energy consists of a layer-compression term, a splay-distortion term, and a surface-tension term, equivalent to the elastic free energy of a two-layer smectic liquid crystal with surface tension. Minimization of the free energy leads to a differential equation that, with boundary conditions, determines the elastic deformation of a bilayer membrane. When a dimeric gramicidin channel is formed in a membrane of thickness greater than the length of the channel, the membrane deformation reduces the stability of the channel. Previously this effect was studied by comparing the variation of channel lifetime with the surface tension of bilayers (Elliott, J. R., D. Needham, J. P. Dilger, and D. A. Hayden, 1983, Biochim. Biophys. Acta, 735:95-103). The tension was assumed to pull a dimer for a distance z before the channel loses ion conductivity. To account for the data, z was found to be 18 A. With the deformation free energy, the data can be accounted for with z less than or approximately to 1 A, which is consistent with the breaking of hydrogen bonds in a dimer dissociation. Increasing the strength of lipid-protein interactions is not the only consequence of the complete free energy compared with the previous discussions. It also changes the shape of membrane deformation around an embedded channel from convex to concave, and increases the range of deformation from less than 10 A to greater than 20 A. Clearly these will be important factors in the general considerations of lipid-protein interactions and membrane-mediated interactions between proteins. In addition, thermal fluctuations of a membrane are calculated; in particular, we calculate the relations between the intrinsic thickness and the experimentally measured values. The experimental parameters of monoolein-squalene membranes are used for quantitative analyses.     

九寨沟针阔混交林能量平衡特征

青藏高原及其周边地区的能量交换过程是推动我国及东亚地区天气过程演变与气候变化的重要因素。青藏高原及其周边山谷地区与青藏高原—四川盆地过渡区具有独特的大气边界层热力结构,其能量收支研究不可忽视,但由于长期观测数据的缺失,该地区的能量平衡特征尚未解明。以青藏高原东北边缘向四川盆地陡跌的过渡地带的典型亚高山河谷九寨沟的针阔混交林为研究对象,利用涡度相关系统,对九寨沟典型针阔混交林2014—2015年各能量通量进行了连续观测,分析了该生态系统能量平衡各分量的变化特征,讨论其能量闭合状况。结果表明:能量平衡各分量均与净辐射有相似的日变化、季节变化特征。与萌芽期、生长期、生长后期相比,冻土期各分量峰现时间均延迟2—3 h;而且各项绝对值大小在不同季节占比不同:冻土期和萌芽期显热通量为能量主要支出项;而生长期与生长后期潜热通量占主导地位。九寨沟2014与2015年生长期潜热通量占净辐射比值分别为0.69、0.75,远高于青藏高原其他地区。两年间研究区能量不闭合,能量闭合度分别为0.75,0.71。对于更好地理解高原山区和从高原到盆地的能量循环机理和动力学有着重要意义。     

Photosynthetic free energy transduction related to the electric potential changes across the thylakoid membrane

A model based on our present knowledge of photosynthetic energy transduction is presented. Calculated electric potential profiles are compared with microelectrode recordings of the thylakoid electric potential during and after actinic illumination periods of intermediate duration. The information content of the measured electric response is disclosed by a comparison of experimental results with calculations. The proton flux through the ATP synthase complex is seen to markedly influence the electric response. Also the imbalance in maximum turnover rate between the two photosystems, common to obligate shade plants like Peperomia metallica used in the microelectrode experiments, is clearly reflected in the electric potential profile.Dedicated to Prof. L.N.M. Duysens on the occasion of his retirement.