Probing the molecular-scale lipid bilayer response to shear flow using nonequilibrium molecular dynamics

A nonequilibrium molecular dynamics simulation of the response of dimyristoylphosphatidylcholine (DMPC) bilayers to a solvent shear flow is presented. Application of shear flow to planar, stationary DMPC bilayers results in a redistribution of the membrane density profile along the bilayer normal due to the alignment of the lipids in the direction of flow and an increase in average lipid chain length. An increase in the intermolecular and intramolecular order of the lipids in response to the shear flow is also observed. This study provides groundwork for understanding the mechanism of the full response of lipid bilayers to externally imposed solvent shear flows, beginning with the response in the absence of collective lipid motions such as undulations and bilayer flow.     

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.     

Molecular dynamics simulation of nonsteroidal antiinflammatory drugs,naproxen and relafen,in a lipid bilayer membrane

Naproxen and relafen, as nonsteroidal antiinflammatory drugs, were simulated in neutral and charged forms and their effects on a lipid bilayer membrane were investigated by molecular dynamics simulation using Groningen machine for chemical simulations software (GROMACS). Simulation of 10 systems was performed, which included different dosages of the drug molecules, naproxen and Relafen, in charged and neutral forms, and a mixture of naproxen and Relafen in neutral forms. The effects of the mixture and the individual drugs' dosages on membrane properties, such as electrostatic potential, order parameter, diffusion coefficients, and hydrogen bond formation, were analyzed. Hydration of the drugs in the membrane system was investigated using radial distribution function analysis. Using fully hydrated dimyristoylphosphatidylcholine (DMPC) as a reference system, 128 lipid molecules and water molecules were simulated exclusively, and the same simulation technique was performed on 10 other systems, including drug mixtures and a DMPC membrane. Angular distributions of lipid chains of the membrane were calculated, and the effects of the drug insertion and chain orientation in the membrane were evaluated. © 2013 Wiley Periodicals, Inc.     

A multiscale coarse-graining method for biomolecular systems

A new approach is presented for obtaining coarse-grained (CG) force fields from fully atomistic molecular dynamics (MD) trajectories. The method is demonstrated by applying it to derive a CG model for the dimyristoylphosphatidylcholine (DMPC) lipid bilayer. The coarse-graining of the interparticle force field is accomplished by an application of a force-matching procedure to the force data obtained from an explicit atomistic MD simulation of the biomolecular system of interest. Hence, the method is termed a "multiscale" CG (MS-CG) approach in which explicit atomistic-level forces are propagated upward in scale to the coarse-grained level. The CG sites in the lipid bilayer application were associated with the centers-of-mass of atomic groups because of the simplicity in the evaluation of the forces acting on them from the atomistic data. The resulting CG lipid bilayer model is shown to accurately reproduce the structural properties of the phospholipid bilayer.     

Enhanced Lipid Diffusion and Mixing in Accelerated Molecular Dynamics

Accelerated molecular dynamics (aMD) is an enhanced sampling technique that expedites conformational space sampling by reducing the barriers separating various low-energy states of a system. Here, we present the first application of the aMD method on lipid membranes. Altogether, ～1.5 μs simulations were performed on three systems: a pure POPC bilayer, a pure DMPC bilayer, and a mixed POPC:DMPC bilayer. Overall, the aMD simulations are found to produce significant speedup in trans-gauche isomerization and lipid lateral diffusion versus those in conventional MD (cMD) simulations. Further comparison of a 70-ns aMD run and a 300-ns cMD run of the mixed POPC:DMPC bilayer shows that the two simulations yield similar lipid mixing behaviors, with aMD generating a 2-3-fold speedup compared to cMD. Our results demonstrate that the aMD method is an efficient approach for the study of bilayer structural and dynamic properties. On the basis of simulations of the three bilayer systems, we also discuss the impact of aMD parameters on various lipid properties, which can be used as a guideline for future aMD simulations of membrane systems.     

Bilayer in small bicelles revealed by lipid-protein interactions using NMR spectroscopy

Intermolecular nuclear Overhauser effects (NOEs) between the integral outer membrane protein OmpX from Escherichia coli and small bicelles of dihexanoyl phosphatidylcholine (DHPC) and dimyristoyl phosphatidylcholine (DMPC) give insights into protein-lipid interactions. Intermolecular NOEs between hydrophobic tails of lipid and protein in the bicelles cover the surface area of OmpX forming a continuous cylindric jacket of approximately 2.7 nm in height. These NOEs originate only from DMPC molecules, and no NOEs from DHPC are observed. Further, these NOEs are mainly from methylene groups of the hydrophobic tails of DMPC, and only a handful of NOEs arise from methyl groups of the hydrophobic tails. The observed contacts indicate that the hydrophobic tails of DMPC are oriented parallel to the surface of OmpX and thus DMPC molecules form a bilayer in the vicinity of the protein. Thus, a bilayer exists in the small bicelles not only in the absence of but also in the presence of a membrane protein. In addition, the number of NOEs between the polar head groups of lipid molecules and protein is increased in the bicelles compared with those in micelles. This observation may be due to the closely packed head groups of the bilayer. Moreover, irregularity of hydrophobic interactions in the middle of the bilayer environment was observed. This observation together with the interactions between polar head groups and proteins gives a possible rationale for structural and functional differences of membrane proteins solubilized in micelles and in bilayer systems and hints at structural differences between protein-free and protein-loaded bilayers.     

Molecular dynamics simulations of rhodopsin in different one-component lipid bilayers

Four 20 ns molecular dynamic simulations of rhodopsin embedded in different one-component lipid bilayers have been carried out to ascertain the importance of membrane lipids on the protein structure. Specifically, dimyristoyl phosphatidylcholine (DMPC), dipalmitoyl phosphatidylcholine (DPPC), palmitoyl oleoyl phosphatidylcholine (POPC), and palmitoyl linoleyl phosphatidylcholine (PLPC) lipid bilayers have been considered for the present work. The results reported here provide information on the hydrophobic matching between the protein and the bilayer and about the differential effects of the protein on the thickness of the different membranes. Furthermore, a careful analysis of the individual protein-lipid interactions permits the identification of residues that exhibit permanent interactions with atoms of the lipid environment that may putatively act as hooks of the protein to the membrane. The analysis of the trajectories also provides information about the effect of the bilayer on the protein structure, including secondary structural elements, salt bridges, and rigid-body motions.     

Structural, dynamic, and electrostatic properties of fully hydrated DMPC bilayers from molecular dynamics simulations accelerated with graphical processing units (GPUs)

We present results of molecular dynamics simulations of fully hydrated DMPC bilayers performed on graphics processing units (GPUs) using current state-of-the-art non-polarizable force fields and a local GPU-enabled molecular dynamics code named FEN ZI. We treat the conditionally convergent electrostatic interaction energy exactly using the particle mesh Ewald method (PME) for solution of Poisson's Equation for the electrostatic potential under periodic boundary conditions. We discuss elements of our implementation of the PME algorithm on GPUs as well as pertinent performance issues. We proceed to show results of simulations of extended lipid bilayer systems using our program, FEN ZI. We performed simulations of DMPC bilayer systems consisting of 17,004, 68,484, and 273,936 atoms in explicit solvent. We present bilayer structural properties (atomic number densities, electron density profiles), deuterium order parameters (S(CD)), electrostatic properties (dipole potential, water dipole moments), and orientational properties of water. Predicted properties demonstrate excellent agreement with experiment and previous all-atom molecular dynamics simulations. We observe no statistically significant differences in calculated structural or electrostatic properties for different system sizes, suggesting the small bilayer simulations (less than 100 lipid molecules) provide equivalent representation of structural and electrostatic properties associated with significantly larger systems (over 1000 lipid molecules). We stress that the three system size representations will have differences in other properties such as surface capillary wave dynamics or surface tension related effects that are not probed in the current study. The latter properties are inherently dependent on system size. This contribution suggests the suitability of applying emerging GPU technologies to studies of an important class of biological environments, that of lipid bilayers and their associated integral membrane proteins. We envision that this technology will push the boundaries of fully atomic-resolution modeling of these biological systems, thus enabling unprecedented exploration of meso-scale phenomena (mechanisms, kinetics, energetics) with atomic detail at commodity hardware prices.     

Systematic implicit solvent coarse graining of dimyristoylphosphatidylcholine lipids

We have used systematic structure‐based coarse graining to derive effective site–site potentials for a 10‐site coarse‐grained dimyristoylphosphatidylcholine (DMPC) lipid model and investigated their state point dependence. The potentials provide for the coarse‐grained model the same site–site radial distribution functions, bond and angle distributions as those computed in atomistic simulations carried out at four different lipid–water molar ratios. It was shown that there is a non‐negligible dependence of the effective potentials on the concentration at which they were generated, which is also manifested in the properties of the lipid bilayers simulated using these potentials. Thus, effective potentials computed at low lipid concentration favor to more condensed and ordered structure of the bilayer with lower average area per lipid, while potentials obtained at higher lipid concentrations provide more fluid‐like structure. The best agreement with the reference data and experiment was achieved using the set of potentials derived from atomistic simulations at 1:30 lipid:water molar ratio providing fully saturated hydration of DMPC lipids. Despite theoretical limitations of pairwise coarse‐grained potentials expressed in their state point dependence, all the resulting potentials provide a stable bilayer structure with correct partitioning of different lipid groups across the bilayer as well as acceptable values of the average lipid area, compressibility and orientational ordering. In addition to bilayer simulations, the model has proven its robustness in modeling of self‐aggregation of lipids from randomly dispersed solution to ordered bilayer structures, bicelles, and vesicles. © 2014 Wiley Periodicals, Inc.     

Magnetic resonance investigations of lipid motion in isotropic bicelles

The dynamics of DMPC in different isotropic bicelles have been investigated by NMR and EPR methods. The local dynamics were obtained by interpretation of 13C NMR relaxation measurements of DMPC in the bicelles, and these results were compared to EPR spectra of spin-labeled lipids. The overall size of the bicelles was investigated by PFG NMR translational diffusion measurements. The dynamics and relative sizes were compared among three different bicelles: [DMPC]/[DHPC] = 0.25, [DMPC]/[DHPC] = 0.5, and [DMPC]/[CHAPS] = 0.5. The local motion is found to depend much more strongly on the choice of the detergent, rather than the overall size of the bicelle. The results provide an explanation for differences in apparent dynamics for different peptides, which are bound to bicelles. This in turn determines under what conditions reasonable NMR spectra can be observed. A model is presented in which extensive local motion, in conjunction with the overall size, affects the spectral properties. An analytical expression for the size dependence of the bicelles, relating the radius of the bilayer region with physical properties of the detergent and the lipid, is also presented.     

Impact on lipid membrane organization by free branched-chain fatty acids

Here, we exploit the non-invasive techniques of solid-state NMR (nuclear magnetic resonance) and differential scanning calorimetry (DSC) to study the effect of free iso and ante-iso branched chain fatty acids (BCFAs) on the physicochemical properties of lipid membranes. Free fatty acids are present in biological membranes at low abundance, but can influence the cellular function by modulating the membrane organization. Solid state NMR spectra of dimyristoylphosphatidylcholine (DMPC) lipid membranes containing either free 12-methyltetradecanoic acid (a15:0) or free 13-methyltetradecanoic acid (i15:0), show significant differences in their impact on the lipid bilayer. Chain order profiles obtained by deuterium NMR on fully deuterated DMPC-d(67) bilayers revealed an ordering effect induced by both fatty acids on the hydrophobic membrane core. This behavior was also visible in the corresponding DSC thermograms where the main phase transition of DMPC bilayers-indicative of the hydrophobic membrane region-was shifted to higher temperatures, with the iso isomer triggering more pronounced changes as compared to the ante-iso isomer. This is probably due to a higher packing density in the core of the lipid bilayer, which causes reduced diffusion across membranes. By utilizing the naturally occurring spin reporters nitrogen-14 and phosphorus-31 present in the hydrophilic DMPC headgroup region, even fatty acid induced changes at the membrane interface could be detected, an observation reflecting changes in the lipid headgroup dynamics.     

Bilayer hydrophobic thickness and integral membrane protein function

The influence of the lipid environment on the function of membrane proteins is increasingly recognized as crucial. Nevertheless, the molecular mechanisms underlying protein-lipid interactions remain obscure. Membrane lipid composition has a regulatory effect on membrane protein activity, and for a number of membrane proteins a clear correlation was found between protein activity and properties of the membrane bilayer such as fluidity. Membrane thickness is an important property of a lipid bilayer. It is expected that hydrophobic thickness match the hydrophobic thickness of transmembrane segments of integral membrane proteins. Any mismatch between the hydrophobic thicknesses of the lipid bilayer and the protein would lead to some modification in either the structure of the protein or the structure of the bilayer, or both. Consequent rearrangements may result in changes in protein activity. Here we review the behavior of several transmembrane proteins whose activity is altered by hydrophobic core thickness.     

Impact of Strong and Weak Lipid–Protein Interactions on the Structure of a Lipid Bilayer on a Gold Electrode Surface

A lipid bilayer deposited on an electrode surface can serve as a benchmark system to investigate lipid–protein interactions in the presence of physiological electric fields. Recoverin and myelin‐associated glycoprotein (MAG) are used to study the impact of strong and weak protein–lipid interactions on the structure of model lipid bilayers, respectively. The structural changes in lipid bilayers are followed using electrochemical polarization modulation infrared reflection–absorption spectroscopy (PM IRRAS). Recoverin contains a myristoyl group that anchors in the hydrophobic part of a cell membrane. Insertion of the protein into the 1,2‐dimyristoyl‐sn‐glycero‐3‐phosphatidylcholine (DMPC)–cholesterol lipid bilayer leads to an increase in the capacitance of the lipid film adsorbed on a gold electrode surface. The stability and kinetics of the electric‐field‐driven adsorption–desorption process are not affected by the interaction with protein. Upon interaction with recoverin, the hydrophobic hydrocarbon chains become less ordered. The polar head groups are separated from each other, which allows for recoverin association in the membrane. MAG is known to interact with glycolipids present on the surface of a cell membrane. Upon probing the interaction of the DMPC–cholesterol–glycolipid bilayer with MAG a slight decrease in the capacity of the adsorbed lipid film is observed. The stability of the lipid bilayer increases towards negative potentials. At the molecular scale this interaction results in minor changes in the structure of the lipid bilayer. MAG causes small ordering in the hydrocarbon chains region and an increase in the hydration of the polar head groups. Combining an electrochemical approach with a structure‐sensitive technique, such as PM IRRAS, is a powerful tool to follow small but significant changes in the structure of a supramolecular assembly.     

Membrane disordering induced by chloroform and carbon tetrachloride

We studied effects of chloroform and carbon tetrachloride on bilayer membranes of dimyristoyl-phosphatidylcholine (DMPC) and egg yolk phosphatidylcholine (Egg-PC) by birefringence, dynamic light scattering and fluorescence methods. It is shown that interference light due to the membrane birefringence considerably decreases by addition of the organohalogen compounds for both lipid membranes, indicating a significant decrease in membrane order. In addition, results of dynamic light scattering and turbidity measurements show a rupture of multilamellar DMPC vesicles induced by addition of chloroform at concentrations above 0.2 v/v%. No rupture of the vesicles is observed within the limit of solubility of carbon tetrachloride in water, but excessive addition of carbon tetrachloride (above 0.2 v/v%) induces the vesicle rupture. Chain orientational order was estimated from the interference light intensity at low concentrations of the organohalogen compounds without the occurrence of the vesicle rupture. The estimation shows a monotonic decrease in the chain order with increasing the concentration. The decreases in DMPC chain order by chloroform and by carbon tetrachloride are about 17% at 0.2 v/v% and 23% at 0.05 v/v%, respectively. The reduction in the chain order is correlated with an increase in the membrane fluidity observed by excimer fluorescence of pyrene incorporated to the membrane. Behavior of membrane disordering of Egg-PC is approximately similar with that of DMPC. This implies the strong interaction between the organohalogen compounds and the lipid chains, whether or not the bilayer has the vacancy resulted from unsaturated double bonds and different chains in length. The results of this work suggest that damages of biological membranes by chloroform and tetrachloride are not only induced by a direct attack on proteins but also by a significant membrane disorder.     

Transmembrane Signaling with Lipid‐Bilayer Assemblies as a Platform for Channel‐Based Biosensing

Artificial and natural lipid membranes that elicit transmembrane signaling is are useful as a platform for channel‐based biosensing. In this account we summarize our research on the design of transmembrane signaling associated with lipid bilayer membranes containing nanopore‐forming compounds. Channel‐forming compounds, such as receptor ion‐channels, channel‐forming peptides and synthetic channels, are embedded in planar and spherical bilayer lipid membranes to develop highly sensitive and selective biosensing methods for a variety of analytes. The membrane‐bound receptor approach is useful for introducing receptor sites on both planar and spherical bilayer lipid membranes. Natural receptors in biomembranes are also used for designing of biosensing methods.     

Insights into the effect of combustion-generated carbon nanoparticles on biological membranes: a computer simulation study

Classical molecular dynamics simulations of atomistic models of combustion-generated carbon nanoparticles and lipid bilayers have been performed to explore their possible structural, dynamical, and thermodynamic effects on biological membranes. The DREIDING generic force field is used for the carbonaceous nanoparticles of different morphologies, as produced from combustion sources, and the united atom model was employed for the dimyristoylphosphatidylcholine (DMPC) bilayer. It is observed that particle shape and structure have significant effects on solvation, mobility, adsorption, and permeation behavior of the particles. While combustion-generated carbon nanoparticles with an aspect ratio close to unity prefer to stay near the membrane center, precursors with other shapes mostly reside within the hydrocarbon tail region of the membrane. Carbon nanoparticles are not trapped in a local region even inside the membranes but move freely with a speed depending on their molecular weight. The adsorption of the particles on the surface of the biological membrane is comparable to thermal fluctuations because the weak segregation effect by water molecules is the main driving force to the adsorption behavior. The bigger the precursors are, the stronger they are bound to the membrane surface. The presence of combustion-generated nanoparticles inside the membrane perturbs local lipid density by pushing the neighboring lipid molecules away from the nanoparticles. This, coupled with thermal fluctuations, can induce an instantaneous membrane pore to allow water protrusion. From the umbrella sampling method, the potential of mean force for the permeation of carbona nanoparticles into the bilayer was also obtained. Surprisingly, elongated particles have a free energy barrier an order of magnitude smaller compared with more round ones. In addition, the round carbon nanoparticles showed strong hysteresis due to the local trapping of water molecules. Although the carbon soot precursors studied in this work are not the well-known carbon nanoparticles such as fullerenes or carbon nanotubes, the qualitative features of this study may be applicable to them as well.     

Hydrogen/deuterium exchange of hydrophobic peptides in model membranes by electrospray ionization mass spectrometry

We demonstrate here that the hydrogen/deuterium solvent exchange (HDX) properties of the transmembrane fragment of the M2 protein of Influenza A (M2-TM) incorporated into lipid vesicles or detergent micelles can be studied with straightforward electrospray (ESI) and nanospray mass spectrometry (MS) configurations provided that key factors, including sample preparation techniques, are optimized. Small unilamellar vesicle preparations were obtained by solubilizing dimyristoyl phosphatidylcholine (DMPC) and the M2-TM peptide in aqueous solution with n-octyl-β-D-glycopyranoside, followed by dialysis to remove the detergent. Electron microscopy experiments revealed that subsequent concentration by centrifugation introduced large multilamellar aggregates that were not compatible with ESI-MS. By contrast, a lyophilization-based concentration procedure, followed by thawing above the liquid crystal transition temperature of the lipid component, maintained the liposome size profile and yielded excellent ion fluxes in both ESI-MS and nano-ESI-MS. Using these methods the global HDX profile of M2-TM in aqueous DMPC vesicles was compared with that in methanol, demonstrating that several amide sites were protected from exchange by the lipid membrane. We also show that hydrophobic peptides can be detected by ESI-MS in the presence of a large molar excess of the detergent Triton X-100. The rate of HDX of M2-TM in Triton X-100 micelles was faster than that in DMPC vesicles but slower than when the peptide had been denatured in methanol. These results indicate that the accessibility of backbone amide sites to the solvent can be profoundly affected by membrane protein structure and dynamics, as well as the properties of model bilayer systems.     

Modification of the CHARMM force field for DMPC lipid bilayer

The CHARMM force field for DMPC lipids was modified in order to improve agreement with experiment for a number of important properties of hydrated lipid bilayer. The modification consists in introduction of a scaling factor 0.83 for 1-4 electrostatic interactions (between atoms separated by three covalent bonds), which provides correct transgauche ratio in the alkane tails, and recalculation of the headgroup charges on the basis of HF/6-311(d,p) ab-initio computations. Both rigid TIP3P and flexible SPC water models were used with the new lipid model, showing similar results. The new model in a 75 ns simulation has shown a correct value of the area per lipid at zero surface tension, as well as good agreement with the experiment for the electron density, structure factor, and order parameters, including those in the headgroup part of lipids.     

Fluorescence study of the fluidity and cooperativity of the phase transitions of zwitterionic and anionic liposomes confined in sol-gel glasses

The current work makes use of different fluorescent reporter molecules and fluorescent spectroscopic techniques to characterize the thermotropic, physical, and dynamical properties of large unilamellar liposomes formed from either 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) or 1,2-dimyristoyl-sn-glycero-3-[phospho-rac-glycerol] (DMPG) encapsulated in sol-gel matrixes. In particular, cooperativity of the phase transition is analyzed from steady-state fluorescence anisotropy of 1,6-diphenyl-1,3,5-hexatriene (DPH), the interfacial properties are studied by measuring the spectral shift of Laurdan, and the structural organization (heterogeneity) of the lipid bilayer is determined from the fluorescence lifetime of trans-parinaric acid (t-PnA). In addition, information regarding order and dynamical properties in the bulk hydrophobic core is obtained from time-resolved fluorescence anisotropy of t-PnA and 3-(4-(6-phenyl)-1,3,5-hexatrienyl)-phenylpropionic acid (PA-DPH). The spectroscopic study reveals that upon encapsulation, the basic thermodynamic properties as well as the fluidity of the lipid bilayer practically remain intact for DMPG liposomes but not for DMPC liposomes, whose lipid bilayer exhibits large gel-fluid heterogeneity. On the basis of these experimental results, electrostatic interactions between phospholipid polar heads and the porous surface of the host matrix seem to play a capital role for the preservation of the structural integrity of encapsulated bilayer.     

Dissipative particle dynamics simulation study of the bilayer-vesicle transition

A bilayer structure is an important immediate for the vesicle formation. However,the mechanism for the bilayer-vesicle transition remains unclear. In this work,a dissipative particle dynamics(DPD) simulation method was employed to study the mechanism of the bilayer-vesicle transition. A coarse-grained model was built based on a lipid molecule termed dimyristoylphosphatidylcholine(DMPC). Simulations were performed from two different initial configurations:a random dispersed solution and a tensionless bilayer. It was found that the bilayer-vesicle transition was driven by the minimization of the water-tail hydrophobic interaction energy,and was accompanied with the increase of the position entropy due to the redistribution of water molecules. The bulk pressure was reduced during the bilayer-vesicle transition,suggesting the evolved vesicle morphology was at the relatively low free energy state. The membrane in the product vesicle was a two-dimensional fluid. It can be concluded that the membrane of a vesicle is not interdigitated and most of the bonds in lipid chains are inclined to orient along the radical axis of the vesicle.