Pivotal Plane Research Articles

Innovative Approaches for Early Alzheimer’s Disease Detection through Novel Analysis of Brain MRI Images

Alzheimer's is one of the most well-known reasons for Dementia. Alzheimer's sickness (AD) is an irreversible, moderate cerebrum issue that gradually obliterates memory and thinking abilities. Alzheimer's and different types of dementia positioned seventh driving reason for death by WHO. Picture handling is broadly utilized in the clinical field to recognize illness and help specialists in dynamics dependent on perception. The paper means to recognize the Alzheimer's sickness at the most punctual with the goal that patients can be forestalled before irreversible changes happen in the mind. We propose the picture handling method to deal with the Magnetic Resonance Imaging (MRI) of the cerebrum from the pivotal plane, coronal plane, and sagittal plane. The picture division is utilized to feature the impacted locale in cerebrum MRI. The analyzed area in mind MRI incorporates the hippocampus and volume of the cerebrum. A similar ID of people impacted with the Alzheimer's illness, Healthy partner, and Mild Cognitive weakness is finished.

Curvature Energetics Determined by Alchemical Simulation on Four Topologically Distinct Lipid Phases.

The relative curvature energetics of two lipids are tested using thermodynamic integration (TI) on four topologically distinct lipid phases. Simulations use TI to switch between choline headgroup lipids (POPC; that prefers to be flat) and ethanolamine headgroup lipids (POPE; that prefer, for example, the inner monolayer of vesicles). The thermodynamical moving of the lipids between planar, inverse hexagonal (HII), cubic (QII; Pn3m space group), and vesicle topologies reveals differences in material parameters that were previously challenging to access. The methodology allows for predictions of two important lipid material properties: the difference in POPC/POPE monolayer intrinsic curvature (ΔJ0) and the difference in POPC/POPE monolayer Gaussian curvature modulus (Δκ̅m), both of which are connected to the energetics of topological variation. Analysis of the TI data indicates that, consistent with previous experiment and simulation, the J0 of POPE is more negative than POPC (ΔJ0 = -0.018 ± 0.001 Å-1). The theoretical framework extracts significant differences in κ̅m of which POPE is less negative than POPC by 2.0 to 4.0 kcal/mol. The range of these values is determined by considering subsets of the simulations, and disagreement between these subsets suggests separate mechanical parameters at very high curvature. Finally, the fit of the TI data to the model indicates that the position of the pivotal plane of curvature is not constant across topologies at high curvature. Overall, the results offer insights into lipid material properties, the limits of a single HC model, and how to test them using simulation.

BUMPy: A Model-Independent Tool for Constructing Lipid Bilayers of Varying Curvature and Composition.

Molecular dynamics is a powerful tool to investigate atomistic and mesoscopic phenomena in lipid bilayer systems. These studies have progressed with the advent of increased computational power, and efforts are now increasingly being directed toward investigating the role of curvature and bilayer morphology, as these are critical features of biological processes. Computational studies of lipid bilayers benefit from tools that can create starting configurations for molecular dynamics simulations, but the majority of such tools are restricted to generating flat bilayers. Generating curved bilayer configurations comes with practical complications and potential ramifications on physical properties in the simulated system if the bilayer is initiated in a high-strain state. We present a new tool for creating curved lipid bilayers that combines flexibility of shape, force field, model resolution, and bilayer composition. A key aspect of our approach is the use of the monolayer pivotal plane location to accurately estimate interleaflet area differences in a curved bilayer. Our tool is named BUMPy (Building Unique Membranes in Python), is written in Python, is fast, and has a simple command line interface.

Determining the Lipid Tilt Modulus by Simulating Membrane Buckles.

Lipid tilt affects the energy of membrane deformations on scales comparable to the membrane's thickness. The surface divergence of the tilt field creates a local spontaneous curvature, while tilt itself is quadratically penalized with a strength given by the tilt modulus. Traditionally, this modulus is determined by measuring the power spectrum of lipid orientation fluctuations. Here we present a novel approach which does not rely on fluctuations but instead exploits the fact that curvature gradients induce a tilt field. Its implementation extends a technique previously developed by us for localizing the position of the pivotal plane in buckling simulations, which quantifies the lipid imbalance across segments cut out from a complete buckle. Lipid tilt affects this count in a predictable way, and the signal can be quantified well enough to back out the tilt modulus-at no additional cost and with about 5% precision for not too coarse models. We apply our technique to three lipid models of very different resolution: the highly coarse grained Cooke model, and two versions of DMPC, using both the (less highly coarse grained) MARTINI and the (united atom) Berger force field. For Cooke, we find an effective bilayer tilt modulus of 29 ± 9 pN/nm, and for the less generic DMPC lipid, we find 115 ± 6 pN/nm for MARTINI and 39 ± 2 pN/nm for Berger, both in reasonable agreement with existing studies for these models. We also show that the position of the pivotal plane for Berger DMPC lies just below the glycerol backbone-unlike for MARTINI DMPC, where this plane lies closer to the middle of the lipid.

Determining the Pivotal Plane of Fluid Lipid Membranes in Simulations

Each leaflet of a curved lipid membrane contains a surface at which the area strain vanishes, the so-called pivotal plane. Its distance z0 from the bilayer's mid-plane arises in numerous membrane structure related contexts, for instance the connection between monolayer and bilayer moduli, stress-profile moments, or area-difference elasticity theories. Experimentally, the pivotal plane is known to lie close to the glycerol backbone of a lipid, but only very few simulations have tried to locate it. Here we propose two precise methods for determining z0, both of which rely on monitoring the lipid imbalance across a curved bilayer. The first method considers the ratio of lipid number between the two leaflets of cylindrical or spherical vesicles and requires lipid flip-flop for equilibration. The second method looks at the leaflet difference across local sections cut out from a buckled membrane and is free of this limitation. Our simulations rely on two different coarse-grained lipid models. First, the generic three-bead solvent-free Cooke model, which is amenable to both methods and gives results for z0 that agree at the percent level. And second, a ten-bead representation of dimyristoylphosphocholine (DMPC) with the explicit solvent MARTINI model, which can only be analyzed with the buckling method. For the latter, the obtained value z0 = 0.850(11) nm lies about 0.4 nm inwards of the glycerol backbone, essentially in the middle of the leaflet, and is hence unexpectedly small. We attribute this to limitations of the coarse-grained description, suggesting that the location of the pivotal plane might be a novel indicator for how well lipid models capture the microscopic origins of curvature elasticity, especially the relative contributions of head and tail regions to the overall curvature modulus.

Amphipathic Helices—Wedge? Or Nae Nae?

Large-scale deformation of lipid membranes is essential to many cellular processes, including vesicular trafficking, organelle formation, and maintenance, and viral entry and exit. These processes are difficult to model, as they are inherently multiscale—i.e., molecular scale interactions manifest as membrane deformations with 100-nm lengthscales. A major challenge is therefore to determine the essential molecular details, so that more coarse-grained approaches (whether continuum- or particle-based) capture the correct biophysics.

Determining the pivotal plane of fluid lipid membranes in simulations.

Each leaflet of a curved lipid membrane contains a surface at which the area strain vanishes, the so-called pivotal plane. Its distance z0 from the bilayer's midplane arises in numerous contexts, for instance the connection between monolayer and bilayer moduli, stress-profile moments, or area-difference elasticity theories. Here, we propose two precise methods for determining the location of the pivotal plane in computer simulations, both of which rely on monitoring the lipid imbalance across a curved bilayer. The first method considers the ratio of lipid number between the two leaflets of cylindrical or spherical vesicles; it hence requires lipid flip-flop for equilibration. The second method looks at the leaflet difference across local sections cut out from a buckled membrane; this observable equilibrates even in the absence of flip-flop. We apply our methods to two different coarse-grained lipid models, the generic three-bead solvent-free Cooke model and a ten-bead representation of dimyristoylphosphocholine with the explicit solvent MARTINI model. The Cooke model is amenable to both methods and gives results that agree at the percent level. Using it, we also show that the pivotal plane moves outward as lipid curvature becomes more positive. The MARTINI model can only be analyzed with the buckling method; the obtained value z0 = 0.850(11) nm lies about 0.4 nm inwards of the glycerol backbone and is hence unexpectedly small. We attribute this to limitations of the coarse-grained description, suggesting that the location of the pivotal plane might be a good indicator for how well lipid models capture the microscopic origins of curvature elasticity. Finally, we also show that the pivotal plane position itself moves as the membrane is bent. The leading correction is linear in curvature, dependent on the Poisson ratio, and can matter when analyzing experimental results obtained from highly curved inverse hexagonal phases.

Bending Free Energy from Simulation: Correspondence of Planar and Inverse Hexagonal Lipid Phases

Simulations of two distinct systems, one a planar bilayer, the other the inverse hexagonal phase, indicate consistent mechanical properties and curvature preferences, with single DOPE leaflets having a spontaneous curvature, R0 = −26 Å (experimentally ∼–29.2 Å) and DOPC leaflets preferring to be approximately flat (R0= –65 Å, experimentally ∼–87.3 Å). Additionally, a well-defined pivotal plane, where a DOPE leaflet bends at constant area, has been determined to be near the glycerol region of the lipid, consistent with the experimentally predicted plane. By examining the curvature frustration of both high and low curvature, the transferability of experimentally determined bending constants is supported. The techniques herein can be applied to predict the effect of biologically active molecules on the mechanical properties of lipid bilayers under well-controlled conditions.

An Anionic Phospholipid Enables the Hydrophobic Surfactant Proteins to Alter Spontaneous Curvature

The hydrophobic surfactant proteins, SP-B and SP-C, greatly accelerate the adsorption of the surfactant lipids to an air/water interface. Previous studies of factors that affect curvature suggest that vesicles may adsorb via a rate-limiting structure with prominent negative curvature, in which the hydrophilic face of the lipid leaflets is concave. To determine if SP-B and SP-C might promote adsorption by inducing negative curvature, we used small-angle x-ray scattering to test whether the physiological mixture of the two proteins affects the radius of cylindrical monolayers in the inverse hexagonal phase. With dioleoyl phosphatidylethanolamine alone, the proteins had no effect on the hexagonal lattice constant, suggesting that the proteins fail to insert into the cylindrical monolayers. The surfactant lipids also contain ∼10% anionic phospholipids, which might allow incorporation of the cationic proteins. With 10% of the anionic dioleoyl phosphatidylglycerol added to dioleoyl phosphatidylethanolamine, the proteins induced a dose-related decrease in the hexagonal lattice constant. At 30°C, the reduction reached a maximum of 8% relative to the lipids alone at ∼1% (w/w) protein. Variation of NaCl concentration tested whether the effect of the protein represented a strictly electrostatic effect that screening by electrolyte would eliminate. With concentrations up to 3 M NaCl, the dose-related change in the hexagonal lattice constant decreased but persisted. Measurements at different hydrations determined the location of the pivotal plane and proved that the change in the lattice constant produced by the proteins resulted from a shift in spontaneous curvature. These results provide the most direct evidence yet that the surfactant proteins can induce negative curvature in lipid leaflets. This finding supports the model in which the proteins promote adsorption by facilitating the formation of a negatively curved, rate-limiting structure.

An Anionic Phospholipid Enables the Hydrophobic Surfactant Proteins to Alter Spontaneous Curvature

The cationic, hydrophobic surfactant proteins, SP-B and SP-C (SPs), promote adsorption of vesicles to an air water interface and greatly increase the rate of forming an alveolar film. The available evidence suggests that the SPs may facilitate adsorption by promoting the generation of a negatively curved intermediate. The studies here tested whether the proteins could change the curvature of phospholipid leaflets in the inverse hexagonal (HII) phase. Experiments with the uncharged dioleoyl phosphatidylethanolamine (DOPE) showed no change in the lattice-constant with added SPs. Pulmonary surfactant contains ∼10% (mol:mol) anionic phospholipids. We therefore also examined mixtures of DOPE with 10% (mol:mol) of the anionic dioleoyl phosphatidylglycerol (DOPG) to investigate selective interactions with the SPs. Small angle X-ray scattering established the phase diagram (temperature - % protein) and lattice-constants for these lipids combined with the physiological mixture of the SPs. The hexagonal lattice-constant decreased linearly with increasing amounts of protein before reaching a temperature-dependent maximum change of 8-14% at ∼1% (w:w) protein. To test whether this effect was strictly electrostatic, NaCl concentrations up to 3M provided electrostatic screening. The salt diminished but did not eliminate the dose-related change in the lattice-constant. Measurements at different hydrations showed that the separation between the pivotal plane and the aqueous core was unaffected by the proteins, indicating that the change in the lattice-constant produced by the proteins reflects a more negative spontaneous curvature. These results provide direct evidence that the hydrophobic surfactant proteins can enhance the negative curvature of lipid leaflets. Studies were conducted at the Stanford Synchrotron Radiation Lightsource.

Lipid Bilayer Curvature Frustration

The free energy of bending of surfaces composed of biological lipids is derived, computed, and compared with experiment. Simulations of two distinct systems, one a planar bilayer, the other the inverse hexagonal phase indicate consistent mechanical properties and curvature preferences, with DOPE having a spontaneous curvature, R0 = −26 Angstroms and DOPC preferring to be approximately flat (R0=-65 Angstroms). Additionally, a well-defined pivotal plane, where a DOPE leaflet bends at constant area, has been determined to be near the glycerol region of the lipid, consistent with the experimentally predicted plane. By examining the curvature frustration of both high and low curvature, the transferability of experimentally determined bending constants is supported. How to predict the effects of biologically active molecules on the mechanical properties of lipid bilayers under well-controlled conditions will be examined.

COMPARATIVE PRECISION OF THE PIVOTAL ESTIMATORS OF PARTICLE SIZE

The pivotal estimators of the surface area and the volume of a generic "particle" are based on a point sampled test line on an isotropic pivotal plane through a fixed point called the pivotal point. The purpose of this paper is to compare the precision of the pivotal estimator of surface area against the surfactor on the one hand, and of the pivotal estimator of volume against the nucleator on the other. For the sake of a tractable but informative model we compute exact variances for a spherical particle with an eccentric nucleolus.

The Pivotal Plane of Phosphatidylethanolamine is Unaffected by the Hydrophobic Surfactant Proteins

Available evidence suggests that the hydrophobic surfactant proteins (SP), SP-B and SP-C, promote adsorption of the surfactant lipids to the alveolar air/water interface by facilitating formation of a rate-limiting negatively-curved structure. In support of this model, the proteins induce several phosphatidylethanolamines to form inverse bicontinuous cubic phases, in which each leaflet has the same saddle-shaped curvature as the hypothetical intermediate. Proteins could promote formation of the cubic phases by altering the spontaneous curvature (c0) of the phospholipids, which would change the dimensions of the inverse hexagonal (HII) phase. With 1,2-dioleoyl phosphatidylethanolamine (DOPE) in excess water, the SP had no effect on the HII phase, suggesting a constant c0. The SP, however, might still change c0 by shifting the location of the pivotal plane at which c0 is calculated. To determine if the proteins shift the pivotal plane, we measured X-ray diffraction from DOPE with 0 - 1% SP at 22 oC with different hydrations. Behavior at the different SP concentrations was indistinguishable. With increasing hydration the hexagonal lattice expanded until reaching the same limiting size at the same limiting hydration, indicating that the location of the Luzatti plane, which defines the boundary between the aqueous core and lipid, was unaffected. Detailed structural analysis of the lattice-dimensions at lower hydrations confirmed the existence of a pivotal plane at all levels of protein, and the derived location of the pivotal plane relative to the Luzatti plane (Vp/Vl) showed no response to protein concentration. Since neither Vp/Vl, nor the location of the Luzatti plane change with SP, the location of the pivotal plane remains constant. Unaffected position of the pivotal plane confirms that the SP induce cubic phases without changing the spontaneous curvature. (Studies conducted at the Stanford Synchrotron Radiation Lightsource).

Elastic deformations in hexagonal phases studied by small-angle X-ray diffraction and simulations

In this study we present experimental and theoretical results which concern the deviations from circularity of the pivotal plane in the inverse hexagonal phases (H(II)) of phospholipid self-assemblies. Due to packing constraints, the cross-section of the polar/apolar interface deviates from a circle, which we studied in minute detail by analysing small-angle X-ray diffraction data of dioleoyl-phosphatidylethanolamine (DOPE) and stearoyl-oleoyl-phosphatidylethanolamine (SOPE), respectively. On this structural basis, Monte Carlo (MC) simulated annealing variations of the free energy were carried out, both on the formation of the H(II)-phase and on the particular shape of the cross-section in the H(II)-phase. The equilibrium of the H(II)-phase pivotal plane contour and the corresponding values of the mean intrinsic curvature, H(m), and the hydrocarbon chain stiffness, τ, were determined from MC calculations. The results of these calculations were tested by solving the corresponding system of non-linear differential equations derived using variational calculus. Here our main aim is to predict the range of possible values of H(m) and τ. Comparing the measured structural data with predictions from MC calculations including lipid anisotropy, and accounting for the elastic deformations of the pivotal plane allowed us to determine a relationship between the bending deformation and stretching of hydrocarbon chains.

The influence of cholesterol on phospholipid membrane curvature and bending elasticity

The behavior of dioleoylphosphatidylethanolamine (DOPE)/cholesterol/tetradecane and dioleoylphosphatidylcholine (DOPC)/cholesterol/tetradecane were examined using x-ray diffraction and the osmotic stress method. DOPE/tetradecane, with or without cholesterol, forms inverted hexagonal (HII) phases in excess water. DOPC/tetradecane forms lamellar phases without cholesterol at lower temperatures. With tetradecane, as little as 5 mol% cholesterol in DOPC induced the formation of HII phases of very large dimension. Increasing levels of cholesterol result in a systematic decrease in the HII lattice dimension for both DOPE and DOPC in excess water. Using osmotic pressure to control hydration, we applied a recent prescription to estimate the intrinsic curvature and bending modulus of the HII monolayers. The radii of the intrinsic curvature, RPO, at a pivotal plane of constant area within the monolayer were determined to be 29.4 A for DOPE/tetradecane at 22 degrees C, decreasing to 27 A at 30 mol% cholesterol. For DOPC/tetradecane at 32 degrees C, RPO decreased from 62.5 A to 40 A as its cholesterol content increased from 30 to 50 mol%. These data yielded an estimate of the intrinsic radius of curvature for pure DOPC of 87.3 A. The bending moduli kc of DOPE/tetradecane and DOPC/tetradecane, each with 30 mol% cholesterol, are 15 and 9 kT, respectively. Tetradecane itself was shown to have little effect on the bending modulus in the cases of DOPE and cholesterol/DOPE. Surprisingly, cholesterol effected only a modest increase in the kc of these monolayers, which is much smaller than estimated from its effect on the area compressibility modulus in bilayers. We discuss possible reasons for this difference.

Measured effects of diacylglycerol on structural and elastic properties of phospholipid membranes

Diacylglycerol, a biological membrane second messenger, is a strong perturber of phospholipid planar bilayers. It converts multibilayers to the reverse hexagonal phase (HII), composed of highly curved monolayers. We have used x-ray diffraction and osmotic stress of the HII phase to measure structural dimensions, spontaneous curvature, and bending moduli of dioleoylphosphatidylethanolamine (DOPE) monolayers doped with increasing amounts of dioleoylglycerol (DOG). The diameter of the HII phase cylinders equilibrated in excess water decreases significantly with increasing DOG content. Remarkably, however, all structural dimensions at any specific water/lipid ratio that is less than full hydration are insensitive to DOG. By plotting structural parameters of the HII phase with changing water content in a newly defined coordinate system, we show that the elastic deformation of the lipid monolayers can be described as bending around a pivotal plane of constant area. This dividing surface includes 30% of the lipid volume independent of the DOG content (polar heads and a small fraction of hydrocarbon chains). As the mole fraction of DOG increases to 0.3, the radius of spontaneous curvature defined for the pivotal surface decreases from 29 A to 19 A, and the bending modulus increases from approximately 11 to 14 (+/-0.5) kT. We derive the conversion factors and estimate the spontaneous curvatures and bending moduli for the neutral surface which, unlike the pivotal plane parameters, are intrinsic properties that apply to other deformations and geometries. The spontaneous curvature of the neutral surface differs from that of the pivotal plane by less than 10%, but the difference in the bending moduli is up to 40%. Our estimate shows that the neutral surface bending modulus is approximately 9kT and practically does not depend on the DOG content.

Stages of the bilayer-micelle transition in the system phosphatidylcholine-C12E8 as studied by deuterium- and phosphorous-NMR, light scattering, and calorimetry

The perturbation of phospholipid bilayer membranes by a nonionic detergent, octaethyleneglycol mono-n-dodecylether (C12E8), was investigated by 2H- and 31P-NMR, static and dynamic light scattering, and differential scanning calorimetry. Preequilibrated mixtures of the saturated phospholipids 1,2-dipalmitoyl-sn-glycero-3-phosphorylcholine (DPPC), 1,2-dimyristoyl-sn-glycero-3-phosphorylcholine (DMPC), and 1,2-dilauroyl-sn-glycero-3-phosphorylcholine (DLPC) with the detergent were studied over a broad temperature range including the temperature of the main thermotropic phase transition of the pure phospholipids. Above this temperature, at a phospholipid/detergent molar ratio 2:1, the membranes were oriented in the magnetic field. Cooling of the mixtures below the thermotropic phase transition temperatures of the pure phospholipids led to micelle formation. In mixtures of DPPC and DMPC with C12E8, a narrow calorimetric signal at the onset temperature of the solubilization suggested that micelle formation was related to the disorder-order transition in the phospholipid acyl chains. The particle size changed from 150 nm to approximately 7 nm over the temperature range of the bilayer-micelle transition. The spontaneous orientation of the membranes at high temperatures enabled the direct determination of segmental order parameters from the deuterium spectra. The order parameter profiles of the phospholipid acyl chains could be attributed to slow fluctuations of the whole membrane and to detergent-induced local perturbations of the bilayer order. The packing constraints in the mixed bilayers that eventually lead to bilayer solubilization were reflected by the order parameters of the interfacial phospholipid acyl chain segments and of the phospholipid headgroup. These results are interpreted in terms of the changing average shape of the component molecules. Considering the decreasing cross sectional areas in the acyl chain region and the increasing hydration of the detergent headgroups, the bilayer-micelle transition is the result of an imbalance in the chain and headgroup repulsion. A neutral or pivotal plane can be defined on the basis of the temperature dependence of the interfacial quadrupolar splittings.