The impact of surface area,volume, curvature,and Lennard–Jones potential to solvation modeling

This article explores the impact of surface area, volume, curvature, and Lennard–Jones (LJ) potential on solvation free energy predictions. Rigidity surfaces are utilized to generate robust analytical expressions for maximum, minimum, mean, and Gaussian curvatures of solvent–solute interfaces, and define a generalized Poisson–Boltzmann (GPB) equation with a smooth dielectric profile. Extensive correlation analysis is performed to examine the linear dependence of surface area, surface enclosed volume, maximum curvature, minimum curvature, mean curvature, and Gaussian curvature for solvation modeling. It is found that surface area and surfaces enclosed volumes are highly correlated to each other's, and poorly correlated to various curvatures for six test sets of molecules. Different curvatures are weakly correlated to each other for six test sets of molecules, but are strongly correlated to each other within each test set of molecules. Based on correlation analysis, we construct twenty six nontrivial nonpolar solvation models. Our numerical results reveal that the LJ potential plays a vital role in nonpolar solvation modeling, especially for molecules involving strong van der Waals interactions. It is found that curvatures are at least as important as surface area or surface enclosed volume in nonpolar solvation modeling. In conjugation with the GPB model, various curvature‐based nonpolar solvation models are shown to offer some of the best solvation free energy predictions for a wide range of test sets. For example, root mean square errors from a model constituting surface area, volume, mean curvature, and LJ potential are less than 0.42 kcal/mol for all test sets. © 2016 Wiley Periodicals, Inc.     

Torocyte shapes of red blood cell daughter vesicles

The shape of the newly described torocyte red blood cell endovesicles induced by octaethyleneglycol dodecylether (C12E8) is characterized. A possible explanation for the origin and stability of the observed torocyte endovesicles is suggested. Three partly complementary mechanisms are outlined, all originating from the interaction of C12E8 molecules with the membrane. The first is a preferential intercalation of the C12E8 molecule into the inner membrane layer, resulting in a membrane invagination which may finally close, forming an inside-out endovesicle. The second is a preference of the C12E8-induced membrane inclusions (clusters) for small local curvature which would favour torocyte endovesicle shape with large regions of small or even negative membrane mean curvatures, the C12E8 membrane inclusion being defined as a complex composed of the embedded C12E8 molecule and some adjacent phospholipid molecules which are significantly distorted due to the presence of the embedded C12E8 molecule. The preference of the C12E8 inclusions for zero or negative local curvature may also lead to the nonhomogeneous lateral distribution of the C12E8 inclusions resulting in their accumulation in the membrane of torocyte endovesicles. The third possible mechanism is orientational ordering of the C12E8-induced inclusions in the regions of torocyte endovesicles with high local membrane curvature deviator.     

Phospholipid-based nonlamellar mesophases for delivery systems: Bridging the gap between empirical and rational design

Phospholipids are ubiquitous cell membrane components and relatively well-accepted ingredients due to their natural origin. Phosphatidylcholine (PC) in particular offers a promising alternative to monoglycerides for lyotropic liquid crystalline (LLC) delivery system applications in the food, cosmetics and pharmaceutical industries, provided its strong tendency to form zero-mean curvature lamellar mesophases in water can be overcome. Higher negative curvatures are usually reached through the addition of a third lipid component, forming a ternary diagram phospholipid/water/oil.     

Experimental evidence to support a theory of lipid membrane fusion

Membrane fusion between two lipid membranes with different curvatures was measured by using a fluorescence fusion assay for lipid vesicle systems and was also obtained by measuring lipid monolayer surface tension upon the fusion of vesicles to monolayer membranes. For such membrane systems, it was found that when lysolipid was incorporated only in the membrane with a greater curvature, membrane fusion was more suppressed than those for the case where the same amount (molar ratio of lysolipid to non-lysolipids) of lysolipid was incorporated only in the membrane with a lower curvature. When lysolipid was incorporated only in a flat membrane (e.g., monolayer) and the fusion of small vesicles (SUV) to the monolayer was measured, suppression of membrane fusion by lysolipid was minimal. It is known that lysolipid lowers the surface energy of curved membranes, which stabilizes energetically such membrane surfaces, and thus suppresses membrane fusion. Our results support our theory of lipid membrane fusion where the membrane fusion occurs through the most curved membrane region at the contact area of two interacting membranes.     

Curvature effect on nanometer-scale surface properties of phospholipid layers

Phospholipid bilayers were formed through liposome fusion on surfaces with different curvatures that were defined with silica spheres deposited on silicon water. Prior to the fusion, the surfaces became hydrophobic with octadecyltrimethoxysilane solution. Using atomic force microscope, surface forces were measured on dipalmitoylphosphatidylcholine (DPPC) layers and dioleoylphosphatidylcholine (DOPC) layers upon the curvature at 25°C. The short-range repulsions were higher at 20 and 100 nm curvatures than other curvatures for the DPPC layer, while they were lower for the DOPC layer. Since it was known that the forces are related to its low mechanical stability of the lipid layer, this opposite behavior was analyzed in terms of stability upon the curvature, which appears to be eventually determined by the correlation between the lipid molecule geometry and the surface curvature.     

Shape transitions in lipid membranes and protein mediated vesicle fusion and fission

In the cell, the plasma membrane is often densely decorated by transmembrane proteins. The morphology and dynamics of the membrane are strongly influenced by the presence of proteins. In this paper, we use a coarse-grained model to explore the composite membrane-protein system and develop a simulation methodology based on thermodynamic integration to examine free energy changes during membrane shape transitions. The authors show that a critical concentration of conical membrane proteins or proteins with nonzero spontaneous curvature can drive the formation of small vesicles. The driving force of vesicle budding stems from the preference of proteins to gather in regions of high curvature. A sufficiently high concentration of proteins therefore can influence the topology of the membrane. The biological significance of our results is discussed.     

Topological analysis of complex molecular surfaces

An algorithm for the calculation of local and global curvatures of molecular surfaces is presented. The analysis is based on a surface representation as a set of points in 3-D space (“dotted surface” representation). The surface data are used to subdivide the surfac into domains with different curvatures. All domains are characterized by a reference point with a corresponding curvature profile specifiying the topological properties in its neighborhood. The curvature profiles provide a method for a systematic comparison of the shapes of different molecules. Such a strategy is important for the treatment of molecular recognition problems. The enzyme-inhibitor complex trypsin/BPTI was chosen to demonstrate the scopes of the method.     

Curvature-modulated phase separation in lipid bilayer membranes

Cellular membranes exhibit a variety of controlled curvatures, with filopodia, microvilli, and mitotic cleavage furrows being only a few of many examples. Coupling between local curvature and chemical composition in membranes could provide a means of mechanically controlling the spatial organization of membrane components. Although this concept has surfaced repeatedly over the years, controlled experimental investigations have proven elusive. Here, we introduce an experimental platform, in which microfabricated surfaces impose specific curvature patterns onto lipid bilayers, that allows quantification of mechanochemical couplings in membranes. We find that, beyond a critical curvature value, membrane geometry governs the spatial ordering of phase-separated domain structures in membranes composed of cholesterol and phospholipids. The curvature-controlled ordering, a consequence of the distinct mechanical properties of the lipid phases, makes possible a determination of the bending rigidity difference between cholesterol-rich and cholesterol-poor lipid domains. These observations point to a strong coupling between mechanical bending and chemical organization that should have wide-reaching consequences for biological membranes. Curvature-mediated patterning may also be useful in controlling complex fluids other than biomembranes.     

Dynamics and instabilities of lipid bilayer membrane shapes

Biological membranes undergo constant shape remodeling involving the formation of highly curved structures. The lipid bilayer represents the fundamental architecture of the cellular membrane with its shapes determined by the Helfrich curvature bending energy. However, the dynamics of bilayer shape transitions, especially their modulation by membrane proteins, and the resulting shape instabilities, are still not well understood. Here, we review in a unifying manner several theories that describe the fluctuations (i.e. undulations) of bilayer shapes as well as their local coupling with lipid or protein density variation. The coupling between local membrane curvature and lipid density gives rise to a ‘slipping mode’ in addition to the conventional ‘bending mode’ for damping the membrane fluctuation. This leads to a number of interesting experimental phenomena regarding bilayer shape dynamics. More importantly, curvature-inducing proteins can couple with membrane shape and eventually render the membrane unstable. A criterion for membrane shape instability is derived from a linear stability analysis. The instability criterion reemphasizes the importance of membrane tension in regulating the stability and dynamics of membrane geometry. Recent progresses in understanding the role of membrane tension in regulating dynamical cellular processes are also reviewed. Protein density is emphasized as a key factor in regulating membrane shape transitions: a threshold density of curvature coupling proteins is required for inducing membrane morphology transitions.     

Amphipathic helices as mediators of the membrane interaction of amphitropic proteins, and as modulators of bilayer physical properties

The amphipathic helix (AH) motif is used by a subset of amphitropic proteins to accomplish reversible and controlled association with the interfacial zone of membranes. Functioning as more than mere membrane anchoring domains, amphipathic helices can serve as autoinhibitory domains to suppress the protein activity in its soluble form, and as sensors or modulators of membrane curvature. Thus amphipathic helices can both respond to and modulate membrane physical properties. These and other features are illustrated by the behavior of CTP: phosphocholine cytidylyltransferase (CCT), a key regulatory enzyme in PC synthesis. A comparison of the physico-chemical features of CCT's AH motif and 10 others reveals similarities and several differences. The importance of these parameters to the particulars of the membrane interaction and to functional consequences requires more systematic exploration. The membrane partitioning of amphitropic proteins with AH motifs can be regulated by various strategies including changes in membrane lipid composition, phosphorylation, ligand-induced conformational changes, and membrane curvature. Several amphitropic proteins that control budding or tubule formation in cells have AH motifs. The insertion of the hydrophobic face of these amphipathic helices generates an asymmetry in the lateral pressure of the two leaflets resulting in an induction of positive curvature. Curvature induction or stabilization may be a universal property of AHA proteins, not just those involved in budding, but this possibility requires further demonstration.     

Surfactant-induced formation of honeycomb pattern on micropipette with curvature gradient

Breath figure (BF) process is a facile method to prepare honeycomb structures by dynamic movements of condensed micrometer-sized water droplets at the interface of volatile fluid. Here, we aim to find answers to understand how the BF process occurs on micropipettes with curvature gradient and to understand the role of the surfactant in obtaining honeycomb patterns. Poly (L-lactic acid) (PLLA) chloroform solution with dioleoylphosphatidylethanolamine (DOPE) as surfactant was utilized. It is found that the honeycomb structure formed on the micropipettes changes remarkably with the gradually increased surface curvature. The variation trends of the arrangement and diameter of pores on the micropipettes with the increasing curvature are similar to the different time stages of BF process: smaller and sparse pores formed at higher curvature are similar to those formed at early stage of BF; regular honeycomb patterns formed at lower curvature are similar to those formed at the late stage of BF. Especially, the "semi-coalescence" hemispherical pores strings are found at high curvatures on PLLA-DOPE films, indicating the surfactant-induced coalescence of water droplets in BF process. The differences of drying speed of polymer solvent on micropipette with gradually increased curvatures make the printing of the pores at different BF stages on polymer film possible. These findings not only strongly support the mechanism of BF array formation, but also elucidate the surfactant-induced coalescence.     

Courbures de Riemann dans le problème plan des trois corps — Stabilité

We develop a method for studying the curvature of the configuration space of a dynamical system equipped with the Maupertuis metric, for a given value of the energy constant, using the symbolic manipulation program Macsyma. We apply this method in the planar three-body problem. Discussion of the sign of the Riemann curvatures enables one to study the stability of particular configurations. For Lagrange's homothetic triangular solution, we found conditions when all the Riemann curvatures are negative. This means that under these conditions, the homothetic Lagrange solution is exponentially unstable.     

Properties of giant vesicles

We have discussed the specific properties of giant vesicles and their use as model systems for fluid interfaces and biomembranes. Recent advances in giant vesicle research include systematic measurements of visco-elastic parameters as a function of membrane composition, experiments with water-soluble amphiphiles and active membranes, as well as the investigation of hydrodynamic interactions. Notably, it has finally been possible to measure spontaneous curvatures of membranes for a variety of different systems. Experimentally, spontaneous curvature has been a somewhat obscure quantity so far. Furthermore, vesicles have been used to construct bioelectronic devices and new classes of vesicles made of polymers were introduced.     

Curvature elasticity of mixed amphiphilic bilayers

Elastic bending constants of mixed amphiphilic bilayers are calculated using a molecular approach. The free energy is expanded up to quadratic order in curvatures and compositions, choosing a flat symmetrical bilayer as the reference state. Bending constants are then calculated from the derivatives of the free energy evaluated at this reference state. Two-component bilayers are considered. As a novelty, the local compositions are allowed to fully relax upon bending so that the 2 monolayers are at chemical equilibrium with each other at every curvature. The compositional degree of freedom is shown to affect the bending constant k, but not the saddle-splay constant k. The influence on the membrane elastic properties of various chain structural features, such as length, volume, and stiffness, is investigated. This may prove useful to model mixed bilayers composed of hydrocarbon/hydrocarbon and hydrocarbon/fluorocarbon chains.     

Model cell membranes: Discerning lipid and protein contributions in shaping the cell

The high complexity of biological membranes has motivated the development and application of a wide range of model membrane systems to study biochemical and biophysical aspects of membranes in situ under well defined conditions. The aim is to provide fundamental understanding of processes controlled by membrane structure, permeability and curvature as well as membrane proteins by using a wide range of biochemical, biophysical and microscopic techniques. This review gives an overview of some currently used model biomembrane systems. We will also discuss some key membrane protein properties that are relevant for protein–membrane interactions in terms of protein structure and how it is affected by membrane composition, phase behavior and curvature.     

Coexistence of menisci and the influence of neighboring pores on capillary displacement curvatures in sphere packings

The methods of calculating meniscus curvatures given by Mayer and Stowe and also independently by Princen are essentially the same. The method is exact for pores defined by rods. From comparison with experimental results, the method provides, for zero contact angle at least, a close approximation for pores defined by spheres. The application of the method to model pores defined by rods and spheres is discussed with particular attention being paid to the effects of neighboring pores. The merits of defining the neighbors of a particular pore as mirror images are discussed together with the effect of neighboring pores on the determination of pore sizes from capillary displacement curvatures. Meniscus curvatures of a family of pore shapes defined by three equal rods and mirror image neighbors are tabulated. A simple correlation was found between these values and estimates of the curvature given by the Haines incircle approximation.     

Nanoporous microbead supported bilayers: stability, physical characterization, and incorporation of functional transmembrane proteins

The introduction of functional transmembrane proteins into supported bilayer-based biomimetic systems presents a significant challenge for biophysics. Among the various methods for producing supported bilayers, liposomal fusion offers a versatile method for the introduction of membrane proteins into supported bilayers on a variety of substrates. In this study, the properties of protein containing unilamellar phosphocholine lipid bilayers on nanoporous silica microspheres are investigated. The effects of the silica substrate, pore structure, and the substrate curvature on the stability of the membrane and the functionality of the membrane protein are determined. Supported bilayers on porous silica microspheres show a significant increase in surface area on surfaces with structures in excess of 10 nm as well as an overall decrease in stability resulting from increasing pore size and curvature. Comparison of the liposomal and detergent-mediated introduction of purified bacteriorhodopsin (bR) and the human type 3 serotonin receptor (5HT3R) are investigated focusing on the resulting protein function, diffusion, orientation, and incorporation efficiency. In both cases, functional proteins are observed; however, the reconstitution efficiency and orientation selectivity are significantly enhanced through detergent-mediated protein reconstitution. The results of these experiments provide a basis for bulk ionic and fluorescent dye-based compartmentalization assays as well as single-molecule optical and single-channel electrochemical interrogation of transmembrane proteins in a biomimetic platform.     

Bending the Curve: Molecular Manifestations of Electron Antisymmetry

As very light fermions, electrons are governed by antisymmetric wave functions that lead to exchange integrals in the evaluation of the energy. Here we use the localized representation of orbitals to decompose the electronic energy in a fashion that isolates the enigmatic exchange contributions and characterizes their distinctive control over electron distributions. The key to this completely general analysis is considering the electrons in groups of three, drawing attention to the curvatures of pair potentials, rather than just their amplitudes and slopes. We show that a positive curvature at short distances is essential for the mutual distancing of electrons and a negative curvature at longer distances is essential to account for the influence of lone pairs on bond torsion. Neither curvature is available in the absence of the exchange contributions. Thus, although exchange energies are much shorter range than Coulomb energies, their influence on molecular geometry is profound and readily understood.     

Riemannian three dimensional molecular spaces

A simple manipulation of the first order density function permits to define a curved 3D Riemannian coordinate set, which can substitute the usual flat 3D Cartesian space, where atoms and molecules are supposed to exist. Several simple models are discussed. Gaussian type orbitals generate a space division with positive and negative curvatures, the later one being near the centre of the functions; contrarily Slater type orbitals provide a positive curvature everywhere.     

Vesicle Tubulation with Self‐Assembling DNA Nanosprings

A major goal of nanotechnology and bioengineering is to build artificial nanomachines capable of generating specific membrane curvatures on demand. Inspired by natural membrane‐deforming proteins, we designed DNA‐origami curls that polymerize into nanosprings and show their efficacy in vesicle deformation. DNA‐coated membrane tubules emerge from spherical vesicles when DNA‐origami polymerization or high membrane‐surface coverage occurs. Unlike many previous methods, the DNA self‐assembly‐mediated membrane tubulation eliminates the need for detergents or top‐down manipulation. The DNA‐origami design and deformation conditions have substantial influence on the tubulation efficiency and tube morphology, underscoring the intricate interplay between lipid bilayers and vesicle‐deforming DNA structures.