Measurement of forces between and within bilayers of neutral phospholipids

Phospholipids in water form lamellar phases made up of alternating layers of water and bimolecular lipid leaflets. Three complementary methods, osmotic, mechanical, and vapour pressures, were used to measure the work of removing water from lamellar phases composed of frozen dipalmitoylphosphatidylcholine ( DPPC ), melted DPPC, egg phosphatidylethanolamine or equimolar mixtures of DPPC and cholesterol ( DPPC/CHOL ), Concurrently the structural changes that resulted from this water removal were measured using X-ray diffraction. The work was divided into that which forces the bilayers together ( F ) and that which compresses the molecules together within the bilayers ( F )# A large repulsive force exists between bilayers composed of each of the lipids studied and this force increases exponentially as bilayer separation is decreased. F is affected by the nature of the head groups, conformation of the acyl chains and heterogeneity of these chains. In general all of the melted phosphatidylcholines ( melted DPPC, egg lecithin and DPPC/CHOL ) have large equilibrium separations in excess water resulting from large repulsive hydration forces between these bilayers. By comparison, egg PE has an increased attractive force, and frozen DPPC has a decreased hydration force; each results in smaller separations in water for these two lipids. The chemical potentials of the water between the bilayers for all these lipids lie on a continuum, indicating that interbilayer water cannot be characterized by two discrete states, usually referred to as "bound" or "non**bound". For all lipids studied a maximum of 25 % of the total work done on the system goes into deforming the bilayers. The method used here viii to separate repulsion from deformation, developed for us by v. A. Parsegian, provides a unique method for the measurement of lateral pressure of a bilayer and its modulus of deformability ( Y ). Lateral pressure is affected by the nature of the head group, conformation and heterogeneity of the acyl chains. For small changes in molecular surface area ( A ) near equilibrium, both melted and frozen DPPC have similar values for the deformability modulus. Thus in this regime it requires about the same force to change the angle of tilt of frozen chains as it does to compress the fluid bilayer. The introduction of cholesterol into bilayers of DPPC reduces dramatically the lateral pressure of the bilayers over a large range of molecular surface areas ( A ). The variation in the magnitude of bilayer repulsion with different phospholipids provides a basis for the mechanism of lipid segregation in mixed lipid systems and suggests that interacting heterogeneous membranes may influence or modulate the composition of the opposing membrane. The measurements of deformabilities of bilayers provides a direct comparison of them with the properties of monolayers.

Measurement of repulsive forces between charged phospholipid bilayers

Electrostatic forces between membranes containing charged lipids were assumed to play an important role in influencing interactions between membranes long before quantitative measurements of such forces were available. ~ur measurements were designed to measure electrostatic forces between layers of lecithin charged with lipi~s carrying ionizable head groups. These experiments have shown that the interactions between charged lipid bila.yere are dominated by electrostatic forces only at separations greater than 30 A. At smaller separations the repulsion between charged bilayers is dominated by strong hydration forces. The net repulsive force between egg lecithin bilayers containing various amounts of cherged lipids (phosphatidylglycerol (PG) 5,10 ano 50 mole%, phosphatidyli. nosi tol (PI) 10 mole% and sodium oleate (Na-Ol) 3,5 and 10 mole%, where mole% gives the ratio of the number of moles' of .charged lipid to the total number of moles of all lipids present in the sample) was stuoied with the help ('If the osmotic streas technique described by LeNeveu et aI, (1977). Also, the forces between pure PG were j_nvestigated in the same manner. The results have been plotted showing variation of force as a function of bilay- _ er separation dw• All curVes 90 obtained called force curves, were found to be similar in sha.pe, showing two distinct regions, one when dw<.30 A is a region cf very rapid iiivariation of force with separation ( it is the region dominated by hydre,tion force) and second when dw> 40 A is a region of very slow variation of force with separB.tion ( it is the region dominated by the electrostatic force). Between these two regions there exists a transition area in which, in most systems studied, a phase separation of lipids into fractions containing different amounts of charged groups, was observed. A qualitative analysis showed that our results were v/ell described by the simple electrostatic double -le.yer theory. For quantitative agreement between measured and calculated force curves however, the charge density for the calculations had to be taken as half of that given by the number density of charged lipids present in the lecithin bilayers. It is not clear at the moment what causes such low apparent degree of ionization among the charged head groups, and further study is needed in this area.

Simultaneous extraction of order parameters and orientational distribution fuctions from 31[superscript]P NMR spectra of magnetically partially oriented phospholipid bilayers

Order parameter profiles extracted from the NMR spectra of model membranes are a valuable source of information about their structure and molecular motions. To al1alyze powder spectra the de-Pake-ing (numerical deconvolution) ~echnique can be used, but it assumes a random (spherical) dist.ribution of orientations in the sample. Multilamellar vesicles are known to deform and orient in the strong magnetic fields of NMR magnets, producing non-spherical orientation distributions. A recently developed technique for simultaneously extracting the anisotropies of the system as well as the orientation distributions is applied to the analysis of partially magnetically oriented 31p NMR spectra of phospholipids. A mixture of synthetic lipids, POPE and POPG, is analyzed to measure distortion of multilamellar vesicles in a magnetic field. In the analysis three models describing the shape of the distorted vesicles are examined. Ellipsoids of rotation with a semiaxis ratio of about 1.14 are found to provide a good approximation of the shape of the distorted vesicles. This is in reasonable agreement with published experimental work. All three models yield clearly non-spherical orientational distributions, as well as a precise measure of the anisotropy of the chemical shift. Noise in the experimental data prevented the analysis from concluding which of the three models is the best approximation. A discretization scheme for finding stability in the algorithm is outlined

Structural effects of neutral lipids on the divalent cation-induced interactions of phosphatidylserine - containing bilayers

As Ca2+ and phosphatidylserine (PS) are known to induce the adhesion of bilayer vesicles and form collapsed multibilayer structures in vitro, it was the aim of this study to examine how that interaction and the resultant structures might be modified by neutral lipid species. X-ray diffraction data from multilamellar systems suggest that phosphatidylcholine (PC) and diacylglycerol (DG) might be in the collapsed phase up to a concentration of -30 mole % and that above this concentration these neutral lipids may modify Ca2+-induced bilayer interactions. Using large unilamellar vesicles and long incubations in excess Ca2+ to ensure equilibration, similar preliminary results were again obtained with PC, and also with phosphatidylethanolamine (PE). A combination of X-ray diffraction, thin-layer chromatography, density gradient centrifugation and freeze-fracture electron microscopy, used in conjunction with an osmotic stress technique, showed that (i) -30 mole % PC can be accomodated in the Ca(DOPS)2 phase; and (ii) higher PC levels modify Ca2+-induced bilayer interactions resulting in single lamellar phases of larger dimension and reduced tendency for REV collapse. Importantly, the data suggest that PC is dehydrated during the rapid collapse process leading. to Ca(DOPS)2 formation and exists with this dehydrated phase. Similar results were obtained using PS isolated from bovine brain. Preliminary studies using two different phosphatidylethanolamine (PE) species indicated accomodation by Ca(DOPS)2 of -25-30 mole 0/0 PE and bulk phase separation, of species favouring a non-bilayer phase, at higher levels. Significantly, all PS/PE vesicles appear to undergo a complete Ca2+-induced collapse, even with contents of up to 90 mole % PE. These data suggest that PE may have an important role in fusion mechanisms in vivo. In sum the data lend both structural and stoichiometric evidence for th~ existence of laterally segregated neutral lipid molecules within the same bilayers as PS domains exposed to Ca2+.

Acyclic 5-Choosability of Planar Graphs Without Adjacent Short Cycles

The conjecture claiming that every planar graph is acyclic 5-choosable[Borodin et al., 2002] has been verified for several restricted classes of planargraphs. Recently, O. V. Borodin and A. O. Ivanova, [Journal of Graph Theory,68(2), October 2011, 169-176], have shown that a planar graph is acyclically 5-choosable if it does not contain an i-cycle adjacent to a j-cycle, where 3<=j<=5 if i=3 and 4<=j<=6 if i=4. We improve the above mentioned result and prove that every planar graph without an i-cycle adjacent to a j-cycle with3<=j<=5 if i=3 and 4<=j<=5 if i=4 is acyclically 5-choosable.

Planar Topological Defects in Unconventional Superconductors

In this work, we consider the properties of planar topological defects in unconventional superconductors. Specifically, we calculate microscopically the interaction energy of domain walls separating degenerate ground states in a chiral p-wave fermionic superfluid. The interaction is mediated by the quasiparticles experiencing Andreev scattering at the domain walls. As a by-product, we derive a useful general expression for the free energy of an arbitrary nonuniform texture of the order parameter in terms of the quasiparticle scattering matrix. The thesis is structured as follows. We begin with a historical review of the theories of superconductivity (Sec. 1.1), which led the way to the celebrated Bardeen-Cooper- Schrieffer (BCS) theory (Sec. 1.3). Then we proceed to the treatment of superconductors with so-called "unconventional pairing" in Sec. 1.4, and in Sec. 1.5 we introduce the specific case of chiral p-wave superconductivity. After introducing in Sec. 2 the domain wall (DW) model that will be considered throughout the work, we derive the Bogoliubov-de Gennes (BdG) equations in Sec. 3.1, which determine the quasiparticle excitation spectrum for a nonuniform superconductor. In this work, we use the semiclassical (Andreev) approximation, and solve the Andreev equations (which are a particular case of the BdG equations) in Sec. 4 to determine the quasiparticle spectrum for both the single- and two-DW textures. The Andreev equations are derived in Sec. 3.2, and the formal properties of the Andreev scattering coefficients are discussed in the following subsection. In Sec. 5, we use the transfer matrix method to relate the interaction energy of the DWs to the scattering matrix of the Bogoliubov quasiparticles. This facilitates the derivation of an analytical expression for the interaction energy between the two DWs in Sec. 5.3. Finally, to illustrate the general applicability our method, we apply it in Sec. 6 to the interaction between phase solitons in a two-band s-wave superconductor.

Edge-choosability of Planar Graphs

According to the List Colouring Conjecture, if G is a multigraph then χ' (G)=χl' (G) . In this thesis, we discuss a relaxed version of this conjecture that every simple graph G is edge-(∆ + 1)-choosable as by Vizing’s Theorem ∆(G) ≤χ' (G)≤∆(G) + 1. We prove that if G is a planar graph without 7-cycles with ∆(G)≠5,6 , or without adjacent 4-cycles with ∆(G)≠5, or with no 3-cycles adjacent to 5-cycles, then G is edge-(∆ + 1)-choosable.

Diastereoselective Synthesis of Planar Chiral N-Substituted Ferrocenes Derived from Epimeric Imidazolones and their Application to Asymmetric Hydrogenation of Quinolines

This thesis describes the synthesis and use of an N-substituted ferrocene bearing a proline-derived chiral directing group and diastereoselective lithiation-electrophile quench of the pro-Sp hydrogen of the ferrocene to give planar chiral products in >95:5 dr. The auxiliary group is found to be stable to lithium bases of types RLi and R2NLi giving the same diastereoselectivity. The anti- epimer of the previously mentioned syn auxiliary induces lithiation of pro Rp rather than pro Sp hydrogen in >95:5 dr. Upon electrophile quench and elimination, the enantiomer of the syn-derived planar chiral imidazolone is obtained. Hence, this method provides a practical way to prepare planar chiral enantiomers in this series without the use of a more expensive D-proline derived starting material. The syn and anti epimers have β, γ-stereogenic centers and the origin of stereoselectivity in lithiation appears to be driven by the conformational bias exerted by the β-silyloxy moiety in each chiral auxiliary. In the thesis, this conclusion is supported using insensitivity of lithiation selectivity to the bulkiness of the base, comparison of enantiomers, deuteration experiments, nOe difference studies and computational modeling of the ground states and lithiation transition states for both substrates. The products are then converted to ligand precursors to make iridium and rhodium complexes. Among them, one of the cationic iridium complex is found to be effective in the asymmetric hydrogenation of 2-substituted quinolines with enantioselectivities up to 80% at pressures as low as 5 atm.