Area per Lipid in DPPC-Cholesterol Bilayers:Analytical Approach

Area per molecule in a DPPC-Cholesterol bilayers depends non-linearly on the cholesterol concentration. Using flexible strings model of lipid membranes we calculate area per molecule in DPPC-Cholesterol mixtures in the biologically relevant concentrations range. Few parameters of the model are optimized for a perfect agreement with the area per lipid data available from molecular dynamics simulations. Lateral pressure at the hydrophilic interface, {gamma}, is taken to be proportional to the cholesterol concentration. Non-linearity arises as a consequence of the non-linear dependence of thermodynamical equilibrium area of molecules on {gamma}. DPPC lipid is modeled as flexible string of finite thickness and a given bending rigidity, while cholesterol molecule is modeled as rigid rod with finite thickness and infinite rigidity. Using parameters fitted to reproduce area per molecule dependence on cholesterol concentration, we had further calculated our model predictions for the NMR order parameter of DPPC lipid chains and coefficient of thermal area expansion. The microscopic nature of the model allows to consider a broad range of thermodynamic phenomena.

Pore formation phase diagrams for lipid membranes

Critical lateral pressure for a pore formation and phase diagram of porous membrane are derived analytically as functions of the microscopic parameters of the lipid chains. The derivation exploits path-integral calculation of the free energy of the ensembles of semi-flexible strings and rigid rods that mimic the hydrophobic tails of lipids in the lipid bilayers and bolalipid membranes respectively. Analytical expressions for the area stretch/compressibility moduli of the membranes are derived in both models.

Flexible-to-semiflexible chain crossover on the pressure-area isotherm of lipid bilayer

We found theoretically that competition between ~Kq^4 and ~Qq^2 terms in the Fourier transformed conformational energy of a single lipid chain, in combination with inter-chain entropic repulsion in the hydrophobic part of the lipid (bi)layer, may cause a crossover on the bilayer pressure-area isotherm P(A)~(A-A_0)^{-n}. The crossover manifests itself in the transition from n=5/3 to n=3. Our microscopic model represents a single lipid molecule as a worm-like chain with finite irreducible cross-section area A_0, flexural rigidity K and stretching modulus Q in a parabolic potential with self-consistent curvature B(A) formed by entropic interactions between hydrocarbon chains in the lipid layer. The crossover area per lipid A* obeys relation Q^2/(KB(A*))~1 . We predict a peculiar possibility to deduce effective elastic moduli K and Q of the individual hydrocarbon chain from the analysis of the isotherm possessing such crossover. Also calculated is crossover-related behavior of the area compressibility modulus K_a, equilibrium area per lipid A_t, and chain order parameter S.

Metallic stripes and the universality of the anomalous half-breathing phonon in high-Tc cuprates

We demonstrate that the strong anomalies in the high frequency LO-phonon spectrum in cuprate superconductors can in principle be explained by the enhanced electronic polarizability associated with the self-organized one dimensionality of metallic stripes. Contrary to the current interpretation in terms of transversal stripe fluctuations, the anomaly should occur at momenta parallel to the stripes. The doping dependence of the anomaly is naturally explained, and we predict that the phonon line-width and the spread of the anomaly in the transverse momentum decrease with increasing temperature while high resolution measurements should reveal a characteristic substructure to the anomaly.