Regulation of Sticholysin II-Induced Pore Formation by Lipid Bilayer Composition, Phase State, and Interfacial Properties

Sticholysin II (StnII) is a pore-forming toxin that uses sphingomyelin (SM) as the recognition molecule in targeting membranes.After StnII monomers bind to SM, several toxin monomers act in concert to oligomerize into a functional pore. The regulation of StnII binding to SM, and the subsequent pore-formation process, is not fully understood. In this study, we examined how the biophysical properties of bilayers, originating from variations in the SM structure, from the presence of sterol species, or from the presence of increasingly polyunsaturated glycerophospholipids,affected StnII-induced pore formation. StnII-induced pore formation, as determined from calcein permeabilization, was fastest in the pure unsaturated SM bilayers. In 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC)/saturated SM bilayers (4:1 molar ratio), pore formation became slower as the chain length of the saturated SMs increased from 14 up to 24 carbons. In the POPC/palmitoyl-SM (16:0-SM) 4:1 bilayers, SM could not support pore formation by StnII if dimyristoyl-PC was included at 1:1 stoichiometry with 16:0-SM, suggesting that free clusters of SM were required for toxin binding and/or pore formation. Cholesterol and other sterols facilitated StnII-induced pore formation markedly, but the efficiency did not appear to correlate with the sterol structure. Benzyl alcohol was more efficient than sterols in enhancing the pore-formation process, suggesting that the effect on pore formation originated from alcohol-induced alteration of the hydrogen-bonding network in the SM-containing bilayers. Finally, we observed that pore formation by StnII was enhanced in the PC/16:0-SM 4:1 bilayers, in which the PC was increasingly unsaturated. We conclude that the physical state of bilayer lipids greatly affected pore formation by StnII. Phase boundaries were not required for pore formation, although SM in a gel state attenuated pore formation.

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).