Phospholipid chain length alters the equilibrium between pore and channel forms of gramicidin

Gramicidin is an excellent model system for studying the passage of ions through biological membranes. The conformation of gramicidin is well defined in many different solvent and lipid systems, as are its conductance and spectroscopic properties. It is a polymorphic molecule that can adopt two different types of structure, the double helical "pore" and the helical dimer "channel". This study investigated the influence of the acyl chain length of membrane phospholipids on the conformations adopted by gramicidin. We used circular dichroism spectroscopy to examine the conformational equilibrium between the pore and channel forms in small unilamellar vesicles of phosphatidylcholine with acyl chain lengths of 18, 20 and 22 carbons. Our results show that in C18 and C20 lipids almost all the gramicidin is in the channel form, while in the longer C22 lipids the equilibrium shifts in favour of pore conformations, such that they form up to 43% of the total population. This change is attributed to the ability of the double helical conformation to tolerate more hydrophobic mismatch than the helical dimer, perhaps due to the greater number of stabilising intermolecular hydrogen bonds.     

Pairings for cryptographers

Many research papers in pairing-based cryptography treat pairings as a “black box”. These papers build cryptographic schemes making use of various properties of pairings. If this approach is taken, then it is easy for authors to make invalid assumptions concerning the properties of pairings. The cryptographic schemes developed may not be realizable in practice, or may not be as efficient as the authors assume.The aim of this paper is to outline, in as simple a fashion as possible, the basic choices that are available when using pairings in cryptography. For each choice, the main properties and efficiency issues are summarized. The paper is intended to be of use to non-specialists who are interested in using pairings to design cryptographic schemes.     

Regularity of Optimal Controls for State Constrained Problems

Conditions are given under which optimal controls are Lipschitz continuous, for dynamic optimization problems with functional inequality constraints. The linear independence condition on active state constraints, present in the earlier literature, can be replaced by a less restrictive, positive linear independence condition, that requires linear independence merely with respect to non-negative weighting parameters. Smoothness conditions on the data are also relaxed. A key part of the proof involves an analysis of the implications of first order optimality conditions in the form of a nonsmooth Maximum Principle.     

On the distribution of the coefficients of normal forms for Frobenius expansions

Frobenius expansions are representations of integers to an algebraic base which are sometimes useful for efficient (hyper)elliptic curve cryptography. The normal form of a Frobenius expansion is the polynomial with integer coefficients obtained by reducing a Frobenius expansion modulo the characteristic polynomial of Frobenius. We consider the distribution of the coefficients of reductions of Frobenius expansions and non-adjacent forms of Frobenius expansions (NAFs) to normal form. We give asymptotic bounds on the coefficients which improve on naive bounds, for both genus one and genus two. We also discuss the non-uniformity of the distribution of the coefficients (assuming a uniform distribution for Frobenius expansions).