Structural characterization of artificial self-assembling porphyrins that mimic the natural chlorosomal bacteriochlorophylls c, d, and e

We report two crystal structures of a synthetic porphyrin molecule which was programmed for self-assembly. The same groups which ensure that bacteriochlorophylls c, d, and e can self-assemble into the chlorosomal nanorods, the photosynthetic antenna system of some green bacteria, have been engineered into desired positions of the tetrapyrrolic macrocycle. In the case of the 5,15-meso-substituted anchoring groups, depending upon the concentration, by using the same crystallization solvents, either a tetragonal or a layered structure of porphyrin stacks were encountered. Surprisingly, pi-pi interactions combined with extensive dispersive interactions, which also encompass cyclohexane, one of the crystallization solvents, win over putative hydrogen bonding. We are aware that our compounds differ considerably from the natural bacteriochlorophylls, but based upon our findings, we now question the hydrogen-bonding network, previously proposed to organize stacks of bacteriochlorophylls. Transmission electron microscopy (TEM), atomic force microscopy (AFM), and small-angle X-ray scattering (SAXS) on various isomeric compounds support our challenge of current models for the chlorosomal antenna as these show structures, astonishingly similar to those of chlorosomes.     

Cycle Action on Treelike Structures

The purpose of this paper is to study the action on cycles of several known classes of oligomorphic groups, that is, infinite permutation groups of countable degree having only finitely many orbits on k-sets for each k. The groups studied here are all related to trees and treelike relational structures. The sequence whose k-th term is the number of orbits in the action on k-cycles is called Parker sequence. It turns out that, if we are dealing with the automorphism group of a suitable relational structure, this sequence counts also the finite substructures admitting a cyclic automorphism; in calculating these sequences for various groups, we shall thus describe and enumerate such substructures.Di più dirò: ch’a gli alberi dà vita [I shall say more: the trees are given life spirito uman che sente e che ragiona. by a human spirit that perceives and reasons.Di più dirò: ch’a gli alberi dà vita spirito uman che sente e che ragiona. Per prova sollo; io n’ho la voce udita che nel cor flebilmente anco mi suona.[I shall say more: the trees are given life by a human spirit that perceives and reasons. I know it by experience: I heard their voice and it still resounds faintly in my heart.]Torquato Tasso, Gerusalemme liberata, XIII, 49     

A characterization of affine hyperquadrics

In this paper, using the existence of special exhaustions that satisfy the complex homogeneous Monge–Ampère equation and curvature properties are given characterizations of the affine hyperquadric and other special Stein manifolds. Mathematics Subject Classification (2000) 32W20, 32V40