Polyene circular

For a circular polyene (a planar monocyclic compounds) such as benzene or cyclobutadiene the secular equation is a circulant ... 

For the circular aromatic or anti-aromatic polyene with n carbon atoms (C H ) the eigenenergies are given by... 

There are relatively few chemotherapeutic drugs which cause permeability increases in membranes such as the antifungal polyenes and the antibacterial circular oligopeptides of the tyrocidin, gramicidin and polymyxin families. Most of these are too toxic for systemic use but polymyxins have been given systemically in severe Pseudomonas infections with an attending risk of renal toxicity. 

Vertut-Croquin A, Bolard J, Chabbert M, Gary-Bobo C. Differences in the interaction of the polyene antibiotic amphotericin B with cholesterol- or ergosterol-containing phospholipid vesicles. A circular dichroism and permeability study. Biochemistry 1983 22(12) 2939 4. 

The nature of the interaction between polyene antibiotics and membrane sterols has also been investigated using UV, fluorescence and circular dichroism spectral studies [155,159,187,188]. The rate and degree of filipin III binding to cholesterol-containing liposomes depended upon the absolute sterol concentration and the mole percent in the bilayer. Binding constants for filipin III and liposomes were also estimated. 

We want to be able to deduce the conformation of a polymer in solution from its measured circular dichroism spectrum. For a linear polymer each ordered conformation must be a helix. The limiting cases for a helix are a straight line and a circle. A helix of identical residues is characterized by very few parameters. These are the radius of the helix, the rise per residue (the distance along the helix axis) and the number of residues per turn. A few examples will make this clear. A planar, all trans polyene will have a radius of zero (the helix is a straight line), a rise of 1.44 A and one residue per turn. A polypeptide a-helix has a radius of 2.28 A at the a-carbon, a rise per residue of 1.50 A and 3.6 residues per turn. One strand of a polynucleotide helix in the Watson-Crick B-form of DNA has a radius of 5.72 A at Cr of deoxyribose, a rise per residue of 3.4 A and 10 residues per turn. 

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