Ethanol Oxidation and Toxicity: Role of Alcohol P-450 Oxygenase

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66172/1/j.1530-0277.1986.tb05179.x.pd

From symmetry to syntopy : a fuzzy-set approach to quasi-symmetric systems

Point symmetry is essentially a discrete concept, whereas molecular structures and their conformational changes display continuous features. Using the formalism of fuzzy-set theory, we propose a continuous extension of the symmetry concept for quasi-symmetric systems. For each point k of the reduced nuclear configuration space M of all N-atom systems having a specified stoichiometry, and for an energy criterion ε suggested by the statics or the dynamics of these systems, we define membership functions µi(k, ε) which generate 'syntopy' fuzzy subsets Si, in the metric space M ; these latter are used to obtain a continuous extension s(k, ε) of the symmetry point groups gi. Illustrations of the procedures used are given on simple examples, and applications of the new concept are outlined