Regularity criteria for linear chains

The structural analysis of linear chains of arbitrary fixed shape is discus sed in the context of a spectral approach. The shape of the chain is charac terized by a set of scalar and pseudoscalar invariants, which remain consta nt under translations and rotations. The statistical properties of the set of invariants are compared with the analogous characteristics for a freely linked chain. The proposed criteria have the self-averaging property for re latively short (similar to 100-300 links) chains and can be used to discern possible latent periodicities and symmetries in a system. As examples, two applications of the theory are considered: the structural analysis of chai ns generated by random walks on a cubic lattice and protein C-alpha backbon es. (C) 1999 American Institute of Physics. [S1063-7761(99)01908-3].