Spectral diagnostics and symmetry mapping of molecular polysequences: Conceptual considerations

Abstract

All polysequences of length L form an additive one-parameter group, Sp(L), that is commutative (or Abelian) with respect to a given structural gauge, subject to well defined selection rules .
By expanding the successive moments (the cumulants) of this additive Abelian structure factor encoding in terns of the corresponding characters of the multiplicative group isomorphic to the original additive group (its so-called character group), it is possible to obtain self-consistent delocalized (or Fourier spectral) signatures of any sequence of length L in the specified structural gauge for each of the successive moments (cumulants). This is possible because the group characters are homomorphisms from the one parameter group Sp(L) to the complex domain, and which therefore form a complete orthogonal basis for any mapping from that group to the complex numbers.
Our group theoretical method can be used in at least two ways: (a) To furnish a self-consistent, discriminative classification scheme for comparing two closely identical polysequences with respect to a structural gauge (or, equivalently, with respect to a functional correlative), and (b) For the synthetic design of polysequences (proteins and polynucleotides) with prespecified spectral signature with respect to a particular structural gauge or functional correlative.