A unique or essentially unique single parametric characterisation of biopolymeric structures.

A generalised method of characterising the three dimensional structure of any biopolymer is proposed. The method makes use of rotation and superposition of identical rigid monomeric units that comprise the polymer. Out of the various parameters involved (refers the seven parametric representation of relating two identical rigid bodies in space), the angle of rotation and superposition termed as 'phi s' turns out to be essentially unique. An ideal biopolymer with n identical rigid units is characterised by (n-1) such unique angles. In applying the results to real biopolymers, the importance of recognising that monomeric units are no more rigid but only quasi-rigid is emphasised. However, by appropriate choice of 'rigid' fraction of the quasi-rigid monomers, one is led, as first approximation, to essentially unique characterisation of the biopolymer with (n-1) such unique angles. The phi s as a function of residue number acts essentially as a finger print of the given polymeric fold and the conformation of the chosen biopolymer. However, the full set of seven parameters are needed for model building. It is emphasised that the method is general in its application to any polymer and the application of the results to proteins and nucleic acids is illustrated.