An Algorithm for Ensuring Data Integrity in Internal Parameters Based Representation of Macromolecular Structure Author

An algorithm is presented for the representation of macromolecular structures in terms of internal parameters (bond lengths, bond angles and dihedral angles). The algorithm ensures maintenance of data integrity and constancy when converting to and from a Cartesian representation. It is hoped that this algorithm will lead to large repositories of macromolecular strucure (including the PDB) being maintained in terms of internal parameters. Such a representation would be of great value in computer based structural biology research. Introduction Macromolecular structure can be expressed in two alternative representations, a) in terms of Cartesian coordinates of the constituent atoms, and b) in terms of a set of internal parameters bond lengths, bond angles, and dihedral angles. Of these the former is used predominantly in structural biology studies today. The popular Protein Data Bank(PDB), for instance, is a repository of Cartesian coordinates of atoms in macromolecules (proteins and nucleic acids) whose three dimensional structures have been determined experimentally (by X-ray crystallography or nmr). The representation in terms of internal parameters has several attractive features. Firstly, it is aesthetically appealing. For instance, the representation of a protein by this method can proceed describing the molecule along the peptide backbone starting from the N–terminal and ending at the C-terminal, and corresponding to the sequence in which it is synthesized in the living cell. A rough and ready molecular structure – a starting point for refinement processing – can be generated easily using standard values for the bond lengths and bond angles, and assigning values for the variable dihedral angles based on well-known principles, like for instance, the (φ, ψ) distribution map for proteins. Similarly, in case the coordinates of the heavy atoms alone are known, from a particular experimental determination and the positions of hydrogen atoms are desired to be included, the side-chains in standard geometry can be easily appended. In the case of representation in terms of Cartesian coordinates, the bonds in the molecule have to be either explicitly specified, or are determined based on inter-atomic distances being shorter than specified limits. In the internal parameters based