IMPLEMENTING KNOT-THEORETICAL CHARACTERIZATION METHODS TO ANALYZE THE BACKBONE STRUCTURE OF PROTEINS - APPLICATION TO CTF L7 L12 AND CARBOXYPEPTIDASE-A INHIBITOR PROTEINS

In this work we apply a recently developed method for characterizing the shape of the tertiary structure of proteins. The approach is based on a combination of graph- and knot-theoretical characterizations of Cartesian projections of the space curve describing the protein backbone. The proposed technique reduces the essential shape features to a topologically based code formed by a sequence of knot symbols and polynomials. These polynomials are topological invariants that describe the overcrossing and knotting patterns of curves derived from the molecular space curve. These descriptors are algorithmically computed. The procedure is applied to describe the structure of the carboxy terminal fragment of the L7/L12 chloroplast ribosomal protein (CTF L7/L12) and the potato carboxypeptidase A inhibitor protein (PCI), which has a set of three disulfide bridges. In the former case, we describe the protein's shape features in terms of its alpha-helices, and a backbone simplified by considering helices without internal structure. An extension of the methodology to describe disulfide bridges is discussed and applied to PCI. Changes in the knot-theoretical characterization due to possible uncertainties in the resolution of the X-ray structure, as well as the inclusion of low-frequency motions of the backbone, are also discussed.