A method for the characterization of foldings in protein ribbon models

The ribbon model of chain macromolecules is a useful tool for analyzing some of the large-scale shape features of these complex systems. Up to now, the ribbon model has been used mostly to produce graphical displays, which are usually analyzed by visual inspection. In this work we suggest a computational method for characterizing automatically, in a concise and algebraic fashion, some of the important shape features of these ribbon models. The procedure is based on a graph-theoretical and knot-theoretical characterization of three well-defined projections of a space curve associated with the ribbon. The labeled graphs can be characterized by the handedness of the crossovers in the ribbon that are the vertices of the graph. The method can be used to provide a fully algebraic representation of the changes occurring when a molecule, such as a protein, undergoes conformational rearrangements (folding), as well as to provide a shape comparison for a pair of related molecular ribbons. This algebraic representation is well suited for easy storage, retrieval, and computer manipulation of the information on the ribbon's shape. Illustrative examples of the method are provided.