K. Onizuka, K. Asai, M. Ishikawa, and S. T. C. Wong
We propose a novel description scheme of protein backbone conformation that can model the important factors of protein structure fox,nation, such as global interaction and geometric constraints. This description scheme represents a protein conformation with several symbolic sequences of multiple levels of abstraction. Each symbol in the sequence denotes the class of abstracted topology of subconformarion with the size specific to the level. Low level sequences of this description represent fine stT"uctures of high resolution, and high level sequences represent the abstracted topologies of large scale. The classification of protein backbone subconformations of various sizes is the most important base for this description scheme. This has never been tried so far due to the complexity in dealing with the number of degrees of freedom in subconformations. However, the proposed technique solved this problem by abstracting the topology of middle and large scale subconformations. This linear expansion technique extracts a fixed number of parameters as the expansion coefficients from the coordinate representation of subconformations. In this case, the simple reverse-transformation from the expansion coefficients reconstructs the three dimensional topology of a subconformation. The analysis of the relation between primary structure structure of a region and the subconfirmation of that region at each level in this description helps to model both local and global interactions of protein structure formation. Further, the statistic analysis of overlapping patterns of two subconformations models the geometric constraints important for a structure prediction system in generating a conformation which is geometrically sound.