Codability criterion for picking proteinlike structures from random three-dimensional configurations

We show that the dominant eigenvectors of real protein structural contact matrices are highly correlated with their amino acid sequences. These results suggests that an ab initio sequence-independent profile exists for every protein structure and that this profile is highly effective in differentiating the ordering of amino acids in natural protein sequences from random sequences. This profile provides a structural code and is a key for understanding the unique behavior of protein structures. Using a lattice model, we show that there are special codable structures highly separated from random structures in the dominant eigenvector space of their structural contact matrices. As an example, we show our results provide a good explanation to the "designable principle" of protein structures.