Measuring the Similarity of Protein Structures Using Image Compression Algorithms

For measuring the similarity of biological sequences and structures such as DNA sequences, protein sequences, and tertiary structures, several compression-based methods have been developed. However, they are based on compression algorithms only for sequential data. For instance, protein structures can be represented by two-dimensional distance matrices. Therefore, it is expected that image compression is useful for measuring the similarity of protein structures because image compression algorithms compress data horizontally and vertically. This paper proposes series of methods for measuring the similarity of protein structures. In the methods, an original protein structure is transformed into a distance matrix, which is regarded as a two-dimensional image. Then, the similarity of two protein structures is measured by a kind of compression ratio of the concatenated image. We employed several image compression algorithms, PEG, GIF, PNG, IFS, and SPC. Since SPC often gave better results among the other image compression methods, and it is simple and easy to be modified, we modified SPC and obtained MSPC. We applied the proposed methods to clustering of protein structures, and performed Receiver Operating Characteristic (ROC) analysis. The results of computational experiments suggest that MSPC has the best performance among existing compression-based methods. We also present some theoretical results on the time complexity and Kolmogorov complexity of image compression-based protein structure comparison.