M. I. Bogachev, A. R. Kayumov

The paper discusses the applicability of a novel method recently introduced by the authors to analyze the primary structure of proteins based on the statistics of return intervals between single amino acids to specify the differences between pathogenic and non-pathogenic bacteria. Recent investigations strongly indicate that the primary structure of proteins exhibits long-range dependence and multifractal properties. However, the origin of these structural properties, due to the general complexity of proteins structure and the integrative character of the fluctuation analysis methods that have been applied to extract multifractal features, remain unknown. Based on our recent findings concerning the statistics of return intervals in multifractal data sets, that are distributed considerably broader than a simple exponential that is a well-known result for random location, we suggest a method to elucidate the main components (amino acids) that contribute to the long-range dependent and multifractal primary structure of proteins. We have shown that in most of the bacterial proteins only a few amino acids are characterized by a broad distribution of return intervals that is a clear manefistation of long-range dependence. We demonstrate that the main components contributing to the long-range structural dependencies in proteins vary significantly among different protein functional classes. We also show that the studied properties differ in pathogenic and non-pathogenic bacteria. We hope that the suggested approach can be used to identify specific properties of pathogenic factors and thus to gain a better understanding of pathogenic mechanisms in bacteria and their relations to proteins structure.