The Nonrandom and Geometric Role of Retroviral DNA in Genome

In this study we analyze the statistical characteristics of the human endogenous retroviruses (ERVs) database focusing on the subcase of positions and lengths of ERVs elements. We show that the positions and sizes of the ERV elements within chromosomes exhibit patterns that can be classified based on their complexity (or nonrandomness) characteristics as prescribed by the convolution of the abstract phase space with the tangible molecular space. A complexity factor, incorporating the Hurst exponent and the Tsallisian q-entropic index (used here as a molecular complexity index), captures evolutionary and physicochemical constraints acting on the geometry of ERV elements, defined by their positions and lengths. This reveals that ERV elements constitute a distinct subsystem that interacts with the entire genome and continuously influences its biological functionality. We found that complexity is more pronounced in positions than in lengths. A machine learning tool clustered the retrieved information to statistically capture chromosome functionality and differentiate between the subsystems of positions and lengths.