Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex

•We uncovered the DNA complexity and self-organization in DNA sequences of MHC.•We showed the extremization of Tsallis qq-entropy.•We showed the strong nonlinearity of the DNA dynamics.•The DNA dynamics is a non-Gaussian dynamical fractional anomalous diffusion process.•We showed the long-range correlations and the memory character of the DNA sequence.

We analyze 4 Mb sequences of the Major Histocompatibility Complex (MHC), which is a DNA segment on chromosome 6 with high gene density, controlling many immunological functions and associated with many diseases. The analysis is based on modern theoretical and mathematical tools of complexity theory, such as nonlinear time series analysis and Tsallis non-extensive statistics. The results revealed that the DNA complexity and self-organization can be related to fractional dynamical nonlinear processes with low-dimensional deterministic chaotic and non-extensive statistical character, which generate the DNA sequences under the extremization of Tsallis qq-entropy principle. While it still remains an open question as to whether the DNA walk is a fractional Brownian motion (FBM), a static anomalous diffusion process or a non-Gaussian dynamical fractional anomalous diffusion process, the results of this study testify for the latter, providing also a possible explanation for the previously observed long-range power law correlations of nucleotides, as well as the long-range correlation properties of coding and non-coding sequences present in DNA sequences.