Physica A 438 (2015) 188–209 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Measuring complexity, nonextensivity and chaos in the DNA sequence of the Major Histocompatibility Complex G.P. Pavlos a , L.P. Karakatsanis a,∗ , A.C. Iliopoulos a , E.G. Pavlos a , M.N. Xenakis a , Peter Clark b , Jamie Duke b , D.S. Monos b a Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Xanthi, Greece b Department of Pathology and Laboratory Medicine, Perelman School of Medicine, University of Pennsylvania and The Children’s Hospital of Philadelphia, Philadelphia, PA 19104, USA highlights • We uncovered the DNA complexity and self-organization in DNA sequences of MHC. • We showed the extremization of Tsallis q-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. article info Article history: Received 11 January 2015 Received in revised form 27 May 2015 Available online 8 July 2015 Keywords: DNA MHC Complexity q-entropy Tsallis q-triplet Multifractality abstract 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 theoret- ical and mathematical tools of complexity theory, such as nonlinear time series analy- sis 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 q-entropy principle. While it still re- mains 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 ex- planation 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. © 2015 Elsevier B.V. All rights reserved. 1. Introduction The nucleic acid sequences are likely the most sophisticated and efficient database created by nature through the dynamic process of evolution. The last three decades there has been an enormous effort by many scientists in unraveling the mysteries of DNA, especially establishing the roles of chance and determinism in genetic evolution and coding. This structure can shed ∗ Corresponding author. E-mail address: lkaraka@gmail.com (L.P. Karakatsanis). http://dx.doi.org/10.1016/j.physa.2015.06.044 0378-4371/© 2015 Elsevier B.V. All rights reserved.