Universal spectrum for DNA base C+G concentration variability in Human chromosome Y.pdf

Universal spectrum for DNA base C+G concentration variability in Human chromosome Y A. M. Selvam1 Deputy Director (Retired) Indian Institute of Tropical Meteorology, Pune 411 008, India Email: amselvam@ Web sites: /amselvam /index.html Abstract The spatial distribution of DNA base sequence A, C, G and T exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law of the form 1/fα where f is the frequency and α the exponent. Inverse power law form for power spectra implies the following: (1) A scale invariant eddy continuum, namely, the amplitudes of component eddies are related to each other by a scale factor alone. In general, the scale factor is different for different scale ranges and indicates a multifractal structure for the spatial distribution of DNA base sequence. (2) Scale invariance of eddies also implies long-range spatial correlations of the eddy fluctuations. Multifractal structure to space-time fluctuations and the associated inverse power law form for power spectra is generic to spatially extended dynamical systems in nature and is a signature of self-organized criticality. Mathematical models for the simulation and prediction of fractal fluctuations of dynamical systems are nonlinear and do not have analytical solutions. Finite precision computer realizations of non-linear mathematical models of dynamical systems also exhibit self-organized criticality manifested as sensitive dependence on initial conditions and give chaotic solutions resulting in ‘deterministic chaos’. The exact physical mechanism for the observed self- organized criticality is not yet identified. The author has developed a general systems theory where quantum mechanical laws emerge as self-consistent explanations for the observed long-range space-time correlations in macro-scale dynamical systems, i.e., the apparently chaotic fractal fluctuations are signatures of quantum-like chaos in dynamical systems. The mo