TITLE:
Dense Fractal Networks, Trends, Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes’ Activity in Living Cells for Medical Diagnostics
AUTHORS:
Nikolay E. Galich
KEYWORDS:
Abnormal Fractals; DNA Activity and Shannon Information Entropy; Fractal Patterns and Fragmentation; Informational Homeostasis; Saturations of Chromosomal Correlations; Multi-Scale Fractal Networks of Shannon Entropy
JOURNAL NAME:
Applied Mathematics,
Vol.4 No.11B,
November
7,
2013
ABSTRACT: We analyze correlations and patterns of oxidative
activity of 3D DNA at DNA fluorescence in complete sets of chromosomes
in neutrophils of peripheral blood. Fluorescence of DNA is registered by method
of flow cytometry with nanometer spatial resolution. Experimental data present
fluorescence of many ten thousands of cells, from different parts of body in
each population, in various blood samples. Data is presented in histograms as
frequency distributions of flashes in the dependence on their intensity.
Normalized frequency distribution of information in these histograms is used as
probabilistic measure for definition of Shannon entropy. Data analysis shows
that for this measure of Shannon entropy common sum of entropy, i.e. total entropy E, for any histogram is invariant and has identical trends of
changes all values of E (r) = lnr at reduction of rank r of histogram. This invariance reflects
informational homeostasis of chromosomes activity inside cells in multi-scale
networks of entropy, for varied ranks r.
Shannon entropy in multi-scale DNA networks has much more dense packing of
correlations than in “small world” networks. As the rule, networks of entropy differ by the mix of
normal D 2 and
abnormal D > 2
fractal dimensions for varied ranks r,
the new types of fractal patterns and hinges for various topology (fractal
dimension) at different states of health. We show that all distributions
of information entropy are divided on three classes, which associated in
diagnostics with a good health or dominants of autoimmune or inflammatory
diseases. This classification based on switching of stability at transcritical
bifurcation in homeostasis regulation. We defined many ways for homeostasis
regulation, coincidences and switching patterns in branching sequences, the
averages of Hölder for deviations of entropy from homeostasis at different
states of health, with various saturation levels the noises of entropy at
activity of all chromosomes in support regulation of homeostasis.