AM  Vol.4 No.11 B , November 2013
Dense Fractal Networks, Trends, Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes’ Activity in Living Cells for Medical Diagnostics
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 H&ouml;lder 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.


Cite this paper
N. Galich, "Dense Fractal Networks, Trends, Noises and Switches in Homeostasis Regulation of Shannon Entropy for Chromosomes’ Activity in Living Cells for Medical Diagnostics," Applied Mathematics, Vol. 4 No. 11, 2013, pp. 30-41. doi: 10.4236/am.2013.411A2006.
References
[1]   M. V. Filatov, E. Y. Varfolomeeva and E. A. Ivanov, “Flow Cytofluorometric Detection of Inflammatory Processes by Measuring Respiratory Burst Reaction of Peripheral Blood Neutrophils,” Biochemistry and Molecular Medicine, Vol. 55, No. 2, 1995, pp. 116-121.
http://dx.doi.org/10.1006/bmme.1995.1041

[2]   N. E. Galich and M. V. Filatov, “Laser Fluorescence Fluctuation Excesses in Molecular Immunology Experiments,” Proceedings of the Society of Photo-Optical Instrumentation, Vol. 6597, 2007, Article ID: 65970L.

[3]   N. E. Galich, “Bifurcations of Averaged Immunofluorescence Distributions Due to Oxidative Activity of DNA in Diagnostics,” Biophysical Reviews and Letters, Vol. 5, No. 4, 2010, pp. 227-240.
http://dx.doi.org/10.1142/S1793048010001196

[4]   N. E. Galich, “Cytometric Distributions and Wavelet Spectra of Immunofluorescence Noise in Medical Diagnostics,” World Congress on Medical Physics and Biomedical Engineering, Munich, 7-12 September 2009, pp. 1936-1939,

[5]   N. E. Galich, “Shannon-Weaver Biodiversity of Neutrophils in Fractal Networks of Immunofluorescence for Medical Diagnostics,” Journal of WASET, Vol. 70, 2010, pp. 504-515.
http://www.waset.org/journals/waset/v45/v45-92.pdf

[6]   N. E. Galich, “Complex Networks, Fractals and Topology Trends for Oxidative Activity of DNA in Cells for Populations of Fluorescing Neutrophils in Medical Diagnostics,” Physics Procedia, Vol. 22, 2011, pp. 177-185.
http://dx.doi.org/10.1016/j.phpro.2011.11.028

[7]   N. E. Galich, “Informational Homeostasis for Shannon Entropy in Complex Networks of Oxidative Activity of DNA in Cells; Fractals, Stability and the Switching in Large-Scale Gene Nets for Fluorescing Neutrophils in Medical Diagnostics,” World Congress on Medical Physics and Biomedical Engineering, Beijing, 26-31 May 2012, pp. 542-545.

[8]   J. Feder, “Fractals,” Plenum Press, New York, 1988.
http://dx.doi.org/10.1007/978-1-4899-2124-6

[9]   T. Gneiting and M. Schlather, “Stochastic Models That Separate Fractal Dimension and the Hurst Effect,” SIAM Review, Vol. 46, No. 2, 2004, pp. 269-282.
http://dx.doi.org/10.1137/S0036144501394387

[10]   B. Mandelbrot, “The Fractal Geometry of Nature,” W.H. Freeman, San Francisco, 1977.

[11]   D. J. Watts and S. H. Strogatz, “Collective Dynamics of Small-World Networks,” Nature, Vol. 393, No. 6684, 1998, pp. 440-442. http://dx.doi.org/10.1038/30918

[12]   L. A. N. Amaral, A. Scala, M. Barthélémy and H. E. Stanley, “Classes of Small-World Networks,” Proceedings of the National Academy of Sciences, Vol. 97, No. 21, 2000, pp. 11149-11152.
http://dx.doi.org/10.1073/pnas.200327197

[13]   A. Wagner and D. A. Fell, “The Small World inside Large Metabolic Networks,” Proceedings of the Royal Society of London. Series B, Vol. 268, No. 1478, 2001, pp. 1803-1810.
http://dx.doi.org/10.1098/rspb.2001.1711

[14]   M. E. J. Newman, “The Structure and Function of Complex Networks,” SIAM Review, Vol. 45, No. 2, 2003, pp. 167-256. http://dx.doi.org/10.1137/S003614450342480

[15]   Y. A. Kuznetsov, “Elements of Applied Bifurcation Theory,” Springer, New York, 1995.

[16]   N. G. Van Kampen, “Stochastic Processes in Physics and Chemistry,” North-Holland Personal Library, 1984.

 
 
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