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We analyze oxidative activity of DNA due to fluorescence of chromosomes inside cells, using flow cytometry method with nanometer spatial resolution. Statistics of fluorescence is presented in histogram as frequency distributions of flashes in the dependence on their intensity and in distributions of Shannon entropy, which was defined on the base of normalized distribution of information in original histogram for frequency of flashes. We show that overall 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 histogram’ rank r. This invariance reflects informational homeostasis of chromosomes activity in multi-scale networks of entropy inside all cells in various samples of blood for DNA inside neutrophils, lymphocytes, inside all leukocytes of human and inside chicken erythrocytes for various dyes, colors and various excitations of fluorescence. Informational homeostasis of oxidative activity of 3D DNA in the full set of chromosomes inside living cells exists for any Shannon-Weaver index of biodiversity of cells, at any state of health different beings. Regulation perturbations in information activity DNA provides informational adaptability and vitality of cells at homeostasis support. Noises of entropy, during regulation of informational homeostasis, depend on the states of health in real time. The main structural reconstructions of chromosomal correlations, corresponding to self-regulation of homeostasis, occur in the most large-scale networks of entropy, for rank r<32. We show that stability of homeostasis is supported by activity of all 46 chromosomes inside cells. Patterns, hidden switching and branching in sequences of averages of H?lder and central moments for noises in regulation of homeostasis define new opportunities in diagnostics of health and immunity. All people and all aerobic beings have one overall homeostatic level for countdown of information activity of DNA inside cells. We noted very bad and dangerous properties of artificial cells with other levels of informational homeostasis for all aerobic beings in foods, medical treatment and in biotechnologies.

There are a variety of different features for large-scale oxidative activity of DNA that determine the body’s vital functions [

We are focused on the minimal presence, until deletion, any statistical hypotheses and assumptions in our nonlinear analysis of experiments for DNA activity in living cells. We don’t use the genomic data for all of humanity as a whole. We oriented on medical diagnostics of health status based on oxidative activity of DNA in cells for everyday clinical practice, for given person at given time. Oxidative activity of DNA is visualized in fluorescence. We analyze experimental data on DNA fluorescence in neutrophils of peripheral blood at biochemical reaction of oxidative burst [

Typical examples of original histograms are shown in

Immune system interconnected with different networks of diverse populations of young and old neutrophils in the human body such as networks of metabolic, geographical, ecological, information, genetics, migration and other processes during blood circulation. The fragments of nuclear and mitochondrial DNA with oxidants determine the basic place for localization of fluorescent dye, its distributions, intensity and statistics of fluorescence. These fragments may belong to the coding and non-coding portions of DNA. The heterogeneities of fluorescence varied chromosomes reflect genetic, special, individual features and immune response to the pathogenic actions. Detailed descriptions our experimental procedures for dyeing DNA by ethidium bromid were presented in [

The inevitable noises of immune fluorescence, shown in Figure1b, are formed by the large-scale correlations at DNA activity in cells and represent an actual ‘terra incognita’, if we don’t use any forced smoothing. These noises differ by the structural peculiarities, up to the changes of positive and negative signs for wavelet spectra of noises at various states of health, as are in the cases with different gene expressions [

Registration of fluorescence with flash duration ~10^{−9}^{ }- 10^{−8} s in the jet of blood flowing through the laser beam with velocity ~1 - 10 m/s provides measurement with spatial scales ~10^{−9}^{ }- 10^{−8} m in the flow direction [

liarities cannot be seen in the optical microscope. Each cell has chaotic Brownian motions and chaotic rotations during jet flow of blood through the laser beam at flow cytometry measurements. Thus, we analyze various experimental data for 3D-correlations of nuclear DNA in large populations ~10^{4} - 10^{5} of fluorescing cells with rather high spatial resolution in the flow direction. As well known real 3D-inner life of genome in various cells [

Recently we had found very important empirical invariant for information nentropy, i.e. unified value of total Shannon entropy E(J), based on frequency distributions of information J(I) = −lnP(I), for fluorescing DNA inside human neutrophils in any samples of blood [

Statistics of immunofluorescence is essentially non-Gaussian [

Now we concentrated on the noises and information transfer for DNA activity in cells. Oddly enough that is now fully absent any definition and account of real noises in the chemical reactions of DNA oxidation for stability and transmission of information in a living cell. Are not defined the functions and roles of these noises in the life and metabolic regulation inside cells, in chromosomal and inter-chromosomal correlations. Variability and regulation the dynamics of life, as and the level of noises, always are the base for definition the key position of reliability and transmission of any information in nature and technology, and in the evolution of people’s daily lives. How estimate quality of DNA communications, information and information entropy of DNA activity inside cells? What need for comparison of various data on informational activity of DNA in cell for given person in real time? How to determine structure of large-scale correlations of information activity of DNA in cells, level of information noises and switching of information transfer inside cells at different states of health?

In the Part 2 of this article we define informational homeostasis as invariance of total Shannon entropy E(J, r), for information J at rank r inside all cells, i.e. as overall empirical rule of E(J, r) = lnr, for entropy E(J, r)) based on the normalized distribution of information J(I) = −lnP(I) for fluorescing DNA inside neutrophils (see equations (1), (2)).

In the Part 3 of the article we present experimental illustrations of informational homeostasis E(J, r) = lnr inside different cells in various samples of blood for DNA inside human neutrophils, lymphocytes, inside all leukocytes of human and inside chicken erythrocytes for various dyes, various colors and various excitations of fluorescence.

In the Part 4 of the article we show that total Shannon entropy for information on DNA activity, i.e. total Shannon entropy E(J, r) = lnr, always more than total Shannon entropy E(P, r) for DNA activity inside cells (Shannon-Weaver biodiversity of cells), i.e. Shannon Weaver biodiversity of cells E(P, r) < E(J, r) is less than biodiversity E(J, r) of information on DNA activity in homeostasis. Here also discussed main physical and information peculiarities of invariance of total Shannon entropy E(J, r) = lnr and possible origin of homeostasis.

In the Part 5 of this article we introduce deviations and noises near homeostatic level E(J, r) = lnr of total Shannon entropy E(J, r). Here define two approaches for description varied regulation of information homeostasis in the dependence on the states of health. We observed various changes in dynamics of decreasing and increasing the sequences of central moments and Holder’s averages for noises of Shannon entropy at different states of health. Switching of these averages from low to very high level reflect different pathology in the states of health. We show that regulation of homeostasis is ensured by common participation and correlations of all 46 chromosomes inside cells.

In the Part 6 of the article we present short conclusions. Here also present a question and discussions the role of information homeostasis for selection of a good and bad artificial life (artificial cells) in a good and bad biotechnologies from the point of view a homeostasis condition in cell life of human and all aerobic beings. Clear criteria of a bad and dangerous biotechnology connected with violation of homeostatic level of entropy E(J, r) = lnr and (or) existence other levels of homeostasis of information entropy for artificial cells inside human body, as in a good substrate.

Adequate and correct correlations for DNA activity in cells, without artificial assumptions and smoothing of any experimental data, must be interconnected with systematic investigations of Shannon’ entropies. Here Shannon; entropies define level of functional and informational constraints for DNA correlations inside cells and are used as the measures of sequences variability. Shannon’ entropies for one and the same experimental data depend on the choice of probabilistic measure based on original histograms for frequency of flashes P(I). Basic probabilistic measure may serve a frequency of flashes P(I) [

}^{2} [

Let us define distributions of Shannon entropy E(J(I)) based on information J(I) = LnP(I) for frequency flashes of fluorescence P(I). Let us consider the probability density

256 channels of intensity measurement. The mean value of

Distribution of information

Let us consider normalized distribution of information

as the probabilistic measure for frequency distributions of Shannon entropy

Three examples of frequency distributions of Shannon entropy

In Figures 2(a) we see a very strong roughness and differences in information

Data analysis for all experiments has shown a conservation of identical values of total Shannon entropy in any cells

Thus, total Shannon entropy E(J) is empirical invariant, for all neutrophils in all donors [_{max} = r. At rank r=256 all experimental data, for all donors give one and the same value of

Decreasing rank r leads to decreasing the value of invariant

Here, as everywhere, are used different terms a rank r and range r for the same value of r. Range of histogram r interconnected with the selection of multistage clusters in networks with structure of bronchial tree; here range r coincides with the number of columns in a histogram or with the number of channels for measurements of fluorescence intensity at given maximal value of dimensionless intensity, i.e. r = I_{max}. In our experiments the number of channels is r = 256. Variations of range r, i.e. rank of histogram r, or variations the scale r, when r = I_{max}, provide the changes in irregularity and brokenness of frequency distribution of fluorescence for histograms of various rank r. Various examples decreasing of histograms rank r presented in [

Frequency distribution of entropy

Total entropy

More detailed approximation of total entropy

Experimental data analysis shows that typical variations different values of dimensionless parameters A and B in approximation (8) are A = 1.015 … 0.978 and B = 0.01… 0.21; maximal variations correspond to multiple diseases with the multiple allergies. Theoretical estimation gives single value of B = 0; for single channel measurements of fluorescence, as lower bound of values B, we have value of rank r = 1, probability of flashes p = 1, information J = 0, information entropy

Interesting to compare Shannon information entropy

Informational homeostasis of total Shannon entropy

In Figures 4(d) and 5(d) shown that informational homeostasis exists for DNA inside human lymphocytes, in all leukocytes of human and inside chicken erythrocytes for various dyes, for green and red glow at different excitations of fluorescence by argon laser beam and light of mercury lamp.

Green (blue-green) fluorescence of DNA inside human lymphocytes at wavelength ~480 nm is ensured by small additive of Hoechst 33342 with concentration 2

Two exampels of red fluorescence of human leukocytes and human neutrophils are shown in Figures 5.

We used the additions of hydroethidine with concentration 150

We observe one and the same behavior of total Shannon entropy

In order to illustrate changeability of immunofluorescence for one and the same healthy donor during one year, in real time, let us consider histograms for fluorescence of neutrophils in

Distributions of entropy are shown in Figures 7.

Data analysis shown that logarithmic behavior in the dependence on range r is typical also for Shannon-Weaver biodiversity of neutrophils _{i}. We can enter the information for the frequency distribution of flashes

Shannon entropy

leus of neutrophils. These correlations reflect various networks for distribution of ethidium bromide in chromosomes and coincide with networks of oxidative activity of fluorescing DNA. The same approach may be used for definition biodiversity of any fluorescing cells. Three illustrations of Shannon-Weaver biodiversity presented in

According to Figures 3, 4(d), 5(d), 7(b) invariant of Shannon entropy

The same inequality is observed for all distributions of fluorescence in Figures 1(a), 4(b), 5(c), 6(a). This inequality observed for all experiments on DNA fluorescence, for all cells, all dyes, all colors, etc. Thus, biodiversity of DNA in cells

The inequality (10) associated also with more high density packing of information entropy E(J, r) [

ing role of abnormal fractal dimensions D > 2 in networks of entropy ^{1/D} between N nodes, i.e. more densely fractal networks of information entropy E(J, r) in cells.

This inequality means that dense of packing of DNA activity inside cells is less than dense of parking for information on DNA activity, i.e. networks of DNA activity and networks for information of DNA activity have different topology, dynamical and structural properties in cells. Combined actions and interconnections of these networks produce regulation of informational homeostasis in any cell. Therefore, condition (10) defines informational adaptability and vitality of cells at informational homeostasis.

Invariance of total entropy

Informational invariant of

Let us consider a question about physical nature of support of informational homeostasis inside cells. We have informational homeostasis and overall pattern

Need specially noted that any forced smoothing distributions of J(I, r)/or P(I, r) leads to the destroy of informational homeostasis of total Shannon entropy E(J, r), i.e. ensures the destruction of correlations in real life of DNA inside cells and leads to the uncontrolled distortions of chromosomes activity in the nuclei of cells. Forced smoothing DNA activity inside cells belongs to the games without rules and meaningful, sensible goals.

We haven’t ideal, absolute, correct homeostasis; absolute constant values of information entropy in real life, in real time exist nowhere and never. We always have various fluctuations during regulation of homeostasis for support of it stability. These fluctuations are very individual and concern reach information on human health at specific regulation the dynamic equilibrium in homeostasis for given human. An example of regulation for arbitrary conditions of homeostasis is described in [

for definition various mean characteristics of individual distortions of Shannon entropy in given sample of blood, where frequency distributions of information entropy

Central moments

where

Two branches with even and odd numbers m of central moments

The exponential decreasing of

The power means or averages of Hölder for deviations or fluctuations of entropy

Here symbol

We observe very strong switching for branches at the largest scale r = 4 in Hölder’s averages in

Mean level of experimental errors in original cytometric histograms for r = 256 is about 2% [

Magnitudes of deviations all distributions of

A very slow growth of Hölder’s averages

Averages of Hölder

Average noise level of information entropy in DNA activity for one chromosome among m chromosomes at given range

for

Distributions of

For more contrast here considered also changeability of health of one and the same healthy donor in real time, during one year, for initial histograms in

One may to compare histograms in Figures 1, 6, 10 and 12.

In

networks of information entropy and their stability remain virtually unchanged [

For rather large rank r > 32, difference between

Thus according to Figures 11 the qualitative changes and restructuring of health conditions connected with the qualitative transformations in the structure of the large-scale correlations of information entropy

Switching between networks of entropy, corresponding to different states of health and inverse transitions, for small fluctuations of entropy near homeostasis are ensured by the processes of unknown nature. According to

Different values of r characterize different scale of clusters for oxidative activity of DNA inside cells. Coincidence of Hölder’s averages

This article is associated with the answers to the four questions on physics for information activity of DNA in cells in the presence complete set of chromosomes and all other components and inner elements of living cells.

1) How to determine and to measure information on oxidative activity of DNA inside cells?

2) What statistical characteristics define various structures of large-scale correlations of information activity of DNA inside cells?

3) What general laws and parameters provide and are define stability and reproduction of information in networks of DNA in cells, adaptability of cells and vitality at variation of environment, heredities, traumas, illness, infection, etc?

4) How to determine information noise, structural trends, specific conditions and stability of information transfer inside living cells for different people in real time?

In this way we come to some very clear answers and conclusions about complexity and information patterns for oxidizing activity of DNA inside cells.

A. We observe only one unified value of total Shannon entropy

B. Invariance of total information entropy

Invariance of total information entropy

C. Biodiversity of DNA activity in cells

D. Fluctuations in DNA activity as and self-regulation of informational homeostasis are associated with cell life in the body as in the open system, for stability support of vitality conditions at varied perturbations of different origin. Real traffic in information activity DNA never can be smooth [

E. We introduce the average standard deviation

F. Existence of only one secluded DNA, as the existence of a hermit in a cave, must be linked with the certain homeostatic conditions. Here exists some interest with respect of availability, changeability or the lack of informational homeostasis of secluded DNA in corresponding environment at different conditions (if we don’t like lonely DNA, living, for instance, in the descriptions of textbooks, in vacuum, far from normal of vital conditions, without metabolism and homeostasis, in epigenetic, in bioinformatics, etc.).

In this case, as one of the result, we come to the artificial life. Various artificial cells and corresponding biotechnologies can have the same and (or) not exactly same informational homeostasis as in a real life, in open systems for all aerobic beings. What to say about sciences, technologies, foods and medical treatments of human body, at using various artificial cells, at absence or change of their informational homeostasis with respect of cells of human and all living beings? This is very bad and dangerous. Nobody likes to live as a substrate, for ensuring variations and mutations in an artificial life of the alien cells. This is another life. Here need to check and control level of total Shannon entropy E(J, r) for any artificial cells in order to ensure informational homeostasis of E(J, r) = lnr for all cells in a human body.

G. Large-scale correlations of information for chromosomal structures in cells not strong depend on specification of different cells. Blood cells live in any parts of body and, therefore, reflect local equilibrium, i.e. identical local noise of entropy near homeostasis, with given part of body and at any travels inside different parts of body; self-consistence of informational communication and information transfer connected with life conditions and biorhythms for any given organism in real time. Therefore, informational homeostasis must have overall level and overall background noise for all living cells in given body for interconnections, reproductions and clear, good, stable reproduction functions of cells. It is very important to check our results for informational homeostasis in the cells of blood as assumptions for all other cells, such as neural cell and brain cell, for cardiac and muscle cells, etc. If our assumptions on invariance of informational entropy are correct and universal for all living cells, then we have a very clear overall association between immune, nervous, the cardiac and other systems on the level of different cells. These associations in information transfer and noise of DNA inside cells and inter cells, during regulation of informational homeostasis, must exist without strong dependence from geography and specification of cells in the human body. In this case various cells produce exchange of information (noises) on DNA activity in chromosomes for maintains a good stability of life or informational homeostasis at local perturbation and change conditions of environment for any given group of cells in the body. Here a regulation of entropy noise near homeostasis interconnected with varied changes of fractal topology, in the types and magnitudes of correlations and structures of multi-scale complex networks for DNA activity [

H. A very strong magic of doctrines, spells and emotional, deeply enigmatic words, about ‘signals of cells’ from biological textbooks here, in this article, have rather clear quantitative definition as noise of Shannon entropy near overall homeostatic level of total entropy E(J, r) = lnr, during regulation of informational homeostasis for oxidative activity of DNA in cells, in equations (5), (6), (7), (11) and in experimental illustrations in Figures 1-12 for various cells living inside different people in real time…..To be continued.

Thanks to M. Filatov for kindly providing the experimental data.