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We analyze fluorescence due to oxidizing activity of DNA in neutrophils of peripheral blood in the large populations ~10^{4} - 10^{5} of cells. Fluorescence is registered by flow cytometry method. Spatial resolution is about a few nanometers for varied complex three-dimensional (3D) DNA nanostructures of all non-coding and coding parts of DNA. It’s shown that oxidative activity of all 3D DNA in the full set of chromosomes inside cells is defined by new standards for complex networks of “exponentially small worlds”, with more dense packing than in the well known networks of “small worlds”. Analysis of various blood samples in vivo and during medical treatment shown that only two classes of Good and Bad Networks of DNA for a good and a bad health existed. This division is defined by any network to one from two classes of “n” or “s” shaped curves for typical deviations and from straight line in perfect networks of “exponentially small worlds”, as for two types of hysteresis curves at phase transitions or at switching of bistability. These deviations coincide with two types of positive and negative trends of changing fractal dimension by changing the scales of multi-scale networks of fluorescing DNA. These trends give the overall assessments of human immunity, including hidden and unidentified diseases, and as a sum of all kinds of health and illness of given person, from the point of view the inner life of neutrophils, living in different parts of human body in given time. Characteristics of deviations associated with type, level and complexity of illness in the dependence on the

We present results of a novel nonlinear analysis of flow cytometry experiments on immunofluorescence with nanometer spatial resolution in the flow direction [^{4} - 10^{5} of neutrophils in the peripheral blood of human. These results are used also for populations of chicken erythrocytes in the blood of young hens. Fluorescence of DNA inside cells is initiated by oxidative burst reaction at using ethidium bromid as a dye [

Let us consider mainly quantitative peculiarities of immunofluorescence. Some applications of oxidative burst reaction in diagnostics, standard biochemical procedures for preparing samples and basic experiments of flow cytometry for blood samples volume ~1 ml are described in [1-4]. The volume of blood is V = 1 - 2 ml. Blood with heparin additives is diluted by physiological solution in a ratio of 1/3. Hydroethidine addition with concentration of 150 μg/ml is used for initiation of DNA fluorescence. At the beginning, hydroethidine is transformed into ethidium bromide as a result of chemical oxidative reactions in the blood cells. Small concentration 100 ng/ml additives of phorbol myristate acetate (PMA) to blood samples ensure the intensive staining of the cell nuclei of polymorph nuclear leukocytes. The staining reflects differences in the ability of cells to produce oxygen radicals, i.e. the respiratory burst activity. The fluorescence is proportional to the ability of neutrophils to produce the active forms of oxygen. Hydroethidine binds with fragments of nuclear DNA and has strong, red fluorescence excited by TEM_{00} mode radiation from Argon laser light at 488 nm wavelengths. Fluorescence is registered by flow cytometry technique. The rate of measurements is about (1 - 2) × 10^{4} cells per/min. The flow velocity is about 1 m/s. The mean time of measurements of one model is about 2 minutes. This empirically selected regime is selfconsistent with noises of various nature and gives statistically stable and reproducible results. The inaccuracy and reproducibility for preparations and measurement procedures usually compose of not more than a few percent or more correctly of ≈2%. Spatial resolution of the instruments in flow cytometry may be very high [^{−9} s in the jet of blood flowing through the laser beam with the velocity ~1 m/s provides measurement with spatial scales ~10^{−9} m in the flow direction [^{−12} s of fluorescence pulses give an increasing of sensitivity and decreasing the lower limit of spatial measurements in the flow direction.

Each experiment reflects a considerable statistics for frequency distribution of flashes for approximately 10^{4} and more than 10^{4} fluorescing neutrophils in the blood of any donor. Corresponding examples for frequency distributions of fluorescence are presented below in Figures 1, 3 and 4. These experiments form various experimental data for 3D-correlations of all chromosomal DNA in large populations ~10^{4} - 10^{5} of cells. We have many new unknown details for inner life of genome and chromosomes inside cells for oxidizing activity of real 3D DNA in nanometer scales. These details cannot be seen in the optical microscope. These details are reflected in histograms of fluorescence, but we don’t know how to extract and decrypt corresponding information. At present, we have no adequate knowledge in mathematics, physics, information theory, medicine and biology for absolutely

correct, coherent, consistent and complete interpretation of this new and significant information about 3D DNA activity inside cells. Some of these unsolved problems may be associated with abnormal fractals; complex networks of 3D-DNA activity; fractals in networks of “exponentially small worlds”; information entropy or Shannon-Weaver index of biodiversity for activity of DNA inside cells; etc.

In the parts 2 and 3 of this article we define fractal property of multi-scale networks of fluorescence and Shannon-Weaver biodiversity of neutrophils. In the parts 4 and 5 we define packing of DNA activity in multi-scale fractal networks in order to classify a good and bad DNA networks, and a good/bad health status, as for two various types of packing and deviations from perfected ideal. In the part 6, we show that large-scale networks for fluorescing DNA in neutrophils of healthy and unhealthy humans are similar to fractal networks for fluorescing DNA of chicken erythrocytes in the blood of healthy and unhealthy young hens and roosters. This similarity caused by the proximity of networks of “real worlds” for oxidative activity of chromosomal DNA in the living cells to standards of “exponentially small worlds”. This new class of complex networks has much denser packaging than well-known [

Here we present some approaches, semi-empirical results and first steps in the direction of practical needs for medical diagnosis and treatment monitoring complex analysis of immunofluorescence. We continue to develop various new methods and approaches [1,3,4,6] to the contemporary nonlinear analysis of modern experiments on oxidative activity and inner life of DNA inside cells.

Three examples of typical cytometry histograms are shown in

These natural peculiarities of immunofluorescence often are accompanied by statistical instabilities of local intensity distributions [1,3,4,6]. Statistical instabilities ensure insolvency and inapplicability of standard methods of data analysis, when there isn’t lawful basis for their applicability. Here statistical instabilities of local intensity distributions mean that the average value of intensity is smaller than dispersion, dispersion is smaller than asymmetry and other higher statistical moments of intensity fluctuations [3,4,6]. The exponential growth of central moments of fluorescence intensity reflects the clear sign of turbulence [

In the case of Gaussian statistics corresponding statistical moments of fluctuations have an opposite trend to rapid exponential increasing. Therefore here domain lower statistical moments, i.e. average and standard deviation.

Thus, statistical instability of immunofluorescence prevents an application of traditional data analysis. Fast exponential growth of higher statistical moments means that even a low level small noise of fluorescence for higher orders of correlation and autocorrelation of noise provides the intermittency of DNA fluorescence, i.e. rare irregular bright flashes in time [

We need to develop a sequence of new nonlinear statistical methods to data analysis of immunofluorescence.

Let us consider some fractal peculiarities of immunofluorescence. Different analogies of various fractal networks such as bronchial tree, structure of oncology tumor, arterials tree, etc. with networks and distributions of immunofluorescence are described in [_{max}. In our experiments maximal number of channels is 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 ranks [

Hurst exponent H [

where R/S is rescaled range (R = S), R is range or maximal deviation of P(I) from local mean level, S is standard deviation of P(I). Illustration of definition Hurst index was presented in [1,4]. Hurst index H for frequency of flashes P(I) connected with fractal (Hausdorff) dimension D [

Examples for three distributions of Hurst index in the hierarchy of fractal clusters with various scales, corresponding to data in

According to

The values of dH/dlnr depend on different states of health or illness and may be use in monitoring the states of health over time in vivo and in medical treatment [

According to Figures 2 and 5, a good and a bad health various people differ a positive and negative overall trends in changes of fractal dimension D(r) or a positive and negative derivatives dD/dr > 0 and dD/dr < 0. The values of (dD/dr) depend on the health status, type of disease and vary in time for one and the same human and for different people.

Thus, we got the empirical rule for classifying the General State of Health in the form of answer Yes/No or healthy/sick, i.e. dD/dr > 0 or dD/dr < 0, for all donors [1,4] from the point of view diverse populations of neutrophils, living in different parts of the human body in different conditions. This response includes the presence

of all kinds of health and illness, including hidden and unidentified diseases. This classification is defined by the change of signs of plus/minus in the overall trends of fractal topology, i.e. in the dynamics and direction of changes of fractal dimension or Hurst index, with a monotonic decrease of scales r of networks or sizes r of clusters in fractal correlations for oxidative activity of DNA inside cells. Sequential analysis of features and causes in systematic changes of fractal topology in networks for oxidative activity of DNA in neutrophils for different samples of blood presented below in this article.

Next comments describe the typicality of normal and abnormal fractals for networks of DNA fluorescence. Normal fractal dimension D corresponds to the interval 1 < D < 2 for positive Hurst index H > 0. Negative Hurst index H < 0 gives the anomalous fractal dimensions D = (2 − H) > 2. Absolute majority of the authors ignore any anomaly fractal dimensions. Nevertheless, negative Hurst index H < 0 does not contradict the main definitions of the power-law correlations for fractal distributions [

Other comments connected with differentiation and classification varied distributions of Hurst index in

Let us define Shannon-Weaver biodiversity of fluorescing neutrophils. The function of P(I) = P_{i} can be considered as density of probability for frequency of flashes P_{i}. We can enter the information for the frequency distribution of flashes and Shannon information entropy, where

Shannon entropy E(r) for frequency distribution of flashes depends on histogram’s range r, which coincides with the maximal number of channels of intensity measurements at given range r. Information is defined by the flash probability P(I) of fluorescing neutrophils with specified intensity in the specified channel. Thus, fluorescence’ histogram visualizes the probability of existence of neutrophils with a specific oxidizing activity of chromosomes in the given sample of blood. Therefore, Shannon entropy E(r) also characterizes the Shannon-Weaver index E(P) [5,6] for the biological diversity of neutrophils. Distinctive features of neutrophils here are determined by different oxidizing activities of various DNA, which are reflected in fluorescence. Distinctions in neutrophil activity for oxygen metabolism and fluorescence interconnected with peculiarities of chromosomes structure and large-scale chromosomal correlations in the nucleus of neutrophils. These correlations reflect the distribution networks of ethidium bromide in chromosomes, coinciding with networks of oxidizing activity of fluorescing DNA. The same approach may be used for definition biodiversity of any other cells.

Biodiversity of Shannon-Weaver E(r) of neutrophils in the blood of various people with different states of health, associated with

These illustrations show that Shannon-Weaver biodiversity for populations of neutrophils E(r) depend on the states of health. These illustrations show also that biodiversity E(r) for neutrophils living inside given person depend on range r, which determined by the scale r of clusters in DNA network, by the resolution of the device with maximal number of channels is equal to r or by parameter r as the governing by the scale of averaging.

Figures 6 show a clear logarithmic growth of Shannon-Weaver biodiversity of neutrophils E(r) with increasing of range r or of maximal number r of measuring channels; dE/dlnr > 0 for any kinds the states of health.

We observe richer biodiversity of neutrophils for oncology and poorer biodiversity for inflammatory disease (bronchial asthma) in

According to

Biodiversity of neutrophils in the blood of patient with complex diseases of cancer and hepatitis B, depends on medical interventions, as can be seen in

The clear decreasing of biodiversity of neutrophils we observe for any inflammations in Figures 6(a) and (c). Thus, a bad health corresponds to decreasing of biodiversity of neutrophils in human body, i.e. leads to a weakness of immune response, just as the sad trend of species extinction successfully ensured by means of a bad ecology.

Let us consider the mean values for overall trends of fractal dimension D = 2 − H for all ranges of r in networks of fluorescing neutrophils with different biodiversity E(r). The negative dependence of fractal dimension D on range r in Figures 2 and 5 for negative sign of derivative dD/dlnr < 0 give very clear criteria of a bad health. The positive sign of derivative dD/dlnr > 0 give very clear criteria of a good health. Shannon-Weaver biodiversity E(r) of neutrophils always defined by the positive logarithmic dependence of E ~ lnr; dE/dlnr > 0 [

According to Figures 2 and 5(b) most notable contribution to the persistent behavior of fractal distributions for unhealthy people brings the value of H(r) < 1/2 at low values of r, corresponding to intercellular correlations [

Shannon-Weaver index for biodiversity of neutrophils E(r), i.e. Shannon information entropy, presents clear parameter reflecting overall immunity condition at monitoring of health.

Networks of DNA activity in cells interconnected with networks of biodiversity in cells’ communities.

Rich biodiversity of neutrophils E(r) prolongs human life for people with a good and bad health status by increasing the diversity of immune reactions. Good immunity is ensured by a care about a high biodiversity of own neutrophils and good conditions of their environment in the human body.

Consider an undirected network, and let us define d as the mean geodesic (i.e., shortest) distance between pairs of vertex or nodes in a network of flashes of fluorescence. The certain number N of synchronized nodes-flashes in networks of DNA fluorescence inside cells are characterized by the intensity I ~ N, where N defines a common number of correlated nodes in network, if every node in fluorescence network has the approximately identical fragment of oxidative activity of DNA with approximately identical quantity of fluorescing dye. More detailed determination of correlated nodes N in the clusters of fluorescence networks of DNA inside cells now is unknown. The correlation length d depends on the network topology. Random networks with a given degree distribution may be the networks of “small worlds” [^{1/D} defines a linear size of D-dimensional lattice or the size of a fractal cluster d ~ N^{1/D}. Therefore estimation of fractal dimension D of fluorescence in the networks of “small worlds” is D(N) ~ lnN/lnlnN. Standard definition of fractal dimension D [8,10].

also gives D(N) ~ lnN/lnlnN in “small worlds” network. We use the experimental data in immunofluorescence histograms to define Hurst index H and fractal dimension D according to Equations (1)-(3). The transformation of “small worlds” due to reduction of range r = I ~ N leads to expression. We used this correlation in the linear approximations of experimental data in

The increasing of the small details in

Let us consider the linear dependencies of as the basic approximations of real correlations of DNA activity. In this case we have networks of “exponentially small worlds” with more dense parking than networks of “small worlds”, where. In our case networks of “exponentially small worlds” are more sensitive for registration of dynamical changes in “real world” networks and deviations from ideal of a good health than networks of “small worlds” presented in [

In

Actual behavior of any functions of in

Moreover, the values of parameter A, for linear regression of y = Ax + B in

to A = 1. This value of A = 1 corresponds to unstable not existing situation. Changeability and variations the values of A are varied in time and depend on the states of health in vivo and in medical treatment, as it is shown in

In

Systematic changes of biodiversity for neutrophils living inside sick man in

Here hysteresis may be connected also with different types of synchronizations in cell cycles for populations of neutrophils living inside healthy and unhealthy body. This is also only hypothetic possibility. Here exist many unstudied and unsolved problems also in information processes and synchronization between coalitions of chromosomal DNA for inter and inner correlations of (in) cells, inside cells and between different cells, such as different neutrophils, lymphocytes and other cells of blood and body, in addition to or instead of epigenetics.

Let us note, also, some fragments of deterministic communications of unknown origin in networks of DNA activity. We often observe mix of fractal and non-fractal correlations for different scales (rank) of r in different samples of blood for unhealthy people. According to Figures 2 and 5(b) most notable contribution to the persistent behavior of fractal distributions for unhealthy people brings the value of H(r) < 1/2 at low range number of r, corresponding to intercellular correlations [

Thus, now we haven’t clear understanding many details of DNA life and activity inside living cells. In this regard let us note some modern approaches, based on new results in the last few years, which no reflected in textbooks, but give important new accents for researchers and for discussions of two classes of features in Figures 2, 5 and 8. At first, in nano-scale range in 3D chaotic coil of nuclear DNA various intra-chromosomal and interchromosomal correlations in the coalitions of DNA may to play the effective role of varied networks consisting from self-organized nanopores for segments of DNA. Nanopores produce various modifications and different switching of multistability in the behavior of various fragments of DNA [

More exotic and hypothetic possibilities of a new regulation in DNA activity connected with building a chromosome segregation machine [

Rather prosaic reasons for existence of two classes the ordering of results in Figures 2, 5 and 8 connected with two dominant types of statistical stability for nonlinear distributions of DNA activity inside cells. Two dominant classes for negative and positive trends in Figures 2 and 5 and for “n” and “s” shaped curves in

Proposed criteria a good and bad health can to use for definition a diagnosis and estimation of health not only a human. Let us consider fractals and diversity in the oxidative activity of DNA inside chicken erythrocytes in the blood of young hens and roosters. Preparation and measurements fluorescence of chicken erythrocytes is the same than fluorescence of human neutrophils. Two examples of typical cytometry histograms for young birds are shown in

Initially we offered that in our experiments participate only healthy chickens. We were sure that we are dealing only with healthy birds. Analysis results which presented in Figures 9(c) and (d), where observed two types of positive and negative trends in topology of DNA networks, as for good and bad health of human in Figures 2, 5 and 8 shows that it is not so.

In Figures 9(a) and (b) multiple peaks (maxima) correspond to different cell adhesion complexes of several cells. Adhesion complexes of several cells are reflected in the structure of networks of DNA fluorescence and in the structure of biodiversity E(r) of cells in

Here more diverse adhesions of cells lead to increasing of Shannon-Weaver biodiversity E(r). Actual biodiversity for lonely erythrocytes of chickens is less than in

tion of health of young birds based on fluorescing DNA inside chicken erythrocytes in Figures 9(c), (d) and 10 similar to those of the classification of human health for fluorescing DNA inside human neutrophils in Figures 2, 5 and 8. Positive and negative trends in topology, Good and Bad DNA Network in chicken erythrocytes are defined as for human neutrophils. These responses reflect the common estimations of chicken immunity, including hidden and unidentified diseases, as for common sum of all kinds of health and illness.

According to

Thus, large-scale fractal networks for fluorescing DNA in neutrophils and erythrocytes of healthy and unhealthy humans and birds are similar. This universality is connected with the proximity of networks of “real worlds” for oxidative activity of chromosomal DNA in the living cells to standards of “exponentially small worlds”. Here observed also similarity in the character of topology trends and deviations from ideal networks of “exponentially small worlds” for a good and bad health of different humans and different birds. Thus, we may to propose that 3D oxidizing activity of real nuclear DNA for complete set of chromosomes inside cells has some universality in the structure and behavior of large-scale correlations for all healthy and unhealthy humans and beings.

In other words, neutrophils are familiar and are meeting with all, without exception, local inflammations, viruses and bacteria, many results of their activities and other inhabitants of human body, biography, heredity, daily life, traditions and structures of master’s biology, architecture and geography for flora and fauna entire ecology and physiology of inner life of human and all its agencies and organs. These knowledge and communications are reflected in changeable structures of large-scale networks for DNA activity inside neutrophils, in various local and individual deformations of correlations in densely packing fractal networks of “exponentially small worlds”, as it is shown in Figures 5, 8 and 9. This response includes the presence of all kinds of health and illnesses, including hidden and unidentified diseases. This response reflects overall estimation of immunity, like for a common sum dominating of influences of positive (good health) or negative (illness) reactions of a given person, from the point of view the inner life of neutrophils’ community, living in different parts of the human body in different conditions.

Main peculiarities of typical distributions for a good and bad health are described like “n” and “s” shaped curves in Figures 2, 5 and 8, as two typical classes of deviations of real situation in health status from violet straight line in networks of “exponentially small worlds” in

Networks of DNA activity for a man with a good health in real life are personal and changeable in time, according to Figures 5(a) and 8(b). Here occurs serial changes in the inner life; various populations of neutrophils, living inside one and the same healthy human during one year, are shown in Figures 4, 5(a) and 8(b), at conservation of a good immunity of human. The conservation of a good immunity of humanity is reflected in the stable behavior of the negative trends and values of A < 1 for linear regressions in Figures 5(a) and 8(b). Here exists also conservation of a rather high level of biodiversity of Shannon-Weaver in all populations of neutrophils, as it is shown in

Shannon-Weaver index for biodiversity of neutrophils E(r), i.e. Shannon information entropy based on distribution of oxidative activity of DNA inside cells, presents clear parameter reflecting overall immunity condition at monitoring of health. Shannon information entropy E(r) for DNA activity in the full set of chromosomes is very important in the cell life. Networks of DNA activity inside cell interconnected with ecological networks for cells’ communities, i.e. with networks of Shannon entropy. Higher values of information entropy or biodiversity E(r) are preferable for a good immunity. A poorness of information, communications or Shannon entropy restricts a life and development of human.

There is an extremely dense packing of information on DNA activity inside cells. Currently, any other information networks, in nature or in computer and information systems, have much less dense packaging of information than new classes of densely packed “exponentially small worlds” for oxidative activity of DNA inside cells, which are introduced here as experimental facts. These empirical facts are illustrated here by the results of experimental data analysis in Figures 8 and 9. These empirical facts define a very high density packaging of DNA activity in the chromosomal networks, existing for ensuring life activity of cells. A level of complexity of these correlations in Figures 8 and 9 is very high; generalization of all fractal correlations exists only in the double-double (quadruple) logarithmic scale. One may say that these are ugly, bad pictures. Forming pictures in Figures 2, 5, 8 and 9 associated with high compression of manifolds of diverse images and fractal correlations, with their fragmentation and intermittency. Real traffic in complex networks never is smooth [15,16].

Here is the sign of a good health associated with the “s” shaped curves, in the chromosomal networks of “exponentially small worlds” and with high ShannonWeaver biodiversity of neutrophils, i.e. with rather high level for Shannon entropy in the information activity of DNA inside cells. More simple criteria for classifying the General State of Health in the form of answer Yes/No or healthy/sick are based on positive or negative trends in fractal topology, i.e. positive dD/dr > 0 or negative dD/dr < 0 trends in multi-scale fractal networks at increasing of scale r in Figures 2 and 5, giving much less details. Good health of human also is reflected in the increasing of fractal dimensions D(r) with increasing of Shannon Weaver biodiversity E(r) ~ lnr of neutrophils. Bad health reflects the opposite trends.

These topological and informational features of fractal patterns in large-scale packing of DNA activity inside cells reflect the experimental facts about two universal classes of Good and Bad DNA networks, which are not needed in the existence of epigenetics or other hypotheses.

Thus, complex networks, information entropy (Shannon Weaver biodiversity) and fractals in large-scale information structures of DNA activity inside cells belong to the basic target of identification and to the main objects of study and analysis in diagnosing the life of cells, human health and human immunity. Here presented only the first steps to understanding of informational laws, patterns and functions of large-scale correlations for oxidative activity of DNA inside cells.

To be continued.

The author thanks M. Filatov, for kindly providing the experimental data. I also would be grateful researchers in physics, medicine and immunology for kindly providing the serial systematic experimental data from clinical studies of cells in oncology, cardiology, inflammations, infections, autoimmune, and neurodegenerative diseases with multichannel recording (more than 1000, 10,000 and more channels) of the DNA activity inside different cells by flow cytometry, scanning electron microscopy, their combinations and other methods of high-resolution of spatial dimensions, for reproducible physical measurements of DNA activity inside any cells.