Homeostasis of Metals in Epidermis: Age Shifts and Possible Connection with Critical (Synchronous) Work of Membrane ATPases

The spectrometric analysis of the level of sodium (Na) and
potassium (K) in the epidermis derivative (hair), which was
performed earlier in 10297 healthy individuals...


Introduction
The spectrometric analysis of the level of sodium (Na) and potassium (K) in the epidermis derivative (hair), which was performed earlier in 10297 healthy individuals (from 2 to 85 years old), revealed the following age-related features in the homeostasis of these metals [1]. In the extreme age groups (from 2 to 9 years and from 60 to 85 years), there was a significant (almost threefold) increase in the content of Na and K as compared with the middle age group (20-49 years). The average concentration values of these metals found using the bootstrap method (since it was not possible to confirm the hypothesis about the normal distribution of spectrometry data), were as follows: for potassium in the extreme age groups -376.9 μg/g (2-9 years) and 121.4 mcg/g (60-85 years old), and in the group of 20 to 49 year-olds -only 47.1 mcg/g; sodium in the extreme age groups -324.9 μg/g (60-85 years) and 293.9 μg/g (2-9 years), and in the group from 20 to 49 years old -only 99.9 μg/g. We lean toward attributing such a difference to the increased production of reactive oxygen and nitrogen forms (ROS and RNS) in childhood [2] and senile age.
It is known that ROS and RNS are activators of Na+, K+-AT-Pase, the main transporter of Na+ and K+ ions through the plasma membrane. The activation of Na+, K+-ATPase with ROS (oxidation) and/or RNS (nitrosylation) occurs upon modification of SH-groups of cysteine in the protein molecule of this enzyme. As a result, the density (quantity) of actively working Na+ and K+ transporters increases on the cell membrane. The use of the term 'density' is not incidental. According to the theory of self-organized criticality (SC) [3], the membrane ATPases pool is a system of oscillators that can be activated by ROS and RNS and 'attune' (synchronize) their own oscillations (given sufficient density of active molecules on the cell membrane), thereby switching to critical condition. Consequently, under conditions of oxidative and/or nitrosative stress with the synchronous operation of membrane pumps, one can expect an increase in the concentration of Na+ and K+ ions in epidermal cells.
We were able to verify the reality of such events by examining metal-ligand homeostasis (MLH) in the epidermis (hair) of 947 healthy individuals and 954 liquidators of the Chernobyl accident [4].
The prooxidant shifts detected in the blood of the liquidators suggested oxidative stress [5], while the results of the EPR analysis of hair (a significant increase in the EPR signal of nitroxide) were indicative of nitrosative stress [6]. The differences revealed in MLH among the Chernobyl liquidators as compared with the control group concerned not only Na and K but also such metals as Ca, V, Zn, Cu, Cd, Fe, Al, Cr, Pb, Li [7]. In addition, another probable discriminator of nitrosative stress was found -the linear correlation coefficient r (Pearson) between the concentration values of K and Zn, which was 1.5 times higher in the liquidators (rK-Zn=-0.42; p<0.05) than in the control group (rK-Zn=-0.28; p<0.05) [7]. It is possible that a linear K-Zn bond, which becomes closer due to nitrosative stress, may indicate that synchronous (critical) mode of operation is inherent in the entire family of membrane ATPases (P-type), which are responsible for metal traffic (not just Na+, K+-ATPases), although the degree of this 'criticality' and the direction of quantitative shifts (up or down) may be different.
We have discovered the following signs of criticality confirming the fact that metal homeostasis in the epidermis is a phenomenon of self-organized criticality ('SC-phenomenon'). First, the presence of stable linear correlation (regardless of sample size) between the concentration values of K and Na. The synchronous work of membrane Na+, K+-ATPases, apparently, should explain the origin of this correlation. Please note that the value of the coefficient rK-Na (Pearson), not exceeding 0.6-0.7 in the total sample (if you do not take into account the Na/K ratio), increased significantly to 0.8-0.9 with a separate definition of rK-Na in groups with Na/K< 1 and Na/ K>1 [8]. At the same time, non-constant (sample size dependent) pairwise linear correlations (both positive and negative) are also found between other metals [9], which does not exclude the possibility of synchronous (critical) operation of their transmembrane transporters (ATPases of P-type). Second, the self-organized criti-cality in the MLH of the epidermis involves not only the synchronous operation of membrane pumps but also a power-law relationship between the number of cells and the metal content in them (in certain ranges of numerical values).
On a graph on a double logarithmic scale, the power-law takes the form of a straight line, which allows this power-law dependence to be identified, and its inherent fractality (independence of scale) enables to identify a power-law dependence at any level which suitable for such analysis. Therefore, if power-law dependence really exists between the number of cells and the content of metals in them, then it should obviously manifest itself not only at the cellular level but also at the level of individuals. This greatly simplifies the research task and, as our experience shows, makes it completely solvable using hair spectrometry. Our analysis of spectrometric data using mathematical statistics methods confirmed the applicability of the power-law for homeostasis of Na, K, Ca, Fe, Cu, Zn [1,10]. The results of similar studies of MLH for such metals as Al, Cd, Pb, V, Li, Cr, are presented in this paper. Third, the degree of synchronization (criticality) in the functioning of membrane ATPases (P-type) can be measured using the so-called synchronization index (SI), which is equal to the area under the curve of numerical values of pair correlations (Pearson) between metals (without taking into account the sign) [11].
It turned out that the SI value under nitrosative stress (accident liquidators) was not only higher than in the control group (6.13 vs The values of SI noticeably differed in these categories of healthy individuals: in the subgroup with a distinct negative K-Zn bond (r = -0.43; p <0.05), the SI was 9.17; and in its absence (r =-0.01), the SI was only 5.18 [11].
However, we still have to answer the following questions: The results of studies undertaken by us to find answers to these and other questions are presented in the article.

Materials and Methods
Atomic emission spectrometry of hair was performed at the  [11], and the linear correlation coefficient (Pearson) between the content of K and Zn in the hair (rK-Zn) was found.
In addition, along with atomic emission spectrometry and determination of SI, EPR analysis of hair was performed to measure the level of NO production by the method used in our previous studies [6] involving 58 Chernobyl liquidators (55 men and 3 women) and 58 healthy subjects (18 men and 40 women).
Then, a comparative analysis of the magnitude of the NO signal on the EPR spectrogram, spectrometry data, and SI was performed in the Chernobyl group and the control group. It should be emphasized that the age medians in the compared groups almost coincided (Me1 = 53 years; Me2 = 54 years, resp.). Using the methods of mathematical statistics, we analyzed the results of hair spectrometry for the content of Al, Cd, Pb, V, Li, and Cr obtained from 10,000 healthy subjects: Moscow residents (5,000 men and 5,000 women) aged 20 to 45. To identify the power-law relationship between the metal content in the epidermis and the number of individuals (a sign of self-organized criticality), the probability density (distribution) function (PDF) was estimated and the distribution was adjusted using the method of linearization. We used a similar mathematical approach in our previous study [10]. For statistical data processing, the MATLAB software package was used.

Results and Discussion
As already mentioned, the power-law dependence takes the x + = Figure 1: An "ideal" random fit case with a Pareto distribution (RND). The blue curve is the density estimate from spectrometry data. The red curve is the fitting of the power-law distribution by linearization. RMSE is the root mean square error. Cthr is the lowest concentration at which fitting begins.
To be able to judge about the quality of the fit, an 'ideal' case of such a fit in random numbers with the Pareto distribution is shown below (Figure 1). To obtain a normalized histogram, the column boundaries were chosen uniformly on a logarithmic scale (30 columns for 10,000 measurements). Indicated above the figures are metal name, RMSE is the standard error, Cthr is the lowest concentration with which the fitting begins (concentration values lower than Cthr are not taken into account). The calculation of the distribution density parameters is presented in Table 1.         One can get an idea of the size of the critical phase in the homeostasis of one or another metal by the percentage of individuals in the total sample who show reliable graphic signs of criticality.
The results of this assessment are shown in Table 2.
As shown in Table 2, the critical phase in K and Na homeostasis is noticeably greater than that of other metals (77.6% and 72.3%, resp.). Perhaps this should explain the high and independent of the sample size rK-Na (0.8-0.9) when it is separately determined in groups with Na/K< 1 and Na/K > 1 [8]. The smallest critical phase size (22.9%) was for vanadium (Figure 7). For other metals, the values of this indicator ranged from 40% (Cr) to 62.5% (Pb). This coincides with the results of our earlier analysis of linear bonds (Pearson), which revealed the unstable (and dependent from sample size) nature of all pair correlations among these metals, with the exception of K and Na [9]. The data of hair spectrometry in the study of MLH, the values of SI and rK-Zn (Pearson) in healthy individuals (n = 300) in different age groups are presented in Table 3. As follows from Table 3, the quantitative shifts in the extreme age groups (I and III) relative to Group II coincided in their direction not only for K and Na, but also for all other metals: Al (↑), Cd (↑), Fe (↑), Cr (↑), Cu (↓), Li (↑), Pb (↑), V (↑), Zn (↓). Moreover, the SI values in Groups I and III are visibly higher than in Group II (12.6 and 12.05 vs 9.5 resp.). It is significant that the direction of quantitative changes in MLH in this case (Table 3) with that of the Chernobyl liquidators (n=954) in relation to control (n=947) [4]. The value of SI in the general group of liquidators, as already mentioned, was also visibly higher than that of healthy individuals (6.13 vs 2.17) [11]. The dynamics of the coefficient rK-Zn (Pearson) is also of interest: rK-Zn in Groups I and III was not only twice as high (in absolute value), but also retained its sign (-) in contrast to Group II, see Table 3 Table 4. Note: *) significance of difference p <0.05.
As Table 4 shows, the quantitative shifts in the MLH of the Cher-  (Table 3). At the same time, the magnitude of the SI (12.05 vs 8.3) and the degree of NO production in the biosubstrate (34.1 vs 19.1) among the liquidators were significantly higher than in the control (Table 4). To explain the data obtained, it is advisable to use the basic principles of the theory of self-organized criticality, according to which membrane pumps -ATPases (P-type), which 2) Unidirectional quantitative shifts in the MLH of the extreme age groups were accompanied by a higher level of paired linear bonds between the concentration values of metals if we evaluate them (bonds) by the SI value (criticality sign). The dynamics of rK-Zn was similar to the dynamics of SI.
3) In the observations where the age factor was excluded (comparative analysis was carried out in identical age groups), the results of EPR spectroscopy of the hair confirmed the relationship between NO production and signs of criticality in the operation of membrane pumps: a significant increase of NO production in the epidermis was associated with an increase in SI and characteristic unidirectional shifts in MLH.
4) The concept of MLH in the epidermis as an SC phenomenon makes it impossible to assess the content of any specific metal in the whole body by the level of this metal in the hair (spectrometry