Using atomic emission spectrometry, the content of Sodium (Na) and Potassium (K) in an epidermal derivative was measured in healthy subjects (n=9991). According to the spectrometry data, 4 groups were formed depending on the value of the Na/K ratio: Group 1: Na/K<1 (n=1834), Group 2: Na/K – 1 to 5 (n=6884), Group 3: Na/K – 5 to 10 (n=893) and Group 4: Na/K>10 (n=380). A correlation analysis (Pearson) of the K-Na bond tightness was conducted in the total sample (n=9991) and in each of the groups with different values of Na/K.

It was found that the correlation coefficient r in the total sample (r_K-Na=0.61; p<0.05) was noticeably lower than in any of the four groups (r_K-Na=0.85-0.97; p<0.05). It was also established that the reduction of r_K-Na was due to the presence of the spectrometry data of Group 1 (where Na/K<1) in the total sample. As a hypothesis, the authors suggest that there is a connection between the brain electrical activity (BEA) and the synchronous (critical) work of membrane K⁺/Na⁺-ATPases in epidermal cells.

Keywords: Na- and K-homeostasis, Electrical activity of the brain, Oxidative/nitrosative stress, Epidermis, Self-organized criticality

INTRODUCTION

In our previous studies [1-8] were obtained evidence accessories for the homeostasis of electrogenic metals (K, Na, Ca) in epidermis to the phenomena of self-organized criticality (SC). This was evidenced by:

1)       Power dependence between the content of K, Na and Ca in epidermis and the number of individuals in certain intervals of concentration values;

2)       Fractal distribution of the spectrometry data of these metals in epidermis;

3)       Synchronous (critical) nature of operation of Na⁺/K⁺-ATPase, which is the main transporter of Na⁺ and K⁺ ions through the cell membrane.

The conclusion about the possibility of synchronous (critical) functioning of Na⁺/K⁺-ATPases was made by us after we had established a reliable and stable linear relationship (Pearson) between the concentration values of these metals (according to the spectrometry data) [9].

However, the r_K-Na coefficient, which ranged from 0.6 to 0.7 in different samples, seemed to us too ‘humble’ for the synchronous (as a ‘single mechanism’) operation of membrane pumps. This parameter, apparently, should be significantly higher if we are talking about critical processes. Therefore, we tried to find out what it was that contributed (directly or indirectly) to the probable ‘understatement’ of the K-Na level.

It is significant that the ratio of the average values of [Na] and [K] (bootstrap-method), according to our data, in such a substrate as hair in 947 healthy individuals was almost identical – 1.5 [7].

At the same time, by spectrometry of epidermis (hair), we observed pronounced scattering of individual metal concentrations: sodium – 0.645 μg/g to 9240 μg/g; and potassium – 0.045 to 6505.1 µg/g [8], which allows for the existence of a spread among the individual values of the [Na]/ [K] ratio. It was interesting to find out the individual [Na]/[K] fluctuations in healthy individuals of most productive working age (20 to 49 years).

At the same time, one cannot exclude the connection between the [Na]/[K]-ration and the critical (synchronous) mode of operation of the membrane Na⁺/K⁺-ATPase. We analyzed correlations between [Na] and [K] depending on the value of [Na]/[K] to confirm or reject such a possibility. The analysis results are presented in this paper.

MATERIALS AND METHODS

Determination of sodium (Na) and potassium (K) in hair was done in a laboratory of the Center for Biotic Medicine (Moscow) using mass spectrometry with inductively coupled plasma (ICP-MS) on a NexION 300D spectrometer (Perkin Elmer Inc., Shelton, CT, USA). Practically healthy Moscow residents aged 20 to 49 were under observation (n=9991), of which 4999 (50.04%) were males and 4992 (49.96%) – females.

Hair samples for the spectrometry study were taken from the subjects following a mandatory informed consent procedure. In the occipital region, a tuft of hair 2 cm long and 0.5 cm thick was cut off close to the scalp.

To minimize the possibility of environmental contamination, hair samples were washed with acetone and then rinsed thrice with deionized water with subsequent air drying at 60°C. Further treatment of the samples was performed using microwave degradation. Specifically, 50 mg hair samples were introduced into a Teflon container and added to 5 ml of concentrated analytical grade HNO₃ (Sigma-Aldrich Co, St. Louis, MO, USA). Decomposition was performed in a Berghof speedwave four system (Berghof Products & Instruments, Germany) for 20 min at 170-180°C. After decomposition, deionized water was added to get a final volume of 15 ml.

A correlation analysis (Pearson) of the obtained data was carried out with determination of the correlation coefficient r_K-Na (pairwise correlations between the concentration values of K and Na in the substrate). We tested the normal distribution hypothesis using the Jarque-Bera test [1] and the Kolmogorov-Smirnov test [4]. Because of this test, it was possible with high probability to refute the hypothesis of normal distribution of chemical elements. Therefore, an alternative approach (the bootstrap method) was used, which does not require a normal distribution of the priori ensemble [2].

The Matlab software tool was used for statistical data processing.

RESULTS AND DISCUSSION

The distribution of individuals depending on the [Na]/[K] ratio was as follows: [Na]/[K]<1 was detected in 1834 subjects (18.4%); [Na]/[K] from 1 to 5 – in 6884 subjects (68.9%); [Na]/[K] from 5 to 10 – in 893 subjects (8.9%); [Na]/[K]>10 – in 380 subjects (3.8%). The correlation coefficient r between [Na] and [K] was found in each of these groups. The results are presented in Table 1.

As can be seen from Table 1, the values of coefficient r were higher in all the four subgroups (regardless of the [Na]/[K] ratio value) as compared to the total sample.

It was interesting to find out which one of the presented subgroups contributed the most to the ‘understatement’ of r in the general sample as compared to all the other subgroups. In that respect, the most ‘suspicious’ was subgroup 1 with the [Na]/[K] ratio<1, which fundamentally distinguished it from all the others.

Therefore, we decided to find out in what way the presence of subgroup 1 in the total sample affected the r coefficient value alone or in conjunction with each of the subgroups or any combinations thereof (Table 2).

The level of Na and K in the epidermis was found as a median with the boundaries of the confidence interval (the bootstrap method). The ratio of medians (Me [Na]/Me [K]) in each age group was as mentioned in Table 5.

In the absolute majority of healthy subjects (Table 5), which we investigated in the cited paper [7], the ratio [Na]/[K] (median) ranged from 2.1 to 2.4 (starting from the age of 20). It is should be noted that it is quite close (2.3) to the same parameter ([Na]/[K]) obtained in the present work for most individuals (68.9%) but using the mean values of [Na] and [K] (Table 3). After replacing the average with the median, the [Na]/[K] ratio was almost unchanged (2.1 vs. 2.3).

The [Na]/[K] ratio in the younger age group (2 to 9 years) turned out to be less than 1 (0.86), i.e. the same ‘inverted’ ratio as in subgroup 1 (Table 3). In Table 3, this ratio (0.65) is calculated from the mean values of [Na] and [K]. The replacement of the average by the median had practically no effect on the value of this parameter (0.68 vs. 0.65).

Why is the fact of ‘inversion’ of [Na]/[K] ratio in children from 2 to 9 years old so important? The answer is that at this age (up to 13 years old) the dominant EEG rhythm is the θ rhythm [3], whose participation in the appearance of the ‘inverted’ [Na]/[K] coefficient in 18.4% of people of mature age (20-49 years) in our observations seems likely. This requires verification and refinement in combined (EEG+spectrometry) studies, but at the same time allows for the possibility of the BEA influence (as an order parameter) on the operation of membrane ATPases. Moreover, this assumption (in addition to the possible ‘synchronizing’ action of BEA on the operation of membrane pumps) will include, as shown by our data, the probability of a significant effect of BEA on the level and the ratio of [Na] and [K] in the substrate.

It is not very clear why the presence of subgroup 1 ([Na]/[K]<1) in the total sample causes a noticeable decrease in the tightness of the relationship between [Na] and [K], whereas in subgroup 1 itself the r_K-Na turned out to be high (0.86; Table 1). One possible explanation for such ‘inconsistency’ can be as follows:

As already mentioned, the [Na]/[K] ratio for the whole body is ~1.3 with the predominant localization of sodium in the extracellular space and potassium - inside the cell [5]. The main membrane pump, Na⁺/K⁺-ATPase, which works against the electrochemical gradient of these metals, under whose influence Na⁺ ions tend to get into the cell and K⁺ ions tend to leave it, provides this distribution. An important feature of the Na⁺/K⁺-ATPase operation is its ability (per unit time) to remove more Na⁺ ions from the cell than K⁺ ions, which this pump has time to ‘pump’ into the cell. By the way, this explains the existence and relative constancy of the membrane potential.

The ratio of [Na] and [K] we found earlier (by average values) in such biosubstrate as hair amounted to 1.5 [7], i.e., almost did not differ from that for the whole body (1.3). Therefore, it seemed that distribution of these metals in the epidermis (with a predominance of Na) is normative and may be found in all healthy individuals without exception. However, that is not confirmed by the data we obtained.

In 18.4% of healthy individuals (subgroup 1, Table 1) [Na]/[K] was <1 (average 0.65). In addition, the presence of this subgroup in the general population explains the noticeable decrease in r_K-Na (down to 0.61), compared with the same parameter in each of the fractions and its average value (r_K-Na=0.9).

Therefore, we are ready to assume that a decrease in the Na content in a substrate with predominance of K may indicate (at least in some individuals with the lowest [Na] value and the highest [K]) significant changes in the distribution of these metals inside and outside the cell. This, in our opinion, may be due to a change in the direction of the electrochemical gradient of Na⁺ and K⁺ ions or, in other words, the reversal of the pump function of Na⁺/K⁺-ATPase (‘pumping’ K⁺ ions from the cell and ‘pumping’ Na⁺ ions into the cell). In this case, the known proportion of ion exchange for a given pump (3 Na⁺ ions vs. 2 K⁺ ions) can be maintained.

It is known that such a reversion (due to changes in the membrane potential and the content of sodium and calcium in the cell) occurs with the sodium-calcium exchanger (NCX) [6].

Due to the high level (0.86) of r_K-Na in individuals with [Na]/[K]<1 (Table 1), technical reasons are less likely to explain the reduction of sodium in the biosubstrate (storage conditions of the sample and/or its processing).

Another aspect of sodium-potassium homeostasis in the epidermis (which is closely related to the results of this work) needs to be discussed. We are talking about the interpretation and diagnostic value of the data of hair spectrometry and the possibility of their extrapolation on the body as a whole.

The results of the study have convinced us that these data do not reflect changes in metal homeostasis at the level of the whole body, and, therefore, they neither allow us to judge about the adequate availability of Na and K, nor help us to identify their dangerous deficit or excess.

Thus, the mean values of [Na] and [K] in all subgroups differ from each other with high reliability (Table 3). At the same time, the average value of [Na] in subgroup 1 is more than twice lower than in subgroup 4, and the average value of [K] in subgroup 1 is almost 12 times higher than in subgroup 4 (!). The scattering of individual values of these metals in the epidermis, which we have already mentioned, is even more impressive: Na – from 0.645 μg/g to 9240 μg/g; K – from 0.045 to 6505.1 µg/g. It must be noted that all the measurements were carried out in practically healthy subjects showing no pathological symptoms.

Therefore, to avoid unjustified generalizations, the results of hair spectrometry, as well as possible changes in metal homeostasis, should only be attributed to the given substrate - epidermis, which, as shown by our experience, can be productively used in studying the complex problems of modern bioelementology.

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