Previously we have shown that nM ouabain-induced activation of cAMP-dependent Na/Ca exchange in reverse (R) mode in cell membrane has age-dependent weakening hydration effect on heart muscle and brain tissues and such Na/Ca exchange is characterized by quantum mechanical sensitivity. As in biological experiments radioactive
45Ca is used for the study of cold
40Ca exchange in cells and organisms, in the present work, the age-dependent effect of physiological solution (PS) containing either
40Ca or
45Ca on tissue hydration in different experimental conditions was studied in order to evaluate the bioequivalence of these two forms of Ca. The obtained data indicate that the intraperitoneal injections of
40Ca PS and 45Ca PS leading to activation of RNa/
40Ca and RNa/
45Ca exchanges, respectively, have different age-dependent effects on heart muscle and brain tissue hydration. As in myocyte membrane, the Na/Ca exchange is more expressed than in neuronal membrane, the age-dependent heart muscle hydration is more sensitive to quantum properties of Ca than brain tissue hydration. The [
45Ca]i, in contrary to [
40Ca]i, has age-dependent weakening and stabilizing effect on tissue hydration and makes the latter insensitive to ouabain. The obtained data bring us to a strong conclusion that RNa/Ca exchange has quantum mechanical properties and in biological experiments radioactive
45Ca cannot be used for adequate estimation of the functional activity of
40Ca ions in cells and organisms.
Rat Brain Heart Muscle <sup>45</sup>Ca Na/Ca Exchange Ouabain1. Introduction
Metabolic control of cell hydration is a fundamental parameter determining its functional activity. Our previous study has shown that the metabolically driven water efflux from the cell is a key mechanism controlling low membrane permeability for Na ions and membrane excitability [1]. Traditionally, the age-dependent increase of intracellular Ca ([Ca]i) contents is considered as a result of activation of Na/Ca exchange in reverse (R) mode in response to Na/K pump dysfunction-induced increase of intracellular Na ([Na]i) [2] [3]. However, we have shown that the activation of RNa/Ca exchange, occurring also upon the impact of extremely weak chemical and physical factors, is unable to change the Na/K pump and ionic channel activities in membrane, which are due to the increase of intracellular cAMP contents [4] [5] [6] [7] [8]. It is notable that, in spite of the fact that RNa/Ca exchange functions in stoichiometry of 3Na:1Ca, its activation, as a result of Na gradient decrease, only leads to cell dehydration, while in case of activation of cAMP-dependent decrease of intracellular Ca ([Ca]i) contents, it has age-dependent weakening hydration effect on heart and brain tissues [9] [10].
Thus, on the basis of the above presented and literature data on the key role of intracellular messengers in regulation of [Ca]i, the cGMP/cAMP-dependent Na/Ca exchange has been suggested as a universal membrane sensor through which the biological effects of weak signals on excitable cells are realized [8] [11] [12].
Our recent studies show that cAMP-dependent RNa/Ca exchange-induced cell hydration has quantum mechanical sensitivity: pM and nM radioactive [3H]-ouabain modulate brain tissue hydration more effectively than the same doses of non-labeled (cold) ouabain [13]. Considering the fact that radioactive 45Ca is widely used for the study of cold 40Ca exchange in cells and organisms, it seems extremely important to evaluate the diversity of their functional activities. It is suggested that the comparative study of age-dependent effects of RNa/Ca exchange on heart muscle hydration (contraction) and brain tissue hydration after intraperitoneal (i/p) injections of physiological solution (PS) containing cold 40Ca and radioactive 45Ca could help to reveal the mechanism(s) through which the 45Ca modulates heart muscle and brain tissue hydration. For this purpose, in the present work, the comparative study of age-dependent effects of RNa/40Ca and RNa/45Ca exchange on heart muscle and brain tissue hydration and 45Ca uptake in different experimental conditions were performed.
2. Materials and Methods2.1. Animals
All procedures performed on animals were carried out following the protocols approved by Animal Care and Use Committee of Life Sciences International Postgraduate Educational Centre (LSIPEC, Yerevan, Armenia).
The experiments were performed on young (6 weeks old) and old (18 months old) mail albino rats. They were regularly examined, kept under control of the veterinarians in LSIPEC and reserved in a specific pathogen-free animal room under optimum conditions of 12 h light/dark cycles, at temperature of 22˚C ± 2˚C, with a relative humidity of 50% and were fed ad libitum on a standard lab chow and water.
2.2. Chemicals
Tyrode’s PS containing (in mM) 137 NaCl, 5.4 KCl, 1.8 CaCl2, 1.05 MgCl2, 5 C6H12O6, 11.9 NaHCO3, and 0.42 NaH2PO4 and adjusted to pH 7.4 was used. PS with radioactive 45Ca (PerkinElmer, Massachusetts, USA) was received by substituting 0.0115 mM of CaCl2 from 1.8 mMCaCl2 with the radioactive one (with 11.2 mCi/l activity). The animals were i/p injected with PS containing 40Ca (named as 40Ca PS) and 45Ca (named as 45Ca PS). The volume of injected solutions was adjusted according to the weight of animals (0.02 ml/g). The ouabain solutions at 10−9 M and 10−4 M were used for incubation of tissue samples. PS with 50% of NaCl was received by replacing 68.5 mM of NaCl from 137 mM NaCl with 2 M mannitol dissolved in PS for maintaining the osmolarity of the solution. These two types of PS in corresponding figures are named as 100% Na PS and 50% Na PS. All chemicals were obtained from “Medisar” Industrial Chemical Importation Company (Yerevan, Armenia).
2.3. Tissue Preparation
The experimental data were received in in vivo and in in vitro conditions. The tissue samples from each experiment were investigated after decapitation. Since anesthetics with different chemical and pharmacological profiles have significantly effects on the metabolic processes in tissues [14] [15], in our experiments the animals were sharply immobilized by liquid nitrogen [16] and decapitated. After this procedure full absence of somatic reflexes was recorded. The heart muscle, brain cortex, subcortex and cerebellum tissues were isolated and dissected according to the corresponding experiments.
2.4. Experimental Design
The determination of tissue hydration and Ca uptake was carried out in in vivo conditions on young and old rats of intact and i/p injected groups. In each young and old animal groups 3 rats were taken. The animals of intact group were immobilized and decapitated at once and 5 samples from each animal’s heart muscle, brain cortex, subcortex and cerebellum tissues were taken. The animals of the next groups were i/p injected with 40Ca PS or 45Ca PS, respectively. After 30 min they were immobilized and decapitated. From each animal, as in case of intact ones, the same number of tissue samples were taken. Thus, from each tissue 15 samples were received, where the water contents and 45Ca uptake were defined. All our experiments were repeated three times.
The comparative effects on tissue hydration after their incubation in ouabain-free and 10−9 M, 10−4 M ouabain mediums were provided on nine young and old animals in control (preliminarily injected with 40Ca PS) and experimental (preliminarily injected with 45Ca PS) groups. From each group of animals 45 samples of heart muscle tissue and the same number of brain cortex samples were received. They were divided into 3 parts and incubated separately for 15 min in ouabain free PS (15 samples), 10−9 M ouabain solution (15 samples) and 10−4 M ouabain solution (15 samples).
The comparative effects on tissue hydration after their incubation in 100% Na PS and 50% Na PS were carried out on two parallel groups of animals. The control group of animals (6 young and 6 old rats) was preliminarily i/p injected with 40Ca PS and from each animal 5 samples of heart muscle and brain cortex tissue were received. After that 15 samples of heart muscle (or brain cortex) tissue were incubated in 100% Na PS for 15 min, while the next 15 samples in 50% Na PS. The identical procedure was repeated on experimental group of young and old animals preliminarily i/p injected with 45Ca PS.
2.5. Definition of Water Content
The water contents of heart muscle, brain cortex, subcortex and cerebellum tissues was determined by traditional “tissue drying” method [17]. After measuring the wet weight (w.w.) of tissue samples they were dried in oven (Factory of Medical Equipment, Odessa, Ukraine) for 24 h at 105˚C for determination of dry weight (d. w.). The quantity of water in 1 g of d.w. tissue was counted by the following equation: (w.w. − d.w.)/d.w.
2.6. Measurement of <sup>45</sup>Ca Uptake
The measurement of 45Ca uptake in tissue samples was carried out after the determination of their dry weights. Tissue samples were homogenized in 50 µl of 68% HNO3 solution. Then 2 ml of Bray’s scintillation fluid was added and chemo luminescence of samples were quantified with 1450-MicroBeta liquid scintillation counter (Wallac, Turku, Finland). The quantity of 45Ca in tissue samples was expressed by cpm/mg d. w.
2.7. Statistical Analysis
Microsoft Excel and Sigma-Plot (Version 8.02A, NY, USA) were used for data analyses. The statistical significance in comparison with the control group was calculated with Student’s t-test with the following symbols (*p < 0.05; **p < 0.01; ***p < 0.001).
3. Results
Figure 1 shows the results of the experiments where the effects of i/p injections of 40Ca PS and 45Ca PS on tissue hydration are compared with those received from intact animals.
As can be seen, 40Ca PS and 45Ca PS have different effects on heart muscle and brain tissues hydration. The injection of 40Ca PS leads to dehydration in all samples of heart muscle and brain tissues (except in cerebellum tissue of old animals),
while the injection of 45Ca PS has dehydration effect on heart muscle tissue of young animals. Meanwhile, in brain tissues of young as well as in heart muscle and brain tissues of old rats the injection of 45Ca PS brings to tissue hydration. Thus, the differences between the effects of 40Ca PS and 45Ca PS on tissue hydration indicate the distinctive nature of hydration mechanisms in heart muscle and brain tissues. In addition, the differences between the effects of 40Ca PS and 45Ca PS in heart muscle and brain cortex tissues have age-dependent increasing character, while in subcortex and cerebellum tissues age-dependent decreasing character was observed (Figure 1(a), Figure 1(b)). Our previous study has shown that the high-affinity ouabain receptors (a3) in the membrane with RNa/Ca exchange function, have more pronounced age-dependent increasing character in brain cortex tissue than in subcortex and cerebellum tissues [9]. Therefore, in the following experiments, brain cortex tissue has been chosen as a subject for the present investigation.
As can be seen in Figure 2, the level of 45Ca uptake in heart muscle tissue is much higher than in brain tissues.
However, the age-dependent decrease of 45Ca uptake by brain tissue is more pronounced than in case of heart muscle tissue.
As Ca uptake by RNa/Ca exchange leads to more effective changes of [Ca]i than by potential-dependent ionic channels [3], we have considered Ca uptake as a result of RNa/45Ca exchange.
It is known that [Ca]i has multisided effects on intracellular metabolism [18] through which it can cause cell hydration, including the oxidative phosphorylation-induced endogenous water formation [19], the stimulation of Ca-Calmoduline-NO-cGMP pathway-induced activation of Na/Ca exchange in forward (F) mode [11] [20] and inhibition of Na/K-pump activity [21]. Therefore, in the next series of experiments the individual role of each above-mentioned pathway in determination of differences between the effects of [40Ca]i and [45Ca]i on heart muscle and brain cortex tissue hydration was studied.
Considering the high expression of RNa/Ca exchange in heart muscle tissue compared with brain cortex one, it was predicted that in heart muscle tissue the differences between the effects of 40Ca and 45Ca on cell hydration would be more pronounced than in brain tissue. Therefore, to evaluate the nature of the mechanisms through which the effects of 40Ca PS and 45Ca PS on tissues hydration are realized, their effects on tissue hydration in various experimental conditions were studied.
The effects of 40Ca PS and 45Ca PS on heart muscle tissue hydration
The results presented in Figure 3 show that in ouabain-free PS the hydration of heart muscle samples of young animals injected with 40Ca PS is more pronounced than that of young animals injected with 45Ca PS.
The hydration of heart muscle samples from old animals injected with 40Ca PS is less than the hydration of samples from old animals injected with 45Ca PS (Figure 3(b)).
As mentioned in the introduction part of the present study, 10−9 M and 10−4 M ouabain activate the RNa/Ca exchange by both the decrease of [Ca]i [7] [11] and the increase of [Na]i [22], respectively.
The incubation of heart muscle tissue samples of young animals preliminarily injected with 40Ca PS (Figure 3(a)) in 10−9 M ouabain solution, having cAMP-dependent activation effect on RNa/40Ca exchange [7], causes pronounced dehydration effect, while in heart muscle tissue samples of young animals injected with 45Ca PS, only slight dehydration effect can be recorded. The same study in old animals injected with 40Ca PS shows more pronounced hydration effects as compared with the injection of 45Ca PS (Figure 3(b)).
The incubation of heart muscle tissue samples of young animals preliminarily injected with 40Ca PS in 10−4 M ouabain solution leads to more pronounced dehydration effect (Figure 3(a)) than in case of 10−9 M ouabain. However, in heart muscle tissue samples of young animals injected with 45Ca PS, 10−4 M ouabain brings to the same level of dehydration as in the case of 10−9 M ouabain (Figure 3(a)).
The same procedures in old animals preliminarily injected with 40Ca PS show that the incubation of their heart muscle tissue samples in 10−4 M ouabain leads to the decrease of hydration in contrast to those incubated in 10−9 M ouabain (Figure 3(b)). On the other hand, in animals preliminarily injected with 45Ca PS the incubation of heart muscle tissue samples in 10−4M ouabain brings to sharp dehydration (Figure 3(b)). The age-dependent reverse character of hydration, in case when heart muscle tissue samples are incubated in ouabain solutions (сompare the continuous lines with the dotted ones in Figure 3(a), Figure 3(b)), is also worth mentioning.
It is known that both 10−9 M and 10−4 M ouabain-induced activations of RNa/Ca exchange are accompanied with the increase of intracellular cAMP contents [12], having an important role in muscle contractility (hydration). Therefore, to exclude the role of cAMP contents in determination of differences between the effects of activation of RNa/40Ca and RNa/45Ca exchange on heart muscle tissue hydration, in the next series of experiments the mentioned differences are studied by the decrease of Na gradient on the membrane. For this purpose, two various ages of animals were preliminarily injected with 40Na PS (40Ca or with 45Ca) and 30 min later their heart muscle tissue samples were separately incubated in 100% Na PS and 50% Na PS.
As can be seen in Figure 4, the decrease of Na ions ([Na]o) concentration by 50% in cell bathing medium leads to more pronounced dehydration in heart
muscle tissue samples than in heart muscle tissue samples incubated in normal 100% Na PS.
However, the dehydration effect induced by 50% Na PS is more expressed in heart muscle tissue samples of animals injected with 45Ca PS than in those injected with 40Ca PS (Figure 4(a), Figure 4(b)).
The effects of 40Ca PS and 45Ca PS on brain cortex tissue hydration
The same protocols of experiments performed on heart muscle tissue were repeated with brain cortex tissue. The data presented in Figure 5 indicate that in ouabain-free PS brain cortex tissue samples of young as well as of old animals preliminarily injected with 40Ca in ouabain-free PS are more dehydrated than those animals injected with 45Ca, while the incubation of brain cortex tissue samples of young rats injected with 40Ca in 10−9 M ouabain shows significantly higher level of hydration as compared with the samples of animals injected with 45Ca (Figure 5(a)).
The incubation of brain cortex tissue samples of young rats injected with 40Ca PS in 10−4 M ouabain leads to dehydration, while the same procedure in young rats injected with 45Ca appears to have less pronounced hydration effect: i.e. there is a slight dose-dependent increase of tissue hydration at ouabain (Figure 5(a)).
As can be seen in Figure 5(b), the incubation of brain cortex tissue samples of old animals preliminarily injected with 40Ca PS in 10−9 M and 10−4 M ouabain medium brings to dose-dependent increase of hydration level, while in case of old animals injected with 45Ca PS brain cortex tissue hydration is slightly increased in 10−9 M ouabain and decreased in 10−4 M ouabain medium.
The effects of 100% Na PS and 50% Na PS on brain cortex tissue hydration are
the same as in the identical case of heart muscle tissue hydration (Figure 4). As is shown in Figure 6(a), Figure 6(b).
The dehydration in brain cortex tissue samples incubated in 50% Na PS is more pronounced in animals of both ages, which are preliminarily injected with 45Ca PS, than in tissue samples of animals preliminarily injected with 40Ca PS.
4. Discussion
It is known that Ca uptake by cells is realized by potential-dependent ionic channels and RNa/Ca exchange. As the threshold of RNa/Ca exchange activation
is incomparable less than of ionic channel activity, in the present experiments, the PS injection-induced stimulation of Ca uptake can mainly be considered as a result of RNa/Ca exchange activation [3]. As the energy source for RNa/Ca exchange is Eca - ENa, it is predicted that E45Ca > E40Ca, because of [45Ca]i, is close to “0” mM. Therefore, it is predicted that the rate of RNa/45Ca exchange must be higher than the rate of RNa/40Ca exchange. However, it is not clear whether the physiological difference between the activations of RNa/40Ca and RNa/45Ca exchange is only due to their different rates or not.
As was noted in introduction part, the activation of RNa/Ca exchange has double effects on cell hydration: passive-dehydration because of its electrogenic character and [Ca]i-induced metabolic effects. The obtained data showing that the activation of RNa/40Ca and RNa/45Ca exchanges has different effects on heart muscle and brain tissue hydration with age-dependent character reveals the different metabolic effects of intracellular [40Ca]i and [45Ca]i on cell hydration (Figure 1).
By previous study it has been shown that the increase of [Ca]i leads to heart muscle hydration because of activation of Ca-Calmoduline-NO-cGMP-induced stimulation of FNa/Ca exchange [22]. The data that in young rats the activation of RNa/45Ca exchange has more pronounced dehydration effect than the activation of RNa/40Ca exchange, and in heart muscle tissue of old rats it leads to more hydration compared with the activation of RNa/40Ca exchange in ouabain-free medium, can support the suggestion that the rate of RNa/45Ca exchange is higher than the rate of RNa/40Ca exchange. The RNa/45Ca exchange-induced brain tissue hydration compared with the activation of RNa/40Ca exchange (Figure 1(a) and Figure 1(b)) can be explained by the same mechanism.
The data on age-dependent decrease of 45Ca uptake by tissues can be considered as a result of aging-induced increase of [Ca]i, which is in harmony with literature data [2]. It is worth noting that in spite of the fact that the expression of RNa/Ca exchange in heart muscle tissue is much higher than in brain tissue, the age-dependent decrease of Ca uptake in brain tissue is more pronounced than in heart muscle tissues (Figure 2). Such a weak age-dependency of Ca uptake in heart muscle tissue probably can be explained by higher [Ca]i-buffering properties of heart muscle tissue as compared with brain tissue. Therefore, we suggest that discussing the comparative results of the effects of 40Ca PS and 45Ca PS on heart muscle and brain tissues could help to evaluate the nature of different metabolic mechanisms of [40Ca]i and [45Ca]i.
The effects of 40Ca PS and 45Ca PS on heart muscle tissue hydration
The obtained data that in ouabain-free medium heart muscle tissue samples from young and old rats injected with 45Ca PS are dehydrated and hydrated, respectively, compared with heart muscle hydration of animals injected with 40Ca PS (Figure 3(a), Figure 3(b)), can be explained by the above mentioned suggestion that the rate of RNa/45Ca exchange is higher than the rate of RNa/40Ca exchange. The results showing that heart muscle tissue samples of 40Ca PS-injected young rats are sharply dehydrated upon the impact of 10−9 M and 10−4 M ouabain, while in the rats injected with 45Ca PS both concentrations of ouabain have slight dehydration effects on muscle (Figure 3(a)), can probably be explained by 45Ca-induced transition of cytoplasm from sol into gel state because of high Ca-dependent phosphorylation of myofibrils in cytosol or by compensation of RNa/45Ca exchange-induced dehydration by hydration of FNa/Ca exchange activation in result of high [45Ca]i-induced activation of Ca-Calmoduline-NO-cGMP pathway [11].
The obtained result that in old rats injected with 45Ca PS heart muscle tissue hydration becomes ouabain-sensitive is probably due to age-dependent weakening of heart muscle contractility leading to abnormal increase of [Ca]i as well as aging-induced dysfunction of intracellular cAMP controlling system.
The 10−9 M ouabain-activation of RNa/Ca exchange which leads to heart muscle hydration can be explained by [Ca]i-induced activation of mitochondrial function leading to stimulation of endogenous water molecules’ formation, which is based on our previous data [19]. The fact that the 10−9 M ouabain-induced activation of RNa/45Ca exchange has less pronounced hydration effects on heart muscle of young animals than the activation of RNa/40Ca exchange (Figure 3) can also be explained by high [45Ca]i leading to depression of 10−9 M induced activation of RNa/Ca exchange.
The strong dehydration effect of RNa/45Ca exchange at 10−4 M ouabain in heart muscle of old animals supports the previous suggestion that the dehydration effect of RNa/45Ca exchange on heart muscle becomes more effective at high [Na]i, when Na/K pump is in inactive state.
The effect of 45Ca-induced stabilization of muscle hydration in young rats and its absence in aged ones seems extremely interesting and the elucidation of its exact mechanism can serve as a subject for a special investigation.
The data revealing that 50% Na PS-induced activation of RNa/45Ca exchange has stronger effects on muscle hydration than RNa/40Caexchange activation (Figure 4) indicate that the rate of RNa/45Ca exchange is higher than that rate of RNa/40Ca exchange.
The effects of R Na/40Ca and R Na/45Ca exchange on brain cortex tissue hydration
As in the case of heart muscle study, the data showing that in ouabain-free PS brain cortex tissue samples of young as well as of old animals preliminarily injected with 40Ca are more dehydrated than of those of animals injected with 45Ca PS (Figure 5) can be explained by high rate of RNa/45Ca exchange compared with rate of RNa/40Ca exchange. The RNa/45Ca exchange brings to hydration through elevation of [45Ca]i than by activation of FNa/Ca exchange and passive dehydration effect on tissue, respectively. The data that in 10−9 M ouabain brain cortex tissue samples of young animals injected with 40Ca PS demonstrate hydration effect through [Ca]i-induced increase of endogenous water formation by mitochondria [19] and in the same conditions the absence of such effect in young animals injected with 45Ca PS and less sensitivity to 10−4 M ouabain (Figure 5(a)) allow us to suggest that [45Ca]i, besides the activation of FNa/Ca exchange, which can balance RNa/Ca exchange-induced tissue dehydration by an unknown mechanism, also causes transformation of cytoplasm from sol into gel state in young animals. The data that in 10−9 M and 10−4 M ouabain mediums the hydration level of brain cortex samples from 40Ca PS-injected old rats has dose-dependent increasing character, while in the case of 45CaPS-injected animals brain cortex tissue hydration is slightly increased in 10−9 M ouabain and decreased in 10−4 M ouabain mediums indicate that [45Ca]i-induced stabilizing mechanism of brain cortex hydration in young animals has age-dependent weakening character.
The data that in both ages of animals the decrease of [Na]o leads to more pronounced dehydration in cortex samples of 45Ca PS-injected animals compared to dehydration in cortex samples from 40Ca PS-injected animals can be an additional support for the aforementioned suggestion that the rate of RNa/45Ca exchange is higher than the rate of RNa/40Ca exchange (6A and B).
5. Conclusions
Thus, the obtained data of the present work bring us to the following conclusions:
· The intraperitoneal injections of 40Ca PS and 45Ca PS which bring to activation of RNa/40Ca and RNa/45Ca exchange, respectively, have different effects on heart muscle and brain tissue hydration with different age-dependent characters.
· These differences between RNa/40Ca and RNa/45Ca exchange-induced tissue hydrations are much more pronounced in heart muscle tissues than in brain tissues as RNa/Ca exchange is expressed incomparably higher in heart muscle tissues than in brain tissues.
· The rate of RNa/45Ca exchange is higher than the rate of RNa/40Ca exchange, because of E45Ca > E40Ca.
· The [45Ca]i and [40Ca]i have different metabolic effects on heart muscle and brain cortex tissue hydration. In young animals tissue hydration in the case of [40Ca]i has dose-dependent ouabain sensitivity, while in the case of [45Ca]i tissue hydration becomes ouabain-insensitive. Upon the impact of [45Ca]i, the heart muscle tissue hydration of old rats becomes ouabain-sensitive, while brain cortex tissue hydration remains significantly less ouabain-sensitive than in the case of [40Ca]i.
· The main summary of this work is that radioactive 45Ca is not bioequivalent to cold 40Ca. Therefore, 45Ca cannot be used in biological experiments for evaluation of the functional role of 40Ca.
Acknowledgements
We express our gratitude to Ani Gyurjinyan from UNESCO Chair in Life Sciences for editorial work.
Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper.
Cite this paper
Nikoghosyan, A., Narinyan, L., Heqimyan, A. and Ayrapetyan, S. (2020) The Radioactive 45Ca Cannot be Used for Adequate Estimation of the Functional Activity of 40Ca Ions in Cells and Organisms. Open Journal of Biophysics, 10, 13-26. https://doi.org/10.4236/ojbiphy.2020.101002
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