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STUDY OF THE SYNCHRONIZATION AND THE TRANSMISSION OF GATING MODULATION IN THE SINGLE POTASSIUM CHANNEL
M.E. Astashev1'2*, A.A. Grinevich2, D.A. Serov1'2, A.V. Simakin1, V.A. Yusim1, A.V. Tankanag2
1 Prokhorov General Physics Institute of the Russian Academy of Sciences, 38 Vavilove St., Moscow, 119991, Russia;
2 Institute of Cell Biophysics of the Russian Academy of Sciences, 3 Institutskaya St., Pushchino, Moscow oblast, 142290, Russia.
* Corresponding author: [email protected]
Abstract. The transition of the ion channel between the open and closed states is traditionally considered random. Current experimental data indicated the presence of oscillatory modes of regulation of open/closed states, and possible connections between these modes. The canonical methods Fourier or wavelet transforms, fractal analysis and mathematical modelling can evaluate open/closed states oscillatory modes, but cannot describe their relationship to each other. We first applied the method of bispectral analysis to solve this problem. The well-described potassium channels potential-dependent Kv, calcium-dependent KCa and the modelled potassium channel KcsA were studied. The relationship between fluctuations open/closed lifetimes at frequencies ~0.1, ~1 and ~10 Hz was shown. These frequencies correspond to rhythmic processes in cardiovascular and nervous systems functioning, including those regulated by potassium channels. The normalised integrated bispectrum index was chosen to quantitatively evaluate the interrelation of ion channel opening/closing states. The normalised bispectrum index notable increased upon alteration of the membrane potential from 0 to 20 mV. The obtained data expand our understanding of ion channel functioning principles and can be used in the search for new approaches to the pathological states (channelopathies) therapy.
Keywords: amplitude-frequency analysis, phase wavelet coherence, correlation analysis, bispectral analysis, potassium channels, single channel patch-voltage-clamp.
List of Abbreviations
DMEM - Dulbecco's Modified Eagle Medium
Hepes - 4-(2-hydroxyethyl)-1-pipera-zineethanesulfonic acid
KcsA - potassium channel of the bacterium Streptomyces lividans
NMDAR - N-methyl-D-aspartate receptor
NMDG - N-methyl-D-glutamine
Introduction
The maintenance of ionic gradients is of paramount importance for the viability and functionality of cells. This is achieved through the transmembrane movement of ions, which enables the integration of all cells within the organism. (González et al., 2012; Melnikov et al., 2009). Potassium channels probably appeared at the dawn of life. They are found in archaea, bacteria and eukaryotes (Moulton et al., 2011; Schrempf et al., 1995). Potassium ions play a major role in the formation of membrane potentials, in the regulation of cell excitability, duration and frequency of the action potential, as well as the processes of muscle cell contraction
and metabolism, in the control of the genome, cell volume and others (Pivovarov et al., 2018; Zorov, 2022). Potassium ion channels in cell membrane are of paramount importance for the regulation of the transmembrane gradient K+ (Hille, 2001), and are also present in present in mitochondrial membranes and endoplasmic reticulum (Belosludtsev et al., 2020; Khodaee et al., 2014; Varlamova et al., 2021).. In addition to the potential-dependent ones, a large set of potassium channels that are little sensitive to membrane potential and are activated or blocked by different ligands have been described (González et al., 2012; Melnikov et al., 2009). Potassium channels are distinguished by an astonishing degree of diversity. About 200 representatives belonging to five major groups have been described: voltage-gated K+-chan-nels, delayed (outward) rectifier K+-channels, inward (abnormal) rectifier K+-channels (Kir), Ca2+-sensitive K+-channels (Kostyuk et al., 1975; Krutetskaya et al., 2003; Shah & Haylett, 2009). The diversity in question pertains to the structure, function, biophysical characteristics, and pharmacological properties of the channels.
The general plan of structure comprises four protein subunits embedded in the cell membrane, which together form a pore (Moulton et al., 2011; Wei et al., 2005). The direct participation of potassium channels of different types regulates physiological processes at the levels from cells to organ systems in the body as a whole, including: regulation of heart rate, temperature sensitivity, skin microcirculation rate, functioning of the central nervous system, etc. (Grandi et al., 2016; Hertel, 2007; Judge et al., 2007; Korogod & Demianenko, 2017). Sufficient evidence has accumulated that a range of diseases are associated with impaired functioning of ion channels and are referred to as chan-nelopathies (Kolesnikova et al., 2022). In particular, potassium channels can be considered as targets in the treatment of neurological diseases such as episodic ataxia and epilepsy (Browne et al., 1994; Du et al., 2005; Nikitin & Vinogradova, 2021). Recent studies have shown that potassium channels may be therapeutic targets in the treatment of Substance Use Disorders such as Alcohol Use Disorder, Cocaine Use Disorder, Methamphetamine Use Disorder Methamphetamine Use Disorder, and Methamphetamine Use Disorder. (Jayanthi et al., 2019; McCoy et al., 2021; Morgan et al., 2002; Padula et al., 2020). Therefore, understanding the mechanisms governing channel transitions between open and closed states is of both fundamental and applied importance and can be applied in the development of new therapeutic approaches to the treatment of chan-nelopathies.
The first potassium channel with a characterised three-dimensional structure is the KcsA channel from Streptomyces lividans (Zakharian & Reusch, 2004). Many types of potassium channel structures are described, including potassium channels with pore-forming domain only (KcsA), voltage-gated, internal rectification channels, tandem pore domains and ligand-gated potassium channels (Kuang et al., 2015). The regulation of ion channel conductance is facilitated by the gate mechanism. The gate mechanism of the ion channel is constituted by an association of structural elements of the macromolecular transmembrane complex of
the ion channel, which is responsible for controlling the magnitude of the ionic current through the selective centre of the channel. The initial concept of the existence of a dedicated gate particle within the channel structure was derived from two sources: firstly, assumptions that formed the basis of the Hodgkin and Huxley model, and secondly, experiments conducted with the proteolytic enzyme pronase, which resulted in the elimination of the inacti-vation process in sodium channels (Armstrong et al., 1973) or mutations that caused the elimination of the inactivation process in the potassium channel (Hoshi et al., 1990).
Consequently, distinct gate particles were incorporated into the functional architectures of ion channels for an extended period (Hille, 2001). Subsequently, it was determined that the inactivation and gate processes of ion channels are facilitated by distinct structural elements. In potassium channels, the inactivation process is mediated by a small globular structure situated at the N-terminus (Zagotta et al., 1990), while the intracellular gate process is regulated by the S6-segment (Kuang et al., 2015). Additionally, an extracellular gate mechanism has been identified (which is more accurately described as a gate mechanism associated with the selective filter) (Imai et al., 2010). All these gate processes, in the experiment, realise the current dynamics in the form of 'all-or-nothing', i.e. the trigger mode of channel switching from a fully conducting state to a fully non-conducting state with switching time less than 1 ms. Analysing the activity of a single channel by recording the current through it traditionally involves selecting 'open' and 'closed' states using a simple threshold algorithm to form arrays of numbered channel lifetimes in the open and closed states (Brazhe et al., 2004). It is worth noting that the open and closed state times of ion channels can vary considerably. In particular, for muscle-type acetylcholine receptors, the open state times can be ~2, ~40, ~150, ~600, or ~1000 p,sec depending on the type and concentration of the ligand (Ljaschenko et al., 2021). However, even during binding to a single ligand at a single concentration, the
probability distribution of the open state times is not uni- but bi- or polymodal. A bi- or tri-modal probability distribution can also be observed for the closed state times (Ljaschenko et al., 2021). A similar phenomenon is characteristic of other receptors, e.g. NMDAR and Kv11.1 (Amin et al., 2021; Mitcheson et al., 2000). In view of this, estimation of the frequency of opening of a single ion channel by the method of expert estimation is difficult, and such methods of studying periodic processes as fractal methods of analysis and/or wavelet transform and mathematical modelling are used for automated estimation of the dynamics of open and closed states of single ion channels and (Astashev et al., 2007; Grinevich & Astashev, 2019; Kamiya et al., 2018).
Previously, we have undertaken extensive studies of 'long-term memory' in the gating process of a single potassium channel. The fact of persistence in the sequence of gate mechanism lifetimes of two types of potassium channels has been established (Kazachenko et al., 2007) and a fractal kinetics model of the potassium channel has been developed (Grinevich & Astahev, 2019).
Questions that were not answered in the course of earlier works: Are the processes of transition of a natural channel from open to closed state and back again related to each other, because structurally, such a relationship is possible? Are there slow (tens of seconds) periodic or resonant processes in the channel activity, which could be manifested in modulation of cellular processes or be their source?
The apparatus of coherent and bispectral analysis should help in the search for answers to these questions (Astashev et al., 2023; Bandrivskyy et al., 2004; Newman et al., 2021). The aim of the present work was to determine whether there are links between the regularities of the natural channel transition processes from open to closed states and vice versa and to search for conditions for changing this link, if it exists. An additional task was to determine the frequency characteristics of coupled periodic processes in the regulation of the times of open and closed states of potassium channels.
Materials and Methods
Cells
Experiments were performed on isolated brain neurons of freshwater gastropod Lymnaea stagnalis and Vero E6 cell line (ATCC CRL-1586). All manipulations with animals were performed in accordance with the regulatory act of the Ministry of Health of the Russian Federation No.199-n 'On Approval of the Rules of Good Laboratory Practice' according to protocols approved by the Ethics Committee of the Institute of Cell Biophysics of the Russian Academy of Sciences (No.12306, 2006). Neurons were isolated after pretreatment of the ganglion ring with 0.35% pronase (Sigma, USA) at 20-22 °C during 20-40 min, according to the method of M.A. Kostenko et al. (Kostenko et al., 1974). Vero cells were cultured in DMEM medium (Gibco, USA) supplemented with 10% (v/v) fetal calf serum (HyClone, USA), 2 mM L-glutamine, 50 U/ml penicillin and 50 p,g/ml streptomycin (all produced by PanEco, Russia).
Single channel patch-voltage-clamp
Currents through potassium channels were recorded by the single channel patch-voltage-clamp technic, which allows us to determine the lifetimes of the closed and open states. The registration of currents through single channels in snail neurons and Vero cells was de- scribed earlier (Kazachenko & Geletyuk, 1984) and is an adaptation of the standard single chan- nel patch-voltage-clamp method in the inside- out configuration. Glass micropipettes were made of borosilicate glass. The micropipette blanks had an outer diameter of 1.6 mm and an inner diameter of 0.86 mm, a length of 100 mm with a myrofilament. Narishige PC-10 puller (Narishige, Japan) was used for drawing. The resistance of the tip of the micropipette was 4 ± 0.5 MQ. The micropipette for recording currents in the control was filled with physiological solution of the following composition (mM): 45 NaCl, 12 KCl, 4 CaCh, 1 MgCh at pH = 7.5 (Hepes - KOH, 2.5 mM) (all reagents produced by Sigma, USA). In experiments with [K+]o = 0, the micropipette was filled with a solution of the following composition (mM): 50 NaCl, 4 CaCl2, 1 MgCh at pH = 7.5 (Hepes
- KOH, 2.5 mM). The solution in experimental chamber in control contained 100 mM KCl at pH = 7.2 (Hepes - KOH, 2.5 mM). The 'inside-out' configuration of membrane fragments was used. The activity was recorded when the solution flow in the chamber was stopped in order to avoid possible influence on the channel activity of the moving solution.
The currents were recorded directly on the hard disc of a personal computer with a low-pass filter of 2.5 kHz. The frequency of data digitisation in the computer was 10 kHz. WinEDR software (J. Demster, Strathclide Electrophysiology Software, UK) adapted by the author of presented work with ADC L-791 (LCard, Russia) was used for recording. An example of the time series of changes in the current flowing through a single ion channel is shown below (Fig. 1 Kv and Kca).
Data processing
The duration of open (to) and closed (tc) channel states was determined at 50% of the current amplitude through the channel (Colquhoun & Sigworth, 1995; Dempster, 1993; Sakmann & Neher, 1995). The determination of the current value corresponding to the open and closed states was carried out using the histogram of the amplitudes of the current records. An example of recognition of open and closed lifetimes is shown in Fig. 1 (Kv and KCa) in color coding (red - open state, blue - closed state). The time series of changes in current through a single ion channel were subjected to spectral analysis based on algorithms implementing continuous adaptive and complex wavelet transforms based on the Morlet wavelet (formula 1), as detailed in works (Tikhonova et al., 2022).
(1)
= e1MQi e
>0t e-f2/2
where ro0 - is a coefficient determining the ratio of accuracy of signal localisation detection by time or frequency.
The sequences of potassium channel lifetimes were analysed by using bispectral analysis based on continuous complex wavelet transform using a log-normal wavelet to obtain information about inter-frequency interactions
and possible nonlinearity in the regulation of the gate mechanism functioning (Astashev et al., 2024; Newman et al., 2021).
Mathematical modelling
The modelling of the times of the open and closed states of the ion channel was performed on the basis of a modified mathematical model of the gate mechanism of a single ion channel KcsA (Grinevich et al., 2007). The model assumes that the gate particles of the channel are rigid rods with dynamics described by the deflection angle of the gate particles during the opening and closing of the channel (Doyle et al., 1998). The time dependence of the deflection angle was modelled using the Langevin equation. An example of the time series of changes in the current flowing through a model ion channel is shown below (Fig. 1 Km). The basic model and its modifications are described in detail in (Grinevich & Astahev, 2019). The discovery of open and closed lifetimes from the model channel time series was carried out by exactly the same method as for natural potassium channels.
Statistical processing
The normality of sample distributions was assessed using the Shapiro-Wilk and Kolmogo-rov-Smirnov tests. The distribution of sample values differed from the normal distribution, therefore, nonparametric statistics methods were used to further analyse the experimental data. The results were presented as median values and interquantile ranges (percentiles of 25 and 75%). The statistical significance of differences between sample values was assessed using the Mann-Whitney test (SigmaPlot v10). Differences between sample values were considered statistically significant at a significance level of p < 0.05.
Results
In this work the currents through two types of ion channels Kv and Kca were investigated by single channel patch clamp. The obtained experimental data were additionally compared with the results of mathematical modelling (Km). Examples of original experimental rec-
ords and wavelet maps for a given record are presented below (Fig. 1). The dynamic series, experimental recordings and modelled data have significant similarities, hence further analysis is applicable for both modelled and experimental data. In order to obtain high coherence, it is necessary to maintain a constant phase shift in the two studied signals at a certain frequency. Given that the calculation of the phase of a wavelet coefficient has nothing to do with the resulting modulus of the same coefficient, the phase is calculated in any case. However, it is obvious that when the modulus is small (i.e., when there are no stable oscillations at a given time-frequency point), the obtained phase value has no informative meaning. Therefore, to ana-
lyse the coherence coefficient, it is important to compare it with the wavelet coefficient modulus maps, as illustrated in the illustration below (Fig. 2). The red colour in the wavelet coefficient modulus maps (Fig. 2 a, b) corresponds to the presence of stable oscillations, and indeed for periods of about 1000 opening-closing periods (which corresponds to an oscillation period of about 11 seconds), bands of red colour corresponding to stable oscillations are observed. At the same time, the phase shift plot (Fig. 2 c) also shows a band of the same colour, which corresponds to a constant shift. This indicates the presence of coherence in the sequences of open and closed lifetimes for a period of 11 seconds in this channel.
50 msec
Open state Close state
Fig. 1. Examples of initial recordings of the currents of potential-dependent (Kv), calcium-dependent (Kca) or model (M) potassium channel. The current through each channel was recorded by single channels patch-voltage-clamp technic. Colour indicates open (red) and closed (blue) channel states for each studied channel. The potential is 20 mV
To obtain information on inter-frequency interactions and possible nonlinearity in the regulation of the functioning of the gate mechanism, the sequences of potassium channel lifetimes were analysed using the bispectral analysis described in study (Newman et al., 2021).
The bispectral analysis shows the interrelationship of frequencies in the signal, thus a function p123(©1, W2) depending on these frequencies appears. An example of the result of bispectral analysis for the dynamics of the open and closed state times of the potential-de-pend-ent potassium channel is shown in Figure
3. The peculiarity of bispectral analysis is that for high values (blue and violet areas) to appear on the two-dimensional bispectral map, several conditions must be fulfilled at once: synchronous presence of oscillations with frequencies roi, ro and an overtone with frequency roi+ro in the signal is necessary, as well as phase coherence of these oscillations, i.e. the phase difference of these oscillations must be constant. In fact, this analysis is adapted to detect harmonics and overtones that may appear when propagating signals with oscillations in a nonlinear medium.
Time, s
Fig. 2. Coherence in the activity of the potential-dependent potassium channel from the L. stagnalis snail neuron (a) wavelet decomposition coefficients of the sequence of open times of life, (b) wavelet decomposition coefficients of the sequence of closed times of life, (c) phase shift of wavelet coefficients of open times relative to closed times. For all graphs: on the abscissa axis is the event number, on the ordinate axis is the oscillation period in units of event pieces. The colour in the graph (a, b) indicates the wavelet coefficient modules: red - high, green - low. The colour on the graph (c) shows the value of phase shift. The average channel opening-closing cycle time is 11 ms
0,001 0,01 0,1 0 400 800 Frequency, Hz Time, §
Fig. 3. The bispectrum (left) and the initial map of wavelet coefficients of the Kv-channel lifetimes (right) in the open state. The solid lines show the main frequencies and the dashed overtone, the phase and amplitude synchronisation of which is necessary for the appearance of a point maximum on the bispectrum for frequencies 0.011 Hz and 0.0012 Hz. That is, in addition to these frequencies, at 0.0122 Hz there must also be an overtone synchronised in phase with the first two. The colours denote the values of the bispectral coefficients and wavelet coefficients. For bispectral coefficients (left): the largest values are shown in blue and zero values in red, for wavelet coefficient moduli (right): dark blue colour - zero values, yellow - largest values
During analysing the 3D-plots of bispectrum indices for the potential-dependent, calcium-dependent and model K+-channel, multiple maxima in a wide range of frequencies are visible (Figure 4) both for a separate comparison of open and closed states sequences and for analysing the interaction between open and closed states sequences. In addition, the similarity of the plots of bispectrum indices for natural and
model channels draws attention: a wide range of frequencies in which the bispectrum index has non-zero values, approximately the same values of maxima. During analysing the dependence of peak values of the bispectrum index obtained for the sequences of the model channel, we can see tendency to increase the peak value for the interaction of sequences of open and closed times (Fig. 4).
open vs open
open vs close
close vs close
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Fig. 4. Bispectra plots for the lifetime sequence of the Kv channel from L. stagnalis (a, b, c), calcium-dependent Kca channel (d, e, f), and model channel (g, h, and i). Transmembrane potential is 10 mV. a d, g - open-state sequence analysis, c, f and i - closed-state sequence analysis, b, e and h - interaction analysis of open-and closed-states sequences. The scale of colour coding is indicated in the graphs as maximum values corresponding to blue, red corresponds to zero
5
A similar analysis performed for natural ion channels also shows the dependence of the peak value of the bispectrum index when analysing the interaction between open and closed state sequences on transmembrane potential in natural ion channels (Fig. 5). However, it can be seen that while this trend is visible within the data for a single channel, the data varies between channels and appropriate normalisation
of the data is required. As such normalisation, we have used the bispectral indices obtained on mixed data series (normalised integral bispec-tral index). This approach is guaranteed to eliminate any phase relationships in the sequence, but leaves the amplitude characteristics of the data series unchanged. Significant differences in the normalised bispectral indices were found (see Fig. 6, inset).
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Transmembrane potential, mV Fig. 5. Dependence of coherence on Vm in model ion channels
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Fig. 6. Dependence of the maximum bispectrum index on the transmembrane potential of natural ion channels when analysing the interaction between open and closed states. The statistical analysis of differences of mixed series of normalised integral bispectral index indices for Kv-dependent transmembrane potentials at 0 mV (n = 3) and 20 mV (n = 6) is shown in the inset. * - p < 0.05 Mann-Whitney test
Discussion
The method of bispectral analysis is a very interesting tool for philologists, as it allows quantifying the degree of interrelation of different physiological rhythmic processes. In particular, the application of bispectral analysis is described in electrophysiology, physiology of higher nervous activity, analysis of skin blood perfusion oscillations (Glass et al., 1997; Newman et al., 2021; Petrucci et al., 2023; Sigl & Chamoun, 1994). The first attempts to analyse the kinetics of closed and open states of ion channels were made at the end of the last century (Mullick & Reddy, 1988). However, the authors only demonstrated the principal possibility of applying the method to the estimation of non-Gaussian signals. The interconnected oscillations of the duration of the open and closed state times of the potassium channel was detected for the first time using bispectral analysis and observed a complex pattern of this relationship. We have detected interconnected oscillations of open and closed state times with frequencies of ~0.1, ~1 ~10 Hz (Fig. 4). For the model channel and the channel from Lymnaea st. a connection was found at a frequency of ~0.03 Hz (period ~30 sec). It is noteworthy that these frequencies coincide with a range of frequencies of physiological processes. In particular, the frequency of 0.1 Hz falls within the ranges of low-frequency oscillations of heart rate variability (Goldstein et al., 2011; Lehrer & Gevirtz, 2014), myogenic rhythm of oscillations of the skin microcirculation rate, realised due to spontaneous contractions of sphincters of arterioles (Golenhofen, 1970; Iskhakova et al., 2016), spontaneous Ca2+ concentration oscillations in neuron-glial culture cells (Mishchenko et al., 2023).
The participation of potassium channels in the regulation of processes at the level of the cardiovascular system is consistent with the literature data (Aziz et al., 2018; Jackson, 2017). Remarkably, the coupling detected on model and invertebrate channels at 0.03 Hz coincides with the central frequency of the neurogenic rhythm of skin microcirculation rate oscillations (Kolosova et al., 2018; Stefanovska et al., 1999; Zharkikh et al., 2023). We assume that
this frequency relationship exists in calcium-dependent Kca-channels (or other K+-channels) of vertebrates and will be observed at sufficient recording length. The presence of this site in other channels may indicate the universality of the mechanisms causing this connection of oscillations of the times of closed and open states. The frequencies of ~0.1 and ~10 Hz are represented at the nervous system level by spontaneous low-frequency activity transients and the alpha rhythm (Klimesch et al., 2007; Vanhatalo et al., 2002). Cytoplasmic calcium concentration in a range of cells can undergo spontaneous oscillations with a frequency of ~0.1 Hz, for example: glial cells, hippocampal neurons and cardiomyocytes (Cohen & Safran, 2020; Fordsmann et al., 2019; Kokoz et al., 2019; Kononov et al., 2012; Maltsev & Kokoz, 2020; Mathiesen et al., 2012; Teplov et al., 2021; Zinchenko et al., 2021). The transition from events at the level of a single channel to the cell level is possible if a cooperative process of their opening is initiated. Such a process has been described for cationic TRPV channels (Mulier et al., 2017).
The correlation between skin microcirculation rhythms has previously been shown to change with age and in functional tests (Tikhonova et al., 2022). The results of the present and previous studies suggest that changes in the correlation between rhythmic processes in the regulation of ion channel conductance may be a novel regulatory mechanism at both the molecular-cellular and organ-organismal levels.
It is noteworthy that the areas with a high bispectral index in the case of the Kv channel from L. stagnalis occupy almost the entire area of the bispectral map and forming a more complex pattern compared to the model channel and Kca-expressed in vertebrate cells. It is possible a consequence (or cause) of functional features of vertebrate and invertebrate neural system, in particular, gastropod mollusks. The vertebrate neural system is characterised by a high number of both neurons themselves and neuronal connections. The invertebrate neural system is characterised by a smaller number of very large neurons, which are capable of providing diverse
functioning at the ganglion level, but the number of connections between such neurons is smaller (Katz et al., 2013; Luisetto, 2019).
Increases in the bispectrum index with increasing transmembrane potential mean either an increase in the nonlinearity or an increase in the phase relationship of the processes of opening and closing of the gate mechanism, both of which can be realised due to an increase in the internal stresses in the channel structure when the transmembrane potential is applied to the voltage sensor. Another possible mechanism for changing the nonlinearity is a change in the structure of interactions of the channel segments due to a change in the local temperature of the protein globule due to the flow of ionic current through the selective filter; however, we should expect a decrease in phase coherence due to thermal noise, which should decrease the bispectrum index with increasing transmembrane potential and current amplitude, respectively.
A sigmoidal dependence of the relative rate of displacement of water molecules from the hydrophobic pore of the channel in the closed state on the value of the transmembrane electric potential was shown earlier (Grinevich & Astahev, 2019). Recently, data has accumulated on the role of voltage-gated ion channels in mediating the effects of alternating magnetic fields at the cellular level (Lisi et al., 2006; Morgado-Valle et al., 1998; Sarimov et al., 2023; Zheng et al., 2021). This has been demonstrated using a combination of magnetic fields and specific ligands, but the exact mechanism of channel-dependent magnetobiological effects is still unclear. We suggest that changes in the interaction between open and closed lifetime sequences may be one of the potential mechanisms for the effects of magnetic fields on ion channel conductance.
Recently, the ability of metallic nanoparti-cles to alter the volt-ampere characteristics and conductivity of potential dependent potassium channels through plasmon resonance has been discovered (Soloviev et al., 2015). In addition, metal nanoparticles can physically close the channel pore, change the physical properties of the cell membrane, release metal ions that act
on the conductivity of ion channels, and cause oxidative stress (Yin et al., 2019). The main mechanism has not yet been elucidated. Possibly, the analysis of the interaction between the sequences of open and closed ion channel lifetimes by bispectral analysis will help to clarify the mechanisms of action of metal nanoparti-cles and their oxides on ion channel permeability. Recently, metal nanoparticles and their oxides have been increasingly used in medicine and agriculture (Gudkov et al., 2023; Nikolova & Chavali, 2020), so understanding all possible health effects of their use is a prerequisite for their safe use.
The large amount of information obtained from 3D maps is both an advantage of this method and a factor that complicates the automated analysis of the obtained data and a set of sample values for adequate statistical analysis. Therefore, it is necessary to look for ways to optimise the data, to search and select a part of the information from the array, the "convolution" of the data. In our work we applied the method of peak value calculation with normalisation to the indicators of mixed series of indicators. This method allowed us to reveal the presence of a low-frequency regulation of the duration of the open state times and the dependence of this low-frequency regulation on the value of the transmembrane potential (Fig. 6).
New methods for automated comparison of 3D map features are needed to provide additional information on the regulation of ion channel open/closed lifetimes and to increase the applicability of bispectral analysis for biological data analysis. For example, the method of principal components, multi-dimensional data analysis, automated pattern recognition may be promising (Hira & Deshpande, 2015; Jolliffe & Cadima, 2016; Ristivojevic et al., 2014).
Investigations of bispectral characteristics of duration oscillation of open and closed states of ion channels (in particular, potassium channels) in native, ligand-bound and/or after modification of the primary sequence of the polypeptide chain will expand knowledge about the etiology of canalopathies and will broaden the area for searching new approaches and methods for the therapy of canalopathies and associated disorders.
Contribution
Concept and research preparation - A.M.E. and G.A.A.; research planning - T.A.V.; research conducting - S.D.A., A.M.E., S.A.V., Y.V.A. and G.A.A.; writing and drafting of article - S.D.A., A.M.E., G.A.A and T.A.V.; project administration - T.A.V. All authors have read and agreed with the published version of the manuscript.
Funding
This work was financially supported by the Russian Science Foundation (RSF) grant № 22-15-00215.
Conflict of Interest
The authors confirm that they have no conflicts of interest.
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