Elucidation of Rapid Synchronization on Electric Discharge by Use of Model Cell Systems Mimicking Electric Organs of Electric Eel

Abstract

The electric organ of a typical electric fish was artificially constructed by use of a model-cell system combining liquid-membrane cells mimicking the function of K⁺ and voltage-gated Na⁺ channels. The relation between the power generation of the electric organ and the rapid synchronization was investigated using the external electric stimulus. As for a model electrocyte, only a K⁺-channel-mimicking cell was set on the head side and both K⁺-channel and voltage-gated Na⁺-channel mimicking cells were placed on the caudal side. The potential difference between one and another side through the electrocyte changed from 0 V to about 0.15 V after the external electric stimulus was applied. In the firing state, the electric current due to the transfer of K⁺ and Na⁺ flowed through the model electrocyte. When multiple model electrocytes were in series, the simultaneous ignitions by opening of voltage-gated Na⁺ channels generate a large voltage through the electrocyte aggregates. In this case, the total voltage was the sum of the potential differences of the respective electrocytes. When several model electrocytes were in parallel, the total current was the sum of the currents of all electrocytes. The rapid synchronization of the electric organ of the electric eel (0.5 ms level) seems to be caused by circulating leak currents among neighboring cells through neural and vascular networks.

1. Introduction

Electric fish, such as electric eels and electric rays, have electric organs in their bodies and use electric signals as a means of attack, defense, and detection.^1–4 The electric organ is composed of many electrocytes, which generate electrical signals by utilizing the difference in concentrations of K⁺ inside and outside the cells and that of Na⁺. The electric eel is a typical electric fish and a freshwater fish that inhabits the Amazon and Orinoco river systems in South America.^4–7 The electric organ of the electric eel (Electrophorus electricus) is composed of layered electrocytes and generates the voltage of up to 600 V or more by simultaneously discharging (firing).^4,6,8–14 These electrocytes in line are covered with the insulating tubular connective tissue and are arranged in a regular pattern. Each electrocyte is placed within the insulating tube, and the membrane potentials at a caudal and head sides individually change.^4,12,15 The caudal cell membrane is rich in both neurotransmitter-dependent ion channels and voltage-gated Na⁺ channels, and changes its membrane potential from the resting potential due to the function of K⁺ channel to the action potential due to the function of Na⁺ channel in response to neural and electrical stimulation.^4,12,15 On the other hand, the cell membrane on the head side does not have these properties, and only K⁺ channel serves as a transporter. When a discharge (firing) signal is transmitted from the nerve to the caudal cell membrane, neurotransmitter-dependent ion channels open and the membrane potential changes in the positive direction with respect to the extracellular fluid on the caudal side. Since voltage-gated Na⁺ channels open simultaneously, Na⁺ mainly flows into the electrocyte and the membrane potential changes to the action potential on the caudal side. On the head side only K⁺ is released, and the membrane potential with respect to the extracellular fluid slightly changes in the positive direction. As a result, a potential difference of about 150 mV is generated through the electrocyte with respect to the caudal side.^4,12 Although each electrocyte generates an electromotive force of about 150 mV, a voltage of 600 V or more is generated by simultaneous connection of more than 4000 electrocytes in series.^4,12 Considering the thickness of each electrocyte (about 100 µm),¹² 4000 cells connected in series would be about 0.4 m. Because it is well-known that the firing of each electrocyte is synchronized within 0.5 ms,¹⁶ the transmission rate of information between electrocytes is estimated to be more than 800 m s⁻¹. This is a considerably large value compared to, for example, the conduction velocity of human motor nerves (100 m s⁻¹),¹⁷ and it is difficult to elucidate the conduction mechanism of electric eels such as the velocity, synchronization of signals, etc. based on the conventional view.

Recently, a model system combining multiple liquid–membrane cells has been applied to examine the propagation mechanism of electrical signals within one cell or among multiple cells by the author’s group.^18–28 It was proved that propagation of the membrane potential was caused by locally circulating currents in the model neuron composed of several liquid-membrane cells mimicking Na⁺ and K⁺ channels.^24–26 The author’s group has pointed out that there are serious problems in conventional concepts of nerve conduction as follows. First, it is not sufficient to consider the influence of neuronal firing at postsynaptic membrane on the propagation of action potential (directional propagation and potential profile along the axon). Next, the facilitated propagation of action potential by inserting long wire electrodes in the axon is not considered in the case measuring the membrane potentials on the axon using the voltage-clamp technique. As for cell-to-cell communication, the possibility of the electric transmission due to not gap junctions but the penetration of the local circulating current among adhering multiple cells is suggested using a model system composing multiple cells.^27,28

In this study, we constructed a model electrocyte using liquid-membrane cells mimicking K⁺ and voltage-gated Na⁺ channels to elucidate the rapid signal conduction of electric eels. By connecting multiple model electrocytes in series or parallel, we examined the influence of both the arrangement of the electrocytes and the current flowing the surrounding area on the rapid signal conduction.

2. Experimental

2.1 Chemicals

Sodium tetrakis[3,5-bis(trifluorometyl)phenyl]borate (NaTFPB) was prepared according to the previously described procedure.²⁹ Potassium tetrakis[3,5-bis(trifluorometyl)phenyl]borate (KTFPB) was obtained by dissolving 1 g of NaTFPB in 100 mL of boiling water and mixing it with 5 mL of an aqueous solution saturated with KCl (about 3.3 M). Here, M denotes mol dm⁻³. The precipitated KTFPB was separated from the solution by filtration and the product was washed with water. After drying under vacuum for several hours, it was used as a reagent. The TFPB⁻ salt of tetraheptylammonium (THpATFPB) was obtained as a precipitate by mixing a methanol solution (100 mL) of NaTFPB (1 g) with a methanol solution (100 mL) of THpACl (1 g) (Tokyo Kasei Chemical Co.). THpATFPB was then recrystallized by adding water to the methanol solution. Nitrobenzene (NB) was purchased from Wako Pure Chemical Co. All other chemicals were of analytical reagent grade and used without further purification. Dibenzo-18-crown-6 (DB18C6) was used as an ionophore to stabilize K⁺ and Na⁺ in the NB phase.

2.2 Apparatus

An electrometer HJE-100 (Hokuto Denko Co.) was used for potential measurements and an ammeter HM-103A (Hokuto Denko Co.) was used for current measurements. All data were recorded at a sampling interval of 2 ms by a logger GL7000 (Graphtec Co.). A potentiostat/galvanostat HA1010mM1A (Hokuto Denko Co.) and a function generator HB-105 (Hokuto Denko Co.) were used for pulse voltammetry, and an A/D converter NI BNC-2120 (National Instruments Corp.) was used for data recording.

An On-Off-On 4-pole twin-throw toggle switch 5669ADBGK (APEM Inc.) was used as a switch to initiate the firing of the electrochemical cell mimicking the electrocyte (model electrocyte). To construct a liquid-membrane cell mimicking the function of voltage-gated Na⁺ channels, an operational amplifier TL061CP (Texas Instruments Inc.), a reed relay SIL05-1A72-BV669 (Meder electronic Inc.), and a timer LM555CN (Texas Instruments Inc.) were used. The threshold to connect the Na⁺ channel mimicking cell with the electric circuit through the relay switch was set at −50 mV, the connection was kept for more than 1 s. The electric circuit of this relay switch is shown in Fig. SI1.

2.3 Construction of model cell systems

On the head side of the cell membrane in the actual electrocytes, K⁺ channels are abundant, but voltage-gated Na⁺ channels are absent, as shown in Fig. 1.^4,12,15

Figure 1.

Scheme of an electric organ of an electric eel (Electrophorus electricus) (a). Ion transport across one electrocyte under the resting condition (b). Ion transport across one electrocyte under the firing condition (c).

In the present study, two types of electrochemical cells mimicking the functions of K⁺ and Na⁺ channels, respectively, were constructed by combination of a liquid-membrane (LM) and two aqueous phases (W1 and W2).^25–27 A porous polytetrafluoroethylene resin (PTFE) membrane filter T300A025A (diameter: 25 mm, pore size: 3.0 µm, thickness: 75 µm) was purchased from Toyo Roshi Kaisya, Ltd., and was used to stabilize the NB solution in the filter as the liquid membrane. Respective cells were named K_h, K_c, and Na cells. Here, W1 and W2 corresponded to the extracellular and intracellular phases, respectively. The subscripts (h, c) in the K_h and K_c cells mean to the head and caudal sides, respectively. Since only K⁺ channels exist in the head side of electrocytes, the K_h cell was set in the head side of the model electrocyte, as shown in Fig. 2a. Similarly, both K⁺ and Na⁺ channels exist in the caudal side of actual electrocytes, K_c and Na cells were set within the caudal side of the model electrocyte. As shown in Fig. SI2, the membrane filter was put between two glass cells (W1 and W2). An O-ring was used to prevent leakage of water. In order to mimic the relation between the membrane potential and the membrane current in the actual electrocytes of electric eels, the ionic compositions of K (K_h and K_c) and Na cells were selected as schemes (i) and (ii), respectively.

  

  

The area of LMs of K_h and Na cells was 2.0 cm² and that of K_c cell was 0.2 cm². The difference in membrane area was adopted to mimic the ratio of the current due to the flow of Na⁺ to that of K⁺ across the model electrocytes. In each liquid membrane phase, K⁺ or Na⁺ was added in the form of KTFPB or NaTFPB, respectively. In order to mimic the function of electrical discharge of one electrocyte, three type cells were prepared in the present model. Ag wires coated with AgCl (Ag|AgCl) were inserted in the respective water phases, and they were electrically connected with each other. MgCl₂ was added to make the Cl⁻ concentrations in all aqueous phases 0.1 M. The potential difference between W1 and W2 across LM (E) was measured using Ag|AgCl electrodes immersed in W1 and W2 of each cell. The Ag|AgCl electrode inserted in W1 was used as a reference (extracellular side). The current due to the flow of cations from W2 to W1 was defined as a positive current at each electrochemical cell, and the current due to the flow of cations from W1 to W2 was recognized as a negative current. The solid black lines in Fig. 2 indicate lead wires connecting all electrochemical cells in the electric circuit. The initial stimulus was given by the connection of the Na cell to the electric circuit through a toggle switch. By turning the toggle switch on, the model electrocyte changed from the quiescent state to the firing state. A resistor (510 Ω) or an electrometer was connected with the external electric circuit, and the electrochemical behavior during the firing state was measured by ammeters and electrometers. Ammeters were connected in series with the K_h and Na cells. Electrometers were connected in parallel to all cells (K_c, K_h, and Na cells) and the resistor.

Figure 2.

Overview of a model electrocyte (a) and model two electrocytes connected in series (b) and in parallel (c).

Two model electrocytes were connected in series or parallel to construct a model electric organ, as shown in Figs. 2b and 2c. Similary to the experiments of one model electrocyte, the toggle switches connected to the Na electrocytes (Na1 and Na2 cells) were set in the electric circuit, and the electrochemical behaviors of the two electrocytes were measured.

When the propagation of the firing state between two electrocytes was investigated, the relay switch was set within electrocyte 2 of Fig. 2 in the electric circuit to mimic the synchronously opening of the voltage-gated Na⁺ channel. The circuit diagram using the relay switch is illustrated in Fig. SI1. The relay switch was connected to the electric circuit when the E value of the K_c2 cell reached the threshold (−50 mV). The connection time of the relay switch to the circuit was longer than 1 s. The E values of all electrochemical cells were observed after the toggle switch of the Na1 electrocyte was manually connected.

3. Results and Discussion

3.1 Electrical characteristics of electrochemical cells mimicking the function of K⁺ and Na⁺ channels

When the only objective ion can transport across the LM between W1 and W2, the membrane potential at i = 0 (E₀) can be expressed by Eq. 1.³⁰

  

\begin{equation} E_{0} = \frac{RT}{zF}\ln \frac{\gamma_{\text{W}1}c_{\text{W}1}}{\gamma_{\text{W}2}c_{\text{W}2}} \end{equation} (1)

where R is the gas constant, T is the absolute temperature, z is the ionic valence, F is Faraday's constant, c_W1 and c_W2 are the concentrations of the objective ion in W1 and W2, respectively, and γ_W1 and γ_W2 are the activity coefficients of the objective ion in W1 and W2, respectively. Assuming γ_W1/γ_W2 ≈ 1, E₀ is calculated from the K⁺ and Na⁺ concentration ratio according to Eq. 1. At T = 298 K, the E₀ of the K_h and K_c cells is estimated to be −77 mV, and the E₀ of the Na cell is 77 mV. In fact, the absolute value of these cells indicated 72–79 mV.

The characteristics of each cell (K_h, K_c, or Na cell) were evaluated by pulse voltammetry, as shown in Fig. 3. Pulse voltammetry was performed by applying the membrane potential and recording the membrane current. The initial potential was set at −77 mV for the K_h and K_c cells and at 77 mV for the Na cell. The membrane current was recorded after 20 s. The potential increment was 20 mV, and the sampling period was 10 s. When the same magnitude of potential difference was applied, the current flow in the K_h cell was about 10 times larger than that in the K_c cell. Since the membrane area of the K_h cell is almost equal to that of the Na cell, the membrane potentials at the head and caudal sides were mainly decided by the K_h and Na cells, respectively, during the power generation.

Figure 3.

Pulse voltammograms for the K_h cell (a), K_c cell (b), and Na cell (c).

3.2 Electrical characteristics of a model electrocyte

First, the model electrocyte was constructed by use of the K_c, K_h, and Na cells and the resistor (510 Ω). The currents in the K_h and Na cells were measured with ammeters, and the current in the K_c cell was calculated by Kirchhoff's law. Figures 4a and 4b indicates the time-courses of E and i of the K_c, K_h, and Na cells. The potential difference (E_total) and the current (i_total) between the head and the caudal sides across the electrocyte were illustrated using long dashed triplicate-dotted line. The resistor was used to mimic mainly a solution resistance of the environmental water where the electric eels live in. The direction of the actual current flow is shown by arrows in Fig. 4c (blue arrows: the current flow at each electrochemical cell, yellow arrows: the current flow across the model electrocyte and that through the outside). The moment when the Na cell was connected to the electric circuit was set to 0.000 s. Before the Na cell was connected (t < 0.000 s), the E values on the head and caudal sides of the model electrocyte were determined by the K_h and K_c cells, respectively (−74.8 mV at t = −0.120 s for both). Since both E values were almost equal, the potential difference between the head (left) and caudal (right) sides of the model electrocyte was about 0 V, and the current flowing through the external circuit (a 510 Ω resistor) was almost 0 A. When the Na cell was connected, positive currents flowed through the K_h and K_c cells and a negative current flowed in the Na cell. Accordingly, a positive current flowed from the caudal to the head side through the entire model electrocyte, as illustrated by yellow arrows. The E values on the head and caudal sides in the firing state were −30.0 mV and 16.5 mV, respectively, at t = 1.000 s, as shown in Fig. 4a. Considering the potential direction of each electrochemical cell, the absolute magnitude of the potential difference across the model electrocyte was almost identical to the potential difference (E_total = 46.1 mV) measured in the external circuit. Similar to the current flows at the head and caudal sides, the current i_total that flowed through the external circuit was 90.4 µA.

Figure 4.

Time-courses of membrane potentials (a) and membrane currents (b) of the model electrocyte using the resistor (R = 510 Ω). Directions of the current flows of all cells and the electric circuit (c).

Next, an electrometer was used as an external circuit instead of the resistor, and E and i were also measured when the Na cell was connected. The i value of the K_h cell was kept at about 0 A, and the E value was −74.5 mV at t = 1.000 s. On the other hand, a positive current flowed in the K_c cell, and a negative current flowed through the Na cell at the same time. The membrane potentials of K_c and Na cells then became to be 53.7 mV at t = 1.000 s. The sum of the absolute values of both membrane potentials of the head and caudal sides was almost equal to the potential difference E_total = 128 mV, and the electrometer connected as an external circuit indicated the same value. When the current flowed through the external circuit is zero, the E_total value can be regarded as the electromotive force of the model electrocyte.

3.3 Charactristics of the model aggregate composing two electrocytes connected in series or parallel

It is predictable that electrical properties of the aggregate of model electrocytes were changed by the connection of their electrocytes in series or parallel. How to change the electrical properties by the connection was investigated in this section. Figures 5 and 6 show the time-courses of the membrane potentials and membrane currents, respectively, of each cell in the model electric organs of which electrocytes were connected in series and parallel, respectively. A 510 Ω resistor was used as an external electrical resistance. Connecting Na1 and Na2 cells to the electric circuit by toggle switches at the same time, two model electrocytes changed to the firing state, as shown in Fig. 7. The direction of the current flow is also shown in the same figure.

Figure 5.

The time-courses of the potential differences across the model electric organ connecting in series (a) and the currents flowed across the model electric organ (b).

Figure 6.

The time-courses of the potential differences across the model electric organ connecting in parallel (a) and the currents flowed across the model electric organ (b).

Figure 7.

Direction of the current flow at each cell and within the electric circuit. The model electric organ connecting in series (a) and that connecting in parallel (b).

Similarly to the case of the single model electrocyte, the positive current flowed in the K_h and K_c cells and the negative current flowed in the Na cell during the connection of the Na cell. Since the absolute value of the K_c cell was smaller than that of the Na cell, the positive current flowed from the caudal side to the head side through the entire model electric organ. The total current i_total was 113 µA in the series circuit and 134 µA in the parallel circuit (t = 1.000 s). The electromotive force E_emf was 259 mV in the series circuit and was 131 mV in the parallel circuit, as indicated in Table 1. These values were measured using an electrometer as an external circuit without the resistor (R = 510 kΩ). The data on the electrical properties of one electrocyte were shown in Fig. SI3. The above results show the characteristics of the model aggregate as a power source. Assuming that the relation E_emf = i_total (r + 510 Ω) holds between the E_emf value and the i_total value, r corresponds to the internal resistance of the model electric organ. The E_emf and r values of each circuit are shown in Table 1. It indicates that additivity of the E_emf values is valid because the E_emf value of the aggregate connecting in series is twice that of the single electrocyte. In addition, when two electrocytes were connected in parallel, the internal resistance was reduced by half. It means that the additivity of the internal conductance is valid. In other words, the electric organ increases its electromotive force by connecting electrocytes in series and reduces its internal resistance by connecting them in parallel. The electric organ can be regarded as a large battery consisting of many small electrocytes connected in series and parallel.

Table 1. The electromotive force (E_emf) and internal electrical resistance (r) of the single model electrocyte and model electric organ connecting two electrocytes in series or parallel.

	Single electrocyte	Two electrocytes in series	Two electrocytes in parallel
Eemf/mV	128	259	131
r/Ω	906	1790	467

Since the surface of the caudal side of the electrocyte is covered with nerve cells, it is thought that stimulation causes the caudal side of almost all electrocytes within the electric organ to change into the action potential simultaneously.^4,12 However, if the neuronal network is partially missing or the stimulation is weak, most electrocytes cannot change into firing states at the same time. Therefore, we investigated the case where one of two electrocytes existing in series or parallel has only a voltage-gated Na⁺ channel and stimulation does not work simultaneously. Specifically, the switch in electrocyte2 was replaced with a relay switch, so that when the membrane potential of K_c2 exceeded the threshold (−50 mV), Na2 cell was connected to the electrical circuit.

First, the switch of the Na2 cell of the model electric organ connecting in series was replaced by a relay switch, as shown in Fig. 8a. When the Na1 cell was manually connected to the electric circuit, the potential difference and current across each cell were changed as shown in Fig. 9. After the Na1 cell was connected, the model Electrocyte1 became a firing state and a positive current flowed from the caudal side to the head side. This current started to flow into the model Electrocyte2 connected in series. Since Electrocyte2 was not a firing state at the time, all the current passed through the K_c2 cell on the caudal side. Considering the relation between the membrane potential and the membrane current of Fig. 3b, it is understandable that the membrane potential of the K_c2 cell varies in the negative direction. Since the relay switch could not connect the Na2 cell, it is predictable that the firing phenomenon of the model electrocyte did not propagate.

Figure 8.

Direction of the current flow at each cell and within the electric circuit. The model electric organ connecting in series (a) and parallel (b). The relay switch was used within the Electrocyte2 instead of the toggle switch. Left side of (b): Just after the firing of Electrocyte1 (0 ms ≤ t ≤ 4 ms). Right side of (b): The moment after the firing of Electrocyte2 (t > 4 ms).

Figure 9.

Time-courses of the potential differences (a) and the current flow (b) across the electric organ connecting in series using a relay switch within electrocyte2.

On the other hand, in the case of the model electric organ connecting in parallel, the firing phenomenon was propagated. The changes in the potential difference and the current of each cell are shown in Fig. 10, and the direction of the current flow is shown in Fig. 8b. In the parallel connection, the current flowing across the Electrocyte1 flowed into both the Ectrocyte2 and the external circuit (510 Ω resistor). The current started to flow from the head side to the caudal side of the Electrocyte2. In the K_c2 cell, the positive current flowed and increased the membrane potential. The membrane potential of the K_c2 cell increased to −15.5 mV at t = 2 ms, exceeding the relay switch threshold value of −50 mV (Fig. SI4). But the negative current flowed in the K_h2 cell just after the connection of the Na1 cell to the electric circuit, and the membrane potential of the K_h2 cell shifted to about −80 mV. After the Na2 cell was connected to the electric circuit, the direction of the current flow across the K_h2 cell was turned because the inflow of Na⁺ across the Na2 cell was larger than the outflow of K⁺ across the K_c2 cell. Therefore, the Electrocyte2 was also fired (t > 4 ms), and the whole electric organ was fired.

Figure 10.

The time-courses of the potential differences across the model electric organ connecting in parallel (a) and the currents flowed across the model electric organ (b) using a relay switch within Electrocyte2.

The above findings can be summarized as follows. The electric organ generates a huge voltage by arranging many electrocytes in series. The current increased by connecting the aggregates in parallel. To generate huge voltages and currents, a large number of electrocytes in the electric organ must fire almost simultaneously. In the electric organ, an electric column is formed by the connection of several hundreds of electrocytes in series within the insulating tube.^1–4 Then, the electric organ is composed of many electric columns. When several electrocytes have already fired, current flows through unfired electrocytes within the electric column where many electrocytes connected in series. The membrane potentials on the caudal side of the unfired electrocytes shift in the negative direction. Therefore, the firing phenomena cannot propagate the whole electric column by only voltage-gated Na⁺ channels, if the receptor type Na⁺ channels are partialy lost or the firing effect is weak. It is proved that the firing phenomena propagate through the unfired electrocytes connected in parallel by the leak current using conductive routes such as gap junctions. However, since the electric columns are separated from each other by an insulating membrane, it is seemed to be difficult to affect each other among neighboring electrocytes. On the other hand, it is well-known that the surface of the caudal side of electrocytes is covered with nerve cells and that the surface of the head side of electrocytes is cover by blood vessels or the membrane resistance is fairly smaller than that of the caudal side.⁴ Since neuron cells and blood vessels penetrate through the insulating membrane, these might be able to serve as leak routes.

Since it has been reported that the firing of each electrocyte is synchronized within 0.5 ms,¹⁶ the transmission rate within the electric organ is estimated to be more than 800 m s⁻¹. This value is much faster than the conduction velocity of human motor nerves (100 m s⁻¹).¹⁷ It is thought that the transmission rate from the center controlling synchronization to each electrocyte is skillfully regulated. For example, the diameter of neurons connected to electrocytes, the length between nodes of Ranvier, and the thickness of myelin sheaths are larger, longer, and thicker on the caudal side than on the head side, respectively.³¹ These factors increase the conduction velocity of the nerves on the caudal side relative to the head side and may synchronize most of electrocytes. However, it is difficult to explain the fast synchronization based on these factors only. It is thought that the fast synchronization is caused by multiplier effect of not only these factors but also the electric stimulation across leak routes using nerve cells and blood vessels.

4. Conclusion

In the present study, the rapid synchronization of electric discharge of electric fishs was investigated using the aggregate of model electrocytes. We prepared the model electrocyte and its aggregate by use of liquid membrane-type cells mimicking the functions of K⁺ and Na⁺ channels. In the resting state, no potential difference occurred between the body fluids through a single electrocyte. On the other hand, the balance of membrane potentials at the head and caudal sides was disrupted in the firing state, and about 130 mV was generated as an electromotive force. When the model electrocytes were connected in series, the electromotive force increased. In the case that they were connected in parallel, the internal conductance increased.

In order to add potential dependence to the Na⁺ channel mimicking cell, a relay switch was fabricated to connect the cell to the circuit when the potential of the cell membrane on the tail side exceeds a threshold value. In a system with two model generator cells connected in series, the behavior of one model generator cell was observed when the relay switch was introduced into the cell and the other model generator cell was forced to fire. In the system in which the model generator cells were connected in series, the current flowing out of the fired cell flowed into the un-fired cell from the tail side toward the head side. This current pushed the membrane potential of the tail side down to the negative side, so the relay switch was not activated and the ignition phenomenon did not propagate. On the other hand, when the model generator cells were connected in parallel, the outflow current from the firing cell flowed from the head side to the tail side into the non-firing cell. This current pushed the membrane potential of the tail side toward the positive side, which activated the relay switch and propagated the firing phenomenon. These results suggest that in the electric fish organ, in which many generator cells are connected in series, synchronization of firing of each generator cell cannot be achieved only by a potential-dependent switch of the cell itself, but requires an external stimulus to fire the cells simultaneously.

Acknowledgment

The authors thank Prof. Kenji Kano for his encouragement and useful comments.

Data Availability Statement

The data that support the findings of this study are openly available under the terms of the designated Creative Commons License in J-STAGE Data at https://doi.org/10.50892/data.electrochemistry.25026791.

• 1) The electric organ of a typical electric fish was artificially constructed by use of a model-cell system combining liquid-membrane cells mimicking the function of K⁺ and voltage-gated Na⁺ channels. The relation between the power generation of the electric organ and the rapid synchronization was investigated using the external electric stimulus. As for a model electrocyte, only a K⁺-channel-mimicking cell was set on the head side and both K⁺-channel and voltage-gated Na⁺-channel mimicking cells were placed on the caudal side. The potential difference between one and another side through the electrocyte changed from 0 V to about 0.15 V after the external electric stimulus was applied. In the firing state, the electric current due to the transfer of K⁺ and Na⁺ flowed through the model electrocyte. When multiple model electrocytes were in series, the simultaneous ignitions by opening of voltage-gated Na⁺ channels generate a large voltage through the electrocyte aggregates. In this case, the total voltage was the sum of the potential differences of the respective electrocytes. When several model electrocytes were in parallel, the total current was the sum of the currents of all electrocytes. The rapid synchronization of the electric organ of the electric eel (0.5 ms level) seems to be caused by circulating leak currents among neighboring cells through neural and vascular networks.

CRediT Authorship Contribution Statement

Yusuke Yamada: Data curation (Lead), Formal analysis (Lead), Investigation (Equal), Methodology (Equal), Resources (Equal), Software (Equal), Writing – original draft (Lead)

Yuki Kitazumi: Conceptualization (Supporting), Data curation (Equal), Formal analysis (Equal), Investigation (Supporting), Methodology (Supporting), Software (Lead), Writing – review & editing (Supporting)

Osamu Shirai: Conceptualization (Lead), Data curation (Supporting), Formal analysis (Equal), Funding acquisition (Lead), Investigation (Lead), Methodology (Lead), Project administration (Lead), Resources (Equal), Supervision (Lead), Validation (Lead), Visualization (Equal), Writing – original draft (Lead), Writing – review & editing (Lead)

Conflict of Interest

The authors declare no conflict of interest in the manuscript.

Footnotes

Y. Kitazumi and O. Shirai: ECSJ Active Members

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