Electrical Potential of Leaping Eels Open Access

The long body of an electric eel (Electrophorus electricus) is composed primarily of electrogenic tissue, providing this South American fish with the most powerful electrical discharge of any species [Grundfest, 1957]. Large specimens produce discharges of up to 600 V, and when short circuited the external current can be as high as 1 A [Brown, 1950; Coates, 1950]. This ability has made electric eels one of the most famous and long-studied species [Williamson and Walsh, 1775; von Humboldt, 1806, 1807; Faraday, 1832; Du Bois-Reymond, 1849; Sachs, 1881; Coates et al., 1940; Nachmansohn et al., 1943; Albe-Fessard, et al., 1951; Keynes and Martins-Ferreira, 1953; Szabo, 1966; Changeux et al., 1970; Bauer, 1979, Westby, 1988; Gotter et al., 1998; Stoddard, 1999; Stoddard and Markham, 2008; Finger and Piccolino, 2011; Markham, 2013; Gallant et al., 2014; Catania, 2016]. But the impressively large voltages and currents quoted for eels removed from the water in a laboratory setting are not experienced by nearby prey, or potential predators, immersed in the water with the eel. Rather the eel's discharge is distributed throughout the surrounding water, falling rapidly in strength by the effect of geometric spreading [Knudsen, 1975; Hopkins, 1999; Nelson, 2005; Nelson and MacIver, 2006] such that only a small fraction of the power impinges on other animals. Clearly, this fraction is sufficient to act as an efficient means of offense and defense. Indeed, the fact that only a small portion of the eel's output can be conveyed to an aquatic target is the most obvious explanation for the evolution of the eel's prodigious electrical power.

However, the recent discovery of an extraordinary defensive behavior by electric eels, during which they leap from the water to directly electrify threats (Fig. 1), casts the total power output of an eel in a new light [Catania, 2016]. The unattenuated values for whole-body output are, in this case, more directly relevant to the circuit produced. The shocking leap of an electric eel can often be elicited by approaching the eel with a partially submerged, large conductor. In the author's experience, nonconductors do not elicit this defensive behavior. This is consistent with the observation that small conductors are attacked as prey, whereas small nonconductors are ignored [Catania, 2015]. Large conductors are apparently interpreted as large animals. A large partially submerged animal could be a terrestrial predator that had encountered an eel in shallow water [e.g., during the Amazonian dry season - Catania, 2016]. The leaping defense is not consistent with eel predation because eels never bite at the large conductors during the leap, and eels are gape-limited predators that cannot dismember prey.

In the course of the leaping defense, an eel rises rapidly from the water with its lower jaw in contact with a threatening conductor, while discharging high-voltage volleys. This behavior is shown in Figure 1a, using a prosthetic arm containing eel-powered light-emitting diodes arranged to represent nerve tracts. Figure 1b shows the current flow schematically. Figure 1c shows the proposed equivalent circuit. The equivalent circuit includes the internal resistance of the eel (r), the electromotive force (ε) of the eel's “battery,” the resistance of the water in which the eel is immersed (R_w), and two resistors in parallel for the return path of current to the water (R_o and R_a). One of the two latter resistances represents the return path through the small, and decreasing, amount of water on the eel's body as it emerges (R_o). It also includes possible return paths through the eel's internal tissues. Because this resistance increases as the eel attains greater height [Catania, 2016], it is represented as a variable resistor. The other resistance represents the target; in this case the arm (R_a).

In this investigation, experiments were designed to determine the electromotive force (ε) of the eel's summed electrocytes, the internal resistance of the eel (r), the resistance of the main body of water, and the range of the variable resistor that represents the return path from the eel's lower jaw to the main body of water (Fig. 2). The resistance of the eel's target was not investigated in this study. Results are presented for four different eels ranging in size from approximately 40 cm to over 1 m.

All procedures were approved by the Vanderbilt Institutional Animal Care and Use Committee. Eels (E. electricus) obtained from commercial fish suppliers were housed in custom-made Plexiglas aquariums ranging in size from 300-480 L with aerated water, gravel bottom, plastic imitation branches, and plants, temperature between 24 and 26°C, pH between 6.5 and 7.0, and conductivity between 100 and 200 µS/cm. Lighting was on a 12-h/ 12-h light/dark cycle, and eels were fed earthworms and fish. Eel sizes were 40 cm (eel A), 66 cm (eel B), 103 cm (eel C), and 113 cm (eel D).

To record voltage and current directly from the eels, each was lifted into the air in a nonconductive net and contacted at the head and tail with silver-thread-conductive therapy gloves (Conductive Therapy Shop®) worn over rubber gloves. The conductive gloves were in turn connected to 16-G, braided copper speaker wire to form a low-resistance pathway to the remaining circuit elements. The leads from the conductive gloves were connected to an 8-channel, 5-V relay module board for Arduino (JBtek). Five of the 8 relays were used and controlled by a Master-8 stimulator (A.M.P.I., Jerusalem, Israel) that was programmed to sequentially activate the 5 relays at 200-ms intervals (including 200 ms with no relay activated giving 6 conditions). The relays were arranged with resistors to sequentially cycle through open circuit and then approximately 1,600, 800, 400, 200, and 0 Ω. The resistors were 5-W, 200-Ω ceramic resistors (±5% accuracy) that were added together by the relays to produce the values listed above during the experiment.

While the animal was contacted, and the circuit progressed through the resistances as described above, voltage and current (from the eel's high-voltage discharge) were simultaneously measured as illustrated schematically in Figure 3a. Voltage was recorded and stored with both a PowerLab 8/35 data acquisition unit (ADInstruments) through a P4100 100:1 probe (Sainsmart, Lenexa Kansas) using LabChart software (version 7; ADInstruments) at a 100-kHz sampling rate and with a Tektronix TBS 2000 digital oscilloscope through a tuned TPP0100, ×10 attenuating probe at a 100-kHz sampling rate - the latter stored as high-resolution jpegs for each data trace. The dual voltage recordings facilitated figure construction because the PowerLab data traces included all the timing information for the current, voltage, camera, and relay states. However, for convenience, all high-voltage values in the figures and data were taken from the easily tuned attenuating probe of the Tectronix oscilloscope.

Current was measured with a model H1-ACDC-72 (Hall effect) current sensor (BDW Enterprises LLC) at a 100-kHz sampling rate. The current sensor produced a voltage proportional to the current that was in turn recorded on a separate channel of the PowerLab 8/35 data acquisition unit. A known calibrating current (measured by a Fluke 115 True RMS multimeter) was passed through the current sensor and recorded prior to every trial. A third channel of the PowerLab 8/35 data acquisition unit recorded a separate output of the Master-8 stimulator, marking the time during which relays were active.

To convert recorded voltages from the model H1-ACDC-72 current sensor into current measures, the relevant area of the LabChart 7 trace was selected, the “min-max” function was used to record the peak from each discharge using the Datapad function, and these values were exported to Microsoft Excel. The deflection from baseline was converted to current values (amperes) based on the previously recorded calibration current. These data, in addition to the corresponding voltages from the oscilloscope, were imported into the JMP statistical program (a unit of SAS, Cary, NC, USA) to determine standard errors and standard deviations (online suppl. Table 1; see www.karger.com/doi/10.1159/000475743) for each resistance value. The means for each value were plotted and a linear fit determined using the “fit line” function, which was used to produce the graphs, and R² values, illustrated in Figure 3 and described in the text.

To estimate the value of water resistance, the aquarium water was brought to a conductivity of 100 μS/cm (measured with a calibrated Ohaus Starter 300C conductivity meter accurate to ±0.5%; Ohuas, Parippany, NJ, USA). Four carbon rods (16 cm in length and 1/3 cm in diameter) were positioned vertically at 25-cm intervals (Fig. 4a) by insertion into holes drilled into a Plexiglas holder on the bottom of the aquarium filled to a depth of 30 cm. Each carbon rod was connected by (insulated) 16-G speaker wire to an 8-channel, 5-V relay module board for Arduino controlled by a Master-8 stimulator as described above. Connection points between wire and rod were insulated with moldable plastic. Four relays were used to successively connect one of the rods to a single 16-G wire that ran to a conductive glove as previously described. A net was modified by adding an extension to the bottom that roughly matched the shape and size of the caudal portion of eel C's body. In this manner, the eel's tail was lowered into the water while each carbon rod was successively switched into the circuit at 250-ms intervals. Current was recorded with a model H1-ACDC-72 (Hall effect) current sensor as described above while the eel was contacted on the head with the conductive glove to complete the circuit. Amperage values were determined from the output of the current sensor as described above. Total resistance for each measure was determined by dividing ε (316 V for eel C) by I (measured for each discharge in the experiment). Water resistance for each distance was determined by subtracting Eel C's internal resistance (438 Ω) from total resistance for each discharge. Results were analyzed in JMP as described above and plotted (with standard deviations shown) in Figure 4c showing water resistance versus distance from the eel's tail for the four carbon rods.

The electric organ discharges were recorded from leaping eels by connecting a split aluminum plate to wires connected to a PowerLab 8/35 data acquisition unit and oscilloscope as described above and illustrated in Figure 5. Water conductivity was 100 μS/cm. Video was collected with a MotionXtra NX7S1 camera (IDT Inc, Tallahassee, FL, USA) with 2 RPS Studio CooLED 100 RS-5610 for lighting at 1,000 frames/s. The synchronization output of the high-speed camera was recorded on a separate PowerLab channel allowing coordination of video plates and voltage recordings. Voltage values were taken from the oscilloscope as described above. To illustrate the eel's output in relationship to eel behavior, data traces were copied at high resolution from the LabChart 7 program into Adobe Illustrator and illustrated with vector graphics to allow scaling to variable final figure sizes. The waveform for each discharge was replaced with a solid line of equivalent height in the illustrations. Single high-speed video frames that corresponded to eel voltages numbered in Figure 5 were determined from the frame marking TTL recorded by the PowerLab unit.

Because this investigation bridges the biology of electric eels and the characteristics of the electrical circuit involved, some brief background regarding the basic physical parameters, and method for their measurement, is included and illustrated. Two fundamental characteristics of the eel's discharge are the electromotive force (electrical potential in volts developed by the electrocytes during a discharge [ε]) and the eel's internal resistance to current flow (r). As with a battery, the values of these parameters can be obtained by short circuiting the eel to measure maximal current flow and by separately measuring the maximal voltage developed during a discharge with a high-impedance voltmeter. Internal resistance can then simply be calculated from V and I by Ohm's law. However, a more accurate value is attained by the experiment illustrated in Figure 2. In this case, an additional resistance is added to the circuit and varied. For each value of resistance, the current and corresponding voltages are recorded and plotted. For internal resistances that follow Ohm's law, a straight line is obtained, with the y-intercept in volts indicating the electromotive force, ε, and the slope equivalent to the negative of the internal resistance (r; Fig. 2c). These values are commonly measured for batteries and have previously been measured for electric eels [Brown, 1950] and other electric fish [Bell et al., 1976; Caputi et al., 1989; Baffa and Correa, 1992]. Previous results indicate that eel electrocytes can be analyzed in this manner as ordinary batteries. Once the values of ε and r have been determined, the values for the other resistances illustrated in Figure 1c can be investigated for any given eel. In the experiments in this study, all voltage and current values refer to the peak value for each of the discharges analyzed, water temperature was 25°C, and water conductivity was 100 μS.

For the present investigation, the technique used was similar to that of the air gap technique of Caputi et al. [1989] but with some modifications. For example, rather than suspending the animal such that only the head and tail were in separate aqueous solutions while the body was in air, or experimenting with an eel on a table [Brown, 1950], the eels were briefly lifted in a nonconductive net and then contacted with soft, conductive gloves connected by wires to the ammeter and voltmeter. This method, combined with modern multichannel data acquisition units, allowed the voltage and current measurements at different resistances to be obtained in only a few seconds. In addition to reducing stress on the experimental animals, this technique reduced the possibility of electrocyte fatigue that could occur for longer-term experiments.

Figure 3a-c illustrates the paradigm and results for eel C, which provided a remarkably clear, long data set as the eel began discharging in bursts (left-most series in Fig. 3b) and then transitioned to a continuous volley while relays cycled the circuit through 6 different resistances, each lasting 200 ms (for zero resistance, there was some resistance of wires and relays, resulting in a small voltage drop present in “zero” columns; Fig. 3b). Some discharges occurred during the short time during which the relays switched resistors, resulting in occasional “open-circuit” conditions between resistor values (arrows; Fig. 3b). The linear relationship between current and voltage is suggested from the raw data trace (Fig. 3b; amperes in green and volts in red in the online version). A plot of volts versus amperes (Fig. 3c) resulted in a straight line (R² = 0.998) with a y- intercept (ε) of 316 V and a slope of -438 (r= 438 Ω).

These results indicate that eel C has an electromotive force of 316 V and an internal resistance of 438 Ω as measured for the peaks of its high-voltage discharge. It should be noted that all electrocytes are active during an eel's high-voltage discharges [Bennett, 1968, 1970]. Thus, electric eels do not have a mechanism to vary the magnitude of their high-voltage discharges during volleys, although it is possible that fatigue causes a reduction in power output over time.

The same experiment was performed for the other 3 eels in the study. Figure 3d, e illustrates the results for a slightly longer eel (eel D). Bursts of high-voltage discharges were more typical of the remaining 3 eels (as illustrated in Fig. 3d), providing fewer data points per unit time than was the case for eel C. Nevertheless, the data were consistent and clear for each animal such that standard errors (and often standard deviations) were too small to illustrate for most points; thus, all bars represent standard deviations. Online supplementary Table 1 provides the number of data points (discharges), standard errors, and standard deviations analyzed for each resistance. For each eel, the relationship between voltage and current was linear, with R² values of 0.987, 0.996, and 0.997 for eels D, B, and A, respectively. Thus, values for ε and r were obtained for each specimen. The results showed the expected relationship between longer eel length and greater electromotive force. The eels were labeled by increasing length (A-D). Eel A was 40 cm long and eel D was 113 cm long. Values for ε were 179, 301, 316, and 382 V for eels A-D, respectively.

The resistance of the water surrounding an electric eel is an important variable that affects the circuit developed when an electric eel leaps in self-defense (Fig. 1c). To estimate this resistance, a custom net was designed that allowed current to be measured as the eel's tail was lowered into the water while its head was contacted by a conductive glove (Fig. 4a). The circuit was completed by connecting the glove to one of the four carbon rods submerged in the water at fixed distances from the eel. A series of relays sequentially switch the connection from the glove to one of the carbon rods, progressing from closest to farthest at 250-ms intervals (water was at 25°C and water conductivity was 100 μS/cm). Under these conditions, eel C once again produced a continuous volley of closely spaced, high-voltage discharges (Fig. 4c). Because ε was known for this eel (316 V) and total current (I) was measured in the experiment, total resistance of the circuit was easily determined for each distance (R = V/I). Subtracting the known internal resistance for the eel (438 Ω) from total resistance for each carbon rod trial provided the resistance for the water at the different distances from tail to carbon rod (Fig. 4d). This particularly clear data set was used to roughly estimate water resistance for all eels based on approximate distance of the tail from other circuit elements in subsequent analysis and discussion.

The next experiment examined the electrical potential (voltage) developed between the lower jaw of the eel and the water as each specimen made shocking leaps. The procedure followed a previously published paradigm [Catania, 2016]. A flat metal plate was divided such that one section could be immersed in the water with only the upper edge protruding. An insulator separated the lower plate from an upper plate; the latter extended well above the water (Fig. 5a). When the lower plate was brought close, the eel usually made an explosive attack. First, contact was made with the lower jaw to the lower plate below the water. Next, the eel followed the lower plate to the water surface and sprang from the water keeping its lower jaw in continual contact as it passed over the insulator and onto the upper plate. Throughout this behavior, a volley of high-voltage discharges was emitted. Voltage was recorded between the two plates as the eel rapidly ascended (Fig. 5). In the course of this behavior, eels often made various contortions of their anterior body to keep the lower jaw in contact with the plate, thus ensuring the circuit was complete for most of the time the eel's head was above water.

As observed in a previous investigation [Catania, 2016], the recorded voltage increased dramatically as the eels ascended the plate. Initial contact with the upper plate, when most of the eel's body was submerged, corresponded to low-amplitude recordings of only a few volts. Highest-recorded voltages generally corresponded to the greatest heights reached by the eel on any given trial. In the examples provided in Figure 5, the recorded peaks for eels A, B, C, and D were 100, 228, 265, and 261 V, respectively. These correspond to a substantial proportion of ε for each specimen.

The values for voltages and resistances provided in the experiments described above allow for an approximation of the other components illustrated in Figure 1c and an estimate of the dynamics of the circuit during the eel's leaping defense. Importantly, the target resistance was not considered in the present analysis. Instead, the circuit elements were considered from the perspective of the voltage recordings from the metal plate during the leap, as measured from a high-impedance voltmeter. Thus, for the conditions of these experiments, the circuit can be considered an unloaded voltage divider.

For brevity, the resulting circuit elements are considered only for eels A and C. In the case of eel C, water resistance was estimated to be 600 Ω, based on the approximate tail distance during the leap illustrated in Figure 5b, c. The peak potential recorded was 265 V (Fig. 5c). Therefore, the voltage drop across the water resistance and internal resistance was ε - 265 V or 51 V. The peak current through the circuit was calculated as 51 V divided by 1,038 Ω (the latter being combined water resistance and internal resistance r) indicating a peak current in the circuit of 0.049 A. From this current, the resistance between the eel's lower jaw and the main body of water could be calculated as R₀ = V₀/I or 265 V/0.049 A ≈ 5,400 Ω. Thus, it was estimated that for eel C, the resistance between the lower jaw and the water (for the leap illustrated in Fig. 5b, c) ranged from approximately 0 to 5,400 Ω as the eel ascended (Fig. 6b). Similar calculations can be made for the other eels. For the smallest eel (eel A), the internal resistance, r, was considerably larger at 707 Ω. The water resistance was estimated to be smaller, based on the closer proximity of the tail to the lower plate (400 Ω). The peak potential of 100 V during the leap (Fig. 5h, i) leads to a calculated resistance between lower jaw and water of approximately 0-1,400 Ω as the eel ascended (Fig. 6c).

The goal of this study was to first measure the electromotive force (ε) and internal resistance (r) for a number of eels. The next goal was to estimate the additional resistances involved in the circuit that are produced when an eel leaps and shocks in self-defense. These values in turn allow for generalizations to other eels in other settings, electrifying variable targets with different resistances.

The simplified circuit that is proposed to develop when an eel emerges from the water to electrify a threat is illustrated in Figure 1c. It consists of a voltage source (ε), an internal resistance (r), the water resistance (R_w), and two resistors in parallel that form return paths to the water. For the purposes of the present study, the eel's target was a high-impedance voltmeter. This simplified the measurements to those of an unloaded voltage divider circuit, for which the voltage drop at R_o can be measured as a resistor in series with the remaining components (addition of the target resistance is discussed below).

ε and r for each eel were determined in the manner often used for batteries, and previously used for electric eels [Brown, 1950], and similar to the air gap technique of Caputi et al. [1989]. Total currents and voltages were measured for each eel in a circuit that included an additional resistance that was varied (Fig. 2, 3). A plot of voltage versus current for each resistance value was linear such that the electromotive force and internal resistance could be determined (Fig. 3). The magnitude of ε ranged from 179 V for the smallest (40-cm) eel to 382 V for the longest eel that was over 1 m in length (Fig. 6a). The electromotive force of each eel was roughly proportional to length, as might be expected for the number of electrocytes in series. The lowest internal resistance (438 Ω) was found for the electric eel that clearly had the greatest girth (eel C) rather than the greatest length. This is consistent with the number of electrocytes that might be arranged in parallel. Caputi et al. [1989] found a similar relationship of increasing power output relative to fish size using the air gap technique to investigate Gymnotus carapo.

Once ε and r were known, total water resistance was estimated (using a single eel) by directly measuring current in a circuit that included water between the eel's tail and conductive carbon rods at four different fixed distances (Fig. 4). When considering water resistance, it should be noted that the eel's leaping behavior brings its tail and body progressively closer to the target as the eel ascends. This would presumably have the effect of reducing total water resistance as the eel attained greater heights on the target. For this study, a single value of 600 Ω was used for eel C, whereas a single value of 400 Ω was used for eel A (the smallest eel). Relatively large (percentage) changes to this value would have little effect on the calculation of return path resistance (see below).

Measurement of the voltage drop across the final resistance to be analyzed was facilitated by the nature of the eel's leaping behavior, during which each specimen voluntarily connects itself to a voltmeter through the conductive plate arrangement illustrated in Figure 5a. High-speed video recordings, coordinated with voltage recordings, allowed for a comparison between eel height and electrical potential during this behavior. Kirchhoff's voltage law (the sum of the voltage drops in the circuit must add to zero) allowed subsequent calculation of this resistance by subtraction of the other components, as outlined in the results. The results indicated that the resistance between the eel's lower jaw and the main body of water increases from (presumably) zero to thousands of ohms as the eel ascends. The examples included in this study reflect the maximum voltage attained from only a few trials for each animal. There is little doubt the resistance of the return path over or through the eel's body may be considerably greater for higher leaps. For example, in the course of observing and photographing eels leaping at diverse stimuli, some instances include examples for which the eel comes most of the way out of the water (Fig. 7). It is possible that eels curtail the behavior when very high resistance is encountered (as in the case of the high-impedance voltmeter, for which negligible current flows between the upper and lower plates). The examples shown in Figure 7 were cases for which current flowed through conductive tape on the prop, through light-emitting diodes, and then through a return path to the water. Feedback to the eel about this completed circuit could indicate a successful, on-target electrification of the threat and hence result in a longer and higher leap. More studies are needed to explore this possibility. But regardless of potential feedback to the eel, greater heights (Fig. 7) would be expected to correspond to greater resistances for the return path than illustrated in Figure 6b, c. Thus, peak resistance values from 5,000-8,000 Ω might be predicted for large electric eels that had risen to half their body length during a shocking leap.

Having explored the electrical circuit involved when an eel leaps in self-defense, the next obvious question is how this circuit affects the target at which the eel is directing its high voltage? This is the case for the complete circuit illustrated in Figure 1c, for which two resistors are in parallel. It represents a current divider circuit, and it is obvious that more current will flow through the path of least resistance. This provides the basis for the selection of the eel's leaping behavior, which progressively decreases the relative resistance of the target as the eel ascends to greater heights (one assumption for this conclusion is that electric eels do not have low-resistance tissues that form an internal return pathway for the electrocytes, as this would make their use of high-voltage discharges unfeasible in general). The familiar formula for determining current through each resistor in parallel is I_N = I_Total (R_Total/R_N).

It is perhaps most informative to consider an example. If we assume a wet human arm (as would inevitably be the case at the contact point between an eel and its target) has a resistance of 2,000 Ω [Reilly, 2012], then a large eel would impart most of the current in the circuit through the human limb at peak height. In the case of eel C, as illustrated for Figure 8, roughly 0.09 A of current would flow through the arm, equivalent to 16 W, in brief pulses corresponding to the peak of each high-voltage discharge. A pulse rate of 200-300 Hz has been used in numerous studies to activate nociceptors in diverse species [Duranti et al., 1983; Anderson et al., 1999; Arendt-Nielsen et al., 2000; Spadavecchia et al., 2002; Kimura et al., 2004] - similar to the eel's high-voltage discharge rate while leaping. Moreover, when humans were stimulated at 300 Hz, pain threshold was reached at a current of roughly 5 mA, with very severe pain at 18 mA. Clearly, 90 mA would cause considerable pain.

It is not clear which potential predators may have led to the evolution of the defensive behavior, or what the particular resistance of the predator's epidermis might be. In a previous report [Catania, 2016], the author reported that eels over 60 cm engaged in this behavior. In the present study, it was discovered that all eels examined over the length of approximately 30 cm (6 juvenile specimens) engaged in the behavior. The behavior was exhibited in full form from these growing juveniles when first observed, but a precise developmental stage at which it emerged was not recorded. Nevertheless, it is clearly a common and innate behavior. It seems most likely that the function of the high-voltage discharges, during shocking leaps, is to activate afferents that would result in a highly aversive experience for potential predators on the receiving end.

This work was supported by NSF grant 1456472 to K.C.C.

The author has no conflict of interests to declare.