Waveform diversity of electric organ discharges: the role of electric organ auto-excitability in Gymnotus spp.

The discovery of weak continuous electric organ discharges [EODs(Lissmann, 1951)] emitted by Gymnarchus niloticus was the first step for solving the question posed by Charles Darwin (Darwin,1866) concerning the function and evolution of electric organs(EOs). Lissmann's article was followed by a series of subsequent articles showing that: (a) the EOD emitted by a fish triggers behavioural responses in other fish (Mohres, 1957); (b)fish can detect and discriminate electromagnetic signals(Lissmann, 1958; Lissmann and Machin, 1958; Machin and Lissmann, 1960);and (c) there are sensory receptor organs tuned for the species-specific EOD waveform (Bullock et al.,1961). These studies beautifully demonstrated that the EOs and their control system constitute a paradigmatic specialisation of the motor system, whose function is to provide a carrier for sensory signals(Bennett and Grundfest, 1959). The theoretical framework already elaborated in the pioneer papers(Lissmann, 1958; Lissmann and Machin, 1958; Machin and Lissmann, 1960) set the basis for understanding this sensory modality and its two roles in animal life: active electrosensory exploration of the environment and electrocommunication with conspecifics.

One of the most salient characteristics of the electric fields generated by electric fish is the species specificity of its waveforms(Coates et al., 1954; Bennett and Grundfest, 1959). Beyond constituting a taxonomic sign for species identification, the biological role of species specificity of the EOD is still a matter of discussion. Several non-exclusive hypotheses have been raised about this point. Some authors suggest that main driving force in the evolution of EOD waveform is a process of cryptic adaptation in order to avoid predation(Stoddard, 1999; Stoddard, 2002). This process tends to increase the number of waves produced in a given time and the EOD power spectra are shifted to a higher frequency range. Other authors suggest that species-specific waveform has a crucial role for species recognition in mating and reproduction (Crampton and Albert, 2005; Albert and Crampton, 2005). Ecologically co-occurring species of gymnotiforms(e.g. Gymnotus carapo and Gymnotus coropinae) often exhibit non-overlapping ranges of far field power spectra suggesting that these species may be able to recognise and discriminate each other on the basis of frequency components of the electrocommunication carrier. However, the ranges of the power spectra of various species co-occurring at floodplain habitats of Central Amazon overlap. A wavelet `signal space' representing features of the head to tail EOD waveform suggests that these species may recognise and discriminate each other on the basis of both frequency and temporal components of the electrocommunication carrier(Crampton et al., 2008). Finally, seasonal control of EOD waveform by environmental and hormonal factors may result in carrier modulation and thus result in gender and dominance signs and/or signals (Bass and Hopkins, 1983; Hopkins et al.,1990; Silva et al.,2002).

Species specificity of the EOD is provided by the evolution of different electromotor control mechanisms and effectors responsible for this control(Bennett and Grundfest, 1959; Bennett, 1971; Bass, 1986; Caputi, 1999; Caputi et al., 2005). While the EOD waveform of African electric fish (Mormyridae) is characteristic of the responses of a homogeneous population of synchronously activated electrogenic units (Hopkins,1999), American electric fish (Gymnotiforms) show a combination of strategies yielding more complex EOD waveforms. Gymnotiforms exhibit a relatively long EO, located in the ventral part of the body from the anal pore to the tip of the tail, covering about 90% of the fish's body length. These EOs can be myogenic or neurogenic, depending on the species. Myogenic organs are composed of longitudinal tubes of connective tissue in which the electrogenic units are aligned in an orderly manner, much like the batteries in a hand flash light (torch) (Bennett and Grundfest, 1959; Couceiro and De Almeida, 1961; Trujillo-Cenóz et al.,1984; Trujillo-Cenóz and Echague, 1989). Each of these electrogenic units (known as electrocytes) is a muscle-derived syncitium, which has lost its contractile machinery but has developed the ability to generate species-specific electrical responses (Bennett,1971; Zakon et al.,2008). In the species with myogenic organs, the EOD can take the form of a sequence of brief pulses separated by silent intervals 4–100 times longer than the duration of the pulse (pulse-emitting fish) or by intervals similar in duration to the pulse (wave-emitting fish). Neurogenic organs, however, are composed of the axons of spinal electromotoneurons, which run longitudinally and are packed in an orderly manner along extended portions of the fish body (Bennett,1971). All known species having neurogenic organs are wave-emitting fish.

In most gymnotid pulse species, the intrinsic properties, the innervation and the activation time of the electrocytes are dependent on electrocyte location (Caputi et al., 1989; Caputi et al., 1994). Thus,the EODs of pulse-emitting species can be likened to complex motor acts characterised by fixed spatio-temporal patterns of electromotive forces. Their comparative analysis may be a useful window for identifying traits in their evolution. We have postulated that waveform diversity arises from either: (a)variations in the intrinsic properties or innervation patterns of the electrocytes; (b) variations in the activation timing of different regions of the EO and the rostral and caudal faces of the individual electrocytes; or (c)the additional occurrence of neurogenic electrogenesis. We also suggested that the `labile links' in the determination of waveform evolution will be related to diversity of this sort in the mechanisms underlying electrogenesis(Rodríguez-Cattáneo et al.,2008).

The most widely accepted hypothesis on waveform generation for pulse gymnotids states that two types of components can be distinguished according to their generation mechanism (Bennett,1971; Caputi et al.,2005).

The first type, direct neurally driven components (V₁,V₂ and V₃ in G. omarorum) originate as the sum of electrocyte responses to a synchronised neural volley that synaptically activates a set of similarly oriented membrane patches. This causes first a synaptic depolarisation of the innervated faces and, potentially, the subsequent firing of a spike in the post-synaptic electrocyte. For example, in G. omarorum, V₁ originates from the sum of post-synaptic potentials generated at the rostral faces of the abdominal electrocytes;V₂ originates from the sum of action potentials generated at the rostral faces of the electrocytes in the mid-body (central) region; and V₃ originates from the sum of action potentials generated at the caudal faces of the electrocytes all along the fish's body(Macadar et al., 1989; Caputi et al., 1989).

The second type of component contributing to the EOD waveform, referred to here as indirectly driven components, is a consequence of the electrocyte membrane activation by longitudinal currents flowing along the EO. The action currents associated with the spikes generating V₃ flow along the EO stimulating the opposite membranes of the electrocyte and passing through the EO as a whole triggering a second spike, which in turn gives rise to V₄ (Bennett and Grundfest,1959; Macadar et al.,1989; Caputi et al.,1989). A similar process gives rise to V₅ in other fish. The electrocytes of G. omarorum have a complex repertoire of channels that are differently distributed in the rostral and caudal faces of the electrocytes (Sierra et al.,2005; Sierra et al.,2007) and this repertoire thus shapes the contribution of each individual electrocyte to the EOD. The longitudinal flow of current is not a local process restricted to a single electrocyte but rather it is a process dependent on the ability of the EO to funnel (and therefore to summate) the currents generated by the neighbouring electrocytes(Albe-Fessard and Buser, 1950). This mechanism, besides depending on excitability, depends also on inter-electrocyte distance and on the space constant of each tube, which in turn depends on the resistances of the connective sheath and the jelly tissue in between the electrocytes.

Thus, the ability of the EO as a whole to generate new components as described above can be altered by the presence of an external load. The electromotive force (EMF) of the equivalent source for the indirectly driven components is highly dependent on the load resistance and consequently is not linear. This is the case of the mormyrid Gnathonemus petersii(Bell et al., 1976) and the gymnotid Brachyhypopomus pinnicaudatus(Caputi et al., 1998).

In this article we describe an example of waveform divergence in two parapatric taxonomic units of Gymnotus spp. endemic to neighbouring regions of Latin America: Gymnotus omarorum (from the south of Uruguay) and Gymnotus sp. (from the west of Rio Grande do Sul,Paraguay and north-eastern Argentina). We found that the waveform differences are mainly determined by the responsiveness of the EO to its previous activity(auto-excitability).

Forty specimens of Gymnotus omarorum(Richer de Forges et al.,2009) and twenty specimens of a still undescribed species Gymnotus sp. were utilised in this study. Both kinds of fish are called `morena' in the local fisherman's jargon. Gymnotus sp. were bought from local dealers in La Paz, Argentina (in March 2008 and 2009) and were presumably recently caught in the affluent of the Paraná River near the border between Paraguay and Argentina. Gymnotus omarorum was captured by the authors in the Laguna del Cisne, Uruguay, in all four seasons of the year from March 2008 to April 2009. In this study, all potentially harmful procedures were conducted under anaesthesia, following IIBCE's regulations for the use of experimental animals and the guidelines of the Comisión Honoraria de Experimentación Animal of the Universidad de la República (CHEA), and the Society for Neuroscience.

The structure of the EO and the distribution of the thin nerve bundles, as well as the arrangement of the electromotor nerve terminals on the surface of the electrocytes, were studied using silver impregnated samples.

Fish were decapitated under deep terminal anaesthesia (MS222 250 mg l^–1, until gilling movements and the EOD ceased). After a combined fixation and decalcification step by immersion in De Castro's solution [formulae in Ramón y Cajal and De Castro(Ramón y Cajal and De Castro,1933)], portions of the fish were silver impregnated by immersion in AgNO₃, 1.5%, for 7 days at 37°C, and this was subsequently reduced in formaldehyde-hydroquinone. We studied: (a) the abdominal walls; (b)a portion of the mid-body region about 50% along the length of the fish body;and (c) a portion of the tail (caudal 10%). Tissues were embedded in a soft mixture of epoxy resin and sectioned using a sliding microtome (30 μm thick) either frontally or parasagitally. Sections were explored under the light microscope, and digital images were made using different optical and CCD resolutions.

Head to tail electric fields produced by the EOD were recorded with the fish resting in the middle of a net pen running between the centres of the short walls (28 cm) of a plastic tank (48×28 cm, filled with water up to 4 cm depth, conductivity 30 μs cm^–1, temperature 24°C). The back and forth movements of the fish were minimised using stitches to adjust the net to the shape of the body. The longitudinal head to tail EOD (htEOD) fields, recorded using two stainless steel electrodes, placed on the middle of each of the short walls of the tank, one facing the head and the other facing the tail. Voltage between the electrodes was measured using a high-input impedance, high-gain, differential amplifier (10–20 kHz band-pass filter, floating ground). Recorded waveforms were sampled(25–50 kHz, depending on the number of channels recorded, 16 bits) and displayed on a computer screen.

Like the htEOD recorded in water, the htEOD recorded in air is a holistic estimate that lacks the necessary spatio-temporal dimensions to describe the electrogenic source in gymnotids. This is because different portions of the fish body emit regional EODs with different waveforms. In these fish the EOs are extended, non-homogeneous structures in which different regions generate different waveforms and, in the case of the wave components generated by non-innervated faces of electrocytes, the voltage vs current plot frequently yields a non-linear relationship, and the EMF is load dependent(Bell et al., 1976; Caputi et al., 1998). Therefore, we used complementary methods to explore spatial waveform pattern of the EOD and the auto-excitability of the EO.

For multiple air gap exploration(Caputi et al., 1993), fish were suspended in air using a custom made electrode array consisting of seven parallel wires perpendicular to the main axis of the body, placed in contact with the skin, one at each extreme of the fish and the others at the limits of the explored regions. Seven regions of the fish body were considered: the head, the abdomen and five consecutive caudal portions (each one equivalent to one-seventh of the fish's length). Voltages recorded between consecutive pairs of wires were amplified to reach adequate amplitude for similar quantization(always larger than 8 bits) and sampled at 25 kHz. In the air gap condition,there was no load, so voltage recordings were considered to be good estimators of the equivalent EMFs generated by different portions of the fish's body. However, this was not the case for all wave components because the equivalent sources of some indirectly neurally driven components are not linear.

The objective of curarisation was to show the similarity of the EOD remnant when the electromotor drive diminishes under the synaptic threshold for eliciting the contribution of electrocyte action potentials to the EOD. This is a necessary condition to verify that the mechanisms involved in the generation of V₁, V₂ and V₃ are similar in both species and that the main differences are in the mechanism underlying V₄. Curarisation allowed us to compare the remnants of the EOD wave components when they achieve a stabilised waveform in which V₄ and V₅ are absent. We used a slow-acting, long-lasting, nicotinic antagonist (d-tubocurarine) to block the electrocyte's end plates in a competitive and progressive way. As it is known from previous studies(Caputi et al., 1989; Caputi et al., 1994; Caputi et al., 1998; Caputi and Aguilera, 1996),the effect of d-tubocurarine occurs in two phases. During the first phase, the EOD become initially disorganised, showing a decay in amplitude and an increase in duration of the components. At the acme of disorganisation phase bursts of supernumerary wavelets following the main EOD are frequently observed. If curare concentration is enough this disorganisation phase is followed by a stable phase where the EOD remnant becomes a new stereotyped waveform that decays in amplitude until all post-synaptic activity is blocked. At this stabilised partial curarisation stage, each of these remnants reflect the sub-threshold post-synaptic activity in which timing, shape, amplitude and spatial origin along the fish body are characteristics of the species.

In three individuals of each taxon we compared the regional EOD in the intact fish with that resulting from partial curarisation at the stable phase(0.5 μg g^–1 of d-tubocurarine, i.m.). Fish tolerated this dose without stopping breathing or modifying their EOD rate but showed large changes in their EODs. We compared recordings, obtained from three portions of the fish (1 or 2 cm long depending on the experiment) located in the abdominal region (between the anal papilla and the origin of the anal fin), at the central region (about the centre of the fish length) and at the tail region(at the most caudal possible portion).

We employed the method described by Bell et al.(Bell et al., 1976) to explore the efficacy of the longitudinal currents generating V₃ for eliciting V₄ at the tail region. This method consists of splitting the load into two parallel `one way' paths of opposite direction using Germanium diodes. While one diode allows the current generating V₃(I₃) to flow through an externally controlled resistive path and blocks the current generating V₄ (I₄),the other diode allows the circulation of I₄ through another externally controlled path, blocking I₃. It is important to note that when the absolute values of peak voltages are lower than the cut-off threshold of the diodes (300 mV) current does not circulate in any direction. However, when the absolute values of peak voltages are larger than the diode threshold, they are controlled by the external load. We used an 11-position step switch to modify an external load connected in series with a diode oriented in such a way that allowed only the flow of I₃ (R2, Fig. 8A). Thus, for a given position of the step switch we clamped the peak value of I₃. For each of the 11 positions of the switch (i.e. for each value of I₃) we explored the voltage–current relationship of V₄ by varying the resistance of a rheostat connected in series with the second diode (R1, Fig. 8A). At the end of this series of experiments, we obtained 11 characteristic curves, one for each position of the switch. Because we found that voltage current was well fitted by a linear decreasing function (see Results) we were able to estimate the EMF generating V₄ (EMF₄) for each clamped value of I₃. In order to compare results from fish of different sizes, we constructed an index of EO auto-excitability defined as the ordinate value of the relative EMF₄. This is equivalent to the quotient between minimum EMF₄ (for very large load resistances, near open circuit) and the maximum EMF₄ (for very low load resistance, near short circuit).

The specimens of G. omarorum and Gymnotus sp. were very similar in their external morphology. Their EOD waveform recorded head to tail in water (24–26°C, 20–50 μS cm^–1),although similar, showed the following differences: (a) while the EOD waveform of G. omarorum exhibited four components [V₁ to V₄ in Fig. 1A(Trujillo-Cenóz et al.,1984)], that of Gymnotus sp. exhibited five, adding a late smooth positive component (V₁ to V₅ in Fig. 1B); (b) the relative peak of V₄ is larger in Gymnotus sp.(V₄/V₃ ratios were 0.463+0.033 and 0.854+0.039, mean and standard deviation for G. omarorum and Gymnotus sp.,respectively, Wilcoxon test P<0.001); and (c) the width of V₄ in G. omarorum is longer than in Gymnotus sp.:the point at which the waveform crosses a threshold set parallel to the abscissa at 20% of the peak ranged from 0.6 to 0.89 ms for G. omarorum and from 0.34 to 0.56 ms for Gymnotus sp. (Wilcoxon test P<0.001). These differences cause an increase in the relative power at higher frequencies in Gymnotus sp.(Fig. 1C, light grey power spectrum).

In the air gap recordings, current amplitude and voltage amplitude of the directly neurally driven wave components changed in opposite directions according to a decaying linear relationship when different external loads were applied (Fig. 2). The voltages vs current plots were referred to as the characteristic function of the source (Fig. 2). The parameters of these functions allowed us to estimate the EMFs as the ordinate intersections and the internal resistances as the slopes(Cox and Coates, 1938; Bell et al., 1976; Caputi et al., 1989).

We did not find any significant differences in the EMF between the two taxa[V₁: 31±5 mV and 26±6 mV; V₂:175±35 mV and 176±44 mV; V₃: 2.78±0.43 V and 2.63±0.33 V; mean and standard deviation for G. omarorum(N=18) and Gymnotus sp. (N=15), respectively,Mann–Whitney U-test P>0.99 in all cases].

Internal resistance decreases with total length due to a scaling effect. Length-normalised resistance, expressed in resistivity units, was calculated as the product of the internal resistance times the total fish length [for fundamentals, see Caputi and Budelli(Caputi and Budelli, 1995)]. These internal resistance indexes were similar in both species(1289±649 kΩ cm for G. omarorum, N=18, and 1349±547 kΩ cm for Gymnotus sp., N=15;Mann–Whitney U-test, P=0.47).

In Gymnotus sp. (14 out of 15 specimens), V₄ (voltage) vs I₄ (current) plots were well fitted by a straight line(Fig. 3A, in all specimens R²>0.99; N always >170). Interestingly, the internal resistance calculated for V₄ was always smaller than the internal resistance calculated for V₃ in the same fish (Wilcoxon test, P<0.01, N=14, note the difference in slope compared with V₃, Fig. 3A). Linearity observed was maintained when the same specimens were recorded again after five months of captivity in the lab (N=2). The V₅(voltage) vs I₅ (current) plot showed always non-linear concave relationship resembling a parabola(Fig. 3A).

In G. omarorum V₄ (voltage) vs I₄(current) plots showed in most cases a non-linear relationship. The slope of the characteristic function became less steep with the increase of load resistance and in some cases became flat or even inverted for very large resistances (Fig. 3B). In such cases the characteristic function resembled a parabola with a maximum.

Consistently, with these differences, the ratio between V₄ and V₃ (in both species) and between V₅ and V₃(in Gymnotus sp.) always decreased as a function of the external load. The range of this ratio and the slope of the function were different for both species (Fig. 3C). This indicates that external load was an important factor for determining waveform,shape and amplitude of V₄ in G. omarorum and also had some influence on V₄ and V₅ in Gymnotus sp. This non-linearity exhibited by V₄ in G. omarorum and the presence of V₅, which is also non-linear, in Gymnotus sp. indicate that waveform differences are related to the mechanisms involved in the generation of non-neurally driven components.

Based on earlier studies (Bennett and Grundfest, 1959; Macadar et al., 1989) showing that in G. carapo and G. omarorum V₄ is generated by the activation of the rostral faces of the electocytes by the action currents generating V₃, we interpreted that the differences between the two studied taxa could be explained by differences in the auto-excitability of the EO and conducted the following experiments to test this hypothesis. First, we showed that V₁, V₂ and V₃ and the EOs were indistinguishable when comparing the two populations under the scope of three different techniques: histological analysis of silver impregnated samples,multiple air gap and multiple air gap under curare. Second, we showed that the amplitude and duration of the late components are functions of the longitudinal currents associated with V₃ (I₃). Whereas in G. omarorum the manipulation of I₃causes a large effect on EMF₄, in Gymnotus sp. it causes a very small effect.

Three different techniques allowed us to show similarities between the innervation patterns of EOs and the early components (V₁ to V₃) of the EOD waveform: (a) histological analysis of silver impregnated tissue samples revealed that the EOs show similar structures and innervation patterns in both species; (b) multiple air gap recordings show that EMF patterns mainly differ in the amplitude and shape of the late wave components (V₄ and V₅); and (c) curarisation allowed us to show the similarity between both taxa when the remnants of the EOD achieved a stabilised waveform in which V₄ and V₅ were absent(see Materials and methods). Figs 4, 5, 6 show only small differences between both taxa in the innervation patterns, the corresponding regional waveforms and their remnants obtained from the same specimen after partial curarisation.

Transverse sections of the abdominal region show that in both species the EO is composed of four tubes (two on each side) located in the abdominal wall. In G. omarorum these tubes are composed of cuboidal electrocytes lying on a single surface parallel to the skin. In Gymnotus sp. these tubes have a triangular section. They are arranged in such a way that the lateral faces of lateral electrocytes have a topological arrangement in regard to the peritoneum, and the inferior faces of medial electrocytes lie against the skin (schemata Fig. 4A). Lateral electrocytes are doubly (rostral and caudally) innervated whereas the medial ones are innervated only on the caudal face(Fig. 4A–D). This similarity between anatomies is well matched with the similar waveforms of the abdominal EOD: a smooth V₁ to V₃ pattern is present in both intact and curarised animals. This V₁ to V₃ pattern is followed in the intact animals by a small V₄. In curarised animals the EODs are relatively much smaller and less sharp. V₃ is smaller because the synaptic potential, as indicated by V₁, which is smaller due to curare, and the smaller synaptic potentials do not evoke action potentials on the innervated faces reliably. In addition, V₁is a long-lasting wave and V₃ occurs during the final portion of V₁ (Fig. 4E).

In the central region of fish of the two taxa, the EOs are composed of eight tubes (four on each side). They are located on parasagittal planes on either side of the midline. Dorsal electrocytes are larger and extend laterally, partially covering the external face of the electrocyte located below. They are doubly (rostral and caudally) innervated while the others are innervated only caudally (Fig. 5A,B for G. omarorum and Gymnotus sp.). Consistently with the presence of doubly innervation, a sharp polyphasic complex was generated at this region in both species. However, while V₂ and V₃ were un-distinguishable both in intact and curarised animals, the amplitudes of V₄ were always larger in the intact specimens of Gymnotus sp. than in G. omarorum(Fig. 5C,D). Once again V₂ and V₃ were reduced while V₄ was abolished in G. omarorum. In Gymnotus sp., a small remnant was observed in one of the experiments. This result may be explained either by the presence of late activated weak synapses on rostral faces of the doubly innervated electrocytes or more likely by a similar mechanism as the second negative peak observed at the abdominal region (because the apparent remnant of V₃ is shorter and smaller than in G. omarorum).

In the caudal region of both taxa the EOs are also composed of eight tubes,four on either side of the midline. Electrocyte density increases markedly in the caudal direction and near the tip of the tail they are very densely packed. Electrocytes are caudally innervated(Fig. 6A,B parasagittal sections) and a large posterior electromotor nerve running rostro-caudally is clearly visible (labelled as PEN in Fig. 6B). The regional EOD is consistent with this innervation pattern(Fig. 6C,D). As before,V₃ is reduced and V₄ is abolished with curare. They are preceded by a small biphasic deflection that corresponds to the activity of the posterior electromotor nerve(Trujillo-Cenóz and Echague,1989; Caputi et al.,1989).

Quantitative analysis of the spatio-temporal pattern in the multiple-air-gap shows similar EOD waveforms in both taxa. The spatio-temporal patterns show that V₁ is generated abdominally, V₂ is generated in the central regions (gaps 2–6), V₃ is generated all along the body and V₄ and V₅ are mainly generated in the caudal two-sevenths of the body (waveforms were normalised to the positive peak in Fig. 7A,B). The regional waveforms (Fig. 7A,B),the absolute amplitudes of each wave component at every portion(Fig. 7C and D), and the ratios V₄/V₃ (Fig. 7E) all show that the main differences between species occur in the indirectly driven components. In central and caudal regions V₄is larger and briefer in Gymnotus sp., consequently the ratios V₄/V₃ are also larger. V₅ is only present in the caudal regions in Gymnotus sp. but not in G. omarorum. No differences between taxa were found in the relative timings of V₃ along the EO (Fig. 7F).

Both head to tail recordings and the anatomo-functional analysis made in the previous sections suggest that the main differences between the EOD waveforms are caused by differences in auto-excitability. To test this hypothesis we used a differential loading method to quantify the efficacy of longitudinal currents generating V₃ (referred to as I₃) for exciting the rostral faces and thus eliciting V₄ (see Materials and methods). We used the same air gap recording apparatus connected in a different mode to explore the generation of V₄ either when the external load was constant or where we clamped the value of V₃ by using different loads for V₃ and V₄. Diodes split the circuit into two parallel `one way' paths of opposite direction (Fig. 8A). When the absolute value of the generated voltage was lower than the thresholds of the Germanium diodes (300 mV), current was minimal. When voltage exceeded 300 mV, current was directed to only one of the paths.

When the head to tail drop of voltage was positive the current I₃ flowed through resistor R2 in series with one of the diodes. When the head to tail drop of voltage was negative the current I₄ flowed through resistor R1 in series with the other diode. This network allowed us to clamp the peak of I₃ at a chosen value by setting the value of resistor R2. We set the value of R2(and consequently clamped the peak current of I₃, max I₃, Fig. 8B) at several values in each of the studied fish (typically from 6 in the field to 11 in the lab). With I₃ clamped, we then constructed a plot of V₄vs I₄ (referred to as the characteristic function plot) by gradually varying the value of the load rheostat R1. As shown in Fig. 8B, the current–voltage plots were superimposed following a slope equal to R2 in the positive–positive quadrant. For negative values of the two variables, the traces followed different slopes as R1 was changed. For each one of the chosen R2 values we constructed a plot of the peak values of V₄vs the peak values of I₄. These plots correspond to the envelopes of the brown and violet graphs of Fig. 8B. We found for all R2 values that this envelope was a line of equal slope but which intersected the ordinate at different values (Fig. 8B and Fig. 9A,B). Thus, non-linearity observed in the simple air gap was a consequence of an increase in EMF₄ due to the increase in the stimulus intensity(I₃). In G. omarorum the ordinate intersection(i.e. the equivalent EMF, EMF₄) increased as a function of the amplitude of I₃ (Fig. 9A,C). This was also true for Gymnotus sp. although the change in electromotive was much smaller and sometimes null(Fig. 9B,C).

EMF₄ data normalised to their maxima were plotted vsnormalised I₃. We compared the relationship exhibited by Gymnotus sp. (Fig. 10A) with the relationships exhibited by G. omarorumgathered at three different seasons (autumn, early spring and late spring, Fig. 10B–D). The auto-excitability may be measured in these plots as the ratio between the minimal EMF measured in open circuit and maximal EMF measured at closed circuit. This auto-excitability index is equivalent to the(I₃=0, R2→∞). The histograms of the auto-excitability indexes show very different shapes: it is unimodal and exhibits small dispersion in Gymnotus sp. and is bimodal and exhibits large dispersion in G. omarorum(Fig. 10E). We found a large difference between medians and dispersion of auto-excitability index between the two taxa (Wilcoxon test, P<0.001; auto-excitability index range: 0.8–1 for Gymnotus sp. and 0.3–0.85 for G. omarorum).

Cumulative frequency plots also show these differences between the two taxa and the similarity between the populations of G. omarorum gathered and studied at different seasons just after capture or in captivity. Two comparisons were performed: (a) fish studied 24–48 h after capture(black symbols, Fig. 10F) with fish under captivity for more than three months (grey symbols, Fig. 10F, Wilcoxon test, P>0.95); and (b) the freshly gathered fish population according to the season of gathering (autumn=circles, spring=squares and late spring=triangles, Fig. 10F,Kruskal–Wallis test P>0.95). Two specimens of Gymnotus sp. were studied twice, immediately after being bought from local dealers in Argentina and after five months in captivity at the lab. Results of both measurements were very similar.

The present study compares two taxonomic units, which may be confused at first sight as members of the same taxon. Indeed, the local names for these fish are `morena' in both Argentine Mesopotamia and Uruguay. However, we found that the electric field and the generation mechanisms of the EOD of animals bought in La Paz, Argentina, have phenotypic traits that make it possible to differentiate them from animals captured in Laguna del Cisne, Uruguay. In addition, parallel research (W. G. R. Crampton and J. S. Albert, personal communication) indicates that these populations may represent different taxa. The population found in Uruguay, previously identified as G. carapo,is the best studied species of Gymnotus and may correspond to a new species, referred to as `omari' as a tribute to Omar Macadar and Omar Trujillo-Cenóz who pioneered research on these fish in Uruguay during the 1980s (Richer de Forges et al.,2009) [for reviews on electromotor and electrosensory systems of this taxon, see Caputi (Caputi,1999) and Caputi et al.(Caputi et al., 2008)]. The population found in Argentina (and also reported in the south of Brazil and Paraguay) may also correspond to a new species, Gymnotus sp.

The main difference between EOD waveforms recorded head to tail in water appears in the late components (V₄ in G. omarorum and V₄ and V₅ in Gymnotus sp.). These differences determine the shift of the power spectrum to a higher frequency range. Previous evidence indicates that V₄ in G. omarorum is generated by the indirect activation of the membranes of the rostral faces of the electrocytes. Intracellular recordings obtained from in vitropreparations of the EO show that action currents generated by the activation of caudal faces triggered the generation of action potentials on the rostral faces (Bennett, 1971; Macadar et al., 1989; Lorenzo et al., 1988; Sierra, 2007) but not on the lateral faces (Sierra, 2007; Markham and Stoddard, 2005). Net action currents generated by the delayed activation of the rostral faces flow from caudal to rostral through the muscle and other non-excitable tissues of the fish, as well as through the surrounding water, and contribute to V₄.

The following evidence indicates that the differences in EOD waveform reported here result from differences in the EO auto-excitability in the two taxa.

Firstly, we did not found major differences in the early components of the EOD waveforms of G. omarorum and Gymnotus sp. either in the intact or curarised specimens. Moreover, curarisation experiments showed that V₄ and V₅ in Gymnotus sp. and V₄ in G.omarorum (Caputi et al., 1989) were abolished at the tail region. This result has been observed in other gymnotids such as B. pinnicaudatus(Caputi et al., 1998), and Rhamphychthys rostratus (Caputi et al., 1994) at the tail region where only caudally innervated electrocytes occur. Curare diminishes the synaptic potentials and thus the likelihood and synchronism of action potentials on the innervated face. This causes a smooth reduction of the V₁, a wave component generated at synaptic potentials, but disorganisation of the sharp complex including V₂, V₃, V₄ and V₅ generated by action currents. When curarisation reaches the stabilised stage the amplitude decays gradually without changes in waveform because the EOD remnant corresponds to sub-threshold synaptic potentials. Thus, the similarity of profiles at this stabilised stage of partial curarisation suggests that the neural activation volleys are similar in both species.

A second indication that the differences in EOD waveform result from differences in auto-excitability comes from the sensitivity of late wave components to load. In the case of the directly neurally driven components(V₂ and V₃), modelling based on linear sources accurately represents the data obtained in the simple air gap experiments. However, in the case of indirectly neurally driven components (V₄and V₅) EMFs were load dependent. The auto-excitability hypothesis also predicts the increase in duration and the relative amplitude decrease of V₄ and V₅ observed in the recordings in air. Because the relative changes in peak amplitude are larger than changes in the overall area of the EOD waveform, this suggests that the main difference between the two taxonomic units is a different degree of synchrony in the activation of the rostral faces. These findings indicate that the EMF₄ depends on the current associated with V₃. This dependence is more marked in G. omarorum and does not vary with either seasonal conditions or time in captivity.

The third and strongest evidence that the differences in EOD waveform results from differences in auto-excitability was obtained by using the technique of differential loading. We showed that when the current associated with V₃ was clamped at a given value (I₃), the data points of the characteristic plot for V₄ were well fitted by a line whose ordinate (or electromotive force, EMF4) depended on the clamped value of I₃. This procedure demonstrates a cause–effect relationship between the process generating V₃and the process generating V₄ and confirms the hypothesis of a generation mechanism based on the auto-excitability of the EO. Due to the smaller value of V₅ and the threshold of 0.3 mV characteristic of Germanium diodes, we were unable to make the same analysis in the case of V₅. Nevertheless, its similar behaviour in the simple air gap suggests that this component is also generated by an auto-excitation mechanism.

The differential loading technique also allowed us to quantify the auto-excitability of the EO using an index that is easy to obtain in the intact fish and therefore a powerful tool for comparing auto-excitability within and between fish populations. Index comparison clearly showed that the differences in waveforms between Gymnotus sp. and G. omarorum reflect the differences in the auto-excitability of their EO. Interestingly, G. omarorum has a wide range of auto-excitability that marginally overlaps with that of Gymnotus sp., showing either a genetic heterogeneity or a local environmental factor affecting genotypic expression. Moreover, the similar distribution of auto-excitability indexes of G. omarorum when comparing fish in captivity vs freshly caught fish or fish gathered in different seasons indicate that wide dispersion is a characteristic of the taxon.

Although this study was not designed to discriminate the contributions of the different factors involved in auto-excitability, our data suggest that the ion channel repertoire, either in the electrocyte membrane or in the connective tissue tubes that encase them, may be the most important element in the taxonomic units that are compared.

We conclude that the differences in the EOD phenotype of the two studied taxa are due to the different expression of a genetic repertoire of voltage-dependent conductances in the rostal electrocyte membranes and/or leakage conductances in the connective sheath encasing the electrocytes. Regardless the possibility of a parapatric speciation process, the observed EOD waveform diversity may be useful for avoiding hybridisation along the borders of neighbouring geographic ranges and for reinforcing pre-existing differences.