AM is a postgraduate student (PEDECIBA, Uruguay) whose thesis is being advised by AAC and RB. AAC and RB conceived and designed the experiments, and contributed reagents/materials/analysis tools. AM performed the experiments. AM, AAC, and RB analyzed the data and wrote the paper.
The authors have declared that no competing interests exist.
Electroreceptive fish detect nearby objects by processing the information contained in the pattern of electric currents through the skin. The distribution of local transepidermal voltage or current density on the sensory surface of the fish's skin is the electric image of the surrounding environment. This article reports a model study of the quantitative effect of the conductance of the internal tissues and the skin on electric image generation in
This paper analyzes the contribution of the body and skin conductance of weakly electric fish in shaping the electric image, using a realistic computational model.
Object recognition, a relevant issue in sensory systems, is not yet fully understood. How pre-receptor mechanisms and interactions between objects shape images is of interest in all sensory systems, leading to general concepts and a specialized jargon. The authors rescue the generality of two concepts for understanding sensory systems. These concepts were introduced early in electroreception research: object perturbed field (change in the basal field generated by the presence of an object), and imprimence (equivalent sources produced at the location of the object). The fish body is an object: generating its imprimence, modifying the basal field, and interacting with other objects. Analogously, the human body interferes, reflecting light or sound in the generation of visual and acoustic images.
The contribution of internal and skin conductivities in image generation has been controversial since the seminal work of Lissmann and Machin in 1958. We show that the high internal conductance of the fish increases and redirects the currents that illuminate objects, increasing and shaping the electric image. Skin resistance mainly influences image magnitude.
Electroreceptive fish detect nearby objects by processing the information contained in the pattern of electric currents through the skin. In weakly electric fish, these currents result from a self-generated field, produced by the electric organ discharge (EOD). Local transepidermal voltage or current density is the effective stimulus for electroreceptors. The distribution of voltage or current on the sensory surface of the fish's skin is the electric image of the surrounding environment [
Theoretical analysis of image generation has yielded realistic models that predict with acceptable accuracy the electrosensory stimulus [
Experimental studies in pulse gymnotids have confirmed theoretical predictions, showing that the high conductivity of the fish body funnels the self-generated current to the perioral region, where an electrosensory fovea has been described on the basis of electroreceptor density, variety, and central representation [
This article describes a realistic modelling study of the effect of the internal and skin conductance on electric image generation in
We generalize two concepts: “object perturbing field” and “imprimence,” introduced early in electroreception research [
Electric fields and images generated by metal objects were described in previous reports (reviewed by [
(A) The coloured background represents the difference in voltage between each point surrounding the fish and an infinitely distant point, using a non-linear arctangent colour scale (used to highlight values close to zero) shown in the colour bar below for the basal field (in the absence of objects). The black line shows the zero equipotential surface, which is perpendicular to the axis of the EO equivalent dipole distribution.
(B) A similar coloured representation shows the perturbing field (i.e., the field in the presence of the object minus the basal field) produced by a metal cube (1 cm3) close to the skin (0.5 mm). The black line shows the zero equipotential surface, which is perpendicular to the axis of the object equivalent dipole distribution.
(C) Electric image of the metal object depicted in a colour map on the modelled realistic fish from a
(D) Electric image along the intersection of the skin with the sagittal plane, illustrating its “Mexican hat” profile.
To study the effect of the skin and internal conductances on the generation of the electric image, we departed from the situation proposed by Lissmann and Machin (1958), in which all fish tissues have the same conductivity as the water. Secondly, we studied the effect of changing internal conductivity, while maintaining a skin conductance that was very high and therefore of negligible effect. Thirdly, for an internal conductivity similar to that experimentally determined, we studied the effect of changing skin conductance as if it were uniform along the fish surface. Finally, we compared results obtained with homogeneous skin conductances and those obtained with the heterogeneous distribution of the skin conductances that is present in
We have proposed that the low resistivity of the fish body is a very important factor for the shaping of the electric image. To assess its contribution, we simulated electric images for fish having a high skin conductance but with different internal conductivities.
We first modelled a fish with an internal conductivity equal to that of the water, as assumed by Lissmann and Machin [
The black bars show the zero equipotential surfaces as in
(A) Basal field (in the absence of objects). (B) Perturbing field produced by the same scene as in
(C) Electric image of the metal object depicted in a colour map on the modelled transparent fish from a
(D) Electric image along the intersection of the skin with the sagittal plane.
Comparison of
(A) Electric image of a dipole placed at 0.5 mm from a “transparent” fish seen from a
(B) Same scene as (A) for fish with realistic internal conductivity.
(C) Electric image (transcutaneous current density) along the intersection of the skin with the sagittal plane (left), and the coronal plane (right), for the same dipole as in (A) and (B). Red traces show the images on a transparent fish, while blue traces correspond to a fish with realistic internal conductivity. Note that the ordinate for the realistic fish (left) is twice that for the transparent fish (right).
(A) Normalized electric images of the same metal cube (identical position) on fish with different internal conductivities. Red: 16.5 μScm−1 (the same as water conductivity), cyan: 165 μScm−1, blue: 1,650 μScm−1, black: 16,500 μScm−1 (normal conductivity), magenta: 165,000 μScm−1. The skin is modelled for all cases, with a homogeneous conductivity of 500,000 μScm−1. The dashed line shows the case of a fish with realistic internal conductivity and skin conductivity distribution. rl, realistic internal conductivity; rlh, realistic internal conductivity, heterogeneous skin distribution.
(B) Peak amplitude of the electric image of a metal cube (1 cm3) placed at 0.5 mm from the fish, as a function of body internal conductivity. The difference in the peak amplitude of the electric image corresponding to the realistic internal conductivity fish shown in this figure and that shown in
To assess the contribution of the skin to image formation, we studied the effect of different uniform skin conductances for a fish with normal internal conductivity. For very low skin conductivity, the transepithelial currents produced by the EO are negligible (
(A) Transcutaneous current density (electric image) of a metal cube (1cm3) placed at 0.5 mm from the skin, modelled on skin with different conductivities. Red: 10 μScm−2, cyan: 100 μScm−2 (similar to mormyromast epithelium), blue: 1,000 μScm−2, black: 10,000 μScm−2, magenta: 100,000 μScm−2. All these fish have an internal conductivity of 3,300 μScm−1. Dashed line shows the case of a fish with realistic internal conductivity and skin conductivity distribution.
(B) Transcutaneous voltage calculated from the transcutaneous current densities shown in (A), using the same colour code.
(C) Current peak (right axis, red trace) and voltage peak (left axis, blue trace) as a function of skin conductivity for fish with homogeneous skin.
(D) Normalized plot for (B), using same colour code. mel, mormyromast epithelium-like conductivity; rlh, realistic internal conductivity, heterogeneous skin distribution.
Animals extract information from the environment and from their own bodies by analyzing changes in the patterns of energy impinging on their sensory surfaces. In that sense, it can be affirmed that to see is to reconstruct visual scenes from a light pattern on the retina or to hear is to extract auditory scenes from sound patterns at the cochlea [
In electrosensory perception, each object generates a signal that results from the deformation that its presence causes in an electric field. This deformation is a virtual field, called “object perturbing field” by Lissmann and Machin [
The “imprimence” of an object, an expression also coined by Lissmann and Machin [
The imaging process consists of two steps: imprimence generation (yellow boxes in
First row, generation of stimulation in the presence of the object; second row, basal stimulation in the absence of objects; third row, sensory image.
(A) Fish with water-like internal conductivity. Imprimence generation (yellow boxes) precedes image generation (purple boxes). A field perturbation (green arrows) is induced as a consequence of the object interaction with the basal field (dark-blue arrows). The electric image is the difference between the perturbing (light-blue arrow) and the basal fields at the skin.
(B) Fish with realistic internal conductivity. The interaction of the body with the field perturbed by the object (red arrows) introduces another component (orange arrow) to the electrosensory stimulus (magenta arrow). The electric image (yellow arrow) is the electrosensory stimulus minus the basal field (blue arrow, representing the sum of the effects of the fish body and the object in the presence of each other). (See Discussion for explanation.)
However, in nature, the basal field is different from that produced by the EO in a homogeneous medium, because it is affected by the inextricable presence of the fish body. Similarly, the object perturbing field is also affected by the fish's body. This interaction (red arrows) produces two extra components that add to the basal electrosensory stimulus (dark-blue arrow): the perturbing field of the object (green arrow) and the perturbing field of the fish body (orange arrow). This resulting field acting on the skin is the electrosensory stimulus (magenta arrow). To calculate the electric image, we subtracted the effect of the basal stimulus (fish body alone, blue arrow). Thus, the electric image (yellow arrow) results from the addition of the perturbing field of the fish's body in the presence of the object (orange arrow) plus the perturbing field of the object in the presence of the fish's body (green arrow). When the object is large enough and surrounds the fish, its effect becomes very important, having a strong influence on the overall pattern of current flow. This is the case when the fish chooses to stay in confined spaces that are frequently its preference in the natural habitat, or in the tube-shaped shelters commonly used in captivity. The fish's positioning of its body in this manner strongly affects the electric images of objects and electrosensory responses [
When the object is relatively small or far from the fish body, the loop between the object and the fish body opens, because the influence of the field of the object on the fish body becomes negligible compared to the basal field. Consequently, the scheme of image generation is the same as in the case of the transparent fish. However, the basal field illuminating the object is different than that in the case of a transparent fish and so is the image.
The skin conductance is the other important factor shaping the electric image. A homogeneous decrease of the skin conductance causes: a) a decrease of the transepithelial current density, b) an increase of the transepithelial voltage up to a maximum at the range of natural skin conductivity, c) a decrease of the relative slope of the flanks of the image, and d) an increase of the centre region of the “Mexican hat” profile.
For measuring electrosensory stimulus, either local field (equivalent to current flow) or transcutaneous voltage has often been used indiscriminately [
Our study also shows a consistent decrease in the relative slope of the flanks of the image and an increase in the centre region of the “Mexican hat” profile with increasing skin resistance (see
Object recognition is an important issue in all sensory systems (including electrical perception), but it is not well understood. The comparative study of different sensory systems leads to general concepts and a language that could potentially be shared by researchers in different systems. In this paper, we focus on peripheral imaging mechanisms, a subject common to sensory systems. We focus in particular on the way in which pre-receptor mechanisms and interactions between different objects in a given scene shape the image.
We emphasize two concepts that were introduced early on in electroreception research [
The imprimence produced by the animal's own body acts as a pre-receptor mechanism. The fish body can be considered as an object that interacts with other objects in the scene, generating an imprimence that through the perturbing field modifies the basal field of the scene and, consequently, the imprimence of the other objects. Many species of fish (including Mormyrids) hear underwater due to the imprimence produced by air-filled sacs such as the swimbladder [
Animal senses explore nature using a limited number of types of energy and receptors with limited dynamic ranges. This constrains and conditions the representation of external reality according to the capabilities of each animal. Humans circumvent these limitations by creating artificial systems, such as radar or sonar, which expand the repertoire of representable qualities of objects. The concepts of imprimence and perturbing field may be applied to the design of artificial sensory systems. It is a common practice to deal with interactions between objects and the perturbations of the fields by the imprimences of other objects as undesirable interference. Nevertheless, evolution has developed neural operations that use images resulting from object interferences as a source of information, in some cases using this to infer object attributes. In these cases, interference between objects may increase the amount of available information contained in the image. Development of the theory of peripheral imaging is a necessary step for the design of computational procedures, allowing the extraction of a larger amount of information from the same signals.
The electric image of an object results from the projection on the skin of a virtual field caused by the presence of an object, in a given electrosensory scene.
The fish's large internal conductance (compared with water) causes a rostral funnelling of the current. This leads to an increase in the imprimence of objects close to the rostral regions of the fish and, consequently, to an increase in the amplitude of their images.
The large difference in conductivity between the inside and outside of the fish forces the field to be almost perpendicular to the sensory surface and, consequently, makes the shape of the image more symmetrical.
An object modifies the field of other objects immersed in the same global field. The fish body itself is a major object, inherent to the process of image generation. Thus, a global field results from the reciprocal interaction between the fish body and nearby objects.
The conductance of the skin changes the shape of the image only slightly, but drives the amplitude (considered as the distribution of transepithelial voltages) close to its maximum, for a given set of other electrical parameters. This result suggests that the high resistance of the mormyromast surface, a property conferred by a thin layer of tightly packed epithelial cells, may serve to optimize object images.
The use of a realistic computational model has allowed us to settle the controversy about the relative importance of the internal and skin conductivities in the determination of the magnitude and shape of the electric image, an issue that has been debated since the seminal paper by Lissmann and Machin [
We propose that the concepts of perturbing field and imprimence [
Simulations were run using a program written to simulate the electric image in weakly electric fish (i.e., the currents through the fish skin), which uses the Boundary Element Method (BEM [
We studied the effect of the skin and internal conductivity on the electric image in the presence of a metallic (high conductance) cube placed symmetrically to the sagittal plane and facing the dorsal skin 0.5 mm away. Water conductivity was kept at 16.5 μScm−1.
To assess the influence of the internal conductivity of the fish body, different values ranging from that equal to surrounding water conductivity (in which case the fish may be considered transparent) to 16,500 μScm−1 were examined, including the value experimentally determined (3,300 μScm−1). In order to maintain a constant electric source, tail and body regions were modelled as independent compartments, maintaining the tail with a realistic internal conductivity while applying different values for the body. In these cases, the conductance across the model skin was set low enough to be considered irrelevant.
To study the influence of the skin conductance, we explored the effect of different skins with homogeneously distributed conductances ranging from 10–100,000 μScm−2 and a natural-like skin with heterogeneous conductance distribution. The internal conductivity in this case was close to that experimentally determined (3,300 μScm−1).
Two singular conditions were used for comparison purposes: a) when the fish model has experimentally determined conductances (where the fish body exerts its normal effect on the electric image); and b) when it has water-like conductances (i.e., where the fish body exerts no effect on the electric image).
The authors would like to thank Dr. Kirsty Grant and the anonymous reviewers for their helpful comments and suggestions of improvement. This work was partially financed by the Comision Sectorial de Investigación Científica (CSIC), Universidad de la República, Montevideo, Uruguay (fellowship for AM and equipment), and a grant for international cooperation from the French Ministère des Affaires Etrangères, (ECOS-Sud U03B01).
electric organ
electric organ discharge