Peripheral electrosensory imaging by weakly electric fish.

Different species have developed different solutions to the problem of constructing a representation of the environment from sensory images projected onto sensory surfaces. Comprehension of how these images are formed is an essential first step in understanding the representation of external reality by a given sensory system. Modeling of the electrical sensory images of objects began with the discovery of electroreception and continues to provide general insights into the mechanisms of imaging. Progress in electric image research has made it possible to establish the physical basis of electric imaging, as well as methods to accurately predict the electric images of objects alone and as a part of a natural electric scene. In this review, we show the following. (1) The internal low resistance of the fish's body shapes the image in two different ways: by funneling the current generated by the electric organ to the sensory surface, it increases the fields rostrally, thus enhancing the perturbation produced by nearby objects; and by increasing the projected image. (2) The electric fish's self-generated currents are modified by capacitive objects in a distinctive manner. These modulations can be detected by different receptor types, yielding the possibility of "electric color." (3) The effects of different objects in a scene interact with each other, generating an image that is different from the simple addition of the images of individual objects, thus causing strong contextual effects.

The electric image in Gnathonemus petersii.

We review modelling and experimental work dealing with the mechanisms of generation of electric image. We discuss: (1) the concept of electric image in the context of the reafference principle; (2) how waveform codes an impedance related qualia of the object image, referred to as "electric colour"; (3) that some characteristics of the spatial profiles generated by pre-receptor mechanisms are suitable for edge detection; (4) which parameters of the spatial profiles provide information for distance discrimination; (5) that electric images are distributed representations of the scene.

Dynamical behavior of a pacemaker neuron model with fixed delay stimulation.

In physiological and pathological conditions, many biological oscillators, such as pacemaker cells, operate under the influence of feedbacks. Fixed delay stimulation is a standard preparation to evaluate the effects of such influences. Through the study of the Hodgkin-Huxley model, we show that such recurrent excitation can lead to regular and irregular discharge trains with interdischarge intervals that are up to several multiples of the period of the oscillator. In other words, we show that recurrent excitation can considerably slow down the firings of the pacemaker. This result contrasts with previous studies of similar preparations that have reported that fixed delay stimulation leads to a bursting pattern in which regimes of high-frequency firing alternate with periods of quiescence. We elucidate the mechanisms underlying the behavior of the oscillator under fixed delay perturbation through the analysis of the dynamics of a well-known two-dimensional oscillator, namely, the Poincaré oscillator.

The electric image in weakly electric fish: perception of objects of complex impedance.

Weakly electric fish explore the environment using electrolocation. They produce an electric field that is detected by cutaneous electroreceptors; external objects distort the field, thus generating an electric image. The electric image of objects of complex impedance was investigated using a realistic model, which was able to reproduce previous experimental data. The transcutaneous voltage in the presence of an elementary object is modulated in amplitude and waveform on the skin. Amplitude modulation (measured as the relative change in the local peak-to-peak amplitude) consists of a 'Mexican hat' profile whose maximum relative slope depends on the distance of the fish from the object. Waveform modulation depends on both the distance and the electrical characteristics of the object. Changes in waveform are indicated by the amplitude ratio of the larger positive and negative phases of the local electric organ discharge on the skin. Using the peak-to-peak amplitude and the positive-to-negative amplitude ratio of this discharge, a perceptual space can be defined and correlated with the capacitance and resistance of the object. When the object is moved away, the perceptual space is reduced but keeps the same proportions (homothetically): for a given object, the positive-to-negative amplitude ratio is a linear function of the peak-to-peak amplitude. This linear function depends on the electrical characteristics of the object. However, there are 'families' of objects with different electrical characteristics that produce changes in the parameters of the local electric organ discharge that are related by the same linear function. We propose that these functions code the perceptual properties of an object related to its impedance.

The electric image in weakly electric fish: physical images of resistive objects in Gnathonemus petersii.

The present study describes a measurement-based model of electric image generation in the weakly electric mormyrid fish Gnathonemus petersii. Measurements of skin impedance, internal resistivity and fish body dimensions have been used to generate an electrical-equivalent model of the fish and to calculate electrical images and equivalent dipole sources for elementary resistive objects. These calculations allow us to understand how exafferent and reafferent signals are sensed by electroreceptors. An object's electric image consists of the modulation of the transcutaneous voltage profile generated by the fish's own discharge. The results suggest a set of rules for electrolocation: (1) the side of the fish where modulation is larger indicates the side on which the object is situated; (2) the object's position in the electroreceptive field is indicated by the point of maximum modulation of the transcutaneous voltage; (3) the degree of focus of the image indicates the distance to the object. In addition, center-surround opposition originating at pre-receptor level is proposed. Both experimental measurements and modeling indicate that fish skin impedance is relatively low (400-11 000 cm²) and mainly resistive. This low skin impedance appears to enhance the local electric organ discharge modulation, the center-surround effect, the signal-to-noise ratio for electrolocation and the active space for electrocommunication.

Two-neuro networks. II. Leaky integrator pacemaker models.

The behavior of two pacemaker neurons simulated by leaky integrators and connected reciprocally by synapses was studied. In every case the firing of both neurons phase-locks. The resulting limit cycle may or may not show simultaneous firing of both neurons. When both synapses are excitatory, phase-locking with simultaneous neuronal firing is always present. When one synapse is excitatory and the other inhibitory, phase-locking is also present always, while the neurons may or may not fire simultaneously. For a restricted set of parameters, bistability appears; the initial conditions determine whether or not the limit cycle presents simultaneous firing. When both synapses are inhibitory, the system phase-locks without simultaneous firing for almost every set of parameters.

The electric image in weakly electric fish: I. A data-based model of waveform generation in Gymnotus carapo.

Understanding how electrosensory images are generated and perceived in actively electrolocating fish requires the study of the characteristics of fish bodies as electric sources. This paper presents a model of Gymnotus carapo based on measurements of the electromotive force generated by the electric organ and the impedance of the passive tissues. A good agreement between simulated and experimentally recorded transcutaneous currents was obtained. Passive structures participate in the transformation of the electromotive force pattern into transcutaneous current profiles. These spatial filtering properties of the fish's body were investigated using the model. The shape of the transcutaneous current profiles depends on tissue resistance and on the geometry and size of the fish. Skin impedance was mainly resistive. The effect of skin resistance on the spatial filtering properties of the fish's body was theoretically analyzed. The model results show that generators in the abdominal and central regions produce most of the currents through the head. This suggests that the electric organ discharge (EOD), generated in the abdominal and central regions is critical for active electrolocation. In addition, the well-synchronized EOD components generated all along the fish produce large potentials in the far field. These components are probably involved in long-distance electrocommunication. Preliminary results of this work were published as a symposium abstract.

Computer simulation of diffusion processes as a teaching aid.

A computer program for the simulation of diffusion processes has been developed. It displays the trajectories of single molecules under Brownian motion. Diffusion of 40 to 100 molecules in a box with or without barriers can be simulated, and concentration-time and concentration-distance functions can be plotted. This program may be useful, when complemented with experimental work and theoretical study, for teaching diffusion and membrane permeability processes.

Is the Na+,K+-ATPase symmetrically distributed in the neuroepithelium of the vestibular system in the axolotl (Ambyostoma mexicanum)?

This study was undertaken to assess the localization of the Na+,K+-ATPase in the neuroepithelial cells of the macula sacculi. In vitro perilymphatic (basolateral) perfusion with ouabain produced a significant drop in the membrane potential. Endolymphatic (apical) application of ouabain had practically no effect on membrane potentials. This suggests that Na+,K+-ATPase is asymmetrically distributed in the neuroepithelial cells.