Mind the gap: the minimal detectable separation distance between two objects during active electrolocation.

In a food-rewarded two-alternative forced-choice procedure, it was determined how well the weakly electric elephantnose fish Gnathonemus petersii can sense gaps between two objects, some of which were placed in front of complex backgrounds. The results show that at close distances, G. petersii is able to detect gaps between two small metal cubes (2 cm × 2 cm × 2 cm) down to a width of c. 1·5 mm. When larger objects (3 cm × 3 cm × 3 cm) were used, gaps with a width of 2-3 mm could still be detected. Discrimination performance was better (c. 1 mm gap size) when the objects were placed in front of a moving background consisting of plastic stripes or plant leaves, indicating that movement in the environment plays an important role for object identification. In addition, the smallest gap size that could be detected at increasing distances was determined. A linear relationship between object distance and gap size existed. Minimal detectable gap sizes increased from c. 1·5 mm at a distance of 1 cm, to 20 mm at a distance of 7 cm. Measurements and simulations of the electric stimuli occurring during gap detection revealed that the electric images of two close objects influence each other and superimpose. A large gap of 20 mm between two objects induced two clearly separated peaks in the electric image, while a 2 mm gap caused just a slight indentation in the image. Therefore, the fusion of electric images limits spatial resolution during active electrolocation. Relative movements either between the fish and the objects or between object and background might improve spatial resolution by accentuating the fine details of the electric images.

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.

Electric fish measure distance in the dark.

Distance determination in animals can be achieved by visual or non-visual cues. Weakly electric fish use active electrolocation for orientation in the dark. By perceiving self-produced electric signals with epidermal electroreceptors, fish can detect, locate and analyse nearby objects. Distance discrimination, however, was thought to be hardly possible because it was assumed that confusing ambiguity could arise with objects of unknown sizes and materials. Here we show that during electrolocation electric fish can measure the distance of most objects accurately, independently of size, shape and material. Measurements of the 'electric image' projected onto the skin surface during electrolocation revealed only one parameter combination that was unambiguously related to object distance: the ratio between maximal image slope and maximal image amplitude. However, slope-to-amplitude ratios for spheres were always smaller than those for other objects. As predicted, these objects were erroneously judged by the fish to be further away than all other objects at an identical distance. Our results suggest a novel mechanism for depth perception that can be achieved with a single, stationary two-dimensional array of detectors.

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.

Two-neurons network. I. Integrate and fire pacemaker models.

The behavior of two pacemakers simulated by integrate and fire oscillators reciprocally connected by synapses is studied. The activation of each synapse produces a sudden potential shift in the post-synaptic neuron. Two sorts of behaviour may occur when at least one synapse is excitatory. Phase-locking occurs for almost every set of parameters, and given certain initial conditions. Repetitive patterns in indifferent equilibrium appear in the presence of a given set of parameters and certain other initial conditions. Quasi-periodic behaviour corresponds to almost every set of parameters when both synapses are inhibitory, although repetitive patterns of firing in indifferent equilibrium occassionally occur.

Food anticipatory yawning rhythm in the rat.

The effect of feeding schedules on the daily rhythm in spontaneous yawning activity was studied in high yawning (HY) Sprague-Dawley rats. If the animals are fed ad libitum and changed from a standard 12-12 light-dark (LD) illumination regime to constant light (LL), the normal predark circadian peak in yawning disappears, to be replaced, after 3 weeks, by two or more ultradian smaller peaks in yawning frequency. Restriction of food availability to 2-2:30 regular hours of the day, in rats under LL conditions, leads to the appearance of a significant preprandial (food anticipatory) peak in yawning. A similar eating-fasting daily cycle of 2-22 h in rats under LD conditions determines the disappearance of the pre-dark peak in yawning activity, and a significant shift in higher yawning frequency towards the couple of hours preceding food availability. This result suggests that restricted feeding is more potent than the LD transition in the entrainment of the daily rhythm in yawning activity.

Serial dependency in the discharge pattern of dorsal spinocerebellar tract neurons: a computer simulation analysis.

We have developed a model in order to analyze the factors eventually responsible for the strong negative serial dependency between successive interspike intervals in the discharge of the Dorsal Spinocerebellar Tract (DSCT) neurons. This dependency is reflected, phenomenologically, by short intervals followed by long ones and, quantitatively, by the first order correlation coefficient (R1-2); which can be lower than -.6 (Jansen, Nicolaysen & Rudjord, 1966; Kröller and Grüsser, 1982). We have found that the lowest values of R1-2 are always related with model parameter values which were very similar to those obtained experimentally. It was observed that EPSP amplitude distribution plays an important role in the discharge patterns of the DSCT neurons. There is one fiber that elicits EPSPs greater than 6 mV, which is responsible for the genesis of the short intervals in the discharge. Long intervals are determined basically by a suprathreshold depolarization and the afterhyperpolarization processes.

Dynamic analysis of the righting reflex in toads; recovery after hemilabyrinthectomy.

Static and dynamic measurements of the righting reflex were performed in intact toads (Bufo arenarum platensis) and at different stages of recovery from hemilabyrinthectomy. Reflex activity was evaluated by the toad's capacity to maintain a horizontal head position while rolled sideways. Static data were obtained from frontal photographs. In dynamic experiments platform position (stimulus) was measured through a potentiometer, while a linear accelerometer glued to the cranium was used to record head tilts. The dynamic study included a linear systems analysis using sinusoids of 0.5-3 Hz with rolls of up to 30° to each side. Hemilabyrinthectomy produced a head tilt towards the lesioned side, and gain decay and phase lag increase in the dynamic response. All postural defects recovered progressively within 30-60 days as already described in other species. Nevertheless, the tonic head deviation produced by dynamic stimuli of frequencies above 1 Hz did not recover. This remnant defect has not been observed in previous studies in which only static observations were performed. The involvement of a frequency-dependent rectifying mechanism in postural compensation is discussed.

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.

Locking, intermittency, and bifurcations in a periodically driven pacemaker neuron: Poincaré maps and biological implications.

Slowly adapting stretch receptor (SAO) pacemaker neurons, driven with periodic tugs, were analyzed by way of Poincaré mappings (Appendix). Two behaviors were apparent. i) Intermittency characterized previously unclear situations: discharges shifted irregularly between prolonged epochs where spike phases (relative to tugs) and intervals barely changed (slid), and brief bursts with marked variations (skipped). ii) Locking was well-known: phases and intervals remained almost fixed, regardless of the initiation. Changing frequencies, map domains with locking (ordered according to spikes/tugs ratios), alternated with intermittent ones. The best fit for any experimental map was a curve, not straight but certainly unidimensional, continuous and monotonic; it varied characteristically with frequency. This suggested relations called diffeomorphisms, implying periodicity and quasi-periodicity. Outcomes, expanding previous knowledge and meaningful biologically, were i) a precise, exhaustive behavior list (including between behavior transitions) and ii) a thorough understanding or model. This, in turn, provides norms for more specific models (single-variable ones suffice), constraints upon basic mechanisms (one variable, reflecting several real ones combined, should behave as the phase), and forecasts for future experimentation (e.g., unexamined tug frequencies and amplitudes).

Is GABA an afferent transmitter in the vestibular system?

This study was undertaken to determine the possible role of GABA as an afferent transmitter in the vestibular system of the axolotl. We studied the effects of GABA, muscimol, bicuculline and picrotoxin on the spontaneous spike discharge of the afferent fibers of the sacculi lagena and anterior semicircular canal. It was found that GABA and muscimol produce a very weak excitatory effect which does not mimic either the temporal course or the amplitude of the response of vestibular afferents to physiological stimuli. The GABA antagonist bicuculline has no significant effect on these fibers, and picrotoxin partially blocks the spontaneous activity in 33% of the fibers studied. These results indicate that GABA is probably not an afferent transmitter in the vestibular system as has previously been proposed.

A spike generator mechanism model simulates utricular afferents response to sinusoidal vibrations.

Using a model of spike generator mechanism (SGM) with a variable threshold we simulate the responses of utricular afferents to sinusoidal vibrations. It reproduces the phase locking characteristics (bifurcations diagrams) and the stimulus frequency firing rate relationships of different types of utricular afferents. We estimate the model parameters selecting the values which best fit the experimental results and we compare them with those from basic mechanisms involved in utricular codification.

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.

Mechanisms of sensory adaptation in the isolated utricle.

The occurrence of receptor adaptation in utricular afferent fibers is now widely recognized. The experiments reported here explored the basic mechanisms of adaptation at the level of the receptor organ. Spike discharges from single utricular afferent fibers were recorded in isolated labyrinths of an elasmobranch, during three types of stimulation: (a) tilts in the gravity field, (b) vibrations, and (c) electrical polarization delivered through the nerve filaments from which recordings were also made. Experimental evidence supported the conclusion that polarization affects the discharge by acting at the level of the spike triggering mechanism, the point of the afferent fiber at which impulses normally arise. Three types of afferent fibers have been described: Types I and II fire spontaneously and show phasic-tonic responses to tilts. Type III fibers do not have spontaneous activity and respond to tilts in a phasic manner. Adaptation to polarizing currents was observed in all afferent fibers. Type II fibers adapted slowly to vibrations whereas types I and III afferent fibers did not. The functional processes situated near the spike triggering site of the sensory axon is referred to as neural whereas those occurring at earlier stages of transduction are called preneural. Adaptation to tilts exhibited two successive components: an early, fast phase and a late, slow one. Our results suggested that these phases can be related to the mechanisms of preneural and neural adaptation, respectively. Because the time course of adaptation to polarizing currents was similar in different afferent fibers, we concluded that preneural adaptation was the origin of the differences among afferent fibers that allowed their classification into phasic, phasic-tonic, and tonic groups. No attempts were made to separate the influence of mechanical coupling and transduction in the production of preneural adaptation.

Motor-pattern production: interaction of chemical and electrical synapses.

A pair of neurons exhibiting postinhibitory rebound, if connected through reciprocally inhibitory chemical synapses, will exhibit a stable pattern of alternating bursts. If two such oscillating pairs, of similar but not identical properties are connected by means of an electrical synapse and an inhibitory chemical synapse between two neurons, one in each pair, the burst patterns may drift, may lock in synchrony, may entrain in antiphase, may entrain at an intermediate phase, or may be suppressed in the inhibited pair. The behavior depends on the strengths of the chemical and electrical coupling as well as on the degree of depression at the chemical synapse. There relationships of the motor patterns are illustrated quantitatively through theoretical calculations.