The complexity of high-frequency electric fields degrades electrosensory inputs: implications for the jamming avoidance response in weakly electric fish

Modeling the Sequential Pattern Variability of the Electromotor Command System of Pulse Electric Fish

Mormyridae, a family of weakly electric fish, use electric pulses for communication and for extracting information from the environment (active electroreception). The electromotor system controls the timing of pulse generation. Ethological studies have described several sequences of pulse intervals (SPIs) related to distinct behaviors (e.g., mating or exploratory behaviors). Accelerations, scallops, rasps, and cessations are four different SPI patterns reported in these fish, each showing characteristic stereotyped temporal structures. This article presents a computational model of the electromotor command circuit that reproduces a whole set of SPI patterns while keeping the same internal network configuration. The topology of the model is based on a simplified representation of the network with four neuron clusters (nuclei). An initial configuration was built to reproduce nucleus characteristics and network topology as described by detailed morphological and electrophysiological studies. Then, a methodology based on a genetic algorithm (GA) was developed and applied to tune the model connectivity parameters to automatically reproduce a whole set of patterns recorded from freely-behaving Gnathonemus petersii specimens. Robustness analyses of input variability were performed to discard overfitting and assess validity. Results show that the set of SPI patterns is consistently reproduced reaching a dynamic balance between synaptic properties in the network. This model can be used as a tool to test novel hypotheses regarding temporal structure in electrogeneration. Beyond the electromotor model itself, the proposed methodology can be adapted to fit models of other biological networks that also exhibit sequential patterns.

Minimal sensor arrays for localizing objects using an electric sense

Weakly electric fish encode perturbations in a self-generated electric field to sense their environment. Localizing objects using this electric sense requires that distance be decoded from a two-dimensional \emph{electric image} of the field perturbations on their skin. Many studies of object localization by weakly electric fish, and by electric sensing in a generic context, have focused on extracting location information from different features of the electric image. Some of these studies have also considered the additional information gained from sampling the electric image at different times, and from different viewpoints. Here, we take a different perspective and instead consider the information available at a single point in space (i.e. a single sensor or receptor) at a single point in time (i.e. constant field). By combining the information from multiple receptors, we show that an object's distance can be unambiguously encoded by as few as four receptors at specific locations on a sensing surface in a manner that is relatively robust to environmental noise. This provides a lower bound on the information (i.e. receptor array size) required to decode the three-dimensional location of an object using an electric sense.

Dynamics of a neuronal pacemaker in the weakly electric fish Apteronotus

The precise timing of neuronal activity is critical for normal brain function. In weakly electric fish, the medullary pacemaker network (PN) sets the timing for an oscillating electric organ discharge (EOD) used for electric sensing. This network is the most precise biological oscillator known, with sub-microsecond variation in oscillator period. The PN consists of two principle sets of neurons, pacemaker and relay cells, that are connected by gap junctions and normally fire in synchrony, one-to-one with each EOD cycle. However, the degree of gap junctional connectivity between these cells appears insufficient to provide the population averaging required for the observed temporal precision of the EOD. This has led to the hypothesis that individual cells themselves fire with high precision, but little is known about the oscillatory dynamics of these pacemaker cells. As a first step towards testing this hypothesis, we have developed a biophysical model of a pacemaker neuron action potential based on experimental recordings. We validated the model by comparing the changes in oscillatory dynamics produced by different experimental manipulations. Our results suggest that this relatively simple model can capture a large range of channel dynamics exhibited by pacemaker cells, and will thus provide a basis for future work on network synchrony and precision.

Electrosensory Contrast Signals for Interacting Weakly Electric Fish

Active sensory systems have evolved to properly encode natural stimuli including those created by conspecifics, yet little is known about the properties of such stimuli. We consider the electrosensory signal at the skin of a fixed weakly electric fish in the presence of a swimming conspecific. The dipole recordings are obtained in parallel with video tracking of the position of the animals. This enables the quantification of the relationships between the recording dipole and the positions of the head, midbody and tail of the freely swimming fish. The contrast of the signal at the skin is shown to be well-fitted by a decreasing exponential function of distance. It is thus anti-correlated with distance; it is also correlated with the second envelope (i.e., the envelope of the envelope) of the raw recorded signal. The variance of the contrast signal is highest at short range. However, the coefficient of variation (CV) of this signal increases with distance. We find a range of position and associated contrast patterns under quasi-2D swimming conditions. This is quantified using global measures of the visit times of the free fish within measurable range, with each visit causing a bump in contrast. The durations of these bumps as well as the times between these bumps are well reproduced by a doubly stochastic process formed by a dichotomous (two-state) noise with Poisson statistics multiplying a colored noise [Ornstein-Uhlenbeck (OU) process]. Certain rapid body movements such as bending or turning are seen to produce contrast drops that may be part of cloaking strategies.

Chirping and asymmetric jamming avoidance responses in the electric fish Distocyclus conirostris

Electrosensory systems of weakly electric fish must accommodate competing demands of sensing the environment (electrolocation) and receiving social information (electrocommunication). The jamming avoidance response (JAR) is a behavioral strategy thought to reduce electrosensory interference from conspecific signals close in frequency. We used playback experiments to characterize electric organ discharge frequency (EODf), chirping behavior and the JAR of Distocyclus conirostris, a gregarious electric fish species. EODs of D. conirostris had low frequencies (∼80-200 Hz) that shifted in response to playback stimuli. Fish consistently lowered EODf in response to higher-frequency stimuli but inconsistently raised or lowered EODf in response to lower-frequency stimuli. This led to jamming avoidance or anti-jamming avoidance, respectively. We compare these behaviors with those of closely related electric fish (Eigenmannia and Sternopygus) and suggest that the JAR may have additional social functions and may not solely minimize the deleterious effects of jamming, as its name suggests.

A model for studying the energetics of sustained high frequency firing

Regulating membrane potential and synaptic function contributes significantly to the energetic costs of brain signaling, but the relative costs of action potentials (APs) and synaptic transmission during high-frequency firing are unknown. The continuous high-frequency (200-600Hz) electric organ discharge (EOD) of Eigenmannia, a weakly electric fish, underlies its electrosensing and communication. EODs reflect APs fired by the muscle-derived electrocytes of the electric organ (EO). Cholinergic synapses at the excitable posterior membranes of the elongated electrocytes control AP frequency. Based on whole-fish O₂ consumption, ATP demand per EOD-linked AP increases exponentially with AP frequency. Continual EOD-AP generation implies first, that ion homeostatic processes reliably counteract any dissipation of posterior membrane E_Na and E_K and second that high frequency synaptic activation is reliably supported. Both of these processes require energy. To facilitate an exploration of the expected energy demands of each, we modify a previous excitability model and include synaptic currents able to drive APs at frequencies as high as 600 Hz. Synaptic stimuli are modeled as pulsatile cation conductance changes, with or without a small (sustained) background conductance. Over the full species range of EOD frequencies (200–600 Hz) we calculate frequency-dependent “Na⁺-entry budgets” for an electrocyte AP as a surrogate for required 3Na⁺/2K⁺-ATPase activity. We find that the cost per AP of maintaining constant-amplitude APs increases nonlinearly with frequency, whereas the cost per AP for synaptic input current is essentially constant. This predicts that Na⁺ channel density should correlate positively with EOD frequency, whereas AChR density should be the same across fish. Importantly, calculated costs (inferred from Na⁺-entry through Nav and ACh channels) for electrocyte APs as frequencies rise are much less than expected from published whole-fish EOD-linked O₂ consumption. For APs at increasingly high frequencies, we suggest that EOD-related costs external to electrocytes (including packaging of synaptic transmitter) substantially exceed the direct cost of electrocyte ion homeostasis.