This model has been tested by stimulating Brienomyrus brachyistius KOs with head-tail or transverse electric field geometries designed to stimulate receptors sequentially, and uniform geometry designed to stimulate them synchronously while recording in vivo evoked potentials from the posterior exterolateral nucleus (ELp), the sole recipient of ELa small cell output. Given that electric field strength was sufficient to drive “all” KOs, we predicted no evoked potentials in ELp under uniform geometry compared to a large evoked potential under head-tail and transverse geometry.

To interpret this experiment, a simulation of certain elements of the neural network was performed. The next sections outline the simulation and some results.

Xu-Friedman MA, Hopkins CD (1999)

Simulation Assumptions


A Matlab program was written to implement the simulation. All of the receptor cells are simulated, the spike trains stored in a compressed format, then all of the small cells are simulated. There are options to build a new fish or to just apply a new stimulus to a fish which was already built. Output plots appear in 3 figures:

The following examples show the model performance under several conditions. All of these examples were run with just 200 small cells, not the usual 1000. All simulations were on the same 'fish'.

  1. The first example is a relatively long stimulus of 1 mSec, medium amplitude (0.3), and head/tail field orientation. Note the different duration receptor voltages depending on the center frequency of the convolution filters. Receptor spikes are bunched around the onset (head receptors) and fall (tail receptors) of the stimulus.

    Small cell input currents below show the size ratio between the large inhibitory and small excitatiory inputs and also show that the excitation is delayed relative to the inhibition. Inhibition is long lasting, so there is only one burst of output spikes.

    Summed APs. This figure is an approximation of recordable data. Note that the relative weighting of the receptor and small cells amplitudes may be wrong.
  2. The second example is a relatively long stimulus of 1 mSec, medium amplitude (0.3), and full-body field orientation. this is the same stimulus as example 1, but is applied to the entire body. Note that virtually all the receptors fire on the rising edge of the outside-positive pulse.

    Only two or three small cells escape from the massive inhibition caused by all the receptors firing at once.

    There is only the smallest AP distribution from the small cells.
  3. The third example is a relatively long stimulus of 1 mSec, low amplitude (0.1), and head-tail orientation. The lower stimulus, combined with the variablity of the convolution filters causes the receptor firing to become multimodal.

  4. The fourth example is a relatively long stimulus of 1 mSec, low amplitude (0.1), and full-body orientation. Again, the lower stimulus, combined with the variablity of the convolution filters causes the receptor firing to become multimodal.

    Because less than 1/2 of the receptors produced an AP, some of the small cells avoid inhibition and fire.

  5. The fifth example is a relatively long stimulus of 1 mSec, high amplitude (1.0), and head-tail orientation.

    Note the full supression of the second AP peak below.

  6. The sixth example is a relatively short stimulus of 0.2 mSec, medium amplitude (0.3), and head-tail orientation. The receptor output is multomodal for a different reason: The rising edge and falling edges overlap.

Possible comparisions between simulation and data

  1. Qualitatively, both the simulation and the data show a block in ELa output for high amplitude, full-body stimulation. The model predicts less block for head-tail stimulation than the real data at high stimulus amplitude.
  2. Laurieanne's data shows that on a plot of evoked potential amplitude versus stimulus amplitude, the biggest response occures at a specific stimulus amplitude (which depends on the fish), independent of the stimulus duration. In the following, fish1 is left, fish2 is right.
    Duration is 0.2 mSec at top and 1.0 mSec at bottom. Purple is full-body, green is head-tail.

    A simple interpretation of this could be: At low stimulus, response amplitude should be proportional to stimulus amplitude because to takes only one receptor to fire a small cell, but concidence with an inhibitory cell to stop firing. For full-body stimulation the response amplitude should go as n*(100-n) where n is the number of responding receptors. If n is proportional to stimulus amplitude (and not duration), there will always be a peak at about 50% activation. The first-pass model does not predict this independence of stimulus duration. This is because the probability of receptor firing is proportional to (stim strength)x(stim duration), not just to the strength. Adding an extra delay to the inhibitory small cell inputs seems to fix this problem (item 2 below). The extra inhibitory delay allows a few excitatory inputs to 'leak through' the inhibition at higher stimulation strength. The second-pass model (item 3 below) partly fixes the problem in a more natural way, by taking into account the long tail on the excitatory delay distribution shown here.
    1. For the first pass case (described in the assumptions above), the biggest response moves to higher amplitude at shorter stimulation duration.
    2. If 200 microseconds extra delay is added to the inhibitory inputs (program), then the stim/response curves look like Laurieanne's. The different duration curves overlap. And the slopes are similar to real data.
    3. For the second pass case (described in the assumptions above), the real distribution of excitatory delays was used (program and datafile of all delays) . The resulting response curves look promising, but the shift in the peak amplitude suggests that there probably needed to be more modeled delay in the inhibitory inputs. the slopes are good, particularly the curvature of the response curve at high amplitude, which resembles real data.
    4. A modification of the second pass added 30 uSec of delay to the inhibitory side. The resulting response curves match the real data fairly well, however The head-tail stimulation flatttens out at a lower level.

      Overlay onto real data. Purple is fullbody, green is head-tail. Note that the horizontal scale was stretched to match one decade. Vertical scale was stretched to approximate peak-to-low value ratio. Model was translated to match peak positions.
  3. Ratio of ELa to ELp peak amplitudes may constrain the simulation.
  4. Multimodal peaks in receptor response may constrain amplitude-center frequency relationship.

Fitting real data

We wrote a modifed program which automatically generated strength-response curves. Laurieanne compared these to real data and found a good fit with an inhibitory delay distribution of mean=250 microsec and The following plots show a case computed with a Gaussian distrbution of inhibitory delays with mean=206+/-61 microseconds. Pulse length was set to 200 microseconds. Four separate fish were generated to check for the effect of random variation due to filter responses and small cell wiring. Horizontal scale is stinulus strength, vertical is peak of simulated evoked potential. (this program generates detailed currents and voltages)

Can the model resolve distance and direction?

A real fish needs to be able to untangle the effects of amplitude and EOD phase to determine the direction of another fish, independently of the distance to the fish. Distance scales the EOD waveform, therefore changing its effect on nonlinear receptors in a complex way. Ideally, the outputs from the small cells should be able to separate the distance from the direction. There are several considerations:

The program presents 20 stimuli to a model fish with 100 receptors and 800 small cells. The 20 stimuli are broken down into 4 directions, each presented at 5 amplitudes. Clustering of HD was initially done by looking at a table, but patterns are hard to see, so a technique called Multidimensional Scaling (MDS) was used to lower the dimensionality. You would expect range/phase data to be two dimensional, since there are just two parameters. So the question comes down to whether the 20-dimensional HD data set fits into two dimentions in an understandable way. The following plots shows that it does. The pulse duration matched the average EOD duration for this species, 300 microseconds. Amplitudes covered a 100:1 range. Stimuli were applied in 4 phases (4 directions). Inhibition delay was set to a Gaussian distribution with mean=200+/-100 microsec.

The first plot shows that all four strength-response curves are essentially identical, impling that there is no particular bias in the model for direction.

The second plot shows the output of all 800 small cells for each of 20 stimuli. This is the raw data entering the MDS caluclation. You can see the low amplitude stimuli are sparse (stimuli 1, 6, 11, 16). you can also see that the higher strength stimuli produce patterns which are similar within direction (e.g. 19, 20), but different between directions (e.g. 19,20 versus 14,15).

The third plot shows that the MDS analysis could find a reasonable 2-dimensional fit to the distance data, and that it make topological sense, because red is front positive, green is back positive, blue is left positive, and cyan is right positive. Only the lowest amplitude stimuli are not direction-resolved. Since fish come in different sizes (and thus amplitude), there is a basic ampliude/distance ambiguity. It seems to me that direction of approach is more important, and is clearly resolved.

The fourth plot shows that there is not much additional information gained by going to a 3-dimensional analysis. The four clumps are all abou the same distance above the floor. There may be some signal amplitude information in the vertical direction, however.


Bell CC and Grant K(1989), Corollary discharge inhibition and preservation of temporal information in a sensory nucleus of mormyrid electric fish, Journal of Neuroscience, Vol 9, 1029-1044,

Friedman MA, Hopkins CD (1998) Neural substrates for species recognition in the time-coding electrosensory pathway of mormyrid electric fish. Journal of Neuroscience 18:1171-1185.

Xu-Friedman MA, Hopkins CD (1999) Central mechanisms of temporal analysis in the knollenorgan pathway of mormyrid electric fish. Journal of Experimental Biology 202:1311-1318

Dent, Laurieanne. Spike Timing Detectors in the Nervous System: Experimental and Theoretical Studies of the Electrosensory System of Mormyrid Fish. Cornell University, 2008.