Eigenmannia: Glass Knife Fish A Weakly Electric Fish

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Eigenmannia Glass Knife FishA Weakly Electric
Fish

• Electrical organ discharges (EODs)
• Individually fixed between 250 and 600 Hz
• Method of electrolocation and communication
• Electroreceptors
• Respond to phase (T-type)
• Respond to amplitude (P-type)

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Jamming Avoidance Response

• Two fish will adjust EOD if frequencies are
  similar enough.
• Before Fish A 304 Hz, Fish B 300 Hz.
• After Fish A 312 Hz, Fish B 292 Hz.
• Uses T-type and P-type receptors to compute
  whether EODs should be raised or lowered.
• Role of T-type well understood. This paper
  examines the role of P-type.

Electrical Field
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The P-type Receptor Cells

• Single afferent projections to Electrosensory
  Lateral Line (ELL) lobe of the medulla
• Tuned to the EOD frequency of the individual
• Loosely phase locked
• Fire lt 1 per electric cycle, though as amplitude
  increase firings/per cycle goes to one

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Stimulus and Electrophysiology

• T Blank Tape Produces White Noise (the
  stimulus)
• Can vary the Standard Deviation
• BF Output passed through low-pass filter with
  variable cut-food frequency
• Can Vary the Cut-Off Frequency (fc)
• FG function generator (next slide)
• Electrodes in Mouth and Near tail produce
  electric field, to which receptors respond

Insert 1A here
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The Function Generator

• A0 is the Mean Amplitude
• s(t) is the white noise after it has passed
  through a filter
• fcarrier is equal to the EOD

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Recordings

• Recordings of P-type receptors at the animals
  trunk
• Identified P-type receptors by 3 criteria
• Probability of firing per cycle lt 1
• Spontaneous activity was irregular
• Units phase locked with large jitter
• 26 units selected
• Recordings of 135 seconds for 3 Protocols
• Spontaneous activity
• Response to wide-band white noise (fc 740 Hz)
• Varying fc, Ao, and standard deviation of s(t) in
  a pseudo random manner

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Theory

• ti spike occurrence time
• X0 mean firing rate.

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• h(t) was chosen to minimize the square error
  between
• the stimulus and the stimulus estimate

• The integration is over the duration of the
  experiment (T135sec)
• fc is cut-off frequency
• Ssx is Fourier transform of the cross
  correlation function of the stimulus and the
  spike train.
• Sxx is the Fourier transform of the auto
  correlation function stimulus and the spike
  train.

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• Now we can determine
• We determine noise, as the distance between the
  original stimulus and the estimated stimulus

• Signal To Noise Ratio, SNR(f), as the power
  spectrum of the
• of the stimulus divided by the power
  spectrum of the noise

Measure the amount of signal power present at a
given frequency relative to the noise.
SNR 1 means that it is impossible to differ the
signal from the noise.
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Measure of rate of mutual information that
is transmitted by the reconstructions about the
stimulus.

• Coding Fraction, a normalized measure of the
  quality
• of reconstruction

(Mean square error in the reconstruction)
( 0 lt ? lt 1 ), and for max error ? is 0

• Dividing by the firing rate ? , yields the mutual
  information transmitted per spike IsIe/ ?

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Data Analysis

• How we obtained the data for the above
  equations
• Spike Sample
• The spike peak occurrences times were selected
  and resample at 2KHz together with the
  stimulus.(2KHz because we saw that we are
  interested in frequencies bellow 740, say 1000
  and then nyquist)
• Filter
• - Estimate of the cross correlation between
  spike trains and stimulus was obtained by Fast
  Fourier transform. (Ssx,Sxx)
• SNR
• - Estimate of the stimulus and spikes power
  spectra were obtained using Fast Fourier
  transform and averaging 130 samples of data, each
  1024msec long.

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• The stimulus estimation were obtained by
  convolving the filter and the spike train in the
  frequency domain using Fast Fourier Transform.
  Here to avoid contamination by the carrier
  frequency of the spike train, they set the filter
  to zero for frequencies greater than fcarrier
  30Hz.
• Experimental errors were either obtained directly
  by repeated measurements or by error propagation

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Results

• Response to sinusoidal stochastic amplitude
  modulations spontaneous activity
• P-type receptor afferent units fire with
  increased probability when the amplitude of the
  external electric field is raised.

10Hz sinusoidal amplitude modulation and the
corresponding poststimulus histogram.
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• The spontaneous activity of P units appears
  consistent with the assumptions of stationary
  probability density for the spike distribution.

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• Increasing mean stimulus amplitude, increase the
  probability of firing.

A1.0, ?233
A0.8, ?208
A0.6, ?174
A0.5, ?152
A0.4, ?112
A0.3, ? 98
A0.2, ? 55
A0.1, ? 24
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• Temporal Bandwidth
• For wide band white noise stimulus 740Hz,
  checking over
• 13 units
• SNR always equal to 1 for frequencies gt 200Hz.
• and reconstruction is poor ? 0.0024 (lt2.5)
• For white noise stimulus 175Hz, while keeping
• power spectrum constant.
• SNR improved and more faithful reconstruction ?
  0.222.

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• Cutoff Frequency
• The coding fraction ? decreased with increasing
  fc.
• Decreasing the fc of the stimulus, increase the
  SNR at lower frequencies.

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• Why?
• 1. The power spectra density was increased in the
  range of frequencies encoded by the units.
• 2. The power spectra density of the signal was
  reduced at high frequencies.
• Two experiments were made to check these
  assumption.
• - fc of the stimulus was kept fixed, and the
  power density was increased.
• - fc of the stimulus was increased, and the
  power density was kept constant.

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• Effect of Mean Firing Rate
• Dynamic Range of mean firing rate from
  spontaneous firing rate to fcarrier (limit
  once/cycle)
• Signal-to-Noise Ratio increases as firing rate
  increases, but saturates at ½ fcarrier

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• Coding Fraction, Information Rate, Information
  Per Spike
• Coding Fraction, Information Rate also increases
  and saturates at the same points (Figure a and
  b), while Information per Spike decreases upon
  saturation (c)
• Lower Cut-Off Frequency ? Steeper slope in Coding
  Fraction
• fc 175 vs. fc 88 Hz
• No significant influence of the spontaneous
  firing rate on the slope of the coding fraction.
  (Fig. A and B)
• Significant coding occurred 20-40 Hz above
  spontaneous discharge

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• Standard Deviation and Signal-to-noise Ratio
• Varying the Standard Deviation is the same as
  increasing the amplitude
• Max. standard deviation set at .25 to avoid phase
  changes
• Signal-to-Noise Ratio increases with standard
  deviation

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• Coding Fraction, Information Rate, Information
• Per Spike
• All three of these increase with Standard
  Deviation
• Dotted lines are one unit at three mean firing
  rates (bottom 70, middle 110, and top 170)
• Larger mean firing rates
• Initial slope larger
• Saturation reached at lower standard deviation

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Discussion

• Studied Encoding Information
• Signal-to-Noise
• Mutual Information Rate
• Coding Fraction
• Despite the Noise, single afferents encode much
  of the stimulus

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• Technical Considerations
• The head and tail electric field geometry most
  effective in jamming avoidance response
• They may have chosen T-Type cells, however their
  data suggest otherwise (P-Type).

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• Reverse Correlation and Linear Reconstruction
  Filter
• Spiked were typically triggered by large positive
  slope in the stimulus.
• Neither the Biophysical interpretation nor the
  computational properties that could be read from
  the filter are obvious.
• The filter h(t) changes when the statistics of
  the stimulus or the mean firing rate of the units
  changes.

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• Their observation of the filter argue against the
  notion that there is a single cell that
  explicitly reconstruct the stimulus.
• The results are true for the assumption that the
  white noise stimuli is coded with stationary
  statistics and that the spike train is stationary
  in response to the stimulus.

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• Existence of nonlinearities
• The experiment show that adding high frequencies
  to the stimulus reduce the signal to noise ratio
  at low frequencies. This indicates that the
  receptors response to electric field amplitude
  modulation is nonlinear.

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• Natural stimuli
• 1. A typical power spectrum of natural
  amplitude modulations around the fish in its
  natural behavior has not been measured.
• 2. Amplitude modulations caused by small moving
  objects have been estimated to be between 2
  80Hz.
• They showed that SNR and fraction of signal
  encoded in single spike trains increase as the
  cutoff frequency of the stimulus decrease between
  740-88Hz. (slide18)
• More experiments were done, decreasing fc to 2,
  20, 50 that verified these results.

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• mean firing rate, dynamic range spontaneous
  activity
• The mean firing rate ?, increase with the mean
  amplitude A0.
• This enable them to study the coding
  performances as function of ? by changing A of
  the stimulus.
• The SNR, mutual information rate and coding
  fraction increased with increasing mean firing
  rate, for firing rates between the spontaneous
  activity and half of fcarrier.
• Coding started for mean firing rates 20-40Htz
  above the spontaneous discharge.

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• Coding fraction and mutual information both
  reached maximum at about half of fcarrier.
• There is a differential sensitivity of the coding
  fraction and the mutual information transmission
  as fc of the stimulus was changed.
• Anesthetized fish have lower spontaneous activity
  and EOD frequency, thus reduced firing rate than
  untreated fish, therefore the measured firing
  rate may not be the optimal one.

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Standard Deviation and Contrast

• Coding Fraction, etc. increased with an increase
  in Standard Deviation
• Because Mean Firing Rate was constant and only
  Standard Deviation changed, better performance
  was not due to more firing

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Upper Bound on Performance

• Upper Bound fcarrier because max of one spike
  per electric cycle
• Coding fraction at upper bound given by equation
  below.
• For these experiments fcarrier 400 Hz and fc
  100 Hz, so coding fraction is 0.75
• P receptors can code gt1/2 the information that
  can be encoded about a stimulus

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Behavioral Relevance

• Information from the P receptors to the CNS
  depends on
• Mean firing rate
• fc of the stimulus, as will as its contrast
• Similar results in mammalian visual system?
• Individual P receptors covey accurate and
  efficient representation
• Convergence makes more accurate and more
  efficient?