131 lines
6.7 KiB
TeX
131 lines
6.7 KiB
TeX
\section*{Electric fish as a real world model system}
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To put the results from our simulations into a real world context, we chose the
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weakly electric fish \textit{Apteronotus leptorhynchus} as a model system.
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\lepto\ uses an electric organ to produce electric fields which it
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uses for orientation, prey detection and communication. Distributed over the skin
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of \lepto\ are electroreceptors which produce action potentials
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in response to electric signals.
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These receptor cells ("p-units") are analogous to the
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simulated neurons we used in our simulations because they do not receive any
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input other than the signal they are encoding. Individual cells fire independently
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of each other and there is no feedback.
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\subsection*{Results}
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Figure \ref{fig:ex_data} A,B and C show three examples for coherence from intracellular
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measurements in \lepto\. Each cell was exposed to up to 128 repetitions of the
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same signal. The response was then averaged over different numbers of trials to
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simulate different population sizes of homogeneous cells. We can see that an increase
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in population size leads to higher coherence. Similar to what we saw in the simulations,
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around the average firing rate of the cell (marked by the red vertical lines), coherence
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decreases sharply. We then aggregated the results for 31 different cells (50 experiments total,
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as some cells were presented with the stimulus more than once).
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Figure \ref{ex_data} D shows that the increase is largest inside the
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high frequency intervals. As we could see in our simulations (figures \ref{fig:popsizenarrow15} C
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and \ref{fig:popsizenarrow10} C), the ratio of coding fraction in a large population
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to the coding fraction in a single cell is larger for higher frequencies.
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%simulation plots are from 200hz/nice coherence curves.ipynb
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\begin{figure}
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\centering
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\includegraphics[width=0.49\linewidth]{img/fish/coherence_example.pdf}
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\includegraphics[width=0.49\linewidth]{img/fish/coherence_example_narrow.pdf}
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\includegraphics[width=0.49\linewidth]{{img/coherence/broad_coherence_15.0_1.0_different_popsizes_0.001}.pdf}
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\includegraphics[width=0.49\linewidth]{{img/coherence/coherence_15.0_0.5_narrow_both_different_popsizes_0.001}.pdf}
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\label{fig:ex_data}
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\caption{A,B,C: examples of coherence in the p-Units of \lepto. Each plot shows
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the coherence of the response of a single cell to a stimulus for different numbers of trials.
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Like in the simulations, increased population sizes lead to a higher coherence.
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D: Encoding of higher frequency intervals profits more from an increase in
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population size than encoding of lower frequency intervals.
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The ratio of the coding fraction for the largest number of trials divided by
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the coding fraction for a single trial for each of six different frequency
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intervals. Shown here are the data for all 50 experiments (31 different cells).
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The orange line signifies the median value for all cells. The box
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extends over the 2nd and 3rd quartile. }
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\end{figure}
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\begin{figure}
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\centering
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broad
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\includegraphics[width=0.48\linewidth]{img/fish/cf_curves/cfN_broad_0.pdf}
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\includegraphics[width=0.48\linewidth]{img/fish/cf_curves/cfN_broad_1.pdf}
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\includegraphics[width=0.48\linewidth]{img/fish/cf_curves/cfN_broad_2.pdf}
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\includegraphics[width=0.48\linewidth]{img/fish/cf_curves/cfN_broad_3.pdf}
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\end{figure}
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%box_script.py, quot_sigma() und quot_sigma_narrow()
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\begin{figure}
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\centering
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broad
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_broad_0_50.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_broad_50_100.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_broad_100_150.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_broad_150_200.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_broad_200_250.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_broad_250_300.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_broad_0_50.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_broad_50_100.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_broad_100_150.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_broad_150_200.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_broad_200_250.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_broad_250_300.pdf}
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narrow
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_narrow_0_50.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_narrow_50_100.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_narrow_150_200.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_narrow_250_300.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/sigma_cf_quot_narrow_350_400.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_narrow_0_50.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_narrow_50_100.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_narrow_150_200.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_narrow_250_300.pdf}
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\includegraphics[width=0.16\linewidth]{img/fish/scatter/check_fr_quot_narrow_350_400.pdf}
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\end{figure}
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\begin{figure}
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\centering
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\includegraphics[width=0.4\linewidth]{img/fish/diff_box.pdf}
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\includegraphics[width=0.4\linewidth]{img/fish/diff_box_narrow.pdf}
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\includegraphics[width=0.4\linewidth]{img/relative_coding_fractions_box.pdf}
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\notedh{needs figure 3.6 from yue and equivalent}
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\end{figure}
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\begin{figure}
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\includegraphics[width=0.49\linewidth]{img/fish/ratio_narrow.pdf}
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\includegraphics[width=0.49\linewidth]{img/fish/broad_ratio.pdf}
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\label{freq_delta_cf}
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\caption{This is about frequency and how it determines $delta_cf$. In other paper I have used $quot_cf$.}
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\end{figure}
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\subsection{Discussion}
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We also confirmed that the results from the theory part of the paper play a role in a
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real world example. Inside the brain of the weakly electric fish
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\textit{Apteronotus leptorhynchus} pyramidal cells in different areas
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are responsible for encoding different frequencies. In each of those areas,
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cells integrate over different numbers of the same receptor cells.
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Artificial populations consisting of different trials of the same receptor cell
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show what we have seen in our simulations: Larger populations help
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especially with the encoding of high frequency signals. These results
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are in line with what is known about the pyramidal cells of \lepto:
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The cells which encode high frequency signals best are the cells which
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integrate over the largest number of neurons.
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