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nonlinearbaseline.tex
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\newcommand{\eqnref}[1]{Eq.~\eqref{#1}}
\newcommand{\eqnsref}[1]{Eqs.~\eqref{#1}}
%%%%% species names %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\Lepto}{\emph{Apteronotus leptorhynchus}}
\newcommand{\lepto}{\emph{A. leptorhynchus}}
\newcommand{\Eigen}{\emph{Eigenmannia virescens}}
\newcommand{\eigen}{\emph{E. virescens}}
%%%%% notes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\note}[2][]{\textbf{[#1: #2]}}
%\newcommand{\note}[2][]{}
@@ -303,7 +297,7 @@ Here we search for such weakly nonlinear responses in electroreceptors of the tw
\subsection{Experimental subjects and procedures}
Within this project, we re-evaluated datasets that were recorded between 2010 and 2023 at the Ludwig Maximilian University (LMU) M\"unchen and the Eberhard-Karls University T\"ubingen. All experimental protocols complied with national and European law and were approved by the respective Ethics Committees of the Ludwig-Maximilians Universität München (permit no. 55.2-1-54-2531-135-09) and the Eberhard-Karls Unversität Tübingen (permit no. ZP 1/13 and ZP 1/16).
The final sample consisted of 172 P-units and 30 ampullary electroreceptor afferents recorded in 80 weakly electric fish of both sexes of the species \lepto{}. Fish were obtained from a commercial supplier for tropical fish (Aquarium Glaser GmbH, Rodgau, Germany) and kept in tanks with a water temperature of $25\pm1\,^\circ$C and a conductivity of around $270\,\micro\siemens\per\centi\meter$ under a 12\,h:12\,h light-dark cycle.
The final sample consisted of 172 P-units and 30 ampullary electroreceptor afferents recorded in 80 weakly electric fish of both sexes of the species \textit{Apteronotus leptorhynchus}. Fish were obtained from a commercial supplier for tropical fish (Aquarium Glaser GmbH, Rodgau, Germany) and kept in tanks with a water temperature of $25\pm1\,^\circ$C and a conductivity of around $270\,\micro\siemens\per\centi\meter$ under a 12\,h:12\,h light-dark cycle.
Before surgery, the animals were deeply anesthetized via bath application of a solution of MS222 (120\,mg/l, PharmaQ, Fordingbridge, UK) buffered with Sodium Bicarbonate (120\,mg/l). The posterior anterior lateral line nerve (pALLN) was exposed by making a small cut into the skin covering the nerve. The cut was placed dorsal of the operculum just before the nerve descends towards the anterior lateral line ganglion (ALLNG). Those parts of the skin that were to be cut were locally anesthetized by cutaneous application of liquid lidocaine hydrochloride (20\,mg/ml, bela-pharm GmbH). During the surgery, water supply was ensured by a mouthpiece to maintain anesthesia with a solution of MS222 (100\,mg/l) buffered with Sodium Bicarbonate (100\,mg/l). After surgery, fish were immobilized by intramuscular injection of from 25\,$\micro$l to 50\,$\micro$l of tubocurarine (5\,mg/ml dissolved in fish saline; Sigma-Aldrich).
Respiration was then switched to normal tank water and the fish was transferred to the experimental tank.
@@ -483,7 +477,7 @@ Both, the reduced intrinsic noise and the RAM stimulus, need to replace the orig
\begin{figure*}[t]
\includegraphics[width=\columnwidth]{twobeats}
\caption{\label{fig:twobeats} Nonlinearity in an electrophysiologically recorded P-unit of \lepto{} in a three-fish setting (cell identifier ``2021-08-03-ac"). Receiver with EOD frequency $f_{\rm EOD} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both foreign signals have the same strength relative to the own field amplitude (10\,\% contrast). Top row: Sketch of signal processing in the nonlinear system (black box). Second row: Superposition of the receiver EOD with the EODs of other fish, colored line highlights the amplitude modulation. Third row: Three trials of spike trains of the recorded P-unit. Fourth row: Firing rate, estimated by convolution of the spike trains with a Gaussian kernel. Bottom row: Power spectrum of the spike trains. \figitem{A} Baseline condition: The cell is driven by the self-generated field alone. The baseline firing rate $r = 139$\,Hz dominates the power spectrum (blue circle). \figitem{B} The receiver's EOD and a single conspecific with an EOD frequency $f_{1}=631$\,Hz are present. Superposition of the two EODs induces a periodic amplitude modulation, referred to as beat, with beat frequency $\Delta f_1=33$\,Hz. The P-unit strongly responds to this beat (purple). \figitem{C} The receiver and a fish with an EOD frequency $f_{2}=797$\,Hz are present. The resulting beat $\Delta f_2=133$\,Hz is faster as the difference between the EOD frequencies is larger. The P-unit response to this faster beat is weaker (green). \figitem{D} All three fish with EOD frequencies $f_{\rm EOD}$, $f_1$, and $f_2$ are present. Additional peaks occur in the power spectrum of the spike response at the sum (orange) and difference (red) of the two beat frequencies, indicating nonlinear interactions between the two frequencies in the P-unit. Note, the spectrum of the raw signal (top row, gray) has power only at the three EOD frequencies $f_{EOD}$, $f_1$, and $f_2$.}
\caption{\label{fig:twobeats} Nonlinearity in an electrophysiologically recorded P-unit of \textit{A. leptorhynchus} in a three-fish setting (cell identifier ``2021-08-03-ac"). Receiver with EOD frequency $f_{\rm EOD} =664$\,Hz encounters fish with EOD frequencies $f_{1}=631$\,Hz and $f_{2}=797$\,Hz. Both foreign signals have the same strength relative to the own field amplitude (10\,\% contrast). Top row: Sketch of signal processing in the nonlinear system (black box). Second row: Superposition of the receiver EOD with the EODs of other fish, colored line highlights the amplitude modulation. Third row: Three trials of spike trains of the recorded P-unit. Fourth row: Firing rate, estimated by convolution of the spike trains with a Gaussian kernel. Bottom row: Power spectrum of the spike trains. \figitem{A} Baseline condition: The cell is driven by the self-generated field alone. The baseline firing rate $r = 139$\,Hz dominates the power spectrum (blue circle). \figitem{B} The receiver's EOD and a single conspecific with an EOD frequency $f_{1}=631$\,Hz are present. Superposition of the two EODs induces a periodic amplitude modulation, referred to as beat, with beat frequency $\Delta f_1=33$\,Hz. The P-unit strongly responds to this beat (purple). \figitem{C} The receiver and a fish with an EOD frequency $f_{2}=797$\,Hz are present. The resulting beat $\Delta f_2=133$\,Hz is faster as the difference between the EOD frequencies is larger. The P-unit response to this faster beat is weaker (green). \figitem{D} All three fish with EOD frequencies $f_{\rm EOD}$, $f_1$, and $f_2$ are present. Additional peaks occur in the power spectrum of the spike response at the sum (orange) and difference (red) of the two beat frequencies, indicating nonlinear interactions between the two frequencies in the P-unit. Note, the spectrum of the raw signal (top row, gray) has power only at the three EOD frequencies $f_{EOD}$, $f_1$, and $f_2$.}
\end{figure*}
We explored a large set of electrophysiological data from primary afferents of the active and passive electrosensory system, P-units and ampullary cells \citep{Grewe2017, Hladnik2023}, that were recorded in the brown ghost knifefish \textit{Apteronotus leptorhynchus}. We re-analyzed this dataset to search for weakly nonlinear responses that have been predicted in previous theoretical work \citep{Voronenko2017}. Additional simulations of LIF-based models of P-unit spiking help to interpret the experimental findings in this theoretical framework. We start with demonstrating the basic concepts using example P-units and respective models and then compare the population of recordings in both cell types.
@@ -679,7 +673,7 @@ The afferents of the passive electrosensory system, the ampullary cells, exhibit
Ampullary stimuli originate from the muscle potentials induced by prey movement \citep{Kalmijn1974, Engelmann2010, Neiman2011fish}. For a single prey item such as \textit{Daphnia}, these potentials are often periodic but the simultaneous activity of a swarm of prey resembles Gaussian white noise \citep{Neiman2011fish}. Linear and nonlinear encoding in ampullary cells has been studied in great detail in the paddlefish \citep{Neiman2011fish}. The power spectrum of the baseline response shows two main peaks: One peak at the baseline firing frequency, a second one at the oscillation frequency of primary receptor cells in the epithelium, plus interactions of both. Linear encoding in the paddlefish shows a gap at the epithelial oscillation frequency, instead, nonlinear responses are very pronounced there.
Ampullary stimulus encoding is somewhat different in \lepto{}. The power spectrum of the spontaneous response is dominated by only the baseline firing rate and its harmonics, a second oscillator is not visible. The baseline firing frequency, however, is outside the linear coding range \citep{Grewe2017} while it is within the linear coding range in paddlefish \citep{Neiman2011fish}. Interestingly, the nonlinear response in the paddlefish ampullary cells increases with stimulus intensity while it disappears in our case (\figrefb{fig:dataoverview}~\panel[ii]{C}) indicating that paddlefish data have been recorded above the weakly-nonlinear regime.
Ampullary stimulus encoding is somewhat different in \textit{A. leptorhynchus}. The power spectrum of the spontaneous response is dominated by only the baseline firing rate and its harmonics, a second oscillator is not visible. The baseline firing frequency, however, is outside the linear coding range \citep{Grewe2017} while it is within the linear coding range in paddlefish \citep{Neiman2011fish}. Interestingly, the nonlinear response in the paddlefish ampullary cells increases with stimulus intensity while it disappears in our case (\figrefb{fig:dataoverview}~\panel[ii]{C}) indicating that paddlefish data have been recorded above the weakly-nonlinear regime.
The population of ampullary cells is very homogeneous with respect to the baseline rate (131$\pm$29\,Hz) and stimulus encoding properties \citep{Grewe2017}. This implies that, if the stimulus contains the appropriate frequency components that sum up to the baseline rate, the resulting nonlinear response appears at the baseline rate that is similar in the full population of ampullary cells and that is outside the linear coding range. Postsynaptic cells integrating ampullary input might be able to extract such nonlinear responses. How such nonlinear effects might influence prey detection should be addressed in future studies.