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\hspace*{\fill} July 18, 2025

\noindent Dear Ana Levina,

we would like to submit our manuscript ``Spike generation in
electroreceptor afferents introduces additional spectral response
components by weakly nonlinear interactions'' for publication in PLoS
Computational Biology. It is the result of a collaborative effort on
the theoretical side, Benjamin Linder, HU Berlin, and the experimental
and numerical modeling side, Jan Grewe and myself at the University of
Tuebingen, within the DFG priority program 2205 ``Evolutionary
optimization of neuronal processing''.

Computational neuroscientists have a strong interest in characterizing non-linearities and study their functional consequences. However, experimental backing of these theoretical findings are scarce. For example, encoding of dynamic stimuli in spike trains often can be well approximated by linear response theory, in particular when driving the neuron in the supra-threshold regime at low signal-to-noise ratios. This has been exploited in numerous theoretical studies. At less noise or stronger stimulus amplitudes non-linear effects become more prominent. In the weakly non-linear regime, the second term of the Volterra series becomes relevant. Benjamin Lindner developed analytical solutions of this term for the leaky integrate-and-fire neuron, which predicts non-linear interactions whenever one or the sum of two stimulus frequencies matches the neuron's baseline firing rate. Until now, however, these fundamental non-linearities arising from the core mechanism of spike generation have not been reported in any experimental data.

With our work we set out to fill this gap. We scan a large set of electrophysiological data measured in two types of electrosensory neurons of the electric fish \textit{Apteronotus leptorhynchus} for signatures of these non-linearities. In ampullary cells, non-linear interaction between two stimulus frequencies are prominent, whereas in P-units they are harder to find. Estimating the second-order susceptibilites from real data turns out to be a hard problem as limited data leads to poor estimates. Comparison with models that have been fitted to individual P-units, we are able to deduce the presence of non-linear interactions also in some of the P-units. Finally, we discuss our findings and the relevance of non-linear interactions in the neuroethological context.

We believe that this analysis of electrophysiological data close to expectations from theoretical work is of strong interest to many readers of PLoS Computational Biology and can inspire future research in other sensory systems.

Best regards,\\%[-2ex]
%\hspace*{0.17\textwidth}\includegraphics[width=0.3\textwidth]{JanBenda-Signature2020}\\
Prof. Dr. Jan Benda, on behalf of all authors

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