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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''.

Non-linearites are at the heart of neural computations in the brain, spike generation, for example, involves a strong non-linearity. Nevertheless, the 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 \textbf{(was superthreshold before...)} regime at low signal-to-noise ratios. This has been exploited in numerous theoretical studies. However, 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. In our manuscript we set out to find signatures of these interactions in electrophysiological data measured in two types of electrosensory neurons of the electric fish \textit{Apteronotus leptorhynchus}. In ampullary cells, these interactions 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 deduce the presence of non-linear interactions also in P-units. Finally, we discuss our findings and the relevance of non-linear interactions in the context of the neuroethological background.

Computational neuroscientists have a strong interest in characterizing non-linearities and study their functional consequences. However, experimental backing of these theoretical findings are scarce. With our work we set out to fill this gap and are able to confirm theoretical findings about the second-order susceptibility in real neurons. We believe that it 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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