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\hspace*{\fill} July 18, 2025

\noindent Dear Ana Levina,

we would like to publish our manuscript ``Spike generation in
electroreceptor afferents introduces additional spectral response
components by weakly nonlinear interactions'' in PLoS Computational
Biology. It is a result of a collaboration between Benjamin Linder, HU
Berlin, and Jan Grewe and myself at the University of Tuebingen, within the DFG priority program 2205 ``Evolutionary optimization of neuronal processing''.

Spike generation involves a strong non-linearity. Nevertheless, the encoding of dynamic stimuli into spike trains often can be well approximated by linear response theory, in particular when driving the neuron in the superthreshold 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 came up with analytical solutions of this term for the leaky integrate-and-fire neuron, which predict 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 the weakly non-linear regime in electrophysiological data measured in two types of electrosensory neurons of the elctric fish \textit{Apteronotus leptorhynchus}. In ampullary cells these interactions are prominent, whereas in P-units these are harder to find. Estimating the second-order susceptibilites from real data turns out to be a hard problem. By comparison with models that have been fitted to individual P-units we are then able to interpret the poor estimates from limited data. Finally, we discuss our findings in the context of behaviorally electrosensory stimuli.

Non-linearites are at the heart of neural computations in the brain. Consequently, computational neuroscientists have a strong interest in characterizing non-linearities and study their functional consequences. However, experimental evidences backing up these theoretical findings are scarce. Our manuscripts fills this gap and thus is of srong interest for many readers of PLoS Computational Biology. We confirm theoretical findings about the second-order susceptibility and by setting our results into a neuroethological background we discuss potential roles of these nonlinear effects in neural processing that require future research.

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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