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\begin{document}
\hspace*{\fill} September 24, 2025

\noindent Dear Arvind Kumar,

we would like to submit our manuscript ``Spike generation in
electroreceptor afferents introduces additional spectral response
components by weakly nonlinear interactions'' for publication in
eNeuro. 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 eNeuro 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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