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TEXBASE=nonlinearbaseline
BIBFILE=references.bib
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@ -277,8 +277,8 @@ Supported by SPP 2205 ``Evolutionary optimisation of neuronal processing'' by th
% 250 words
\section{Abstract}
Spiking thresholds in neurons or rectification at synapses are essential for neuronal computations rendering neuronal processing inherently nonlinear. Nevertheless, linear response theory has been instrumental for understanding, for example, the impact of noise or neuronal synchrony on signal transmission, or the emergence of oscillatory activity, but is valid only at low stimulus amplitudes or large levels of intrinsic noise. At higher signal-to-noise ratios, however, nonlinear response components become relevant. Theoretical results for leaky integrate-and-fire neurons in the weakly nonlinear regime suggest strong responses at the sum of two input frequencies if these frequencies or their sum match the neuron's baseline firing rate.
We here analyze nonlinear responses in two types of primary electroreceptor afferents, the P-units of the active and the ampullary cells of the passive electrosensory system of the wave-type electric fish \textit{Apteronotus leptorhynchus}. In our combined experimental and modeling approach we identify these predicted nonlinear responses in low-noise P-units and, much stronger, in ampullary cells. Our results provide experimental evidence for nonlinear responses of spike generators in the weakly nonlinear regime. We conclude that such nonlinear responses occur in any sensory neuron that operates in similar regimes particularly at near-threshold stimulus conditions.
Spiking thresholds in neurons or rectification at synapses are essential for neuronal computations rendering neuronal processing inherently nonlinear. Nevertheless, linear response theory has been instrumental for understanding, for example, the impact of noise or neuronal synchrony on signal transmission, or the emergence of oscillatory activity, but is valid only at low stimulus amplitudes or large levels of intrinsic noise. At higher signal-to-noise ratios, however, nonlinear response components become relevant. Theoretical results for leaky integrate-and-fire neurons in the weakly nonlinear regime suggest strong responses at the sum of two input frequencies if one of these frequencies or their sum match the neuron's baseline firing rate.
We here analyze nonlinear responses in two types of primary electroreceptor afferents, the P-units of the active and the ampullary cells of the passive electrosensory system of the wave-type electric fish \textit{Apteronotus leptorhynchus}. In our combined experimental and modeling approach we identify these predicted nonlinear responses primarily in low-noise P-units and in more than every second ampullary cell. Our results provide experimental evidence for nonlinear responses of spike generators in the weakly nonlinear regime. We conclude that such nonlinear responses occur in any sensory neuron that operates in similar regimes particularly at near-threshold stimulus conditions.
% max 120 words
\section{Significance statement}
@ -289,7 +289,7 @@ The generation of action potentials involves a strong threshold nonlinearity. Ne
\begin{figure*}[t]
\includegraphics[width=\columnwidth]{lifsuscept}
\caption{\label{fig:lifsuscept} First- and second-order response functions of the leaky integrate-and-fire model. \figitem{A} Magnitude of the first-order (linear) response function $|\chi_1(f)|$, also known as the ``gain'' function, quantifies the response amplitude relative to the stimulus amplitude, both measured at the same stimulus frequency. \figitem{B} Magnitude of the second-order (nonlinear) response function $|\chi_2(f_1, f_2)|$ quantifies the response at the sum of two stimulus frequencies. Because frequencies can also be negative, the sum is actually a difference in the upper-left and lower-right quadrants, since $f_2 + f_1 = f_2 - |f_1|$ for $f_1 < 0$. For linear systems, the second-order response function is zero, because linear systems do not create new frequencies and thus there is no response at the sum of the two frequencies. The plots show the analytical solutions from \citet{Lindner2001} and \citet{Voronenko2017} with $\mu = 1.1$ and $D = 0.001$. Note that the leaky integrate-and-fire model is formulated without dimensions, frequencies are given in multiples of the inverse membrane time constant.}
\caption{\label{fig:lifsuscept} First- and second-order response functions of the leaky integrate-and-fire model. \figitem{A} Magnitude of the first-order (linear) response function $|\chi_1(f)|$, also known as the ``gain'' function, quantifies the response amplitude relative to the stimulus amplitude, both measured at the same stimulus frequency. $r$ marks the neuron's baseline firing rate. \figitem{B} Magnitude of the second-order (nonlinear) response function $|\chi_2(f_1, f_2)|$ quantifies the response at the sum of two stimulus frequencies. Because frequencies can also be negative, the sum is actually a difference in the upper-left and lower-right quadrants, since $f_2 + f_1 = f_2 - |f_1|$ for $f_1 < 0$. For linear systems, the second-order response function is zero, because linear systems do not create new frequencies and thus there is no response at the sum of the two frequencies. The plots show the analytical solutions from \citet{Lindner2001} and \citet{Voronenko2017} with $\mu = 1.1$ and $D = 0.001$. Note that the leaky integrate-and-fire model is formulated without dimensions, frequencies are given in multiples of the inverse membrane time constant.}
\end{figure*}
We like to think about signal encoding in terms of linear relations with unique mapping of a given input value to a certain output of the system under consideration. Indeed, such linear methods, for example the transfer function or first-order susceptibility shown in \subfigref{fig:lifsuscept}{A}, have been widely and successfully applied to describe and predict neuronal responses and are an invaluable tools to characterize neural systems \citep{Eggermont1983,Borst1999}. Nonlinear mechanisms, on the other hand, are key on different levels of neural processing. Deciding for one action over another is a nonlinear process on the systemic level. On the cellular level, spiking neurons are inherently nonlinear. Whether an action potential is elicited depends on the membrane potential to exceed a threshold \citep{Hodgkin1952, Koch1995}. Because of such nonlinearities, understanding and predicting neuronal responses to sensory stimuli is in general a difficult task.
@ -322,8 +322,7 @@ For monitoring the EOD without the stimulus, two vertical carbon rods ($11\,\cen
\subsection{Stimulation}\label{rammethods}
Electric stimuli were attenuated (ATN-01M, npi-electronics, Tamm, Germany), isolated from ground (ISO-02V, npi-electronics, Tamm, Germany) and delivered via two horizontal carbon rods (30 cm length, 8 mm diameter) located $15\,\centi\meter$ laterally to the fish.
The fish were stimulated with band-limited white noise stimuli with a cut-off frequency of 150\,Hz (ampullary), 300 or 400\,Hz (P-units). The stimulus intensity is given as a contrast, i.e. the standard deviation of the noise stimulus relative to the fish's EOD amplitude. The contrast varied between 1 and 20\,\% (median 5\,\%) for P-units and 2.5 and 20\,\% (median 5\,\%) for ampullary cells. Only noise stimuli with a duration of at least 2\,s (maximum of 50\,s, median 10\,s) and enough repetitions to results in at least 100 FFT segments (see below, P-units: 100--1520, median 313, ampullary cells: 105 -- 3648, median 722) were included into the analysis. When ampullary cells were recorded, the white noise was directly applied as the stimulus. To create random amplitude modulations (RAM) for P-unit recordings, the noise stimulus was first multiplied with the EOD of the fish (MXS-01M; npi electronics).
Electric stimuli were attenuated (ATN-01M, npi-electronics, Tamm, Germany), isolated from ground (ISO-02V, npi-electronics, Tamm, Germany) and delivered via two horizontal carbon rods (30 cm length, 8 mm diameter) located $15\,\centi\meter$ parallel to each side of the fish. The fish were stimulated with band-limited white noise stimuli with a cut-off frequency of 150\,Hz (ampullary), 300 or 400\,Hz (P-units). The stimulus intensity is given as a contrast, i.e. the standard deviation of the noise stimulus relative to the fish's EOD amplitude. The contrast varied between 1 and 20\,\% (median 5\,\%) for P-units and 2.5 and 20\,\% (median 5\,\%) for ampullary cells. Only noise stimuli with a duration of at least 2\,s (maximum of 50\,s, median 10\,s) and enough repetitions to results in at least 100 FFT segments (see below, P-units: 100--1520, median 313, ampullary cells: 105 -- 3648, median 722) were included into the analysis. When ampullary cells were recorded, the white noise was directly applied as the stimulus. To create random amplitude modulations (RAM) for P-unit recordings, the noise stimulus was first multiplied with the EOD of the fish (MXS-01M; npi electronics).
\subsection{Data analysis} Data analysis was done in Python 3 using the packages matplotlib \citep{Hunter2007}, numpy \citep{Walt2011}, scipy \citep{scipy2020}, pandas \citep{Mckinney2010}, nixio \citep{Stoewer2014}, and thunderlab (\url{https://github.com/bendalab/thunderlab}).
@ -522,7 +521,7 @@ P-units fire action potentials probabilistically phase-locked to the self-genera
\begin{figure*}[p]
\includegraphics[width=\columnwidth]{punitexamplecell}
\caption{\label{fig:punit} Linear and nonlinear stimulus encoding in example P-units. \figitem{A} Interspike interval (ISI) distribution of a cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field (cell identifier ``2020-10-27-ag''). This cell has a rather high baseline firing rate $r=405$\,Hz and an intermediate CV$_{\text{base}}=0.49$ of its interspike intervals. \figitem{B} Power spectral density of the cell's baseline response with marked peaks at the cell's baseline firing rate $r$ and the fish's EOD frequency $f_{\text{EOD}}$. \figitem{C} Random amplitude modulation (RAM) stimulus (top, red, with cutoff frequency of 300\,Hz) and evoked responses (spike raster, bottom) of the same P-unit for two different stimulus contrasts (right). The stimulus contrast quantifies the standard deviation of the RAM relative to the fish's EOD amplitude. \figitem{D} Gain of the transfer function (first-order susceptibility), \eqnref{linearencoding_methods}, computed from the responses to 10\,\% (light blue) and 20\,\% contrast (dark blue) RAM stimulation of 5\,s duration. \figitem{E} Absolute value of the second-order susceptibility, \eqnref{chi2}, for both the low and high stimulus contrast. At the lower stimulus contrast an anti-diagonal where the sum of the two stimulus frequencies equals the neuron's baseline frequency clearly sticks out of the noise floor. \figitem{F} At the higher contrast, the anti-diagonal is much weaker. \figitem{G} Second-order susceptibilities projected onto the diagonal (averages over all anti-diagonals of the matrices shown in \panel{E, F}). The anti-diagonals from \panel{E} and \panel{F} show up as a peak close to the cell's baseline firing rate $r$. The susceptibility index, SI($r$) \eqnref{siindex}, quantifies the height of this peak relative to the values in the vicinity. \figitem{H} ISI distributions (top) and second-order susceptibilities (bottom) of two more example P-units (``2021-06-18-ae'', ``2017-07-18-ai'') showing an anti-diagonal, but not the full expected triangular structure. \figitem{I} Most P-units, however, have a flat second-order susceptibility and consequently their SI($r$) values are close to one (cell identifiers ``2018-08-24-ak'', ``2018-08-14-ac'').}
\caption{\label{fig:punit} Linear and nonlinear stimulus encoding in example P-units. \figitem{A} Interspike interval (ISI) distribution of a cell's baseline activity, i.e. the cell is driven only by the unperturbed own electric field (cell identifier ``2020-10-27-ag''). This cell has a rather high baseline firing rate $r=405$\,Hz and an intermediate CV$_{\text{base}}=0.49$ of its interspike intervals. \figitem{B} Power spectral density of the cell's baseline response with marked peaks at the cell's baseline firing rate $r$ and the fish's EOD frequency $f_{\text{EOD}}$. \figitem{C} Random amplitude modulation (RAM) stimulus (top, red, with cutoff frequency of 300\,Hz) and evoked responses (spike raster, bottom) of the same P-unit for two different stimulus contrasts (right). The stimulus contrast quantifies the standard deviation of the RAM relative to the fish's EOD amplitude. \figitem{D} Gain of the transfer function (first-order susceptibility), \eqnref{linearencoding_methods}, computed from the responses to 10\,\% (light blue) and 20\,\% contrast (dark blue) RAM stimulation of 5\,s duration. \figitem{E} Absolute value of the second-order susceptibility, \eqnref{chi2}, for the low stimulus contrast. An anti-diagonal where the sum of the two stimulus frequencies equals the neuron's baseline frequency clearly sticks out of the noise floor. \figitem{F} At the higher contrast, the anti-diagonal in the absolute value of the second-order susceptibility is much weaker. \figitem{G} Second-order susceptibilities projected onto the diagonal (averages over all anti-diagonals of the matrices shown in \panel{E, F}). The anti-diagonals from \panel{E} and \panel{F} show up as a peak close to the cell's baseline firing rate $r$. The susceptibility index, SI($r$) \eqnref{siindex}, quantifies the height of this peak relative to the values in the vicinity. \figitem{H} ISI distributions (top) and second-order susceptibilities (bottom) of two more example P-units (``2021-06-18-ae'', ``2017-07-18-ai'') showing an anti-diagonal, but not the full expected triangular structure. \figitem{I} Most P-units, however, have a flat second-order susceptibility and consequently their SI($r$) values are close to one (cell identifiers ``2018-08-24-ak'', ``2018-08-14-ac'').}
\end{figure*}
Noise stimuli, here random amplitude modulations (RAM) of the EOD (\subfigref{fig:punit}{C}, top trace, red line), have been commonly used to characterize stimulus-driven responses of sensory neurons using transfer functions (first-order susceptibility), spike-triggered averages, or stimulus-response coherences. Here, we additionally estimate from existing recordings the second-order susceptibility to quantify nonlinear encoding. P-unit spikes align more or less clearly with fluctuations in the RAM stimulus. A higher stimulus intensity, here a higher contrast of the RAM relative to the EOD amplitude (see methods), entrains the P-unit response more clearly (light and dark blue for low and high contrast stimuli, respectively, \subfigrefb{fig:punit}{C}). Linear encoding, quantified by the first-order susceptibility or transfer function, \eqnref{linearencoding_methods}, is similar for the two RAM contrasts in this low-CV P-unit (\subfigrefb{fig:punit}{D}), as expected for a linear system. The first-order susceptibility is low for low frequencies, peaks in the range below 100\,Hz and then falls off again \citep{Benda2005}.

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punitexamplecell.py
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@ -141,11 +141,13 @@ def plot_response(ax, s, eodf, time1, stimulus1, contrast1, spikes1,
eod = np.sin(2*np.pi*eodf*time1) * (1 + stim)
else:
eod = np.sin(2*np.pi*eodf*time1) + stim
ax.plot(time1, 4*eod + 7, **s.lsEOD)
ax.plot(time1, 4*(1 + stim) + 7, **s.lsAM)
ax.plot(time1, 4*eod + maxtrials - 1, **s.lsEOD)
ax.plot(time1, 4*(1 + stim) + maxtrials - 1, **s.lsAM)
ax.set_xlim(t0, t1)
ax.set_ylim(-2*maxtrials - 0.5, 14)
ax.xscalebar(1, -0.05, 0.01, None, '10\\,ms', ha='right')
ax.text(t1 + 0.003, maxtrials - 1 + 4, f'${100*contrast1:.0f}$\\,\\%',
va='center', color=s.lsAM['color'])
ax.text(t1 + 0.003, -0.5*maxtrials, f'${100*contrast1:.0f}$\\,\\%',
va='center', color=s.cell_color1)
ax.text(t1 + 0.003, -1.55*maxtrials, f'${100*contrast2:.0f}$\\,\\%',

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\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{textcomp}
\usepackage{xcolor}
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\usepackage[left=25mm, right=25mm, top=20mm, bottom=20mm]{geometry}
\setlength{\parskip}{2ex}
\usepackage[mediumqspace,Gray,squaren]{SIunits} % \ohm, \micro
\usepackage{natbib}
%\bibliographystyle{jneurosci}
\usepackage[breaklinks=true,bookmarks=true,bookmarksopen=true,pdfpagemode=UseNone,pdfstartview=FitH,colorlinks=true,citecolor=blue,urlcolor=blue]{hyperref}
\newcommand{\issue}[1]{\textbf{#1}}
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\begin{document}
\issue{\large Reviewer \#1}
\issue{The manuscript "Spike generation in electroreceptor afferents
introduces additional spectral response components by weakly
nonlinear interactions" submitted to eNeuro represents a noteworthy
advancement in the field, as it elucidates that, under an often
naturally occurring scenario the non linear responses of the pair
electroreceptor-primary afferent ensemble may intervene in signal
encoding. The manuscript shows that during the reception of signals
originating distantly from multiple individual conspecifics,
electroreceptor primary afferents may exhibit nonlinear responses
allowing the fish to guess the presence of more than one
individual. This is articulated with clarity through a
straightforward leaky-integrate-and-fire model of electroreceptor
responsiveness. The illustrations are both lucid and enhance the
comprehension of the results section. The discussion is
sound. However, the intrinsic value of the manuscript would likely
be obscure without a more "biologist-friendly" approach. I would
like to offer several suggestions that may serve to either enhance
the manuscript or inspire future research endeavors.}
\response{}
\issue{First, I should point out that beyond the presence of a
threshold-induced nonlinearity, the complex structure of the
axon-like dendritic innervation receptor cell terminals within the
electroreceptor organ. This analogical nonlinear response may have
its origin in the branched anatomy of the dendrite-axon terminals,
easily verifiable by anatomical studies, and the presence, hardly
demonstrable but plausible, of ion channel diversity; see, for
example, Trigo, F. F. (2019) Antidromic analog signaling. Frontiers
in Cellular Neuroscience, 13, 354. for a discussion of the general
case and the study by Troy Smith, Unguez and Weber (2006, Fig. 3) in
which receptor cells of tuberous electroreceptor organs and their
afferents from Apteronotus leptorhinchus were labeled to varying
degrees by six anti-Kv1 antibodies. Kv1.1 and Kv1.4 immunoreactivity
was intense in the afferent axons of electroreceptor organs. It is
noteworthy that Kv1 are low-threshold channels and, in some cases,
exhibit a prolonged refractory period (Nogueira and Caputi,
2013). These sources of nonlinearity could be mentioned to
strengthen the links between well-written theoretical analysis and
the practical field of experimental physiology.}
\response{READ PAPERS AND CITE THEM}
\issue{Second, and along the same lines, the discussion could be
improved by mentioning the effects and significance of these
nonlinearities when the recipient fish makes changes in its EOD
frequency in at least two cases: a) sustained changes, as in
interference avoidance responses, and b) transient changes, as in
chirps.}
\response{THINK ABOUT IT AND ADD TO DISCUSSION}
\issue{Finally, the precise description of the methods could be
expanded for reaching a broader biology audience; in particular, the
purpose of some procedures should be explained in some way. While
the meaning seems clear as the reader scrolls through the results, a
first reading of the methods, although accurate, does not offer the
biology reader a quick and intuitive approach to the study.}
\response{IMPROVE METHOD DESCRIPTION AS DESCRIBED BELOW}
\issue{Next, I list some minor more detailed comments that may clarify
the design and methods and facilitate their understanding by a
broader audience.}
\issue{In general, you referenced P receptors and ampullary
structures; however, what about T receptors? How can one distinguish
between T and P in the recordings? Might it be possible that the
negative results observed in certain receptors are attributable to
the type of receptor (P or T)? Did you postulate, as suggested by
Viancour (1979), that there exists a continuum of responsiveness
between the extreme profiles of P (signal amplitude) and T (signal
slope)?}
\response{SAY SOMETHING ABOUT T-UNITS AND THAT WE DEFINITELY EXCLUDED THEM}
\issue{In line 147, rather than using the term
"laterally," I believe it would enhance clarity to state "parallel
to each side of the fish," as the orientation of the electrodes may
otherwise remain ambiguous.}
\response{Done.}
\issue{Furthermore, no commentary or discussion is provided regarding
the fact that the stimulation procedure, which is transverse to the
main axis of the body, neglects to account for the effects on the
field foveal perioral region where the majority of receptors are
located.}
\response{ADD SOMETHING TO STIMULATION SECTION}
\issue{Line 148, the phrase "band limited white noise" lacks
clarity. Upon my initial reading, I assumed that the cutoff limit
you referenced pertained to a low pass filter applicable to both
ampullary and P-type tuberous receptors; however, it could indeed be
interpreted as the opposite. In a strict sense, all "white noise
stimuli" are band-passed. The duration of the stimulus establishes a
lower cutoff for the band pass in one instance, while the
responsiveness of the stimulation apparatus delineates the upper
cutoff limits in another. Nevertheless, once one comprehends the
objective of the experiment, the implicit significance of the white
noise filtering becomes exceedingly apparent. Thus, this description
could benefit from greater clarity to avoid the need to explore the
results first in order to understand well.}
\response{STATE TYPE OF FILTERING IN STIMULATION SECTION, CITE ALES SKORJANC}
\issue{Line 154. This procedure elicits a modulation of the envelope
of the reafferent signal. To achieve this, you adopted distinct
approaches for the ampullary and P receptors: a) in the case of
ampullary receptors, you presented white noise and incrementally
elevated its amplitude (variance) until the mean amplitude of the
averaged sine wave recorded via local electrodes adjacent to the
gills exhibited an increase of 1 to 5\%, is this correct?}
\response{NO! EXPLAIN AND ENHANCE STIMULATION SECTION}
\issue{b) with regard to P receptors, you multiplied the head-to-tail
ongoing signal by a white noise signal and played the resultant
output, adjusting the amplitude until the local signal experienced
an enhancement of 1 to 5\% in average, is this interpretation
accurate? Since the head to tail EOD and the local signals over the
body are out of phase this process induces both amplitude and phase
modulation of the stimulus signal, which will be contingent upon the
phase lag of the local EOD at the receptor site in relation to the
head-to-tail EOD. This phase lag, as reported in the literature,
exhibits a shift ranging from pi to 2pi between a receptor situated
at the head and another at the tail. (I posit that this may not
significantly impact individual receptors response; however, how
does this influence the relative timing among distinct receptors,
and what is its correlation with jamming avoidance mechanisms?)
Furthermore, does this form of noise modulation exert a comparable
effect on the flanks (i.e., the apex of the derivative) as it does
on the peaks of the signal themselves? How does this affect the
recruitment of P and T receptors?}
\response{ALL THESE DETAILS DO NOT MATTER AT THE LEVL OF INDIVIDUAL P-UNITS. SEE HLADNIK.}
\issue{Line 238. Are you referring to the terminal non-myelinated
branches that connect receptor cells to the initial Ranvier node?
The peripheral afferent constitutes a myelinated and active dendrite
whose distal branches receive synapses from receptor
cells. Consequently, there exists a summation occurring at some
juncture, likely at the first node, that facilitates the generation
of an action potential. Otherwise, the signal would not be
effectively propagated from the receptors to the ganglia where the
somata reside. Receptors across various species exhibit notable
differences; some are myelinated within the electroreceptor organ,
while others display the first node external to the electroreceptor
organ. Could you discuss this aspect, considering the anatomical
structure of the receptor in your species?}
\response{READ LITERATURE AND SAY A FEW WORDS}
\issue{\large Reviewer \#2}
\issue{This work is a nice contribution to our general understanding
of nonlinearities in sensory coding, and to our detailed
understanding of behaviorally relevant information processing in the
electrosensory systems of weakly electric fish. I have several
suggestions for the authors.}
\response{}
\issue{(1) Abstract, line 29. "...if these frequencies or their sum
match the neuron's baseline firing rate" is not quite accurate
because "these frequencies" implies BOTH input frequencies must
match the baseline firing rate. I think you mean to state, "...if
one of these frequencies or their sum match the neuron's baseline
firing rate."}
\response{Your are right! We changed the sentence as suggested.}
\issue{(2) Abstract, line 33. The wording here is unclear,
specifically what you mean by "much stronger." Much stronger what
exactly? I think you mean to refer to the fact that these nonlinear
responses were more common and stronger in ampullary units than
P-units, but "much stronger" does not clearly convey this,
especially in the abstract.}
\response{We changed the sentence to ``... we identify these predicted nonlinear responses primarily in low-noise P-units and in more than every second ampullary cell.''}
\issue{(3) Figure 1A. "r" needs to be clearly defined here. Based on
the text, it seems to be the baseline firing rate of the neuron, but
this needs to be made clear in the figure legend.}
\response{We added a brief sentence to the caption.}
\issue{(4) Figure 1B. "Because frequencies can also be negative..."
This is unclear and needs more explanation, especially because there
are no negative frequencies in your actual data. How can frequencies
be negative?}
\response{UH... LETS WRITE SOMETHING}
\issue{(5) Figure 3 and 4. Why are the power spectra clipped at such
low frequencies? This makes it impossible to see peaks due to
potential df2 harmonics and fEOD. Figure 5 extends to higher
frequencies to illustrate these and it is not clear why these are
clipped in these two figures.}
\response{HM. LETS CHECK HOW IT LOOKS LIKE. BUT THIS LOW FREQUENCY RANGE IS THE RELEVANT ONE FOR CODING.}
\issue{(6) Figure 3. Why are these example firing rates based on
convolution with a 1 ms Gaussian kernel if the analyses were based
on convolution with a 2 ms Gaussian kernel (line 169)? It seems that
example data should effectively illustrate how the data were
actually analyzed. More fundamentally, why would a 2-fold difference
in kernel width be appropriate for presentation vs. analysis?}
\response{DAMN. LETS REDO THE FIGURE.}
\issue{(7) Figure 3D legend. The relationship between 2nd order AM
(envelope) and the two nonlinear peaks should be made clear. I
believe the envelope is represented by both peaks, correct?}
\response{ADD SENTENCE.}
\issue{(8) Line 302. "not-small amplitude" is arbitrary and
vague. Please be clearer and more precise.}
\response{}
\issue{(9) Figures 5C and 6C. For the stimuli with the red RAM
waveforms, please make it clear which contrast is being represented
by these traces, as responses to two different contrasts are shown.}
\response{We added the shown stimulus contrast to the figure.}
\issue{(10) Figure 5E, F. The legend states that second-order
susceptibility for both the low and high stimulus contrasts are
shown in E, but E shows the low contrast and F shows the high
contrast.}
\response{Good catch! Fixed.}
\issue{(11) Lines 453-465, Figure 8. This section was confusing to
me. Why does second-order susceptibility decrease as stimulus
contrast increases, when theory predicts that higher signal-to-noise
ratios should result in larger nonlinearities?}
\response{NOT WEAK ANY MORE. DEVIATION FROM SQUARE DEPENDENCE. BENJI!}
\issue{(12) Lines 655-675. This was a very nice end to the discussion,
but I would like to see more. I would like the broader significance
of this study to be expanded upon with respect to (1) behavioral
relevance for signal detection in weakly electric fish, and (2)
comparative relevance for other modalities and species. Speculation
is fine so long as it is clearly indicated as such. It might work
best to expand upon and distribute the information in lines 655-666
throughout the discussion at relevant points, rather than as an
afterthought. The conclusion section in lines 667-675 could then
reiterate these points briefly and delve into more detail on
comparative considerations.}
\response{UH. LETS THINK ABOUT IT.}
\end{document}