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nonlinearbaseline.tex

@@ -256,10 +256,9 @@ Spiking thresholds in neurons or rectification at synapses are essential for neu
 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.
 
 % Please keep the Author Summary between 150 and 200 words
-% Use the first person. PLOS ONE authors please skip this step. 
-% Author Summary not valid for PLOS ONE submissions.   
-%\section{Author summary}
-%Weakly electric fish use their self-generated electric field to detect a wide range of behaviorally relevant stimuli. Intriguingly, they show detection performances of stimuli that are (i) extremely weak and (ii) occur in the background of strong foreground signals, reminiscent of what is often described as the cocktail party problem. Such performances are achieved by boosting the signal detection through nonlinear mechanisms. We here analyze nonlinear encoding in two different populations of primary electrosensory afferents of the weakly electric fish. We derive the rules under which nonlinear effects can be observed in both electrosensory subsystems. In a combined experimental and modeling approach we generalize the approach of nonlinear susceptibility to systems that respond to amplitude modulations of a carrier signal.
+% Use the first person.
+\section{Author summary}
+The generation of action potentials involves a strong threshold non-linearity. Nevertheless, the encoding of stimuli with small amplitudes by neurons with sufficient intrinsic noise can be well described as a linear system. As the stimulus amplitude is increased, non-linear effects start to appear. Initially, in the so-called weakly non-linear regime new spectral components at the sum and the difference of two stimulus frequencies start to appear. This regime has been well characterized by theoretical analysis based on simple neuron models like the leaky integrate-and-fire model. These findings predict non-linear interactions whenever one or the sum of two stimulus frequencies matches a neuron's baseline firing rate. We set out to find these signatures in a large set of electrophysiological recordings from electroreceptive neurons of a weakly electric fish. In ampullary cells these interactions are prominent, whereas in P-units they are harder to find. Estimating non-linear response kernels from limited 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. The non-linear response components could boost sensory responses to weak signals emitted by distant conspecifics.
 
   
 \section{Introduction}
@@ -496,11 +495,6 @@ The weakly nonlinear interactions in low-CV P-units could facilitate the detecta
 We have demonstrated pronounced nonlinear responses in primary electrosensory afferents at weak stimulus amplitudes and sufficiently low intrinsic noise levels. The observed nonlinearities match the expectations from previous theoretical studies \citep{Voronenko2017,Franzen2023}. The resulting nonlinear components introduce spectral components not present in the original stimulus, that may provide an edge in the context of signal detection problems at stimulus amplitudes close to threshold \citep{Schlungbaum2023}. Electrosensory afferents share an evolutionary history with hair cells \citep{Baker2019} and share many response properties with mammalian auditory nerve fibers \citep{Barayeu2023, Joris2004}. Thus, we expect weakly nonlinear responses for near-threshold stimulation in auditory nerve fibers as well.
 
 
-\section{Acknowledgements}
-Supported by SPP 2205 ``Evolutionary optimisation of neuronal processing'' by the DFG, project number 430157666.
-We thank Tim Hladnik, Henriette Walz, Franziska Kuempfbeck, Fabian Sinz, Laura Seidler, Eva Vennemann, and Ibrahim Tunc for the data they recorded over the years in our lab
-
-
 \section{Methods}
 
 \subsection{Experimental subjects and procedures}
@@ -677,6 +671,12 @@ Based on the Furutsu-Novikov theorem \citep{Furutsu1963,Novikov1965,Lindner2022,
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 Both, the reduced intrinsic noise and the RAM stimulus, need to replace the original intrinsic noise. Because the RAM stimulus is band-limited and undergoes some transformations before it is added to the reduced intrinsic noise, it is not \textit{a priori} clear, what the amplitude of the RAM should be. We bisected the amplitude of $s_\xi(t)$, until the CV of the resulting interspike intervals matched the one of the original model's baseline activity. The second-order cross-spectra, \eqnref{crossxss}, were computed between the RAM stimulus $s_{\xi}(t)$ and the spike train $x(t)$ it evoked. In this way, the effective signal-to-noise ratio can be increased while maintaining the total noise in the system. 
 
+
+\section{Acknowledgements}
+Supported by SPP 2205 ``Evolutionary optimisation of neuronal processing'' by the DFG, project number 430157666.
+We thank Tim Hladnik, Henriette Walz, Franziska Kuempfbeck, Fabian Sinz, Laura Seidler, Eva Vennemann, and Ibrahim Tunc for the data they recorded over the years in our lab
+
+
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