diff --git a/susceptibility1.tex b/susceptibility1.tex index 2ffbd49..cded7e7 100644 --- a/susceptibility1.tex +++ b/susceptibility1.tex @@ -1,6 +1,8 @@ \documentclass[10pt,letterpaper]{article} -\title{Weakly nonlinear responses at low intrinsic noise levels in two types of electrosensory primary afferents} +\title{Spike generation in electroreceptor afferents introduces additional spectral response components by weakly nonlinear interactions} + +%\title{Weakly nonlinear interactions of the spike generator introduce additional spectral response components in electroreceptor afferents} \author{Alexandra Barayeu\textsuperscript{1}, Maria Schlungbaum\textsuperscript{2,3}, @@ -398,7 +400,10 @@ % Please keep the abstract below 300 words \section{Abstract} -Neuronal processing is inherently nonlinear --- spiking thresholds or rectification in synapses are central to neuronal computations. Nevertheless, linear response theory has been instrumental in understanding, for example, the impact of noise or synchronous spikes on signal transmission, or the emergence of oscillatory activity. At higher signal-to-noise ratios, however, the second order in the Volterra \notebl{Volterra wurde noch nicht erwaehnt} series becomes relevant. This second-order susceptibility captures nonlinear interactions between pairs of stimulus frequencies. Theoretical results for leaky integrate-and-fire neurons suggest strong responses at the sum of two input frequencies only when these frequencies or their sum match the neuron's baseline firing rate. We here analyze second-order susceptibilities in two types of primary electroreceptor afferents, P-units of the active and ampullary cells of the passive electrosensory system of the wave-type electric fish \textit{Apteronotus leptorhynchus}. In our combined experimental and modeling approach we find the predicted weakly nonlinear responses in some P-units with very low baseline interspike-interval variability and much stronger in all ampullary cells, which are less noisy than P-units. Such nonlinear responses boost responses to weak sinusoidal stimuli and are therefore of immediate relevance for wave-type electric fish that are exposed to superpositions of many frequencies in social contexts. +Neuronal processing is inherently nonlinear --- spiking thresholds or rectification in synapses is essential to neuronal computations. Nevertheless, linear response theory has been instrumental in understanding, for example, the impact of noise or synchronous spikes 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 the predicted nonlinear responses in low-noise P-units and much stronger in all 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. + +% Such nonlinear responses boost responses to weak sinusoidal stimuli and are therefore of immediate relevance for wave-type electric fish that are exposed to superpositions of many frequencies in social contexts. % Please keep the Author Summary between 150 and 200 words % Use the first person. PLOS ONE authors please skip this step. @@ -407,9 +412,6 @@ Neuronal processing is inherently nonlinear --- spiking thresholds or rectificat %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. -\notejb{Check use of $f_2$ versus $\Delta f_2$ in the results section, in particular in fig 4 and following} - - \section{Introduction} \begin{figure*}[t] @@ -546,7 +548,7 @@ The population of ampullary cells is generally more homogeneous, with lower base \section{Discussion} -Theoretical work \citep{Voronenko2017,Franzen2023} derived analytical expressions for weakly-nonlinear responses in LIF and theta model neurons driven by two sine waves with distinct frequencies. We here looked for such nonlinear responses in two types of electroreceptor afferents that differ in their intrinsic noise levels \citep{Grewe2017} using white-noise stimuli to estimate second-order susceptibilities. Following \citet{Voronenko2017} we expected to observe increased levels of second-order susceptibility where either of the stimulus frequencies alone or the sum of the stimulus frequencies matches the baseline firing rate ($f_1=\fbase{}$, $f_2=\fbase{}$ or \fsumb{}). We find traces of these nonlinear responses in most of the low-noise ampullary afferents and only those P-units with very low intrinsic noise levels. Complementary model simulations demonstrate, in the limit to vanishing stimulus amplitudes and extremely high number of repetitions, that the second order susceptibilities estimated from the electrophysiological data are indeed indicative of the theoretically expected weakly nonlinear responses. +Theoretical work \citep{Voronenko2017,Franzen2023} derived analytical expressions for weakly-nonlinear responses in LIF and theta model neurons driven by two sine waves with distinct frequencies. We here investigated such nonlinear responses in two types of electroreceptor afferents that differ in their intrinsic noise levels \citep{Grewe2017} using white-noise stimuli to estimate second-order susceptibilities. Following \citet{Voronenko2017} we expected to observe increased levels of second-order susceptibility where either of the stimulus frequencies alone or the sum of the stimulus frequencies matches the baseline firing rate ($f_1=\fbase{}$, $f_2=\fbase{}$ or \fsumb{}). We find traces of these nonlinear responses in most of the low-noise ampullary afferents and only those P-units with very low intrinsic noise levels. Complementary model simulations demonstrate, in the limit to vanishing stimulus amplitudes and extremely high number of repetitions, that the second order susceptibilities estimated from the electrophysiological data are indeed indicative of the theoretically expected weakly nonlinear responses. With this, we provide experimental evidence for nonlinear responses of a spike generator at low stimulus amplitudes. % EOD locking: % Phase-locking to the own field also leads to a representation of \feod{} in the P-unit firing rate (see \figref{fig:punit}\panel{B}) \citep{Sinz2020}.