diff --git a/nonlinearbaseline.tex b/nonlinearbaseline.tex index 5dc7de5..40fcfc4 100644 --- a/nonlinearbaseline.tex +++ b/nonlinearbaseline.tex @@ -467,7 +467,7 @@ Is it possible to predict nonlinear responses in a three-fish setting based on s \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 investigated such nonlinear responses in two types of electroreceptor afferents that differ in their intrinsic noise levels \citep{Grewe2017} using band-limited white-noise stimuli to estimate second-order susceptibilities. Following \citet{Voronenko2017} we expected to observe distinct ridges in the second-order susceptibility where either of the stimulus frequencies alone or their sum matches the baseline firing rate. We find traces of these nonlinear responses in the majority of ampullary afferents. In P-units, however, only a minority of the recorded cells, i.e. those characterized by low intrinsic noise levels and low output noise, show signs of such nonlinear responses. Complementary model simulations demonstrate in the limit of high numbers of FFT segments, that the estimates from the electrophysiological data are indeed indicative of the theoretically expected triangular structure of supra-threshold weakly nonlinear responses. With this, we provide experimental evidence for nonlinear responses of a spike generator at low intrinsic noise levels or low stimulus amplitudes. \notejg{not sure, if i like this last sentence} +Theoretical work \citep{Voronenko2017,Franzen2023} derived analytical expressions for weakly-nonlinear responses of spike generating 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 band-limited white-noise stimuli to estimate second-order susceptibilities. Following \citet{Voronenko2017} we expected to observe distinct ridges in the second-order susceptibility where either of the stimulus frequencies alone or their sum matches the baseline firing rate. We find traces of these nonlinear responses in the majority of ampullary afferents. In P-units, however, only a minority of the recorded cells, i.e. those characterized by low intrinsic noise levels and low output noise, show signs of such nonlinear responses. Complementary model simulations demonstrate in the limit of high numbers of FFT segments, that the estimates from the electrophysiological data are indeed indicative of the theoretically expected triangular structure of supra-threshold weakly nonlinear responses. With this, we provide evidence for weakly-nonlinear responses of a spike generator at low intrinsic noise levels or low stimulus amplitudes in real sensory neurons. \subsection{Intrinsic noise limits nonlinear responses} The weakly nonlinear regime with its triangular pattern of elevated second-order susceptibility resides between the linear and a stochastic mode-locking regime. Too strong intrinsic noise linearizes the system and wipes out the triangular structure of the second-order susceptibility \citep{Voronenko2017}. Our electrophysiological recordings match this theoretical expectation. The lower the coefficient of variations of the P-units' baseline interspike intervals, the more cells show the expected nonlinearities (\subfigref{fig:dataoverview}{B})\notejg{There's something wrong here}. Still, only 18\,\% of the P-units analyzed in this study show relevant nonlinear responses. On the other hand, the majority of the ampullary cells have generally lower CVs (median of 0.09) and indeed we can observe nonlinear responses in the majority of ampullary afferents (74\,\%, \subfigrefb{fig:dataoverview}{C}).