worked on data overview text

nonlinearbaseline.tex

@@ -501,7 +501,7 @@ In the example recordings shown above (\figsrefb{fig:punit} and \fref{fig:ampull
   \caption{\label{fig:noisesplit} Estimation of second-order susceptibilities. \figitem{A} \suscept{} (right) estimated from $N=198$ 256\,ms long FFT segments of an electrophysiological recording of another P-unit (cell ``2017-07-18-ai'', $r=78$\,Hz, CV$_{\text{base}}=0.22$) driven with a RAM stimulus with contrast 5\,\% (left). \figitem[i]{B} \textit{Standard condition} of model simulations with intrinsic noise (bottom) and a RAM stimulus (top). \figitem[ii]{B} \suscept{} estimated from simulations of the cell's LIF model counterpart (cell ``2017-07-18-ai'', table~\ref{modelparams}) based on the same RAM contrast and number of $N=100$ FFT segments. As in the electrophysiological recording only a weak anti-diagonal is visible. \figitem[iii]{B} Same as \panel[ii]{B} but using $10^6$ FFT segments. Now, the expected triangular structure is revealed. \figitem[iv]{B} Convergence of the \suscept{} estimate as a function of FFT segments. \figitem{C} At a lower stimulus contrast of 1\,\% the estimate did not converge yet even for $10^6$ FFT segments. The triangular structure is not revealed yet. \figitem[i]{D} Same as in \panel[i]{B} but in the \textit{noise split} condition: there is no external RAM signal (red) driving the model. Instead, a large part (90\,\%) of the total intrinsic noise is treated as a signal and is presented as an equivalent amplitude modulation ($s_{\xi}(t)$, orange, 10.6\,\% contrast), while the intrinsic noise is reduced to 10\,\% of its original strength (bottom, see methods for details). \figitem[i]{D} 100 FFT segments are still not sufficient for estimating \suscept{}. \figitem[iii]{D} Simulating one million segments reveals the full expected trangular structure of the second-order susceptibility. \figitem[iv]{D} In the noise-split condition, the \suscept{} estimate converges already at about $10^{4}$ FFT segments.}
 \end{figure*}
 
-One simple reason could be the lack of data, i.e. the estimation of the second-order susceptibility is not good enough. Electrophysiological recordings are limited in time, and therefore only a limited number of trials, here repetitions of the same frozen RAM stimulus, are available. In our data set we have 1 to 199 trials (median: 10) of RAM stimuli with a duration ranging from 2 to 5\,s (median: 8\,s), resulting in a total duration of 30 to 400\,s. Using a resolution of 0.5\,ms and FFT segments of 512 samples this yields 105 to 1520 available FFT segments for a specific RAM stimulus. As a consequence, the cross-spectra, \eqnref{eq:crosshigh}, are insufficiently averaged and the full structure of the second-order susceptibility might be hidden in finite-data noise. This experimental limitation can be overcome by using a computational model for the P-unit, a stochastic leaky integrate-and-fire model with adaptation current, dendritic preprocessing, and parameters fitted to the experimentally recorded P-unit (\figrefb{flowchart}) \citep{Barayeu2023}. The model faithfully reproduces the second-order susceptibility of the P-unit estimated from the same low number of FFT (fast fourier transform) segments as in the experiment ($N=100$, compare faint anti-diagonal in the bottom left corner of the second-order susceptibility in \panel[ii]{A} and \panel[ii]{B} in \figrefb{fig:noisesplit}).
+One simple reason could be the lack of data, i.e. the estimation of the second-order susceptibility is not good enough. Electrophysiological recordings are limited in time, and therefore only a limited number of trials, here repeated presentations of the same frozen RAM stimulus, are available. In our data set we have 1 to 199 trials (median: 10) of RAM stimuli with a duration ranging from 2 to 5\,s (median: 8\,s), resulting in a total duration of 30 to 400\,s. Using a resolution of 0.5\,ms and FFT segments of 512 samples this yields 105 to 1520 available FFT segments for a specific RAM stimulus. As a consequence, the cross-spectra, \eqnref{eq:crosshigh}, are insufficiently averaged and the full structure of the second-order susceptibility might be hidden in finite-data noise. This experimental limitation can be overcome by using a computational model for the P-unit, a stochastic leaky integrate-and-fire model with adaptation current, dendritic preprocessing, and parameters fitted to the experimentally recorded P-unit (\figrefb{flowchart}) \citep{Barayeu2023}. The model faithfully reproduces the second-order susceptibility of the P-unit estimated from the same low number of FFT (fast fourier transform) segments as in the experiment ($N=100$, compare faint anti-diagonal in the bottom left corner of the second-order susceptibility in \panel[ii]{A} and \panel[ii]{B} in \figrefb{fig:noisesplit}).
 
 In model simulations we can increase the number of FFT segments beyond what would be experimentally possible, here to one million (\figrefb{fig:noisesplit}\,\panel[iii]{B}). Then the estimate of the second-order susceptibility indeed improves. It gets less noisy, the diagonal at $f_ + f_2 = r$ is emphasized, and the vertical and horizontal ridges at $f_1 = r$ and $f_2 = r$ are revealed. Increasing the number of FFT segments also reduces the order of magnitude of the susceptibility estimate until close to one million the estimate levels out at a low values (\subfigrefb{fig:noisesplit}\,\panel[iv]{B}).
 
@@ -592,10 +592,13 @@ Overall, observing SI($r$) values greater than about 1.8, even for a number of F
 \end{figure*}
 
 \subsection{Low CVs and weak stimuli are associated with distinct nonlinearity in recorded electroreceptive neurons}
-Now we are prepared to evaluate our pool of 39 P-unit model cells, 159 P-units, and 30 ampullary afferents recorded in 75 specimen of \textit{Apteronotus leptorhynchus}.
-\notejb{We need to state the number of trials}
+Now we are prepared to evaluate our pool of 39 P-unit model cells, 159 P-units, and 30 ampullary afferents recorded in 75 specimen of \textit{Apteronotus leptorhynchus}. For comparison across cells we condensed the structure of the second-order susceptibilities into SI($r$) values, \eqnref{eq:nli_equation}, computed from FFTs based on 100 segments of 512 samples at a temporal resolution of 0.5\,ms.
+
+In the P-unit models, each model cell contributed with three RAM stimulus presentations with contrasts of 1, 3, and 10\,\%, resulting in $n=117$ data points. 19 (16\,\%) had SI($r$) values larger than 1.8, indicating the expected ridges at the baseline firing rate in their second-order susceptiility . The lower the cell's baseline CV, i.e. the less intrinsic noise, the higher the SI($r$) (\figrefb{fig:dataoverview}\,\pane[i]{A}). Also, the lower the response modulation, i.e. the weaker the effective stimulus, the higher the S($r$) (\figrefb{fig:dataoverview}\,\pane[ii]{A}). Cells with high SI($r$) values are the ones with baseline firing rate below 200\,Hz (\figrefb{fig:dataoverview}\,\pane[iii]{A}). In comparison to the experimentally measured P-unit recordings, the model cells are skewed to lower baseline CVs (Mann-Whitney $U=12924$, $p=1.3\times 10^{-7}$), because the models are not able to reproduce bursting, which we observe in many P-units and which leads to high CVs. Also the response modulation of the models is skewed to lower values (Mann-Whitney $U=12846$, $p=9.1\times 10^{-8}$), because in the measured cells, response modulation is positively correlated with baseline CV \notejb{(XXX)}, i.e. bursting cells are more sensitive. \notejb{cehck baseline firing rate differences.}
+
+
 \notejb{We need to know which contrasts}
-For comparison across cells we quantify the structure of the second-order susceptibilities by the SI($r$), \eqnref{eq:nli_equation}, that quantifies the expected ridge of the second-order susceptibility at the baseline firing rate (e.g. \subfigref{fig:punit}{G}).
+
 
 Three P-units stand out with \nli{} values exceeding two, but additional \notejb{XXX} cells have \nli{} values greater than 1.8. Based on our insights from the P-unit models these would have the expected triangular structure in their susceptibilities when estimated with a sufficiently high number of segments. However, we can only speculate how many of the cells with lower \nli{} values are false negatives. \notejb{because also many have been measured at too strong contrasts}.
 The \nli{} values of the P-unit population correlate weakly with the CV of the baseline ISIs. Cells with lower baseline CVs tend to have more pronounced peaks in their projections than those that have high baseline CVs (\subfigrefb{fig:dataoverview}{A}). This negative correlation is more pronounced against the CV measured during stimulation (\subfigrefb{fig:dataoverview}{C}).