added notes from our discussion

manuscript.tex

@@ -103,7 +103,6 @@ Nils A. Koch\textsuperscript{1,2}, Lukas Sonnenberg\textsuperscript{1,2}, Jan Be
 
 \textsuperscript{1}Institute for Neurobiology, University of Tuebingen, 72072 Tuebingen, Germany\\
 \textsuperscript{2}Bernstein Center for Computational Neuroscience Tuebingen, 72076 Tuebingen, Germany
-\notels{shouldn't Nils' current position be on here, too?} \notenk{I don't think so, I didn't perform the work there}
 
 \subsection{Author Contributions - Each author must be identified with at least one of the following: Designed research, Performed research, Contributed unpublished reagents/ analytic tools, Analyzed data, Wrote the paper.}
 \notenk{Adjust as you deem appropriate}\\
@@ -132,7 +131,7 @@ NK, LS, JB Wrote the paper
 Authors report no conflict of interest.
 \\\textbf{A.} The autthors declare no competing financial interests.
 \subsection{Funding sources}
-\notenk{Add as appropriate - I don't know this information}
+\notenk{Add as appropriate - I don't know this information}\notejb{SmartStart}
 \newpage{}
 
 
@@ -281,48 +280,55 @@ To examine the role of cell-type specific ionic current environments on the impa
 \end{figure}
 
 \subsection*{Variety of model neurons}
-Neuronal firing is heterogenous across the CNS and a set of neuronal models with heterogenous firing due to different ionic currents is desirable to reflect this heterogeneity. The set of single-compartment, conductance-based neuronal models used here has considerable diversity as evident in the variability seen across neuronal models both in spike trains and their fI curves (\Cref{fig:diversity_in_firing}). The models chosen all fire tonically and do not exhibit bursting. See methods for details and naming of the models. Some models, such as Cb stellate and RS inhibitory models, display type I firing whereas others such as Cb stellate \(\Delta\)\Kv and STN models have type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) generated through a saddle-node on invariant cycle bifurcation. Type II firing is characterized by a discontinuity in the fI curve (i.e. a jump occurs from no firing to firing at a certain frequency) due to sub-critical Hopf bifurcation \cite{ERMENTROUT2002, ermentrout_type_1996}. The other models used here lie on a continuum between these prototypical firing classifications. Most neuronal models exhibit hysteresis with ascending and descending ramps eliciting spikes at different current thresholds, however the STN +\Kv, STN \(\Delta\)\Kv, and Cb stellate \(\Delta\)\Kv models have large hysteresis (\Cref{fig:diversity_in_firing}, \Cref{fig:ramp_firing}). This prominent hysteresis despite a continues but steep fI curve, together with the long delays of the first spike hint at a homoclinic bifurcation for the STN models \citep{Izhikevich2006} \notejb{add paper by Susanne Schreiber and Jan-Hendrik Schleimer}.
+Neuronal firing is heterogenous across the CNS and a set of neuronal models with heterogenous firing due to different ionic currents is desirable to reflect this heterogeneity. The set of single-compartment, conductance-based neuronal models used here has considerable diversity as evident in the variability seen across neuronal models both in spike trains and their fI curves (\Cref{fig:diversity_in_firing}). The models chosen all fire tonically and do not exhibit bursting. See methods for details and naming of the models. Some models, such as Cb stellate and RS inhibitory models, display type I firing whereas others such as Cb stellate \(\Delta\)\Kv and STN models have type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) generated through a saddle-node on invariant cycle bifurcation. Type II firing is characterized by a discontinuity in the fI curve (i.e. a jump occurs from no firing to firing at a certain frequency) due to sub-critical Hopf bifurcation \cite{ERMENTROUT2002, ermentrout_type_1996}. The other models used here lie on a continuum between these prototypical firing classifications. Most neuronal models exhibit hysteresis with ascending and descending ramps eliciting spikes at different current thresholds, however the STN +\Kv, STN \(\Delta\)\Kv, and Cb stellate \(\Delta\)\Kv models have large hysteresis (\Cref{fig:diversity_in_firing}, \Cref{fig:ramp_firing}). This prominent hysteresis despite a continues but steep fI curve, together with the long delays of the first spike hint at a homoclinic bifurcation for the STN models \citep{Izhikevich2006} \notejb{add paper by Susanne Schreiber and Jan-Hendrik Schleimer}. \notejb{No bifurctions, but mention different dynamics!}
 
 \subsection*{Characterization of Neuronal Firing Properties}
 \begin{figure}[tp]
         \centering
         \includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf}
         \\\notejb{Hab die ? durch LOF/GOF? ersetzt.}
+        \\\notejb{Add arrows to indicate change, make red fI curve in the bottom left smaller. Alternative: legend below the panel.}
         \linespread{1.}\selectfont
         \caption[]{Characterization of firing with AUC and rheobase. (A) The area under the curve (AUC) of the repetitive firing frequency-current (fI) curve. (B) 
 Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy 4 quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in blue with respect to a reference fI curve (black) depict the general changes associated with each quadrant.}
         \label{fig:firing_characterizaton}
 \end{figure}
 
-Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between conditions. Here we focus on two aspects of firing: rheobase, the smallest injected current at which the cell fires an action potential, and the initial \notejb{is ``initially'' ment temporally or with respect to currents?} shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for a fixed range of input currents above rheobase (\Cref{fig:firing_characterizaton}A). The characterization of firing by rheobase and AUC allows to characterize both a neuron's excitability in the sub-threshold regime (rheobase) and periodic firing in the super-threshold regime (AUC). Note that AUC is essentially quantifying the slope of a neuron's fI curve.
+Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between conditions. Here we focus on two aspects of firing: rheobase, the smallest injected current at which the cell fires an action potential, and the shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for a fixed range of input currents above rheobase (\Cref{fig:firing_characterizaton}A). \notejb{this way we make the AUC independent from changes in rheobase} The characterization of firing by rheobase and AUC allows to characterize both a neuron's excitability in the sub-threshold regime (rheobase) and periodic firing in the super-threshold regime (AUC). Note that AUC is essentially quantifying the slope of a neuron's fI curve.
 
-Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, $\Delta$rheobase, and in AUC, $\Delta$AUC, relative to the wild type neuron. $\Delta$AUC is in addition normalized to the AUC if the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by $\Delta$rheobase and \notejb{$\Delta$AUC$_C$} (\Cref{fig:firing_characterizaton}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\Delta\)rheobase), unambigously indicating an increased firing that clearly might be classified as a GOF of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\Delta\)rheobase), indicating a decreased, LOF firing. In the lower left (\(-\Delta\)AUC and \(-\Delta\)rheobase) and upper right (\(+\Delta\)AUC and \(+\Delta\)rheobase) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability. In these cases it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionaly generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant. \notejb{These latter sentences could also go into the discussion. On the other hand they pave the way for the reader.}
+Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, $\Delta$rheobase, and in AUC, $\Delta$AUC, relative to the wild type neuron. $\Delta$AUC is in addition normalized to the AUC if the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by $\Delta$rheobase and \notejb{normalized $\Delta$AUC} (\Cref{fig:firing_characterizaton}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\Delta\)rheobase), unambigously indicating an increased firing that clearly might be classified as a GOF of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\Delta\)rheobase), indicating a decreased, LOF firing. In the lower left (\(-\Delta\)AUC and \(-\Delta\)rheobase) and upper right (\(+\Delta\)AUC and \(+\Delta\)rheobase) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability. In these cases it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionaly generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant.
 
 \subsection*{Sensitivity Analysis}
 Sensitivity analyses are used to understand how input model parameters contribute to determining the output of a model \citep{Saltelli2002}. In other words, sensitivity analyses are used to understand how sensitive the output of a model is to a change in input or model parameters. One-factor-a-time sensitivity analyses involve altering one parameter at a time and assessing the impact of this parameter on the output. This approach enables the comparison of given alterations in parameters of ionic currents across models.
 
-For example, when shifting the half-activation voltage \(V_{1/2}\) of the potassium current in the FS +\Kv model to more depolarized values, then the rheobase of the resulting fI curves shifts to lower currents \(-\Delta\)rheobase), making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves is reduced (\(-\Delta\)AUC), reducing firing rate (\Cref{fig:AUC_correlation}~A). Plotting the corresponding changes in AUC against the change in \(V_{1/2}\) results in a monotonously falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we get a different relation between the changes in AUC and the shifts in \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterize each of these curve by a single number, the \( \text{Kendall} \tau \) correlation coefficient. A monotonously increasing curve results in a \( \text{Kendall} \tau \) close to $+1$, a monotounsly decreasing curve in \( \text{Kendall} \tau \approx -1 \), and a non-monotonous, non-linear relation relation in \( \text{Kendall} \tau \) close to zero (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C).
+For example, when shifting the half-activation voltage \(V_{1/2}\) of the potassium current in the FS +\Kv model to more depolarized values, then the rheobase of the resulting fI curves shifts to lower currents \(-\Delta\)rheobase), making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves is reduced (\(-\Delta\)AUC), reducing firing rate (\Cref{fig:AUC_correlation}~A). \notejb{Refer to Fig 2B} Plotting the corresponding changes in AUC against the change in \(V_{1/2}\) results in a monotonously falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we get a different relation between the changes in AUC and the shifts in \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterize each of these curve by a single number, the \( \text{Kendall} \tau \) correlation coefficient. A monotonously increasing curve results in a \( \text{Kendall} \tau \) close to $+1$, a monotounsly decreasing curve in \( \text{Kendall} \tau \approx -1 \), and a non-monotonous, non-linear relation relation in \( \text{Kendall} \tau \) close to zero (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C).
 
 Changes in gating \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance affect AUC (\Cref{fig:AUC_correlation}), but how exactly AUC is affected usually depends on the specific models. Increasing, for example, the slope factor of the \Kv activation curve, increases the AUC in all models (\( \text{Kendall} \tau \approx +1\)), but with different slopes (\Cref{fig:AUC_correlation}~B). Similar consistent positive correlations can be found for shifts in A-current activation \(V_{1/2}\). Changes in \Kv activation \(V_{1/2}\) and in A-current conductance result in negative correlations with the AUC in all models (\( \text{Kendall} \tau \approx -1\)).
 
 Qualitative differences can be found, for example, when increasing the conductance of the delayed rectifier (\Cref{fig:AUC_correlation}~C). In some model neurons this increased AUC (\( \text{Kendall} \tau \approx +1\)), whereas in others AUC is decreased (\( \text{Kendall} \tau \approx -1\)). In the STN +\Kv model, AUC depends in a non-linear way on the conductance of the delayed rectifier, resulting in an \( \text{Kendall} \tau \) close to zero. Even more dramatic qualitative differences between models result from shifts of the activation curve of the delayed rectifier, as discussed already above (\Cref{fig:AUC_correlation}~A). Some model neurons do almost not depend on changes in K-current activation \(V_{1/2}\) or show strongly non-linear dependencies, both resulting in \( \text{Kendall} \tau\) close to zero. Many model neurons show strongly negative correlations, and a few show positive correlations with shifting the activation curve of the delayed rectifier.
 
-\notejb{the slope factor has a name (``slope factor'', but \(V_{1/2}\) not. How is this called, ``midpoint potential''?}\notenk{How about ``half-maximal potential''?}
+\notejb{the slope factor has a name (``slope factor''), but \(V_{1/2}\) not. How is this called, ``midpoint potential''? ``half activation potential/voltage''}\notenk{How about ``half-maximal potential''?}
+
+\notejb{``maximum conductance''}
 
 
 \begin{figure}[tp]
         \centering
         \includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf}
+        \\\notejb{y-labels: normalized $\Delta$AUC}
         \\\notejb{tick labels too small!}\notenk{Is this better?}\notejb{Make them as large as possible. You still have a bit of room before they start overlapping.}
-        \\\notejb{By the way: all figures should be included with their original size, so that the fonts have the same size in all the figures!}
+        \\\notejb{By the way: all figures should be included with their original size, so that the fonts have the same size in all the figures! - Should be ok by now.}
         \\\notejb{The colored boxes need to be a bit higher with the topic edge having some distance to the plot title}
         \\\notejb{To make referencing in the text simpler we should tag each panel}
         \\\notejb{Normalized AUC is called ``$AUC_{contrast}$'' in the methods...}
+        \\\notejb{second column: x-label are wrong, i.e. $k/k_{WT}$, $g/g_{WT}$}
+        \\\notejb{Make subplot size exactly like in Figure 4}
         \linespread{1.}\selectfont
         \caption[]{Effects of altered channel kinetics on AUC in various neuron models. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in \(V_{1/2}\) and AUC, slope factor k and AUC as well as current conductances and AUC for each model are shown on the right in (A), (B) and (C) respectively. The relationships between AUC and \(\Delta V_{1/2}\), slope (k) and conductance (g) for the Kendall \(\tau\) coefficients highlights by the black box are depicted in the middle panel. The fI curves corresponding to one of the models are shown in the left panels.}
         \label{fig:AUC_correlation}
 \end{figure}
 
+\notejb{Add more detailed step-by-step description what we did here, like for AUC.}
 The rheobase is also affected by changes in channel kinetics (\Cref{fig:rheobase_correlation}). In contrast to AUC, most alterations result in similar changes of rheobase in all models, but there are some noteable exceptions. Changing the slope factor of Na-current inactivation, \Kv-current inactivation, and A-current activation affect rheobase both with positive and negative correlations in different models (\Cref{fig:rheobase_correlation}B). Departures from monotonic relationships occur in some models as a result of K-current activation, \Kv-current inactivation, and A-current activation in some models \notejb{which parameters are changed?}. Maximum conductance affects rheobase similarly across models (\Cref{fig:rheobase_correlation}C). However, identical changes in current gating properties such as activation or inactivation \(V_{1/2}\) or slope factor \(k\) can have differing effects on firing depending on the model in which they occur. \notejb{This we just have said...}
 
 \begin{figure}[tp]
@@ -340,9 +346,8 @@ Mutations in \Kv are associated with episodic ataxia type~1 (EA1) and have been
         \centering
         \includegraphics[width=\linewidth]{Figures/simulation_model_comparison.pdf}
         \\\notejb{Font sizes...}
-        \\\notejb{The mutation symbols and colors are not the same in all subplots!}
         \linespread{1.}\selectfont
-        \caption[]{Effects of episodic ataxia type~1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (\(AUC_{contrast}\)) and rheobase (\(\Delta\)rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kv (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kv (I) models. V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively.}
+        \caption[]{Effects of episodic ataxia type~1 associated \Kv mutations on firing. \notejb{Note that marker shape indicates model type/firing type} Effects of \Kv mutations on AUC (\(AUC_{contrast}\)) and rheobase (\(\Delta\)rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kv (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kv (I) models. V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively.}
         \label{fig:simulation_model_comparision}
 \end{figure}