merge

Figures/firing_characterization-jb.py

@@ -227,7 +227,7 @@ def plot_quadrant(ax):
     ax.spines['left'].set_position('zero')
     ax.spines['bottom'].set_position('zero')
     ax.text(1.2, 0.05, '$\\Delta$ rheobase', ha='right')
-    ax.text(-0.05, 0.75, '$\\Delta$ AUC', ha='right', rotation=90)
+    ax.text(-0.03, 0.7, '$\\Delta$ AUC', ha='right', rotation=90)
     ax.tick_params(length=0)
     ax.set_xlim(-1, 1)
     ax.set_ylim(-1, 1)
@@ -268,8 +268,8 @@ ax1.text(-0.25, 1.2, string.ascii_uppercase[0], transform=ax1.transAxes, size=16
 ax3.text(-0.02, 1.05, string.ascii_uppercase[1], transform=ax3.transAxes, size=16, weight='bold')
 
 show_spines(ax3, '')
-ax3.set_ylabel('$\Delta$ AUC')
+#ax3.set_ylabel('$\\Delta$ AUC', rotation='vertical')
-ax3.set_xlabel('$\Delta$ rheobase')
+#ax3.set_xlabel('$\\Delta$ rheobase')
 plot_quadrant(ax3) # plot delineation into quadrants
 
 
@@ -301,4 +301,4 @@ plot_diff_sqrt(ax3_BR, b2=0.4, c2=75)
 ax3_BR.set_ylim(inset_ylim)
 fig.set_size_inches(cm2inch(8.17,12))
 fig.savefig('./Figures/firing_characterization.pdf', dpi=fig.dpi) #bbox_inches='tight', dpi=fig.dpi
-plt.show()
+plt.show()

manuscript.tex

@@ -272,18 +272,20 @@ The code/software described in the paper is freely available online at [URL reda
 
 To examine the role of cell-type specific ionic current environments on the impact of altered ion channel properties on firing behaviour a set of neuronal models was used and properties of channels common across models were altered systematically one at a time. The effects of a set of episodic ataxia type~1 associated \Kv mutations on firing was then examined across different neuronal models with different ionic current environments.
 
-\subsection*{Firing Characterization}
+\subsection*{Characterization of Neuronal Firing Properties}
-\begin{figure}[tp]
+\begin{figure}[t]
         \centering
         \includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf}
-        \\\notejb{Das mit den LOF, GOF und ? in B ist mal ein Vorschlag, der erstens noch verbessert werden kann, aber der auch gerne wieder rueckgaengig gemacht werden kann.}\notenk{Ich wurde LOF, GOF  und ? rueckgaengig machen weil wir argumentieren dass LOF und GOF fuer da Feuerverhalten nicht so geeignet sind}
+        \\\notejb{Das mit den LOF, GOF und ? in B ist mal ein Vorschlag, der erstens noch verbessert werden kann, aber der auch gerne wieder rueckgaengig gemacht werden kann.}\notenk{Ich wurde LOF, GOF  und ? rueckgaengig machen weil wir argumentieren dass LOF und GOF fuer da Feuerverhalten nicht so geeignet sind} \notejb{Ja, und genau die Fragezeichen unterstreichen das schon an dieser Stelle. Spaeter bei den Ergebnissen gibt Beispiele, die genau diese Problem haben (Fig 3.A links), da wuerde ich dann darauf hinweisen.}
         \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 (smallest injected current at which the cell fires an action potential) and the initial shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for input currents above rheobase (\Cref{fig:firing_characterizaton}A). The characterization of firing with AUC and rheobase enables determination of general increases or decreases in firing based on current-firing relationships. The upper left quadrant (\(+\Delta\)AUC and \(-\Delta\)rheobase) indicates an increased firing whereas the bottom right quadrant (\(-\Delta\)AUC and \(+\Delta\)rheobase) indicates decreased firing (\Cref{fig:firing_characterizaton}B). 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 and cannot uniquely be described as a gain or loss of excitability.
+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 (smallest injected current at which the cell fires an action potential) and the initial 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.
+
+In the upper left quadrant of \Cref{fig:firing_characterizaton}B, 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. Im 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.
 
 \begin{figure}[tp]
         \centering
@@ -293,8 +295,7 @@ Neuronal firing is a complex phenomenon and a quantification of firing propertie
         \label{fig:diversity_in_firing}
 \end{figure}
 
-
+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. Bursting would add a third dimension to the characterization of neuronal firing properties, in addition to rheobase and AUC. 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. \notejb{The STN models could be a homoclinic bifurcation (long delay but type 2 like firing), maybe cite Izhikevic book for this.} 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}).\notejb{This hysteresis also supports the homoclinic bifurcation. It is like Type II but with a saddle producing long delays and low rates like Type I. Just adding homoclinic to the Hopf is not quite right... I'll think about it. \citep{Izhikevich2006}}
-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 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. 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 curve (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 or homoclinic bifurcation \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}. The other models used here lie on a continuum between these prototypical firing classifications. \notejb{The STN models could be a homoclinic bifurcation (long delay but type 2 like firing), maybe cite Izhikevic book for this.}\notenk{I added ``or homoclinic'' and cited Izhikevich} Most neuronal models exhibit hysteresis with ascending and descending ramps eliciting spikes with different 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}).
 
 \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. Changes in gating \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance affect AUC (\Cref{fig:AUC_correlation} A, B and C). Heterogeneity in the correlation between gating and conductance changes and AUC occurs across models for most ionic currents. In these cases some of the models display non-monotonic relationships or no relationship (\( |\text{Kendall} \tau | \approx 0\)). However, shifts in A-current activation \(V_{1/2}\), changes in \Kv activation \(V_{1/2}\) and slope factor \(k\), and changes in A-current conductance display consistent monotonic relationships across models  (\( |\text{Kendall} \tau | \ne 0\)). The impact of a similar change in \(V_{1/2}\), slope factor \(k\), or conductance of different currents will impact firing behaviour differently not just within but also between models.
@@ -451,6 +452,7 @@ Accordingly, for accurate modelling and predictions of the effects of mutations
         \centering
         \includegraphics[width=\linewidth]{Figures/ramp_firing.pdf}
         \linespread{1.}\selectfont
+        \\\notejb{You should add the ramp stimulus at the bottom. To be able to see the hysteresis one needs to know where the symmetry axis is. (I gues it is in the center, but better is to see that.}
         \caption[]{Diversity in Neuronal Model Firing Responses to a Current Ramp. Spike trains for Cb stellate (A), RS inhibitory (B), FS (C), RS pyramidal (D), RS inhibitory +\Kv (E), Cb stellate +\Kv (F), FS +\Kv (G), RS pyramidal +\Kv (H), STN +\Kv (I), Cb stellate \(\Delta\)\Kv (J), STN \(\Delta\)\Kv (K), and STN (L) neuron models in response to a slow ascending current ramp followed by the descending version of the current ramp. The current at which firing begins in response to an ascending current ramp and the current at which firing ceases in response to a descending current ramp are depicted on the frequency current (fI) curves in \Cref{fig:diversity_in_firing} for each model.}
         \label{fig:ramp_firing}
 \end{figure}