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Changed model names to model A,B,C,... in the text

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g_table.tex
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@ -11,6 +11,7 @@
% in mS/cm^2
\Xhline{1\arrayrulewidth}
& \begin{tabular}[x]{@{}c@{}} RS\\Pyra-\\midal\\(+\Kv) \end{tabular} & \begin{tabular}[x]{@{}c@{}} RS\\Inhib-\\itory\\(+\Kv)\end{tabular} & \begin{tabular}[x]{@{}c@{}}FS\\(+\Kv) \end{tabular}& \begin{tabular}[x]{@{}c@{}} Cb\\Stellate \end{tabular}& \begin{tabular}[x]{@{}c@{}}Cb\\Stellate\\+\Kv \end{tabular} & \begin{tabular}[x]{@{}c@{}}Cb\\Stellate\\\(\Delta\)\Kv \end{tabular} & STN &\begin{tabular}[x]{@{}c@{}} STN\\+\Kv \end{tabular} &\begin{tabular}[x]{@{}c@{}} STN\\\(\Delta\)\Kv \end{tabular} \\
Model & D (H) & B (E) & C (G) & A & F & J & L & I & K \\
\Xhline{1\arrayrulewidth}
\(g_{Na}\) & \(56\) & \(10\) & \(58\) & \(3.4\) & \(3.4\) & \(3.4\) & \(49\) & \(49\) & \(49\) \\
\(g_{K}\) & \(6\) (\(5.4\)) & 2.1 (\(1.89\)) & 3.9 (\(3.51\)) & \(9.0556\) & \(8.15\) &\(9.0556\) & \(57\) & \(56.43\) & \(57\) \\
@ -26,7 +27,7 @@
\Xhline{1\arrayrulewidth}
\end{tabular}}
\caption[Cell properties and conductances of neuronal models]{Cell properties and conductances of regular spiking pyramidal neuron (RS Pyramidal), regular spiking inhibitory neuron (RS Inhibitory), fast spiking neuron (FS) each with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (RS Pyramidal +\Kv, RS Inhibitory +\Kv, FS +\Kv respectively), cerebellar stellate cell (Cb Stellate), with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (Cb Stellate +\Kv) and with \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) replacement of \(\textrm{I}_\textrm{A}\) (Cb Stellate \(\Delta\)\Kv), and subthalamic nucleus neuron (STN), with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (STN +\Kv) and with \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) replacement of \(\textrm{I}_{\textrm{A}}\) (STN \Kv) models. All conductances are given in \(\textrm{mS}/\textrm{cm}^2\). Capacitances (\(C_m\)) and \(\tau_{max, M}\) are given in pF and ms respectively.}
\caption[Cell properties and conductances of neuronal models]{Cell properties and conductances of regular spiking pyramidal neuron (RS Pyramidal; model D), regular spiking inhibitory neuron (RS Inhibitory; model B), fast spiking neuron (FS; model C) each with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (RS Pyramidal +\Kv; model H, RS Inhibitory +\Kv; model E, FS +\Kv; model G respectively), cerebellar stellate cell (Cb Stellate; model A), with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (Cb Stellate +\Kv; model F) and with \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) replacement of \(\textrm{I}_\textrm{A}\) (Cb Stellate \(\Delta\)\Kv; model J), and subthalamic nucleus neuron (STN; model L), with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (STN +\Kv; model I) and with \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) replacement of \(\textrm{I}_{\textrm{A}}\) (STN \Kv; model K) models. All conductances are given in \(\textrm{mS}/\textrm{cm}^2\). Capacitances (\(C_m\)) and \(\tau_{max, M}\) are given in pF and ms respectively.}
\label{tab:g}
\end{table}

12
gating_table.tex
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@ -8,12 +8,12 @@
& Gating & \(V_{1/2}\) [mV]& \(k\) & \(j\) & \(a\) \\
\Xhline{1\arrayrulewidth}
%Pospischil
& \(\textrm{I}_{\textrm{Na}}\) activation &\(-34.33054521\) & \(-8.21450277\) & \(1.42295686\) & --- \\
RS pyramidal, & \(\textrm{I}_{\textrm{Na}}\) inactivation &\(-34.51951036\) & \(4.04059373\) & \(1\) & \(0.05\) \\
RS inhibitory, & \(\textrm{I}_{\textrm{Kd}}\) activation &\(-63.76096946\) & \(-13.83488194\) & \(7.35347425\) & --- \\
FS & \(\textrm{I}_{\textrm{L}}\) activation &\(-39.03684525\) & \(-5.57756176\) & \(2.25190197\) & --- \\
& \(\textrm{I}_{\textrm{L}}\) inactivation &\(-57.37\) & \(20.98\) & \(1\) & --- \\
& \(\textrm{I}_{\textrm{M}}\) activation &\(-45\) & \(-9.9998807337\) & \(1\) & --- \\ %-45 with 10 mV shift to contributes to resting potential
Models & \(\textrm{I}_{\textrm{Na}}\) activation &\(-34.33054521\) & \(-8.21450277\) & \(1.42295686\) & --- \\
B, C, D, E, G, H & \(\textrm{I}_{\textrm{Na}}\) inactivation &\(-34.51951036\) & \(4.04059373\) & \(1\) & \(0.05\) \\
& \(\textrm{I}_{\textrm{Kd}}\) activation &\(-63.76096946\) & \(-13.83488194\) & \(7.35347425\) & --- \\
(RS pyramidal,& \(\textrm{I}_{\textrm{L}}\) activation &\(-39.03684525\) & \(-5.57756176\) & \(2.25190197\) & --- \\
RS inhibitory, & \(\textrm{I}_{\textrm{L}}\) inactivation &\(-57.37\) & \(20.98\) & \(1\) & --- \\
FS) & \(\textrm{I}_{\textrm{M}}\) activation &\(-45\) & \(-9.9998807337\) & \(1\) & --- \\ %-45 with 10 mV shift to contributes to resting potential
% & & & & &\\
\Xhline{1\arrayrulewidth}
\(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\ \) & \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\ \) activation &\(-30.01851852\) & \(-7.73333333\) & \(1\) & --- \\

26
manuscript.tex
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@ -206,11 +206,11 @@ All modelling and simulation was done in parallel with custom written Python 3.8
% @ 2.60 GHz Linux 3.10.0-123.e17.x86_64.
\subsection*{Different Cell Models}
A group of neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal), regular spiking inhibitory (RS inhibitory), and fast spiking (FS) cells were used \citep{pospischil_minimal_2008}. Additionally, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added to each of these models (RS pyramidal +\Kv, RS inhibitory +\Kv, and FS +\Kv respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate) in this study. This cell model was also extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (Cb stellate +\Kv) or by replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv). A subthalamic nucleus (STN) neuron model as described by \citet{otsuka_conductance-based_2004} was also used. The STN cell model was additionally extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (STN+\Kv) or by replacing the A-type potassium current (STN \(\Delta\)\Kv). The properties and maximal conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models \citep{alexander_cerebellar_2019, otsuka_conductance-based_2004}. For enabling the comparison of models with the typically reported electrophysiological data fitting reported and for ease of further gating curve manipulations, a modified Boltzmann function
A group of neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal; model D), regular spiking inhibitory (RS inhibitory; model B), and fast spiking (FS; model C) cells were used \citep{pospischil_minimal_2008}. Additionally, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added to each of these models (RS pyramidal +\Kv; model H, RS inhibitory +\Kv; model E, and FS +\Kv; model G respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate; model A) in this study. This cell model was also extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (Cb stellate +\Kv; model F) or by replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv; model J). A subthalamic nucleus (STN; model L) neuron model as described by \citet{otsuka_conductance-based_2004} was also used. The STN cell model (model L) was additionally extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (STN +\Kv; model I) or by replacing the A-type potassium current (STN \(\Delta\)\Kv; model K). The properties and maximal conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate (model A) and STN (model L) models \citep{alexander_cerebellar_2019, otsuka_conductance-based_2004}. For enabling the comparison of models with the typically reported electrophysiological data fitting reported and for ease of further gating curve manipulations, a modified Boltzmann function
\begin{equation}\label{eqn:Boltz}
x_\infty = {\left(\frac{1-a}{1+{\exp\left[{\frac{V-V_{1/2}}{k}}\right]}} +a\right)^j}
\end{equation}
with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted to the original formulism for RS pyramidal, RS inhibitory and FS models from \citet{pospischil_minimal_2008}. The properties of \IKv were fitted to the mean wild type biophysical parameters of \Kv described in \citet{lauxmann_therapeutic_2021}. Each of the original single-compartment models used here can reproduce physiological firing behavior of the neurons they represent (\Cref{fig:diversity_in_firing}; \citealt{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004}) and capture key aspects of the dynamics of these cell types.
with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted to the original formulism for RS pyramidal (model D), RS inhibitory (model B) and FS (model C) models from \citet{pospischil_minimal_2008}. The properties of \IKv were fitted to the mean wild type biophysical parameters of \Kv described in \citet{lauxmann_therapeutic_2021}. Each of the original single-compartment models used here can reproduce physiological firing behavior of the neurons they represent (\Cref{fig:diversity_in_firing}; \citealt{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004}) and capture key aspects of the dynamics of these cell types.
\input{g_table}
@ -273,7 +273,9 @@ 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 for this study 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 exhibit type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) whereas 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) \cite{ermentrout_type_1996, Rinzel_1998}. 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}). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, 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 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 for this study 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 exhibit type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) whereas 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) \cite{ermentrout_type_1996, Rinzel_1998}. 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}). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, 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 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 for this study all fire tonically and do not exhibit bursting (see methods for details and naming of the models). Some models, such as models A and B, display type I firing, whereas others such as models J and L exhibit type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) whereas 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) \cite{ermentrout_type_1996, Rinzel_1998}. 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 models I, J, and K have large hysteresis (\Cref{fig:diversity_in_firing}, \Cref{fig:ramp_firing}). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}.
\subsection*{Characterization of Neuronal Firing Properties}
\begin{figure}[tp]
@ -294,11 +296,15 @@ Using these two measures we quantify the effects a changed property of an ionic
\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 delayed rectifier potassium current in the FS +\Kv model to more depolarized values, then the rheobase of the resulting fI curves shifted to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves was reduced (\(-\)\ndAUC), which resulted in a reduced firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in FS neurons is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we got a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterized each of these curves by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient\textsuperscript{a}. A monotonically increasing curve resulted in a \( \text{Kendall} \ \tau \) close to \(+1\)\textsuperscript{a}, a monotonously decreasing curve in \( \text{Kendall} \ \tau \approx -1 \)\textsuperscript{a}, and a non-monotonous, non-linear relation in \( \text{Kendall} \ \tau \) close to zero\textsuperscript{a} (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 delayed rectifier potassium current in the FS +\Kv model to more depolarized values, then the rheobase of the resulting fI curves shifted to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves was reduced (\(-\)\ndAUC), which resulted in a reduced firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in FS neurons is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we got a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterized each of these curves by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient\textsuperscript{a}. A monotonically increasing curve resulted in a \( \text{Kendall} \ \tau \) close to \(+1\)\textsuperscript{a}, a monotonously decreasing curve in \( \text{Kendall} \ \tau \approx -1 \)\textsuperscript{a}, and a non-monotonous, non-linear relation in \( \text{Kendall} \ \tau \) close to zero\textsuperscript{a} (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 delayed rectifier potassium current in the model G to more depolarized values, then the rheobase of the resulting fI curves shifted to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves was reduced (\(-\)\ndAUC), which resulted in a reduced firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in model C is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we got a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterized each of these curves by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient\textsuperscript{a}. A monotonically increasing curve resulted in a \( \text{Kendall} \ \tau \) close to \(+1\)\textsuperscript{a}, a monotonously decreasing curve in \( \text{Kendall} \ \tau \approx -1 \)\textsuperscript{a}, and a non-monotonous, non-linear relation in \( \text{Kendall} \ \tau \) close to zero\textsuperscript{a} (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C).
Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affected the AUC (\Cref{fig:AUC_correlation}), but how exactly the AUC was affected usually depended on the specific neuronal model. Increasing the slope factor of the \Kv activation curve for example increased the AUC in all models (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), but with different slopes (\Cref{fig:AUC_correlation}~D,E,F). Similar consistent positive correlations can be found for shifts in A-current activation \(V_{1/2}\). Changes in \Kv half activation \(V_{1/2}\) and in maximal A-current conductance resulted in negative correlations with the AUC in all models (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}).
Qualitative differences can be found, for example, when increasing the maximal conductance of the delayed rectifier (\Cref{fig:AUC_correlation}~G,H,I). In some model neurons this increased AUC (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), whereas in others AUC was decreased (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}). In the STN +\Kv model, AUC depended in a non-linear way on the maximal conductance of the delayed rectifier, resulting in a \( \text{Kendall} \ \tau \) close to zero\textsuperscript{a}. Even more dramatic qualitative differences between models resulted from shifts of the activation curve of the delayed rectifier, as discussed already above (\Cref{fig:AUC_correlation}~A,B,C). Some model neurons did almost not depend on changes in K-current half activation \(V_{1/2}\) or showed strong non-linear dependencies, both resulting in \( \text{Kendall} \ \tau\) close to zero\textsuperscript{a}. Many model neurons showed strongly negative correlations, and a few displayed positive correlations with shifting the activation curve of the delayed rectifier.
%Qualitative differences can be found, for example, when increasing the maximal conductance of the delayed rectifier (\Cref{fig:AUC_correlation}~G,H,I). In some model neurons this increased AUC (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), whereas in others AUC was decreased (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}). In the STN +\Kv model, AUC depended in a non-linear way on the maximal conductance of the delayed rectifier, resulting in a \( \text{Kendall} \ \tau \) close to zero\textsuperscript{a}. Even more dramatic qualitative differences between models resulted from shifts of the activation curve of the delayed rectifier, as discussed already above (\Cref{fig:AUC_correlation}~A,B,C). Some model neurons did almost not depend on changes in K-current half activation \(V_{1/2}\) or showed strong non-linear dependencies, both resulting in \( \text{Kendall} \ \tau\) close to zero\textsuperscript{a}. Many model neurons showed strongly negative correlations, and a few displayed positive correlations with shifting the activation curve of the delayed rectifier.
Qualitative differences can be found, for example, when increasing the maximal conductance of the delayed rectifier (\Cref{fig:AUC_correlation}~G,H,I). In some model neurons this increased AUC (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), whereas in others AUC was decreased (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}). In model I, AUC depended in a non-linear way on the maximal conductance of the delayed rectifier, resulting in a \( \text{Kendall} \ \tau \) close to zero\textsuperscript{a}. Even more dramatic qualitative differences between models resulted from shifts of the activation curve of the delayed rectifier, as discussed already above (\Cref{fig:AUC_correlation}~A,B,C). Some model neurons did almost not depend on changes in K-current half activation \(V_{1/2}\) or showed strong non-linear dependencies, both resulting in \( \text{Kendall} \ \tau\) close to zero\textsuperscript{a}. Many model neurons showed strongly negative correlations, and a few displayed positive correlations with shifting the activation curve of the delayed rectifier.
\begin{figure}[tp]
@ -309,9 +315,13 @@ Qualitative differences can be found, for example, when increasing the maximal c
\label{fig:AUC_correlation}
\end{figure}
Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affected rheobase (\Cref{fig:rheobase_correlation}). However, in contrast to AUC, qualitatively consistent effects on rheobase across models could be observed. An increasing of the maximal conductance of the leak current in the Cb stellate model increased the rheobase (\Cref{fig:rheobase_correlation}~G). When these changes were plotted against the change in maximal conductance a monotonically increasing relationship was evident (thick teal line in \Cref{fig:rheobase_correlation}~H). This monotonically increasing relationship was evident in all models (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), but with different slopes (thin lines in \Cref{fig:rheobase_correlation}~H). Similarly, positive correlations were consistently found across models for maximal conductances of delayed rectifier K, \Kv, and A type currents, whereas the maximal conductance of the sodium current was consistently associated with negative correlations (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}; \Cref{fig:rheobase_correlation}~I), i.e. rheobase decreased with increasing maximum conductance in all models.
%Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affected rheobase (\Cref{fig:rheobase_correlation}). However, in contrast to AUC, qualitatively consistent effects on rheobase across models could be observed. An increasing of the maximal conductance of the leak current in the Cb stellate model increased the rheobase (\Cref{fig:rheobase_correlation}~G). When these changes were plotted against the change in maximal conductance a monotonically increasing relationship was evident (thick teal line in \Cref{fig:rheobase_correlation}~H). This monotonically increasing relationship was evident in all models (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), but with different slopes (thin lines in \Cref{fig:rheobase_correlation}~H). Similarly, positive correlations were consistently found across models for maximal conductances of delayed rectifier K, \Kv, and A type currents, whereas the maximal conductance of the sodium current was consistently associated with negative correlations (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}; \Cref{fig:rheobase_correlation}~I), i.e. rheobase decreased with increasing maximum conductance in all models.
Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affected rheobase (\Cref{fig:rheobase_correlation}). However, in contrast to AUC, qualitatively consistent effects on rheobase across models could be observed. An increasing of the maximal conductance of the leak current in the model A increased the rheobase (\Cref{fig:rheobase_correlation}~G). When these changes were plotted against the change in maximal conductance a monotonically increasing relationship was evident (thick teal line in \Cref{fig:rheobase_correlation}~H). This monotonically increasing relationship was evident in all models (\( \text{Kendall} \ \tau \approx +1\)\textsuperscript{a}), but with different slopes (thin lines in \Cref{fig:rheobase_correlation}~H). Similarly, positive correlations were consistently found across models for maximal conductances of delayed rectifier K, \Kv, and A type currents, whereas the maximal conductance of the sodium current was consistently associated with negative correlations (\( \text{Kendall} \ \tau \approx -1\)\textsuperscript{a}; \Cref{fig:rheobase_correlation}~I), i.e. rheobase decreased with increasing maximum conductance in all models.
%Although changes in half maximal potential \(V_{1/2}\) and slope factor \(k\) generally correlated with rheobase similarly across model there were some exceptions. Changing the slope factor of Na-current inactivation, \Kv-current inactivation, and A-current activation affected the rheobase both with positive and negative correlations in different models \textcolor{red}{\noteuh{Würde diese hier noch mal benennen, damit es klar wird. }}\notenk{Ich mache das ungern, weil ich für jedes (Na-current inactivation, \Kv-current inactivation, and A-current activation) 2 Liste habe (+ und - rheobase Aenderungen} (\Cref{fig:rheobase_correlation}~F). Departures from monotonic relationships also occurred in some models as a result of K-current activation \(V_{1/2}\) and slope factor \(k\), \Kv-current inactivation slope factor \(k\), and A-current activation slope factor \(k\) in some models \textcolor{red}{\noteuh{Auch hier die unterschiedlcihen betroffenen cell type models benennen, einfach in Klammer dahinter.}}\notenk{Hier mache ich das auch ungern, für ähnlichen Gründen}. Thus, identical changes in current gating properties such as the half maximal potential \(V_{1/2}\) or slope factor \(k\) can have differing effects on firing depending on the model in which they occur.
Although changes in half maximal potential \(V_{1/2}\) and slope factor \(k\) generally correlated with rheobase similarly across model there were some exceptions. Changing the slope factor of Na-current inactivation, \Kv-current inactivation, and A-current activation affected the rheobase both with positive and negative correlations in different models \textcolor{red}{\noteuh{Würde diese hier noch mal benennen, damit es klar wird. }}\notenk{Ich mache das ungern, weil ich für jedes (Na-current inactivation, \Kv-current inactivation, and A-current activation) 2 Liste habe (+ und - rheobase Aenderungen} (\Cref{fig:rheobase_correlation}~F). Departures from monotonic relationships also occurred in some models as a result of K-current activation \(V_{1/2}\) and slope factor \(k\), \Kv-current inactivation slope factor \(k\), and A-current activation slope factor \(k\) in some models \textcolor{red}{\noteuh{Auch hier die unterschiedlcihen betroffenen cell type models benennen, einfach in Klammer dahinter.}}\notenk{Hier mache ich das auch ungern, für ähnlichen Gründen}. Thus, identical changes in current gating properties such as the half maximal potential \(V_{1/2}\) or slope factor \(k\) can have differing effects on firing depending on the model in which they occur.
Although changes in half maximal potential \(V_{1/2}\) and slope factor \(k\) generally correlated with rheobase similarly across model there were some exceptions. Rheobase was affected with both with positive and negative correlations in different models as a result of changing slope factor of \textcolor{red}{Na-current inactivation (positive: models A-H and J; negative: models I, K and L), \Kv-current inactivation (positive: models I and K; negative: models E-G, J, H), and A-current activation (positive: models A,F and L; negative: model I)} (\Cref{fig:rheobase_correlation}~F). Departures from monotonic relationships also occurred in some models as a result of \textcolor{red}{K-current activation \(V_{1/2}\) (e.g. model J) and slope factor \(k\) (models F and G), \Kv-current inactivation slope factor \(k\) (model K), and A-current activation slope factor \(k\) (model L) }. Thus, identical changes in current gating properties such as the half maximal potential \(V_{1/2}\) or slope factor \(k\) can have differing effects on firing depending on the model in which they occur.
\begin{figure}[tp]
@ -358,7 +368,7 @@ To capture the diversity in neuronal ion channel expression and its relevance in
To our knowledge, no comprehensive evaluation of how ionic current environment and cell type affect the outcome of ion channel mutations have been reported. However, comparisons between the effects of such mutations between certain cell types were described. For instance, the R1648H mutation in SCN1A does not alter the excitability of cortical pyramidal neurons, but causes hypoexcitability of adjacent inhibitory GABAergic neurons \citep{Hedrich14874}. In the CA3 region of the hippocampus, the equivalent mutation in \textit{SCN8A}, R1627H, increases the excitability of pyramidal neurons and decreases the excitability of parvalbumin positive interneurons \cite{makinson_scn1a_2016}. Additionally, the L858H mutation in \(\textrm{Na}_\textrm{V}\textrm{1.7}\), associated with erythermyalgia, has been shown to cause hypoexcitability in sympathetic ganglion neurons and hyperexcitability in dorsal root ganglion neurons \citep{Waxman2007, Rush2006}. The differential effects of L858H \(\textrm{Na}_\textrm{V}\textrm{1.7}\) on firing is dependent on the presence or absence of another sodium channel, namely the \(\textrm{Na}_\textrm{V}\textrm{1.8}\) subunit \citep{Waxman2007, Rush2006}. These findings, in concert with our findings emphasize that the ionic current environment in which a channelopathy occurs is vital in determining the outcomes of the channelopathy on firing.
Cell type specific differences in ionic current properties are important in the effects of ion channel mutations. However within a cell type heterogeneity in channel expression levels exists \noteuh{Meinst du damit die “realen” Zellen oder die Modelle?}\notenk{Beides, ``realen'' Zellen und dann die Modelle die daraus entstehen} and it is often desirable to generate a population of neuronal models and to screen them for plausibility to biological data in order to capture neuronal population diversity \citep{marder_multiple_2011} \textcolor{red}{\notenk{add temperature sensitivity-> within cell-type heterogeneity exists - Marder paper?}}. The models we used here are originally generated by characterization of current gating properties and by fitting of maximal conductances to experimental data \citep{pospischil_minimal_2008, ranjan_kinetic_2019, alexander_cerebellar_2019, otsuka_conductance-based_2004}. This practice of fixing maximal conductances based on experimental data is limiting as it does not reproduce the variability in channel expression and neuronal firing behavior of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a neuronal sub-population within the stomatogastric ganglion, the so-called "one-spike bursting" neurons fire three spikes instead of one per burst due to an L-shaped distribution of sodium and potassium conductances \citep{golowasch_failure_2002}.
Cell type specific differences in ionic current properties are important in the effects of ion channel mutations. However within a cell type heterogeneity in channel expression levels exists and it is often desirable to generate a population of neuronal models and to screen them for plausibility to biological data in order to capture neuronal population diversity \citep{marder_multiple_2011} \textcolor{red}{\notenk{add temperature sensitivity-> within cell-type heterogeneity exists - Marder paper?}}. The models we used here are originally generated by characterization of current gating properties and by fitting of maximal conductances to experimental data \citep{pospischil_minimal_2008, ranjan_kinetic_2019, alexander_cerebellar_2019, otsuka_conductance-based_2004}. This practice of fixing maximal conductances based on experimental data is limiting as it does not reproduce the variability in channel expression and neuronal firing behavior of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a neuronal sub-population within the stomatogastric ganglion, the so-called "one-spike bursting" neurons fire three spikes instead of one per burst due to an L-shaped distribution of sodium and potassium conductances \citep{golowasch_failure_2002}.
Multiple sets of conductances can give rise to the same patterns of activity also termed degeneracy and differences in neuronal dynamics may only be evident with perturbations \citep{marder_multiple_2011, goaillard_ion_2021}.
The variability in ion channel expression often correlates with the expression of other ion channels \citep{goaillard_ion_2021} and neurons whose behavior is similar may possess correlated variability across different ion channels resulting in stability in the neuronal phenotype \citep{lamb_correlated_2013, soofi_co-variation_2012, taylor_how_2009}.
The variability of ionic currents and degeneracy of neurons may account, at least in part, for the observation that the effect of toxins within a neuronal type is frequently not constant \citep{khaliq_relative_2006, puopolo_roles_2007, ransdell_neurons_2013}.