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@ -88,6 +88,52 @@
\vspace{-1em}
\date{}
\section*{Titlepage for eNeuro - will be put into Word file provided for submission}
\subsection{Manuscript Title (50 word maximum)}
Loss or Gain of Function? Ion Channel Mutation Effects on Neuronal Firing Depend on Cell Type
\subsection{Abbreviated Title (50 character maximum)}
Ion Channel Mutation Effects Depend on Cell Type
\subsection{List all Author Names and Affiliations in order as they would appear in the published article}
Nils A. Koch\textsuperscript{1,2}, Lukas Sonnenberg\textsuperscript{1,2}, Jan Benda\textsuperscript{1,2}
\textsuperscript{1}Institute for Neurobiology, University of Tuebingen, 72072 Tuebingen, Germany\\
\textsuperscript{2}Bernstein Center for Computational Neuroscience Tuebingen, 72076 Tuebingen, Germany
\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- Each author must be identified with at least one of the following: Designed research, Performed research, Contributed unpublished reagents/ analytic tools, Analyzed data, Wrote the paper.}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}\\
NK, LS, JB Designed Research;
NK, LS, JB Wrote the paper;
NK Performed research;
NK, LS Analyzed data
\subsection{Correspondence should be addressed to (include email address)}
\ \notenk{Nils oder Jan?}
\subsection{Number of Figures}
5
\subsection{Number of Tables}
2
\subsection{Number of Multimedia}
0
\subsection{Number of words for Abstract}
\notenk{Added when manuscript is finalized}
\subsection{Number of Words for Significance Statement}
\notenk{Added when manuscript is finalized}
\subsection{Number of words for Discussion}
\notenk{Added when manuscript is finalized}
\subsection{Acknowledgements}
\subsection{Conflict of Interest}
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}
\newpage{}
\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
@ -98,12 +144,11 @@
\doublespacing
\sloppy
\section*{Abstract (250 Words Maximum - Currently 231)}
\section*{Abstract (250 Words Maximum - Currently 232)}
%\textit{It should provide a concise summary of the objectives, methodology (including the species and sex studied), key results, and major conclusions of the study.}
Ion channels determine neuronal excitability and disruption in ion channel properties in mutations can result in neurological disorders called channelopathies. Often many mutations are associated with a channelopathy, and determination of the effects of these mutations are generally done at the level of currents. The impact of such mutations on neuronal firing is vital for selecting personalized treatment plans for patients, however whether the effect of a given mutation on firing can simply be inferred from current level effects is unclear. The general impact of the ionic current environment in different neuronal types on the outcome of ion channel mutations is vital to understanding of the impacts of ion channel mutations and effective selection of personalized treatments.
Using a diverse collection of neuronal models, the effects of changes in ion current properties on firing is assessed systematically and for episodic ataxia type~1 associated \Kv mutations. The effects of ion current property changes or mutations on firing is dependent on the current environment, or cell type, in which such a change occurs in. Characterization of ion channel mutations as loss or gain of function is useful at the level of the ionic current, however the effects of channelopathies on firing is dependent on cell type. To further the efficacy of personalized medicine in channelopathies, the effects of ion channel mutations must be examined in the context of the appropriate cell types.
Using a diverse collection of neuronal models, the effects of changes in ion current properties on firing is assessed systematically and for episodic ataxia type~1 associated \Kv mutations. The effects of ion current property changes or mutations on firing is dependent on the ionic current environment, or cell type, in which such a change occurs in. Characterization of ion channel mutations as loss or gain of function is useful at the level of the ionic current, however the effects of channelopathies on firing is dependent on cell type. To further the efficacy of personalized medicine in channelopathies, the effects of ion channel mutations must be examined in the context of the appropriate cell types.
\par\null
@ -114,16 +159,15 @@ Ion channels determine neuronal excitability and mutations that alter ion channe
\par\null
\notejb{LOF or LoF? GOF or GoF?}
\notejb{LOF or LoF? GOF or GoF?} \notels{LOF and GoF!!! (I think it is usually all big letters, not 100\% sure though)}
\section*{Introduction} %(750 Words Maximum - Currently \textcolor{red}{837})}
\section*{Introduction (750 Words Maximum - Currently 592)}
%\textit{The Introduction should briefly indicate the objectives of the study and provide enough background information to clarify why the study was undertaken and what hypotheses were tested.}
Voltage-gated ion channels are vital in determining neuronal excitability, action potential generation and firing patterns \citep{bernard_channelopathies_2008, carbone_ion_2020}. In particular, the properties and combinations of ion channels and their resulting currents determine the firing properties of the neuron \citep{rutecki_neuronal_1992, pospischil_minimal_2008}. However, ion channel function can be disturbed, resulting in altered ionic current properties and altered neuronal firing behaviour \citep{carbone_ion_2020}. Ion channel mutations are a common cause of such channelopathies and are often associated with hereditary clinical disorders including ataxias, epilepsies, pain disorders, dyskinesias, intellectual disabilities, myotonias, and periodic paralyses among others \citep{bernard_channelopathies_2008, carbone_ion_2020}.
The effects of channelopathies on ionic-current kinetics are frequently assessed by transfection of heterologous expression systems without endogenous currents \citep{Balestrini1044, Noebels2017, Dunlop2008} \textcolor{red}{(cite more stuff?)} and are categorized into loss-of-function (LOF) or gain-of-function (GOF) effects. With these caterogies it is possible to estimate changes in neuronal firing. These estimates are important for understanding the pathophysiology of these disorders and for identification of potential therapeutic targets \textcolor{red}{(cite some stuff)}. Experimentally, the effects of channelopathies on neuronal firing can also be assessed using primary neuronal cultures \citep{Scalmani2006, Smith2018, Liu2019} \textcolor{red}{(cite more stuff?)} or \textit{in vitro} recordings from transgenic mouse lines \textcolor{red}{(cite some stuff)}.
\notels{LOF and GOF are usually not explained in detail, should we still do this here or is it ok to just mention them?}
\notenk{Are there any obvious citations missing from the following section?}
The effects of channelopathies on ionic current kinetics are frequently assessed by transfection of heterologous expression systems without endogenous currents \citep{Balestrini1044, Noebels2017, Dunlop2008}, and are frequently classified as either a loss of function (LOF) or a gain of function (GOF) with respect to \textcolor{green}{changes in }the \textcolor{green}{amount of} ionic current \citep{Musto2020, Kullmann2002, Waxman2011}. \notenk{Do you think we need to discuss LOF and GOF more than this?} \notels{LOF and GOF are usually not explained in detail, I would think it's fine} These classes can be used to make rough estimates of the effects on neuronal firing \textcolor{red}{(papers?)}, which is important for understanding the pathophysiology of these disorders and for identification of potential therapeutic targets \citep{Orsini2018, Yang2018}. Experimentally, the effects of channelopathies on neuronal firing can be assessed using primary neuronal cultures \citep{Scalmani2006, Smith2018, Liu2019} or \textit{in vitro} recordings from transgenic mouse lines \citep{Mantegazza2019, Xie2010,Lory2020, Habib2015, Hedrich2019}.
%However the effect of a given channelopathy on different neuronal types across the brain is often unclear and not feasible to experimentally obtain. This is especially true when large numbers of distinct mutations are present and personalized medicine approaches are desired.
@ -131,7 +175,9 @@ The effects of channelopathies on ionic-current kinetics are frequently assessed
%General understanding of the effects of changes in current properties on neuronal firing may help to fill the need to understand the impacts of ion channel mutations on neuronal firing.
However the effect of a given channelopathy on different neuronal types across the brain is often unclear and not feasible to experimentally obtain. Different neuron types differ in their composition of ionic currents \citep{yao2021taxonomy} \textcolor{red}{(cite Berens)} and therefore likely respond differently to changes in the properties of one ionic current. The expression level of an affected gene can correlate with firing behaviour in the simplest case \citep{Layer2021} \textcolor{red}{(cite other Papers?)}, however if a gating property is altered substantially this can have complex consequences.
However the effect of a given channelopathy on different neuronal types across the brain is often unclear and not feasible to experimentally obtain. Different neuron types differ in their composition of ionic currents \citep{yao2021taxonomy, Cadwell2016, BICCN2021, Scala2021} and therefore likely respond differently to changes in the properties of one ionic current.
% \textcolor{red}{In the simplest case, the influence on the firing behaviour should correlate with the expression level of the affected gene \textcolor{red}{(cite Niko , other Papers)}. But if a \textcolor{red}{ kinetic parameter} is changed too much, it can have unforseen consequences. }
The expression level of an affected gene can correlate with firing behaviour in the simplest case \citep{Layer2021} \textcolor{red}{(cite other Papers?)} \notenk{Not sure if Lukas had some in mind}, however if a gating property is altered substantially this can have complex consequences.
For instance, altering relative amplitudes of ionic currents can dramatically influence the firing behaviour and dynamics of neurons \citep{rutecki_neuronal_1992, pospischil_minimal_2008,Kispersky2012, golowasch_failure_2002, barreiro_-current_2012, Noebels2017, Layer2021}, however other properties of ionic currents impact neuronal firing as well. In extreme cases, a mutation can have opposite effects on different neuron types. For example, the R1629H SCN1A mutation is associated which increased firing in interneurons, but decreases pyramidal neuron excitability \citep{Hedrich14874,makinson2016scn1a}
@ -223,21 +269,21 @@ The code/software described in the paper is freely available online at [URL reda
% \textit{The results section should clearly and succinctly present the experimental findings. Only results essential to establish the main points of the work should be included.\\
% Authors must provide detailed information for each analysis performed, including population size, definition of the population (e.g., number of individual measurements, number of animals, number of slices, number of times treatment was applied, etc.), and specific p values (not > or <), followed by a superscript lowercase letter referring to the statistical table provided at the end of the results section. Numerical data must be depicted in the figures with box plots.}
To examine the role of cell specific environments of ionic currents on the impact of altered ion channel properties on firing behaviour a set of neuronal models is used and properties of channels common across models are 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 current environments.
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 is used and properties of channels common across models are 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}
\begin{figure}[ht!]
\centering
\includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf}
\\\notejb{Nils, can you put the python script of this figure into the git? I have some ideas I would like to try.}
\\\notenk{Should already be in \path{./Figures}, specifically file: \path{./Figures/firing_characterization.py}}
\notenk{Should already be in \path{./Figures}, specifically file: \path{./Figures/firing_characterization.py}}
\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, with the upper left quadrant (+\(\Delta\)AUC and -\(\Delta\)rheobase) indicating a increased firing and the bottom right quadrant (-\(\Delta\)AUC and +\(\Delta\)rheobase) indicating decreased firing (\Cref{fig:firing_characterizaton}B). In the lower left and upper right quadrants, the effects on firing are less clear-cut and cannot easily 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 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 a 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 easily be described as a gain or loss of excitability.
\begin{figure}[ht!]
\centering
@ -248,10 +294,10 @@ Neuronal firing is a complex phenomenon and a quantification of firing propertie
\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 neuronal models used here has considerable diversity as evident in the variability seen across neuronal models both in representative spike trains and their fI curves (\Cref{fig:diversity_in_firing}). The models chosen all fire repetitively 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 is continuous) generated through a saddle-node on invariant cycle bifurcation and 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 a sub-critical Hopf bifurcation \cite{ERMENTROUT2002, ermentrout_type_1996}. Other models lie on a continuum between these prototypical firing classifications. 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}).
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 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 with different thresholds, however the STN +\Kv, STN \(\Delta\)\Kv, and Cb stellate \(\Delta\)\Kv models have large hysteresis (\Cref{fig:diversity_in_firing}).
\subsection*{Sensitivity Analysis}
Sensitivity analyses are used to understand how input model parameters contribute to 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 analysis involve altering one parameter at a time and enable the comparison of a given alteration 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 (i.e. \( |\text{Kendall} \tau | \approx 0\)\notejb{is this right?} \notenk{Yes, although it is perhaps a bit misleadingly written as this is not the only situation in which the Kendall \(\tau \approx 0\). Kendall \(\tau\) is a measure of monotonic relationships so if there is no relationship or the relationship is completely non-monotonic (i.e. a parabola) then the Kendall \(\tau\) is zero.}). 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.
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 (i.e. \( |\text{Kendall} \tau | \approx 0\)\notejb{is this right?} \notenk{Yes, although it is perhaps a bit misleadingly written as this is not the only situation in which the Kendall \(\tau \approx 0\). Kendall \(\tau\) is a measure of monotonic relationships so if there is no relationship or the relationship is completely non-monotonic (i.e. a parabola) then the Kendall \(\tau\) is zero. I added ``or no relationship'' to make this clearer}). 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. The impact of a similar change in \(V_{1/2}\), slope factor \(k\), or conductance of different currents will impact firing behaviour dfferently not just within and between models.
\begin{figure}[ht!]
\centering
@ -261,20 +307,20 @@ Sensitivity analyses are used to understand how input model parameters contribut
\label{fig:AUC_correlation}
\end{figure}
Alterations in gating \(V_{1/2}\) and slope factor $k$ as well as the maximum conductance also play a role in determining rheobase (\Cref{fig:rheobase_correlation} A, B and C). Shifts in half activation of gating properties are similarly correlated with rheobase across models, however Kendall \(\tau\) values departing from $-1$ indicate non-monotonic relationships between K-current \(V_{1/2}\) and rheobase in some models (\Cref{fig:rheobase_correlation}A). Changes in Na-current inactivation, \Kv-current inactivation, and A-current activation affect rheobase 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. Maximum conductance affects rheobase similarly across models (\Cref{fig:rheobase_correlation}C).
Alterations in gating \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance also play a role in determining rheobase (\Cref{fig:rheobase_correlation} A, B and C). Shifts in half activation of gating properties are similarly correlated with rheobase across models, however Kendall \(\tau\) values departing from \(-1\) indicate non-monotonic or no relationships between K-current \(V_{1/2}\) and rheobase in some models (\Cref{fig:rheobase_correlation}A). Changes in Na-current inactivation, \Kv-current inactivation, and A-current activation affect rheobase 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. 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.
\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{Figures/rheobase_correlation.pdf}
\\\notejb{Oben rechts: linebreak in ``A inactivation'' is weird}
\\\notenk{Habe ich fuer dieses und das AUC Abbildung (Figure 3) geaendert}
\notenk{Habe ich fuer dieses und das AUC Abbildung (Figure 3) geaendert}
\linespread{1.}\selectfont
\caption[]{The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in \(V_{1/2}\) and rheobase, slope factor k and AUC as well as current conductances and rheobase for each model are shown on the right in (A), (B) and (C) respectively. The relationships between rheobase 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:rheobase_correlation}
\end{figure}
\subsection*{\Kv Mutations}
Mutations in \Kv are associated with episodic ataxia type~1 (EA1) and have been characterized biophysically. They are used here as a case study in the effects of various ionic-current environments on neuronal firing and on the outcomes of channelopathies. The changes in AUC and rheobase from wild type values for reported EA1 associated \Kv mutations are heterogenous across models containing \Kv, but generally show decreases in rheobase (\Cref{fig:simulation_model_comparision}A-I). Pairwise non-parametric Kendall \(\tau\) rank correlations between the simulated effects of these \Kv mutations on rheobase are highly correlated across models (\Cref{fig:simulation_model_comparision}J). However, the effects of the \Kv mutations on AUC are more heterogenous as reflected by both weak and strong positive and negative pairwise correlations between models (\Cref{fig:simulation_model_comparision}K), suggesting that the effects of ion-channel variant on super-threshold neuronal firing depend on the specific composition of ionic currents in a given neuron.
Mutations in \Kv are associated with episodic ataxia type~1 (EA1) and have been characterized biophysically \citep{lauxmann_therapeutic_2021}. They are used here as a case study in the effects of various ionic current environments on neuronal firing and on the outcomes of channelopathies. The changes in AUC and rheobase from wild type values for reported EA1 associated \Kv mutations are heterogenous across models containing \Kv, but generally show decreases in rheobase (\Cref{fig:simulation_model_comparision}A-I). Pairwise non-parametric Kendall \(\tau\) rank correlations between the simulated effects of these \Kv mutations on rheobase are highly correlated across models (\Cref{fig:simulation_model_comparision}J) indicating that EA1 associated \Kv mutations generally decrease rheobase across diverse cell-types. However, the effects of the \Kv mutations on AUC are more heterogenous as reflected by both weak and strong positive and negative pairwise correlations between models (\Cref{fig:simulation_model_comparision}K), suggesting that the effects of ion-channel variant on super-threshold neuronal firing depend on the specific composition of ionic currents in a given neuron.
\begin{figure}[ht!]
\centering
@ -285,7 +331,7 @@ Mutations in \Kv are associated with episodic ataxia type~1 (EA1) and have been
\end{figure}
\section*{Discussion (3000 Words Maximum - Currently 2010)}
\section*{Discussion (3000 Words Maximum - Currently 2139)}
% \textit{The discussion section should include a brief statement of the principal findings, a discussion of the validity of the observations, a discussion of the findings in light of other published work dealing with the same or closely related subjects, and a statement of the possible significance of the work. Extensive discussion of the literature is discouraged.}\\
Using a set of diverse conductance-based neuronal models, the effects of changes to properties of ionic currents and conductances on firing were determined to be heterogenous for the AUC of the steady state fI curve but more homogenous for rheobase. For a known channelopathy, episodic ataxia type~1 associated \Kv mutations, the effects on rheobase is consistent across model cell types, whereas the effect on AUC depends on cell type. Our results demonstrate that LoF and GoF on the biophysical level cannot be uniquely transfered to the level of neuronal firing.
@ -298,27 +344,27 @@ Additionally, the single-compartment models do not take into consideration diffe
The firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis. These could be seen as further dimensions to analyze the influence of mutations on neuronal firing and can only increase the uncertainty of these estimations.
Despite all these shortcomings of the models we used in our simulations, they do not touch our main conclusion. The quantitative as well as qualitative effects of a given ionic-current variant in general depend on the specific properties of all the other ionic currents expressed in a given cell.
Despite all these shortcomings of the models we used in our simulations, they do not touch our main conclusion that the quantitative as well as qualitative effects of a given ionic current variant in general depend on the specific properties of all the other ionic currents expressed in a given cell.
\subsection*{Ionic-Current Environments Determine the Effect of Ion Channel Mutations}
\subsection*{Ionic Current Environments Determine the Effect of Ion Channel Mutations}
One-factor-at-a-time (OFAT) sensitivity analyses such as the one performed here are predicated on assumptions of model linearity, and cannot account for interactions between factors \citep{czitrom_one-factor-at--time_1999, saltelli_how_2010}. OFAT approaches are local and not global (i.e. always in reference to a baseline point in the parameter space) and therefore cannot be generalized to the global parameter space unless linearity is met \citep{saltelli_how_2010}. The local space around the wild type neuron is explored with an OFAT sensitivity analysis without taking interactions between parameters into account. Comparisons between the effects of changes in similar parameters across different models can be made at the wild type locale indicative of experimentally observed neuronal behaviour. In this case, the role of deviations in the ionic current properties from their wild type in multiple neuronal models presented here provides a starting point for understanding the general role of these current properties in neurons. However, a more global approach would provide a more holistic understanding of the parameter space and provide insight into interactions between properties.
Characterization of the effects of a parameter on firing with non-parametric Kendall \(\tau\) correlations takes into account the sign and monotonicity of the correlation. In other words Kendall \(\tau\) coefficients provide information as to whether changing a parameter is positively or negatively correlated with AUC or rheobase as well as the extent to which this correlation is positive or negative across the parameter range examined. Therefore, Kendall \(\tau\) coefficients provide general information as to the sensitivity of different models to a change in a given current property, however more nuanced difference between the sensitivities of models to current property changes, such as the slope of the relationship between parameter change and firing are not included in our analysis.
% The inter-model differences seen with the OFAT sensitivity analysis highlight the need for cell specific models. The observed dependence of neuronal firing on voltage-gated sodium channels and delayed-rectifier potassium channels is known \citep{verma_computational_2020, arhem_channel_2006} and substantiated by OFAT analysis across models. It is suggested that variability in these currents may underlie within cell population variability in neuronal firing behaviour \citep{verma_computational_2020}. Although increases in low-voltage activated inward currents are generally accepted to increase firing rates and outward currents to decrease firing rates \citep{nowacki_sensitivity_2011}, this was not always observed in AUC. The heterogeneity in outcomes of model OFAT analysis, especialy with AUC, suggest that the effects of changes in current properties are neuronal dependent and the current environment encompassing the relative conductances, gating \(V_{1/2}\) positions, and gating slopes of other currents plays an important role in modulating firing behaviour and in determining the outcome of a current property change such as a mutation.
Although, to our knowledge, no comprehensive evaluation of how current environment and cell type affect the outcome of ion channel mutations, comparisons between the effects of such mutations in certain cells have been reported. For instance, mutations in the SCN1A gene encoding \(\textrm{Na}_{\textrm{V}}\textrm{1.1}\) result in epileptic phenotypes by selective hypoexcitability of inhibitory but not excitatory neurons in the cortex resulting in circuit hyperexcitability \citep{Hedrich14874}. In CA3 of the hippocampus, mutation of \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) similarly results in increased excitability of pyramidal neurons and decreased 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 \(\textrm{Na}_\textrm{V}\textrm{1.8}\) \citep{Waxman2007, Rush2006}. In a modelling study, it was found that altering the sodium conductance in 2 stomatogastric ganglion neuron models from a population models decreases rheobase in both models, however the initial slope of the fI curves (proportional to AUC) is increased in one model and decreased in the other suggesting that the magnitude of other currents in these models (such as \(\textrm{K}_\textrm{d}\)) determines the effect of a change in sodium current \citep{Kispersky2012}. 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.
Although, to our knowledge, no comprehensive evaluation of how ionic current environment and cell type affect the outcome of ion channel mutations, comparisons between the effects of such mutations in certain cells have been reported. For instance, mutations in the SCN1A gene encoding \(\textrm{Na}_{\textrm{V}}\textrm{1.1}\) result in epileptic phenotypes by selective hypoexcitability of inhibitory but not excitatory neurons in the cortex resulting in circuit hyperexcitability \citep{Hedrich14874}. In CA3 of the hippocampus, mutation of \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) similarly results in increased excitability of pyramidal neurons and decreased 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 \(\textrm{Na}_\textrm{V}\textrm{1.8}\) \citep{Waxman2007, Rush2006}. In a modelling study, it was found that altering the sodium conductance in 2 stomatogastric ganglion neuron models from a population models decreases rheobase in both models, however the initial slope of the fI curves (proportional to AUC) is increased in one model and decreased in the other suggesting that the magnitude of other currents in these models (such as \(\textrm{K}_\textrm{d}\)) determines the effect of a change in sodium current \citep{Kispersky2012}. 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 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}. 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 behaviour of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a sub-population of stomatogastric ganglion "one-spike bursting" neurons fires 3 spikes instead of 1 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}. 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 behaviour of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a sub-population of stomatogastric ganglion "one-spike bursting" neurons fires 3 spikes instead of 1 per burst due to an L shaped distribution of sodium and potassium conductances \citep{golowasch_failure_2002}.
Multiple sets of current 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}.
Variability in ion channel expression often correlates with the expression of other ion channels \citep{goaillard_ion_2021} and neurons whose behaviour is similar may possess correlated variability across different ion channels resulting in stability in neuronal phenotype \citep{lamb_correlated_2013, soofi_co-variation_2012, taylor_how_2009}.
The variability of ion 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}.
\subsection*{Effects of KCNA1 Mutations}
Moderate changes in delayed rectifier potassium currents change the bifurcation structure of Hodgkin Huxley model, with changes analogous to those seen with \Kv mutations resulting in increased excitability due to reduced thresholds for repetitive firing \citep{hafez_altered_2020}. Although the Hodgkin Huxley delayed rectifier lacks inactivation, the increases in excitability seen are in line with simulation-based predictions of the outcomes of \textit{KCNA1} mutations. LOF KCNA1 mutations generally increase neuronal excitability, however the different effects of KCNA1 mutations across models on AUC are indicative that a certain cell type specific complexity exists. Increased excitability seen experimentally with \Kv null mice \citep{smart_deletion_1998, zhou_temperature-sensitive_1998}, with pharmacological \Kv block \citep{chi_manipulation_2007, morales-villagran_protection_1996}, by \citet{hafez_altered_2020} and with simulation-based predictions of KCNA1 mutations. Contrary to these results, \citet{zhao_common_2020} predicted \textit{in silico} that the depolarizing shifts seen as a result of KCNA1 mutations broaden action potentials and interfere negatively with high frequency action potential firing, however \textcolor{green}{they varied stimulus duration between different models and therefore} comparability of firing rates is lacking in this study.
Moderate changes in delayed rectifier potassium currents change the bifurcation structure of Hodgkin Huxley model, with changes analogous to those seen with \Kv mutations resulting in increased excitability due to reduced thresholds for repetitive firing \citep{hafez_altered_2020}. Although the Hodgkin Huxley delayed rectifier lacks inactivation, the increases in excitability seen are in line with simulation-based predictions of the outcomes of \textit{KCNA1} mutations. LOF KCNA1 mutations generally increase neuronal excitability, however the different effects of KCNA1 mutations across models on AUC are indicative that a certain cell type specific complexity exists. Increased excitability seen experimentally with \Kv null mice \citep{smart_deletion_1998, zhou_temperature-sensitive_1998}, with pharmacological \Kv block \citep{chi_manipulation_2007, morales-villagran_protection_1996}, by \citet{hafez_altered_2020} and with simulation-based predictions of KCNA1 mutations. Contrary to these results, \citet{zhao_common_2020} predicted \textit{in silico} that the depolarizing shifts seen as a result of KCNA1 mutations broaden action potentials and interfere negatively with high frequency action potential firing, however they varied stimulus duration between different models and therefore comparability of firing rates is lacking in this study.
Different current properties, such as the difference in \(\textrm{I}_\textrm{A}\) and \IKv in the Cb stellate and STN model families alter the impact of KCNA1 mutations on firing highlighting that knowledge of the biophysical properties of a current and its neuronal expression is vital for holistic understanding of the effects of a given ion channel mutation both at a single cell and network level.
\subsection*{Loss or Gain of Function Characterizations Do Not Fully Capture Ion Channel Mutation Effects on Firing}
The effects of changes in current properties depend in part on the neuronal model in which they occur and can be seen in the variance of correlations (especially in AUC) across models for a given current property change. Therefore, relative conductances and gating properties of currents in the current environment in which an alteration in current properties occurs plays an important role in determining the outcome on firing. The use of loss of function (LOF) and gain of function (GOF) is useful at the level of ion channels and whether a mutation results in more or less ionic current, however the extension of this thinking onto whether mutations induce LOF or GOF at the level of neuronal firing based on the ionic current LOF/GOF is problematic due to the dependency of neuronal firing changes on the current environment. Thus the direct leap from current level LOF/GOF characterizations to effects on firing without experimental or modelling-based evidence, although tempting, should be refrained from and viewed with caution when reported. This is especially relevant in the recent development of personalized medicine for channelopathies, where a patients specific channelopathy is identified and used to tailor treatments \citep{Weber2017, Ackerman2013, Helbig2020, Gnecchi2021, Musto2020, Brunklaus2022}. However, the effects of specific ion channel mutations are often characterized in expression systems and classified as LOF or GOF to aid in treatment decisions \citep{johannesen_genotype-phenotype_2021, Brunklaus2022, Musto2020}. Interestingly, both LOF and GOF \(\textrm{Na}_{\textrm{V}}\textrm{1.1}\) mutations can benefit from treatment with sodium channel blockers \citep{johannesen_genotype-phenotype_2021}, suggesting that the relationship between effects at the level of ion channels and effects at the level of firing and therapeutics is not linear or evident without further contextual information. Therefore, this approach must be used with caution and the cell type which expressed the mutant ion channel must be taken into account. Experimental assessment of the effects of a patients specific ion channel mutation \textit{in vivo} is not feasible at a large scale due to time and cost constraints, modelling of the effects of patient specific channelopathies is a desirable approach.
The effects of changes in current properties depend in part on the neuronal model in which they occur and can be seen in the variance of correlations (especially in AUC) across models for a given current property change. Therefore, relative conductances and gating properties of currents in the ionic current environment in which an alteration in current properties occurs plays an important role in determining the outcome on firing. The use of loss of function (LOF) and gain of function (GOF) is useful at the level of ion channels and whether a mutation results in more or less ionic current, however the extension of this thinking onto whether mutations induce LOF or GOF at the level of neuronal firing based on the ionic current LOF/GOF is problematic due to the dependency of neuronal firing changes on the ionic current environment. Thus the direct leap from current level LOF/GOF characterizations to effects on firing without experimental or modelling-based evidence, although tempting, should be refrained from and viewed with caution when reported. This is especially relevant in the recent development of personalized medicine for channelopathies, where a patients specific channelopathy is identified and used to tailor treatments \citep{Weber2017, Ackerman2013, Helbig2020, Gnecchi2021, Musto2020, Brunklaus2022}. However, the effects of specific ion channel mutations are often characterized in expression systems and classified as LOF or GOF to aid in treatment decisions \citep{johannesen_genotype-phenotype_2021, Brunklaus2022, Musto2020}. Interestingly, both LOF and GOF \(\textrm{Na}_{\textrm{V}}\textrm{1.1}\) mutations can benefit from treatment with sodium channel blockers \citep{johannesen_genotype-phenotype_2021}, suggesting that the relationship between effects at the level of ion channels and effects at the level of firing and therapeutics is not linear or evident without further contextual information. Therefore, this approach must be used with caution and the cell type which expressed the mutant ion channel must be taken into account. Experimental assessment of the effects of a patients specific ion channel mutation \textit{in vivo} is not feasible at a large scale due to time and cost constraints, modelling of the effects of patient specific channelopathies is a desirable approach.
Accordingly, for accurate modelling and predictions of the effects of mutations on neuronal firing, information as to the type of neurons containing the affected channel, and the properties of the affected and all currents in the affected neuronal type is needed. When modelling approaches are sought out to overcome the limitations of experimental approaches, care must be taken to account for model dependency and the generation of relevant cell-type or cell specific populations of models should be standard in assessing the effects of mutations in specific neurons.
\par\null

237
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file = {Full Text PDF:https\://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/epi.14700:application/pdf},
keywords = {Dravet syndrome, epilepsy, FHM, GABA, genetic epilepsy with febrile seizures plus, migraine, remodeling, seizures},
language = {en},
shorttitle = {{SCN1A}/{NaV1}.1 channelopathies},
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urldate = {2022-05-06},
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address = {Berlin, Heidelberg},
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file = {:Habib2015 - Sodium Channels and Pain.html:URL},
keywords = {Voltage-gated sodium channels, Channelopathy, Transgenic mice, Analgesia, Chronic pain, Sensory neurons},
language = {en},
urldate = {2022-05-06},
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author = {Lory, Philippe and Nicole, Sophie and Monteil, Arnaud},
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keywords = {Calcium channels, T-type, Calcium channelopathies, Epilepsy, Ataxia, Autism, Schizophrenia, Primary aldosteronism},
language = {en},
shorttitle = {Neuronal {Cav3} channelopathies},
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urldate = {2022-05-06},
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volume = {60},
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file = {Full Text PDF:https\://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/epi.14731:application/pdf},
keywords = {developmental and epileptic encephalopathy, genotype-phenotype correlation, NaV1.2 channel defect, pathomechanisms, SCN2A channelopathies},
language = {en},
shorttitle = {{SCN2A} channelopathies},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/epi.14731},
urldate = {2022-05-06},
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title = {Personalized medicine in epilepsy patients},
year = {2018},
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volume = {2},
abstract = {Personalized medicine in epilepsy patients},
doi = {10.20517/jtgg.2018.14},
file = {:Orsini2018 - Personalized Medicine in Epilepsy Patients.pdf:PDF},
language = {en},
publisher = {OAE Publishing Inc.},
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urldate = {2022-05-06},
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author = {Yang, Yang and Mis, Malgorzata A. and Estacion, Mark and Dib-Hajj, Sulayman D. and Waxman, Stephen G.},
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pages = {258--275},
volume = {39},
abstract = {Chronic pain is a global unmet medical need. Most existing treatments are only partially effective or have side effects that limit their use. Rapid progress in elucidating the contribution of specific genes, including those that encode peripheral voltage-gated sodium channels, to the pathobiology of chronic pain suggests that it may be possible to advance pain pharmacotherapy. Focusing on voltage-gated sodium channel NaV1.7 as an example, this article reviews recent progress in developing patient-specific induced pluripotent stem cells (iPSCs) and their differentiation into sensory neurons, together with advances in structural modeling, that have provided a basis for first-in-human translational studies. These new approaches will hopefully transform the treatment of pain from trial-and-error toward genomically guided, precision pharmacotherapy.},
doi = {10.1016/j.tips.2017.11.010},
file = {ScienceDirect Full Text PDF:https\://www.sciencedirect.com/science/article/pii/S0165614717302274/pdfft?md5=6ce5432529c56341b86bf0d8c60c20ba&pid=1-s2.0-S0165614717302274-main.pdf&isDTMRedir=Y:application/pdf},
language = {en},
shorttitle = {{NaV1}.7 as a {Pharmacogenomic} {Target} for {Pain}},
url = {https://www.sciencedirect.com/science/article/pii/S0165614717302274},
urldate = {2022-05-06},
}
@Article{Kullmann2002,
author = {Kullmann, Dimitri M.},
journal = {Brain},
title = {The neuronal channelopathies},
year = {2002},
issn = {0006-8950},
month = jun,
number = {6},
pages = {1177--1195},
volume = {125},
abstract = {This review addresses the molecular and cellular mechanisms of diseases caused by inherited mutations of ion channels in neurones. Among important recent advances is the elucidation of several dominantly inherited epilepsies caused by mutations of both voltage‐gated and ligand‐gated ion channels. The neuronal channelopathies show evidence of phenotypic convergence; notably, episodic ataxia can be caused by mutations of either calcium or potassium channels. The channelopathies also show evidence of phenotypic divergence; for instance, different mutations of the same calcium channel gene are associated with familial hemiplegic migraine, episodic or progressive ataxia, coma and epilepsy. Future developments are likely to include the discovery of other ion channel genes associated with inherited and sporadic CNS disorders. The full range of manifestations of inherited ion channel mutations remains to be established.},
doi = {10.1093/brain/awf130},
file = {:Kullmann2002 - The Neuronal Channelopathies.pdf:PDF},
url = {https://doi.org/10.1093/brain/awf130},
urldate = {2022-05-06},
}
@article{makinson2016scn1a,
title={An Scn1a epilepsy mutation in Scn8a alters seizure susceptibility and behavior},
@ -1417,6 +1633,27 @@ SIGNIFICANCE: Bromide is most effective and is a well-tolerated drug among DS pa
doi={10.1016/j.expneurol.2015.09.008}
}
@Article{Waxman2011,
author = {Waxman, Stephen G.},
journal = {Nature},
title = {Channelopathies have many faces},
year = {2011},
issn = {1476-4687},
month = apr,
number = {7342},
pages = {173--174},
volume = {472},
abstract = {A sodium channel known for its role in the perception of pain also seems to be necessary for olfaction. The multiple roles of this channel and the diverse effects of its mutations raise intriguing questions. See Article p.186},
copyright = {2011 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
doi = {10.1038/472173a},
file = {Full Text PDF:https\://www.nature.com/articles/472173a.pdf:application/pdf},
keywords = {Animal behaviour, Channelopathies, Physiology},
language = {en},
publisher = {Nature Publishing Group},
url = {https://www.nature.com/articles/472173a},
urldate = {2022-05-06},
}
@Comment{jabref-meta: databaseType:bibtex;}