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TEXBASE=manuscript
BIBFILE=ref.bib
REBUTTALBASE=
TEXFILE=$(TEXBASE).tex
PDFFILE=$(TEXBASE).pdf
TXTFILE=$(TEXBASE).txt
REVISION=0691c71d176511c294f39d84c89864fa8c141e4a
PDFFIGURES=$(shell sed -n -e '/^[^%].*includegraphics/{s/^.*includegraphics.*{\(.*\)}/\1.pdf/;p}' $(TEXFILE))
ifdef REBUTTALBASE
REBUTTALTEXFILE=$(REBUTTALBASE).tex
REBUTTALPDFFILE=$(REBUTTALBASE).pdf
endif
REBUTTALREVISION=68900a1
# all ###########################################################
ifdef REBUTTALBASE
all: bib rebuttalbib
else
all: bib
endif
# main manuscript #################################################
bib: $(TEXBASE).bbl
$(TEXBASE).bbl: $(TEXFILE) $(BIBFILE) # $(PDFFIGURES)
pdflatex $(TEXFILE)
bibtex $(TEXBASE)
pdflatex $(TEXFILE)
pdflatex $(TEXFILE)
pdflatex $(TEXFILE)
@echo
@echo "BibTeX log:"
@sed -n -e '1,/You.ve used/p' $(TEXBASE).blg
pdf: $(PDFFILE)
$(PDFFILE) : $(TEXFILE) # $(PDFFIGURES)
pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
again :
pdflatex $(TEXFILE)
# watch files #######################################################
watchpdf :
while true; do ! make -s -q pdf && make pdf; sleep 0.5; done
# make diffs ########################################################
diff :
#latexdiff-git -r $(REVISION) --pdf $(TEXFILE)
latexdiff-git -r $(REVISION) $(TEXFILE)
-pdflatex $(TEXBASE)-diff$(REVISION)
-bibtex $(TEXBASE)-diff$(REVISION)
-pdflatex $(TEXBASE)-diff$(REVISION)
-pdflatex $(TEXBASE)-diff$(REVISION)
-pdflatex $(TEXBASE)-diff$(REVISION)
mv $(TEXBASE)-diff$(REVISION).pdf $(TEXBASE)-diff.pdf
mv $(TEXBASE)-diff$(REVISION).tex $(TEXBASE)-diff.tex
mv $(TEXBASE)-diff$(REVISION).bbl $(TEXBASE)-diff.bbl
rm $(TEXBASE)-diff$(REVISION).*
# convert to txt file ################################################
txt: $(PDFFILE)
#dvi2tty -w 132 -v 500000 -e-60 -q $(DVIFILE) | sed -n -e '/\cL/,+2!p' > $(TXTFILE)
pdftotext -nopgbrk $(PDFFILE) - | fold -s > $(TXTFILE)
# convert to rtf file ################################################
rtf :
latex2rtf $(TEXFILE)
# remove all fancy commands from the tex file:
simplify :
sed -e '/overall style/,/page style/d; /setdoublespacing/,+1d; /usepackage.*caption/s/{\(.*\)}/\1/; /figure placement/,/^%/d; /ifthenelse.*nofigs/,/#1/d; /begin{multicols}/d; /end{multicols}/d; /begin{keywords}/,/end{keywords}/d; /begin{contributions}/,/end{contributions}/d; /figurecaptions/d; /linenomath/d; s/captionc/caption/' $(TEXFILE) | perl -00 -lpe 's/\\showfigure{((\s|.)*?)}/$$1/' > $(TEXBASE)-simplified.tex
# statistics #########################################################
stats: $(PDFFILE)
# use \pagestyle{empty} and don't include any pictures!
pdftotext -nopgbrk $(PDFFILE) - | fold -s > tmp.txt
@echo
@echo " words: " `wc -w tmp.txt 2> /dev/null | cut -d ' ' -f 1`
@echo "characters: " `wc -c tmp.txt 2> /dev/null | cut -d ' ' -f 1`
rm tmp.txt
# rebuttal ##########################################################
ifdef REBUTTALBASE
rebuttalbib: $(REBUTTALBASE).bbl
$(REBUTTALBASE).bbl: $(REBUTTALTEXFILE) $(BIBFILE)
pdflatex $(REBUTTALTEXFILE)
bibtex $(REBUTTALBASE)
pdflatex $(REBUTTALTEXFILE)
pdflatex $(REBUTTALTEXFILE)
pdflatex $(REBUTTALTEXFILE)
@echo
@echo "BibTeX log:"
@sed -n -e '1,/You.ve used/p' $(REBUTTALBASE).blg
rebuttal: $(REBUTTALPDFFILE)
$(REBUTTALPDFFILE) : $(REBUTTALTEXFILE)
pdflatex -interaction=scrollmode $< | tee /dev/stderr | fgrep -q "Rerun to get cross-references right" && pdflatex -interaction=scrollmode $< || true
watchrebuttal :
while true; do ! make -q rebuttal && make rebuttal; sleep 0.5; done
rebuttaldiff :
latexdiff-git -r $(REBUTTALREVISION) --append-textcmd="response,issue" --pdf $(REBUTTALTEXFILE)
mv $(REBUTTALBASE)-diff$(REBUTTALREVISION).pdf $(REBUTTALBASE)-diff.pdf
rm $(REBUTTALBASE)-diff$(REBUTTALREVISION).*
endif
# git ##############################################################
pull :
git pull origin master
ifdef REBUTTALBASE
edit : pull
emacs $(TEXFILE) $(BIBFILE) $(REBUTTALTEXFILE) Makefile &
sleep 1
okular $(REBUTTALPDFFILE) $(PDFFILE) &
prepare : pull bib diffrev rebuttalbib rebuttaldiff
else
edit : pull
emacs $(TEXFILE) $(BIBFILE) Makefile &
sleep 1
okular $(PDFFILE) &
prepare : pull bib diffrev
endif
push : prepare
git commit -a
git push origin master
# convert figures to png files #######################################
figures:
./latexfigures2png $(TEXFILE)
# convert pdf figures to eps #########################################
epsfigures:
#for i in $(PDFFIGURES); do echo $$i; rm -f $${i%.pdf}.eps; pdftops -level3 -eps $$i $${i%.pdf}.eps; done
for i in $(PDFFIGURES); do echo $$i; rm -f $${i%.pdf}.eps; gs -q -dNOCACHE -dNOPAUSE -dBATCH -dSAFER -sDEVICE=epswrite -sOutputFile=$${i%.pdf}.eps $$i; done
# clean up ############################################################
clean:
rm -rf auto *~ *.aux *.blg *.bbl *.dvi *.log *.out *.fff *.ttt $(PDFFIGURES) __pycache__
cleanall: clean
rm -f $(PDFFILE) figure-??.png
# help ################################################################
help :
@echo -e \
"make pdf: make the pdf file of the paper.\n"\
"make bib: run bibtex and make the pdf file of the paper.\n"\
"make again: run pdflatex and make the pdf file of the paper,\n"\
" no matter whether you changed the .tex file or not.\n"\
"make watchpdf: make the pdf file of the paper\n"\
" whenever the tex file is modified.\n"\
"make diff: make a diff file against the specified revision (REVISION variable)\n"\
"make txt: make a plain text version of the paper ($(TXTFILE)).\n"\
"make rtf: convert the paper ($(TXTFILE)) to rtf format.\n"\
"make simplify: strip all fancy commands from the paper ($(TXTFILE))\n"\
"make stats: print number of words and characters.\n"\
"make rebuttalbib: run bibtex and make the pdf file of the rebuttal.\n"\
"make rebuttal: make the pdf file of the rebuttal.\n"\
"make watchrebuttal: make the pdf file of the rebuttal\n"\
" whenever the tex file is modified.\n"\
"make rebuttaldiff: make a diff file of the rebuttal against the specified revision\n"\
" (REBUTTALREVISION variable).\n"\
"make pull: pull from the git repository.\n"\
"make edit: pull and open emacs and okular with te relevant files.\n"\
"make prepare: pull and make the pdfs and diffs of the manuscript and the rebuttal.\n"\
"make push: prepare, commit, and push to the git repository.\n"\
"make figures : convert all figures to png files.\n"\
"make epsfigures: convert all included pdf figures to eps files.\n"\
"make clean: remove all intermediate files,\n"\
" just leave the source files and the final .pdf files.\n"\
"make cleanup: remove all intermediate files as well as\n"\
" the final .pdf files.\n"\

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@ -65,9 +65,9 @@
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}
\newcommand{\Kv}{\(\textrm{K}_{\textrm{V}}\textrm{1.1}\ \)}
\newcommand{\Kvnospace}{\(\textrm{K}_{\textrm{V}}\textrm{1.1}\)}
\newcommand{\IKv}{\(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\ \)}
\usepackage{xspace}
\newcommand{\Kv}{\(\textrm{K}_{\textrm{V}}\textrm{1.1}\)\xspace}
\newcommand{\IKv}{\(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\)\xspace}
\DeclareFloatingEnvironment[fileext=lop]{Extended Data}
\newcommand{\beginsupplement}{
@ -76,6 +76,12 @@
\setcounter{table}{0}
\renewcommand{\thetable}{S\arabic{table}}}
%%%%% notes %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newcommand{\note}[2][]{\textbf{[#1: #2]}}
\newcommand{\notenk}[1]{\note[NK]{#1}}
\newcommand{\notels}[1]{\note[LS]{#1}}
\newcommand{\notejb}[1]{\note[JB]{#1}}
\begin{document}
\title{Loss or Gain of Function? Ion Channel Mutation Effects on Neuronal Firing Depend on Cell Type}
@ -97,7 +103,7 @@
%\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 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
@ -107,12 +113,15 @@ Using a diverse collection of neuronal models, the effects of changes in ion cur
Ion channels determine neuronal excitability and mutations that alter ion channel properties result in neurological disorders called channelopathies. Although the genetic nature of such mutations as well as their effects on the ion channel's biophysical properties are routinely assessed experimentally, determination of the role in altering neuronal firing is more difficult. Computational modelling bridges this gap and demonstrates that the cell type in which a mutation occurs is an important determinant in the effects of firing. As a result, classification of ion channel mutations as loss or gain of function is useful to describe the ionic current but care should be taken when applying this classification on the level of neuronal firing.
\par\null
\notejb{LOF or LoF? GOF or GoF?}
\section*{Introduction} %(750 Words Maximum - Currently \textcolor{red}{837})}
%\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}.
Although the effects of channelopathies on ion current kinetics are frequently assessed by transfection of heterologous expression systems without endogenous currents \citep{Balestrini1044, Noebels2017, Dunlop2008} \textcolor{red}{(cite more stuff?)}, the effect of these changes in current biophysics on neuronal firing is 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 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)}.
Although 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?)}, the effect of these changes on neuronal firing is 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 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)}.
%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.
@ -120,17 +129,17 @@ Although the effects of channelopathies on ion current kinetics are frequently a
%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 have different ion current compositions \citep{yao2021taxonomy} \textcolor{red}{(cite Berens)} and therefore likely respond differently to changes in the properties of one current.
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.
% \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?)}, however if a gating property is altered substantially this can have complex consequences.
For instance, altering relative current amplitudes 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 current parameters 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}\textcolor{red}{(and the other paper?)}. %not sure which paper you mean Lukas
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}\textcolor{red}{(and the other paper?)}. %not sure which paper you mean Lukas
%However, the effect on the firing behaviour of different neurons is often unclear \textcolor{red}{(and always incomplete)}. Generally, different neuron types have different ionic current compositions and therefore could react in different ways to changes in one ionic current. In the simpler cases, the respective firing behaviour should mostly correlate with expression level of the affected current and scale with it \textcolor{red}{(cite some stuff, cite NikoPaper)}. \textcolor{red}{If the change in gating kinetics is too strong, the firing behaviour can change qualitatively.} Altering the relative current amplitudes in neuronal models leads to dramtic changes in their firing behaviour and dynamics \citep{rutecki_neuronal_1992, pospischil_minimal_2008,Kispersky2012, golowasch_failure_2002, barreiro_-current_2012, Noebels2017}. \textcolor{red}{The same could happen for other parameters too. \citet{Liu2019} reported a drastically slowed inacitvaiton time constant for a mutation in \textcolor{red}{Na$_V$1.6}, which led to huge depolarization plateaus after an action potential, that lasted several 100 milliseconds.} The most drastic example known to us would be the R1629H mutation in \textcolor{red}{SCN2A}. This mutation increases the excitability of interneurons, but decreases it in pyramidal neurons \textcolor{red}{(cite Hedrich2014 and the other paper)}. \textcolor{red}{Some neuron types may be closer to certain transitions between firing states than other, making these observations even more unpredictable \textcolor{red}{(cite some bifurcation stuff?)}.}
Computational modelling approaches can be used to assess the impacts of current property changes on firing behaviour, bridging the gap between changes in the biophysical properties induced by mutations, firing and clinical symptoms. Conductance-based neuronal models enable insight into the effects of ion channel mutations with specific effects of the resulting ionic current as well as enabling \textit{in silico} assessment of the relative effects of changes in biophysical properties of ionic currents on neuronal firing. Furthermore, modelling approaches enable predictions of the effects of specific mutation and drug induced biophysical property changes.
Computational modelling approaches can be used to assess the impacts of changed properties of ionic currents on firing behaviour, bridging the gap between changes in the biophysical properties induced by mutations, firing and clinical symptoms. Conductance-based neuronal models enable insight into the effects of ion channel mutations with specific effects of the resulting ionic current as well as enabling \textit{in silico} assessment of the relative effects of changes in biophysical properties of ionic currents on neuronal firing. Furthermore, modelling approaches enable predictions of the effects of specific mutation and drug induced biophysical property changes.
We therefore investigate the role that neuronal type plays on the outcome of ion current kinetic changes on firing by simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as to episodic ataxia type 1 associated \Kv mutations.
We therefore investigate the role that neuronal type plays on the outcome of ionic current kinetic changes on firing by simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as to episodic ataxia type~1 associated \Kv mutations.
%In this study we want to get an insight into how changes in ion current kinetics change firing behaviour dependent on neuron type. We will simulate a repertoire of different neuronal models and compare their response to changes in single parameters and to changes as they were observed for mutations in \textcolor{red}{KCNA1}, causing ataxia.
@ -141,10 +150,10 @@ We therefore investigate the role that neuronal type plays on the outcome of ion
%Ion channel transfection of primary neuronal cultures can overcome some of the limitations of cell culture expression. In transfected neuronal cell cultures firing can more readily be assessed as endogenous currents are present, however the expressed and endogenous versions of the same ion channel are present in the cell \cite{Scalmani2006, Smith2018}. To avoid the confound of both expressed and endogenous current contributing to firing, a drug resistance can be introduced to the transfected ion channel and the endogenous version of this current can be pharmacologically silenced \cite{Liu2019}. Although addition of TTX-resistance to \(\textrm{Na}_{\textrm{V}}\) does not alter the gating properties of these channels \cite{Leffler2005}, the relative expression of the transfected ion channel in relation to endogenous currents can be variable and non-specific blocking of ion channels not affected by the channelopathy may occur. As the firing behaviour and dynamics of neuronal models can be dramatically altered by altering relative current amplitudes \citep{rutecki_neuronal_1992, pospischil_minimal_2008,Kispersky2012, golowasch_failure_2002, barreiro_-current_2012, Noebels2017}, primary neuronal cultures provide a useful general indication as to the effects of ion channel mutations but do not provide definitive insight into the effects of a channelopathy on \textit{in vivo} firing.
%The generation of mice lines is costly and behavioural characterization of new mice lines is required to assess similarities to patient symptoms. Although the generation of mouse lines is desirable for a clinical disorder characterized by a specific ion channel mutation, this approach becomes impractical for personalized treatment for large numbers of distinct mutations. 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. Specifically, modelling approaches can be used to assess the impacts of current property changes on firing behaviour, bridging the gap between changes in the biophysical properties induced by mutations and clinical symptoms. Conductance-based neuronal models enable insight into the effects of ion channel mutations with specific effects of the resulting ionic current as well as enabling \textit{in silico} assessment of the relative effects of changes in biophysical properties of ionic currents on neuronal firing. The effects of altered voltage-gated potassium channel \Kv function is of particular interest in this study as it gives rise to the \IKv current and is associated with episodic ataxia type 1. Furthermore, modelling approaches enable predictions of the effects of specific mutation and drug induced biophysical property changes.
%The generation of mice lines is costly and behavioural characterization of new mice lines is required to assess similarities to patient symptoms. Although the generation of mouse lines is desirable for a clinical disorder characterized by a specific ion channel mutation, this approach becomes impractical for personalized treatment for large numbers of distinct mutations. 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. Specifically, modelling approaches can be used to assess the impacts of current property changes on firing behaviour, bridging the gap between changes in the biophysical properties induced by mutations and clinical symptoms. Conductance-based neuronal models enable insight into the effects of ion channel mutations with specific effects of the resulting ionic current as well as enabling \textit{in silico} assessment of the relative effects of changes in biophysical properties of ionic currents on neuronal firing. The effects of altered voltage-gated potassium channel \Kv function is of particular interest in this study as it gives rise to the \IKv current and is associated with episodic ataxia type~1. Furthermore, modelling approaches enable predictions of the effects of specific mutation and drug induced biophysical property changes.
%\Kv channels, encoded by the KCNA1 gene, play a role in repolarizing the action potential, neuronal firing patterns, neurotransmitter release, and saltatory conduction \citep{dadamo_episodic_1998} and are expressed throughout the CNS \citep{tsaur_differential_1992, wang_localization_1994, veh_immunohistochemical_1995}.
%Altered \Kv channel function as a result of KCNA1 mutations in humans is associated with episodic ataxia type 1 (EA1) which is characterized by period attacks of ataxia and persistent myokymia \citep{parker_periodic_1946, van_dyke_hereditary_1975}.
%Altered \Kv channel function as a result of KCNA1 mutations in humans is associated with episodic ataxia type~1 (EA1) which is characterized by period attacks of ataxia and persistent myokymia \citep{parker_periodic_1946, van_dyke_hereditary_1975}.
%Onset of EA1 is before 20 years of age \citep{brunt_familial_1990,rajakulendran_episodic_2007,van_dyke_hereditary_1975, jen_primary_2007}, is associated with a 10 times higher prevalence of epileptic seizures\citep{zuberi_novel_1999} and significantly impacts patient quality of life \citep{graves_episodic_2014}.
%\Kv null mice have spontaneous seizures without ataxia starting in the third postnatal week although impaired balance has been reported \citep{smart_deletion_1998, zhang_specific_1999} and neuronal hyperexcitability has been demonstrated in these mice \citep{smart_deletion_1998, brew_hyperexcitability_2003}. However, the lack of ataxia in \Kv null mice raises the question if the hyperexcitability seen is representative of the effects of EA1 associated \Kv mutations.
@ -163,12 +172,10 @@ All modelling and simulation was done in parallel with custom written Python 3.8
% 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}. To each of these models, a \Kv current (\IKv); \cite{ranjan_kinetic_2019}) was added. A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate). This model was also used with a \Kv current (\IKv; \cite{ranjan_kinetic_2019}) in addition to the A-type potassium current (Cb stellate +\Kv) or replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv). A subthalamic nucleus neuron model as described by \citet{otsuka_conductance-based_2004} are used (STN) and with a \Kv current (\IKv; \cite{ranjan_kinetic_2019}) in addition to the A-type potassium current (STN +\Kv) or replacing the A-type potassium current (STN \(\Delta\)\Kv). The properties and conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models. For comparability to typical electrophysiological data fitting reported and for ease of further gating curve manipulations, a Boltzmann function
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}. To each of these models, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added. A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate). This model was also used with a \Kv current \citep{ranjan_kinetic_2019} in addition to the A-type potassium current (Cb stellate +\Kv) or replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv). A subthalamic nucleus neuron model as described by \citet{otsuka_conductance-based_2004} are used (STN) and with a \Kv current (\IKv; \citealp{ranjan_kinetic_2019}) in addition to the A-type potassium current (STN +\Kv) or replacing the A-type potassium current (STN \(\Delta\)\Kv). The properties and conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models. For comparability to typical electrophysiological data fitting reported and for ease of further gating curve manipulations, a Boltzmann function
\begin{equation}\label{eqn:Boltz}
x_\infty = {\left(\frac{1-a}{1+{exp[{\frac{V-V_{1/2}}{k}}]}} +a\right)^j}
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 for the RS pyramidal, RS inhibitory and FS models \cite{pospischil_minimal_2008}. The properties of \IKv were fitted to the mean wild type biophysical parameters of \Kv \citep{lauxmann_therapeutic_2021}.
@ -190,7 +197,7 @@ with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}
% Sensitivity analyses enable investigation into how different sources of uncertainty in a model result in uncertainty in model outputs \citep{saltelli_sensitivity_2002} and provide information on the relative impact of model inputs \citep{saltelli_why_2019}. We recently used a one-factor-at-a-time (OFAT) sensitivity analysis approach to evaluate the relative impacts of currents on neuronal firing and developed a scoring system for SCN8A mutations that correlated (p = 0.0077, r = 0.64) with the clinical severity of epilepsy in patients with these mutations \citep{johannesen_genotype-phenotype_2021}. This was done in an isolated neuronal model and suggests that even with disregard of network level effects of mutations, the single cell level outcomes of mutations are relevant to disease phenotypes. OFAT sensitivity analyses indicate which factors have or do not have influence, with uninfluential factors never detected as relevant \citep{saltelli_how_2010}. OFAT sensitivity analyses can be used to screen factors that are influential on model outcomes and provide a mechanism by which factors and their relative influence can be easily identified and used in predictive applications.
Current properties of currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{Leak}\)) were systematically altered in a one-factor-at-a-time sensitivity analysis for all models. The gating curves for each current were shifted (\(\Delta V_{1/2}\)) from -10 to 10\,mV in increments of 1\,mV. The slope (\(k\)) of the gating curves were altered from half to twice the initial slope. Similarly, the maximal current conductance (\(g\)) was also scaled from half to twice the initial value. For both slope and conductance alterations, alterations consisted of 21 steps spaced equally on a \(\textrm{log}_2\) scale.
Properties of ionic currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{Leak}\)) were systematically altered in a one-factor-at-a-time sensitivity analysis for all models. The gating curves for each current were shifted (\(\Delta V_{1/2}\)) from -10 to 10\,mV in increments of 1\,mV. The slope (\(k\)) of the gating curves were altered from half to twice the initial slope. Similarly, the maximal current conductance (\(g\)) was also scaled from half to twice the initial value. For both slope and conductance alterations, alterations consisted of 21 steps spaced equally on a \(\textrm{log}_2\) scale.
\subsection*{Model Comparison}
Changes in rheobase (\(\Delta rheobase\)) are calculated in relation to the original model rheobase. The contrast of each AUC value (\(AUC_i\)) was computed in comparison to the AUC of the unaltered wild type model (\(AUC_{wt}\))
@ -198,12 +205,12 @@ with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}
AUC_{contrast} = \frac{AUC_i - AUC_{wt}}{AUC_{wt}}
\end{equation}
To assess whether the effects of a given alteration on \(AUC_{contrast}\) or \(\Delta rheobase\) are robust across models, the correlation between \(AUC_{contrast}\) or \(\Delta rheobase\) and the magnitude of current property alteration was computed for each alteration in each model and compared across alteration types.
To assess whether the effects of a given alteration on \(AUC_{contrast}\) or \(\Delta rheobase\) are robust across models, the correlation between \(AUC_{contrast}\) or \(\Delta rheobase\) and the magnitude of the alteration of a current property was computed for each alteration in each model and compared across alteration types.
The Kendall's \(\tau\) coefficient, a non-parametric rank correlation, is used to describe the relationship between the magnitude of the alteration and AUC or rheobase values. A Kendall \(\tau\) value of -1 or 1 is indicative of monotonically decreasing and increasing relationships respectively.
\subsection*{KCNA1/\Kv Mutations}\label{subsec:mut}
Known episodic ataxia type 1 associated KCNA1 mutations and their electrophysiological characterization reviewed in \citet{lauxmann_therapeutic_2021}. The mutation-induced changes in \IKv amplitude and activation slope (\(k\)) were normalized to wild type measurements and changes in activation \(V_{1/2}\) were used relative to wild type measurements. The effects of a mutation were also applied to \(\textrm{I}_{\textrm{A}}\) when present as both potassium currents display prominent inactivation. In all cases, the mutation effects were applied to half of the \Kv or \(\textrm{I}_{\textrm{A}}\) under the assumption that the heterozygous mutation results in 50\% of channels carrying the mutation. Frequency-current curves for each mutation in each model were obtained through simulation and used to characterize firing behaviour as described above. For each model the differences in mutation AUC to wild type AUC were normalized by wild type AUC (\(AUC_{contrast}\)) and mutation rheobases are compared to wild type rheobase values (\(\Delta rheobase\)). Pairwise Kendall rank correlations (Kendall \(\tau\)) are used to compare the the correlation in the effects of \Kv mutations on AUC and rheobase between models.
Known episodic ataxia type~1 associated KCNA1 mutations and their electrophysiological characterization reviewed in \citet{lauxmann_therapeutic_2021}. The mutation-induced changes in \IKv amplitude and activation slope (\(k\)) were normalized to wild type measurements and changes in activation \(V_{1/2}\) were used relative to wild type measurements. The effects of a mutation were also applied to \(\textrm{I}_{\textrm{A}}\) when present as both potassium currents display prominent inactivation. In all cases, the mutation effects were applied to half of the \Kv or \(\textrm{I}_{\textrm{A}}\) under the assumption that the heterozygous mutation results in 50\% of channels carrying the mutation. Frequency-current curves for each mutation in each model were obtained through simulation and used to characterize firing behaviour as described above. For each model the differences in mutation AUC to wild type AUC were normalized by wild type AUC (\(AUC_{contrast}\)) and mutation rheobases are compared to wild type rheobase values (\(\Delta rheobase\)). Pairwise Kendall rank correlations (Kendall \(\tau\)) are used to compare the the correlation in the effects of \Kv mutations on AUC and rheobase between models.
@ -216,35 +223,34 @@ 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 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 current environments.
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.
\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.}
\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 classification of firing is required for comparisons of firing across cell types and between conditions. Here we focus on the classification of 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. The quantification of the inital shape of the fI curve using by computing the area under the curve (AUC) is a measure of the initial firing at 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) indicate an increase in firing, whereas the bottom right quadrant (-\(\Delta\)AUC and +\(\Delta\)rheobase) is indicative of decreased firing (\Cref{fig:firing_characterizaton}B). In the lower left and upper right quadrants, the effects on firing are more nuance 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, 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.
\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{Figures/diversity_in_firing.pdf}
\linespread{1.}\selectfont
\caption[]{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) 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 \(\Delta\)\Kvnospace (J), STN \(\Delta\)\Kvnospace (K), and STN (L) neuron models. Black marker on the fI curves indicate the current step at which the spike train occurs. The green marker indicates the current at which firing begins in response to an ascending current ramp, whereas the red marker indicates the current at which firing ceases in response to a descending current ramp (see \Cref{fig:ramp_firing}).}
\caption[]{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) 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. Black marker on the fI curves indicate the current step at which the spike train occurs. The green marker indicates the current at which firing begins in response to an ascending current ramp, whereas the red marker indicates the current at which firing ceases in response to a descending current ramp (see \Cref{fig:ramp_firing}).}
\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 ion 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 \(\Delta\)\Kvnospace 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 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 STN +\Kv, STN \(\Delta\)\Kv, Cb stellate \(\Delta\)\Kv 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 current parameters across models. Changes in gating \(V_{1/2}\) and slope factor k as well as the current 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 currents. In these cases some of the models display non-monotonic relationships (i.e. \( |\)Kendall \(\tau | \neq\) ). However, shifts in A current activation \(V_{1/2}\), changes in \Kv activation \(V_{1/2}\) and slope, and changes in A current conductance display consistent monotonic relationships across models.
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}).
\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?} ). 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.
\begin{figure}[ht!]
\centering
@ -254,47 +260,53 @@ 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 current 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 have 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. Current conductance magnitude alterations affect 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 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).
\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{Figures/rheobase_correlation.pdf}
\\\notejb{Oben rechts: linebreak in ``A inactivation'' is weird}
\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 in \Kv are associated with episodic ataxia type 1 (EA1) have been characterized biophysically and are used here as a case study in the effects of current environment on the outcomes of channelopathies on firing. 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).
\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.
\begin{figure}[ht!]
\centering
\includegraphics[width=\linewidth]{Figures/simulation_model_comparison.pdf}
\linespread{1.}\selectfont
\caption[]{Effects of episodic ataxia type 1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (\(AUC_{contrast}\)) and rheobase (\(\Delta\)rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kvnospace (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kvnospace (I) models V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively.}
\caption[]{Effects of episodic ataxia type~1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (\(AUC_{contrast}\)) and rheobase (\(\Delta\)rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kv (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kv (I) models V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively.}
\label{fig:simulation_model_comparision}
\end{figure}
\section*{Discussion (3000 Words Maximum - Currently 2010)}
% \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 current properties 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 cell types, whereas the effect on AUC is cell type dependent.
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.
\subsection*{Validity of Neuronal Models}
Our findings are based on simulations of a range of single-compartment conductance-based models. Many aspects of these models can be questioned.
\subsection*{Validity of Neuronal Models \textcolor{red}{ - put this section in a less prominent place?}}
The \Kv model from \cite{ranjan_kinetic_2019} is based on expression of only \Kv in CHO cells and represents the biophysical properties of \Kv homotetramers and not heteromers. Thus the \Kv model used here neglects the complex reality of these channels \textit{in vivo} including their expression as heteromers and the altered biophyiscal properties of these heteromers \citep{wang__1999, roeper_nip_1998, coleman_subunit_1999, ruppersberg_heteromultimeric_1990, isacoff_evidence_1990, rettig_inactivation_1994}. Furthermore, dynamic modulation of \Kv channels, although physiologically relevant, is neglected here. For example, \(\textrm{K}_{\textrm{V}}\upbeta\)2 plays a role in \(\textrm{K}_{\textrm{V}}\textrm{1}\) channel trafficking and cell membrane expression \citep{shi_efficacy_2016, campomanes_kv_2002, manganas_identification_2001} and \Kv phosphorylation increases cell membrane \Kv \citep{jonas_regulation_1996}. It should be noted that the discrete classification of potassium currents into delayed rectifier and A-type is likely not biological, but rather highlights the characteristics of a spectrum of potassium channel inactivation that arises in part due to additional factors such as heteromer composition \citep{stuhmer_molecular_1989, glasscock_kv11_2019}, non-pore forming subunits (e.g. \(\textrm{K}_{\textrm{V}}\upbeta\) subunits) \citep{rettig_inactivation_1994, xu_kv2_1997}, and temperature \citep{ranjan_kinetic_2019} modulating channel properties.
Additionally, the single-compartment model does not take into consideration differential effects on neuronal compartments (i.e. axon, soma, dendrites), possible different spatial cellular distribution of channel expression across and within these neuronal compartments or across CNS regions nor does it consider different channel types (e.g \(\textrm{Na}_{\textrm{V}}\text{1.1}\) vs \(\textrm{Na}_{\textrm{V}}\text{1.8}\)). More realistic models would consist of multiple compartments, take more currents into account and take the spatial distribution of channels into account, however these models are more computationally expensive, require current specific models and knowledge of the distribution of conductances across the cell. Despite these limitations, each of the models can reproduce physiological firing behaviour of the neurons they represent \citep{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004} and capture key aspects of the dynamics of these cell types.
Additionally, the single-compartment models do not take into consideration differential effects on neuronal compartments (i.e. axon, soma, dendrites), possible different spatial cellular distribution of channel expression across and within these neuronal compartments or across CNS regions nor does it consider different channel types (e.g \(\textrm{Na}_{\textrm{V}}\text{1.1}\) vs \(\textrm{Na}_{\textrm{V}}\text{1.8}\)). More realistic models would consist of multiple compartments, take more ionic currents into account and take the spatial distribution of channels into account, however these models are more computationally expensive, require current specific models and knowledge of the distribution of conductances across the cell. Despite these limitations, each of the models can reproduce physiological firing behaviour of the neurons they represent \citep{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004} and capture key aspects of the dynamics of these cell types.
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.
The firing characterization was performed on steady-state firing and as such processes that cause adaption 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.
\subsection*{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 suggest that the 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 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 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}.
@ -354,13 +366,13 @@ Accordingly, for accurate modelling and predictions of the effects of mutations
\setcounter{figure}{0}
\captionof{figure}{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.}
\captionof{figure}{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) 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 \(\Delta\)\Kvnospace (J), STN \(\Delta\)\Kvnospace (K), and STN (L) neuron models. Black marker on the fI curves indicate the current step at which the spike train occurs. The green marker indicates the current at which firing begins in response to an ascending current ramp, whereas the red marker indicates the current at which firing ceases in response to a descending current ramp.}
\captionof{figure}{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) 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. Black marker on the fI curves indicate the current step at which the spike train occurs. The green marker indicates the current at which firing begins in response to an ascending current ramp, whereas the red marker indicates the current at which firing ceases in response to a descending current ramp.}
\captionof{figure}{The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in \(V_{1/2}\) and AUC, slope factor k and AUC as well as current conductances and AUC for each model are shown on the right in (A), (B) and (C) respectively. The relationships between AUC and \(\Delta V_{1/2}\), slope (k) and conductance (g) for the Kendall \(\tau\) coefficients highlights by the black box are depicted in the middle panel. The fI curves corresponding to one of the models are shown in the left panels.}
\captionof{figure}{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.}
\captionof{figure}{Effects of episodic ataxia type 1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (\(AUC_{contrast}\)) and rheobase (\(\Delta\)rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kvnospace (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kvnospace (I) models V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively.}
\captionof{figure}{Effects of episodic ataxia type~1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (\(AUC_{contrast}\)) and rheobase (\(\Delta\)rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kv (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kv (I) models V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively.}
\newpage
\subsection*{Tables}
@ -381,7 +393,7 @@ Accordingly, for accurate modelling and predictions of the effects of mutations
\centering
\includegraphics[width=\linewidth]{Figures/ramp_firing.pdf}
\linespread{1.}\selectfont
\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 \(\Delta\)\Kvnospace (J), STN \(\Delta\)\Kvnospace (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.}
\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}