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@ -90,7 +90,7 @@ def plot_spike_train(ax, model='RS Pyramidal', stop=750):
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ax.plot(model_spiking['t'][0:stop_ind], model_spiking[model][0:stop_ind], 'k', linewidth=1.5)
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ax.set_ylabel('V')
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ax.set_xlabel('Time [s]')
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ax.set_ylim(-80, 60)
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ax.set_ylim(-85, 60)
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ax.axis('off')
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ax.set_title(model, fontsize=10)
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@ -176,11 +176,11 @@ for i in range(len(models)):
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plot_fI(fI_axs[i], model=models[i])
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# add scalebars
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add_scalebar(ax11_spikes, matchx=False, matchy=False, hidex=True, hidey=True, sizex=100, sizey=50, labelx='100 ms',
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labely='50 mV', loc=3, pad=-0.5, borderpad=-1.0, barwidth=2, bbox_to_anchor=Bbox.from_bounds(-0.2, -0.05, 1, 1),
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add_scalebar(ax11_spikes, matchx=False, matchy=False, hidex=True, hidey=True, sizex=100, sizey=50, labelx='100\u2009ms',
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labely='50\u2009mV', loc=3, pad=-0.5, borderpad=-1.0, barwidth=2, bbox_to_anchor=Bbox.from_bounds(-0.2, -0.05, 1, 1),
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bbox_transform=ax11_spikes.transAxes)
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add_scalebar(ax12_spikes, matchx=False, matchy=False, hidex=True, hidey=True, sizex=100, sizey=50, labelx='100 ms',
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labely='50 mV', loc=3, pad=-0.5, borderpad=-1.0, barwidth=2, bbox_to_anchor=Bbox.from_bounds(-0.2, -0.05, 1, 1),
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add_scalebar(ax12_spikes, matchx=False, matchy=False, hidex=True, hidey=True, sizex=100, sizey=50, labelx='100\u2009ms',
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labely='50\u2009mV', loc=3, pad=-0.5, borderpad=-1.0, barwidth=2, bbox_to_anchor=Bbox.from_bounds(-0.2, -0.05, 1, 1),
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bbox_transform=ax12_spikes.transAxes)
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# add subplot labels
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for i in range(0,len(models)):
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g_table.tex
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g_table.tex
@ -4,27 +4,28 @@
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\centering
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% \begin{tabular}[x]{@{}l@{}} \\ \end{tabular}
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\linespread{1.}\selectfont
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\linespread{1.5}\selectfont
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\fontsize{10pt}{12pt}\selectfont{
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\begin{tabular}{c|c|c|c|c|c|c|c|c|c|}
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\begin{tabular}{cccccccccc}
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% in mS/cm^2
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& \begin{tabular}[x]{@{}c@{}} RS\\Pyra-\\midal \end{tabular} & \begin{tabular}[x]{@{}c@{}} RS\\Inhib-\\itory\end{tabular} & FS & \begin{tabular}[x]{@{}c@{}} Cb\\Stellate \end{tabular}& \begin{tabular}[x]{@{}c@{}}Cb\\Stellate\\+\Kv \end{tabular} & \begin{tabular}[x]{@{}c@{}}Cb\\Stellate\\\(\Delta\)\Kv \end{tabular} & STN &\begin{tabular}[x]{@{}c@{}} STN\\+\Kv \end{tabular} &\begin{tabular}[x]{@{}c@{}} STN\\\(\Delta\)\Kv \end{tabular}
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\\\Xhline{3\arrayrulewidth}
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\Xhline{1\arrayrulewidth}
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& \begin{tabular}[x]{@{}c@{}} RS\\Pyra-\\midal \end{tabular} & \begin{tabular}[x]{@{}c@{}} RS\\Inhib-\\itory\end{tabular} & FS & \begin{tabular}[x]{@{}c@{}} Cb\\Stellate \end{tabular}& \begin{tabular}[x]{@{}c@{}}Cb\\Stellate\\+\Kv \end{tabular} & \begin{tabular}[x]{@{}c@{}}Cb\\Stellate\\\(\Delta\)\Kv \end{tabular} & STN &\begin{tabular}[x]{@{}c@{}} STN\\+\Kv \end{tabular} &\begin{tabular}[x]{@{}c@{}} STN\\\(\Delta\)\Kv \end{tabular} \\
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\Xhline{1\arrayrulewidth}
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\(g_{Na}\) & 56 & 10 & 58 & 3.4 & 3.4 & 3.4 & 49 & 49 & 49 \\
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\(g_{K}\) & 5.4 & 1.89 & 3.51 & 9.0556 & 8.15 &9.0556 & 57 & 56.43 & 57 \\
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\(g_{K_V1.1}\) & 0.6 & 0.21 & 0.39 & - & 0.90556 & 1.50159 & - & 0.57 & 0.5 \\
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\(g_{A}\) & - & - & - & 15.0159 & 15.0159 & - & 5 & 5 & - \\
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\(g_{M}\) & 0.075 & 0.0098 &0.075 & - & - & - & - & - & - \\
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\(g_{L}\) & - & - & - & - & - & - & 5 & 5 & 5 \\
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\(g_{T}\) & - & - & - & 0.45045 & 0.45045 & 0.45045 & 5 & 5 & 5 \\
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\(g_{Ca,K}\) & - & - & - & - & - & - & 1 & 1 & 1 \\
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\(g_{K_V1.1}\) & 0.6 & 0.21 & 0.39 & --- & 0.90556 & 1.50159 & --- & 0.57 & 0.5 \\
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\(g_{A}\) & --- & --- & --- & 15.0159 & 15.0159 & --- & 5 & 5 & --- \\
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\(g_{M}\) & 0.075 & 0.0098 &0.075 & --- & --- & --- & --- & --- & --- \\
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\(g_{L}\) & --- & --- & --- & --- & --- & --- & 5 & 5 & 5 \\
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\(g_{T}\) & --- & --- & --- & 0.45045 & 0.45045 & 0.45045 & 5 & 5 & 5 \\
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\(g_{Ca,K}\) & --- & --- & --- & --- & --- & --- & 1 & 1 & 1 \\
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\(g_{Leak}\) &0.0205 & 0.0205 & 0.038 & 0.07407 & 0.07407 & 0.07407 & 0.035 & 0.035 & 0.035 \\%\Xhline{1\arrayrulewidth}
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\(\tau_{max_M}\)& 608 & 934 & 502 & - & - & - & - & - & - \\
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\(\tau_{max, M}\)& 608 & 934 & 502 & --- & --- & --- & --- & --- & --- \\
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\(C_m\) & 118.44 & 119.99 & 101.71& 177.83 & 177.83 & 177.83 & 118.44& 118.44& 118.44 \\
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\Xhline{1\arrayrulewidth}
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\end{tabular}}
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\caption[Cell properties and conductances of neuronal models]{Cell properties and conductances of regular spiking pyramidal neuron (RS Pyramidal), regular spiking inhibitory neuron (RS Inhibitory), fast spiking neuron (FS), cerebellar stellate cell (Cb Stellate), with additional \(I_{K_V1.1}\) (Cb Stellate \(\Delta\)\Kv) and with \(I_{K_V1.1}\) replacement of \(I_A\) (Cb Stellate \(\Delta\)\Kv), and subthalamic nucleus neuron (STN), with additional \(I_{K_V1.1}\) (STN \(\Delta\)\Kv) and with \(I_{K_V1.1}\) replacement of \(I_A\) (STN \Kv) models. All conductances are given in \(mS/cm^2\). Capacitances (\(C_m\)) and \(\tau_{max_p}\) are given in \(pF\) and \(ms\) respectively.}
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\caption[Cell properties and conductances of neuronal models]{Cell properties and conductances of regular spiking pyramidal neuron (RS Pyramidal), regular spiking inhibitory neuron (RS Inhibitory), fast spiking neuron (FS), cerebellar stellate cell (Cb Stellate), with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (Cb Stellate \(\Delta\)\Kv) and with \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) replacement of \(\textrm{I}_\textrm{A}\) (Cb Stellate \(\Delta\)\Kv), and subthalamic nucleus neuron (STN), with additional \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) (STN \(\Delta\)\Kv) and with \(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\) replacement of \(\textrm{I}_{\textrm{A}}\) (STN \Kv) models. All conductances are given in \(\textrm{mS}/\textrm{cm}^2\). Capacitances (\(C_m\)) and \(\tau_{max, M}\) are given in pF and ms respectively.}
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\label{tab:g}
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\end{table}
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manuscript.tex
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manuscript.tex
@ -44,6 +44,7 @@
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\usepackage{booktabs,array,multirow}
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\usepackage{caption}
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\usepackage{newfloat}
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\usepackage{upgreek}
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\let\cite\citep
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@ -60,11 +61,12 @@
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\providecommand\citealt{\cite}
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\newif\iflatexml\latexmlfalse
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\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%
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\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}
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\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}
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\newcommand{\Kv}{\(\textrm{K}_{\textrm{V}}\textrm{1.1}\ \)}
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\newcommand{\Kvnospace}{\(\textrm{K}_{\textrm{V}}\textrm{1.1}\)}
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\newcommand{\IKv}{\(\textrm{I}_{\textrm{K}_{\textrm{V}}\textrm{1.1}}\ \)}
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\DeclareFloatingEnvironment[fileext=lop]{Extended Data}
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\newcommand{\beginsupplement}{
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@ -94,14 +96,14 @@
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%\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.}
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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.
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Using a diverse collection of neuronal models, the effects of changes in ion current properties on firing is assessed sytematically 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.
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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.
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\par\null
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\section*{Significant Statement (120 Words Maximum - Currently 105)}
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\section*{Significant Statement (120 Words Maximum - Currently 112)}
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%\textit{The Significance Statement should provide a clear explanation of the importance and relevance of the research in a manner accessible to researchers without specialist knowledge in the field and informed lay readers. The Significance Statement will appear within the paper below the abstract.}
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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 should not be blindly extended to firing.
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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.
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\par\null
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\section*{Introduction (750 Words Maximum - Currently 673)}
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@ -109,50 +111,17 @@ Ion channels determine neuronal excitability and mutations that alter ion channe
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Neuronal 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 disturb 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 \citep{bernard_channelopathies_2008, carbone_ion_2020}. The effects of these mutations are frequently determined at a biophysical level, however assessment of the impact of mutations on neuronal firing and excitability is more difficult. Experimentally, transfection of cell cultures or the generation of mutant mice lines are common approaches. Cell culture transfection does not replicate the exact interplay of endogenous currents nor does it take into account the complexity of the nervous system including factors such as expression patterns, intracellular regulation and modulation of ion channels as well as network effects. Transfected currents are characterized in isolation and the role of these isolated currents in the context of other currents in a neuron cannot be definitively inferred. The effects of individual currents \textit{in vivo} also depend on the neuron type they are expressed in and which roles these neurons have in specific circuits. Complex interactions between different cell types \textit{in vivo} are neglected in transfected cell culture. Additionally, transfected currents are not present with the neuron-type specific cellular machinery present \textit{in vivo} and are even transfected in cells of different species. Furthermore, culture conditions can shape ion channel expression \citep{ponce_expression_2018}.
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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 disorders associated with a collection of distinct mutations in a single ion channel. Because of the lack of adequate experimental approaches, a great need is present for the ability to assess the impacts of ion channel mutations on neuronal firing. A more general understanding of the effects of changes in current properties on neuronal firing may help to understand the impacts of ion channel mutations. 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 \(I_{K_V1.1}\) 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.
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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 into the ion channel that is transfected and the drug is used to silence the endogenous version of this current \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 and conductance 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}, 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.
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\Kv channels, encoded by the \textit{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}.
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Altered \Kv channel function as a result of \textit{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}.
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Onset of EA1 is before 20 years of age \citep{brunt_familial_1990,rajakulendran_episodic_2007,van_dyke_hereditary_1975, jen_primary_2007} and is associated with a 10 times higher prevalence of epiletic seizures\citep{zuberi_novel_1999}. EA1 significantly impacts patient quality of life \citep{graves_episodic_2014}.
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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 disorders associated with a collection of distinct mutations in a single ion channel. Because of the lack of adequate experimental approaches, a great need is present for the ability to assess the impacts of ion channel mutations on neuronal firing. A more general understanding of the effects of changes in current properties on neuronal firing may help to understand the impacts of ion channel mutations. 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.
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\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}.
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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}.
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Onset of EA1 is before 20 years of age \citep{brunt_familial_1990,rajakulendran_episodic_2007,van_dyke_hereditary_1975, jen_primary_2007} and is associated with a 10 times higher prevalence of epileptic seizures\citep{zuberi_novel_1999}. EA1 significantly impacts patient quality of life \citep{graves_episodic_2014}.
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\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.
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Using a diverse set of conductance-based neuronal models we examine the role of current environment on the impact of alterations in channels properties on firing behavior generally and for EA1 associated \Kv mutations.
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% \subsection*{Voltage-gated \Kv Potassium Channel} %\textcolor{red}{\textit{KCNA1} and \Kv Ion Channels}
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% \Kv channels, encoded by the \textit{KCNA1} gene, play a role in repolarizing the action potential, neuronal firing patterns, neurotransmitter release, and saltatory conduction \citep{dadamo_episodic_1998}. \Kv is expressed throughout the CNS \citep{tsaur_differential_1992, wang_localization_1994} including in the cerebellum where Purkinje cells, granule cells, large Golgi cells, basket cell terminals and deep cerebellar nuclei cells express \Kv \citep{veh_immunohistochemical_1995, tsaur_differential_1992}. Cortical expression of \Kv is strongest in deep and superficial layers \citep{tsaur_differential_1992}. In the periphery, \Kv is expressed in myelinated axons and is reported to be highly expressed at juxtaparanodal regions where they modulate the ability of axons to repetitively fire \citep{mi_differential_1995, rasband_potassium_1998, wang_localization_1994}.
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% % \Kv inactivation/ heterooligomer/trafficking
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% \Kv channels do not possess the ball and chain domain responsible for fast inactivation in \textit{Drosophila Shaker} channels and thus have slow inactivation (100s of ms) on their own \citep{glasscock_kv11_2019}. At room temperature when no \Kv fast inactivation is present, the complexing of \Kv with another subunit can confer fast inactivation (10s of ms) to \Kv containing heteromers \citep{glasscock_kv11_2019}. Specifically, \(\textrm{K}_{\textrm{V}}\beta\)1 \citep{rettig_inactivation_1994} and \(\textrm{K}_{\textrm{V}}1.4\) \(\alpha\) \citep{stuhmer_molecular_1989} subunits can confer fast inactivation to \Kv containing channels. Interestingly it has been reported that \(\textrm{K}_{\textrm{V}}\beta\)2 subunits may inhibit the \(\textrm{K}_{\textrm{V}}\beta\)1 induced rapid inactivation, adding further complexity as \(\textrm{K}_{\textrm{V}}\beta\)1 and \(\textrm{K}_{\textrm{V}}\beta\)2 have overlapping expression patterns in mammals \citep{xu_kv2_1997}. However, \Kv inactivation is temperature dependent and at more physiological temperatures (35\(^{\circ}\)C) than typical measurement temperatures (room temperature), fast inactivation is seen in \Kv channels \citep{ranjan_kinetic_2019}. %also \citep{sutachan_effects_2005} at room temp
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% Heteromeric \Kv channels such as those found \textit{in vivo} with \(\textrm{K}_{\textrm{V}}1.2\), \(\textrm{K}_{\textrm{V}}1.4\) and \(\textrm{K}_{\textrm{V}}1.6\) \citep{wang__1999, roeper_nip_1998, coleman_subunit_1999}, have different biophysical properties than homomeric \Kv channels \citep{ruppersberg_heteromultimeric_1990, isacoff_evidence_1990,rettig_inactivation_1994}.
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% \(\textrm{K}_{\textrm{V}}\beta\)2 plays a role in \(\textrm{K}_{\textrm{V}}1\) channel trafficking and expression in the cell membrane \citep{shi_efficacy_2016, campomanes_kv_2002, manganas_identification_2001} and in phosphorylation of \Kv increases cell membrane \Kv \citep{jonas_regulation_1996}.
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% Altered \Kv channel function as a result of \textit{KCNA1} mutations in humans is associated with type 1 episodic ataxia where patient have episodes of discoordination as well as with epilepsy and elevated muscle activity \citep{van_dyke_hereditary_1975, jen_primary_2007}.
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% \Kv knock-out or 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}. \Kv null mice show incoordination after a cold water swim not correlated with seizures or with cold-induced muscle hyperexitability (neuromyotonia; \cite{zhou_temperature-sensitive_1998}). Increased neuronal excitability is present in \Kv null mice as evident by the reduction seizure latency after exposure to a convulsant agent \citep{smart_deletion_1998} and increased neuronal firing rates \citep{brew_hyperexcitability_2003}. Nerve excitability is likewise increased in \Kv null mice with repetitive firing observed \citep{smart_deletion_1998, zhou_temperature-sensitive_1998}. The increased action potential arrival in basket cell terminals results in increased neurotransmitter in \Kv null mice \citep{zhang_specific_1999}. Heterozygous mice show vulnerability to seizures intermediate to that of wild type and null mice suggesting that a 50\% reduction in \Kv is sufficient to affect neuronal excitability \citep{smart_deletion_1998, rho_developmental_1999}.
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% \Kv null mice are a model for sudden unexpected death in epilepsy as about half die suddenly in postnatal weeks 3-5 with several having seizures preceding death \citep{smart_deletion_1998, mishra_scn2a_2017}. Interestingly, in these mice a heterozygous deletion of the SCN2A gene encoding the \(\textrm{Na}_{\textrm{V}}\textrm{1.2}\ \) sodium channel increases survival two-fold and decreases seizure duration \citep{mishra_scn2a_2017} suggesting that reduction in sodium currents may in part be able to compensate for reductions in \Kv currents. Missense mutations in the CACNA1A gene encoding for P/Q-type calcium channels causes absence seizures, however in double mutant mice with missense Cacna1a and knocked out \textit{KCNA1} phenotypes associated with each mutation are attenuated \citep{glasscock_masking_2007}. It is suggested that the increase in excitability induced by lack of KCNA1 expression and impaired synaptic transmission caused by CACNA1A mutation may result in an intermediate level of excitability in the large population of neurons expressing both genes \citep{glasscock_masking_2007}. Therefore, loss of \Kv function and the associated increased excitability may be compensated for by alterations in other currents.
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% \Kv channels do not possess the ball and chain domain responsible for fast inactivation in \textit{Drosophila Shaker} channels and thus have slow inactivation (100s of ms) on their own \citep{glasscock_kv11_2019}. At room temperature when no \Kv fast inactivation is present, the complexing of \Kv with another subunit can confer fast inactivation (10s of ms) to \Kv containing heteromers \citep{glasscock_kv11_2019}. Specifically, \(\textrm{K}_{\textrm{V}}\beta\)1 \citep{rettig_inactivation_1994} and \(\textrm{K}_{\textrm{V}}1.4\) \(\alpha\) \citep{stuhmer_molecular_1989} subunits can confer fast inactivation to \Kv containing channels. Interestingly it has been reported that \(\textrm{K}_{\textrm{V}}\beta\)2 subunits may inhibit the \(\textrm{K}_{\textrm{V}}\beta\)1 induced rapid inactivation, adding further complexity as \(\textrm{K}_{\textrm{V}}\beta\)1 and \(\textrm{K}_{\textrm{V}}\beta\)2 have overlapping expression patterns in mammals \citep{xu_kv2_1997}. However, \Kv inactivation is temperature dependent and at more physiological temperatures (35\(^{\circ}\)C) than typical measurement temperatures (room temperature), fast inactivation is seen in \Kv channels \citep{ranjan_kinetic_2019}. %also \citep{sutachan_effects_2005} at room temp
|
||||
|
||||
% Heteromeric \Kv channels such as those found \textit{in vivo} with \(\textrm{K}_{\textrm{V}}1.2\), \(\textrm{K}_{\textrm{V}}1.4\) and \(\textrm{K}_{\textrm{V}}1.6\) \citep{wang__1999, roeper_nip_1998, coleman_subunit_1999}, have different biophysical properties than homomeric \Kv channels \citep{ruppersberg_heteromultimeric_1990, isacoff_evidence_1990,rettig_inactivation_1994}. \(\textrm{K}_{\textrm{V}}\beta\)2 plays a role in \(\textrm{K}_{\textrm{V}}1\) channel trafficking and expression in the cell membrane \citep{shi_efficacy_2016, campomanes_kv_2002, manganas_identification_2001} and in phosphorylation of \Kv increases cell membrane \Kv \citep{jonas_regulation_1996}.
|
||||
|
||||
%where patients have episodes of discoordination as well as with epilepsy and elevated muscle activity \citep{van_dyke_hereditary_1975, jen_primary_2007}.
|
||||
%symptoms
|
||||
%EA1 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} and is associated with a 10 times higher prevalence of epiletic seizures\citep{zuberi_novel_1999}. EA1 significantly impacts patient quality of life \citep{graves_episodic_2014}.
|
||||
%\Kv null mice show incoordination after a cold water swim not correlated with seizures or with cold-induced muscle hyperexitability (neuromyotonia; \cite{zhou_temperature-sensitive_1998}).
|
||||
%Increased neuronal excitability is present in \Kv null mice as evident by the reduction seizure latency after exposure to a convulsant agent \citep{smart_deletion_1998} and increased neuronal firing rates \citep{brew_hyperexcitability_2003}.
|
||||
%Nerve excitability is likewise increased in \Kv null mice with repetitive firing observed \citep{smart_deletion_1998, zhou_temperature-sensitive_1998}.
|
||||
%The increased action potential arrival in basket cell terminals results in increased neurotransmitter in \Kv null mice \citep{zhang_specific_1999}.
|
||||
%Heterozygous mice show vulnerability to seizures intermediate to that of wild type and null mice suggesting that a 50\% reduction in \Kv is sufficient to affect neuronal excitability \citep{smart_deletion_1998, rho_developmental_1999}.
|
||||
|
||||
% \Kv null mice are a model for sudden unexpected death in epilepsy as about half die suddenly in postnatal weeks 3-5 with several having seizures preceding death \citep{smart_deletion_1998, mishra_scn2a_2017}. Interestingly, in these mice a heterozygous deletion of the SCN2A gene encoding the \(\textrm{Na}_{\textrm{V}}\textrm{1.2}\ \) sodium channel increases survival two-fold and decreases seizure duration \citep{mishra_scn2a_2017} suggesting that reduction in sodium currents may in part be able to compensate for reductions in \Kv currents. Missense mutations in the CACNA1A gene encoding for P/Q-type calcium channels causes absence seizures, however in double mutant mice with missense Cacna1a and knocked out \textit{KCNA1} phenotypes associated with each mutation are attenuated \citep{glasscock_masking_2007}. It is suggested that the increase in excitability induced by lack of KCNA1 expression and impaired synaptic transmission caused by CACNA1A mutation may result in an intermediate level of excitability in the large population of neurons expressing both genes \citep{glasscock_masking_2007}.
|
||||
%Therefore, loss of \Kv function and the associated increased excitability may be compensated for by alterations in other currents.
|
||||
|
||||
% Myokymia consists of spontaneous involuntary muscle contractions that produce a rippling quality in the bodies of patients with this episodic ataxia \citep{rajakulendran_episodic_2007, van_dyke_hereditary_1975}.
|
||||
% EA1 has an age of onset earlier than age 20 and attack frequencies that often decline with age \citep{brunt_familial_1990,rajakulendran_episodic_2007,van_dyke_hereditary_1975, jen_primary_2007}.
|
||||
% Episodic attacks can be triggered by shock, sudden movement, physical or emotional stress, and chemical stressors \citep{rajakulendran_episodic_2007, brunt_familial_1990,van_dyke_hereditary_1975} and impact quality of life \citep{graves_episodic_2014}. EA1 patients sometimes have preceding sensory warnings of impending attacks \citep{van_dyke_hereditary_1975, brunt_familial_1990}. Epileptic seizures can occur with EA1 \citep{rajakulendran_episodic_2007, jen_primary_2007} with epilepsy being 10 times more prevalent in individuals with EA1 than individuals without EA1 \citep{zuberi_novel_1999}.
|
||||
|
||||
\par\null
|
||||
|
||||
@ -166,12 +135,21 @@ 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 (\(I_{K_V1.1}\); \cite{ranjan_kinetic_2019}) was added. A cerebellar stellate cell model from \cite{alexander_cerebellar_2019} is used (Cb Stellate). This model was also used with a \Kv current (\(I_{K_V1.1}\); \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 \cite{otsuka_conductance-based_2004} are used (STN) and with a \Kv current (\(I_{K_V1.1}\); \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 models. The properties of \(I_{K_V1.1}\) were fitted to the mean wild type biophysical parameters of \Kv \citep{lauxmann_therapeutic_2021}.
|
||||
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 \cite{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 \cite{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
|
||||
|
||||
\begin{equation}\label{eqn:Boltz}
|
||||
x_\infty = {\left(\frac{1-a}{1+{exp[{\frac{V-V_{1/2}}{k}}]}} +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}.
|
||||
|
||||
|
||||
\input{g_table}
|
||||
|
||||
\input{gating_table}
|
||||
|
||||
\subsection*{Firing Frequency Analysis}
|
||||
The membrane responses to 200 equidistant two second long current steps were simulated using the forward-Euler method with a \(\Delta t = 0.01\)ms from steady state. Current steps ranged from 0 to 1 \(nA\) for all models except for the RS inhibitory neuron models where a range of 0 to 0.35 \(nA\) was used to ensure repetitive firing across the range of input currents. For each current step, action potentials were detected as peaks with at least 50 mV prominence and a minimum interspike interval of 1 ms. The interspike interval was computed and used to determine the instantaneous firing frequencies elicited by the current step. The steady-state firing frequency were defined as the mean firing frequency in 0.5 seconds after the first action potential in the last second of the current step respectively and was used to construct frequency-current (fI) curves.
|
||||
The membrane responses to 200 equidistant two second long current steps were simulated using the forward-Euler method with a \(\Delta \textrm{t} = 0.01\) ms from steady state. Current steps ranged from 0 to 1 nA for all models except for the RS inhibitory neuron models where a range of 0 to 0.35 nA was used to ensure repetitive firing across the range of input currents. For each current step, action potentials were detected as peaks with at least 50 mV prominence and a minimum interspike interval of 1 ms. The interspike interval was computed and used to determine the instantaneous firing frequencies elicited by the current step. The steady-state firing frequency were defined as the mean firing frequency in 0.5 seconds after the first action potential in the last second of the current step respectively and was used to construct frequency-current (fI) curves.
|
||||
|
||||
The smallest current at which steady state firing occurs was identified and the current step interval preceding the occurrence of steady state firing was simulated at higher resolution (100 current steps) to determine the current at which steady state firing began. Firing was simulated with 100 current steps from this current upwards for 1/5 of the overall current range.
|
||||
Over this range a fI curve was constructed and the integral, or area under the curve (AUC), of the fI curve over this interval was computed with the composite trapezoidal rule and used as a measure of firing rate independent from rheobase.
|
||||
@ -184,21 +162,20 @@ All modelling and simulation was done in parallel with custom written Python 3.8
|
||||
|
||||
% 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 (\(I_{Na}\), \(I_K\), \(I_A\)/\(I_{K_V1.1}\), and \(I_{Leak}\)) 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 \(log_2\) scale.
|
||||
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.
|
||||
|
||||
\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 (\(AUC_{wt}\))
|
||||
\begin{equation}\label{eqn:AUC_contrast}
|
||||
AUC_{contrast} = \frac{AUC_i - AUC_{wt}}{AUC_{wt}}
|
||||
\end{equation}
|
||||
% Correlation across alterations within models
|
||||
|
||||
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.
|
||||
|
||||
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*{\textit{KCNA1}/\Kv Mutations}\label{subsec:mut}
|
||||
Known episodic ataxia type 1 associated \textit{KCNA1} mutations and their electrophysiological characterization reviewed in \cite{lauxmann_therapeutic_2021}. The mutation-induced changes in \(I_{K_V1.1}\) 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 \(I_A\) when present as both potassium currents display prominent inactivation. In all cases, the mutation effects were applied to half of the \(I_{K_V1.1}\) or \(I_A\) 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.
|
||||
\subsection*{KCNA1/\Kv Mutations}\label{subsec:mut}
|
||||
Known episodic ataxia type 1 associated KCNA1 mutations and their electrophysiological characterization reviewed in \cite{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.
|
||||
|
||||
|
||||
|
||||
@ -211,18 +188,22 @@ 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.
|
||||
|
||||
\subsection*{Firing Characterization}
|
||||
\begin{figure}[ht!]%described
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf}
|
||||
\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.}
|
||||
\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}
|
||||
|
||||
The quantification of the fI curve using the AUC is seen in \Cref{fig:firing_characterizaton}A. The characterization of firing with AUC and rheobase is seen in \Cref{fig:firing_characterizaton}B, where 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. 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.
|
||||
|
||||
\begin{figure}[ht!]%described
|
||||
Neuronal firing is a complex phenomenon and classification of firing is needed for comparability across cell types. 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.
|
||||
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{Figures/diversity_in_firing.pdf}
|
||||
\linespread{1.}\selectfont
|
||||
@ -231,13 +212,13 @@ The quantification of the fI curve using the AUC is seen in \Cref{fig:firing_cha
|
||||
\end{figure}
|
||||
|
||||
|
||||
The diversity in the neuronal models used is seen in \Cref{fig:diversity_in_firing}. Considerable variability is seen across neuronal models both in representative spike trains and their fI curves. 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. 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 as shown by the green and red markers in \Cref{fig:diversity_in_firing} respectively.
|
||||
Considerable diversity is present in the set of neuronal models used 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}
|
||||
A one-factor-a-time sensitivity analysis enables the comparison of a given alteration in current parameters across models. The effect of changes in gating \(V_{1/2}\) and slope factor k as well as the current conductance on AUC is shown in \Cref{fig:AUC_correlation} A, B and C respectively. 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 \(\tau | \neq\) 1). 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.
|
||||
A one-factor-a-time sensitivity analysis enables 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 \(\tau | \neq\) 1). 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.
|
||||
|
||||
|
||||
\begin{figure}[ht!]%described
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf}
|
||||
\linespread{1.}\selectfont
|
||||
@ -247,11 +228,10 @@ A one-factor-a-time sensitivity analysis enables the comparison of a given alter
|
||||
|
||||
|
||||
|
||||
The effect of changes in gating \(V_{1/2}\) and slope factor k as well as the current conductance on rheobase is shown in \Cref{fig:rheobase_correlation} A, B and C respectively.
|
||||
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).
|
||||
|
||||
\begin{figure}[ht!]%described
|
||||
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).
|
||||
|
||||
\begin{figure}[ht!]
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{Figures/rheobase_correlation.pdf}
|
||||
\linespread{1.}\selectfont
|
||||
@ -260,8 +240,8 @@ Changes in Na current inactivation, \Kv current inactivation and A current activ
|
||||
\end{figure}
|
||||
|
||||
\subsection*{\Kv}
|
||||
The changes in AUC and rheobase from wild-type values for reported episodic ataxia type 1 (EA1) associated \Kv mutations are seen in every model containing \Kv in \Cref{fig:simulation_model_comparision}A-I. Pairwise non-parametric Kendall \(\tau\) rank correlations between the simulated effects of these \Kv mutations on rheobase and AUC in different models are seen in \Cref{fig:simulation_model_comparision} J and K respectively. The effects of EA1 associated \Kv mutations on rheobase are highly correlated across models. The effects of the \Kv mutations on AUC are more heterogenous as reflected by both weak and strong positive and negative correlations between models \Cref{fig:simulation_model_comparision}K
|
||||
\begin{figure}[ht!]%described
|
||||
The changes in AUC and rheobase from wild-type values for reported episodic ataxia type 1 (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).
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\begin{figure}[ht!]
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\centering
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\includegraphics[width=\linewidth]{Figures/simulation_model_comparison.pdf}
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\linespread{1.}\selectfont
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@ -270,34 +250,34 @@ The changes in AUC and rheobase from wild-type values for reported episodic atax
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\end{figure}
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\section*{Discussion (3000 Words Maximum - Currently 1559)}
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\section*{Discussion (3000 Words Maximum - Currently 1780)}
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% \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.}\\
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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.
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\subsection*{Validity of Neuronal Models}
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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, \(\textrm{K}_{\textrm{V}}\beta\)2 plays a role in \(K_V1\) 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. \(\textrm{K}_{\textrm{V}}\beta\) subunits) \citep{rettig_inactivation_1994, xu_kv2_1997}, and temperature \citep{ranjan_kinetic_2019} modulating channel properties.
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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.
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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.
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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. The firing characterization was performed on adapted firing and as such currents that cause adaptation are neglected in our analysis.
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\subsection*{Current Environments Determine the Effect of Ion Channel Mutations}
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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 and additivity are 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.
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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.
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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.
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% 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.
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Although, to our knowldege, 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}. Additionallly, 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 \(K_d\)) 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.
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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.
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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}.
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The models used here are generated by characterization of current gating properties and by fitting of maximal conductances to experimental data. 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}.
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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}.
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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}.
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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}.
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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}.
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\subsection*{Effects of \textit{KCNA1} Mutations}
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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 both score-based and simulation-based predictions of the outcomes of \textit{KCNA1} mutations. Recently, \cite{zhao_common_2020} predicted \textit{in silico} that the depolarizing shifts seen as a result of \textit{KCNA1} mutations broaden action potentials and interfere negatively with high frequency action potential firing. However, comparability of firing rates is lacking in this study. Furthermore the 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 \cite{hafez_altered_2020} and with score-based and simulation-based predictions of \textit{KCNA1} mutations are contrary to the claims of \cite{zhao_common_2020}. LOF \textit{KCNA1} mutations generally increase neuronal excitability, however the different effects of \textit{KCNA1} mutations across models on AUC are indicative that a certain cell type specific complexity exists.
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Different current properties, such as the difference in \(I_A\) and \(I_{K_V1.1}\) in the Cb stellate and STN model families alter the impact of \textit{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.
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\subsection*{Effects of KCNA1 Mutations}
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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 both score-based and 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 \cite{hafez_altered_2020} and with simulation-based predictions of KCNA1 mutations. Contrary to these results, \cite{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 comparability of firing rates is lacking in this study.
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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.
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\subsection*{Loss or Gain of Function Characterizations Do Not Fully Capture Ion Channel Mutation Effects on Firing}
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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}. 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}. However, 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.
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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}. 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.
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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.
|
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\par\null
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