clean up old comments in manuscript.tex
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@ -180,60 +180,28 @@ Voltage-gated ion channels are vital in determining neuronal excitability, actio
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\notenk{Are there any obvious citations missing from the following section?}
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The effects of channelopathies on ionic current kinetics are frequently assessed by transfection of heterologous expression systems without endogenous currents \citep{Balestrini1044, Noebels2017, Dunlop2008}, and are frequently classified as either a loss of function (LOF) or a gain of function (GOF) with respect to changes in the magnitude of ionic currents flowing through the channels \citep{Musto2020, Kullmann2002, Waxman2011, Kim2021}. This classification of the effects on ionic currents is often directly used to predict the effects on neuronal firing \citep{Niday2018, Wei2017, Wolff2017} \textcolor{red}{(any other Papers?)}, which in turn is important for understanding the pathophysiology of these disorders and for identification of potential therapeutic targets \citep{Orsini2018, Yang2018}. Genotype-phenotype relationships are complex and the understanding of the relationships between these is still evolving \citep{Wolff2017, johannesen_genotype-phenotype_2021}. Experimentally, the effects of channelopathies on neuronal firing can be assessed using primary neuronal cultures \citep{Scalmani2006, Smith2018, Liu2019} or \textit{in vitro} recordings from transgenic mouse lines \citep{Mantegazza2019, Xie2010,Lory2020, Habib2015, Hedrich2019}.
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%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.
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%Linking the effects of modified currents to neuronal firing is crucial for understanding the disease and finding possible treatments. There are many widely accepted approaches. Transfection of heterologous expression systems without endogenous currents reveals changes in ionic current kinetics \textcolor{red}{(cite some stuff)}. Simulations of these effects can predict their effect on neuronal firing \textcolor{red}{(cite some stuff)}. Or the influence on firing behaviour can be directly measured in transfected primary neuronal cultures \textcolor{red}{(cite some stuff)} or in brain slice recordings of mouse lines \textcolor{red}{(cite some stuff)}.
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%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.
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However the effect of a given channelopathy on firing behavior of different neuronal types across the brain is often unclear and not feasible to experimentally obtain. Different neuron types differ in their composition of ionic currents \citep{yao2021taxonomy, Cadwell2016, BICCN2021, Scala2021} and therefore likely respond differently to changes in the properties of a single ionic current.
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% \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. }
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The expression level of an affected gene can correlate with firing behaviour in the simplest case \citep{Layer2021} \textcolor{red}{(any other Papers?)}, however if gating kinetics are affected this can have complex consequences.
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However the effect of a given channelopathy on firing behavior of different neuronal types across the brain is often unclear and not feasible to experimentally obtain. Different neuron types differ in their composition of ionic currents \citep{yao2021taxonomy, Cadwell2016, BICCN2021, Scala2021} and therefore likely respond differently to changes in the properties of a single ionic current. The expression level of an affected gene can correlate with firing behaviour in the simplest case \citep{Layer2021} \textcolor{red}{(any other Papers?)}, however if gating kinetics are affected this can have complex consequences.
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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,makinson_scn1a_2016}
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%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?)}.}
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Computational modelling approaches can be used to assess the impacts of changed ionic current properties 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.
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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 more complex changes as they were observed for specific mutations. For this task we chose mutations in KCNA1, encoding for the potassium channel \Kv, that are associated with episodic ataxia type~1 \citep{lauxmann_therapeutic_2021}.
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%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.
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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 presumed \cite{Balestrini1044} or determined at a biophysical level, however assessment of the impact of mutations on neuronal firing and excitability is more difficult. Experimentally, 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 \cite{Balestrini1044, Noebels2017}. 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 \cite{Dunlop2008, Noebels2017}. Additionally, transfected currents are not expressed in the presence of physiologically present auxillary proteins 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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% Complex interactions between different cell types and circuit level effects \textit{in vivo} are neglected in transfected cell culture.
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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 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.
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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 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.
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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}, 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}.
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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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\par\null
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\section*{Materials and Methods}
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% \textit{The materials and methods section should be brief but sufficient to allow other investigators to repeat the research (see also Policy Concerning Availability of Materials). Reference should be made to published procedures wherever possible; this applies to the original description and pertinent published modifications. }
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\par\null
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All modelling and simulation was done in parallel with custom written Python 3.8 software, run on a Cent-OS 7 server with an Intel(R) Xeon (R) E5-2630 v2 CPU.
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% @ 2.60 GHz
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% Linux 3.10.0-123.e17.x86_64.
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% @ 2.60 GHz Linux 3.10.0-123.e17.x86_64.
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\subsection*{Different Cell Models}
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A group of neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal), regular spiking inhibitory (RS inhibitory), and fast spiking (FS) cells were used \citep{pospischil_minimal_2008}. Additionally, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added to each of these models (RS pyramidal +\Kv, RS inhibitory +\Kv, and FS +\Kv respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate). 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 maximal conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models. For comparability to typical electrophysiological data fitting reported and for ease of further gating curve manipulations, a modified Boltzmann function
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\begin{equation}\label{eqn:Boltz}
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x_\infty = {\left(\frac{1-a}{1+{\exp\left[{\frac{V-V_{1/2}}{k}}\right]}} +a\right)^j}
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\end{equation}
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A group of neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal), regular spiking inhibitory (RS inhibitory), and fast spiking (FS) cells were used \citep{pospischil_minimal_2008}. Additionally, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added to each of these models (RS pyramidal +\Kv, RS inhibitory +\Kv, and FS +\Kv respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate). 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 maximal conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models. For comparability to typical electrophysiological data fitting reported and for ease of further gating curve manipulations, a modified Boltzmann function
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\begin{equation}\label{eqn:Boltz}
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x_\infty = {\left(\frac{1-a}{1+{\exp\left[{\frac{V-V_{1/2}}{k}}\right]}} +a\right)^j}
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\end{equation}
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with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted to the original formulism for RS pyramidal, RS inhibitory and FS models from \citet{pospischil_minimal_2008}. The properties of \IKv were fitted to the mean wild type biophysical parameters of \Kv \citep{lauxmann_therapeutic_2021}. Each of the original single-compartment models used here 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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@ -242,43 +210,32 @@ with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}
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\input{gating_table}
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\subsection*{Firing Frequency Analysis}
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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, or the relative height above the lowest contour line encircling it, 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\,s after the first action potential in the last second of the current step respectively and was used to construct frequency-current (fI) curves. Alteration in current magnitudes can have different effects on rheobase and the initial slope of the fI curve \citep{Kispersky2012}.
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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, or the relative height above the lowest contour line encircling it, 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\,s after the first action potential in the last second of the current step respectively and was used to construct frequency-current (fI) curves. Alteration in current magnitudes can have different effects on rheobase and the initial slope of the fI curve \citep{Kispersky2012}.
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For this reason, we quantify neuronal firing with the rheobase as well as the area under the curve (AUC) of the initial portion of the fI curve as a measure of the initial slope of the fI curve.
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%\textcolor{red}{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 of the fI-curve) 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} \notels{I don't see this in the paper. As far as I understood, they start with one model type and then only work with the other and state that they behave qualitatively the same} \notenk{Yes you are right. I looked at the paper again and I'm not sure why I wrote that. I think the key thing I was trying to get at is that the effect of an increase in sodium conductan on the fI curve can be different at different parts of the fI curve, because at higher firing rates \(\textrm{K}_\textrm{d}\) plays a role. As such changes or heterogeneity in \(\textrm{K}_\textrm{d}\) could alter the effect of such an increase in sodium conductance at these higher firing rates.}. \notenk{Do you think that this is a more accurate representation? ``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 shape of the fI curves especially at high firing rates is altered due other currents in these models such as \(\textrm{K}_\textrm{d}\) \citep{Kispersky2012}.''} \notenk{Could move this to methods as a justification as to why we use rheobase and AUC as measures for firing}}
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%\notenk{add as justification as to why we use AUC and rheobase. Previously, changes in fI curves have shown differences ....}
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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.
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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.
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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.
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To obtain the rheobase, the current step interval preceding the occurrence of action potentials was explored at higher resolution with 100 current steps spanning the interval. Membrane responses to these current steps were then analyzed for action potentials and the rheobase was considered the lowest current step for which an action potential was elicited.
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To obtain the rheobase, the current step interval preceding the occurrence of action potentials was explored at higher resolution with 100 current steps spanning the interval. Membrane responses to these current steps were then analyzed for action potentials and the rheobase was considered the lowest current step for which an action potential was elicited.
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All models exhibit tonic firing and any instances of bursting were excluded to simplify the characterization of firing. Firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis.
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\subsection*{Sensitivity Analysis and Comparison of Models}
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% 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.
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Properties of ionic currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{\textrm{Leak}}\)) 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 voltage dependence of the time constant associated with the shifted gating curve was correspondingly shifted. 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. We neglect variation of time constants for the practical reason that estimation and assessment of time constants and changes to them is not straightforward \citep{Clerx2019, Whittaker2020}.
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Properties of ionic currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{\textrm{Leak}}\)) 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 voltage dependence of the time constant associated with the shifted gating curve was correspondingly shifted. 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. We neglect variation of time constants for the practical reason that estimation and assessment of time constants and changes to them is not straightforward \citep{Clerx2019, Whittaker2020}.
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%Although a number of methods have been used to fit ionic currents including different approaches in estimate time constants either from summary data or from full current traces, and are limited by the available data \citep{Clerx2019, Whittaker2020}. On one hand, specialized equipment and great experimental care is often required to estimate time constants \citep{Whittaker2020}. As a result summary data is often not recorded for voltage ranges in which time constants are fast. On the other hand, lack of availability of full current traces for each mutation limits the alternative current trace fitting approach. For these practical reasons, we neglect the effect of mutation altered time constants despite acknowledging that time constant changes are likely important in determining the outcome of a given mutation on firing.}
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\subsection*{Model Comparison}
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Changes in rheobase (\drheo) 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 (\(AUC_{wt}\))
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\begin{equation}\label{eqn:AUC_contrast}
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\textrm{normalized } \Delta \textrm{AUC} = \frac{AUC_i - AUC_{wt}}{AUC_{wt}}
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\end{equation}
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To assess whether the effects of a given alteration on \ndAUC or \drheo are robust across models, the correlation between \ndAUC or \drheo and the magnitude of the alteration of a current property was computed for each alteration in each model and compared across alteration types.
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\subsection*{Model Comparison}
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Changes in rheobase (\drheo) 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 (\(AUC_{wt}\))
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\begin{equation}\label{eqn:AUC_contrast}
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\textrm{normalized } \Delta \textrm{AUC} = \frac{AUC_i - AUC_{wt}}{AUC_{wt}}
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\end{equation}
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To assess whether the effects of a given alteration on \ndAUC or \drheo are robust across models, the correlation between \ndAUC or \drheo and the magnitude of the alteration of a current property was computed for each alteration in each model and compared across alteration types.
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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.
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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.
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\subsection*{KCNA1/\Kv Mutations}\label{subsec:mut}
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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 (\ndAUC) and mutation rheobases are compared to wild type rheobase values (\drheo). 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.
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\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 (\ndAUC) and mutation rheobases are compared to wild type rheobase values (\drheo). 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.
|
||||
|
||||
|
||||
|
||||
@ -307,7 +264,6 @@ Neuronal firing is heterogenous across the CNS and a set of neuronal models with
|
||||
\subsection*{Characterization of Neuronal Firing Properties}
|
||||
\begin{figure}[tp]
|
||||
\centering
|
||||
% \includegraphics[width=0.5\linewidth]{Figures/firing_characterization.pdf}
|
||||
\includegraphics[width=0.5\linewidth]{Figures/firing_characterization_arrows.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)
|
||||
@ -316,7 +272,6 @@ Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occup
|
||||
\end{figure}
|
||||
|
||||
Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between conditions. Here we focus on two aspects of firing: rheobase, the smallest injected current at which the cell fires an action potential, and the shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for a fixed range of input currents above rheobase (\Cref{fig:firing_characterization}A). The characterization of firing by rheobase and AUC allows to characterize both a neuron's excitability in the sub-threshold regime (rheobase) and periodic firing in the super-threshold regime (AUC) by two independent measures. Note that AUC is essentially quantifying the slope of a neuron's fI curve.
|
||||
%\notenk{This enables a AUC measurement independent from rheobase.}\notejb{I added a few words to the next sentence. Would this be enough or should we make it more explicit by an extra sentence als Nils suggests it?} \notenk{I think that this is enough - we can always expand if a reviewer asks}
|
||||
|
||||
Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, \drheo, and in AUC, \(\Delta\)AUC, relative to the wild type neuron. \(\Delta\)AUC is in addition normalized to the AUC of the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by \drheo and \ndAUC (\Cref{fig:firing_characterization}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\)\drheo), unambigously indicating an increased firing that clearly might be classified as a GOF of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\)\drheo), indicating a decreased, LOF firing. In the lower left (\(-\Delta\)AUC and \(-\)\drheo) and upper right (\(+\Delta\)AUC and \(+\)\drheo) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability. In these cases it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionally generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant.
|
||||
|
||||
@ -342,9 +297,6 @@ Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) a
|
||||
|
||||
Although changes in half maximal potential \(V_{1/2}\) and slope factor \(k\) generally correlate with rheobase similarly across model there are some exceptions. Changing the slope factor of Na-current inactivation, \Kv-current inactivation, and A-current activation affect rheobase both with positive and negative correlations in different models (\Cref{fig:rheobase_correlation}~F). Departures from monotonic relationships also occur in some models as a result of K-current activation \(V_{1/2}\) and slope factor \(k\), \Kv-current inactivation slope factor \(k\), and A-current activation slope factor \(k\) in some models. Thus, identical changes in current gating properties such as the half maximal potential \(V_{1/2}\) or slope factor \(k\) can have differing effects on firing depending on the model in which they occur.
|
||||
|
||||
%The rheobase is also affected by changes in channel kinetics (\Cref{fig:rheobase_correlation}). In contrast to AUC, most alterations result in similar changes of rheobase in all models, but there are some noteable exceptions. Changing the slope factor of Na-current inactivation, \Kv-current inactivation, and A-current activation affect rheobase both 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 \notejb{which parameters are changed?}. Maximum conductance affects rheobase similarly across models (\Cref{fig:rheobase_correlation}~C). However, identical changes in current gating properties such as the half maximal potential \(V_{1/2}\) or slope factor \(k\) can have differing effects on firing depending on the model in which they occur. \notejb{This we just have said...}
|
||||
|
||||
|
||||
|
||||
\begin{figure}[tp]
|
||||
\centering
|
||||
@ -371,25 +323,17 @@ Mutations in \Kv are associated with episodic ataxia type~1 (EA1) and have been
|
||||
|
||||
To compare the effects of changes to properties of ionic currents on neuronal firing of different neuron types, a diverse set of conductance-based models was simulated. Changes to single ionic current properties, as well as known episodic ataxia type~1 associated \Kv mutations showed consistent effects on the rheobase across cell types, whereas the effects on AUC of the steady-state fI-curve depend on cell type. Our results demonstrate that LOF and GOF on the biophysical level cannot be uniquely transferred to the level of neuronal firing. The effects depend on the properties of the other currents expressed in a cell and are therefore depending on cell type.
|
||||
|
||||
%Using a set of diverse conductance-based neuronal models, the effects of changes to properties of ionic currents on neuronal 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 are consistent across model cell types, whereas the effects on AUC depend on cell type. Our results demonstrate that LOF and GOF on the biophysical level cannot be uniquely transferred to the level of neuronal firing. The effects depend on the properties of the other currents expressed in a cell and are therefore depending on cell type.
|
||||
|
||||
\subsection*{Neuronal Diversity}
|
||||
%\notejb{Before we start questioning our models we should have a paragraph pointing out that neurons are diverse and differ in their ion channel composition. Cite for example those recent Nature/Science papers where Phillip Berens is part of on neuron types in cerebellum. Thomas Euler Retina ganglien cell types. Then the paper defining Regular/fast spiking interneurons. And many more... like Eve Marder as you have it in a paragraph further down.}\\
|
||||
%\notenk{Added this section - it needs more work, but what do you think of the direction I'm going?} \notenk{Also I'm not sure which regular/fast spiking interneuron paper you mean}\\
|
||||
|
||||
The nervous system consists of a vastly diverse and heterogenous collection of neurons with variable properties and characteristics including diverse combinations and expression levels of ion channels which are vital for neuronal firing dynamics.
|
||||
|
||||
Advances in high-throughput techniques have enabled large-scale investigation into single-cell properties across the CNS \citep{Poulin2016} that have revealed large diversity in neuronal gene expression, morphology and neuronal types in the motor cortex \citep{Scala2021}, neocortex \cite{Cadwell2016, Cadwell2020}, GABAergic neurons \citep{Huang2019} and interneurons \citep{Laturnus2020}, cerebellum \citep{Kozareva2021}, spinal cord \citep{Alkaslasi2021}, visual cortex \citep{Gouwens2019} as well as the retina \citep{Baden2016, Voigt2019, Berens2017, Yan2020a, Yan2020b}.
|
||||
|
||||
% Functional differences: reg/fat spiking, Ephys, models
|
||||
Diversity across neurons is not limited to gene expression and can also be seen electrophysiologically \citep{Tripathy2017, Gouwens2018, Tripathy2015, Scala2021, Cadwell2020, Gouwens2019, Baden2016, Berens2017} with correlations existing between gene expression and electrophysiological properties \citep{Tripathy2017}. At the ion channel level, diversity exists not only between the specific ion channels cell types express but heterogeneity also exists in ion channel expression levels within cell types \citep{marder_multiple_2011, goaillard_ion_2021,barreiro_-current_2012}. As ion channel properties and expression levels are key determinents of neuronal dynamics and firing \citep{Balachandar2018, Gu2014, Zeberg2015, Aarhem2007, Qi2013, Gu2014a, Zeberg2010, Zhou2020, Kispersky2012} neurons with different ion channel properties and expression levels display different firing properties.
|
||||
|
||||
%Taken together, the nervous system consists of a vastly diverse and heterogenous collection of neurons with variable properties and characteristics including diverse combinations and expression levels of ion channels which are vital for neuronal firing dynamics.
|
||||
|
||||
To capture the diversity in neuronal ion channel expression and its relevance in the outcome of ion channel mutations, we used multiple neuronal models with different ionic currents and underlying firing dynamics here.
|
||||
|
||||
|
||||
|
||||
|
||||
\subsection*{Ionic Current Environments Determine the Effect of Ion Channel Mutations}
|
||||
|
||||
To our knowledge, no comprehensive evaluation of how ionic current environment and cell type affect the outcome of ion channel mutations have been reported. However, comparisons between the effects of such mutations between certain cell types were described. For instance, the R1628H mutation in SCN1A results in selective hyperexcitability of cortical pyramidal neurons, but causes hypoexcitability of adjacent inhibitory GABAergic neurons \citep{Hedrich14874}. In CA3 of the hippocampus, the equivalent mutation in SCN8A, R1648H, increases excitability of pyramidal neurons and decreases 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}. 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.
|
||||
@ -398,70 +342,20 @@ Cell type specific differences in ionic current properties are important in the
|
||||
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}.
|
||||
% 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
|
||||
% mutation of \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) similarly results in increased excitability of pyramidal neurons and decreased excitability of parvalbumin positive interneurons
|
||||
|
||||
\subsection*{Effects of KCNA1 Mutations}
|
||||
Changes in delayed rectifier potassium currents, analogous to those seen in \Kv mutations, change the underlying firing dynamics of the Hodgkin Huxley model result in reduced thresholds for repetitive firing and thus contribute to increased excitability \citep{hafez_altered_2020}. Although the Hodgkin Huxley delayed rectifier lacks inactivation, the increases in excitability seen by \citet{hafez_altered_2020} are in line with our simulation-based predictions of the outcomes of \Kv mutations. LOF KCNA1 mutations generally increase neuronal excitability, however the varying susceptibility on rheobase and different effects on AUC of the fI-curve of KCNA1 mutations across models are indicative that a certain cell type specific complexity exists. Increased excitability is 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} and by \citet{hafez_altered_2020} with simulation-based predictions of KCNA1 mutations. Contrary to these results, \citet{zhao_common_2020} predicted \textit{in silico} that the depolarizing shifts seen as a result of KCNA1 mutations broaden action potentials and interfere negatively with high frequency action potential firing, however they varied stimulus duration between different models and therefore comparability of firing rates is lacking in this study.
|
||||
|
||||
In our simulations, different current properties alter the impact of KCNA1 mutations on firing in our simulations as evident in the differences seen in the impact of \(\textrm{I}_\textrm{A}\) and \IKv in the Cb stellate and STN model families on KCNA1 mutation firing. This highlights 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.
|
||||
|
||||
%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.
|
||||
%Moderate changes in delayed rectifier potassium currents change the bifurcation structure \notels{firing dynamics} of Hodgkin Huxley model, with changes analogous to those seen with KV1.1 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 KCNA1 mutations.
|
||||
|
||||
\subsection*{Loss or Gain of Function Characterizations Do Not Fully Capture Ion Channel Mutation Effects on Firing}
|
||||
The effects of changes in current properties depend in part on the neuronal model in which they occur and can be seen in the variance of correlations (especially in AUC of the fI-curve) across models for a given current property change. Therefore, relative conductances and gating properties of currents in the ionic current environment in which an alteration in current properties occurs plays an important role in determining the outcome on firing. The use of loss of function (LOF) and gain of function (GOF) is useful at the level of ion channels and whether a mutation results in more or less ionic current, however the extension of this thinking onto whether mutations induce LOF or GOF at the level of neuronal firing based on the ionic current LOF/GOF is problematic due to the dependency of neuronal firing changes on the ionic current environment. Thus the direct leap from current level LOF/GOF characterizations to effects on firing without experimental or modelling-based evidence, although tempting, should be refrained from and viewed with caution when reported. This is especially relevant in the recent development of personalized medicine for channelopathies, where a patients specific channelopathy is identified and used to tailor treatments \citep{Weber2017, Ackerman2013, Helbig2020, Gnecchi2021, Musto2020, Brunklaus2022}. However, the effects of specific ion channel mutations are often characterized in expression systems and classified as LOF or GOF to aid in treatment decisions \citep{johannesen_genotype-phenotype_2021, Brunklaus2022, Musto2020}. Interestingly, both LOF and GOF \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) 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 should be used with caution and the cell type which expressed the mutant ion channel may provide valuable insight into the functional consequences of an ion channel mutation. Where experimental assessment of the effects of a patient's specific ion channel mutation \textit{in vivo} is not feasible at a large scale, modelling approaches investigating the effects of patient specific channelopathies provides an alternative bridge between characterization of changes in biophysical properties of ionic currents and the firing consequences of these effects. In both experimental and modelling investigation of firing level effects of channelopathies cell-type dependency should be considered.
|
||||
|
||||
%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.
|
||||
|
||||
The effects of altered ion channel properties on firing is generally influenced by the other ionic currents in the cell. In channelopathies the effect of a given ion channel mutation on neuronal firing therefore depends on the cell type in which those changes occur \citep{Hedrich14874, makinson_scn1a_2016, Waxman2007, Rush2006}. Although certain complexities of neurons such as differences in cell-type sensitivities to current property changes, interactions between ionic currents, cell morphology and subcellular ion channel distribution are neglected here, it is likely that this increased complexity \textit{in vivo} would contribute to the cell-type dependent effects on neuronal firing. Cell-type dependent firing effects of channelopathies may underlie shortcomings in treatment approaches in patients with channelopathies and accounting for cell-type dependent firing effects may provide an opportunity to further the efficacy and precision in personalized medicine approaches.
|
||||
|
||||
|
||||
|
||||
%
|
||||
%\subsection*{Validity of Neuronal Models}
|
||||
%
|
||||
%\notejb{The following three paragraphs are rather technical and if possible should be shorter.}\\ \notenk{shortened single vs multicompartment model paragraphs. We could remove the \Kv paragraph I've shortened - see below}\\
|
||||
%Our findings are based on simulations of a range of single-compartment conductance-based models. 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. More realistic models are more computationally expensive, and require knowledge of the distribution of conductances across the cell. However, each of the single-compartment models used here 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.
|
||||
%%Many aspects of these models can be questioned.
|
||||
%\notels{in a few sentences in the methods}
|
||||
%
|
||||
%%\notenk{We could remove this paragraph about \Kv}
|
||||
%The \Kv model from \cite{ranjan_kinetic_2019} is based on expression of only \Kv in CHO cells and simplifies the complex reality of these channels \textit{in vivo} including their function as heteromers, and dynamic modulation and regulation \citep{wang__1999, roeper_nip_1998, coleman_subunit_1999, ruppersberg_heteromultimeric_1990, isacoff_evidence_1990, rettig_inactivation_1994, shi_efficacy_2016, campomanes_kv_2002, manganas_identification_2001, jonas_regulation_1996, stuhmer_molecular_1989, glasscock_kv11_2019, xu_kv2_1997, ranjan_kinetic_2019}.
|
||||
|
||||
|
||||
|
||||
|
||||
%\notejb{If this could be enriched with some citations than fine. Otherwise move this as a half sentence into methods/results} \notenk{moved steady-state firing characterization to methods}
|
||||
%The firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis. These could be seen as further dimensions to analyze the influence of mutations on neuronal firing and can only increase the uncertainty of these estimations.
|
||||
|
||||
%Despite all these shortcomings of the models we used in our simulations, they do not touch our main conclusion that the quantitative as well as qualitative effects of a given ionic current variant in general depend on the specific properties of all the other ionic currents expressed in a given cell.
|
||||
|
||||
%%\notenk{We could add a brief discussion somewhere in this section about time constants and why we neglect them despite likely being important in determining the outcome of a mutation.} \notejb{If we have citations for the time constant issue then yes, do it.}\\
|
||||
%%\notenk{I'm not sure I like the section I wrote here. I would tend towards leaving it out.}
|
||||
%%Although a number of methods have been used to fit ionic currents including different approaches in estimate time constants either from summary data or from full current traces, and are limited by the available data \citep{Clerx2019, Whittaker2020}. On one hand, specialized equipment and great experimental care is often required to estimate time constants \citep{Whittaker2020}. As a result summary data is often not recorded for voltage ranges in which time constants are fast. On the other hand, lack of availability of full current traces for each mutation limits the alternative current trace fitting approach.
|
||||
%%For these practical reasons, we neglect the effect of mutation altered time constants despite acknowledging that time constant changes are likely important in determining the outcome of a given mutation on firing.
|
||||
%%
|
||||
%%
|
||||
%%\notejb{Too technical, shorter! These aspects do not questions our result.} \notenk{Made a little shorter}
|
||||
%%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 current parameter space around the wild type neuron is explored here with a one-factor-at-a-time (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. \notels{methods: time constants are difficult to obtain (clerx et al 2019), therefore we ignore them}
|
||||
%%
|
||||
%% \notels{we measured OFAT, and it would only get more complicated, if we would look at interactions}
|
||||
%%
|
||||
%%\notejb{Too technical, shorter! These aspects do not questions our result.} \notenk{Tried to shorten, not sure about it...}
|
||||
%%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.
|
||||
%%Kendall \(\tau\) coefficients provide general information as to whether different models exhibit positive or negative correlation of AUC or rheobase to a change in a given current property, however more nuanced difference between the sensitivities of models to current property changes, such which models show faster/slower increases/decreases in firing properties in response to a given current property change are not included in our analysis. \notels{formulate more understandable}
|
||||
%% 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.
|
||||
|
||||
|
||||
\par\null
|
||||
|
||||
|
||||
|
||||
\selectlanguage{english}
|
||||
\newpage
|
||||
\FloatBarrier
|
||||
|
||||
Loading…
Reference in New Issue
Block a user