small changes and comments added

manuscript.tex

@@ -169,7 +169,7 @@ Ion channels determine neuronal excitability and mutations that alter ion channe
 Voltage-gated ion channels are vital in determining neuronal excitability, action potential generation and firing patterns \citep{bernard_channelopathies_2008, carbone_ion_2020}. In particular, the properties and combinations of ion channels and their resulting currents determine the firing properties of the neuron \citep{rutecki_neuronal_1992, pospischil_minimal_2008}. However, ion channel function can be disturbed, resulting in altered ionic current properties and altered neuronal firing behaviour \citep{carbone_ion_2020}. Ion channel mutations are a common cause of such channelopathies and are often associated with hereditary clinical disorders including ataxias, epilepsies, pain disorders, dyskinesias, intellectual disabilities, myotonias, and periodic paralyses among others  \citep{bernard_channelopathies_2008, carbone_ion_2020}.
 
 \notenk{Are there any obvious citations missing from the following section?}
-The effects of channelopathies on ionic current kinetics are frequently assessed by transfection of heterologous expression systems without endogenous currents  \citep{Balestrini1044, Noebels2017, Dunlop2008}, and are frequently classified as either a loss of function (LOF) or a gain of function (GOF) with respect to \textcolor{green}{changes in }the \textcolor{green}{amount of} ionic current \citep{Musto2020, Kullmann2002, Waxman2011}. \notenk{Do you think we need to discuss LOF and GOF more than this?} \notels{LOF and GOF are usually not explained in detail, I would think it's fine}  These classes can be used to make rough estimates of the effects on neuronal firing \textcolor{red}{(papers?)}, which is important for understanding the pathophysiology of these disorders and for identification of potential therapeutic targets \citep{Orsini2018, Yang2018}. Experimentally, the effects of channelopathies on neuronal firing can be assessed using primary neuronal cultures  \citep{Scalmani2006, Smith2018, Liu2019}  or \textit{in vitro} recordings from transgenic mouse lines \citep{Mantegazza2019, Xie2010,Lory2020, Habib2015,  Hedrich2019}.
+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 amount of ionic current \citep{Musto2020, Kullmann2002, Waxman2011}. \notenk{Do you think we need to discuss LOF and GOF more than this?} \notels{LOF and GOF are usually not explained in detail, I would think it's fine}  This classification can be used to make rough estimates of the effects on neuronal firing \textcolor{red}{(papers?)}, which in turn is important for understanding the pathophysiology of these disorders and for identification of potential therapeutic targets \citep{Orsini2018, Yang2018}. Experimentally, the effects of channelopathies on neuronal firing can be assessed using primary neuronal cultures  \citep{Scalmani2006, Smith2018, Liu2019}  or \textit{in vitro} recordings from transgenic mouse lines \citep{Mantegazza2019, Xie2010,Lory2020, Habib2015,  Hedrich2019}.
 
 
 %However the effect of a given channelopathy on different neuronal types across the brain is often unclear and not feasible to experimentally obtain. This is especially true when large numbers of distinct mutations are present and personalized medicine approaches are desired.
@@ -182,7 +182,7 @@ However the effect of a given channelopathy on different neuronal types across t
 % \textcolor{red}{In the simplest case, the influence on the firing behaviour should correlate with the expression level of the affected gene \textcolor{red}{(cite Niko , other Papers)}. But if a \textcolor{red}{ kinetic parameter} is changed too much, it can have unforseen consequences. }
   The expression level of an affected gene can correlate with firing behaviour in the simplest case \citep{Layer2021} \textcolor{red}{(cite other Papers?)} \notenk{Not sure if Lukas had some in mind}, however if a gating property is altered substantially this can have complex consequences.
 
-For instance, altering relative amplitudes of ionic currents can dramatically influence the firing behaviour and dynamics of neurons \citep{rutecki_neuronal_1992, pospischil_minimal_2008,Kispersky2012, golowasch_failure_2002, barreiro_-current_2012, Noebels2017, Layer2021}, however other properties of ionic currents impact neuronal firing as well. In extreme cases, a mutation can have opposite effects on different neuron types. For example, the R1629H SCN1A mutation is associated which increased firing in interneurons, but decreases pyramidal neuron excitability \citep{Hedrich14874,makinson_2016_scn1a}
+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}
 
 %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?)}.}
 
@@ -222,11 +222,11 @@ All modelling and simulation was done in parallel with custom written Python 3.8
     
 \subsection*{Different Cell Models}
     A group of neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal), regular spiking inhibitory (RS inhibitory), and fast spiking (FS) cells were used \citep{pospischil_minimal_2008}. To each of these models, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added. A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate). This model was also used with a \Kv current \citep{ranjan_kinetic_2019} in addition to the A-type potassium current (Cb stellate +\Kv) or replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv). A subthalamic nucleus neuron model as described by \citet{otsuka_conductance-based_2004} are used (STN) and with a \Kv current (\IKv; \citealp{ranjan_kinetic_2019}) in addition to the A-type potassium current (STN +\Kv) or replacing the A-type potassium current (STN \(\Delta\)\Kv). The properties and conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models. For comparability to typical electrophysiological data fitting reported and for ease of further gating curve manipulations, a Boltzmann function
-    \notels{is this still a Boltzmann function?}
+    \notels{is this still a Boltzmann function?}\notenk{I'm not sure, we could always say ``a Boltzmann function raise to a power''}
     \begin{equation}\label{eqn:Boltz}
          x_\infty = {\left(\frac{1-a}{1+{\exp\left[{\frac{V-V_{1/2}}{k}}\right]}} +a\right)^j} 
     \end{equation}
-with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted for the RS pyramidal, RS inhibitory and FS models \cite{pospischil_minimal_2008} \notels{this reference could be missleading, they didnt't fit these parameters and the model origin is cited above}.  The properties of \IKv  were fitted to the mean wild type biophysical parameters of \Kv \citep{lauxmann_therapeutic_2021}.
+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} \notels{this reference could be missleading, they didnt't fit these parameters and the model origin is cited above} \notenk{how about ``... 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}.
 
     
 \input{g_table}
@@ -247,7 +247,7 @@ with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}
     
 % Sensitivity analyses enable investigation into how different sources of uncertainty in a model result in uncertainty in model outputs \citep{saltelli_sensitivity_2002} and provide  information on the relative impact of model inputs \citep{saltelli_why_2019}. We recently used a one-factor-at-a-time (OFAT) sensitivity analysis approach to evaluate the relative impacts of currents on neuronal firing and developed a scoring system for SCN8A mutations that correlated (p = 0.0077, r = 0.64) with the clinical severity of epilepsy in patients with these mutations \citep{johannesen_genotype-phenotype_2021}. This was done in an isolated neuronal model and suggests that even with disregard of network level effects of mutations, the single cell level outcomes of mutations are relevant to disease phenotypes. OFAT sensitivity analyses indicate which factors have or do not have influence, with uninfluential factors never detected as relevant \citep{saltelli_how_2010}. OFAT sensitivity analyses can be used to screen factors that are influential on model outcomes and provide a mechanism by which factors and their relative influence can be easily identified and used in predictive applications. 
     
-    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 slope (\(k\)) of the gating curves were altered from half to twice the initial slope. Similarly, the maximal current conductance (\(g\)) was also scaled from half to twice the initial value. For both slope and conductance alterations, alterations consisted of 21 steps spaced equally on a \(\textrm{log}_2\) scale.
+    Properties of ionic currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{\textrm{Leak}}\)) 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.
     
     \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 (\(AUC_{wt}\))
@@ -341,6 +341,7 @@ Using a set of diverse conductance-based neuronal models, the effects of changes
 
 \subsection*{Validity of Neuronal Models}
 \notels{should we move this to a less prominent position? How much of this part could be counted as common knowledge and be left out?, for example model complexity in terms of currents and compartments, I just think that this part might be too harsh on the models, even if the criticism doesn't apply for the main points of the paper}
+\notenk{I think a large part of this section, although hgihlighting the problems with the models, helps make the case that there is a vast amount of complexity and heterogeneity not just in what we show with the models, but also unaccounted for by the models. That is to say that we are in a sense underestimating the amount of variability in responses of different cells to the same mutation. Perhaps it would be good to change this section to emphasize that perspective?}
 
 Our findings are based on simulations of a range of single-compartment conductance-based models. Many aspects of these models can be questioned.
 
@@ -353,6 +354,7 @@ The firing characterization was performed on steady-state firing and as such ada
 Despite all these shortcomings of the models we used in our simulations, they do not touch our main conclusion that the quantitative as well as qualitative effects of a given ionic current variant in general depend on the specific properties of all the other ionic currents expressed in a given cell.
     
 \subsection*{Ionic Current Environments Determine the Effect of Ion Channel Mutations}
+\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.}
 One-factor-at-a-time (OFAT) sensitivity analyses such as the one performed here are predicated on assumptions of model linearity, and cannot account for interactions between factors \citep{czitrom_one-factor-at--time_1999, saltelli_how_2010}. OFAT approaches are local and not global (i.e. always in reference to a baseline point in the parameter space) and therefore cannot be generalized to the global parameter space unless linearity is met \citep{saltelli_how_2010}. The local space around the wild type neuron is explored with an OFAT sensitivity analysis without taking interactions between parameters into account. Comparisons between the effects of changes in similar parameters across different models can be made at the wild type locale indicative of experimentally observed neuronal behaviour. In this case, the role of deviations in the ionic current properties from their wild type in multiple neuronal models presented here provides a starting point for understanding the general role of these current properties in neurons. However, a more global approach would provide a more holistic understanding of the parameter space and provide insight into interactions between properties.
 
 Characterization of the effects of a parameter on firing with non-parametric Kendall \(\tau\) correlations takes into account the sign and monotonicity of the correlation. In other words Kendall \(\tau\) coefficients provide information as to whether changing a parameter is positively or negatively correlated with AUC or rheobase as well as the extent to which this correlation is positive or negative across the parameter range examined. Therefore, Kendall \(\tau\) coefficients provide general information as to the sensitivity of different models to a change in a given current property, however more nuanced difference between the sensitivities of models to current property changes, such as the slope of the relationship between parameter change and firing are not included in our analysis. 

ref.bib

@@ -1620,18 +1620,6 @@ SIGNIFICANCE: Bromide is most effective and is a well-tolerated drug among DS pa
 }
 
 
-%@article{makinson2016scn1a,
-%  title={An Scn1a epilepsy mutation in Scn8a alters seizure susceptibility and behavior},
-%  author={Makinson, Christopher D and Dutt, Karoni and Lin, Frank and Papale, Ligia A and Shankar, Anupama and Barela, Arthur J and Liu, Robert and Goldin, Alan L and Escayg, Andrew},
-%  journal={Experimental neurology},
-%  volume={275},
-%  pages={46--58},
-%  year={2016},
-%  publisher={Elsevier},
-%  language = {en},
-%  url={https://doi.org/10.1016/j.expneurol.2015.09.008},
-%  doi={10.1016/j.expneurol.2015.09.008}
-%}
 
  
 @Article{Waxman2011,