Added more context and transitions to the results section

manuscript.tex

@@ -113,7 +113,7 @@ Neuronal ion channels are vital in determining neuronal excitability, action pot
 
 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. 
    
-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.
+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.
 
 \Kv channels, encoded by the KCNA1 gene, play a role in repolarizing the action potential, neuronal firing patterns, neurotransmitter release, and saltatory conduction \citep{dadamo_episodic_1998} and are expressed throughout the CNS  \citep{tsaur_differential_1992, wang_localization_1994, veh_immunohistochemical_1995}.   
 Altered \Kv channel function as a result of KCNA1 mutations in humans is associated with episodic ataxia type 1 (EA1) which is characterized by period attacks of ataxia and persistent myokymia \citep{parker_periodic_1946, van_dyke_hereditary_1975}. 
@@ -201,7 +201,7 @@ Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occup
 \end{figure}
 
 
-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.
+Neuronal firing is a complex phenomenon and classification of firing is required for comparisons of firing across cell types and between conditions. Here we focus on the classification of two aspects of firing: rheobase (smallest injected current at which the cell fires an action potential) and the initial shape of the frequency-current (fI) curve. The quantification of the inital shape of the fI curve using by computing the area under the curve (AUC) is a measure of the initial firing at currents above rheobase (\Cref{fig:firing_characterizaton}A). The characterization of firing with AUC and rheobase enables determination of general increases or decreases in firing based on current-firing relationships, with the upper left quadrant (+\(\Delta\)AUC and -\(\Delta\)rheobase) indicate an increase in firing, whereas the bottom right quadrant (-\(\Delta\)AUC and +\(\Delta\)rheobase) is indicative of decreased firing (\Cref{fig:firing_characterizaton}B). In the lower left and upper right quadrants, the effects on firing are more nuance and cannot easily be described as a gain or loss of excitability.
 
 \begin{figure}[ht!]
         \centering
@@ -212,10 +212,10 @@ Neuronal firing is a complex phenomenon and classification of firing is needed f
 \end{figure}
 
 
-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}).
+Neuronal firing is heterogenous across the CNS and a set of neuronal models with heterogenous firing due to different ion currents is desirable to reflect this heterogeneity. The set of neuronal models used here has considerable diversity as evident in the variability seen across neuronal models both in representative spike trains and their fI curves (\Cref{fig:diversity_in_firing}). The models chosen all fire repetitively and do not exhibit bursting. Some models, such as Cb stellate and RS inhibitory models, display type I firing whereas others such as Cb stellate \(\Delta\)\Kvnospace and STN models have type II firing. Type I firing is characterized by continuous fI curve (i.e. firing rate is continuous) generated through a saddle-node on invariant cycle bifurcation and type II firing is characterized by a discontinuity in the fI curve (i.e. a jump occurs from no firing to firing at a certain frequency) due to a Hopf bifurcation \cite{ERMENTROUT2002, ermentrout_type_1996}. Other models lie on a continuum between these prototypical firing classifications. Most neuronal models exhibit hysteresis with ascending and descending ramps eliciting spikes with different thresholds, however STN +\Kv, STN \(\Delta\)\Kv, Cb stellate \(\Delta\)\Kv have large hysteresis (\Cref{fig:diversity_in_firing}).
 
 \subsection*{Sensitivity analysis}
-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.
+Sensitivity analyses are used to understand how input model parameters contribute to the output of a model \citep{Saltelli2002}. In other words, sensitivity analyses are used to understand how sensitive the output of a model is to a change in input or model parameters. One-factor-a-time sensitivity analysis involve altering one parameter at a time and enable the comparison of a given alteration in current parameters across models. Changes in gating \(V_{1/2}\) and slope factor k as well as the current conductance affect AUC (\Cref{fig:AUC_correlation} A, B and C). Heterogeneity in the correlation between gating and conductance changes and AUC occurs across models for most currents. In these cases some of the models display non-monotonic relationships (i.e. \( |\)Kendall \(\tau | \neq\) ). However, shifts in A current activation \(V_{1/2}\), changes in \Kv activation \(V_{1/2}\) and slope, and changes in A current conductance display consistent monotonic relationships across models.
 
 
 \begin{figure}[ht!]
@@ -226,9 +226,6 @@ A one-factor-a-time sensitivity analysis enables the comparison of a given alter
         \label{fig:AUC_correlation}
 \end{figure}
 
-
-
-
 Alterations in gating \(V_{1/2}\) and slope factor k as well as the current conductance also play a role in determining rheobase (\Cref{fig:rheobase_correlation} A, B and C).  Shifts in half activation of gating properties are similarly correlated with rheobase across models, however Kendall \(\tau\) values departing from -1 indicate non-monotonic relationships between K current \(V_{1/2}\) and rheobase in some models (\Cref{fig:rheobase_correlation}A). Changes in Na current inactivation, \Kv current inactivation and A current activation have affect rheobase with positive and negative correlations in different models (\Cref{fig:rheobase_correlation}B). Departures from monotonic relationships occur in some models as a result of K current activation, \Kv current inactivation and A current activation in some models. Current conductance magnitude alterations affect rheobase similarly across models (\Cref{fig:rheobase_correlation}C).
 
 \begin{figure}[ht!]
@@ -240,7 +237,7 @@ Alterations in gating \(V_{1/2}\) and slope factor k as well as the current cond
 \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 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).
+Mutations in \Kv are associated with episodic ataxia type 1 (EA1) have been characterized biophysically and are used here as a case study in the effects of current environment on the outcomes of channelopathies on firing. The changes in AUC and rheobase from wild-type values for reported EA1 associated \Kv mutations are heterogenous across models containing \Kv, but generally show decreases in rheobase (\Cref{fig:simulation_model_comparision}A-I).  Pairwise non-parametric Kendall \(\tau\) rank correlations between the simulated effects of these \Kv mutations on rheobase are highly correlated across models (\Cref{fig:simulation_model_comparision}J). However, the effects of the \Kv mutations on AUC are more heterogenous as reflected by both weak and strong positive and negative pairwise correlations between models (\Cref{fig:simulation_model_comparision}K).
 \begin{figure}[ht!]
         \centering
         \includegraphics[width=\linewidth]{Figures/simulation_model_comparison.pdf}

ref.bib

@@ -1,3 +1,5 @@
+
+
 @Article{chi_manipulation_2007,
   author   = {Chi, Xian Xuan and Nicol, G. D.},
   title    = {Manipulation of the {Potassium} {Channel} {Kv1}.1 and {Its} {Effect} on {Neuronal} {Excitability} in {Rat} {Sensory} {Neurons}},
@@ -1298,3 +1300,24 @@ SIGNIFICANCE: Bromide is most effective and is a well-tolerated drug among DS pa
   month     = nov,
   year      = {2001},
 }
+
+ 
+@Article{Saltelli2002,
+  author   = {Saltelli, Andrea},
+  journal  = {Risk Analysis},
+  title    = {Sensitivity {Analysis} for {Importance} {Assessment}},
+  year     = {2002},
+  issn     = {1539-6924},
+  number   = {3},
+  pages    = {579--590},
+  volume   = {22},
+  abstract = {We review briefly some examples that would support an extended role for quantitative sensitivity analysis in the context of model-based analysis (Section 1). We then review what features a quantitative sensitivity analysis needs to have to play such a role (Section 2). The methods that meet these requirements are described in Section 3; an example is provided in Section 4. Some pointers to further research are set out in Section 5.},
+  doi      = {10.1111/0272-4332.00040},
+  file     = {Full Text PDF:https\://onlinelibrary.wiley.com/doi/pdfdirect/10.1111/0272-4332.00040:application/pdf},
+  keywords = {Uncertainty analysis, quantitative sensitivity analysis, computational models, assessment of importance, risk analysis},
+  language = {en},
+  url      = {https://onlinelibrary.wiley.com/doi/abs/10.1111/0272-4332.00040},
+  urldate  = {2022-04-12},
+}
+
+@Comment{jabref-meta: databaseType:bibtex;}