emphasize more ionic current composition

Frontiers_manuscript/For_Submission/Koch_frontiers_revised.tex

@@ -61,15 +61,11 @@ $^{3}$Department of Neurology and Epileptology, Hertie Institute for Clinical Br
 
 
 \begin{abstract}
-\section{}
-Clinically relevant mutations to voltage-gated  ion channels, called channelopathies, alter ion channel function, properties of ionic currents and neuronal firing.  The effects of ion channel mutations are routinely assessed and characterized as loss of function (LOF) or gain of function (GOF) at the level of ionic currents. However, emerging personalized medicine approaches based on LOF/GOF characterization have limited therapeutic success. Potential reasons are among others that the translation from this binary characterization to neuronal firing is currently not well understood ---  especially when considering different neuronal cell types. Here we investigate the impact of neuronal cell type on the firing outcome of ion channel mutations with simulations of a diverse collection of conductance-based neuron models. We systematically analyzed the effects of changes in ion current properties on firing in different neuronal types.  Additionally, we simulated the effects of known mutations in the \textit{KCNA1} gene encoding the \Kv potassium channel subtype associated with episodic ataxia type~1 (EA1). These simulations revealed that the outcome of a given change in ion channel properties on neuronal excitability depends on neuron type, i.e. the properties and expression levels of the unaffected ionic currents. Consequently, neuron-type specific effects are vital to a full understanding of the effects of channelopathies on neuronal excitability and are an important step towards improving the efficacy and precision of personalized medicine approaches.
+\noindent Clinically relevant mutations to voltage-gated  ion channels, called channelopathies, alter ion channel function, properties of ionic currents and neuronal firing.  The effects of ion channel mutations are routinely assessed and characterized as loss of function (LOF) or gain of function (GOF) at the level of ionic currents. However, emerging personalized medicine approaches based on LOF/GOF characterization have limited therapeutic success. Potential reasons are among others that the translation from this binary characterization to neuronal firing is currently not well understood ---  especially when considering different neuronal cell types. Here we investigate the impact of neuronal cell type on the firing outcome of ion channel mutations. To this end we simulated a diverse collection of single-compartment, conductance-based neuron models that differed in their composition of ionic currents. We systematically analyzed the effects of changes in ion current properties on firing in different neuronal types.  Additionally, we simulated the effects of known mutations in the \textit{KCNA1} gene encoding the \Kv potassium channel subtype associated with episodic ataxia type~1 (EA1). These simulations revealed that the outcome of a given change in ion channel properties on neuronal excitability depends on neuron type, i.e. the properties and expression levels of the unaffected ionic currents. Consequently, neuron-type specific effects are vital to a full understanding of the effects of channelopathies on neuronal excitability and are an important step towards improving the efficacy and precision of personalized medicine approaches.
 
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-\tiny
  \keyFont{ \section{Keywords:} Channelopathy, Epilepsy, Ataxia, Potassium Current, Neuronal Simulations, Conductance-based Models, Neuronal heterogeneity } 
 \end{abstract}
+
 \section{Introduction}
 The properties and combinations of voltage-gated ion channels are vital in determining neuronal excitability \citep{bernard_channelopathies_2008, carbone_ion_2020, rutecki_neuronal_1992, pospischil_minimal_2008}. However, ion channel function can be disturbed, for instance through genetic alterations, resulting in altered neuronal firing behavior \citep{carbone_ion_2020}. In recent years, next generation sequencing has led to an increase in the discovery of clinically relevant ion channel mutations and has provided the basis for pathophysiological studies of genetic epilepsies, pain disorders, dyskinesias, intellectual disabilities, myotonias, and periodic paralyses \citep{bernard_channelopathies_2008, carbone_ion_2020}.
 Ongoing efforts of many research groups have contributed to the current understanding of underlying disease mechanism in channelopathies. However, a complex pathophysiological landscape has emerged for many channelopathies and is likely a reason for limited therapeutic success with standard care.              
@@ -80,18 +76,16 @@ Neuron-type specificity is likely vital for successful precision medicine treatm
 
 Taken together, these examples demonstrate the need to study the effects of ion channel mutations in many different neuron types --- a daunting if not impossible experimental challenge. In the context of this diversity, simulations of conductance-based neuronal models are a powerful tool bridging the gap between altered ionic currents and firing in a systematic and efficient way. Furthermore, simulations allow to predict the potential effects of drugs needed to alleviate the pathophysiology of the respective mutation \citep{johannesen_genotype-phenotype_2021, lauxmann_therapeutic_2021, Bayraktar}. 
 
-In this study, we therefore investigated how the outcome of ionic current kinetic changes on firing depend on neuronal cell type by (1) characterizing firing responses with two measures, (2) simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as (3) to more complex changes in this case as they were observed for specific \textit{KCNA1} mutations that are associated with episodic ataxia type~1 \citep{Browne1994, Browne1995, lauxmann_therapeutic_2021}.
+In this study, we therefore investigated how the outcome of ionic current kinetic changes on firing depend on neuronal cell type, i.e. on the composition of ionic currents, by (1) characterizing firing responses with two measures, (2) simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as (3) to more complex changes in this case as they were observed for specific \textit{KCNA1} mutations that are associated with episodic ataxia type~1 \citep{Browne1994, Browne1995, lauxmann_therapeutic_2021}.
 
 \section{Material and Methods}
 All modelling and simulation was done in parallel with custom written Python 3.8  (Python Programming Language; RRID:SCR\_008394) software, run on a Cent-OS 7 server with an Intel(R) Xeon (R) E5-2630 v2 CPU.
     
 \subsection{Different Neuron Models}
-A group of neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal; model D), regular spiking inhibitory (RS inhibitory; model B), and fast spiking (FS; model C) neurons 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; model H, RS inhibitory +\Kv; model E, and FS +\Kv; model G respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate; model A) in this study. This neuron model was also extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (Cb stellate +\Kv; model F) or by replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv; model J). A subthalamic nucleus (STN; model L) neuron model as described by \citet{otsuka_conductance-based_2004} was also used. The STN neuron model (model L) was  additionally extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (STN +\Kv; model I) or by replacing the A-type potassium current (STN \(\Delta\)\Kv; model K). Model letter naming corresponds to panel lettering in Figure \ref{fig:diversity_in_firing}. The anatomical origin of each model is shown in Figure \ref{fig:diversity_in_firing}~M. The properties and maximal conductances of each model are detailed in Table \ref{tab:g} and depicted in Figure \ref{fig:model_g}. The gating properties are unaltered from the original Cb stellate (model A)  and STN (model L) models \citep{alexander_cerebellar_2019, otsuka_conductance-based_2004}. For enabling the comparison of models with the typically reported electrophysiological data fitting reported and for ease of further gating curve manipulations, a modified Boltzmann function
-
+A set of single-compartment, conductance-based neuronal models representing the major classes of cortical and thalamic neurons including regular spiking pyramidal (RS pyramidal; model D), regular spiking inhibitory (RS inhibitory; model B), and fast spiking (FS; model C) neurons 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; model H, RS inhibitory +\Kv; model E, and FS +\Kv; model G respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate; model A) in this study. This neuron model was also extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (Cb stellate +\Kv; model F) or by replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv; model J). A subthalamic nucleus (STN; model L) neuron model as described by \citet{otsuka_conductance-based_2004} was also used. The STN neuron model (model L) was  additionally extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (STN +\Kv; model I) or by replacing the A-type potassium current (STN \(\Delta\)\Kv; model K). Model letter naming corresponds to panel lettering in Figure \ref{fig:diversity_in_firing}. The anatomical origin of each model is shown in Figure \ref{fig:diversity_in_firing}~M. The properties and maximal conductances of each model are detailed in Table \ref{tab:g} and depicted in Figure \ref{fig:model_g}. The gating properties are unaltered from the original Cb stellate (model A)  and STN (model L) models \citep{alexander_cerebellar_2019, otsuka_conductance-based_2004}. For enabling the comparison of models with the typically reported electrophysiological data fitting reported and for ease of further gating curve manipulations, a modified Boltzmann function
 \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 to the original formulism for RS pyramidal (model D), RS inhibitory (model B) and FS (model C) models from \citet{pospischil_minimal_2008}. The properties of \IKv  were fitted to the mean wild type biophysical parameters of \Kv described in \citet{lauxmann_therapeutic_2021}. The fitted gating parameters are detailed in Table \ref{tab:gating}. Each of the original single-compartment models used here can reproduce physiological firing behavior of the neurons they represent (Figure \ref{fig:diversity_in_firing}; \citealt{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004}) and capture key aspects of the dynamics of these neuron types. 
     
 \subsection{Firing Frequency Analysis} 
@@ -132,7 +126,7 @@ To examine the role of neuron-type specific ionic current environments on the im
 (1) firing responses were characterized with rheobase and \(\Delta\)AUC, (2) a set of neuronal models was used and properties of channels common across models were altered systematically one at a time, and (3) the effects of a set of episodic ataxia type~1 associated \textit{KCNA1} mutations on firing was then examined across different neuronal models with different ionic current environments.
 
 \subsection{Variety of model neurons}
-Neuronal firing is heterogeneous across the CNS and a set of neuronal models with heterogeneous firing due to different ionic currents is desirable to reflect this heterogeneity. The set of single-compartment, conductance-based neuronal models used here has considerable diversity as evident in the variability seen across neuronal models both in spike trains and their fI curves (Figure \ref{fig:diversity_in_firing}). The models chosen for this study all fire tonically and do not exhibit bursting (see methods for details and naming of the models). Models are qualitatively sorted based on their firing curves and labeled model A through L accordingly. Model B ceases firing with large current steps (Figure \ref{fig:diversity_in_firing}~B) indicating depolarization block. Some models, such as models A and B, display type I firing, whereas others such as models J and L exhibit type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) whereas 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; \citealt{ermentrout_type_1996, Rinzel_1998}). The other models used here lie on a continuum between these prototypical firing classifications. Most neuronal models exhibit hysteresis with ascending and descending ramps eliciting spikes at different current thresholds. However, the models  I, J, and K have large hysteresis (Figure \ref{fig:diversity_in_firing} and Supplementary Figure S1). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}. This broad range of single-compartmental models represents the distinct dynamics of various neuron types across diverse brain regions.
+Neuronal firing is heterogeneous across the CNS and a set of neuronal models with heterogeneous firing due to different ionic currents is desirable to reflect this heterogeneity. The set of single-compartment, conductance-based neuronal models used here has considerable diversity as evident in the variability seen across neuronal models both in spike trains and their fI curves (Figure \ref{fig:diversity_in_firing}). The models chosen for this study all fire tonically and do not exhibit bursting (see methods for details and naming of the models). Models are qualitatively sorted based on their firing curves and labeled model A through L accordingly. Model B ceases firing with large current steps (Figure \ref{fig:diversity_in_firing}~B) indicating depolarization block. Some models, such as models A and B, display type I firing, whereas others such as models J and L exhibit type II firing. Type I firing is characterized by continuous fI curves (i.e. firing rate increases from 0 in a continuous fashion) whereas 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; \citealt{ermentrout_type_1996, Rinzel_1998}). The other models used here lie on a continuum between these prototypical firing classifications. Most neuronal models exhibit hysteresis with ascending and descending ramps eliciting spikes at different current thresholds. However, the models  I, J, and K have large hysteresis (Figure \ref{fig:diversity_in_firing} and Supplementary Figure S1). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}. This broad range of single-compartmental models represents the distinct dynamics of various neuron types across diverse brain regions, but does not take into account differences in morphology or synaptic input.
 
 \subsection{Characterization of Neuronal Firing Properties}
 Neuronal firing is a complex phenomenon, and a quantification of firing properties is required for comparisons across neuron types and between different conditions. Here we focus on two aspects of firing that are routinely measured in clinical settings \citep{Bryson_2020}: rheobase, the smallest injected current at which the neuron 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 (Figure \ref{fig:firing_characterization}~A). The characterization of the firing properties of a neuron by using 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.
@@ -159,13 +153,15 @@ Mutations in \textit{KCNA1} are associated with episodic ataxia type~1 (EA1) and
 
 \section{Discussion}
 
-To compare the effects of ion channel mutations on neuronal firing of different neuron types, we used a diverse set of conductance-based models to systematically characterize the effects of changes in individual channel properties. Additionally, we simulated the effects of specific episodic ataxia type~1 associated (EA1) \textit{KCNA1} mutations. Changes to single ionic current properties, as well as known EA1 associated \textit{KCNA1} mutations showed consistent effects on the rheobase across neuron types, whereas the effects on the slope of the steady-state fI-curve depended on the neuron type. Our results demonstrate that loss of function (LOF) and gain of function (GOF) on the biophysical level cannot be uniquely transferred to the level of neuronal firing. Thus, the effects caused by different mutations depend on the properties of the other ion channels expressed in a neuron and are therefore depend on the channel ensemble of a specific neuron type. 
+To compare the effects of ion channel mutations on neuronal firing of different neuron types, we used a diverse set of conductance-based models, that differ in their composition of ionic currents, to systematically characterize the effects of changes in individual channel properties. Additionally, we simulated the effects of specific episodic ataxia type~1 associated (EA1) \textit{KCNA1} mutations. Changes to single ionic current properties, as well as known EA1 associated \textit{KCNA1} mutations showed consistent effects on the rheobase across neuron types, whereas the effects on the slope of the steady-state fI-curve depended on the neuron type. Our results demonstrate that loss of function (LOF) and gain of function (GOF) on the biophysical level cannot be uniquely transferred to the level of neuronal firing. Thus, the effects caused by different mutations depend on the properties of the other ion channels expressed in a neuron and are therefore depend on the channel ensemble of a specific neuron type. 
 
 \subsection{Firing Frequency Analysis}
-Although differences in neuronal firing can be characterized by an area under the curve of the fI curve for a fixed current range, this approach characterizes firing as a mixture of key features: rheobase and the initial slope of the fI curve. By probing rheobase directly and using an AUC relative to rheobase, we disambiguate these features and enable insights into the effects on rheobase and initial fI curve steepness. This increases the specificity of our understanding of how ion channel mutations alter firing across neuron types and enable classification as described in Figure \ref{fig:firing_characterization}. Importantly, in cases when ion channel mutations alter rheobase and initial fI curve steepness in ways that oppose effects on firing (upper left and bottom right quadrants of Figure \ref{fig:firing_characterization}~B), this disambiguation is important for understanding the outcome of the mutation. In these cases, the regime the neuron is operating in is vital in determining the neuron's firing outcome. If it is in its excitable regime and only occasionally generates an action potential, then the effect on the rheobase is more important. If it is firing periodically with high rates, then the change in AUC might be more relevant. 
+Although differences in neuronal firing can be characterized by an area under the curve of the fI curve for a fixed current range, this approach characterizes firing as a mixture of two key features: rheobase and the initial slope of the fI curve. By probing rheobase directly and using an AUC relative to rheobase, we disambiguate these features and enable insights into the effects on rheobase and initial fI curve steepness. This increases the specificity of our understanding of how ion channel mutations alter firing across neuron types and enable classification as described in Figure \ref{fig:firing_characterization}. Importantly, in cases when ion channel mutations alter rheobase and initial fI curve steepness in ways that oppose effects on firing (upper left and bottom right quadrants of Figure \ref{fig:firing_characterization}~B), this disambiguation is important for understanding the outcome of the mutation. In these cases, the regime the neuron is operating in is vital in determining the neuron's firing outcome. If it is in its excitable regime and only occasionally generates an action potential, then the effect on the rheobase is more important. If it is firing periodically with high rates, then the change in AUC might be more relevant. 
 
 \subsection{Modelling Limitations}
-The models used here are simple and they all capture key aspects of the firing dynamics for their respective neuron. The simple models fall short of capturing the complex physiology, biophysics and heterogeneity of real neurons, nor do they take into account subunit stoichiometry, auxillary subunits, membrane composition which influence the biophysics of ionic currents \citep{Al-Sabi_2013, Oliver_2004, Pongs_2009, Rettig1994}. However, for the purpose of understanding how different neuron-types, or current environments, contribute to the diversity in firing outcomes of ion channel mutations, the fidelity of the models to the physiological neurons they represent is of a minor concern. For exploring possible neuron-type specific effects, variety in currents and dynamics across models is of utmost importance. With this context in mind, the collection of models used here are labelled as models A-L to highlight that the physiological neurons they represent is not of chief concern, but rather that the collection of models with different attributes respond heterogeneously to the same perturbation. Additionally, the development of more realistic models is a high priority and will enable neuron-type specific predictions that may aid precision medicine approaches. Thus, weight should not be put on any single predicted firing outcome here in a specific model, but rather on the differences in outcomes that occur across the neuron-type spectrum the models used here represent. Further investigation and analysis of the neuron-type effects of ion channel mutations including with animal experiments is essential for validation of the results presented here and for furthering the understanding of the effects of channelopathies at multiple levels of scale.
+The single-compartment models used here all capture key aspects of the firing dynamics for their respective neuron. The models fall short of capturing the morphology, complex physiology, biophysics and heterogeneity of real neurons, nor do they take into account subunit stoichiometry, auxillary subunits, or membrane composition which influence the biophysics of ionic currents \citep{Al-Sabi_2013, Oliver_2004, Pongs_2009, Rettig1994}. However, these simplified models allow to study the effect of different compositions of ionic currents on the diversity in firing outcomes of ion channel mutations in isolation.
+
+Our results demonstrate that for exploring possible neuron-type specific effects, variety in currents and dynamics across models is of utmost importance. With this context in mind, the collection of models used here are labelled as models A-L to highlight that the physiological neurons they represent is not of chief concern, but rather that the collection of models with different attributes respond heterogeneously to the same perturbation. Additionally, the development of more realistic models is a high priority and will enable neuron-type specific predictions that may aid precision medicine approaches. Thus, weight should not be put on any single predicted firing outcome here in a specific model, but rather on the differences in outcomes that occur across the neuron-type spectrum the models used here represent. Further investigation and analysis of the neuron-type effects of ion channel mutations including with animal experiments is essential for validation of the results presented here and for furthering the understanding of the effects of channelopathies at multiple levels of scale.
 
 \subsection{Neuronal Diversity}
 The nervous system consists of a vastly diverse and heterogeneous collection of neurons with variable properties and characteristics including diverse combinations and expression levels of ion channels which are vital for neuronal firing dynamics.
@@ -208,7 +204,7 @@ With this study we suggest that neuron-type specific effects are vital to a full
         \centering
         \includegraphics[width=\linewidth]{diversity_in_firing_diagram.jpg}
         \linespread{1.}\selectfont
-        \caption[]{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) for Cb stellate  \textbf{(A)}, RS inhibitory  \textbf{(B)}, FS \textbf{(C)}, RS pyramidal  \textbf{(D)}, RS inhibitory +\Kv  \textbf{(E)}, Cb stellate +\Kv  \textbf{(F)}, FS +\Kv  \textbf{(G)}, RS pyramidal +\Kv  \textbf{(H)}, STN +\Kv  \textbf{(I)}, Cb stellate \(\Delta\)\Kv  \textbf{(J)}, STN \(\Delta\)\Kv  \textbf{(K)}, and STN  \textbf{(L)} neuron models. Models are sorted qualitatively based on their fI curves. Black markers on the fI curves indicate the current step at which the spike train occurs. The green marker indicates the current at which firing begins in response to an ascending current ramp, whereas the red marker indicates the current at which firing ceases in response to a descending current ramp (see Supplementary Figure S1). A schematic illustrating the anatomical locations of the models is included \textbf{(M)}, however single compartment models are used for each cell type.} 
+        \caption[]{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) for Cb stellate  \textbf{(A)}, RS inhibitory  \textbf{(B)}, FS \textbf{(C)}, RS pyramidal  \textbf{(D)}, RS inhibitory +\Kv  \textbf{(E)}, Cb stellate +\Kv  \textbf{(F)}, FS +\Kv  \textbf{(G)}, RS pyramidal +\Kv  \textbf{(H)}, STN +\Kv  \textbf{(I)}, Cb stellate \(\Delta\)\Kv  \textbf{(J)}, STN \(\Delta\)\Kv  \textbf{(K)}, and STN  \textbf{(L)} neuron models. Models are sorted qualitatively based on their fI curves. Black markers on the fI curves indicate the current step at which the spike train occurs. The green marker indicates the current at which firing begins in response to an ascending current ramp, whereas the red marker indicates the current at which firing ceases in response to a descending current ramp (see Supplementary Figure S1). A schematic illustrating the anatomical locations of the models is included \textbf{(M)}, however single-compartment models are used for each cell type.} 
         \label{fig:diversity_in_firing}
 \end{figure}