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manuscript.tex
@ -160,7 +160,7 @@ Nils A. Koch\textsuperscript{1,2}, Lukas Sonnenberg\textsuperscript{1,2}, Ulrike
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\section*{Abstract (250 Words Maximum - Currently )}
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%\textit{It should provide a concise summary of the objectives, methodology (including the species and sex studied), key results, and major conclusions of the study.}
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Ion channels determine neuronal excitability and disruption in ion channel properties caused by mutations can result in neurological disorders called channelopathies. Often, mutations within one gene are associated with a specific channelepothy and the effects of these mutations on channel function, i.e. the gating current of the affected ion channel, are generally determined using heterologous expression systems. Nevertheless, the impact of such mutations on neuronal firing is essential not only for determining brain function, but also for selecting personalized treatment options for the affected patient. The effect of ion channel mutations on firing in different cell types has been mostly neglect and it is unclear whether the effect of a given mutation on firing can simply be inferred from the effects identified at the current level. Here we use a diverse collection of computational neuronal models to determine that ion channel mutation effects at the current level cannot be indiscriminantly used to infer firing effects without consideration of cell-type. In particular, systematic simulation and evaluation of the effects of changes in ion current properties on firing properties in different neuronal types as well as for mutations in the \textit{KCNA1} gene encoding the \Kv potassium channel subtype associated with episodic ataxia type~1 (EA1) was performed. The effects of changes in ion current properties generally and due to mutations in the \Kv channel subtype on the firing of a neuron depends on the ionic current environment, or the neuronal cell type, in which such a change occurs in. Thus, while characterization of ion channel mutations as loss or gain of function is useful at the level of the ionic current, this characterization should not be extended to the level of neuronal excitability as the effects of ion channel mutations on the firing of a cell is dependent on the cell type and the composition of different ion channels and subunits therein. To further the efficacy of personalized medicine in channelopathies, the effects of ion channel mutations must be examined in the context of the appropriate cell types in which these mutations occur.
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Ion channels determine neuronal excitability and disruption in ion channel properties caused by mutations can result in neurological disorders called channelopathies. Often, mutations within one gene are associated with a specific channelepothy and the effects of these mutations on channel function, i.e. the gating current of the affected ion channel, are generally determined using heterologous expression systems. Nevertheless, the impact of such mutations on neuronal firing is essential not only for determining brain function, but also for selecting personalized treatment options for the affected patient. The effect of ion channel mutations on firing in different cell types has been mostly neglect and it is unclear whether the effect of a given mutation on firing can simply be inferred from the effects identified at the current level. Here we use a diverse collection of computational neuronal models to determine that ion channel mutation effects at the current level cannot be indiscriminantly used to infer firing effects without consideration of cell-type. In particular, systematic simulation and evaluation of the effects of changes in ion current properties on firing properties in different neuronal types as well as for mutations in the \textit{KCNA1} gene encoding the \Kv potassium channel subtype associated with episodic ataxia type~1 (EA1) was performed. The effects of changes in ion current properties generally and due to mutations in the \Kv channel subtype on the firing of a neuron depends on the ionic current environment, or the neuronal cell type, in which such a change occurs in. Thus, while characterization of ion channel mutations as loss or gain of function is useful at the level of the ionic current, this characterization should not be extended to the level of neuronal excitability as the effects of ion channel mutations on the firing of a cell is dependent on the cell type and the composition of different ion channels and subunits therein. For increased efficiency and efficacy of personalized medicine approaches in channelopathies, the effects of ion channel mutations must be examined in the context of the appropriate cell types in which these mutations occur.
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%Using a diverse collection of computational neuronal models, the effects of changes in ion current properties on firing properties of different neuronal types were simulated systematically and for mutations in the \textit{KCNA1} gene encoding the \Kv potassium channel subtype associated with episodic ataxia type~1 (EA1). The effects of changes in ion current properties or changes due to mutations in the \Kv channel subtype on the firing of a neuron depends on the ionic current environment, or the neuronal cell type, in which such a change occurs in. Characterization of ion channel mutations as loss or gain of function is useful at the level of the ionic current. However, the effects of mutations causing channelopathies on the firing of a cell is dependent on the cell type and thus on the composition of different ion channels and subunits. To further the efficacy of personalized medicine in channelopathies, the effects of ion channel mutations must be examined in the context of the appropriate cell types in which these mutations occur.
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\par\null
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@ -205,7 +205,7 @@ All modelling and simulation was done in parallel with custom written Python 3.8
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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; model D), regular spiking inhibitory (RS inhibitory; model B), and fast spiking (FS; model C) 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; 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 cell 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 cell 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). 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 (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
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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) 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; 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 cell 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 cell 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 \Cref{fig:diversity_in_firing}. 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 (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
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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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@ -348,9 +348,9 @@ Mutations in \textit{KCNA1} are associated with episodic ataxia type~1 (EA1) and
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\section*{Discussion (3000 Words Maximum - Currently )}
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% \textit{The discussion section should include a brief statement of the principal findings, a discussion of the validity of the observations, a discussion of the findings in light of other published work dealing with the same or closely related subjects, and a statement of the possible significance of the work. Extensive discussion of the literature is discouraged.}\\
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Changes to single ionic current properties, as well as known episodic ataxia type~1 associated \textit{KCNA1} mutations showed consistent effects on the rheobase across cell types, whereas the effects on AUC of the steady-state fI-curve depended on the cell 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 cell and are therefore depend on the channel ensemble of a specific cell type.
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%Changes to single ionic current properties, as well as known episodic ataxia type~1 associated \textit{KCNA1} mutations showed consistent effects on the rheobase across cell types, whereas the effects on AUC of the steady-state fI-curve depended on the cell 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 cell and are therefore depend on the channel ensemble of a specific cell type.
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To compare the effects ion channel mutations on neuronal firing of different neuron types, a diverse set of conductance-based models was simulated, by simulating the effect of changes in individual channel properties across conductance-based neuronal models and by simluating the effects of 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 cell types, whereas the effects on AUC of the steady-state fI-curve depended on the cell 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 cell and are therefore depend on the channel ensemble of a specific cell type.
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To compare the effects ion channel mutations on neuronal firing of different neuron types, a diverse set of conductance-based models was used and the effect of changes in individual channel properties across conductance-based neuronal models and the effects of episodic ataxia type~1 associated (EA1) \textit{KCNA1} mutations were simulated. Changes to single ionic current properties, as well as known EA1 associated \textit{KCNA1} mutations showed consistent effects on the rheobase across cell types, whereas the effects on AUC of the steady-state fI-curve depended on the cell 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 cell and are therefore depend on the channel ensemble of a specific cell type.
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\subsection*{Firing Frequency Analysis}
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Although, firing differences can be characterized by an area under the curve of the fI curve for fixed current steps 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 cells types and enable classification as described in \Cref{fig:firing_characterization}. Importanty, in cases when ion channel mutations alter rheobase and initial fI curve sleepness in ways that opposing effects on firing (upper left and bottom right quadrants of \Cref{fig:firing_characterization}B) this disamgibuation is important for understanding the outcome of the mutation. In these cases, the regime the neuron is operating in is vital in determining the cells 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.
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@ -370,11 +370,11 @@ To capture the diversity in neuronal ion channel expression and its relevance in
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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 R1648H mutation in SCN1A does not alter the excitability of cortical pyramidal neurons, but causes hypoexcitability of adjacent inhibitory GABAergic neurons \citep{Hedrich14874}. In the CA3 region of the hippocampus, the equivalent mutation in \textit{SCN8A}, R1627H, increases the excitability of pyramidal neurons and decreases the 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, namely the \(\textrm{Na}_\textrm{V}\textrm{1.8}\) subunit \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.
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Cell type specific differences in ionic current properties are important in the effects of ion channel mutations. However within a cell type heterogeneity in channel expression levels exists and it is often desirable to generate a population of neuronal models and to screen them for plausibility to biological data in order to capture neuronal population diversity \citep{marder_multiple_2011} \textcolor{red}{\notenk{add temperature sensitivity-> within cell-type heterogeneity exists - Marder paper?}}. The models we used here are originally generated by characterization of current gating properties and by fitting of maximal conductances to experimental data \citep{pospischil_minimal_2008, ranjan_kinetic_2019, alexander_cerebellar_2019, otsuka_conductance-based_2004}. This practice of fixing maximal conductances based on experimental data is limiting as it does not reproduce the variability in channel expression and neuronal firing behavior of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a neuronal sub-population within the stomatogastric ganglion, the so-called "one-spike bursting" neurons fire three spikes instead of one per burst due to an L-shaped distribution of sodium and potassium conductances \citep{golowasch_failure_2002}.
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Cell type specific differences in ionic current properties are important in the effects of ion channel mutations. However within a cell type heterogeneity in channel expression levels exists and it is often desirable to generate a population of neuronal models and to screen them for plausibility to biological data in order to capture neuronal population diversity \citep{marder_multiple_2011}. The models we used here are originally generated by characterization of current gating properties and by fitting of maximal conductances to experimental data \citep{pospischil_minimal_2008, ranjan_kinetic_2019, alexander_cerebellar_2019, otsuka_conductance-based_2004}. This practice of fixing maximal conductances based on experimental data is limiting as it does not reproduce the variability in channel expression and neuronal firing behavior of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a neuronal sub-population within the stomatogastric ganglion, the so-called "one-spike bursting" neurons fire three spikes instead of one per burst due to an L-shaped distribution of sodium and potassium conductances \citep{golowasch_failure_2002}.
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Multiple sets of conductances can give rise to the same patterns of activity also termed degeneracy and differences in neuronal dynamics may only be evident with perturbations \citep{marder_multiple_2011, goaillard_ion_2021}.
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The variability in ion channel expression often correlates with the expression of other ion channels \citep{goaillard_ion_2021} and neurons whose behavior is similar may possess correlated variability across different ion channels resulting in stability in the neuronal phenotype \citep{lamb_correlated_2013, soofi_co-variation_2012, taylor_how_2009}.
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The variability of ionic currents and degeneracy of neurons may account, at least in part, for the observation that the effect of toxins within a neuronal type is frequently not constant \citep{khaliq_relative_2006, puopolo_roles_2007, ransdell_neurons_2013}.
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% \textcolor{red}{\notenk{add temperature sensitivity-> within cell-type heterogeneity exists - Marder paper?}}
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\subsection*{Effects of \textit{KCNA1} Mutations}
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Changes in delayed rectifier potassium currents, analogous to those seen in LOF \textit{KCNA1} 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 observed by \citet{hafez_altered_2020} are in line with our simulation-based predictions of the outcomes of \textit{KCNA1} mutations. LOF \textit{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 \textit{KCNA1} mutations. Contrary to these results, \citet{zhao_common_2020} predicted \textit{in silico} that the depolarizing shifts seen as a result of \textit{KCNA1} mutations broaden action potentials and interfere negatively with high frequency action potential firing. However, they varied stimulus duration between different models and therefore comparability of firing rates is lacking in this study.
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@ -388,7 +388,7 @@ Therefore, this approach should be used with caution and the cell type which exp
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The effects of altered ion channel properties on firing is generally influenced by the other ionic currents present 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.
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\subsection*{Limitations}
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The models used here are simple and while they all capture key aspects of the firing dynamics for their respective cell, they fall short of capturing the complex physiology and biophysics of real cells. However, for the purpose of understanding how different cell-types, or current environments, contribute to diversity in firing outcomes of ion channel mutations, the fidelity of the models to the physiological cells they represent is of a minor concern and the variety in currents and dynamics across models is of utmost importance. Additionally, the development of more realistic models is a high priority and will enable cell-type specific predictions that may aid in precision medicine approaches. Thus, weight should not be put on any single predicted firing outcome here, but rather on the differences in outcomes that occur across the cell-type spectrum the models used here represent.
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The models used here are simple and while they all capture key aspects of the firing dynamics for their respective cell, they fall short of capturing the complex physiology and biophysics of real cells. However, for the purpose of understanding how different cell-types, or current environments, contribute to diversity in firing outcomes of ion channel mutations, the fidelity of the models to the physiological cells they represent is of a minor concern and the variety in currents and dynamics across models is of utmost importance. With this context, models are labelled as models A-L here to highlight that the physiological cells they represent is not of chief concern, but rather that the collection of models with different attributes results in heterogenous firing responses to the same perturbation. Additionally, the development of more realistic models is a high priority and will enable cell-type specific predictions that may aid in 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 cell-type spectrum the models used here represent.
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\par\null
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@ -436,51 +436,51 @@ The models used here are simple and while they all capture key aspects of the fi
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% Remove top and right borderlines that to not contain measuring metrics from all graph/histogram figure panels (i.e., do not box the panels in). Do not include any two-bar graphs/histograms; instead state those values in the text.
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% All illustrations documenting results must include a bar to indicate the scale. All labels used in a figure should be explained in the legend. The migration of protein molecular weight size markers or nucleic acid size markers must be indicated and labeled appropriately (e.g., “kD”, “nt”, “bp”) on all figure panels showing gel electrophoresis.}
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\setcounter{figure}{0}
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\begin{figure}[tp]
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\centering
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\includegraphics[width=\linewidth]{Figures/diversity_in_firing.pdf}
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\linespread{1.}\selectfont
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\caption[]{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) for Cb stellate (A), RS inhibitory (B), FS (C), RS pyramidal (D), RS inhibitory +\Kv (E), Cb stellate +\Kv (F), FS +\Kv (G), RS pyramidal +\Kv (H), STN +\Kv (I), Cb stellate \(\Delta\)\Kv (J), STN \(\Delta\)\Kv (K), and STN (L) neuron models. Black marker 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 \Cref{fig:ramp_firing}).}
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\label{fig:diversity_in_firing}
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\end{figure}
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\begin{figure}[tp]
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\centering
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\includegraphics[width=0.5\linewidth]{Figures/firing_characterization_arrows.pdf}
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\linespread{1.}\selectfont
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\caption[]{Characterization of firing with AUC and rheobase. (A) The area under the curve (AUC) of the repetitive firing frequency-current (fI) curve. (B)
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Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy 4 quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in red with respect to a reference fI curve (blue) depict the general changes associated with each quadrant.}
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\label{fig:firing_characterization}
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\end{figure}
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\begin{figure}[tp]
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\centering
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\includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf}
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\linespread{1.}\selectfont
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\caption[]{Effects of altered channel kinetics on AUC in various neuron models. The fI curves corresponding to shifts in FS \(+\)\Kv model delayed rectifier K half activation \(V_{1/2}\) (A), changes \Kv activation slope factor \(k\) in the FS \(+\)\Kv model (B), and changes in maximal conductance of delayed rectifier K current in the STN \(+\)\Kv model (C) are shown. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); B), \Kv activation slope factor \(k\) (k/\(\textrm{k}_{WT}\); E) and maximal conductance \(g\) of the delayed rectifier K current (g/\(\textrm{g}_{WT}\); H) for all models (thin lines) with relationships from the fI curve examples (A, D, G respectively) highlighted by thick lines with colors corresponding to the box highlighting each set of fI curves. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in half maximal potential \(V_{1/2}\) and \ndAUC (C), slope factor k and \ndAUC (F) as well as maximal current conductances and \ndAUC (I) for each model and current property is computed. The relationships between \(\Delta V_{1/2}\), k/\(\textrm{k}_{WT}\), and g/\(\textrm{g}_{WT}\) and \ndAUC for the Kendall rank correlations highlighted in the black boxes are depicted in (B), (E) and (H) respectively.}
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\label{fig:AUC_correlation}
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\end{figure}
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\begin{figure}[tp]
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\centering
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\includegraphics[width=\linewidth]{Figures/rheobase_correlation.pdf}
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\linespread{1.}\selectfont
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\caption[]{Effects of altered channel kinetics on rheobase. The fI curves corresponding to shifts in FS \(+\)\Kv model \Kv activation \(V_{1/2}\) (A), changes \Kv inactivation slope factor \(k\) in the Cb stellate \(+\)\Kv model (B), and changes in maximal conductance of the leak current in the Cb stellate model (C) are shown. The \drheo of fI curves is plotted against \Kv half activation potential (\(\Delta V_{1/2}\); B), \Kv inactivation slope factor \(k\) (k/\(\textrm{k}_{WT}\); E) and maximal conductance \(g\) of the leak current (g/\(\textrm{g}_{WT}\); H) for all models (thin lines) with relationships from the fI curve examples (A, D, G respectively) highlighted by thick lines with colors corresponding to the box highlighting each set of fI curves. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in half maximal potential \(V_{1/2}\) and \drheo (C), slope factor k and \drheo (F) as well as maximal current conductances and \drheo (I) for each model and current property is computed. The relationships between \(\Delta V_{1/2}\), k/\(\textrm{k}_{WT}\), and g/\(\textrm{g}_{WT}\) and \drheo for the Kendall rank correlations highlighted in the black boxes are depicted in (B), (E) and (H) respectively..}
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\label{fig:rheobase_correlation}
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\end{figure}
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\begin{figure}[tp]
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\centering
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\includegraphics[width=\linewidth]{Figures/simulation_model_comparison.pdf}
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\linespread{1.}\selectfont
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\caption[]{Effects of episodic ataxia type~1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (percent change in normalized \(\Delta\)AUC) and rheobase (\(\Delta\)Rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kv (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kv (I) models. V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively. Marker shape is indicative of model/firing type, and grey dashed lines denote the quadrants of firing characterization (see \Cref{fig:firing_characterization}).}
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\label{fig:simulation_model_comparision}
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\end{figure}
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%\setcounter{figure}{0}
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%
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%\begin{figure}[tp]
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% \centering
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% \includegraphics[width=\linewidth]{Figures/diversity_in_firing.pdf}
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% \linespread{1.}\selectfont
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% \caption[]{Diversity in Neuronal Model Firing. Spike trains (left), frequency-current (fI) curves (right) for Cb stellate (A), RS inhibitory (B), FS (C), RS pyramidal (D), RS inhibitory +\Kv (E), Cb stellate +\Kv (F), FS +\Kv (G), RS pyramidal +\Kv (H), STN +\Kv (I), Cb stellate \(\Delta\)\Kv (J), STN \(\Delta\)\Kv (K), and STN (L) neuron models. Black marker 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 \Cref{fig:ramp_firing}).}
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% \label{fig:diversity_in_firing}
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%\end{figure}
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%
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%
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%\begin{figure}[tp]
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% \centering
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% \includegraphics[width=0.5\linewidth]{Figures/firing_characterization_arrows.pdf}
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% \linespread{1.}\selectfont
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% \caption[]{Characterization of firing with AUC and rheobase. (A) The area under the curve (AUC) of the repetitive firing frequency-current (fI) curve. (B)
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%Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy 4 quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in red with respect to a reference fI curve (blue) depict the general changes associated with each quadrant.}
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% \label{fig:firing_characterization}
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%\end{figure}
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%
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%
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%\begin{figure}[tp]
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% \centering
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% \includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf}
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% \linespread{1.}\selectfont
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% \caption[]{Effects of altered channel kinetics on AUC in various neuron models. The fI curves corresponding to shifts in FS \(+\)\Kv model delayed rectifier K half activation \(V_{1/2}\) (A), changes \Kv activation slope factor \(k\) in the FS \(+\)\Kv model (B), and changes in maximal conductance of delayed rectifier K current in the STN \(+\)\Kv model (C) are shown. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); B), \Kv activation slope factor \(k\) (k/\(\textrm{k}_{WT}\); E) and maximal conductance \(g\) of the delayed rectifier K current (g/\(\textrm{g}_{WT}\); H) for all models (thin lines) with relationships from the fI curve examples (A, D, G respectively) highlighted by thick lines with colors corresponding to the box highlighting each set of fI curves. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in half maximal potential \(V_{1/2}\) and \ndAUC (C), slope factor k and \ndAUC (F) as well as maximal current conductances and \ndAUC (I) for each model and current property is computed. The relationships between \(\Delta V_{1/2}\), k/\(\textrm{k}_{WT}\), and g/\(\textrm{g}_{WT}\) and \ndAUC for the Kendall rank correlations highlighted in the black boxes are depicted in (B), (E) and (H) respectively.}
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% \label{fig:AUC_correlation}
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%\end{figure}
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%
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%
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%\begin{figure}[tp]
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% \centering
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% \includegraphics[width=\linewidth]{Figures/rheobase_correlation.pdf}
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% \linespread{1.}\selectfont
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% \caption[]{Effects of altered channel kinetics on rheobase. The fI curves corresponding to shifts in FS \(+\)\Kv model \Kv activation \(V_{1/2}\) (A), changes \Kv inactivation slope factor \(k\) in the Cb stellate \(+\)\Kv model (B), and changes in maximal conductance of the leak current in the Cb stellate model (C) are shown. The \drheo of fI curves is plotted against \Kv half activation potential (\(\Delta V_{1/2}\); B), \Kv inactivation slope factor \(k\) (k/\(\textrm{k}_{WT}\); E) and maximal conductance \(g\) of the leak current (g/\(\textrm{g}_{WT}\); H) for all models (thin lines) with relationships from the fI curve examples (A, D, G respectively) highlighted by thick lines with colors corresponding to the box highlighting each set of fI curves. The Kendall rank correlation (Kendall \(\tau\)) coefficients between shifts in half maximal potential \(V_{1/2}\) and \drheo (C), slope factor k and \drheo (F) as well as maximal current conductances and \drheo (I) for each model and current property is computed. The relationships between \(\Delta V_{1/2}\), k/\(\textrm{k}_{WT}\), and g/\(\textrm{g}_{WT}\) and \drheo for the Kendall rank correlations highlighted in the black boxes are depicted in (B), (E) and (H) respectively..}
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% \label{fig:rheobase_correlation}
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%\end{figure}
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%
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%\begin{figure}[tp]
|
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% \centering
|
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% \includegraphics[width=\linewidth]{Figures/simulation_model_comparison.pdf}
|
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% \linespread{1.}\selectfont
|
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% \caption[]{Effects of episodic ataxia type~1 associated \Kv mutations on firing. Effects of \Kv mutations on AUC (percent change in normalized \(\Delta\)AUC) and rheobase (\(\Delta\)Rheobase) compared to wild type for RS pyramidal +\Kv (A), RS inhibitory +\Kv (B), FS +\Kv (C), Cb stellate (D), Cb stellate +\Kv (E), Cb stellate \(\Delta\)\Kv (F), STN (G), STN +\Kv (H) and STN \(\Delta\)\Kv (I) models. V174F, F414C, E283K, and V404I mutations are highlighted in color for each model. Pairwise Kendall rank correlation coefficients (Kendall \(\tau\)) between the effects of \Kv mutations on rheobase and on AUC are shown in J and K respectively. Marker shape is indicative of model/firing type, and grey dashed lines denote the quadrants of firing characterization (see \Cref{fig:firing_characterization}).}
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% \label{fig:simulation_model_comparision}
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%\end{figure}
|
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|
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|
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%\captionof{figure}{Characterization of firing with AUC and rheobase. (A) The area under the curve (AUC) of the repetitive firing frequency-current (fI) curve. (B) Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy 4 quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in blue with respect to a reference fI curve (black) depict the general changes associated with each quadrant.}
|
||||
|
||||
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Reference in New Issue
Block a user