Changes from meeting with Jan and Lukas
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@ -196,7 +196,9 @@ For instance, altering relative amplitudes of ionic currents can dramatically in
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Computational modelling approaches can be used to assess the impacts of altered ionic current properties on firing behavior, bridging the gap between changes in the biophysical properties induced by mutations, firing and clinical symptoms. Conductance-based neuronal models enable insight into the effects of ion channel mutations with specific effects of the resulting ionic current as well as enabling \textit{in silico} assessment of the relative effects of changes in biophysical properties of ionic currents on neuronal firing. Furthermore, modelling approaches enable predictions of the effects of specific mutation and drug induced biophysical property changes \citep{Layer2021,Liu2019,johannesen_genotype-phenotype_2021, lauxmann_therapeutic_2021}. \textcolor{red}{\notenk{added citation to make this clearer - other papers not from us?}} \noteuh{Hiermit möchtest du sagen, dass man quasi den Block eines bestimmtem Kanaltyps auf das Feuern untersuchen kann? Oder was genau meinst du damit?} \notenk{Ja, nicht nur Mutation oder Block alleine, aber auch ob ein bestimmten Block das Feuern richtung Wildtyp bringen kann (bzw. Unser Paper mit Carbamazepine und Riluzul in KCNA1)}
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In this study, we therefore investigated the role that a specific neuronal cell type plays on the outcome of ionic current kinetic changes on firing \noteuh{Eher andresrum, oder? Es wurde untersucht, wie die Veränderungen in der Kinetik sich auf das Feuern unterschiedlicher Neuronentypen auswirken.} \notenk{I'm not sure I understand this comment - I think I have done what Uli is suggesting?} \textcolor{red}{\notenk{Re-write this to make it clearer? how the firing of various neuron cell types is affected by changes in ionic current kinetics}} by simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as to more complex changes as they were observed for specific mutations. For this task we chose mutations in the \textit{KCNA1} gene, encoding the potassium channel subunit \Kv, that are associated with episodic ataxia type~1 \citep{Browne1994, Browne1995, lauxmann_therapeutic_2021}.
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\textit{In this study, we therefore investigated the role that a specific neuronal cell type plays on the outcome of ionic current kinetic changes on firing \noteuh{Eher andresrum, oder? Es wurde untersucht, wie die Veränderungen in der Kinetik sich auf das Feuern unterschiedlicher Neuronentypen auswirken.} \notenk{Re-written below to make it clearer} by simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as to more complex changes as they were observed for specific mutations. }
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In this study, we therefore investigated how the outcome of ionic current kinetic changes on firing depend on neuronal cell type by simulating the response of a repertoire of different neuronal models to changes in single current parameters as well as to more complex changes as they were observed for specific mutations. For this task we chose mutations in the \textit{KCNA1} gene, encoding the potassium channel subunit \Kv, that are associated with episodic ataxia type~1 \citep{Browne1994, Browne1995, lauxmann_therapeutic_2021}.
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\noteuh{Warum hast du die UE den immer als „Formel“ eingefügt? (\Kv) Geht auch einfach als normaler Text. (Kv1.1) } \notenk{Ich habe die IUPHAR Nomenklatur mit "V" tiefgestellt benutzt}
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\par\null
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@ -208,11 +210,11 @@ 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), regular spiking inhibitory (RS inhibitory), and fast spiking (FS) cells were used \citep{pospischil_minimal_2008}. Additionally, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added to each of these models (RS pyramidal +\Kv, RS inhibitory +\Kv, and FS +\Kv respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate) 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) or by replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv). A subthalamic nucleus (STN) neuron model as described by \citet{otsuka_conductance-based_2004} was also used. The STN cell model was additionally extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (STN+\Kv) or by replacing the A-type potassium current (STN \(\Delta\)\Kv). The properties and maximal conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models \citet{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), regular spiking inhibitory (RS inhibitory), and fast spiking (FS) cells were used \citep{pospischil_minimal_2008}. Additionally, a \Kv current (\IKv; \citealt{ranjan_kinetic_2019}) was added to each of these models (RS pyramidal +\Kv, RS inhibitory +\Kv, and FS +\Kv respectively). A cerebellar stellate cell model from \citet{alexander_cerebellar_2019} is used (Cb stellate) 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) or by replacing the A-type potassium current (Cb stellate \(\Delta\)\Kv). A subthalamic nucleus (STN) neuron model as described by \citet{otsuka_conductance-based_2004} was also used. The STN cell model was additionally extended by a \Kv current \citep{ranjan_kinetic_2019}, either in addition to the A-type potassium current (STN+\Kv) or by replacing the A-type potassium current (STN \(\Delta\)\Kv). The properties and maximal conductances of each model are detailed in \Cref{tab:g} and the gating properties are unaltered from the original Cb stellate and STN models \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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with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted to the original formulism for RS pyramidal, RS inhibitory and FS models from \citet{pospischil_minimal_2008}. The properties of \IKv were fitted to the mean wild type biophysical parameters of \Kv described in \citet{lauxmann_therapeutic_2021}. Each of the original single-compartment models used here can reproduce physiological firing behavior of the neurons they represent \citep{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004} and capture key aspects of the dynamics of these cell types.
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with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted to the original formulism for RS pyramidal, RS inhibitory and FS models from \citet{pospischil_minimal_2008}. The properties of \IKv were fitted to the mean wild type biophysical parameters of \Kv described in \citet{lauxmann_therapeutic_2021}. Each of the original single-compartment models used here can reproduce physiological firing behavior of the neurons they represent (\Cref{fig:diversity_in_firing}; \citealt{pospischil_minimal_2008, alexander_cerebellar_2019, otsuka_conductance-based_2004}) and capture key aspects of the dynamics of these cell types.
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\input{g_table}
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@ -220,13 +222,23 @@ with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}
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\input{gating_table}
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\subsection*{Firing Frequency Analysis}
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The membrane responses to 200 equidistant two second long current steps were simulated using the forward-Euler method with a \(\Delta \textrm{t} = 0.01\)\,ms from steady state. Current steps ranged from 0 to 1\,nA (stepsize 5pA) \noteuh{Wie groß war den die Step-size?}\notenk{Es gab 200 schrite (siehe erster Satz) also 0.005nA von 0 bis 1 nA } \notenk{added step size for both to make it explicit} for all models except for the RS inhibitory neuron models where a range of 0 to 0.35 nA (stepsize 1.75pA) was used to ensure repetitive firing across the range of input currents. For each current step, action potentials were detected as peaks with at least 50\,mV prominence, or the relative height above the lowest contour line encircling it, and a minimum interspike interval of 1\,ms. The interspike interval was computed and used to determine the instantaneous firing frequencies elicited by the current step. The steady-state firing frequency was defined as the mean firing frequency 0.5\,s after the first action potential \noteuh{Warum nur in den ersten 0.5 s ? da würde man auch schon sehen, ob es zu einer spike frequency adaptation kommt? Aber das hattest du nicht angeschaut, oder? Ist ja auch wichtig für das Feuerverhalten unterschiedlichen Neurone. } \notenk{Die 0.5s ist in der letzte sekunde des steps, damit die adaption keine Rolle spielt. Wenn mann die ISIs hat fuer den ganzen Step, kann mann nicht einfach die letzte sekunde nehmen weil es nicht unbedingt (bzw fast nie) einen spike genau am Anfang oder am Ende gibt. Dies bedeutet das mann irgendwie nur ein Teil des erstes/letztes ISI im durchschnitt mit rechnen muss. Um das zu vermeiden habe ich nur 0.5s benutzt die vom ersten spike in der letzte sekund anfaengt. Ich hoffe das dass Sinn macht?} \textcolor{red}{\notenk{Reason: at low firing rates a fixed time interval can miss spikes (i.e. get F=0Hz when F is small}} in the last second of the current step respectively \textcolor{red}{to ensure a uniform time interval sampling across models and at low firing rates} and was used to construct frequency-current (fI) curves. Alteration in current magnitudes can have different effects on rheobase and the initial slope of the fI curve \citep{Kispersky2012}.
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For this reason, we quantified neuronal firing using the rheobase as well as the area under the curve (AUC) of the initial portion of the fI curve as a measure of the initial slope of the fI curve.
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The membrane responses to 200 equidistant two second long current steps were simulated using the forward-Euler method with a \(\Delta \textrm{t} = 0.01\)\,ms from steady state. Current steps ranged from 0 to 1\,nA (stepsize 5\,pA) \noteuh{Wie groß war den die Step-size?}\notenk{Es gab 200 schritte (siehe erster Satz) also 0.005nA von 0 bis 1 nA } \notenk{added step size for both to make it explicit} for all models except for the RS inhibitory neuron models where a range of 0 to 0.35\,nA (stepsize 1.75\,pA) was used to ensure repetitive firing across the range of input currents. For each current step, action potentials were detected as peaks with at least 50\,mV prominence, or the relative height above the lowest contour line encircling it, and a minimum interspike interval of 1\,ms. The interspike interval was computed and used to determine the instantaneous firing frequencies elicited by the current step.
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To ensure a uniform time interval sampling across models, accurate firing frequencies at low firing rates, and reduced spike sampling bias steady-state firing was defined as the mean firing frequency in a 500\,ms window in the last second of the current steps starting at the inital action potential in this last second.
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Firing characterization was performed in the last second of current steps to ensure steady-state firing is captured and adaptation processes are neglected in our analysis. Alteration in current magnitudes can have different effects on rheobase and the initial slope of the fI curve \citep{Kispersky2012}.
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For this reason, we quantified neuronal firing using the rheobase as well as the area under the curve (AUC) of the initial portion of the fI curve as a measure of the initial slope of the fI curve \Cref{fig:firing_characterization}A.
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The smallest current at which steady state firing occured was identified and the current step interval preceding the occurrence of steady state firing was simulated at higher resolution (100 current steps) to determine the current at which steady state firing began. Firing was simulated with 100 current steps from this current upwards for 1/5 of the overall current range. Over this range a fI curve was constructed and the integral, or area under the curve (AUC), of the fI curve over this interval was computed with the composite trapezoidal rule and used as a measure of firing rate independent from rheobase.
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To obtain the rheobase at a higher current resolution than the fI curve, the current step interval preceding the occurrence of action potentials was explored at higher resolution with 100 current steps spanning the interval (stepsizes of 0.05 pA and 0.0175 pA respectively) \notenk{To address the comment below I added the reason and step sizes to make it clearer why this was done}. Membrane responses to these current steps were then analyzed for action potentials and the rheobase was considered the lowest current step for which an action potential was elicited. \noteuh{Ich verstehe aber nicht so ganz, was dann der Unterschied zu oben ist? Ab wann hast du den steady-state definiert? Wie viele Aktionspotentiale mussten mindestens auftreten? Das ist mir unklar. Und für die Rheobas hast du dann geschaut, wann min. 1 AP aufgetreten ist, oder?} \notenk{Der Unterschied zu oben ist dass oben die Ziel Stromschrit gefunden wird wo das Feuern anfaengt (z.B. 0.07 kein feuern, 0.08 feuern). Dieser Stromschrit wird dann wieder Simuliert mit kleinere schritte (z.B. 0.007, 0.00701, 0.00702, …, 0.0799, 0.08). Die Rheobas wird dann von diese kleiner schritte gefunden wo min 1 AP aufgreten ist (damit die Rheobase feiner aufgeloest ist)}
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All models exhibited tonic firing and any instances of periodic bursting were excluded to simplify the characterization of firing. \noteuh{Die Pyramidenzellen haben auch nie am Anfang einen kurzen „burst“ gezeigt? Ich frage nur, weil das in Zellen bei einigen Pyramidenzellen der Fall ist. Die hast du auch alles ausgeschlossen, um die Variabilität zu minimieren?} \notenk{Mit bursting meine ich hier repetitiven bursts, bzw. Periodisches bursting mit interburst Intervale. Den Fall wo die Pyramidenzellen am Anfang einen kurzen "burst" haben ist vorgekommen, wird aber hier nicht analysiert weil wir das "steady state" feuern hier betrachten - added ``periodic'' to make this clear} Firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis.
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All models exhibited tonic steady-state firing with default parameters. In limited instances, variations of parameters elicited periodic bursting, however these instances were excluded from further analysis.
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\notenk{Italics sections below are replaced above}
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\textit{The steady-state firing frequency was defined as the mean firing frequency 0.5\,s after the first action potential in the last second of the current step respectively \textcolor{red}{to ensure a uniform time interval sampling across models and at low firing rates} and was used to construct frequency-current (fI) curves. }
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\textit{\noteuh{Warum nur in den ersten 0.5 s ? da würde man auch schon sehen, ob es zu einer spike frequency adaptation kommt? Aber das hattest du nicht angeschaut, oder? Ist ja auch wichtig für das Feuerverhalten unterschiedlichen Neurone. } \notenk{Die 0.5s ist in der letzte sekunde des steps, damit die adaption keine Rolle spielt. Wenn mann die ISIs hat fuer den ganzen Step, kann mann nicht einfach die letzte sekunde nehmen weil es nicht unbedingt (bzw fast nie) einen spike genau am Anfang oder am Ende gibt. Dies bedeutet das mann irgendwie nur ein Teil des erstes/letztes ISI im durchschnitt mit rechnen muss. Um das zu vermeiden habe ich nur 0.5s benutzt die vom ersten spike in der letzte sekund anfaengt. Ich hoffe das dass Sinn macht?} \textcolor{red}{\notenk{Reason: at low firing rates a fixed time interval can miss spikes (i.e. get F=0Hz when F is small}}}
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\textit{All models exhibited tonic firing and any instances of periodic bursting were excluded to simplify the characterization of firing. \noteuh{Die Pyramidenzellen haben auch nie am Anfang einen kurzen „burst“ gezeigt? Ich frage nur, weil das in Zellen bei einigen Pyramidenzellen der Fall ist. Die hast du auch alles ausgeschlossen, um die Variabilität zu minimieren?} \notenk{Mit bursting meine ich hier repetitiven bursts, bzw. Periodisches bursting mit interburst Intervale. Den Fall wo die Pyramidenzellen am Anfang einen kurzen "burst" haben ist vorgekommen, wird aber hier nicht analysiert weil wir das "steady state" feuern hier betrachten - added ``periodic'' to make this clear}}
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\subsection*{Sensitivity Analysis and Comparison of Models}
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@ -265,12 +277,12 @@ To examine the role of cell-type specific ionic current environments on the impa
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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 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 \Cref{fig:ramp_firing}). \noteuh{Würde jeweils noch ein Leerzeichen nach dem „+“ machen. Oder davor und danach weglassen.}\notenk{Ist vielleicht weil pandoc von LaTeX zu Word immer + Kv1.1 statt \Kv in der Word datei getan hat} \noteuh{Bricht das Feuern der Zellen wirklich schon bei einer Strominjektion von 0.3nA ab? Und die Feuerfrequenz ist so hoch? War das bei den bereits publizierten RS inhibitory neurons ebenfalls so?}\notenk{Ja das Feuern des Modells bricht von 0.3nA ab und feuert mit hoehe Feuerfrequenz. Das eine (RS inhibitory ist das original publizierte model (die von Experimentelle Daten gefitted wurde), und das RS inhibitory +\Kv hat niedriger Feuerfrequenz. }}
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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 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 \Cref{fig:ramp_firing}). \noteuh{Bricht das Feuern der Zellen wirklich schon bei einer Strominjektion von 0.3nA ab? Und die Feuerfrequenz ist so hoch? War das bei den bereits publizierten RS inhibitory neurons ebenfalls so?}\notenk{Ja das Feuern des Modells bricht von 0.3nA ab und feuert mit hoehe Feuerfrequenz. Das eine (RS inhibitory ist das original publizierte model (die von Experimentelle Daten gefitted wurde), und das RS inhibitory +\Kv hat niedriger Feuerfrequenz. }}
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\label{fig:diversity_in_firing}
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\end{figure}
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\subsection*{Variety of model neurons}
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Neuronal firing is heterogenous across the CNS and a set of neuronal models with heterogenous 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 (\Cref{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). Some models, such as Cb stellate and RS inhibitory models, display type I firing, whereas others such as Cb stellate \(\Delta\)\Kv and STN models 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) \notenk{\cite{ermentrout_type_1996}?}. 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 STN +\Kv, STN \(\Delta\)\Kv, and Cb stellate \(\Delta\)\Kv models have large hysteresis (\Cref{fig:diversity_in_firing}, \Cref{fig:ramp_firing}). Different types of underlying current dynamics \textcolor{red}{\notenk{current dynamics or dynamics - ask Jan?}} \textcolor{red}{\noteuh{wie zum Beispiel? Könnte dann in der Diskussion evtl. aufgegriffen werden}} are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}.
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Neuronal firing is heterogenous across the CNS and a set of neuronal models with heterogenous 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 (\Cref{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). Some models, such as Cb stellate and RS inhibitory models, display type I firing, whereas others such as Cb stellate \(\Delta\)\Kv and STN models 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) \cite{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 STN +\Kv, STN \(\Delta\)\Kv, and Cb stellate \(\Delta\)\Kv models have large hysteresis (\Cref{fig:diversity_in_firing}, \Cref{fig:ramp_firing}). Different types of underlying current dynamics \textcolor{red}{\noteuh{wie zum Beispiel? Könnte dann in der Diskussion evtl. aufgegriffen werden}} are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}.
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\subsection*{Characterization of Neuronal Firing Properties}
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\begin{figure}[tp]
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@ -278,13 +290,15 @@ Neuronal firing is heterogenous across the CNS and a set of neuronal models with
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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 four quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in red with respect to a reference (or wild type) fI curve (blue) depict the general changes associated with each quadrant.\textcolor{red}{\noteuh{Evtl. könntest du schon in den Methoden auf Fig. 2A verweisen?}}}
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Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occupy four quadrants separated by no changes in AUC and rheobase. Representative schematic fI curves in red with respect to a reference (or wild type) 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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Neuronal firing is a complex phenomenon, and a quantification of firing properties is required for comparisons across cell types and between different conditions. Here we focus on two aspects of firing: rheobase, the smallest injected current at which the cell fires an action potential, and the shape of the frequency-current (fI) curve as quantified by the area under the curve (AUC) for a fixed range of input currents above rheobase (\Cref{fig:firing_characterization}A). The characterization of 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.
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Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, \drheo, and in AUC, \(\Delta\)AUC, relative to the wild type neuron. \(\Delta\)AUC is in addition normalized to the AUC of the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by \drheo and \ndAUC (\Cref{fig:firing_characterization}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\)\drheo), unambigously indicating an increased firing that clearly might be classified as a gain of function (GOF) of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\)\drheo), indicating a decreased, loss of function (LOF) firing. In the lower left (\(-\Delta\)AUC and \(-\)\drheo) and upper right (\(+\Delta\)AUC and \(+\)\drheo) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability. In these cases, it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionally generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant. \textcolor{red}{\noteuh{Das sind ja eigentlich schon Hypothesen, sollte eher in die Diskussion oder dort zumindest noch mal aufgegriffen werden. Kommt ja vermutlich noch ;-)}} \textcolor{red}{\notenk{Add to dicussion? As intro and explanation as to why we characterize firing?}}
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Using these two measures we quantify the effects a changed property of an ionic current has on neural firing by the differences in both rheobase, \drheo, and in AUC, \(\Delta\)AUC, relative to the wild type neuron. \(\Delta\)AUC is in addition normalized to the AUC of the wild type neuron, see Eq.~\eqref{eqn:AUC_contrast}. Each fI curve resulting from an altered ionic current is a point in a two-dimensional coordinate system spanned by \drheo and \ndAUC (\Cref{fig:firing_characterization}B). An fI curve similar to the one of the wild type neuron is marked by a point close to the origin. In the upper left quadrant, fI curves become steeper (positive difference of AUC values: \(+\Delta\)AUC) and are shifted to lower rheobases (negative difference of rheobases: \(-\)\drheo), unambigously indicating an increased firing that clearly might be classified as a gain of function (GOF) of neuronal firing. The opposite happens in the bottom right quadrant where the slope of fI curves decreases (\(-\Delta\)AUC) and the rheobase is shifted to higher currents (\(+\)\drheo), indicating a decreased, loss of function (LOF) firing. In the lower left (\(-\Delta\)AUC and \(-\)\drheo) and upper right (\(+\Delta\)AUC and \(+\)\drheo) quadrants, the effects on firing are less clear-cut, because the changes in rheobase and AUC have opposite effects on neuronal firing. Changes in a neuron's fI curves in these two quadrants cannot uniquely be described as a gain or loss of excitability.
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\notenk{Moved to discussion section ``Firing Frequency Analysis} \textit{In these cases, it depends on the regime the neuron is operating in. If it is in its excitable regime and only occasionally generates an action potential, then the effect on the rheobase matters more. If it is firing periodically with high rates, then the change in AUC might be more relevant. \textcolor{red}{\noteuh{Das sind ja eigentlich schon Hypothesen, sollte eher in die Diskussion oder dort zumindest noch mal aufgegriffen werden. Kommt ja vermutlich noch ;-)}} \textcolor{red}{\notenk{Add to dicussion? As intro and explanation as to why we characterize firing?}}}
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\subsection*{Sensitivity Analysis}
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Sensitivity analyses are used to understand how input model parameters contribute to determining 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 analyses involve altering one parameter at a time and assessing the impact of this parameter on the output. This approach enables the comparison of given alterations in parameters of ionic currents across models.
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@ -300,7 +314,7 @@ Qualitative differences can be found, for example, when increasing the maximal c
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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 (D), and changes in maximal conductance of delayed rectifier K current in the STN \(+\)\Kv model (G) are shown. The fI curves corresponding to the smallest and largest alterations are seen in grey and black respectively for (A,D, and G) in accordance to the x-axis in B, E, and H. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); D), \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. \noteuh{Den Unterschied zwischen den dicken und dünnen Linien kann man relativ schlecht sehen. Obwohl ja die dicke Linie auch der Farbe des Kastens entspricht. Aber wenn man B/W druckt, dann sieht man das halt schlecht…} \notenk{Added color gradient x-axis in B, E, H to indicate color scale in A,D,G, and added a tence to legend to make this clearer}}
|
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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 (D), and changes in maximal conductance of delayed rectifier K current in the STN \(+\)\Kv model (G) are shown. The fI curves from the smallest and largest alterations are seen from grey to black respectively for (A,D, and G) in accordance to the x-axis in B, E, and H. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); D), \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. \noteuh{Den Unterschied zwischen den dicken und dünnen Linien kann man relativ schlecht sehen. Obwohl ja die dicke Linie auch der Farbe des Kastens entspricht. Aber wenn man B/W druckt, dann sieht man das halt schlecht…} \notenk{Added color gradient x-axis in B, E, H to indicate color scale in A,D,G, and added a tence to legend to make this clearer}}
|
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\label{fig:AUC_correlation}
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||||
\end{figure}
|
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|
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@ -313,7 +327,7 @@ Although changes in half maximal potential \(V_{1/2}\) and slope factor \(k\) ge
|
||||
\centering
|
||||
\includegraphics[width=\linewidth]{Figures/rheobase_correlation.pdf}
|
||||
\linespread{1.}\selectfont
|
||||
\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 (D), and changes in maximal conductance of the leak current in the Cb stellate model (G) are shown. The fI curves corresponding to the smallest and largest alterations are seen in grey and black respectively for (A,D, and G) in accordance to the x-axis in B, E, and H. 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. \notenk{Added color gradient x-axis in B, E, H to indicate color scale in A,D,G and added a sentence to make it clearer.}}
|
||||
\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 (D), and changes in maximal conductance of the leak current in the Cb stellate model (G) are shown. The fI curves from the smallest and largest alterations are seen from grey to black respectively for (A,D, and G) in accordance to the x-axis in B, E, and H. 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. \notenk{Added color gradient x-axis in B, E, H to indicate color scale in A,D,G and added a sentence to make it clearer.}}
|
||||
\label{fig:rheobase_correlation}
|
||||
\end{figure}
|
||||
|
||||
@ -338,9 +352,11 @@ Changes to single ionic current properties, as well as known episodic ataxia typ
|
||||
|
||||
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.
|
||||
|
||||
\subsection*{Firing Frequency Analysis}
|
||||
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.
|
||||
|
||||
|
||||
\subsection*{Neuronal Diversity}
|
||||
\noteuh{Der Abschnitt gefällt mir sehr gut!}
|
||||
The nervous system consists of a vastly diverse and heterogenous collection of neurons with variable properties and characteristics including diverse combinations and expression levels of ion channels which are vital for neuronal firing dynamics.
|
||||
|
||||
Advances in high-throughput techniques have enabled large-scale investigation into single-cell properties across the CNS \citep{Poulin2016} that have revealed large diversity in neuronal gene expression, morphology and neuronal types in the motor cortex \citep{Scala2021}, neocortex \cite{Cadwell2016, Cadwell2020}, GABAergic neurons in the cortex and retina \citep{Huang2019, Laturnus2020} \noteuh{Wie sind den hier die Unterschiede zwischen GABAergen Neuronen und Interneuronen festgelegt? Und von welchen Gehrinbereichen ist dann hier die Rede?} \notenk{Stimmt, habe ich schlecht geschrieben. Das sind Interneuronen vom neocortex in Huang und Paul und V1 und bipolar cells in der Retina in Laturnus}\notenk{Change to ``GABAergic neurons in the cortex and retina''}, cerebellum \citep{Kozareva2021}, spinal cord \citep{Alkaslasi2021}, visual cortex \citep{Gouwens2019} as well as the retina \citep{Baden2016, Voigt2019, Berens2017, Yan2020a, Yan2020b}.
|
||||
|
||||
11
ref.bib
11
ref.bib
@ -2193,4 +2193,15 @@ SIGNIFICANCE: Bromide is most effective and is a well-tolerated drug among DS pa
|
||||
urldate = {2022-09-03},
|
||||
}
|
||||
|
||||
@InBook{Rinzel_1998,
|
||||
author = {John Rinzel and GB Ermentrout},
|
||||
editor = {C Koch and I Segev},
|
||||
pages = {135--169},
|
||||
publisher = {MIT Press},
|
||||
title = {Analysis of neural excitability and oscillations},
|
||||
year = {1989},
|
||||
booktitle = {Methods in neuronal modeling},
|
||||
language = {English (US)},
|
||||
}
|
||||
|
||||
@Comment{jabref-meta: databaseType:bibtex;}
|
||||
|
||||
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