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\newcommand{\ndAUC}{normalized \(\Delta\)AUC\xspace}
\Crefformat{Extended Data}{#2Extended Data #1#3}
\DeclareFloatingEnvironment[fileext=lop]{Extended Data}
\newcommand{\beginsupplement}{
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\newcommand{\notenk}[1]{\note[NK]{#1}}
\newcommand{\notels}[1]{\note[LS]{#1}}
\newcommand{\notejb}[1]{\note[JB]{#1}}
\newcommand{\noteuh}[1]{\note[UBSH]{#1}}
\begin{document}
\title{Loss or Gain of Function? Effects of Ion Channel Mutations on Neuronal Firing Depend on the Cell Type}
@ -258,7 +256,7 @@ To examine the role of cell-type specific ionic current environments on the impa
(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 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). Models are qualitatively sorted based on their firing curves and labeled model A through L accordingly. 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; \citet{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 (\Cref{fig:diversity_in_firing,fig:ramp_firing}). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}.
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). Models are qualitatively sorted based on their firing curves and labeled model A through L accordingly. 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 (\Cref{fig:diversity_in_firing,fig:ramp_firing}). Different types of underlying current dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}.
\subsection*{Characterization of Neuronal Firing Properties}
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.