diff --git a/manuscript.tex b/manuscript.tex index 261ac2f..5dbc2f2 100644 --- a/manuscript.tex +++ b/manuscript.tex @@ -144,7 +144,7 @@ % \item \textbf{Neuronal Excitability}; % \item Sensory and Motor Systems; % \item Integrative Systems; -% \item Cognition and Behavior; +% \item Cognition and Behavior % \item Novel Tools and Methods; % \item Disorders of the Nervous System; % \item or History, Teaching, and Public Awareness. @@ -245,7 +245,9 @@ The Kendall's \(\tau\) coefficient, a non-parametric rank correlation, is used t Known episodic ataxia type~1 associated \textit{KCNA1} mutations and their electrophysiological characterization have been reviewed in \citet{lauxmann_therapeutic_2021}. The mutation-induced changes in \IKv amplitude and activation slope (\(k\)) were normalized to wild type measurements and changes in activation \(V_{1/2}\) were used relative to wild type measurements. Although initially described to lack fast activation, \Kv displays prominent inactivation at physiologically relevant temperatures \citep{ranjan_kinetic_2019}. The effects of a mutation were also applied to \(\textrm{I}_{\textrm{A}}\) when present as both potassium currents display inactivation. In all cases, the mutation effects were applied to half of the \Kv or \(\textrm{I}_{\textrm{A}}\) under the assumption that the heterozygous mutation results in 50\% of channels carrying the mutation. Frequency-current curves for each mutation in each model were obtained through simulation and used to characterize firing behavior as described above. For each model the differences in mutation AUC to wild type AUC were normalized by wild type AUC (\ndAUC) and mutation rheobases were compared to wild type rheobase values (\drheo). Pairwise Kendall rank correlations (Kendall \(\tau\)) were used to compare the correlation in the effects of \Kv mutations on AUC and rheobase between models. \subsection*{Code Accessibility} -The code/software described in the paper is freely available online at [URL redacted for double-blind review]. The code is available as \Cref{code_zip}. +%The code/software described in the paper is freely available online at [URL redacted for double-blind review]. The code is available as \Cref{code_zip}. +The code/software described in the paper is freely available online at \newline \href{https://github.com/nkoch1/LOFGOF2023}{https://github.com/nkoch1/LOFGOF2023}. The code is available as \Cref{code_zip}. + % The type of computer and operating system on which the code was run to obtain the results in the manuscript must be stated in the Materials and Methods section.\\ @@ -267,7 +269,7 @@ Using these two measures we quantified the effects a changed property of an ioni \subsection*{Sensitivity Analysis} 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. -For example, when shifting the half activation voltage \(V_{1/2}\) of the delayed rectifier potassium current in the model G to more depolarized values, then the rheobase of the resulting fI curves shifted to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves was reduced (\(-\)\ndAUC), which resulted in a reduced firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in model C is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we got a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterized each of these curves by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient. A monotonically increasing curve resulted in a \( \text{Kendall} \ \tau \) close to \(+1\) a monotonously decreasing curve in \( \text{Kendall} \ \tau \approx -1 \), and a non-monotonous, non-linear relation in \( \text{Kendall} \ \tau \) close to zero (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C). +For example, when shifting the half activation voltage \(V_{1/2}\) of the delayed rectifier potassium current in the model G to more depolarized values, then the rheobase of the resulting fI curves shifted to lower currents \(-\)\drheo, making the neuron more sensitive to weak inputs, but at the same time the slope of the fI curves was reduced (\(-\)\ndAUC), which resulted in a reduced firing rate (\Cref{fig:AUC_correlation}~A). As a result the effect of a depolarizing shift in the delayed rectifier potassium current half activation \(V_{1/2}\) in model G is in the bottom left quadrant of \Cref{fig:firing_characterization}~B and characterization as LOF or GOF in excitability is not possible. Plotting the corresponding changes in AUC against the change in half activation potential \(V_{1/2}\) results in a monotonically falling curve (thick orange line in \Cref{fig:AUC_correlation}~B). For each of the many models we got a different relation between the changes in AUC and the shifts in half maximal potential \(V_{1/2}\) (thin lines in \Cref{fig:AUC_correlation}~B). To further summarize these different dependencies of the various models we characterized each of these curves by a single number, the \( \text{Kendall} \ \tau \) correlation coefficient. A monotonically increasing curve resulted in a \( \text{Kendall} \ \tau \) close to \(+1\) a monotonously decreasing curve in \( \text{Kendall} \ \tau \approx -1 \), and a non-monotonous, non-linear relation in \( \text{Kendall} \ \tau \) close to zero (compare lines in \Cref{fig:AUC_correlation}~B with dots in black box in panel C). Changes in gating half activation potential \(V_{1/2}\) and slope factor \(k\) as well as the maximum conductance \(g\) affected the AUC (\Cref{fig:AUC_correlation}), but how exactly the AUC was affected usually depended on the specific neuronal model. Increasing the slope factor of the \Kv activation curve for example increased the AUC in all models (\( \text{Kendall} \ \tau \approx +1\)), but with different slopes (\Cref{fig:AUC_correlation}~D,E,F). Similar consistent positive correlations could be found for shifts in A-current activation \(V_{1/2}\). Changes in \Kv half activation \(V_{1/2}\) and in maximal A-current conductance resulted in negative correlations with the AUC in all models (\( \text{Kendall} \ \tau \approx -1\)). @@ -286,7 +288,7 @@ Mutations in \textit{KCNA1} are associated with episodic ataxia type~1 (EA1) and To compare the effects of 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. Additionally, 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. \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}. Importantly, in cases when ion channel mutations alter rheobase and initial fI curve steepness 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. +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}. Importantly, in cases when ion channel mutations alter rheobase and initial fI curve steepness in ways that oppose effects on firing (upper left and bottom right quadrants of \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 cell's firing outcome. If it is in its excitable regime and only occasionally generates an action potential, then the effect on the rheobase is more important. If it is firing periodically with high rates, then the change in AUC might be more relevant. \subsection*{Modelling Limitations} The models used here are simple and 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. For exploring possible cell-type specific effects, variety in currents and dynamics across models is of utmost importance. With this context in mind, the collection of models used here are labelled as models A-L to highlight that the physiological cells they represent is not of chief concern, but rather that the collection of models with different attributes respond heterogeneously to the same perturbation. Additionally, the development of more realistic models is a high priority and will enable 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. @@ -374,7 +376,7 @@ Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occup \centering \includegraphics[width=\linewidth]{Figures/AUC_correlation.pdf} \linespread{1.}\selectfont - \caption[]{Effects of altered channel kinetics on AUC in various neuron models. The fI curves corresponding to shifts in model G delayed rectifier K half activation \(V_{1/2}\) (A), changes \Kv activation slope factor \(k\) in model G (D), and changes in maximal conductance of delayed rectifier K current in the model I (G) are shown. The fI curves from the smallest (grey) to the largest (black) alterations are seen for (A,D, and G) in accordance to the greyscale of 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. } + \caption[]{Effects of altered channel kinetics on AUC in various neuron models. The fI curves corresponding to shifts in model G delayed rectifier K half activation \(V_{1/2}\) (A), changes \Kv activation slope factor \(k\) in model G (D), and changes in maximal conductance of delayed rectifier K current in the model I (G) are shown. The fI curves from the smallest (grey) to the largest (black) alterations are seen for (A,D, and G) in accordance to the greyscale of the x-axis in B, E, and H. The \ndAUC of fI curves is plotted against delayed rectifier K half activation potential (\(\Delta V_{1/2}\); 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. } \label{fig:AUC_correlation} \end{figure} @@ -420,7 +422,7 @@ Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occup % \textit{A legend for the code file, labeled as “Extended Data 1,” should be at the end of the manuscript.\\} % The code files must be packaged into a single ZIP file, uploaded to the submission system as a “Multimedia/Extended Data” file type.} -\captionof{Extended Data}{Python code for simulations and analysis in zip file. Simulation code for each model, the sensitvity analysis of each model, the simulation of \textit{KCNA1} mutations in each model, and all analysis are provided herein.} +\captionof{Extended Data}{Python code for simulations and analysis in zip file. Simulation code for each model, the sensitivity analysis of each model, the simulation of \textit{KCNA1} mutations in each model, and all analysis are provided herein.} \label{code_zip} \end{document}