diff --git a/manuscript.tex b/manuscript.tex index 5f0bddf..007f317 100644 --- a/manuscript.tex +++ b/manuscript.tex @@ -165,7 +165,7 @@ Ion channels determine neuronal excitability and mutations that alter ion channe \par\null -\section*{Introduction (750 Words Maximum - Currently 675)} +\section*{Introduction (750 Words Maximum - Currently 689)} %\textit{The Introduction should briefly indicate the objectives of the study and provide enough background information to clarify why the study was undertaken and what hypotheses were tested.} Voltage-gated ion channels are vital in determining neuronal excitability, action potential generation and firing patterns \citep{bernard_channelopathies_2008, carbone_ion_2020}. In particular, the properties and combinations of ion channels and their resulting currents determine the firing properties of a neuron \citep{rutecki_neuronal_1992, pospischil_minimal_2008}. However, ion channel function can be disturbed, resulting in altered ionic current properties and altered neuronal firing behaviour \citep{carbone_ion_2020}. Ion channel mutations are a common cause of such channelopathies and are often associated with hereditary clinical disorders including ataxias, epilepsies, pain disorders, dyskinesias, intellectual disabilities, myotonias, and periodic paralyses among others \citep{bernard_channelopathies_2008, carbone_ion_2020}. @@ -229,6 +229,9 @@ All modelling and simulation was done in parallel with custom written Python 3.8 \end{equation} with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2}\)), exponent \(j\), and persistent current \(0 \leq a \leq 1\) were fitted to the original formulism for RS pyramidal, 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 \citep{lauxmann_therapeutic_2021}. +\notenk{add this?} + \textcolor{red}{Each of the original single-compartment models used here can reproduce physiological firing behaviour 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. } + \input{g_table} @@ -241,14 +244,16 @@ with slope \(k\), voltage for half-maximal activation or inactivation (\(V_{1/2} 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. To obtain the rheobase, the current step interval preceding the occurrence of action potentials was explored at higher resolution with 100 current steps spanning the interval. 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. - - All models exhibit tonic firing and any instances of bursting were excluded to simplify the characterization of firing. Firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis. \notenk{This last sentence moved here from discussion} + All models exhibit tonic firing and any instances of bursting were excluded to simplify the characterization of firing. Firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis. \subsection*{Sensitivity Analysis and Comparison of Models} % Sensitivity analyses enable investigation into how different sources of uncertainty in a model result in uncertainty in model outputs \citep{saltelli_sensitivity_2002} and provide information on the relative impact of model inputs \citep{saltelli_why_2019}. We recently used a one-factor-at-a-time (OFAT) sensitivity analysis approach to evaluate the relative impacts of currents on neuronal firing and developed a scoring system for SCN8A mutations that correlated (p = 0.0077, r = 0.64) with the clinical severity of epilepsy in patients with these mutations \citep{johannesen_genotype-phenotype_2021}. This was done in an isolated neuronal model and suggests that even with disregard of network level effects of mutations, the single cell level outcomes of mutations are relevant to disease phenotypes. OFAT sensitivity analyses indicate which factors have or do not have influence, with uninfluential factors never detected as relevant \citep{saltelli_how_2010}. OFAT sensitivity analyses can be used to screen factors that are influential on model outcomes and provide a mechanism by which factors and their relative influence can be easily identified and used in predictive applications. - Properties of ionic currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{\textrm{Leak}}\)) were systematically altered in a one-factor-at-a-time sensitivity analysis for all models. The gating curves for each current were shifted (\(\Delta V_{1/2}\)) from -10 to 10\,mV in increments of 1\,mV. The voltage dependence of the time constant associated with the shifted gating curve was correspondingly shifted. The slope (\(k\)) of the gating curves were altered from half to twice the initial slope. Similarly, the maximal current conductance (\(g\)) was also scaled from half to twice the initial value. For both slope and conductance alterations, alterations consisted of 21 steps spaced equally on a \(\textrm{log}_2\) scale. + Properties of ionic currents common to all models (\(\textrm{I}_{\textrm{Na}}\), \(\textrm{I}_{\textrm{K}}\), \(\textrm{I}_{\textrm{A}}\)/\IKv, and \(\textrm{I}_{\textrm{Leak}}\)) were systematically altered in a one-factor-at-a-time sensitivity analysis for all models. The gating curves for each current were shifted (\(\Delta V_{1/2}\)) from -10 to 10\,mV in increments of 1\,mV. The voltage dependence of the time constant associated with the shifted gating curve was correspondingly shifted. The slope (\(k\)) of the gating curves were altered from half to twice the initial slope. Similarly, the maximal current conductance (\(g\)) was also scaled from half to twice the initial value. For both slope and conductance alterations, alterations consisted of 21 steps spaced equally on a \(\textrm{log}_2\) scale.\textcolor{red}{We neglect of altered time constants for the practical reason that estimation and assessment of time constants and changes to them is not straightforward \citep{Clerx2019, Whittaker2020}.} + + +%Although a number of methods have been used to fit ionic currents including different approaches in estimate time constants either from summary data or from full current traces, and are limited by the available data \citep{Clerx2019, Whittaker2020}. On one hand, specialized equipment and great experimental care is often required to estimate time constants \citep{Whittaker2020}. As a result summary data is often not recorded for voltage ranges in which time constants are fast. On the other hand, lack of availability of full current traces for each mutation limits the alternative current trace fitting approach. For these practical reasons, we neglect the effect of mutation altered time constants despite acknowledging that time constant changes are likely important in determining the outcome of a given mutation on firing.} \subsection*{Model Comparison} Changes in rheobase (\drheo) are calculated in relation to the original model rheobase. The contrast of each AUC value (\(AUC_i\)) was computed in comparison to the AUC of the unaltered wild type model (\(AUC_{wt}\)) @@ -285,7 +290,7 @@ To examine the role of cell-type specific ionic current environments on the impa \end{figure} \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 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 have 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). 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}). \notejb{No bifurcations: How about this?} \notenk{I like it!} Different types of the underlying voltage and gating 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 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 have 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). 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 the underlying voltage and gating dynamics are known to generate these different firing types and hysteresis \cite{ERMENTROUT2002, ermentrout_type_1996, Izhikevich2006}. \subsection*{Characterization of Neuronal Firing Properties} \begin{figure}[tp] @@ -299,7 +304,8 @@ Changes in firing as characterized by \(\Delta\)AUC and \(\Delta\)rheobase occup \label{fig:firing_characterization} \end{figure} -Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between 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). \notenk{This enables a AUC measurement independent from rheobase.}\notejb{I added a few words to the next sentence. Would this be enough or should we make it more explicit by an extra sentence als Nils suggests it?} \notenk{I think that this is enough - we can always expand if a reviewer asks} The characterization of firing by 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. +Neuronal firing is a complex phenomenon and a quantification of firing properties is required for comparisons across cell types and between 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 firing by 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. +%\notenk{This enables a AUC measurement independent from rheobase.}\notejb{I added a few words to the next sentence. Would this be enough or should we make it more explicit by an extra sentence als Nils suggests it?} \notenk{I think that this is enough - we can always expand if a reviewer asks} 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 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, 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 occasionaly 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. @@ -357,10 +363,10 @@ Mutations in \Kv are associated with episodic ataxia type~1 (EA1) and have been \end{figure} -\section*{Discussion (3000 Words Maximum - Currently 2145)} +\section*{Discussion (3000 Words Maximum - Currently 1871)} % \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.}\\ -\notels{change AUC to "fI-AUC" or "AUC of the fI-curve"} +\notels{change AUC to "fI-AUC" or "AUC of the fI-curve"} \notenk{Done for Discussion, not sure if this makes sense to do in the results as well} To compare the effects of changes to properties of ionic currents on neuronal firing of different neuron types, a diverse set of conductance-based models were simulated. Changes to single ionic current properties, as well as known episodic ataxia type~1 associated \Kv mutations showed consistent effects on the rheobase across cell types, whereas the effects on AUC of the steady-state fI-curve depend on cell type. Our results demonstrate that LOF and GOF on the biophysical level cannot be uniquely transfered to the level of neuronal firing. The effects depend on the properties of the other currents expressed in a cell and are therefore depending on cell type. @@ -368,65 +374,24 @@ To compare the effects of changes to properties of ionic currents on neuronal fi %Using a set of diverse conductance-based neuronal models, the effects of changes to properties of ionic currents on neuronal firing were determined to be heterogenous for the AUC of the steady state fI curve but more homogenous for rheobase. For a known channelopathy, episodic ataxia type~1 associated \Kv mutations, the effects on rheobase are consistent across model cell types, whereas the effects on AUC depend on cell type. Our results demonstrate that LOF and GOF on the biophysical level cannot be uniquely transfered to the level of neuronal firing. The effects depend on the properties of the other currents expressed in a cell and are therefore depending on cell type. \subsection*{Neuronal Diversity} -\notejb{Before we start questioning our models we should have a paragraph pointing out that neurons are diverse and differ in their ion channel composition. Cite for example those recent Nature/Science papers where Phillip Berens is part of on neuron types in cerebellum. Thomas Euler Retina ganglien cell types. Then the paper defining Regular/fast spiking interneurons. And many more... like Eve Marder as you have it in a paragraph further down.}\\ -\notenk{Added this section - it needs more work, but what do you think of the direction I'm going?} \notenk{Also I'm not sure which regular/fast spiking interneuron paper you mean}\\ +%\notejb{Before we start questioning our models we should have a paragraph pointing out that neurons are diverse and differ in their ion channel composition. Cite for example those recent Nature/Science papers where Phillip Berens is part of on neuron types in cerebellum. Thomas Euler Retina ganglien cell types. Then the paper defining Regular/fast spiking interneurons. And many more... like Eve Marder as you have it in a paragraph further down.}\\ +%\notenk{Added this section - it needs more work, but what do you think of the direction I'm going?} \notenk{Also I'm not sure which regular/fast spiking interneuron paper you mean}\\ Advances in high-throughput techniques have enable 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 \citep{Huang2019} and interneruons \citep{Laturnus2020}, cerebellum \citep{Kozareva2021}, spinal cord \citep{Alkaslasi2021}, visual cortex \citep{Gouwens2019} as well as the retina \citep{Baden2016, Voigt2019, Berens2017, Yan2020a, Yan2020b}. % Functional differences: reg/fat spiking, Ephys, models Diversity across neurons is not limited to gene expression and can also be seen electrophysiologically \citep{Tripathy2017, Gouwens2018, Tripathy2015, Scala2021, Cadwell2020, Gouwens2019, Baden2016, Berens2017} with correlations existing between gene expression and electrophysiological properties \citep{Tripathy2017}. At the ion channel level, diversity exists not only between the specific ion channels cell types express but heterogeneity also exists in ion channel expression levels within cell types \citep{marder_multiple_2011, goaillard_ion_2021,barreiro_-current_2012}. As ion channel properties and expression levels are key determinents of neuronal dynamics and firing \citep{Balachandar2018, Gu2014, Zeberg2015, Aarhem2007, Qi2013, Gu2014a, Zeberg2010, Zhou2020, Kispersky2012} neurons with different ion channel properties and expression levels display different firing properties. -Taken together, 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. +Taken together, 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. \notels{with our models we tried to get this diversity and it's relevant} +To capture the diversity in neuronal ion channel expression and its relevance in the outcome of ion channel mutations, multiple neuronal models with different ionic currents and underlying firing dynamics are used here. - - - -\subsection*{Validity of Neuronal Models} -\notels{should we move this to a less prominent position? How much of this part could be counted as common knowledge and be left out?, for example model complexity in terms of currents and compartments, I just think that this part might be too harsh on the models, even if the criticism doesn't apply for the main points of the paper} -\notenk{I think a large part of this section, although highlighting the problems with the models, helps make the case that there is a vast amount of complexity and heterogeneity not just in what we show with the models, but also unaccounted for by the models. That is to say that we are in a sense underestimating the amount of variability in responses of different cells to the same mutation. Perhaps it would be good to change this section to emphasize that perspective?} - - - -\notejb{The following three paragraphs are rather technical and if possible should be shorter.}\\ \notenk{shortened single vs multicompartment model paragraphs. We could remove the \Kv paragraph I've shortened - see below}\\ -Our findings are based on simulations of a range of single-compartment conductance-based models. Single-compartment models do not take into consideration differential effects on neuronal compartments (i.e. axon, soma, dendrites), possible different spatial cellular distribution of channel expression across and within these neuronal compartments. More realistic models are more computationally expensive, and require knowledge of the distribution of conductances across the cell. However, each of the single-compartment models used here can reproduce physiological firing behaviour 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. -%Many aspects of these models can be questioned. -\notels{in a few sentences in the methods} - -%\notenk{We could remove this paragraph about \Kv} -%The \Kv model from \cite{ranjan_kinetic_2019} is based on expression of only \Kv in CHO cells and simplifies the complex reality of these channels \textit{in vivo} including their function as heteromers, and dynamic modulation and regulation \citep{wang__1999, roeper_nip_1998, coleman_subunit_1999, ruppersberg_heteromultimeric_1990, isacoff_evidence_1990, rettig_inactivation_1994, shi_efficacy_2016, campomanes_kv_2002, manganas_identification_2001, jonas_regulation_1996, stuhmer_molecular_1989, glasscock_kv11_2019, xu_kv2_1997, ranjan_kinetic_2019}. - - - - -%\notejb{If this could be enriched with some citations than fine. Otherwise move this as a half sentence into methods/results} \notenk{moved steady-state firing characterization to methods} -%The firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis. These could be seen as further dimensions to analyze the influence of mutations on neuronal firing and can only increase the uncertainty of these estimations. - -%Despite all these shortcomings of the models we used in our simulations, they do not touch our main conclusion that the quantitative as well as qualitative effects of a given ionic current variant in general depend on the specific properties of all the other ionic currents expressed in a given cell. \subsection*{Ionic Current Environments Determine the Effect of Ion Channel Mutations} -\notenk{We could add a brief discussion somewhere in this section about time constants and why we neglect them despite likely being important in determining the outcome of a mutation.} \notejb{If we have citations for the time constant issue then yes, do it.}\\ -\notenk{I'm not sure I like the section I wrote here. I would tend towards leaving it out.} -Although a number of methods have been used to fit ionic currents including different approaches in estimate time constants either from summary data or from full current traces, and are limited by the available data \citep{Clerx2019, Whittaker2020}. On one hand, specialized equipment and great experimental care is often required to estimate time constants \citep{Whittaker2020}. As a result summary data is often not recorded for voltage ranges in which time constants are fast. On the other hand, lack of availability of full current traces for each mutation limits the alternative current trace fitting approach. -For these practical reasons, we neglect the effect of mutation altered time constants despite acknowledging that time constant changes are likely important in determining the outcome of a given mutation on firing. +Although, to our knowledge, no comprehensive evaluation of how ionic current environment and cell type affect the outcome of ion channel mutations, comparisons between the effects of such mutations in certain cells have been reported. For instance, mutations in the SCN1A gene encoding \(\textrm{Na}_{\textrm{V}}\textrm{1.1}\) result in epileptic phenotypes by selective hypoexcitability of inhibitory but not excitatory neurons in the cortex resulting in circuit hyperexcitability \citep{Hedrich14874}. In CA3 of the hippocampus, mutation of \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) similarly results in increased excitability of pyramidal neurons and decreased 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 \(\textrm{Na}_\textrm{V}\textrm{1.8}\) \citep{Waxman2007, Rush2006}. In a modelling study, it was found that altering the sodium conductance in 2 stomatogastric ganglion neuron models from a population models decreases rheobase in both models, however the initial slope of the fI curves (proportional to AUC of the fI-curve) is increased in one model and decreased in the other suggesting that the magnitude of other currents in these models (such as \(\textrm{K}_\textrm{d}\)) determines the effect of a change in sodium current \citep{Kispersky2012}. 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. -\notejb{Too technical, shorter! These aspects do not questions our result.} \notenk{Made a little shorter} -%One-factor-at-a-time (OFAT) sensitivity analyses such as the one performed here are predicated on assumptions of model linearity, and cannot account for interactions between factors \citep{czitrom_one-factor-at--time_1999, saltelli_how_2010}. OFAT approaches are local and not global (i.e. always in reference to a baseline point in the parameter space) and therefore cannot be generalized to the global parameter space unless linearity is met \citep{saltelli_how_2010}. -The local current parameter space around the wild type neuron is explored here with a one-factor-at-a-time (OFAT) sensitivity analysis without taking interactions between parameters into account. Comparisons between the effects of changes in similar parameters across different models can be made at the wild type locale indicative of experimentally observed neuronal behaviour. In this case, the role of deviations in the ionic current properties from their wild type in multiple neuronal models presented here provides a starting point for understanding the general role of these current properties in neurons. However, a more global approach would provide a more holistic understanding of the parameter space and provide insight into interactions between properties. \notels{methods: time constants are difficult to obtain (clerx et al 2019), therefore we ignore them} - - \notels{we measured OFAT, and it would only get more complicated, if we would look at interactions} - -\notejb{Too technical, shorter! These aspects do not questions our result.} \notenk{Tried to shorten, not sure about it...} -%Characterization of the effects of a parameter on firing with non-parametric Kendall \(\tau\) correlations takes into account the sign and monotonicity of the correlation. In other words Kendall \(\tau\) coefficients provide information as to whether changing a parameter is positively or negatively correlated with AUC or rheobase as well as the extent to which this correlation is positive or negative across the parameter range examined. -Kendall \(\tau\) coefficients provide general information as to whether different models exhibit positive or negative correlation of AUC or rheobase to a change in a given current property, however more nuanced difference between the sensitivities of models to current property changes, such which models show faster/slower increases/decreases in firing properties in response to a given current property change are not included in our analysis. \notels{formulate more understandable} -% The inter-model differences seen with the OFAT sensitivity analysis highlight the need for cell specific models. The observed dependence of neuronal firing on voltage-gated sodium channels and delayed-rectifier potassium channels is known \citep{verma_computational_2020, arhem_channel_2006} and substantiated by OFAT analysis across models. It is suggested that variability in these currents may underlie within cell population variability in neuronal firing behaviour \citep{verma_computational_2020}. Although increases in low-voltage activated inward currents are generally accepted to increase firing rates and outward currents to decrease firing rates \citep{nowacki_sensitivity_2011}, this was not always observed in AUC. The heterogeneity in outcomes of model OFAT analysis, especialy with AUC, suggest that the effects of changes in current properties are neuronal dependent and the current environment encompassing the relative conductances, gating \(V_{1/2}\) positions, and gating slopes of other currents plays an important role in modulating firing behaviour and in determining the outcome of a current property change such as a mutation. - -\notejb{Super important paragraph!} \notels{move to top of paragraph} -Although, to our knowledge, no comprehensive evaluation of how ionic current environment and cell type affect the outcome of ion channel mutations, comparisons between the effects of such mutations in certain cells have been reported. For instance, mutations in the SCN1A gene encoding \(\textrm{Na}_{\textrm{V}}\textrm{1.1}\) result in epileptic phenotypes by selective hypoexcitability of inhibitory but not excitatory neurons in the cortex resulting in circuit hyperexcitability \citep{Hedrich14874}. In CA3 of the hippocampus, mutation of \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) similarly results in increased excitability of pyramidal neurons and decreased 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 \(\textrm{Na}_\textrm{V}\textrm{1.8}\) \citep{Waxman2007, Rush2006}. In a modelling study, it was found that altering the sodium conductance in 2 stomatogastric ganglion neuron models from a population models decreases rheobase in both models, however the initial slope of the fI curves (proportional to AUC) is increased in one model and decreased in the other suggesting that the magnitude of other currents in these models (such as \(\textrm{K}_\textrm{d}\)) determines the effect of a change in sodium current \citep{Kispersky2012}. 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. - -\notejb{Also important, also see my comment at the beginning of the Discussion} 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 behaviour of a heterogeneous neuron population \citep{verma_computational_2020}. For example, a model derived from the mean conductances in a sub-population of stomatogastric ganglion "one-spike bursting" neurons fires 3 spikes instead of 1 per burst due to an L shaped distribution of sodium and potassium conductances \citep{golowasch_failure_2002}. Multiple sets of current 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}. Variability in ion channel expression often correlates with the expression of other ion channels \citep{goaillard_ion_2021} and neurons whose behaviour is similar may possess correlated variability across different ion channels resulting in stability in neuronal phenotype \citep{lamb_correlated_2013, soofi_co-variation_2012, taylor_how_2009}. @@ -438,20 +403,62 @@ The variability of ion currents and degeneracy of neurons may account, at least %in excitability seen are in line with both score-based and simulation-based predictions %of the outcomes of KCNA1 mutations. -Moderate changes in delayed rectifier potassium currents change the bifurcation structure \notels{firing dynamics} of Hodgkin Huxley model, analogous to those seen in \Kv mutations, result in reduced thresholds for repetitive firing and thus contribute to increased excitability \citep{hafez_altered_2020} \notejb{I do not get this first sentence. Where are the bifurcations (citation?) and why is the increased excitatbility a bifurcation?} \notenk{I have tried to fix this section to make it more understandable. The bifurcations change by changing the delayed rectifier in the HH model and as a result of that there is a lower threshold for tonic firing. This lower threshold is what they (Hafez and Gottschalk) use to say that excitability has changed.}. Although the Hodgkin Huxley delayed rectifier lacks inactivation, the increases in excitability seen by \citet{hafez_altered_2020}\notejb{seen where? Here in this manuscript or in which citation?} are in line with our simulation-based predictions of the outcomes of \Kv mutations \notejb{our simulations?}\notenk{Yes}. -LOF KCNA1 mutations generally increase neuronal excitability, however the varying susceptibility on rheobase and different effects on AUC of KCNA1 mutations across models are indicative that a certain cell type specific complexity exists. +Changes in delayed rectifier potassium currents, analogous to those seen in \Kv 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 seen by \citet{hafez_altered_2020} are in line with our simulation-based predictions of the outcomes of \Kv mutations. +LOF 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. %LOF KCNA1 mutations generally increase neuronal excitability, however the different effects of KCNA1 mutations across models on AUC 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 KCNA1 mutations. Contrary to these results, \citet{zhao_common_2020} predicted \textit{in silico} that the depolarizing shifts seen as a result of 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. -Different current properties, such as the difference in \(\textrm{I}_\textrm{A}\) and \IKv in the Cb stellate and STN model families alter the impact of KCNA1 mutations on firing highlighting that knowledge of the biophysical properties of a current and its neuronal expression is vital for holistic understanding of the effects of a given ion channel mutation both at a single cell and network level. \notels{our data show} +In our simulations, different current properties alter the impact of KCNA1 mutations on firing in our simulations as evident in the differences seen in the impact of \(\textrm{I}_\textrm{A}\) and \IKv in the Cb stellate and STN model families on KCNA1 mutation firing. This highlights that knowledge of the biophysical properties of a current and its neuronal expression is vital for holistic understanding of the effects of a given ion channel mutation both at a single cell and network level. \subsection*{Loss or Gain of Function Characterizations Do Not Fully Capture Ion Channel Mutation Effects on Firing} -The effects of changes in current properties depend in part on the neuronal model in which they occur and can be seen in the variance of correlations (especially in AUC) across models for a given current property change. Therefore, relative conductances and gating properties of currents in the ionic current environment in which an alteration in current properties occurs plays an important role in determining the outcome on firing. The use of loss of function (LOF) and gain of function (GOF) is useful at the level of ion channels and whether a mutation results in more or less ionic current, however the extension of this thinking onto whether mutations induce LOF or GOF at the level of neuronal firing based on the ionic current LOF/GOF is problematic due to the dependency of neuronal firing changes on the ionic current environment. Thus the direct leap from current level LOF/GOF characterizations to effects on firing without experimental or modelling-based evidence, although tempting, should be refrained from and viewed with caution when reported. This is especially relevant in the recent development of personalized medicine for channelopathies, where a patients specific channelopathy is identified and used to tailor treatments \citep{Weber2017, Ackerman2013, Helbig2020, Gnecchi2021, Musto2020, Brunklaus2022}. However, the effects of specific ion channel mutations are often characterized in expression systems and classified as LOF or GOF to aid in treatment decisions \citep{johannesen_genotype-phenotype_2021, Brunklaus2022, Musto2020}. Interestingly, both LOF and GOF \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) mutations can benefit from treatment with sodium channel blockers \citep{johannesen_genotype-phenotype_2021}, suggesting that the relationship between effects at the level of ion channels and effects at the level of firing and therapeutics is not linear or evident without further contextual information. Therefore, this approach must be used with caution and the cell type which expressed the mutant ion channel must be taken into account. Experimental assessment of the effects of a patient's specific ion channel mutation \textit{in vivo} is not feasible at a large scale due to time and cost constraints, modelling of the effects of patient specific channelopathies is a desirable approach. -Accordingly, for accurate modelling and predictions of the effects of mutations on neuronal firing, information as to the type of neurons containing the affected channel, and the properties of the affected and all currents in the affected neuronal type is needed. When modelling approaches are sought out to overcome the limitations of experimental approaches, care must be taken to account for model dependency and the generation of relevant cell-type or cell specific populations of models should be standard in assessing the effects of mutations in specific neurons. +The effects of changes in current properties depend in part on the neuronal model in which they occur and can be seen in the variance of correlations (especially in AUC of the fI-curve) across models for a given current property change. Therefore, relative conductances and gating properties of currents in the ionic current environment in which an alteration in current properties occurs plays an important role in determining the outcome on firing. The use of loss of function (LOF) and gain of function (GOF) is useful at the level of ion channels and whether a mutation results in more or less ionic current, however the extension of this thinking onto whether mutations induce LOF or GOF at the level of neuronal firing based on the ionic current LOF/GOF is problematic due to the dependency of neuronal firing changes on the ionic current environment. Thus the direct leap from current level LOF/GOF characterizations to effects on firing without experimental or modelling-based evidence, although tempting, should be refrained from and viewed with caution when reported. This is especially relevant in the recent development of personalized medicine for channelopathies, where a patients specific channelopathy is identified and used to tailor treatments \citep{Weber2017, Ackerman2013, Helbig2020, Gnecchi2021, Musto2020, Brunklaus2022}. However, the effects of specific ion channel mutations are often characterized in expression systems and classified as LOF or GOF to aid in treatment decisions \citep{johannesen_genotype-phenotype_2021, Brunklaus2022, Musto2020}. Interestingly, both LOF and GOF \(\textrm{Na}_{\textrm{V}}\textrm{1.6}\) mutations can benefit from treatment with sodium channel blockers \citep{johannesen_genotype-phenotype_2021}, suggesting that the relationship between effects at the level of ion channels and effects at the level of firing and therapeutics is not linear or evident without further contextual information. Therefore, this approach should be used with caution and the cell type which expressed the mutant ion channel may provide valuable insight into the functional consequences of an ion channel mutation. Where experimental assessment of the effects of a patient's specific ion channel mutation \textit{in vivo} is not feasible at a large scale, modelling approaches investigating the effects of patient specific channelopathies provides an alternative bridge between characterization of changes in biophysical properties of ionic currents and the firing consequences of these effects. In both experimental and modelling investigation of firing level effects of channelopathies cell-type dependency should be considered. + +%Accordingly, for accurate modelling and predictions of the effects of mutations on neuronal firing, information as to the type of neurons containing the affected channel, and the properties of the affected and all currents in the affected neuronal type is needed. When modelling approaches are sought out to overcome the limitations of experimental approaches, care must be taken to account for model dependency and the generation of relevant cell-type or cell specific populations of models should be standard in assessing the effects of mutations in specific neurons. \notels{move small sentences down here} \notels{Conclusion, ionic current composition defines how changes in ionic current properties affect neurons, personalized medicin could benefit from simulations of simulating cell types} +The effects of altered ion channel properties on firing is generally influenced by the other ionic currents 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. 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. + + + +% +%\subsection*{Validity of Neuronal Models} +% +%\notejb{The following three paragraphs are rather technical and if possible should be shorter.}\\ \notenk{shortened single vs multicompartment model paragraphs. We could remove the \Kv paragraph I've shortened - see below}\\ +%Our findings are based on simulations of a range of single-compartment conductance-based models. Single-compartment models do not take into consideration differential effects on neuronal compartments (i.e. axon, soma, dendrites), possible different spatial cellular distribution of channel expression across and within these neuronal compartments. More realistic models are more computationally expensive, and require knowledge of the distribution of conductances across the cell. However, each of the single-compartment models used here can reproduce physiological firing behaviour 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. +%%Many aspects of these models can be questioned. +%\notels{in a few sentences in the methods} +% +%%\notenk{We could remove this paragraph about \Kv} +%The \Kv model from \cite{ranjan_kinetic_2019} is based on expression of only \Kv in CHO cells and simplifies the complex reality of these channels \textit{in vivo} including their function as heteromers, and dynamic modulation and regulation \citep{wang__1999, roeper_nip_1998, coleman_subunit_1999, ruppersberg_heteromultimeric_1990, isacoff_evidence_1990, rettig_inactivation_1994, shi_efficacy_2016, campomanes_kv_2002, manganas_identification_2001, jonas_regulation_1996, stuhmer_molecular_1989, glasscock_kv11_2019, xu_kv2_1997, ranjan_kinetic_2019}. + + + + +%\notejb{If this could be enriched with some citations than fine. Otherwise move this as a half sentence into methods/results} \notenk{moved steady-state firing characterization to methods} +%The firing characterization was performed on steady-state firing and as such adaptation processes are neglected in our analysis. These could be seen as further dimensions to analyze the influence of mutations on neuronal firing and can only increase the uncertainty of these estimations. + +%Despite all these shortcomings of the models we used in our simulations, they do not touch our main conclusion that the quantitative as well as qualitative effects of a given ionic current variant in general depend on the specific properties of all the other ionic currents expressed in a given cell. + +%%\notenk{We could add a brief discussion somewhere in this section about time constants and why we neglect them despite likely being important in determining the outcome of a mutation.} \notejb{If we have citations for the time constant issue then yes, do it.}\\ +%%\notenk{I'm not sure I like the section I wrote here. I would tend towards leaving it out.} +%%Although a number of methods have been used to fit ionic currents including different approaches in estimate time constants either from summary data or from full current traces, and are limited by the available data \citep{Clerx2019, Whittaker2020}. On one hand, specialized equipment and great experimental care is often required to estimate time constants \citep{Whittaker2020}. As a result summary data is often not recorded for voltage ranges in which time constants are fast. On the other hand, lack of availability of full current traces for each mutation limits the alternative current trace fitting approach. +%%For these practical reasons, we neglect the effect of mutation altered time constants despite acknowledging that time constant changes are likely important in determining the outcome of a given mutation on firing. +%% +%% +%%\notejb{Too technical, shorter! These aspects do not questions our result.} \notenk{Made a little shorter} +%%One-factor-at-a-time (OFAT) sensitivity analyses such as the one performed here are predicated on assumptions of model linearity, and cannot account for interactions between factors \citep{czitrom_one-factor-at--time_1999, saltelli_how_2010}. OFAT approaches are local and not global (i.e. always in reference to a baseline point in the parameter space) and therefore cannot be generalized to the global parameter space unless linearity is met \citep{saltelli_how_2010}. +%%The local current parameter space around the wild type neuron is explored here with a one-factor-at-a-time (OFAT) sensitivity analysis without taking interactions between parameters into account. Comparisons between the effects of changes in similar parameters across different models can be made at the wild type locale indicative of experimentally observed neuronal behaviour. In this case, the role of deviations in the ionic current properties from their wild type in multiple neuronal models presented here provides a starting point for understanding the general role of these current properties in neurons. However, a more global approach would provide a more holistic understanding of the parameter space and provide insight into interactions between properties. \notels{methods: time constants are difficult to obtain (clerx et al 2019), therefore we ignore them} +%% +%% \notels{we measured OFAT, and it would only get more complicated, if we would look at interactions} +%% +%%\notejb{Too technical, shorter! These aspects do not questions our result.} \notenk{Tried to shorten, not sure about it...} +%%Characterization of the effects of a parameter on firing with non-parametric Kendall \(\tau\) correlations takes into account the sign and monotonicity of the correlation. In other words Kendall \(\tau\) coefficients provide information as to whether changing a parameter is positively or negatively correlated with AUC or rheobase as well as the extent to which this correlation is positive or negative across the parameter range examined. +%%Kendall \(\tau\) coefficients provide general information as to whether different models exhibit positive or negative correlation of AUC or rheobase to a change in a given current property, however more nuanced difference between the sensitivities of models to current property changes, such which models show faster/slower increases/decreases in firing properties in response to a given current property change are not included in our analysis. \notels{formulate more understandable} +%% The inter-model differences seen with the OFAT sensitivity analysis highlight the need for cell specific models. The observed dependence of neuronal firing on voltage-gated sodium channels and delayed-rectifier potassium channels is known \citep{verma_computational_2020, arhem_channel_2006} and substantiated by OFAT analysis across models. It is suggested that variability in these currents may underlie within cell population variability in neuronal firing behaviour \citep{verma_computational_2020}. Although increases in low-voltage activated inward currents are generally accepted to increase firing rates and outward currents to decrease firing rates \citep{nowacki_sensitivity_2011}, this was not always observed in AUC. The heterogeneity in outcomes of model OFAT analysis, especialy with AUC, suggest that the effects of changes in current properties are neuronal dependent and the current environment encompassing the relative conductances, gating \(V_{1/2}\) positions, and gating slopes of other currents plays an important role in modulating firing behaviour and in determining the outcome of a current property change such as a mutation. + + \par\null