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\date{}
\title{Nils Koch}
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\begin{document}

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        \Huge \textbf{Update on Figures}}}\\ 
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\section*{Firing Characterization:}
\label{sec:orgefc49e8}
\subsection*{Question figure addresses:}
\label{sec:org08ca3c5}
Firing is a complicated phenomenon. How can it be simply characterized to compare the
effects of changes in current properties?

\subsection*{Method by which data is generated:}
\label{sec:org68edbd3}
Schematic diagram that does not contain underlying data - contains different square
root functions.

\subsection*{Conclusion from Figure:}
\label{sec:org320d05e}
Firing can be characterized by the rheobase and the AUC (proprotional to the increase in
firing after the rheobase). The rheobase and firing in a small range above it (AUC) are
likely important for determining network excitability (I think this makes sense,
would need references to support this).

\begin{figure}[H]
\includegraphics[align=c,width=10cm]{firing_characterization.pdf}
\caption{A. Demonstrates AUC in cyan. B. Demonstrates what combinations of increased and
decreased rheobase and AUC look like in terms of fI curves.}
\label{fig:firing_charact}
\end{figure}

\section*{Diversity in Model Firing:}
\label{sec:org411197c}
We have used a number of neuronal models that do not burst to look at the effects
of changes in current properties in firing given different cell types/current
environments

\subsection*{Question figure addresses:}
\label{sec:orge37c0bb}
Which model is used?
\subsection*{Rationale:}
\label{sec:orga9c3a57}
The effect of a change in a current property cannot be assessed in only one cell
type to understand the general effects of this change and to assess whether differences
occur across cell types.
\subsection*{Method by which data is generated:}
\label{sec:orga107703}
Models from different sources are used and an example spike train is shown for each model
along with a fI curve. The black dot on the fI curve indicates where the spike train is
taken from and the green and red dots indicate the current at which the first and last
spike occurs from an increasing and decreasing current ramp respectively. (These ramps
can be seen in the ramp figure at the end).
\subsection*{Conclusion from Figure:}
\label{sec:org8a15a73}
The models use are diverse and display a variety of spike shapes, firing behaviours, and
fI curve shapes.

\begin{figure}[H]
\includegraphics[align=c,width=18cm]{diversity_in_firing.pdf}
\caption{Spike trains and corresponding fI curves from: A. Cb stellate, B. RS Inhibitory,
C. FS, D. RS Pyramidal, E. RS Inhibitory +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\),
F. Cb stellate +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\), 
G. FS +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\),
H. RS Pyramidal +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\), I. STN +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\),
J.Cb stellate \(\Delta\)\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\) , K. STN \(\Delta\)\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\), L. STN,
where +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\) indicates the addition of Kv1.1 to the model
and \(\Delta\)\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\) indicates the exchange of the A type K+ current for Kv1.1. The black
dot on the fI curve indicates where the spike train is taken from and the green and red
dots indicate the current at which the first and last spike occurs from an increasing and
decreasing current ramp respectively.}
\label{fig:div_firing}
\end{figure}


\section*{Rheobase Sensitivity Analysis:}
\label{sec:org1e03320}
I am not yet happy with this figure's layout
\subsection*{Question figure addresses:}
\label{sec:org696855b}
How is rheobase affected by changes in current properties across models? Is the change
in rheobase always in the same direction across models?
\subsection*{Method by which data is generated:}
\label{sec:org09129b8}
A one factor at a time (OFAT) sensitivity analysis was performed on the currents common
to all or most models, where one current property was changed systematically at a time,
the firing responses simulated and the fI curves computed. From this fI curve the
largest injected current at which no firing occurs and the smallest injected
current at which firing occurs were obtained. This current interval was then simulated
to obtain the rheobase at greater resolution.
\subsection*{Conclusion from Figure:}
\label{sec:orga1ee38f}
Generally the effect on rheobase is similar across all models/current environments

\begin{figure}[H]
\includegraphics[align=c,width=18cm]{rheobase_correlation.pdf}
\caption{}
\label{fig:rheo}
\end{figure}

\section*{AUC Sensitivity Analysis:}
\label{sec:orgea61060}
I prefer the first layout
\subsection*{Question figure addresses:}
\label{sec:org73643ea}
How is AUC affected by changes in current properties across models? Is the change
in AUC rheobase always in the same direction across models?

\subsection*{Method by which data is generated:}
\label{sec:org4e1eb8f}
A one factor at a time (OFAT) sensitivity analysis was performed on the currents common
to all or most models, where one current property was changed systematically at a time,
the firing responses simulated and the steady-state fI curves computed. From this fI
curve the largest injected current at which no firing occurs was obtained and the
integral from this current using the composite trapezoidal rule for 1/5 of the current
range.

\subsection*{Conclusion from Figure:}
\label{sec:org8eb1892}
A given current property change does not necessarily cause the same
change in rheobase and as such the outcome of a given change is dependent on the
current environment or cell type.

\begin{figure}[H]
\includegraphics[align=c,width=18cm]{AUC_correlation.pdf}
\caption{}
\label{fig:AUC}
\end{figure}


\section*{Kv1.1 mutation simulation:}
\label{sec:org095a1ae}
\subsection*{Question figure addresses:}
\label{sec:org12e9ebc}
Do mutations of Kv1.1 cause similar effects on firing across cell types or is the effect
cell type (and thus neuronal network) dependent?
\subsection*{Method by which data is generated:}
\label{sec:org094b162}
Published Kv1.1 mutations (Lauxmann et al 2021) are simulated in all models containing
Kv1.1 or an inactivating K\^{}+ current by altering the current properties according to
those experimentally measured for each mutation. The firing of each model for each
mutation are then simulated and the rheobase and AUC are computed.
\subsection*{Conclusion from Figure:}
\label{sec:orgd0738e2}
The effects of Kv1.1 mutations on rheobase are highly correlated across models indicating
that these mutations affect the rheobase in a similar fashion. However, the effect of
Kv1.1 mutations vary across models as seen by the different correlation magnitudes
between models. Thus although these mutations affect rheobase in a similar manner, the
effect on AUC cannot easily be generalized and depends on cell type.

Furthermore, this Figure demonstrates why characterization of mutations in terms of
LOF or GOF in relation to firing overlooks potentially important characteristics of
the changes in firing seen in different cell types. Thus, the characterization LOF
and GOF is useful at a channel level to characterize the effects of a mutation on
the current, but cannot and should not be blindly extended to characterize the
effects of the mutation on firing as LOF and GOF, not only because the current
environment in which this mutation occurs is a key determinant of the firing outcome,
but also that firing is complex and not easily characterized as LOF or GOF.

\begin{figure}[H]
\includegraphics[align=c,width=18cm]{simulation_model_comparison.pdf}
\caption{}
\label{fig:kv11}
\end{figure}

\section*{Ramp Firing - For Supplements?:}
\label{sec:orge8a0957}
\subsection*{Question figure addresses:}
\label{sec:org46e89c4}
How does the firing of the models look like with a ramp protocol?
\subsection*{Method by which data is generated:}
\label{sec:org878a189}
A 4 second ramp with the same current range as the step currents used to obtain fI
plots is used and the firing of all models is simulated. The resulting spike trains
are plotted.
\subsection*{Conclusion from Figure:}
\label{sec:org22fe40d}
The diversity of firing seen with step currents is also seen with current ramps. The
ramps highlight the hysteresis in models.

\begin{figure}[H]
\includegraphics[align=c,width=20cm]{ramp_firing.pdf}
\caption{A. Cb stellate, B. RS Inhibitory,
C. FS, D. RS Pyramidal, E. RS Inhibitory +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\),
F. Cb stellate +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\), 
G. FS +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\),
H. RS Pyramidal +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\), I. STN +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\),
J.Cb stellate \(\Delta\)\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\) , K. STN \(\Delta\)\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\), L. STN,
where +\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\) indicates the addition of Kv1.1 to the model
and \(\Delta\)\(\mathrm{K}_{\mathrm{V}}\mathrm{1.1}\) indicates the exchange of the A type K+
current for Kv1.1.}
\label{fig:ramp}
\end{figure}
\end{document}
