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#+TITLE: Nils Koch
#+DATE: <2021-08-16 Mon>
#+EMAIL: nils.koch@mail.mcgill.ca
#+TAGS: noexport(n)
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#+BEGIN_EXPORT latex
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        \Huge \textbf{Update on Figures}}}\\ 
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* Firing Characterization:
** Question figure addresses:
   Firing is a complicated phenomenon. How can it be simply characterized to compare the
   effects of changes in current properties?

** Method by which data is generated:
   Schematic diagram that does not contain underlying data - contains different square
   root functions.

** Conclusion from Figure:
   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_EXPORT latex
\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}
#+END_EXPORT

* Diversity in Model Firing:
   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

** Question figure addresses:
   Which model is used?
** Rationale:
   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.
** Method by which data is generated:
   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).
** Conclusion from Figure:
   The models use are diverse and display a variety of spike shapes, firing behaviours, and
   fI curve shapes.

#+BEGIN_EXPORT latex
\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}
#+END_EXPORT


* IB model issue:                                                  :noexport:
** Issue Background:
   IB (intrinsicially bursting) model from Pospischil et al. 2008 uses a leak conductance
   of 0.1. This results in bursting like firing initially (see bottom right of Figure
   \ref{fig:IB}) and requires large currents to be injected (> 0.75 nA). When the Kv1.1
   current is added to this model (bottom right Figure \ref{fig:IB}) the bursting
   behaviour is diminished but the currents needed to get firing are still high. As a
   result I decreased the leak conductance by a factor of 10 to 0.01 as seen in the
   upper right of Figure \ref{fig:IB}. This is the model that I used for the sensitivity
   analysis and modelling of Kv1.1 mutations. However, when the original IB model has a
   reduced leak current (of 0.01) it bursts and only for a small current range (see upper
   left of Figure \ref{fig:IB}).
** Issue:
   Which model to use? To use the model with reduced leak that has nice properties with
   Kv1.1 added, the bursting and weird fI curve of the model without Kv1.1 needs to be
   addressed (bursting is not well captured by the analysis methods). To use the model with
   the large leak current (the original model), the large input currents is concerning and
   the sensitivity analysis and Kv1.1 mutation modelling would need to be re-done for this
   model with and without Kv1.1 (with 20/24 cores on the Kraken this would take 2-3 days
   I think). Alternatively, as neither option really sits well with me, we could remove this
   model from all figure and discussion and focus on the other models that in their
   original states (and with Kv1.1 added) have repetitive firing without bursting.
#+BEGIN_EXPORT latex
\begin{figure}[H]
\includegraphics[align=c,width=15cm]{IB_issue_plot.pdf}
\caption{The fI curves and exampling spike trains from the IB model with different
Leak conductances without and with (+Kv1.1) Kv1.1 conductance.}
\label{fig:IB}
\end{figure}
#+END_EXPORT

* Rheobase Sensitivity Analysis:
  I am not yet happy with this figure's layout
** Question figure addresses:
   How is rheobase affected by changes in current properties across models? Is the change
   in rheobase always in the same direction across models?
** Method by which data is generated:
   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.
** Conclusion from Figure:
   Generally the effect on rheobase is similar across all models/current environments

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

* AUC Sensitivity Analysis:
  I prefer the first layout
** Question figure addresses:
   How is AUC affected by changes in current properties across models? Is the change
   in AUC rheobase always in the same direction across models?

** Method by which data is generated:
   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.

** Conclusion from Figure:
   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_EXPORT latex
\begin{figure}[H]
\includegraphics[align=c,width=18cm]{AUC_correlation.pdf}
\caption{}
\label{fig:AUC}
\end{figure}
#+END_EXPORT


* Kv1.1 mutation simulation:
** Question figure addresses:
   Do mutations of Kv1.1 cause similar effects on firing across cell types or is the effect
   cell type (and thus neuronal network) dependent?
** Method by which data is generated:
   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.
** Conclusion from Figure:
   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_EXPORT latex
\begin{figure}[H]
\includegraphics[align=c,width=18cm]{simulation_model_comparison.pdf}
\caption{}
\label{fig:kv11}
\end{figure}
#+END_EXPORT

* Ramp Firing - For Supplements?:
** Question figure addresses:
   How does the firing of the models look like with a ramp protocol?
** Method by which data is generated:
   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.
** Conclusion from Figure:
   The diversity of firing seen with step currents is also seen with current ramps. The
   ramps highlight the hysteresis in models.
  
#+BEGIN_EXPORT latex
\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_EXPORT