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[activation curve] adapted notation

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projects/project_activation_curve/activation_curve.tex
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Estimation of the activation curve} \section{Estimation of activation curves of sodium channels}
Mutations in genes, encoding for ion channels, can result in a variety of neurological diseases like epilepsy, autism and intellectual disability. One way to find a possible treatment is to compare the voltage dependent kinetics of the mutated channel with its corresponding wild-type. These kinetics are described in voltage-clamp experiments and the subsequent data analysis. Mutations in genes encoding ion channels can result in a variety of
neurological diseases like epilepsy, autism, or intellectual
In this task you will compute and compare the activation curves of the Nav1.6 wild-type channel and a variation named A1622D (the amino acid Alanine (A) at the 1622nd position is replaced by Aspartic acid (D)) that causes intellectual disability in humans. disability. One way to find a possible treatment is to compare the
voltage dependent kinetics of the mutated channel with its
corresponding wild-type (non-mutated channel). Voltage-clamp
experiments are used to measure and describe the kinetics.
In the project you will compute and compare the activation curves of
the Nav1.6 wild-type (WT) channel and the A1622D mutation (the amino
acid Alanine (A) at the 1622nd position is replaced by Aspartic acid
(D)) that causes intellectual disability in humans.
\begin{questions} \begin{questions}
\question In the accompanying datasets you find recordings of cells with WT or A1622D transfections. The cells were all clamped to -70mV for some time to bring all ion channels in the same closed states. They are activated by a step change in the command voltage to a value described in the "steps" vector. The corresponding recorded current (in pA) and time (in ms) traces are also saved in the files. \question In the accompanying datasets you find recordings of both
wildtype and A1622D transfected cells. The cells were all clamped to
\begin{parts} a holding potential of $-70$\,mV for some time to bring all ion
\part Plot the current traces of a WT and a A1622D cell. Because the number of transfected channels can vary the peak values have little value. Normalize the curves accordingly (what kind of normalization would be appropriate?). Can you already spot differences between the cells? channels in the same closed states. Then the channels were activated
by a step change in the command voltage to a value described in the
\part \textbf{IV curve}: Find the peak values for each voltage step and plot them against the steps. \code{steps} vector. The corresponding recorded current \code{I} (in
pA) and time \code{t} (in ms) traces are also saved in the files.
\part \textbf{Reversal potential}: Use the IV-curve to estimate the reversal potential of the sodium current. Consider a linear interpolation to increase the accuracy of your estimation.
\begin{parts}
\part \textbf{Activation curve}: The activation curve is a representation of the voltage dependence of the sodium conductivity. It is computed with a variation of Ohm's law: \part Plot all the current traces of a single WT and a single
A1622D cell in two plots. Because the number of transfected
channels can vary the peak values have little value. Normalize the
curves accordingly (what kind of normalization would be
appropriate?). Can you already spot differences between the cells?
\part \textbf{I-V curve}: Find the peak values (minimum or maximum)
for each voltage step and plot them against the steps.
\part \textbf{Reversal potential}: Use the $I$-$V$-curve to
estimate the reversal potential $E_\text{Na}$ of the sodium
current. Consider a linear interpolation to increase the accuracy
of your estimation.
\part \textbf{Activation curve}: The activation curve is a
representation of the voltage dependence of the sodium
conductivity. It is computed with a variation of Ohm's law:
\begin{equation} \begin{equation}
g_{Na}(V) = \frac{I_{peak}}{V - V_{reversal}} g_\text{Na}(V) = \frac{I_{peak}}{V - E_\text{Na}}
\end{equation} \end{equation}
\part \textbf{Compare the two variants}: To compare WT and A1622D activation curves you should first parameterise your data. Fit a sigmoid curve \part \textbf{Comparison of the two ion channel types}: To compare
WT and A1622D activation curves you should first parameterize your
data. Fit a sigmoidal function
\begin{equation} \begin{equation}
g_{Na}(V) = g_{max,Na} / ( 1 + e^{ - \frac{V-V_{1/2}}{k}} ) g_{Na}(V) = \frac{\bar g_\text{Na}}{1 + e^{ - \frac{V-V_{1/2}}{k}}}
\end{equation} \end{equation}
to the activation curves. With $g_{max,Na}$ being the maximum conductivity, $V_{1/2}$ the half activation voltage and $k$ a slope factor. Now you can compare the two variants with a few simple parameters. What do the differences mean? to the activation curves. With $\bar g_\text{Na}$ being the
maximum conductivity, $V_{1/2}$ the half activation voltage and
\part \textbf{BONUS question}: Take a good look at your raw data. What other differences can you see? How could you analyse these? $k$ a slope factor (how these parameters influence the
curve?). Now you can compare the two variants with three simple
parameters. What do the differences mean? Which differences are
statistically significant?
\part \textbf{BONUS question}: Take a closer look at your raw
data. What other differences can you see between the two types of
sodium currents? How could you analyze these?
\end{parts} \end{parts}
\end{questions} \end{questions}