\documentclass[a4paper,12pt,pdftex]{exam}

\newcommand{\ptitle}{Activation curve}
\input{../header.tex}
\firstpagefooter{Supervisor: Lukas Sonnenberg}{}%
{email: lukas.sonnenberg@student.uni-tuebingen.de}

\begin{document}

\input{../instructions.tex}

Mutations in genes encoding ion channels can result in a variety of
neurological diseases like epilepsy, autism, or 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 (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
sodium channel, in particular 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}
  \question In the accompanying datasets you find recordings of both
  wildtype and A1622D transfected cells. The cells were all clamped to
  a holding potential of $-70$\,mV for some time to bring all ion
  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
  \code{steps} vector. The corresponding recorded current \code{I} (in
  pA) and time \code{t} (in ms) traces are also saved in the files.

  \begin{parts}
    \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}
      g_\text{Na}(V) = \frac{I_{peak}}{V - E_\text{Na}}
    \end{equation}

    \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}
      g_{Na}(V) = \frac{\bar g_\text{Na}}{1 + e^{ - \frac{V-V_{1/2}}{k}}}
    \end{equation} 
    to the activation curves. With $\bar g_\text{Na}$ being the
    maximum conductivity, $V_{1/2}$ the half activation voltage and
    $k$ 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{questions}

\end{document}