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[project] fixes to input resistance project

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Jan Grewe 2017-01-22 13:55:59 +01:00
parent 19f25248ae
commit 90cae6c018
1 changed files with 18 additions and 13 deletions
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projects/project_input_resistance/input_resistance.tex
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@ -30,18 +30,20 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section*{Estimating cellular properties of different cell types.}
You will analyse data from intracellular \texit{in vitro} recordings
You will analyze data from intracellular \textit{in vitro} recordings
of pyramidal neurons from two different maps of the electrosensory
lateral line lobe (ELL) of the weakly electric fish
\textit{Apteronotus leptorhynchus}. The resistance and capacitance of
the membrane are typically estimated by injecting hyperpolarizing
current pulses into the cell. From the respective responses we can
calculate the membrane resistance by applying Ohm's law ($U = R \cdot
I$). To estimate the membrane capacitance we need to fit an
exponential function $y = a \cdot e^{(b \cdot x)}$to the response to
get the membrane time-constant $\tau$. With the knowledge of $R$ and
$\tau$ we can estimate the capacitance $C$ from the simple relation
$\tau = R \cdot C$.
\textit{Apteronotus leptorhynchus}. The membrane resistance and the
membrane capacitance are fundamental properties of a neuron that have
a great influence on the coding properties of the cell. They are
typically estimated by injecting pulses of hyperpolarizing current
into the cell. From the respective responses we can calculate the
membrane resistance by applying Ohm's law ($U = R \cdot I$). To
estimate the membrane capacitance we need to fit an exponential
function of the form $y = a \cdot e^{(-x/\tau)}$ to the response to get the
membrane time-constant $\tau$. With the knowledge of $R$ and $\tau$ we
can estimate the capacitance $C$ from the simple relation $\tau = R
\cdot C$.
\begin{questions}
\question{} The accompanying dataset (input\_resistance.zip)
@ -59,13 +61,16 @@ $\tau = R \cdot C$.
a function of time. This plot should also show the across-trial
variability. Also plot the time-course of the injected
current. \\[0.5ex]
\part{} Estimate the imput resistances of each cell.\\[0.5ex]
\part{} Estimate the input resistances of each cell.\\[0.5ex]
\part{} Fit an exponential to the initial few milliseconds of the
current-on response. Use a gradient-descent approach to do
this.\\[0.5ex]
this.\\ It is very important to understand the exponential decay
function. If you are unsure, play with the function and understand
how the parameters influence the decay. (Hint: It might be
necessary to transform the data a bit.)\\[0.5ex]
\part{} Estimate the membrane capacitance of each cell. Compare
$R$, $I$ and $\tau$ between cells of the two segments.\\[0.5ex]
\part{} Optional: use a double exponential and see, if the fit gets better.
\part{} Optional: use a double exponential and see, if the fit improves.
\end{parts}
\end{questions}