60 lines
2.7 KiB
TeX
60 lines
2.7 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Cellular properties}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
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{email: jan.grewe@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\section*{Estimating cellular properties of different cell types.}
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You will analyze data from intracellular \textit{in vitro} recordings
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of pyramidal neurons from two different maps of the electrosensory
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lateral line lobe (ELL) of the weakly electric fish
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\textit{Apteronotus leptorhynchus}. The membrane resistance and the
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membrane capacitance are fundamental properties of a neuron that have
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a great influence on the coding properties of the cell. They are
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typically estimated by injecting pulses of hyperpolarizing current
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into the cell. From the respective responses we can calculate the
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membrane resistance by applying Ohm's law ($U = R \cdot I$). To
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estimate the membrane capacitance we need to fit an exponential
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function of the form $y = a \cdot e^{(-x/\tau)}$ to the response to get the
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membrane time-constant $\tau$. With the knowledge of $R$ and $\tau$ we
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can estimate the capacitance $C$ from the simple relation $\tau = R
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\cdot C$.
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\begin{questions}
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\question{} The accompanying dataset (input\_resistance.zip)
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contains datasets from cells originating from two different parts of
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the ELL, the medial segment (MS) and the centro-medial segment
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(CMS). Each mat-file contains four variables. (i) \textit{V} the
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average membrane potential of 20 repeated current injections, (ii)
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\textit{V\_std} the across-trial standard deviation of the
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responses, (iii) \textit{t} a vector representing the recording
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time (in ms), and (iv) \textit{I} a vector containing the time-course of the
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injected current.
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\begin{parts}
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\part{} Create plots of the raw data. Plot the average response as
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a function of time. This plot should also show the across-trial
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variability. Also plot the time-course of the injected
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current. \\[0.5ex]
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\part{} Estimate the input resistances of each cell.\\[0.5ex]
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\part{} Fit an exponential to the initial few milliseconds of the
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current-on response. Use a gradient-descent approach to do
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this.\\ It is very important to understand the exponential decay
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function. If you are unsure, play with the function and understand
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how the parameters influence the decay. (Hint: It might be
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necessary to transform the data a bit.)\\[0.5ex]
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\part{} Estimate the membrane capacitance of each cell. Compare
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$R$, $I$ and $\tau$ between cells of the two segments.\\[0.5ex]
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\part{} Optional: use a double exponential and see, if the fit improves.
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\end{parts}
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\end{questions}
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\end{document}
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