79 lines
2.9 KiB
TeX
79 lines
2.9 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{f-I curves}
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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{Quantifying the responsiveness of a neuron using the f-I
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curve}
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The responsiveness of a neuron is often quantified using an $f$-$I$
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curve. The $f$-$I$ curve plots the \textbf{f}iring rate of the neuron
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as a function of the stimulus \textbf{I}ntensity.
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In the accompanying datasets you find the \textit{spike\_times} of an
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P-unit electroreceptor of the weakly electric fish \textit{Apteronotus
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leptorhynchus} to a stimulus of a certain intensity, i.e. the
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\textit{contrast}. The spike times are given in milliseconds relative
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to the stimulus onset.
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\begin{questions}
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\question Estimate the $f$-$I$-curve for the onset and the steady
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state response.
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\begin{parts}
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\part Estimate for each stimulus intensity the time course of the
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trial-averaged response (PSTH) and plot it. You will see that
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there are three parts: (i) The first 200\,ms is the baseline (no
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stimulus) activity. (ii) During the next 1000\,ms the stimulus was
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switched on. (iii) After stimulus offset the neuronal activity was
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recorded for further 825\,ms.
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\part Extract the neuron's activity (mean over trials and standard
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deviation) in 50\,ms time windows before stimulus onset (baseline
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activity), immediately after stimulus onset (onset response), and
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50\,ms before stimulus offset (steady state response).
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Plot the resulting $f$-$I$ curves by plotting the three computed
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firing rates against the corresponding stimulus intensities
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(contrasts).
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\end{parts}
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\question Fit a Boltzmann function to the onset and steady-state
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$f$-$I$-curves. The Boltzmann function is a sigmoidal function and
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is defined as
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\begin{equation}
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f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
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\end{equation}
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$x$ is the stimulus intensity, $\alpha$ is the starting firing rate,
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$\beta$ the saturation firing rate, $x_0$ defines the position of
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the sigmoid, and $k$ (together with $\alpha-\beta$) sets the slope.
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\begin{parts}
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\part Before you do the fitting, familiarize yourself with the
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four parameters of the Boltzmann function. What is its value for
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very large or very small stimulus intensities? How does the
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Boltzmann function change if you change the parameters?
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\part Can you get good initial estimates for the parameters?
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\part Do the fits and show the resulting Boltzmann functions
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together with the corresponding data.
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\part Use a statistical test to evaluate which of the onset and
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steady-state responses differ significantly from the baseline
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activity.
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\part Discuss you results with respect to encoding of different
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stimulus intensities.
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\end{parts}
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\end{questions}
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\end{document}
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