76 lines
3.0 KiB
TeX
76 lines
3.0 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 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 as a
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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
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\textit{Apteronotus leptorhynchus} to a stimulus of a certain
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intensity, i.e. the \textit{contrast}. The spike times are given in
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milliseconds relative to the stimulus onset.
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\begin{questions}
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\question{Estimate the FI-curce for the onset and the steady state response.}
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\begin{parts}
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\part Estimate for each stimulus intensity the average response
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(PSTH) and plot it. You will see that there are three parts. (i)
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The first 200\,ms is the baseline (no stimulus) activity. (ii)
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During the next 1000\,ms the stimulus was switched on. (iii) After
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stimulus offset the neuronal activity was recorded for further
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825\,ms.
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\part Extract the neuron's activity in a 50\,ms time window immediately
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after stimulus onset (onset response) and 50\,ms before stimulus offset (steady state response).
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For each plot the resulting F-I curve by plotting the
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computed firing rates against the corresponding stimulus
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intensity, respectively the contrast.
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\end{parts}
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\question{} Fit a Boltzmann function to each of the F-I-curves. The
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Boltzmann function is a sigmoidal function and 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
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firing rate, $\beta$ the saturation firing rate, $x_0$ defines the
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position of the sigmoid, and $k$ (together with $\alpha-\beta$)
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sets the slope.
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\begin{parts}
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\part{} Before you do the fitting, familiarize yourself with the four
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parameters of the Boltzmann function. What is its value for very
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large or very small stimulus intensities? How does the Boltzmann
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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 together
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with the corresponding data.
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\part{} Illustrate how fit to the F-I curves changes during the fitting
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process. You can plot the parameters as a function fit iterations.
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Which parameter stay the same, which ones change with time?
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Support your conclusion with appropriate statistical tests.
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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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