108 lines
4.2 KiB
TeX
108 lines
4.2 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{Neural tuning and noise}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Benda}{}{email: jan.benda@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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You are recording the activity of neurons that differ in the strength
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of their intrinsic noise in response to constant stimuli of intensity
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$I$ (think of that, for example, as a current $I$ injected via a
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patch-electrode into the neuron).
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We first characterize the neurons by their tuning curves (also called
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intensity-response curves). That is, what is the mean firing rate of
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the neuron's response as a function of the constant input current $I$?
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In the second part we demonstrate how intrinsic noise can be useful
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for encoding stimuli on the example of the so called ``subthreshold
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stochastic resonance''.
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The neuron is implemented in the file \texttt{lifspikes.m}. Call it
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with the following parameters:\\[-7ex]
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\begin{lstlisting}
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trials = 10;
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tmax = 50.0;
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current = 10.0; % the constant input current I
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Dnoise = 1.0; % noise strength
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spikes = lifspikes(trials, current, tmax, Dnoise);
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\end{lstlisting}
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The returned \texttt{spikes} is a cell array with \texttt{trials}
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elements, each being a vector of spike times (in seconds) computed for
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a duration of \texttt{tmax} seconds. The input current is set via the
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\texttt{current} variable, the strength of the intrinsic noise via
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\texttt{Dnoise}. If \texttt{current} is a single number, then an input
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current of that intensity is simulated for \texttt{tmax}
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seconds. Alternatively, \texttt{current} can be a vector containing an
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input current that changes in time. In this case, \texttt{tmax} is
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ignored, and you have to provide a value for the input current for
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every 0.0001\,seconds.
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Think of calling the \texttt{lifspikes()} function as a simple way of
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doing an electrophysiological experiment. You are presenting a
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stimulus with a constant intensity $I$ that you set. The neuron
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responds to this stimulus, and you record this response. After
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detecting the timepoints of the spikes in your recordings you get what
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the \texttt{lifspikes()} function returns. In addition you can record
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from different neurons with different noise properties by setting the
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\texttt{Dnoise} parameter to different values.
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\begin{questions}
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\question Tuning curves
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\begin{parts}
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\part First set the noise \texttt{Dnoise=0} (no noise). Compute
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and plot the neuron's $f$-$I$ curve, i.e. the mean firing rate
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(number of spikes within the recording time \texttt{tmax} divided
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by \texttt{tmax} and averaged over trials) as a function of the
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input current for inputs ranging from 0 to 20.
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How are different stimulus intensities encoded by the firing rate
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of this neuron?
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\part Compute the $f$-$I$ curves of neurons with various noise
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strengths \texttt{Dnoise}. Use for example $D_{noise} = 10^{-3}$,
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$10^{-2}$, and $10^{-1}$. Depending on the resulting curves you
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might want to try additional noise levels.
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How does the intrinsic noise level influence the tuning curves?
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What are possible sources of this intrinsic noise?
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\part Show spike raster plots and interspike interval histograms
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of the responses for some interesting values of the input and the
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noise strength. For example, you might want to compare the
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responses of the different neurons to the same input, or by the
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same resulting mean firing rate.
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How do the responses differ?
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\end{parts}
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\question Subthreshold stochastic resonance
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Let's now use a 1\,s long sine wave $I(t) = I_0 + A \sin(2\pi f t)$
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with offset current $I_0$, amplitude $A$, and frequency $f$. Set
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$I_0=5$, $A=4$, and $f=5$\,Hz as an input to the neuron.
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\begin{parts}
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\part Do you get a response of the noiseless ($D_{noise}=0$) neuron?
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\part What happens if you increase the noise strength?
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\part What happens at really large noise strengths?
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\part Generate some example plots that illustrate your findings.
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\part Explain the encoding of the sine wave based on your findings
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regarding the $f$-$I$ curves.
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\part Why is this phenomenon called ``subthreshold stochastic resonance''?
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\end{parts}
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\end{questions}
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\end{document}
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