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projects/project_ficurves/ficurves.tex
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@ -11,33 +11,37 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
\section{Quantifying the responsiveness of a neuron by its F-I curves} \section{Quantifying the responsiveness of a neuron using the F-I curve}
The responsiveness of a neuron is often quantified using an F-I The responsiveness of a neuron is often quantified using an F-I
curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a
function of the stimulus \textbf{I}ntensity. function of the stimulus \textbf{I}ntensity.
In the accompanying datasets you find the \textit{spike\_times} of an
P-unit electroreceptor of the weakly electric fish
\textit{Apteronotus leptorhynchus} to a stimulus of a certain
intensity, i.e. the \textit{contrast}. The spike times are given in
milliseconds relative to the stimulus onset.
\begin{questions} \begin{questions}
\question In the accompanying datasets you find the \question{Estimate the FI-curce for the onset and the steady state response.}
\textit{spike\_times} of an P-unit electroreceptor of the weakly
electric fish \textit{Apteronotus leptorhynchus} to a stimulus of a
certain intensity, i.e. the \textit{contrast}. The spike times are
given in milliseconds relative to the stimulus onset.
\begin{parts} \begin{parts}
\part For each stimulus intensity estimate the average response \part Estimate for each stimulus intensity the average response
(PSTH) and plot it. You will see that there are three parts. (i) (PSTH) and plot it. You will see that there are three parts. (i)
The first 200\,ms is the baseline (no stimulus) activity. (ii) The first 200\,ms is the baseline (no stimulus) activity. (ii)
During the next 1000\,ms the stimulus was switched on. (iii) After During the next 1000\,ms the stimulus was switched on. (iii) After
stimulus offset the neuronal activity was recorded for further stimulus offset the neuronal activity was recorded for further
825\,ms. 825\,ms.
\part Extract the neuron's activity for every 50\,ms after \part Extract the neuron's activity in a 50\,ms time window immediately
stimulus onset and for one 50\,ms slice before stimulus onset. after stimulus onset (onset response) and 50\,ms before stimulus offset (steady state response).
For each time slice plot the resulting F-I curve by plotting the For each plot the resulting F-I curve by plotting the
computed firing rates against the corresponding stimulus computed firing rates against the corresponding stimulus
intensity, respectively the contrast. intensity, respectively the contrast.
\part Fit a Boltzmann function to each of the F-I-curves. The \end{parts}
\question{} Fit a Boltzmann function to each of the F-I-curves. The
Boltzmann function is a sigmoidal function and is defined as Boltzmann function is a sigmoidal function and is defined as
\begin{equation} \begin{equation}
f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; . f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; .
@ -47,26 +51,24 @@ function of the stimulus \textbf{I}ntensity.
position of the sigmoid, and $k$ (together with $\alpha-\beta$) position of the sigmoid, and $k$ (together with $\alpha-\beta$)
sets the slope. sets the slope.
Before you do the fitting, familiarize yourself with the four \begin{parts}
parameter of the Boltzmann function. What is its value for very \part{} Before you do the fitting, familiarize yourself with the four
large or very small stimulus intensities? How does the Boltzmann parameters of the Boltzmann function. What is its value for very
function change if you change either of the parameter? large or very small stimulus intensities? How does the Boltzmann
function change if you change the parameters?
How could you get good initial estimates for the parameter?
Do the fits and show the resulting Boltzmann functions together
with the corresponding data.
\part Illustrate how the F-I curves change in time also by means \part{} Can you get good initial estimates for the parameters?
of the parameter you obtained from the fits with the Boltzmann \part{} Do the fits and show the resulting Boltzmann functions together
function. with the corresponding data.
Which parameter stay the same, which ones change with time? \part{} Illustrate how fit to the F-I curves changes during the fitting
process. You can plot the parameters as a function fit iterations.
Which parameter stay the same, which ones change with time?
Support your conclusion with appropriate statistical tests. Support your conclusion with appropriate statistical tests.
\part Discuss you results with respect to encoding of different \part{} Discuss you results with respect to encoding of different
stimulus intensities. stimulus intensities.
\end{parts} \end{parts}
\end{questions} \end{questions}