Final task
We will base our decision about your marks on your solutions of this task.
People who do not send me a solution of this task but who attended the course
regularly (at least 70% of the total course time), submitted several homework tasks
and discussed them in the seminar have the choice
 To get a letter of confirmation about their course attendance
 To get an “ausreichend” as grade that is send to the Prüfungsamt.
Rules:
 The final task has to be solved individually, not in groups.
 It is ok to use help from Wikipedia, the Matlab help etc, as long the Help does
not come from another course member, your big brother or is downloaded
from the internet.
 If you have questions please contact Sirko Straube (sirko.straube@unioldenburg.de), Julia Furche (julia.furche@mail.uni-oldenburg.de or me
(jutta.kretzberg@uni-oldenburg.de, Raum W4-0-078, Tel 798 3314)
 I will accept also incomplete solutions and descriptions of ways how to solve
the task. If you send me programs that do not work properly, please also
submit a description of what does work and what does not.
 Solutions must be send by email to me jutta.kretzberg@uni-oldenburg.de until
October 11, 2009. I will reconfirm by email when I receive your program.
 I will contact you when I am finished with reading, testing and comparing all
programs. If necessary, I will ask you to come to my office to discuss your
solution. (It might take some weeks until you hear from me.)
Criteria for giving marks:
 Completeness and correctness of the solution
 Amount of extensions
 Generality of the programs (applicable to other data sets)
 Documentation (comments, help texts, variable names…)
 “Elegance” of the solution (structure of the program in sub-programs, usage of
input and output arguments, loops vs. vecorized solutions…)
 Design of the user interface (user inputs, monitor outputs, figure labels…)
 Error tolerance (reaction to unwanted user inputs or input arguments)
Exam Task SS 2009
Your task is to program two methods for the analysis of neuronal data.
I would like to give you the advice to first solve the preparation exercises. They will
help you a lot when you try to solve the two main tasks. You should first program the
basic versions for both tasks and after that start to work on the extensions.
Background:
Neurons (nerve cells) transmit information via changes in their membrane voltage.
They communicate with each other by generating so-called action potentials (or
“spikes”). Spikes are fast, stereotypic changes of the membrane potential, which last
for approximately one millisecond. Since spikes of the same neuron always look very
similar, most people consider the exact shape of the spike to be irrelevant. It is only
relevant if a spike occurred or not.
One of the tasks of action potentials is to transfer information about visual
impressions (pictures) from the eye to the brain. Based on the action potential
sequences of many thousands of retinal ganglion cells the brain has to find out what
the picture that elicited these responses looked like. Our impression of what we (or
the laboratory animal) see originates from these signals.
In the neurosciences it is an important question how the brain solves this task: Which
features of the neural action potential sequences encode the stimulus? Most
neuroscientists assume from the fact that in particular the spike rate (the number of
the action potentials which appear in a period of certain length) plays an important
role for stimulus encoding. The goal is to find the relationship between a stimulus
parameter (in our case the velocity of a moving dot pattern) and the neural response,
measured as the number of spikes in a time window of certain length.
Data set:
The matrix [CellResp.mat] contains example data from a neurophysiological
experiment in which responses of retinal ganglion cells were measured. This data set
contains responses of 20 simultaneously recorded retinal ganglion cells. The
recording lasted for 180 seconds. The responses are stored in time bins of 1 ms.
Each element of the matrix contains one of two possible values: If CellResp(17,
3089) is equal to 1, neuron 17 has generated a spike in time step 3089. If it is equal
to 0 no spike was generated at this time. (You will see that the matrix contains more
0 than 1).
These neuronal responses were elicited by a moving dot pattern. This pattern moved
for 500 ms with a constant speed in the same direction. After this period it randomly
changed its speed and sometimes also its direction and stayed constant again for
500 ms. The movement had one of 9 different velocities: -2.5, - 1.875, -1.25, -0.625,
0, 0.625, 1.25, 1.875, 2.5 [mm/s]
The sign of the values indicates in which of two possible directions (left versus right)
the pattern moved. 0 means that the pattern was standing still for 500 ms. The
sequence of pattern velocities is stored in [StimVec.mat]. Each element of this vector
means that the pattern moved for 500 ms with this velocity, stimulating the 20
neurons contained in the data set.
Preparation tasks:
I would suggest that you practice to handle the data before you start to work on the
task. It is not so easy to take a look at the data because the data set is relatively big.
Practice by calculating:
a. How many spikes were generated in total by each of the neurons?
b. How many spikes were generated during the first 500 ms (during the
presentation of the first stimulus) by each of the neurons?
c. How many spikes did all neurons together generate during the first 500 ms?
d. Does the first 250 ms half of this time period contain more or less spikes than
the second half?
e. Use imagesc to take a look at the responses of all neurons during the first 500
ms. (Each spike appears as a red line on blue background.) Does the data
you see match the numbers you calculated before?
f. How many times was each of the 9 velocities presented to the retina?
g. Generate a vector that contains the stimulus velocity for each millisecond and
plot this vector. (How long does it have to be?) Also plot only the first 10
seconds of the stimulus velocity.
h. How many spikes were generated by neuron 3 when the stimulus velocity -2.5
was present for the first time?
i. How many spikes were generated by neuron 3 in response to each of
presentations of the stimulus velocity -2.5?
Task 1: Tuning curves
A tuning curve shows how the number of spikes a neuron generates depends on a
stimulus property. For our example we want to find out how the typical number of
spikes a neuron generates in 500 ms depends on the stimulus velocity.
Write a function that plots for one individual neuron the mean and the standard
deviation of the response spike counts versus the velocities of the stimulus pattern.
Task 2: Population responses
The population response is the average of the responses of all recorded neurons to a
stimulus. This type of analysis assumes that it is not important which neuron
generates which spike.
Write a program that calculates for each of the 500 ms long response sequences the
population average of the responses of all neurons. (You will obtain one number for
each 20x500 sub-matrix.) Plot the time sequence of the average responses.
(Remember to use adequate figure labels.)
Design your program in a flexible way, so that the user can choose the length of the
time window.
Possible extensions:
General:
a. Keep in mind that your programs should be written as general as possible.
You should be able to use them for a different data set with as few efforts as
possible. The next data set could contain a different number of cells, a
different stimulus sequence, or even stimuli of different length.
b. Design you programs in a user-friendly way. Think about the questions which
outputs could be interesting for the user and where the user should be able to
influence the calculations by providing input values.
c. Special additional task: If you have a lot of time and are interested in
programming in general, you could program a graphical user interface (GUI).
You will find a tutorial how to program GUIs in the Matlab help. (This task is
not easy and takes a lot of time. It is really meant as a special add-on, you do
not need to program a GUI to get top marks.)
Tuning curves:
d. Use your function to calculate a tuning curve of one neuron to calculate the
tuning curves for all neurons. Alternatively you could program a user dialogue
in which the user can choose which tuning curve to display.
e. Analyze the distributions of the spike numbers generated by the individual
cells in response to repeated identical stimulation. Would it be more useful to
calculate the median instead of the mean to generate the tuning curves of
these neurons?
f. Tuning can also be calculated for shorter response times than the full 500 ms
during which a neuron responds to a constant stimulus velocity. Generalize
your programs to make it possible to use shorter time windows (e.g. only the
first 100 ms after the stimulus changes). Is the tuning different for different
window lengths? Is it different if you use the last part of the responses (e.g.
the last 100 ms) before the stimulus changes again instead of using the first
part?
g. Use curve fitting to find functions, which describe the tuning curves you
calculated. Which polynome order is optimal to fit the tuning curves? What are
the differences between the polynomes you find?
h. ** The tuning curves can be grouped into two classes: neurons with
symmetrical tuning (approximately equal spike rates for stimulus movement in
both directions) and direction selective neurons (which respond with more
spikes to movement in one direction than in the other). Try to find a criterion
and an algorithm to separate the two classes automatically by assigning each
of the tuning curves to one of the classes.
Population responses:
i. Adjust your program to show on the x-axis of the plot the time in seconds.
Moreover make sure that you get average response vectors of equal lengths
independent of the time window used for averaging.
j. Systematically vary the length of the time window used for averaging. Do you
find a temporal structure also within the 500 ms long periods of constant
stimulus conditions? What is the shortest averaging time window for which this
method is still useful?
k. Use a relatively short averaging time window (e.g. 20 ms or 50 ms) to
calculate the time course of the average population responses of all cells in
response to all presentations of each of the 9 stimulus velocities.
l. ** Try to find an algorithm to use this mean time course for each of the 9
stimulus velocities to classify the population responses. Your task is the same
as the task of the brain: you have to estimate based on the population
response to a single presentation of a stimulus which of the stimuli it was. Do
some statistics how often your program estimates the correct stimulus.