Lecture 1: Neurons Lecture 2: Coding with spikes Lecture 3 ... · There will be a doodle-poll link posted to schedule meetings to talk about the assignment. Please fill in your available
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Lecture 1: Neurons
Lecture 2: Coding with spikes
Lecture 3: Tuning curves and receptive fields
Lecture 4: Population vectors
To gain a basic understanding of how population vectors are constructed
4 credit students:
First assignment is posted. You have one week to work on it. You can work in groups as long as all contribute and eachstudent submits its own write up.
There will be a doodle-poll link posted to schedule meetingsto talk about the assignment. Please fill in your available timesas soon as possible.
180o right
90o up
0o left
0 45 90 135 180 225 270 369
Firin
g fr
eque
ncy
Movement angle
“Best” angle for a given cell (angle smax that elicits maximal response rmax)
Vectors
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Firin
g fr
eque
ncy
Movement angle
20
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5
0
s0 s1 s2 s3 s4
smax = 135o
90o
x
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0o 180o
10 Hz
135o
s3
90o
x
y
0o 180o
10 Hz
135o
s2
90o
x
y
0o 180o
10 Hz
135o
s4
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Firin
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eque
ncy
N1 N2
N3 N4 N5
smax(N1) = 40o
smax(N2) = 110o
smax(N3) = 135o
smax(N4) = 180o
smax(N5) = 230o
s1 s3s2
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90o
x
y
0o 180oN1
N2 N3
N4
N5
90o
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0o 180o
N2 N3
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y
0o 180o
N2
N3
N2+N3
0 45 90 135 180 225 270 369
Firin
g fr
eque
ncy
N1 N2
N3N4 N5
smax(N1) = 40o
smax(N2) = 110o
smax(N3) = 135o
smax(N4) = 180o
smax(N5) = 230o
s1 s3s2
10
90o
x
y
0o 180o
N2
N3
90o
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0o 180o
N2
0 45 90 135 180 225 270 369
Firin
g fr
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ncy N1 N2
N3
N4 N5
s1 s3s2
10
Exercise: You recorded from three neurons during a monkey’s movement. You have approximated each response curve with a cosine function. Each neuron’s response is normalized to its OWN maximal response.
0.10.20.30.40.50.60.70.80.91.0
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Movement angle
Nor
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ized
firin
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A B C
0.10.20.30.40.50.60.70.80.91.0
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Movement angle
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firin
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A B C
You now use your recordings to predict what the monkey is going to do. The numbers I will give you will be in normalized firing rate. You record the following: A = 1.0, B = 0.0, C = 0.0. What is the best estimate for the angle of movement?
0.10.20.30.40.50.60.70.80.91.0
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Movement angle
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firin
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A B C
You record A = 0.9, B = 0.6. Use three different methods to estimate the angle of the movement from these numbers. Discuss which is best and why.
0.10.20.30.40.50.60.70.80.91.0
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Movement angle
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firin
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A B C
You record A=0, B = 0.6 and C = 0. What is your best estimate? How accurate do you think this could be?
0.10.20.30.40.50.60.70.80.91.0
0 20 40 60 80 100 120 140
Movement angle
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firin
g ra
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A B C
You notice that all your predictions are off by several degrees. State several reasons why this could be the case. How well would a labeled line vs population code decoding strategy work in this case? What would happen if you could increase the number of neurons by 100 fold?
R
G
B
Yellow light ~ 590 nm
nm425 525 625
Deuteranomaly, caused by a similar shift in the green retinal receptors, is by far the most common type of color vision deficiency, mildly affecting red–green hue discrimination in 5% of males. It is hereditary and sex-linked.
R
G
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Yellow light ~ 590 nm
nm425 525 625
nm425 525 625
R
G
Bangle is close
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B
Red light ~ 625 nm
nm425 525 625
nm425 525 625
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G
B
Angle is changed, color perception changes
J. E. LewisSensory processing and the network mechanismsfor reading neuronal population codes
a, Schematic of the local bend network that processes the location S of a touch stimulus to produce a bend directed away from the touch. The network is contained in a single segmental ganglion of the leech nervous system. There are three layers of neurons in the network. The number of neurons at sensory and motor levels is indicated by the number of circles. The exact number of interneurons is not known, although 17 have been identified so far8. b, The tuning properties of the mechanosensory P neurons to stimulus location. Shown are curves fitted to data described in Lewis9 and given by Pi(S) = F(cos(S - Pi
*)) where S is the stimulus location, Pi(S) is the normalized spike count, F(x) = 0 for x 0 and F(x) = x for x > 0. The perimeter of the cross-sectional body wall is roughly circular. We define a location = 0° as the dorsal midline, = 180° = -180° as the ventral midline and = -90° and = 90° as the left and right lateral midlines, respectively. c, To emphasize the directionality of the neural responses and to allow comparison with the behavioural responses discussed later, the same P neuron tuning curves are expressed in a polar coordinate system. The Pi
*are the stimulus locations where the peak response occurs (that is, preferred locations). Pi
* = (45°,135°,-135°,-45°) for i = (1,...,4).
In all panels, solid lines drawn in the polar coordinate system are unit vectors (directed toward the origin) corresponding to the bend direction. Dotted lines correspond to the mean bend direction. a, The responses to a touch stimulus at S = 45° (denoted by the arrow). b, The responses to intracellular current injection in the P2 neuron (denoted by the icon). c, The responses elicited by simultaneous delivery of both stimuli. The data shown are from 15–16 trials in four animals.
a, Summary of the errors produced by the model for different numbers of interneurons (NI) and noise levels, k. Also shown for reference are the experimentally measured behaviouralerror (dotted line) and the P neuron decoding error (solid line). The filled circles show the results for zero noise level (k = 0). b, The minimum number of interneurons (NI) required so that the model is more accurate than the experimentally observed behaviour. Minimum NI increases almost linearly with the noise level. c, The responses of the model (NI = 16) for 20 trials at a stimulus location of S = 90° (compare with Fig. 2c).
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