Tuning tuning curves So far: Receptive fields Representation of - PowerPoint PPT Presentation

Tuning tuning curves So far: Receptive fields Representation of stimuli Population vectors Today: Contrast enhancment, cortical processing

90 o y N 3 N 4 s max (N 1 ) = 40 o Firing frequency N 5 N 2 N 1 s max (N 2 ) = 110 o 10 s max (N 3 ) = 135 o s max (N 4 ) = 180 o N 2 N 3 s max (N 5 ) = 230 o 0 45 90 135 180 225 270 369 N 1 180 o 0 o N 4 x N 5 s1 90 o 90 o y y N 2 +N 3 N 3 N 2 N 2 N 3 180 o 0 o 180 o 0 o x x

90 o y N 3 N 4 s max (N 1 ) = 40 o Firing frequency N 5 N 2 N 1 s max (N 2 ) = 110 o 10 s max (N 3 ) = 135 o s max (N 4 ) = 180 o N 2 N 3 s max (N 5 ) = 230 o 0 45 90 135 180 225 270 369 N 1 180 o 0 o N 4 x N 5 s1 90 o 90 o y y N 2 +N 3 N 3 N 2 N 2 N 3 Winner take all 180 o 0 o 180 o 0 o x x

In many sensory systems, the tuning curves of neurons are not identical to the receptive fields projected to these neurons by sensory neurons. They may be more narrow, include inhibitory parts of the curve, they may be wider or more separated from each other. There are a number of processes that “tune” tuning curves, these include interactions between neurons such as inhibition, excitation and feedback interactions. As we noted before, sensory receptive fields are often broad and relatively non-specific, for example frequency tuning curves in the auditory nerve can span a large range of frequencies.

100 Firing rate (Hz) 80 60 40 20 0 1 2 3 4 5 6 7 8 9 10 Stimulus Frequency (100 Hz) 100 Firing rate (Hz) 80 60 40 N1 = 20-50 = -30 (=0) 20 N2 = 50 – 20 – 10 = 20 N3 = 10-50 = -40 (=0) Stimulus 0 1 2 3 4 5 6 7 8 9 10 Frequency (100 Hz)

Exercise: Assuming linear interactions and all synaptic weights being zero, construct the approximate resulting receptive fields for these neurons and this network: Excitatory neurons N1, N2, N3 100 output frequency 80 N3 N2 60 N1 40 20 0 100 200 300 400 500 600 frequency for all neurons: x = in Inhibitory neurons I1, I2, I3 for all synapses: w=-1 100 output frequency 80 N3 N2 60 N1 40 20 0 100 200 300 400 500 600 frequency

Exercise: Look at the recordings below. Think about what you could learn from these and what additional information you would need to get useful information from this experiment. Firing rate Stimulus 1 Stimulus 2 Stimulus 2

Because of broad receptive fields and tuning curves, neural circuits are thought to enhance “contrast” or increase the difference between sensory stimuli in order to make them more easily recognizable, their features more salient, more distinguishable from each other. Exercise: (a) You have a number of chairs and a number of tables. List features these have in common. Now list features that differentiate them. Write a list of yes no questions that would allow you to decide (i) if an object does belong to either category and (ii) if it is a chair or a table. Now find some examples that would not easily be classified. Create a neural network with a layer of feature detectors (respond to a specific feature), a layer of inhibitory neurons and one or two more layers of neurons including a layer of output neurons. At the output, you want to know if the object you detect is a chair or a table. Think about which features you want to suppress (inhibit) and which you want to have compete against each other.

Exercise: (a) You have a number of chairs and a number of tables. List features these have in common. Now list features that differentiate them. Write a list of yes no questions that would allow you to decide (i) if an object does belong to either category and (ii) if it is a chair or a table. Now find some examples that would not easily be classified. Create a neural network with a layer of feature detectors (respond to a specific feature), a layer of inhibitory neurons and one or two more layers of neurons including a layer of output neurons. At the output, you want to know if the object you detect is a chair or a table. Think about which features you want to suppress (inhibit) and which you want to have compete against each other.

activity activity activity #of carbons #of carbons #of carbons U4 U4 U4 U4 U4 U4 (6)CHO (6)CHO (6)CHO (5)CHO (5)CHO (5)CHO (4)CHO (4)CHO (4)CHO U3 U3 U3 U3 U3 U3 U3 U3 U3 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U4 U3 U3 U3 U3 U3 (4)CHO (4)CHO U3 U3 U3 U3 U3 U3 U3 U3 U3 U3 U3 (5)CHO (5)CHO -(4)CHO -(4)CHO (5)CHO (5)CHO (5)CHO -(4)CHO -(4)CHO -(4)CHO (6)CHO (6)CHO -(5)CHO -(5)CHO (6)CHO (6)CHO (6)CHO -(5)CHO -(5)CHO -(5)CHO (4)CHO (4)CHO (4)CHO -(6)CHO -(6)CHO -(6)CHO (4)CHO-(6)CHO (4)CHO-(6)CHO = = = − − − 2 2 2 Distance: Distance: Distance: Dot product AB = A * B * cos( α ) Dot product AB = A * B * cos( α ) D D D ( ( ( U U U 3 3 3 U U U 4 4 4 ) ) ) (5)-(4) < (4) (5)-(4) < (4) -(5) < (5) -(5) < (5) -(6) -(6)

How to compare vectors

activity #of carbons U4 U4 (6)CHO U3 U3 U3 U4 U4 U4 U4 U4 U4 U3 U3 (4)CHO U3 U3 U3 U3 (5)CHO -(4)CHO (5)CHO -(4)CHO (6)CHO -(5)CHO (6)CHO -(5)CHO (4)CHO-(6)CHO (4)CHO -(6)CHO = − 2 Distance: Dot product AB = A * B * cos( α ) ( 3 4 ) D U U (5)-(4) < (4) -(5) < (5) -(6)

Exercise: What happens to the distance measure and dot product measure if the vectors are “normalized” first (this means they all have length 1.0 and span the unit circle).

Acetylcholine Noradrenaline Serontonine Dopamine Association cortex Peptides .... Secondary visual Secondary auditory Hippocampus cortex cortex Primary auditory Primary visual cortex Olfactory cortex cortex LGN in thalamus MGN in thalamus ? Other retinal neurons Brain stem neurons Olfactory bulb Photoreceptors in eye Auditory receptors in Olfactory receptors cochlea in nose

I. Molecular Layer I. Molecular Layer II. External Granular Layer II. External Granular Layer III. III. External Pyramidal Layer External Pyramidal Layer Line of Line of Kaes Kaes- -Bechterew Bechterew IV. IV. Internal Granular Layer Internal Granular Layer Outer band of Outer band of Baillarger Baillarger - Line of Line of Gennari Gennari in area 17 in area 17 - V. Internal Pyramidal Layer V. Internal Pyramidal Layer Giant pyramidal cell of Betz Giant pyramidal cell of Betz Inner Band of Baillarger Baillarger Inner Band of VI. VI. Polymorphic Layer Polymorphic Layer Golgi Nissl Weigert Golgi Nissl Weigert

Inputs Outputs

Cell body Pyramidal cell

Piriform cortex circuitry Afferent Input from OB mitral cells (LOT) afferent input from Ia olfactory bulb Ib association fibers from other pyramidal cells II cell body layer P P P deep interneurons P III output Association Fibers Haberly, L.B. Chem. Senses, 10: 219 -38 (1985)

Piriform cortex circuitry Afferent Input from OB mitral cells (LOT) afferent input from Ia olfactory bulb Ib association fibers from other pyramidal cells II cell body layer P P P deep interneurons P III output Association Fibers Haberly, L.B. Chem. Senses, 10: 219 -38 (1985)

Piriform cortex circuitry Afferent Input from OB mitral cells (LOT) afferent input from Feedforward FF Ia olfactory bulb interneurons Ib association fibers from other pyramidal cells II cell body layer P P P deep interneurons P FB III Feedback interneurons output Association Fibers Haberly, L.B. Chem. Senses, 10: 219 -38 (1985)

Piriform cortex circuitry Afferent Input from OB mitral cells (LOT) afferent input from Feedforward FF Ia olfactory bulb interneurons Ib association fibers from other pyramidal cells II cell body layer P P P deep interneurons P FB III Feedback interneurons output Association Fibers Haberly, L.B. Chem. Senses, 10: 219 -38 (1985) Neuromodulatory inputs Other association fiber inputs

Layer II (cell bodies) Layer Ib Layer Ia

Stimulus : citronellal activity pattern across mitral cells activity pattern acrosspyramidal cells

Stimulus : citronellal activity pattern across mitral cells feedforward inhibition activity pattern across pyramidal cells

Stimulus : citronellal activity pattern across mitral cells feedforward inhibition association fibers between pyramidal cells activity pattern across pyramidal cells

x sj = cos( α -offset j ) when cos( α -offsetj) >= θ and X sj = 0.0 when cos( α -offset j ) < θ where offset j = 0, -30, -60, -90 and -120. Sensory neurons Local interneurons Pyram idal cells α

I pj = x sj ; I ij = x sj x pj = I pj and x ij = I ij if I > θ and xpj = 0 and x ij = 0 if I < θ . Sensory neurons Local interneurons Pyram idal cells α