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Computational cognitive neuroscience:

4. Synaptic Plasticity

Lubica Beňušková

Centre for Cognitive Science, FMFI Comenius University in Bratislava

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Learning and the brain plasticity

• Synaptic plasticity underlies the brain plasticity, which is a lifelong ability of the brain to reorganize neural circuits based on new experience.

• Organism's ability to store, retain, and subsequently recall information is called a memory.

• The process of acquisition of memories is called learning.

• We distinguish short-term and long-term memory, which are based on short-term and long-term synaptic plasticity, respectively:

– Long-term strengthening of synapses is called long-term potentiation (LTP)

– Long-term weakening of synapses is called long-term depression (LTD)

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“We are what we can remember”

• We have several types of memory (short-term, long-term, explicit,

implicit, working, etc.). All are based on changes in synaptic weights.

• It is widely accepted that long-term memories of all kinds are stored in

the brain in the patterns of synaptic weights in the relevant brain areas

(i.e. cortex, hippocampus, cerebellum, etc.).

• Do all different brain areas posses the same ability of plastic synaptic

changes throughout the whole life?

• It turns out that the so-called primary sensory areas exhibit synaptic

plasticity only during the so-called critical periods of time after birth

whereas associative areas of the cortex are plastic all the time.

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Synaptic plasticity models

• Developmental plasticity during the critical period in V1

─ Normal rearing: both eyes receive normal visual stimuli

─ binocular deprivation : both eyes are closed (sutured)

─ monocular deprivation: one eye is closed (sutured)

─ Reverse suture: after suturing one eye for some time, it is opened and the

previously opened one is sutured.

• Bienenstock, Cooper and Munro (BCM) theory

─ Application to visual cortex V1

─ Experimental support

• BCM theory and the STDP (Spike-timing dependent plasticity)

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Primate visual system

• Visual signals travel from neurons in the eye retina through the optic nerve to

the LGN (lateral geniculate nucleus) in the thalamus and from there to the

primary visual cortex V1.

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Receptive fields of V1 cells are oriented bars

• Recording neural activity in V1 neurons in response to stimuli of different

shapes revealed that neurons respond to the light bars of different

orientations (Nobel Prize to Hubel and Wiesel), thus their “receptive fields”

have the shape of light bars of different angles.

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Micro-organisation of the primary visual cortex V1

• Ocular dominance stripes: cells respond either to the left or right eye or both, especially where stripes change, i.e. on the “borders” between the stripes.

• Orientation selective cells: all neurons within a single cortical column respond to the bars of the same angle. Columns covering all angles from both eyes comprise a macro-column. (“Blobs” are cells sensitive to color.)

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Left

Right

Right Left

Receptive field of simple cells in V1

• Cells in all layers of a single column in V1 have the same orientation selectivity,

i.e. the same tuning curves, for bar-like stimuli from the left and/or right eye.

• Ocular dominance may vary within a cortical column, e.g. in this example the

left eye is more dominant than the right eye. This means the response to the left

eye is bigger than the response to the right eye, while the neuron responds to

the same orientation (angle) of a bar-like light stimulus presented to both eyes.

Tuning curves

0 180 360 90 270

Receptive Field Plasticity (Harel Shouval):

http://www.physics.brown.edu/physics/researchpages/Ibns/index.html

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Right eye Left eye

Right eye Left eye

Development of ocular (eye) dominance

• Normal rearing (NR)

– Normal distribution of ocular dominance in NR. The eye dominance responsivity follows a normal (Gaussian) distribution.

• Binocular deprivation (BD)

– Closing both eyes for a long period (several weeks) after birth causes blindness even if they are later opened again. Neurons in V1 are permanently not responsive to visual stimuli.

Receptive Field Plasticity (Harel Shouval): http://www.physics.brown.edu/physics/researchpages/Ibns/index.html

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Orientation selectivity of V1 simple cells in BD is lost

Binocular Deprivation

Normal

Adult

angle angle

Tuning curve (angles)

Adult


angle angle

Neu

ron

’s re

spo

nse

Neu

ron

’s re

spo

nse

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Monocular deprivation (MD) effect on ocular dominance

Right eye Left eye

Right eye Left eye

• After the period of normal rearing

when the cells in V1 normally

develop their ocular dominance and

orientation selectivity, one eye is

closed.

• Closing the eye for a brief period (1-

2 weeks) causes a shift in the ocular

dominance towards the open eye.

• At the same time, there is less cells

responding to closed eye.


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Monocular Deprivation Normal

Left Right

% o

f ce

lls

group group

Tuning

curves

(angle)

1 2 3 4 5 6 7

10

15

Right

Left


Orientation selectivity in MD is lost for the closed eye

View

from

below

Neu

ron

’s re

spo

nse

Neu

ron

’s re

spo

nse

angle angle

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Left

retina

LGN

Right

retina

LGN

Synapses

from LGN

to V1 Synapses

from LGN

to V1

Computational model

• The neural network model of the

development of ocular dominance

and orientation selectivity in V1

– set up the circuitry reflecting the

anatomy of the modelled visual

system

– choose model of a neuron in V1

– implement the synaptic plasticity

rule for synapses between LGN

and V1 cortical neuron

– Define the activity patterns

coming from LGN

– simulate the model

image

Picture taken from Receptive Field Plasticity (Harel Shouval): http://www.physics.brown.edu/physics/researchpages/Ibns/index.html

Neuron in V1

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x1

x2

xn

o w ·x

w1

w2

·

·

·

wn

Rate model of a neuron

utput y

y = f(S wi xi)

inputs

• Individual inputs represent instantaneous frequencies of input spikes, thus

synaptic weights are wj; synaptic inputs xj and y is the output frequency.

• Input is comprised of a “patterned” input (from some input pattern) plus

random noise, i.e. xj = x’j + random noise. (i.e. small random number)

• If the eye is closed then the input is just a random noise: xj = random noise.

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),( Mj

jyx

dt

dw

2yM

Bienenstock, Cooper & Munro (BCM) theory

jj j xwy

)(),( MM yyy

• Dependent variables: synaptic weights wj; synaptic inputs xj; y is the output

frequency; is the learning speed, is the modification function.

• Value of the modification threshold M depends on the average of the square

of neuron’s past activity over the time interval , i.e. y2 .

is a proportionality constant

• This is called metaplasticity: the outcome of synaptic plasticity depends on

the previous activity of a neuron (Abraham and Bear, TINS, 1996)

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The BCM rule of synaptic plasticity wj= xj

Modification

function

= y(y M)

Moving plasticity threshold

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Neurons that fire out of sync lose their link.

Right

Left

Neurons that fire together wire together.

Output

Right

Left

Output

Let us apply the Hebb rule to right and left eye experiments

• When an axon of cell A is near enough to excite a cell B and repeatedly or persistently takes part in firing it, some growth process or metabolic change takes place in one or both cells such that A's efficiency, as one of the cells firing B, is increased.”

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Right eye Left eye

Right eye Left eye

Right eye (open, relays patterned activity)

Left eye (open, relays the same patterns)

Simulations of the model for NR

• Normal development of OD in NR (normal rearing) is Hebbian

• Synapses of the right and left eyes drive the cortical cell in sync and they strengthen

• Initial conditions and other factors (e.g., chance) cause the spectrum of OD

Output in sync with both eyes spikes

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Right eye Left eye

Right eye Left eye

Right eye (open, relays patterned activity)

Left eye (closed, relays only noise)

Model of MD

• The shift in OD in MD is Hebbian

• Synapses of the right eye that drive the cortical cell strengthen

• Synapses from the left eye (the closed one) weaken

Output in sync with the right eye spikes

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Right eye Left eye

Right eye Left eye

Right eye Left eye

Reverse suture: not Hebbian

• Can the Hebbian learning explain reverse suture experimental results, when formerly closed eye becomes dominant ?

• Not really

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Success in RS simulation due to dynamic M

• After closing the right eye

and opening the left eye,

modification threshold M

slides to the left, because the

overall activity level drops due

to the fact that newly closed

eye relays only noise.

• Newly opened eye relays

proper activity but its synapses

are still very weak. The shift in

M to the left allows the weak

left eye synapses to strengthen.

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Results of the BCM model: NR

• During NR both eyes receive the same patterned input

• The cortical cell develops the same orientation selectivity for both eyes

• In this example both eyes are equally dominant (the cell response is proportional to the weights of the inputs synapses)

Picture taken from Clothiaux, Bear, Cooper (1991) Journal of Neurophysiology, vol. 66, No. 5, pp. 1785-1804.

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Results of the BCM model: MD after NR

• During MD after NR, first both eyes develop OD and OS and then only the open eye receives patterned input, while the closed eye relays only random uncorrelated noise through its synapses.

• Synapses belonging to the closed (left) eye weaken and so does the responsiveness of the cortical cell to stimulation of the closed eye.

• The synapses belonging to the open eye become stronger.


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Results of the BCM model: RS after MD

• During RS after MD, first the

newly closed (right) eye looses

dominance and orientation

selectivity because its synapses

relay only noise

• The newly opened (left) eye

starts to relay patterned activity

to the cortical cell but its

synapses began to strengthen

only after the synapses of the

formerly open eye have had

weakened first.


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Experimental evidence for M

• It is easier to obtain synaptic potentiation in the cortex of dark-reared animals

and it is harder to induce synaptic depression in these cortices (cyan curve).

• The opposite is true for light-reared (NR) visual neurons in V1 (green curve).

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Timing (Markram et al., Science, 1997)

• In 1997, a new phenomenon was discovered – that the sign and magnitude of

synaptic weight change depend also on the precise relative timing of pre- and

postsynaptic spikes.

• Experimental protocol of Spike-Timing Dependent Plasticity: Pre and Post-

synaptic neurons are forced to emit spikes with a pre-defined time difference,

while the modification of the synaptic strength is monitored.

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STDP: spike-timing dependent plasticity

• Depending on the precise time difference t between pre- and post-synaptic

spike, the synaptic weight can be either depressed or potentiated and the

magnitude of change depends on t.

/

/

t

t

eAw

eAw

t = tpost tpre (ms)

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STDP spike interactions

• A+ and + is the amplitude and decay for LTP, respectively, and

• A_ and _ is the amplitude and decay for LTD, respectively.

A

A

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NEUR301

Abigail Morrison, Markus Diesmann,

Wulfram Gerstner:

Possible

implementations

of STDP

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STDP leads to the BCM LTD/LTP threshold

• Izhikevich and Desai (2003) showed STDP leads to the BCM threshold

for the nearest neighbour STDP, i.e. w(t+1) = w(t) (1 + w+ w)

• A’s and ’s are amplitudes and decays for LTP/LTD windows, respectively;

• This threshold equals to the frequency of input stimulation where LTD

changes into LTP, and thus there is no overall change.

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LTP

LTD

post-pre

pre-post

STDP+dynamic BCM (Benuskova & Abraham, 2007)

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yAA

yAA

Homeostatic properties:

y2 is proportional to the

prior time-averaged

postsynaptic activity (as a

spike count or somatic

voltage).

y2 varies for all excitatory

synapses on the postsynaptic

cell (i.e. homeostasis is a

whole-cell property).

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Summary

• All the changes like NR, BD, MD, RS and happen only during the

critical period after birth. After this period is over the plasticity in V1

ceases.

• Critical periods were observed for plasticity in all primary cortices, i.e.

visual and auditory, albeit of different duration and sharpness of

termination.

• Many cortical and brain areas are plastic during the whole life, i.e.

somatosensory, motor, frontal and associative areas, etc.

• Izhikevich and Desai showed that STDP leads to the BCM threshold for

nearest spikes interaction – making the threshold depending on the

previous postsynaptic activity was introduced by Benuskova & Abraham.