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1
Computational cognitive neuroscience:
4. Synaptic Plasticity
Lubica Beňušková
Centre for Cognitive Science, FMFI Comenius University in Bratislava
2
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)
3
“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.
4
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)
5 5
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.
6
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.
7
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.)
8
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
9
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
10
Orientation selectivity of V1 simple cells in BD is lost
Binocular Deprivation
Normal
Adult
angle angle
Tuning curve (angles)
Adult
Receptive Field Plasticity (Harel Shouval): http://www.physics.brown.edu/physics/researchpages/Ibns/index.html
angle angle
Neu
ron
’s re
spo
nse
Neu
ron
’s re
spo
nse
11
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.
Receptive Field Plasticity (Harel Shouval): http://www.physics.brown.edu/physics/researchpages/Ibns/index.html
12
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
Receptive Field Plasticity (Harel Shouval): http://www.physics.brown.edu/physics/researchpages/Ibns/index.html
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
13
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
14
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.
15
),( 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)
16
The BCM rule of synaptic plasticity wj= xj
Modification
function
= y(y M)
Moving plasticity threshold
17
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.”
18
18
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
19
19
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
20
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
21
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.
22
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.
23
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.
Picture taken from Clothiaux, Bear, Cooper (1991) Journal of Neurophysiology, vol. 66, No. 5, pp. 1785-1804.
24
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.
Picture taken from Clothiaux, Bear, Cooper (1991) Journal of Neurophysiology, vol. 66, No. 5, pp. 1785-1804.
25
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).
26
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.
27
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)
28
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
29
NEUR301
Abigail Morrison, Markus Diesmann,
Wulfram Gerstner:
Possible
implementations
of STDP
30
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.
31
LTP
LTD
post-pre
pre-post
STDP+dynamic BCM (Benuskova & Abraham, 2007)
20
20
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).
32
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.