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Synaptic Plasticity Emerging from ChemicalReactions: Spike-Timing Dependent Plasticityof Basal Ganglia Neurons
Ilya ProkinPh.D. defenseLyon2/12/2016
Ph.D. CommitteeGuillaume BeslonJeanette KotaleskiKrasimira Tsaneva-AtanasovaMichael GraupnerHugues Berry
How do you know what is next?
2
Cell A
Cell B
“When an axon of cell A is near enough to excitea cell B and repeatedly or persistently takes partin firing it, some growth process or metabolic
change takes place in one or both cells such that A’sefficiency, as one of the cells firing B, is increased.”
Hebb, D.O., The Organization of Behavior (1949) 3
Synaptic transmission
Presynapticaction potential
+40
0
–55–70
Threshold
mV
Ca2+
Post-synapticcell
Cell B
Cell A
Synapse
1 ms
Kandel (2013) 4
Synaptic transmission
Presynapticaction potential
+40
0
–55–70
Threshold
mV
Ca2+
Post-synapticcell
Glutamate
1 ms
Kandel (2013) 5
Synaptic transmission
Excitatorypostsynapticpotential
Presynapticaction potential
+40
0
–55–70
Threshold
mV
Ca2+
Presynaptic nerveterminal
Receptor-channel
Post-synapticcell
Na+ Na+ Na+
–55
–70
Threshold
1 msDelay
mV
Glutamate
1 ms
Kandel (2013)
AEPSP
6
Synaptic transmission
Excitatorypostsynapticpotential
Presynapticaction potential
+40
0
–55–70
Threshold
mV
Ca2+
Presynaptic nerveterminal
Receptor-channel
Post-synapticcell
Na+ Na+ Na+
–55
–70
Threshold
1 msDelay
mV
Glutamate
1 ms
Kandel (2013)
AEPSP
6
Synaptic Plasticity: LTP and LTD
Plasticity induced by presynaptic stimulation
• LTP (increase) of AEPSPinduced byHigh-Frequency Stimulation15 Hz during 15 s(Bliss and Lømo 1973)
post
pre
• LTD (decrease) of AEPSPinduced byLow-Frequency Stimulation1 Hz during 100 s(Dunwiddie and Lynch 1978)
post
pre
7
Synaptic Plasticity: LTP and LTD
Plasticity induced by presynaptic stimulation
• LTP (increase) of AEPSPinduced byHigh-Frequency Stimulation15 Hz during 15 s(Bliss and Lømo 1973)
post
pre
• LTD (decrease) of AEPSPinduced byLow-Frequency Stimulation1 Hz during 100 s(Dunwiddie and Lynch 1978)
post
pre
7
A new experimental protocol
Δt > 0Time
post
pre
8
A new experimental protocol
...
Period=1/Frequency
Δt > 0
1 2 3 4 Npairings
post
pre
9
A new experimental protocol
Npairings
Frequency
Spike-timing (Δt)
...
Period=1/Frequency
Δt < 0
1 2 3 4 Npairings
from 60 to 100
1 Hz
from -100 to +100 ms
Protocol described by: Typical values are:
post
pre
10
Spike-timing dependent plasticity (STDP)
Spike timing, Δt (ms)
0 40 80-40-80
Chan
ge in E
PSC
am
plit
ude (
%)
-60
0
-20
20
100
60
Δt < 0 Δt > 0
Time
post
pre
Time
post
pre
Spike timin
0-40-80
Chan
ge in E
PSC
am
plit
ude (
%)
-60
0
-20
20
100
60
Δt < 0
Time
post
pre
Bi and Poo (1998) 11
Spike-timing dependent plasticity (STDP)
Spike timing, Δt (ms)
0 40 80-40-80
Chan
ge in E
PSC
am
plit
ude (
%)
-60
0
-20
20
100
60
Δt < 0 Δt > 0
Time
post
pre
Time
post
pre
Bi and Poo (1998)
Hebbian STDP
12
Spike-timing dependent plasticity (STDP)
Spike timing, Δt (ms)
0 40 80-40-80
Chan
ge in E
PSC
am
plit
ude (
%)
-60
0
-20
20
100
60
Δt < 0 Δt > 0
Time
post
pre
Time
post
pre
Bi and Poo (1998)
Hebbian STDP
12
STDP comes in various shapes
Excitatory to inhibitory
20
Excitatory to excitatory
Δt (ms)
Inhibitory to excitatory
25
50
Caporale and Dan (2008)
anti-Hebbian STDP
Why STDP is so variable?
13
STDP comes in various shapes
Excitatory to inhibitory
20
Excitatory to excitatory
Δt (ms)
Inhibitory to excitatory
25
50
Caporale and Dan (2008)
anti-Hebbian STDP
Why STDP is so variable?
13
STDP comes in various shapes
Excitatory to inhibitory
20
Excitatory to excitatory
Δt (ms)
Inhibitory to excitatory
25
50
Caporale and Dan (2008)
anti-Hebbian STDP
Why STDP is so variable?
13
Basal Ganglia
Cortex
Striatum
BasalGanglia
• Learning of skills• Habit learning• Reinforcement learning
• Parkinson’s disease• Huntington’s disease• Tourette syndrome• OCD
14
Basal Ganglia
Cortex
Striatum
BasalGanglia
• Learning of skills• Habit learning• Reinforcement learning
• Parkinson’s disease• Huntington’s disease• Tourette syndrome• OCD
14
Basal Ganglia
BasalGanglia
Cortex
Striatum
15
Typical experimental protocol of STDP induction
pre
post
Mean amplitude of EPSC
Mean amplitude of EPSCW
total=
...1 2 3 4 ... 100
1 s
0<Δt<+30 ms
Time (min)
prepost
Cui et al. (2015) 16
Typical experimental protocol of STDP induction
pre
post
Mean amplitude of EPSC
Mean amplitude of EPSCW
total=
...1 2 3 4 ... 100
1 s
0<Δt<+30 ms
Time (min)
prepost
prepost -30<Δt<0 ms
Cui et al. (2015) 17
Experimental results on STDP of cortico-striatal synapses
pre
post
pre
post
0
100
200
300
Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
Long-Term DepressionLTD
Long-Term PotentiationLTP
Cui et al (2015) 18
Experimental results on STDP of cortico-striatal synapses
pre
post
pre
post
0
100
200
300
Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
50
100
150
200
Npairings0 05 001
Wto
tal(
%) 10<Δt<25 ms
Long-Term DepressionLTD
Long-Term PotentiationLTP
Cui et al (2015) 19
Experimental results on STDP of cortico-striatal synapses
pre
post
pre
post
0
100
200
300
Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
50
100
150
200
Npairings0 05 001
Wto
tal(
%) 10<Δt<25 ms
50
100
150
200
0 100Npairings
50
Wto
tal(
%) -25<Δt<-10 ms
Long-Term DepressionLTD
Long-Term PotentiationLTP
Cui et al (2015) 20
Experimental results on STDP of cortico-striatal synapses
pre
post
Npairings = 100
EPSC
am
plit
ude
(% o
f co
ntr
ol)
-25<Δt<0 ms
NpairingsEPSC
am
plit
ude
(% o
f co
ntr
ol)
LTP isNMDAR
dependent
Cui et al (2015) 21
Experimental results on STDP of cortico-striatal synapses
pre
post
Npairings = 10 Npairings = 100
EPSC
am
plit
ude
(% o
f co
ntr
ol)
EPSC
am
plit
ude
(% o
f co
ntr
ol)
-25<Δt<0 ms
NpairingsEPSC
am
plit
ude
(% o
f co
ntr
ol)
LTP isendocannabinoid
dependent
LTP isNMDAR
dependent
Cui et al (2015) 22
???
• How can we explain new LTP and its dependence on Npairings?• How does it depend on parameters of the protocol and
experimental conditions?• Why STDP is so variable?
23
Outline
Building model
Model validation
STDP and spiking patterns
Conclusions and Perspectives
24
What do we need?
endocannabinoidplasticity
NMDARplasticity
25
What do we need?
endocannabinoidplasticity
NMDARplasticityGlutamate
Calcium
26
Model of postsynaptic plasticity
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticity
PostsynapticMedium-SizedSpiny Neuron
Graupner & Brunel (2007)
dI1dt = dPP1
dt − νCaN I1 + νPKAI10
dPP1dt = −k11I1 · PP1 + k−11(PP10 − PP1)
νx (CaM) = k0x + kx
1 + (Kx/CaM)nx
x = CaN,PKA • 15 ODE• 23 Parameters
27
Model of postsynaptic plasticity
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticity
PostsynapticMedium-SizedSpiny Neuron
Graupner & Brunel (2007)
dI1dt = dPP1
dt − νCaN I1 + νPKAI10
dPP1dt = −k11I1 · PP1 + k−11(PP10 − PP1)
νx (CaM) = k0x + kx
1 + (Kx/CaM)nx
x = CaN,PKA
• 15 ODE• 23 Parameters
27
Model of postsynaptic plasticity
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticity
PostsynapticMedium-SizedSpiny Neuron
Graupner & Brunel (2007)
dI1dt = dPP1
dt − νCaN I1 + νPKAI10
dPP1dt = −k11I1 · PP1 + k−11(PP10 − PP1)
νx (CaM) = k0x + kx
1 + (Kx/CaM)nx
x = CaN,PKA • 15 ODE• 23 Parameters
27
Model of postsynaptic plasticity needs input
leak
IP3R
Ca
SERCACaER
bτVSCC TRPV1
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticity
Calcium
CICR
NMDAR
PostsynapticMedium-SizedSpiny Neuron
• 20 ODE• 65 Parameters
28
Model of postsynaptic plasticity needs input
leak
IP3R
Ca
SERCACaER
bτVSCC TRPV1
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticity
Calcium
CICR
NMDAR
PostsynapticMedium-SizedSpiny Neuron
De Pittà et al. (2009)
• 23 ODE• 88 Parameters
29
Model of postsynaptic plasticity needs input
leak
IP3R
PIP2
IP3
Ca
SERCACaER
PLCβ
bτVSCC
Glutamate
TRPV1
IP3-3K
IP-5P
NMDAR
AMPAR
mGluR
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticityGlutamate
Calcium
PostsynapticMedium-SizedSpiny Neuron
• 24 ODE• 94 Parameters
30
Model of postsynaptic plasticity needs input
leak
IP3R
PIP2
IP3
Ca
SERCACaER
PLCβ
bτVSCC
Glutamate
TRPV1
IP3-3K
IP-5P
NMDAR
AMPAR
mGluR
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
NMDARplasticityGlutamate
Calcium
bAP
Postsynapticintracellular
stimulation ofMSN
Presynapticextracellular
corticalstimulation
Glutamatetransient
PostsynapticMedium-SizedSpiny Neuron
• 24 ODE• 103 Parameters
31
Model with endocannabinoid signaling
leak
IP3R
DAG
PIP2
IP3
DAGLα
2-AG
Ca
SERCACaER
PLCδPLCβ
bτVSCC
MAGL
Glutamate
TRPV1
AEA
CB1R
IP3-3K
IP-5P DAGK
NMDAR
AMPAR
mGluR
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
endocannabinoid
plasticity?
NMDARplasticityGlutamate
Calcium
yCB1R
PostsynapticMedium-SizedSpiny Neuron
• 30 ODE• 121 Parameters
• Numerical integrationwith LSODA
• Sensitivity Analysiswith Monte-Carlo samplingand SRC
• Parameter Fittingwith Differential Evolution
32
Model with endocannabinoid signaling
leak
IP3R
DAG
PIP2
IP3
DAGLα
2-AG
Ca
SERCACaER
PLCδPLCβ
bτVSCC
MAGL
Glutamate
TRPV1
AEA
CB1R
IP3-3K
IP-5P DAGK
NMDAR
AMPAR
mGluR
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
endocannabinoid
plasticity?
NMDARplasticityGlutamate
Calcium
yCB1R
PostsynapticMedium-SizedSpiny Neuron
• 30 ODE• 121 Parameters
• Numerical integrationwith LSODA
• Sensitivity Analysiswith Monte-Carlo samplingand SRC
• Parameter Fittingwith Differential Evolution
32
Model with endocannabinoid signaling
PostsynapticMedium-SizedSpiny Neuron
leak
IP3R
DAG
PIP2
IP3
DAGLα
2-AG
Ca
SERCACaER
PLCδPLCβ
bτVSCC
MAGL
Glutamate
TRPV1
AEA
CB1R
IP3-3K
IP-5P DAGK
NMDAR
AMPAR
mGluR
PP1
I1*
CaNPKA
CaMKII*
CaM
I1
CaMKII
Ca
endocannabinoid
plasticity?
NMDARplasticityGlutamate
Calcium
bAP
Postsynapticintracellular
stimulation ofMSN
Presynapticextracellular
corticalstimulation
Glutamatetransient
yCB1R
• 30 ODE• 121 Parameters
33
Calcium transients depend on stimulation protocol
pre
post
pre
post
0 50 1000.0
0.5
1.0
1.5
Calc
ium
(μ
M)
−40 0 400.0
0.5
1.0
1.5
peak
Ca (μ
M)
after x10
after x100
Npairings Δt (ms)
Δt = -15 ms
Δt = +20 ms
34
Endocannabinoid receptor activation depends on stimulationprotocol
pre
post
pre
post
Calcium Model yCB1R
−40 0 40peak
CB
1R
act
ivati
on
(y)
(a.u
.)C
B1
R
0.00
0.05
0.10
after x10
after x100
0 50 1000.00
0.05
0.10
CB
1R
act
ivati
on
(y)
(a.u
.)C
B1
R
Δt (ms)Npairings
Δt = -15 ms
Δt = +20 ms
35
The hypothesis of endocannabinoid-controlled plasticity
CB1R activation (yCB1R) (a.u.)
Wp
re c
hange (
%)
36
The hypothesis of endocannabinoid-controlled plasticity
Wpre
wante
d (
%)
1.0
-25<Δt<0 ms
NpairingsEPS
C a
mp
litud
e(%
of
con
trol)
0 50 1000.00
0.05
0.10
CB
1R
act
ivati
on (
y)
(a.u
.)C
B1
R
LTD
LTP
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
Δt = -15 ms
Δt = +20 ms
Npairings
37
Two pathways together
CB1R activation (yCB1R) (a.u.)
Wpre
change (
%)
Ω(y
CB1R
)
d Wpre
dt =Ω(yCB1R) − Wpre
τWpre(zCB1R) ; Wpost = 1 + 3.5 CaMKII∗
CaMKII∗max
Wtotal = Wpre Wpost
38
Outline
Building model
Model validation
STDP and spiking patterns
Conclusions and Perspectives
39
Fitting model to the data
pre
post
pre
post
0
100
200
300 Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
STDPexperiments
Model
NpairingsFrequencySpike-timing (Δt)
40
Fitting model to the data
pre
post
pre
post
0
100
200
300 Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
0
100
200
300Npairings = 10
02- 402004- 0
Wto
tal(
%)
Δt (ms)
STDPexperiments
Model
NpairingsFrequencySpike-timing (Δt)
41
Fitting model to the data
50
100
150
200
Npairings0 05 001
Wto
tal(
%) 10<Δt<25 ms
50
100
150
200
0 100Npairings
50
Wto
tal(
%) -25<Δt<-10 ms
pre
post
pre
post
0
100
200
300 Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
0
100
200
300Npairings = 10
02- 402004- 0
Wto
tal(
%)
Δt (ms)
STDPexperiments
Model
NpairingsFrequencySpike-timing (Δt)
42
Fitting model to the data
pre
post
pre
post
50
100
150
200
Npairings0 05 001
Wto
tal(
%) 10<Δt<25 ms
50
100
150
200
0 100Npairings
50
Wto
tal(
%) -25<Δt<-10 ms
0 25 50 75 100
30
15
0
-15
-30
Npairings
Δt
(ms)
0
100
200
300 Npairings = 100
002- 402004-
Wto
tal(
%)
Δt (ms)
0
100
200
300Npairings = 10
02- 402004- 0
Wto
tal(
%)
Δt (ms)
LTPLTD50 100 250
Wtotal (%)STDPexperiments
Model
NpairingsFrequencySpike-timing (Δt)
43
The model predicts endocannabinoid-dependent LTP
50
100
150
200
0 100Npairings
50
Wto
tal(
%) -25<Δt<-10 ms
CB1R activation (yCB1R) (a.u.)Wpre
change (
%)
0
100
200
300
Contro
lMAG
L inh.
MAG
L inh.&
CB1R K
O
Wto
tal(
%)
44
The model predicts endocannabinoid-dependent LTP
50
100
150
200
0 100Npairings
50
Wto
tal(
%) -25<Δt<-10 ms
CB1R activation (yCB1R) (a.u.)Wpre
change (
%)
0
100
200
300
Contro
lMAG
L inh.
MAG
L inh.&
CB1R K
O
150
100
50 13 9 5
ns
*
ns
*
EP
SC
am
plitu
de (pA
)
Contro
l
ns
Wto
tal(
%)
JZL1
84
JZL1
84&
AM25
1
45
Outline
Building model
Model validation
STDP and spiking patterns
Conclusions and Perspectives
46
STDP depends on the protocol
Timepostpre
Timeprepost
LTP
LTD50
100
250
Wtotal
(%)
50 100pairingsN
2
4
6
8
10
Freq
uency
(H
z)
50 100pairingsN
2
4
6
8
10
Freq
uency
(H
z)
Δt = +20 msΔt = -15 ms
NpairingsFrequencySpike-timing (Δt)
47
STDP depends on the protocol
Frequency = 1.5 Hz
Npairings = 20
Frequency = 1 Hz
Npairings = 55
Npairings = 50
Npairings = 3
010 110 210Time (s)
0
100
μC
aM
KII*
(M
)Time
pre
post
Δt = -15 ms
LTP
nothing
~ W
post
48
STDP depends on the protocol
Frequency = 1.5 Hz
Npairings = 20
Frequency = 1 Hz
Npairings = 55
Npairings = 50
Npairings = 3
Time
pre
post
Δt = -15 ms
CB
1R
CB
1R
act
ivati
on (
y)
(a.u
.)
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
010 110 210Time (s)
0.00
0.05
0.10
nothing
LTP
~ W
pre
49
STDP is not fixed
50 100 150pairingsN
0
2
4
6
8
10
Frequency
(H
z)
Npairings Frequency Spike-timing (Δt)
−40 0 40Δt (ms)
0100
300
W (
%) Wpre
Wpost
Wtotal −40 0 400
100
300
W (
%) Wpre
Wpost
Wtotal
Δt (ms)
50
STDP is not fixed
50 100 150pairingsN
0
2
4
6
8
10Fr
equency
(H
z)
Npairings Frequency Spike-timing (Δt)
−50 0 500
100
350preW
postW
Δt (ms)
W (
%)
51
STDP is not fixed
50 100 150pairingsN
0
2
4
6
8
10Fr
equency
(H
z)
Npairings Frequency Spike-timing (Δt)
−50 0 500
100
350preW
postW
Δt (ms)
W (
%)
52
Towards realistic situation
1/Frequency(period)
regula
rSTD
P p
roto
col
wit
h jit
ter
From this:
To this:
...
...
...
...
pre
post
pre
post
t ipost
(with jitter) = t ipost
(regular) + ∆t ijitter
53
Towards realistic situation
0 2 4 6 8 10
100
200
300
tota
lW
(%
)
Frequency = 1 Hz
STDPexperiments
Model
Timeprepost
Npairings = 10Npairings = 100
Npairings = 10Npairings = 100
Δtjitter (ms)max
-30<Δt<0 ms
54
Towards realistic situation
From this: To this:
x1 CaMKII* << Threshold
0 50 100Time (s)
0
50
100
150
200
CaM
KII*
(μM
)
Frequency = 1.0 HzΔt = 5 msm
jittaexr
0 50 100Time (s)
0
50
100
150
200
CaM
KII*
(μM
)
Frequency = 1.0 HzΔt = 0 msm
jittaexr
Δt = -15 ms
Δt = 20 ms
55
Towards realistic situation
From this: To this:
x1 CB1R activation ~ Threshold
0 50 100Time (s)
0.00
0.05
0.10
CB
1R
act
ivati
on (
y),
a.u
.C
B1
R
LTD
LTP
Frequency = 1.0 HzΔt = 0 msm
jittaexr
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
0 50 100Time (s)
0.00
0.05
0.10
CB
1R
act
ivati
on (
y),
a.u
.C
B1
R
LTD
LTP
Frequency = 1.0 HzΔt = 5 msm
jittaexr
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
Δt = -15 ms
Δt = 20 ms
56
Outline
Building model
Model validation
STDP and spiking patterns
Conclusions and Perspectives
57
Conclusions
• Endocannabinoid system supports bidirectional plasticity, notjust LTD
• STDP is not fixed• At low frequency, endocannabinoid-dependent STDP is more
robust than NMDAR/CaMKII-dependent plasticity
• Activation of presynaptic dopamine D2 receptor modulatesplasticity induction
• Glutamate uptake prevents excess LTP
58
Conclusions
• Endocannabinoid system supports bidirectional plasticity, notjust LTD
• STDP is not fixed• At low frequency, endocannabinoid-dependent STDP is more
robust than NMDAR/CaMKII-dependent plasticity
• Activation of presynaptic dopamine D2 receptor modulatesplasticity induction
• Glutamate uptake prevents excess LTP
58
Perspectives: postsynaptic dopamine signaling
leak
IP3R
DAG
PIP2
IP3
DAGLα
2-AG
Ca
SERCACaER
PLCδPLCβ
bτVSCC
MAGL
Glutamate
TRPV1
AEA
CB1R
IP3-3K
IP-5P DAGK
NMDAR
AMPAR
mGluR
PP1
CaNPKA
CaMKII*
CaM
CaMKII
Ca
yCB1R
DARPP-32
D1/D2
receptor
Dopamine
59
Perspectives: a new model of STDP
pre
post...
Plasticity
InputOutput
x60 1 Hz
Δt
W
60
Perspectives: a new model of STDP
pre
post...
Plasticity
InputOutput
x60 1 Hz
Δt
W
60
Perspectives: a new model of STDP
Δt
ΔW
pre
post...
Plasticity?
Input
x60 1 Hz
Output
Δt
W
60
Perspectives: a new model of STDP
Δt
ΔW
Plasticity?
Input
Output
pre
post
60
Perspectives: a new model of STDP
pre
post...
Input
x60 1 Hz
50 100 150pairingsN
0
2
4
6
8
10
Freq
uency (
Hz)
−50 0 500
100
350preW
postW
Δt (ms)W
(%
)
Plasticity Output
Δt
W
60
Perspectives: a new model of STDP
pre
post
Input
50 100 150pairingsN
0
2
4
6
8
10
Freq
uency (
Hz)
−50 0 500
100
350preW
postW
Δt (ms)W
(%
)
Plasticity Output
???
60
Perspectives
• Postsynaptic dopamine and DARPP-32 signaling forreinforcement learning
• Spike-pattern dependent plasticity instead of STDP andplasticity under more realistic conditions
• Reduced model for network simulations, and possiblyunsupervised learning algorithms
61
Thank you!
62
Modulation of endocannabinoid plasticity by presynaptic D2R
0 25 50 75 100
−30
−15
0
15
30
Npairings
50 100 250
W total (%)
∆t(
ms)
LTPLTD
10
0 0
100% 0%
10 20 30−30
−20
−10
0
Npairings
10 20 30−30
−20
−10
0
80 90 10070
10
20
30
80 90 10070
10
20
30
D2R activation (% of control)
Δt
(ms)
Δt
(ms)CB1R
D2R DA
yG
Wpre
2-AG
PLCδPLCβ
bτVSCC
I1
I1
P
CaMKII P
CaMKII
Wpost
(Ca)4 CM
PP1AEA
TRPV1
CaER
SERCA
Ca
yG
D2R activation (% of control)
Time (ms)
yG
(a.u
.)
0.00
0.05
0.10
0 10 20 30
100% 0%
63
Modulation by astrocytic EAAT2
GlutamateNMDAR
AMPAR
mGluR
EAAT2(GLT-1)
Presynapticneuron
Postsynapticneuron
Astrocyte
Wpost
Wpre
64
Modulation by astrocytic EAAT2
0.9 1.0 1.1Frequency (Hz)
−400
−200
0
200
400
Δt
(ms)
Control
0.9 1.0 1.1Frequency (Hz)
−400
−200
0
200
400
Δt
(ms)
EAAT2 block
LTPLTD50 100 250
W total (%)
EAAT2(GLT-1)
EAAT2(GLT-1)
65
Modulation by astrocytic EAAT2
−200 −100 0 100 200Δt (ms)
0
2
4
6
8
peak
of μ
CaM
KII*
(M
)
A B
−200 −100 0 100 200Δt (ms)
0.00
0.02
0.04
0.06
peak
of
Gi/o a
ctiv
ati
on y
G (
a.u
.)
Control
EAAT2 block
66
GHK vs Ohm’s law
Ste
ad
y-st
ate
calc
ium
(μ
M)
Ste
ad
y-st
ate
norm
aliz
ed
calc
ium
flux (
a.u
.)
NMDAR
TRPV1
T-type VSCC
L-type v1.3 VSCC
−80 −60 −40 −20 0 20 40
V (mV)
0.0
0.2
0.4
Ohm's law
GHK
both NMDAR andTRPV1 with:
−80 −60 −40 −20 0 20 40V (mV)
−2
−1
0
1both NMDAR and TRPV1 with Ohm's law
−80 −60 −40 −20 0 20 40V (mV)
0.0
0.5
1.0both NMDAR and TRPV1 with GHK
−80 −60 −40 −20 0 20 400 0.5
Tim
e (
s)
0.2
20
.26
0.3
0
ONMDAR
bAP+EPSP
Δt = −15 msΔt = +15 ms 67
Frequency-∆t
-100 -50 10050
200
300
-100 -50 10050
200
300
B
-100 -50 10050
200
300C
DN
orm
aliz
ed E
PS
C (%
)
Nor
mal
ized
EP
SC
(%
)
Nor
mal
ized
EP
SC
(%
)E
Nor
mal
ized
EP
SC
(%
)
10 pairings at 0.1Hz
-100 -50 10050
200
300
A40
20
0
-20
-40
0
LTP
LTD
50
100
250
W total (%)
1 2 3 4 5Frequency of the pairings (Hz)
10 pairings at 1Hz
10 pairings at 2.5Hz 10 pairings at 4Hz
Model
STDP experiments
Δt (tAP-tEPSP) (ms) Δt (tAP-tEPSP) (ms)
Δt (tAP-tEPSP) (ms) Δt (tAP-tEPSP) (ms)
Δt
(ms)
68
Robustness
C
SR
C
1D
β CB
1RT
B
AM
PAg
2D
1P
τ bA
P
θs Lt To Dp4PLTD
AFAA
HKD
AG
KrD
AG
LK
dur
DCm
ax
APε C
B1R
VSC
Cpθ
s Lt Ta DrtdB
K
ξ VSC
C
ν AT
max
G3PPr
DG
Lr
LTP
Amax
DC
Krα
α CB
1R
FAA
HrM
AG
LrC
B1R
kNM
DA
gξ TR
PV1
γ CB
1RCn
ξ NM
DA
TRPV
1
gθs Lt Ta Prtτ G
τb
Catot
CaM
bC
a
Θ LTP
0.00
0.02
0.04
0.06
0.08
0.10
0.12
tot
CaM
K
B
0
30
15
0
-15
-30
25 50 75 100
LTP
LTD50
100
250
W (%)total
Npairings
Δt
(ms)
LTP
LTD
ΘLTP
startΘLTD
stopΘLTD
start
0.00 0.05 0.10
0
CB1R activation (yCB1R) (a.u.)Wpre
chang
e (
%)A
30
15
0
-15
-30
100 200 300 400
LTP
LTD50
100
250
W (%)total
Npairings
Δt
(ms)
LTP
LTD
0.00 0.05 0.10
0
ΘLTD
stopΘLTD
start
Wpre
chang
e (
%)
CB1R activation (yCB1R) (a.u.)
ΘLTP
start
69
Predictions
200
150
100
Time (min)02 04 6001- 0
5x post-pre (n=17)EP
SC
am
plitu
de (%
)
B1200
100
0
**
**
*
ns
B2
0
100
200
300
Time (min)0.0 0.1 0.2
A1 A2
0
100
200
300
Contro
lMAG
L inh.
MAG
L inh.&
CB1R K
O
Contro
l
****
5x post-preMAGL inhibited
W to
tal(
%)
W to
tal(
%)
EP
SC
am
plitu
de (%
)
60
Model
STDP experiments
17 6 5
stimulation post stimulation
5x post-preJZL184 (n=6)
JZL1
84
JZL1
84&
AM25
1
5x post-pre(Control)
70
Jitter
Npairings10010
1.25
1
Freq
uency
(Hz)
A1 A2
B1 B2
LTD LTP
0 20 40 60 80−100
−50
0
50
100
Δt
(ms)
0 20 40 60 80−100
−50
0
50
100
Δt
(ms)
0 20 40 60 80−100
−50
0
50
100
Δt
(ms)
0 20 40 60 80−100
−50
0
50
100
Δt
(ms)
Δ jittert (ms)maxΔ jittert (ms)max
Δ jittert (ms)max Δ jittert (ms)max
71
Jitter: Higher-Frequency
0 50 100Time (s)
0
50
100
150
200
μC
aM
KII*
(M
)
0 50 100Time (s)
0.00
0.05
0.10CB
1R
CB
1R
act
ivati
on (
y)
(a.u
.)
LTD
LTP
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
0 50 100Time (s)
0
50
100
150
200
μC
aM
KII*
(M
)
0 50 100Time (s)
0.00
0.05
0.10CB
1R
CB
1R
act
ivati
on (
y)
(a.u
.)
LTD
LTP
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
0 50 100Time (s)
0
50
100
150
200
μC
aM
KII*
(M
)
0 50 100Time (s)
0.00
0.05
0.10CB
1R
CB
1R
act
ivati
on (
y)
(a.u
.)
LTD
LTP
ΘsLtTaDrt
ΘsLtToDp
ΘsLtTaPrt
Frequency = 1.25 Hz
Δt = −15 msΔt = +20 ms
20
100
5
A1 B1
A2 B2
A3 B3
Δtjitter(ms)
max
72
Jitter explanation
5
20
100
−100 0 100Δt (ms)
0
2
4
6
peak
of μ
CaM
KII*
(M
)
−100 0 100Δt (ms)
0.00
0.01
0.02
0.03
0.04
0.05
peak
of C
B1
RC
B1
R a
ctiv
ati
on (
y)
(a.u
.)
−100 0 100Δt (ms)
0
2
4
6
peak
of μ
CaM
KII*
(M
)
−100 0 100Δt (ms)
0.00
0.01
0.02
0.03
0.04
0.05
peak
of C
B1
RC
B1
R a
ctiv
ati
on (
y)
(a.u
.)
A1 B1
A2 B2
A3 B3
-15 20
−100 0 100Δt (ms)
0.00
0.01
0.02
0.03
0.04
0.05
peak
of C
B1
RC
B1
R a
ctiv
ati
on (
y)
(a.u
.)
−100 0 100Δt (ms)
0
2
4
6
peak
of μ
CaM
KII*
(M
)
Δtjitter(ms)
max
73
Pathways of eCB-plasticity
moderateCB1R activation
CaN
eCB-LTD
strongCB1R activation
PKA
eCB-LTP
PKACaN
74
Poisson spike trains
−40 −20 0 20 40Δt (ms)
100
200to
tal
W (
%)
R=0.1refractory period=10 ms
−40 −20 0 20 40Δt (ms)
100
200
tota
lW
(%
)
R=0.1refractory period=50 ms
−20 0 20Δt (ms)
100
200
tota
lW
(%
)
R=0.1refractory period=200 ms
−40 −20 0 20 40Δt (ms)
100
200
tota
lW
(%
)
R=0.5refractory period=10 ms
−40 −20 0 20 40Δt (ms)
100
200
tota
lW
(%
)
R=0.5refractory period=50 ms
−20 0 20Δt (ms)
100
200
tota
lW
(%
)
R=0.5refractory period=200 ms
−40 −20 0 20 40Δt (ms)
100
200
tota
lW
(%
)
R=0.9refractory period=10 ms
−40 −20 0 20 40Δt (ms)
100
200
tota
lW
(%
)
R=0.9refractory period=50 ms
−20 0 20Δt (ms)
100
200
tota
lW
(%
)
R=0.9refractory period=200 ms
75
Typical way to model STDP
Δt
ΔW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
Typical way to model STDP
pre
post
Time Δt
ΔWW
76
