lecture 14: the biology of learning
DESCRIPTION
Lecture 14: The Biology of Learning. References: H Shouval, M F Bear, L N Cooper, PNAS 99 , 10831-10836 (2002) H Shouval, G Castellani, B Blais, L C Yeung, L N Cooper, Biol Cybernetics 87 , 383-391 (2002) W Senn, H Markram, M Tsodyks, Neural Computation 13 , 35-67 (2001) - PowerPoint PPT PresentationTRANSCRIPT
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Lecture 14: The Biology of Learning
References:
H Shouval, M F Bear, L N Cooper, PNAS 99, 10831-10836 (2002)
H Shouval, G Castellani, B Blais, L C Yeung, L N Cooper, Biol
Cybernetics 87, 383-391 (2002) W Senn, H Markram, M Tsodyks, Neural Computation 13, 35-67 (2001)
Dayan and Abbott, Sects 8.1, 8.2
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Learning = long-term synaptic changes
Long-term potentiation (LTP) and long-term depression (LTD)
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Learning = long-term synaptic changes
Long-term potentiation (LTP) and long-term depression (LTD)
CA1 region of rat hippocampus
![Page 4: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/4.jpg)
Learning = long-term synaptic changes
Long-term potentiation (LTP) and long-term depression (LTD)
CA1 region of rat hippocampus
Requires NMDA receptors, postsynaptic depolarization (notnecessarily postsynaptic firing)
![Page 5: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/5.jpg)
Timing dependence
Spike-timing dependent plasticity (STDP)
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Timing dependence
Spike-timing dependent plasticity (STDP)
(Markram et al, 1997)
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Timing dependence
Spike-timing dependent plasticity (STDP)
(Markram et al, 1997) (Zhang et al, 1998)
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Model I: Ca control modelShouval et al:
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Model I: Ca control modelShouval et al:
Everything depends on Ca concentration
![Page 10: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/10.jpg)
Model I: Ca control modelShouval et al:
Everything depends on Ca concentration
Ca flows in through NMDA channels
![Page 11: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/11.jpg)
Model I: Ca control modelShouval et al:
Everything depends on Ca concentration
Ca flows in through NMDA channels
“Back-propagating” action potential (BPAP) after postsynaptic spike(with slow tail)
![Page 12: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/12.jpg)
Model I: Ca control modelShouval et al:
Everything depends on Ca concentration
Ca flows in through NMDA channels
“Back-propagating” action potential (BPAP) after postsynaptic spike(with slow tail)
Ca dynamics:
][)(
][ CatI
dtCad
![Page 13: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/13.jpg)
Ca control model (2)
NMDA channel current (after spike at t = 0):
![Page 14: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/14.jpg)
Ca control model (2)
NMDA channel current (after spike at t = 0):
)ee)(()()e)57.3/]([1
1)( //
062.000sf t
st
frVNMDA IItVV
MggPtI
![Page 15: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/15.jpg)
Ca control model (2)
NMDA channel current (after spike at t = 0):
)ee)(()()e)57.3/]([1
1)( //
062.000sf t
st
frVNMDA IItVV
MggPtI
![Page 16: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/16.jpg)
Ca control model (2)
NMDA channel current (after spike at t = 0):
)ee)(()()e)57.3/]([1
1)( //
062.000sf t
st
frVNMDA IItVV
MggPtI
![Page 17: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/17.jpg)
Ca control model (3)Synaptic strength (conductance) obeys
)][])(([ WCaCadt
dW
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Ca control model (3)Synaptic strength (conductance) obeys
)][])(([ WCaCadt
dW
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Ca control model (3)Synaptic strength (conductance) obeys
)][])(([ WCaCadt
dW
Back-propagating action potential:
]e)1(e[)( //0
bss
bsf tbs
ftbs
fBS IIVtV
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Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
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Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
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Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
![Page 23: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/23.jpg)
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
IImRI AkAk
dtdA
![Page 24: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/24.jpg)
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
IImRI AkAk
dtdA
const TIm AAA
![Page 25: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/25.jpg)
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
IImRI AkAk
dtdA
const TIm AAA
)(1
)( mmmTImRm AAAAkAk
dtdA
![Page 26: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/26.jpg)
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
IImRI AkAk
dtdA
const TIm AAA
)(1
)( mmmTImRm AAAAkAk
dtdA
where
RI
ImIR kk
kAkk
;
1
![Page 27: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/27.jpg)
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
IImRI AkAk
dtdA
const TIm AAA
)(1
)( mmmTImRm AAAAkAk
dtdA
where
RI
ImIR kk
kAkk
;
1
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How it works
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Need the slow tail of the BPAP
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LTD if presynaptic spike is too far in advance of postsynaptic one
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LTD if presynaptic spike is too far in advance of postsynaptic one
(unavoidable consequence of model assumptions)
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Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
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Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc):
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Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
![Page 35: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/35.jpg)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
(recall (Lect 6) treatment of synaptic facilitation: y = P(release|vesicle)
![Page 36: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/36.jpg)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
(recall (Lect 6) treatment of synaptic facilitation: y = P(release|vesicle)Here (SMT notation): call it disP
![Page 37: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/37.jpg)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
(recall (Lect 6) treatment of synaptic facilitation: y = P(release|vesicle)Here (SMT notation): call it
Actual changes in build up slowly over ca 20 min,
disP
disP
![Page 38: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/38.jpg)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
(recall (Lect 6) treatment of synaptic facilitation: y = P(release|vesicle)Here (SMT notation): call it
Actual changes in build up slowly over ca 20 min,
)(1
disdisPM
dis PPdt
dP
disP
disP
![Page 39: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/39.jpg)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
(recall (Lect 6) treatment of synaptic facilitation: y = P(release|vesicle)Here (SMT notation): call it
Actual changes in build up slowly over ca 20 min,
)(1
disdisPM
dis PPdt
dP
But changes faster, on the scale of ~1 s or less
disP
disP
disP
![Page 40: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/40.jpg)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc): What is changed, (at least on the 1-hour timescale) is the probability
of transmitter release
(recall (Lect 6) treatment of synaptic facilitation: y = P(release|vesicle)Here (SMT notation): call it
Actual changes in build up slowly over ca 20 min,
)(1
disdisPM
dis PPdt
dP
But changes faster, on the scale of ~1 s or less
Here we try to describe the dynamics of
disP
disP
disP
disP
![Page 41: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/41.jpg)
2-messenger model (2)
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2-messenger model (2)
NMDA receptorsHave 3 states
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2-messenger model (2)
NMDA receptorsHave 3 states
2nd messenger#1
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2-messenger model (2)
NMDA receptorsHave 3 states
2nd messenger#2
2nd messenger#1
![Page 45: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/45.jpg)
NMDA receptorsKinetic equations:
![Page 46: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/46.jpg)
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
![Page 47: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/47.jpg)
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
)( sppostrec
NdN
d
dd ttNrN
dt
dN
![Page 48: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/48.jpg)
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
)( sppostrec
NdN
d
dd ttNrN
dt
dN
1 recud NNN
![Page 49: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/49.jpg)
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
)( sppostrec
NdN
d
dd ttNrN
dt
dN
1 recud NNN
8.0
ms100
,
,
NNdu
NN
du
rr
![Page 50: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/50.jpg)
2nd messengers
Activation driven by Nu,d
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2nd messengers
Activation driven by Nu,d
)()1( sppostuuSS
u
uu ttSNrS
dt
dS
![Page 52: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/52.jpg)
2nd messengers
Activation driven by Nu,d
)()1( sppostuuSS
u
uu ttSNrS
dt
dS
)()1( relpreddSS
d
dd ttSNrS
dt
dS
![Page 53: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/53.jpg)
2nd messengers
Activation driven by Nu,d
)()1( sppostuuSS
u
uu ttSNrS
dt
dS
)()1( relpreddSS
d
dd ttSNrS
dt
dS
4.0
ms300,
S
SS
du
r
![Page 54: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/54.jpg)
Effect on release probability
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Effect on release probability
)(][
)(])[1(
relpredddis
Pd
sppostuudis
Pu
dis
ttSSPr
ttSSPrdt
dP
![Page 56: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/56.jpg)
Effect on release probability
)(][
)(])[1(
relpredddis
Pd
sppostuudis
Pu
dis
ttSSPr
ttSSPrdt
dP
)(][ xxx
![Page 57: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/57.jpg)
Effect on release probability
)(][
)(])[1(
relpredddis
Pd
sppostuudis
Pu
dis
ttSSPr
ttSSPrdt
dP
)(][ xxx
)1();1( ddSdduuSuu SNrSSSNrSS where
are active concentrations of 2nd messengers right after post/pre spikes
![Page 58: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/58.jpg)
Effect on release probability
)(][
)(])[1(
relpredddis
Pd
sppostuudis
Pu
dis
ttSSPr
ttSSPrdt
dP
)(][ xxx
)1();1( ddSdduuSuu SNrSSSNrSS
)(1
disdisPM
dis PPdt
dP
where
are active concentrations of 2nd messengers right after post/pre spikes
Finally,
![Page 59: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/59.jpg)
State diagram:
![Page 60: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/60.jpg)
Qualitative summary
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Qualitative summary
Pre followed by post:
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Qualitative summary
Pre followed by post:move N to up state (pre)
![Page 63: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/63.jpg)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)
![Page 64: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/64.jpg)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
![Page 65: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/65.jpg)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
Post followed by pre:
![Page 66: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/66.jpg)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
Post followed by pre:move N to down state (post)
![Page 67: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/67.jpg)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
Post followed by pre:move N to down state (post)activate Sd (pre)
![Page 68: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/68.jpg)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
Post followed by pre:move N to down state (post)activate Sd (pre)downregulate Pdis (pre)
![Page 69: Lecture 14: The Biology of Learning](https://reader036.vdocuments.mx/reader036/viewer/2022062803/56814871550346895db57d3c/html5/thumbnails/69.jpg)
Simulation vs exptPre/post vs post/pre:
model expt
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Simulation vs expt (2)
model expt