Lecture 14: The Biology of Learning References: H Shouval, M F Bear, L N Cooper, PNAS 99,...
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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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Transcript of Lecture 14: The Biology of Learning References: H Shouval, M F Bear, L N Cooper, PNAS 99,...
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
Learning = long-term synaptic changes
Long-term potentiation (LTP) and long-term depression (LTD)
Learning = long-term synaptic changes
Long-term potentiation (LTP) and long-term depression (LTD)
CA1 region of rat hippocampus
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)
Timing dependence
Spike-timing dependent plasticity (STDP)
Timing dependence
Spike-timing dependent plasticity (STDP)
(Markram et al, 1997)
Timing dependence
Spike-timing dependent plasticity (STDP)
(Markram et al, 1997) (Zhang et al, 1998)
Model I: Ca control modelShouval et al:
Model I: Ca control modelShouval et al:
Everything depends on Ca concentration
Model I: Ca control modelShouval et al:
Everything depends on Ca concentration
Ca flows in through NMDA channels
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)
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
Ca control model (2)
NMDA channel current (after spike at t = 0):
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
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
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
Ca control model (3)Synaptic strength (conductance) obeys
)][])(([ WCaCadt
dW
Ca control model (3)Synaptic strength (conductance) obeys
)][])(([ WCaCadt
dW
Ca control model (3)Synaptic strength (conductance) obeys
)][])(([ WCaCadt
dW
Back-propagating action potential:
]e)1(e[)( //0
bss
bsf tbs
ftbs
fBS IIVtV
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
Possible basis of equation for synaptic changes
AMPA receptors – in membrane (active) and in cytoplasm (inactive)
Kinetic equations:
IImRm AkAk
dtdA
IImRI AkAk
dtdA
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
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
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
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
How it works
Need the slow tail of the BPAP
LTD if presynaptic spike is too far in advance of postsynaptic one
LTD if presynaptic spike is too far in advance of postsynaptic one
(unavoidable consequence of model assumptions)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Model II (2 second messengers)(Senn, Markram, Tsodyks, 2001)
Markram-Tsodyks experiments (rat barrel cortex, exc-exc):
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
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)
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
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
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
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
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
2-messenger model (2)
2-messenger model (2)
NMDA receptorsHave 3 states
2-messenger model (2)
NMDA receptorsHave 3 states
2nd messenger#1
2-messenger model (2)
NMDA receptorsHave 3 states
2nd messenger#2
2nd messenger#1
NMDA receptorsKinetic equations:
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
)( sppostrec
NdN
d
dd ttNrN
dt
dN
NMDA receptorsKinetic equations:
)( relprerec
NuN
u
uu ttNrN
dt
dN
)( sppostrec
NdN
d
dd ttNrN
dt
dN
1 recud NNN
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
2nd messengers
Activation driven by Nu,d
2nd messengers
Activation driven by Nu,d
)()1( sppostuuSS
u
uu ttSNrS
dt
dS
2nd messengers
Activation driven by Nu,d
)()1( sppostuuSS
u
uu ttSNrS
dt
dS
)()1( relpreddSS
d
dd ttSNrS
dt
dS
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
Effect on release probability
Effect on release probability
)(][
)(])[1(
relpredddis
Pd
sppostuudis
Pu
dis
ttSSPr
ttSSPrdt
dP
Effect on release probability
)(][
)(])[1(
relpredddis
Pd
sppostuudis
Pu
dis
ttSSPr
ttSSPrdt
dP
)(][ xxx
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
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,
State diagram:
Qualitative summary
Qualitative summary
Pre followed by post:
Qualitative summary
Pre followed by post:move N to up state (pre)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
Qualitative summary
Pre followed by post:move N to up state (pre)activate Su (post)upregulate Pdis (post)
Post followed by pre:
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)
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)
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)
Simulation vs exptPre/post vs post/pre:
model expt
Simulation vs expt (2)
model expt
