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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
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)
(Markram et al, 1997) (Zhang et al, 1998)
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):
)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
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
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)
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
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
)()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
)(][
)(])[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,
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)