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Beyond Vanilla LTP
Spike-timing-dependent-plasticityor
STDP
Hebbian learning rule
aSN MNWMN,aSN
Δwij = μ xj (vi - φ) learning threshold under which LTD can occur
Stimulation electrodeR di l d ( ll l )Recording electrode (extracellular)
Recording electrode (intracellular)
100%
Baseline
5 sec
100 Hz tetanus
... 2 hours
Tetanustetanus
postsynaptic activation > threshold to increase wij
Δwij = μ xj (vi - φ)
Recording electrode (extracellular)
Recording electrode (intracellular)
5 sec
... 2 hours
100%
Baseline 20 Hz 20 Hz
postsynaptic activation < threshold to decrease wij
Δwij = μ xj (vi - φ)
vivi
xj
time
Δwij = μ * xj * (vi-φ) time100 Hz
vi
xj
time
itime20 Hz
vi
xj
time
time10 Hz10 Hz
Induction of LTP or LTD depends not only on firing frequency butInduction of LTP or LTD depends not only on firing frequency but also on precise temporal relationship between the pre- and postsynaptic action potentials.
Paired
PrePost
Paired
Pre or post only
tpost - tpre = 5ms
Paired
PrePost
Paired
Pre or post only
tpost - tpre = 5ms
Paired
PrePost
Paired
Pre or post only
Baseline
tpost - tpre = 5ms
Repeated pairing (20x)
Pre Post
Paired
pre-onlypost-only
Experimental manipulation
pre and post AP's separated by 5 ms
pre
post10x
< 20 Hz: no LTP> 20 Hz: more LTP
pre20 Hz 20 Hz
4 seconds
Markram et al Regulation of synaptic efficacy by coincidence ofpostsynaptic APs and EPSPsMarkram et al. Regulation of synaptic efficacy by coincidence ofpostsynaptic APs and EPSPs.Science. 1997 Jan 10;275(5297):213-5.
1. Stimulate cell1: > burst of action potentials in cell1
(1) Lets assume a burst of action potentialsis first evoked in cell 1. This burst of action
cell 1 cell 2-> burst of action potentials in cell1-> EPSPs in cell2
potentials will evoke an EPSP in cell 2.
(2)Subsequently a burst of action potentials is evoked in cell 2, which will evoke and EPSP in cell 1.
(1)(2)
In the example shown here, (1) and (2) are separatedby 100 ms. Because the cells are reciprocally connected, in each cell, the burst of action potentials and evoked EPSPs are separated by 100ms. In cell 1, the burst of action potentials precceeds the EPSP by
(1)
(2)
Bursts of AP triggered 10 ms
p p y100 ms and in cell 2, the EPSP preceeds the actionpotentials by 100 ms.
(2)
apart
1. Stimulate cell1: > burst of action potentials in cell1
(1) Lets assume a burst of action potentialsis first evoked in cell 1. This burst of action
cell 1 cell 2-> burst of action potentials in cell1-> EPSPs in cell2
potentials will evoke an EPSP in cell 2.
(2)Subsequently a burst of action potentials is evoked in cell 2, which will evoke and EPSP in cell 1.
(1)(2)
2. Stimulate cell2: -> burst of action potentials in cell2-> EPSPs in cell1
In the example shown here, (1) and (2) are separatedby 100 ms. Because the cells are reciprocally connected, in each cell, the burst of action potentials and evoked EPSPs are separated by 100ms. In cell 1, the burst of action potentials precceeds the EPSP by
(1)
(2)
Bursts of AP triggered 10 ms
p p y100 ms and in cell 2, the EPSP preceeds the actionpotentials by 100 ms.
(2)
apart
1. Stimulate cell1: > burst of action potentials in cell1
(1) Lets assume a burst of action potentialsis first evoked in cell 1. This burst of action
cell 1 cell 2-> burst of action potentials in cell1-> EPSPs in cell2
potentials will evoke an EPSP in cell 2.
(2)Subsequently a burst of action potentials is evoked in cell 2, which will evoke and EPSP in cell 1.
(1)(2)
2. Stimulate cell2: -> burst of action potentials in cell2-> EPSPs in cell1
In the example shown here, (1) and (2) are separatedby 100 ms. Because the cells are reciprocally connected, in each cell, the burst of action potentials and evoked EPSPs are separated by 100ms. In cell 1, the burst of action potentials precceeds the EPSP by
(1)
(2)
Cell1: APs 100ms before EPSPs
Bursts of AP triggered 10 ms
p p y100 ms and in cell 2, the EPSP preceeds the actionpotentials by 100 ms.
(2) Cell2: EPSPs 100ms before APs
apart
1. Stimulate cell1: > burst of action potentials in cell1
(1) Lets assume a burst of action potentialsis first evoked in cell 1. This burst of action
cell 1 cell 2-> burst of action potentials in cell1-> EPSPs in cell2
potentials will evoke an EPSP in cell 2.
(2)Subsequently a burst of action potentials is evoked in cell 2, which will evoke and EPSP in cell 1.
(1)(2)
2. Stimulate cell2: -> burst of action potentials in cell2-> EPSPs in cell1
In the example shown here, (1) and (2) are separatedby 100 ms. Because the cells are reciprocally connected, in each cell, the burst of action potentials and evoked EPSPs are separated by 100ms. In cell 1, the burst of action potentials precceeds the EPSP by
(1)
(2)
Cell1: APs 100ms before EPSPs
Bursts of AP triggered 10 ms
p p y100 ms and in cell 2, the EPSP preceeds the actionpotentials by 100 ms.
(2) Cell2: EPSPs 100ms before APs
EPSP : input from presynaptic cellapart
EPSP : input from presynaptic cellAP: output from postsynaptic cell
EPSP followed by AP: pre before post: tpre - tpost < 0y p p pre postAP followed by EPSP: post before pre: tpre - tpost > 0
cell 1 cell 2
Strengtheningof synaptic strength was obtainedh th t t ll fi d 10 ft it EPSPAP before EPSP: weakening
when the postsynaptc cell fired 10 ms after its EPSP
Weakening of synaptic strength was obtained when the postsynaptic cell fired 10 ms before its EPSP
No change in synaptic strength was obtained when the
of synaptic strength
EPSP before AP: strengthening
Bursts of AP triggered 100 ms apart Bursts of AP triggered 10 ms
No change in synaptic strength was obtained when the postsynaptic EPSP and AP were separated by 100ms in either direction.
EPSP before AP: strengthening of synaptic strength
Bursts of AP triggered 100 ms apart Bursts of AP triggered 10 ms apart
Summary:Summary:
1) If a pre-synaptic cell fires BEFORE a connected postsynaptic cell, the synapse connecting them increases in strength
2) If pre-synaptic cell fires AFTER a connected postsynaptic cell, the synpase between them decreases in strength
t tpre post
pre
pre post
pre p
post
p
post
Consider our previous example on classical conditioning: p p g
Sensory input
Motor output
Food
F
S
Mpre before post
The change in EPSC (exitatory postsynapticThe change in EPSC (exitatory postsynapticcurrent) is plotted as a function of the time elapsed between the postsynaptic actionpotential and the the postsynaptic EPSP duringsimultaneous stimulation of pre- and postsynaptic
llcells.
Bi, GQ and Poo, MM. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type.J Neurosci. 1998 Dec 15;18(24):10464-72.
b f tpre before post
post before pre
Δt = timepre - timepost
Bi, GQ and Poo, MM. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing synaptic Song Miller and Abbott Competitive Hebbianhippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type.J Neurosci. 1998 Dec 15;18(24):10464-72.
Song, Miller and Abbott, Competitive Hebbian learning through spike-timing-dependent synaptic plasticity.Nat Neurosci. 2000 Sep;3(9):919-26.
Δw
pre
post
5 ms 20 ms
.
. N
1
.
N presynaptic spike trainsN synaptic weight
.
. N
1
.
N presynaptic spike trainsN synaptic weight
leaky integrate and fire current due to excitatory inputs
current due to excitatory inputs
[τ dv/dt = -v + inputs]
excitatory inputs excitatory inputs
When Vm >= -54 mV
.
. N
1 When Vm >= -54 mV, neuron fires and Vm = -70 mV
.
N presynaptic spike trainsN synaptic weight
leaky integrate and fire current due to excitatory inputs
current due to excitatory inputsexcitatory inputs excitatory inputs
Vrest = -70 mV, Eex = 0 mV; Ein = -70 mV
postsynaptic spikestra
ins
naps
es .. N
napt
ic sp
ike
syn .
N presynaptic spike trains
pres
yn
time weights
postsynaptic spikes
pre before post
b f
train
s
naps
es .. N
Δt = timepre - timepost
post before pre
napt
ic sp
ike
syn .
N presynaptic spike trains
pres
yn
time weights
NO LEARNING: A+ = 0 and A- = 0
A+ >0 and A- = 0 A+ =0 and A- > 0
A+ ~= A- A+ < A-
Stabilizes Hebbian learningIntroduces competition Favors synchronous presynaptic events
Δt = time - time tΔt timepre timepost
Issues:
At high firing rates, when pre and postsynaptic neuronsare phase-locked both parts of the learning ruleare phase locked, both parts of the learning rule apply for any given spike!
20 ms (50 Hz)
pre
30 mspost
10 ms
Issues:
At high firing rates, when pre and postsynaptic neuronsare phase-locked, both parts of the learning rule apply for any given spike! pp y y g p
20 ms (50 Hz)
pre
post+
++
+ --
postsynaptic spikes interacts with eachpostsynaptic spikes interacts with each presynaptic spike and effects sum up linearly!
Issues:
At high firing rates, when pre and postsynaptic neuronsare phase-locked, both parts of the learning rule apply for any given spike! pp y y g p
20 ms (50 Hz)
pre
post++ -
postsynaptic spikes interacts only withpostsynaptic spikes interacts only withimmediatly preceeding presynaptic spikes
Here we have systematically varied the rate, timing and number of coincident afferents in order to explore the rules that govern induction of long-term plasticity b t ti ll t d thi k t ft d L5 i t i l tbetween monosynaptically connected thick, tufted L5 neurons in rat visual cortex. Our experiments reveal a joint dependence of plasticity on timing and rate, as well as a novel form of cooperativity operating even when the postsynaptic AP is evoked by current injection Based on these experiments we have constructed aevoked by current injection. Based on these experiments we have constructed a quantitative description, which accurately predicts the build-up of potentiation and depression during random firing.
Sjostrom PJ, Turrigiano GG, and Nelson SB. Rate, timing, and cooperativityjointly determine cortical synaptic plasticity. Neuron 32: 1149-1164, 2001.
presynaptic
t tipostsynaptic
measure for strength of synapse
1) LTP depends on stimulation frequency
40 Hz 0.1 Hz
1) LTP depends on stimulation frequency
40 Hz 0.1 Hz
1) LTP depends on stimulation frequency
40 Hz 0.1 Hz
At high frequencies, LTP always dominates!
At high frequencies, LTP always dominates!
All spike interactions
li l
Only nearest spike
All spike interactions sum linearly, but if LTP
sum linearly spike interactions count
y,is present, LTD is not applied
All three models used frequency and voltage dependencies determinedfrom data in this paper.
Models tested with new data NOT used for fitting!