Beyond Vanilla LTP Spike-timing-dependent-plasticity or STDP
Hebbian learning rule aSN W MN,aSN MN learning threshold under which LTD can occur Δ w ij = μ x j (v i - φ )
Stimulation electrode Recording electrode (extracellular) R di l d ( ll l ) Recording electrode (intracellular) 100% 5 sec ... 2 hours Baseline 100 Hz Tetanus tetanus tetanus postsynaptic activation > threshold to increase w ij Δ w ij = μ x j (v i - φ )
Recording electrode (extracellular) Recording electrode (intracellular) 100% 5 sec ... 2 hours Baseline 20 Hz 20 Hz postsynaptic activation < threshold to decrease w ij Δ w ij = μ x j (v i - φ )
v i v i time Δ w ij = μ * x j * (v i - φ ) x j time 100 Hz v i time x j time i 20 Hz v i time x j time 10 Hz 10 Hz
Induction of LTP or LTD depends not only on firing frequency but Induction of LTP or LTD depends not only on firing frequency but also on precise temporal relationship between the pre- and postsynaptic action potentials.
Pre or post only Paired Paired t post - t pre = 5ms Post Pre
Pre or post only Paired Paired t post - t pre = 5ms Post Pre
Paired Paired Pre Post Pre or post only Baseline t post - t pre = 5ms Repeated pairing (20x)
Paired pre-only Pre Post post-only Experimental manipulation pre and post AP's separated by 5 ms < 20 Hz: no LTP post > 20 Hz: more LTP 10x pre pre 20 Hz 20 Hz 4 seconds Markram et al Regulation of synaptic efficacy by coincidence of Markram et al. Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs postsynaptic APs and EPSPs. Science. 1997 Jan 10;275(5297):213 -5.
1. Stimulate cell1: -> burst of action potentials in cell1 > burst of action potentials in cell1 cell 2 cell 1 -> EPSPs in cell2 (1) Lets assume a burst of action potentials is first evoked in cell 1. This burst of action potentials will evoke an EPSP in cell 2. (1) (2)Subsequently a burst of action potentials is evoked (2) in cell 2, which will evoke and EPSP in cell 1. In the example shown here, (1) and (2) are separated by 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, (1) the burst of action potentials precceeds the EPSP by p p y (2) (2) 100 ms and in cell 2, the EPSP preceeds the action potentials by 100 ms. Bursts of AP triggered 10 ms apart
1. Stimulate cell1: -> burst of action potentials in cell1 > burst of action potentials in cell1 cell 2 cell 1 -> EPSPs in cell2 (1) Lets assume a burst of action potentials is first evoked in cell 1. This burst of action potentials will evoke an EPSP in cell 2. 2. Stimulate cell2: (1) -> burst of action potentials in cell2 (2)Subsequently a burst of action potentials is evoked (2) -> EPSPs in cell1 in cell 2, which will evoke and EPSP in cell 1. In the example shown here, (1) and (2) are separated by 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, (1) the burst of action potentials precceeds the EPSP by p p y (2) (2) 100 ms and in cell 2, the EPSP preceeds the action potentials by 100 ms. Bursts of AP triggered 10 ms apart
1. Stimulate cell1: -> burst of action potentials in cell1 > burst of action potentials in cell1 cell 2 cell 1 -> EPSPs in cell2 (1) Lets assume a burst of action potentials is first evoked in cell 1. This burst of action potentials will evoke an EPSP in cell 2. 2. Stimulate cell2: (1) -> burst of action potentials in cell2 (2)Subsequently a burst of action potentials is evoked (2) -> EPSPs in cell1 in cell 2, which will evoke and EPSP in cell 1. In the example shown here, (1) and (2) are separated by 100 ms. Because the cells are reciprocally Cell1: APs 100ms before EPSPs connected, in each cell, the burst of action potentials and evoked EPSPs are separated by 100ms. In cell 1, (1) the burst of action potentials precceeds the EPSP by p p y (2) (2) Cell2: EPSPs 100ms before APs 100 ms and in cell 2, the EPSP preceeds the action potentials by 100 ms. Bursts of AP triggered 10 ms apart
1. Stimulate cell1: -> burst of action potentials in cell1 > burst of action potentials in cell1 cell 2 cell 1 -> EPSPs in cell2 (1) Lets assume a burst of action potentials is first evoked in cell 1. This burst of action potentials will evoke an EPSP in cell 2. 2. Stimulate cell2: (1) -> burst of action potentials in cell2 (2)Subsequently a burst of action potentials is evoked (2) -> EPSPs in cell1 in cell 2, which will evoke and EPSP in cell 1. In the example shown here, (1) and (2) are separated by 100 ms. Because the cells are reciprocally Cell1: APs 100ms before EPSPs connected, in each cell, the burst of action potentials and evoked EPSPs are separated by 100ms. In cell 1, (1) the burst of action potentials precceeds the EPSP by p p y (2) (2) Cell2: EPSPs 100ms before APs 100 ms and in cell 2, the EPSP preceeds the action potentials by 100 ms. EPSP : input from presynaptic cell EPSP : input from presynaptic cell Bursts of AP triggered 10 ms apart AP: output from postsynaptic cell EPSP followed by AP: pre before post: t pre - t post < 0 y p p pre post AP followed by EPSP: post before pre: t pre - t post > 0
cell 2 cell 1 AP before EPSP: weakening Strengthening of synaptic strength was obtained when the postsynaptc cell fired 10 ms h th t t ll fi d 10 after its EPSP ft it EPSP of synaptic strength Weakening of synaptic strength was obtained when before its EPSP the postsynaptic cell fired 10 ms EPSP before AP: strengthening EPSP before AP: strengthening No change in synaptic strength was obtained when the No change in synaptic strength was obtained when the postsynaptic EPSP and AP were separated by 100ms of synaptic strength in either direction. Bursts of AP triggered 10 ms Bursts of AP triggered 10 ms Bursts of AP triggered 100 ms apart Bursts of AP triggered 100 ms apart 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 pre post t pre post t pre p pre p post post
Consider our previous example on classical conditioning: p p g Sensory input Motor output Food F S M pre before post
The change in EPSC (exitatory postsynaptic The change in EPSC (exitatory postsynaptic current) is plotted as a function of the time elapsed between the postsynaptic action potential and the the postsynaptic EPSP during simultaneous stimulation of pre- and postsynaptic cells. ll 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.
pre before post b f t post before pre Δ t = time pre - time post Bi, GQ and Poo, MM. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic hippocampal neurons: dependence on spike timing synaptic Song Miller and Abbott Competitive Hebbian Song, Miller and Abbott, Competitive Hebbian learning through spike -timing-dependent synaptic strength, and postsynaptic cell type. plasticity. J Neurosci. 1998 Dec 15;18(24):10464-72. Nat Neurosci. 2000 Sep;3(9):919 -26.
Δ w pre post 20 ms 5 ms
1 . . N . N synaptic weight N presynaptic spike trains
1 . . N . N synaptic weight N presynaptic spike trains current due to current due to leaky integrate and fire excitatory inputs excitatory inputs excitatory inputs excitatory inputs [τ dv/dt = -v + inputs]
When Vm >= -54 mV When Vm >= -54 mV, 1 neuron fires and Vm = -70 mV . . N . N synaptic weight N presynaptic spike trains current due to current due to leaky integrate and fire excitatory inputs excitatory inputs excitatory inputs excitatory inputs V rest = -70 mV, E ex = 0 mV; E in = -70 mV
N N presynaptic spike trains . . . weights napses syn time postsynaptic spikes trains naptic spike presyn
pre before post postsynaptic spikes post before pre b f trains napses . Δ t = time pre - time post . N naptic spike syn . N presynaptic spike trains presyn 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 learning Introduces competition Favors synchronous presynaptic events Δ t = time Δ t time pre time post - time t
Issues: At high firing rates, when pre and postsynaptic neurons are phase-locked both parts of the learning rule are phase locked, both parts of the learning rule apply for any given spike! 20 ms (50 Hz) pre 30 ms post 10 ms
Issues: At high firing rates, when pre and postsynaptic neurons are 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 each postsynaptic spikes interacts with each presynaptic spike and effects sum up linearly!
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