64 Spike-timing dependent plasticity
A guide to the interactive demonstration
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A single self-contained HTML file sitting next to this guide. Everything runs in your browser — nothing to install, nothing uploaded, works offline.
This is the companion to the Hebbian plasticity demo. That one shows what plasticity does to a neuron over thousands of milliseconds; this one zooms in on a single pairing and shows how the synapse decides.
65 The question this answers
The Hebbian demo established that a synapse changes only when presynaptic activity coincides with a postsynaptic spike, and that reversing the order of those two events reverses the sign of the change. It treated that rule as given.
The obvious question is how a synapse could possibly know any of this. It is a sub-micron structure at the end of a dendrite. It has no access to the soma, no clock, and no way to observe the cell as a whole. What it does have is an NMDA receptor, and that is enough.
66 The mechanism
You have already seen NMDA receptors as coincidence detectors. The demonstration makes the two coincident signals explicit and lets you slide them past each other.
66.1 Signal one: glutamate binding
When the presynaptic terminal releases glutamate, it binds to NMDA receptors on the spine. Binding alone does nothing — the pore is plugged by a Mg²⁺ ion sitting in the channel, and no current flows. What binding does is start a clock. The receptors stay bound and available for a few tens of milliseconds, then let go.
In the demo this is the orange trace, labelled glutamate bound. It jumps when glutamate is released and decays with a 20 ms time constant.
66.2 Signal two: depolarisation
The Mg²⁺ block is voltage-dependent. Depolarise the spine and the ion is electrostatically expelled, unplugging the channel. The depolarisation that matters here arrives from the backpropagating action potential: when the cell fires, the spike does not only travel down the axon, it also propagates back up the dendritic tree and briefly depolarises every spine on it.
In the demo this is the violet trace, labelled Mg²⁺ block relieved. It jumps about 2 ms after the somatic spike — the time the bAP takes to reach the spine — and decays with a 20 ms time constant.
Notice what this signal is: a single global broadcast, identical at every synapse on the cell. It carries no information about which synapse did what.
66.3 The product
Calcium enters only where the two overlap. Glutamate without depolarisation leaves the channel plugged; depolarisation without glutamate leaves it closed. The calcium influx is therefore the product of the two signals, drawn as the dark shaded region in the demo.
\[ \text{Ca}^{2+}\text{ influx}(t) \;\propto\; \underbrace{G(t)}_{\text{glutamate bound}} \times \underbrace{D(t)}_{\text{block relieved}} \]
The peak of that product is the coincidence, reported as a percentage. With both signals decaying at \(\tau = 20\) ms, it works out to a clean exponential:
\[ \text{coincidence} = e^{-|\Delta t + 2| / 20} \]
where \(\Delta t = t_{\text{post}} - t_{\text{pre}}\), the same convention as the pairing-delay slider in the Hebbian demo. The magnitude of the weight change is proportional to this, and matches the rule used in that demo to within 0.016 mV across the whole window.
The +2 in that expression is the 2 ms the backpropagating spike takes to reach the spine. What the receptor detects is the order of events at the spine, not at the soma, so the window is centred at Δt = −2 ms. The demo marks this on the curve as order reverses here.
This is a small effect at a proximal synapse and a large one at a distal dendrite, which is one reason the measured STDP window depends on where on the dendritic tree you record.
66.4 Where the sign comes from — and where it does not
A coincidence detector is symmetric. The product of two exponentials with the same time constant gives exactly the same peak whether glutamate leads the spike by 15 ms or trails it by 15 ms. The mechanism above cannot tell you the sign of the change. You can confirm this in the demo: at Δt = +8 and Δt = −12 (both 10 ms from the centre of the window) the coincidence readout is identical at 61%, but one produces LTP and the other LTD.
What differs is the order in which the two conditions were met, and you can see it directly in the signals panel:
- Glutamate first. The gate is already open and decaying when the spike arrives. Calcium influx begins at the moment of the spike and rises sharply to its peak.
- Spike first. The depolarisation is already decaying when glutamate arrives. Calcium influx begins when glutamate arrives, and reaches a lower peak more slowly.
A large, fast calcium transient preferentially activates CaMKII and drives potentiation; a smaller, more prolonged one preferentially activates phosphatases such as calcineurin and drives depression. The demonstration asserts this sign rule rather than deriving it — it is an experimental result about downstream signalling, and the details are still argued about. Be explicit with students about which part of the model is mechanism and which part is summary; the honest version is more interesting than a seamless one.
67 Reading the display
67.1 The cell
Two dendrites, each ending in a spine. Head size is the synaptic weight, on the same scale as the Hebbian demo (starting at 1.2 mV, floor 0.3, ceiling 5.0).
During a pairing you see three things at each spine, keyed at the foot of the panel: an orange ring for glutamate bound, a violet halo for the Mg²⁺ block being relieved, and a dark core for calcium entering. The violet bAP travels out both dendrites and down the axon.
Watch what happens at synapse B. It receives the same bAP, at the same instant, and its halo is just as bright as A’s. What it does not have is glutamate bound at the right moment. Same global signal, different local state, opposite outcome — that is synapse specificity, made concrete.
67.2 Signals at the spine
The three traces described above, plotted against time relative to the somatic spike, with the calcium peak marked and labelled with the coincidence percentage. The dashed detection floor is the level below which the change is too small to measure; a real induction experiment has one too.
The tabs switch the panel between synapse A and synapse B.
67.3 The STDP window
Weight change per pairing against Δt. The solid line is the model’s prediction across the whole range; the dots are the pairings you have actually run — orange for synapse A, teal for synapse B, small grey ones from the sweep.
By the end of protocol 5 the class has plotted a textbook STDP curve from a mechanism, rather than being shown one and told to believe it.
68 The five protocols
68.1 Glutamate, no spike
Both synapses receive glutamate; the cell never fires. The NMDA receptors bind glutamate and stay plugged. Coincidence 0%, no calcium, no change.
The point: this is the single-receptor version of protocol 2 in the Hebbian demo, where a perfectly synchronised input pattern presented for a full minute changed nothing. Now you can see why. Presynaptic activity satisfies exactly one of the two conditions the receptor requires.
68.2 Glutamate 10 ms before the spike
Synapse A: coincidence 55%, potentiation. Synapse B, on the same cell and the same action potential, gets Δt = −10 ms and depresses.
The point: one spike, two synapses, opposite outcomes, decided entirely by which one had glutamate bound when the depolarisation arrived.
68.3 Spike 10 ms before glutamate
The mirror image. Watch the dark calcium region in the signals panel: it now starts when glutamate arrives rather than at the spike.
The point: the amount of overlap is nearly the same as in protocol 2 — the sign changed, not the magnitude. This is the observation that motivates Section 66.4.
68.4 Too far apart (60 ms)
Both events occur, in the right order, 60 ms apart. The gate has closed before the spike arrives, the coincidence falls below the detection floor, and nothing measurable happens at either synapse.
The point: coincidence detection has a deadline, and the deadline is set by how long the receptors hold glutamate.
68.5 Sweep the whole window
Every Δt from −70 to +70 ms, measured without inducing any plasticity. The dots fill in the full curve.
The point: the shape is not an assumption. It follows from two exponentially decaying signals multiplied together, and its width is the NMDA receptor’s own time constant.
69 Things to try
Predict before running. Set the slider somewhere unusual — Δt = −3, say — and ask the class which way the synapse will go and how strongly, before pressing Run.
Slow the playback to 0.02×. Each pairing then takes about twelve seconds, and you can talk through the two signals arriving while the animation is still running.
Use Repeat ×20. A single pairing changes the weight by less than 0.1 mV, which is invisible. Twenty pairings at Δt = +10 ms takes synapse A from 1.2 to about 2.5 mV while synapse B is driven to its floor, and the size difference in the cell panel becomes obvious. Real induction protocols use 60 to 100 pairings for the same reason.
Find the crossover by hand. Step the slider through −5, −4, −3, −2, −1, 0 and watch the verdict flip between −2 and −1. Then ask why it is not at zero.
Compare the two demos. In the Hebbian demo, set the pairing delay to +10 ms and run protocol 3, then set it to −10 ms and run protocol 4. Those are the same two conditions as protocols 2 and 3 here, played out over thousands of pairings instead of one.
70 Where the model simplifies
- The sign is asserted, not derived. See Section 66.4. This is the model’s largest gap and the most honest thing to say out loud.
- NMDA deactivation is faster here than in life. Real NMDA receptor currents decay over 50–200 ms, considerably longer than the 20 ms used here. The measured STDP window is nevertheless only tens of milliseconds wide, and reconciling those two facts is an active question. The 20 ms figure was chosen to match the window and to agree with the companion demo.
- One pairing, in isolation. Real STDP depends on the frequency of pairing as well as the interval: the same Δt repeated at 50 Hz and at 0.5 Hz gives different outcomes, because calcium and the receptor state from one pairing are still present when the next arrives. Nothing here carries over between pairings.
- No explicit calcium concentration or enzyme cascade. Calcium influx is shown; the concentration it produces, the CaMKII and phosphatase pathways it recruits, and the structural changes that follow are all compressed into a single number.
- AMPA receptors are ignored. The EPSP’s own depolarisation does relieve some Mg²⁺ block in a real spine, so glutamate alone produces a little calcium rather than none. Here it produces none, which makes protocol 1 crisper than reality.
- The spine is a point on an unbranched dendrite, and the bAP arrives undiminished. In a real neuron the bAP attenuates with distance and can fail entirely in distal branches — which is precisely why some synapses are much harder to potentiate than others.
None of these affect the three things the demonstration exists to show: that a synapse detects coincidence through a single receptor, that the width of the window is that receptor’s own time constant, and that the order of the two events determines the sign of the change.