Spike-Timing Spine Plasticity (2D)

Pairing Protocol

Timing offset Δt (post − pre) +10 ms

Pairing frequency 5.0 Hz

Test Spine (yours)

Ca²⁺ trace

0.00

Head volume V

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State

thin

Pairs fired

Thin / labile spine

Mushroom — stabilized (LTP)

Retracting (LTD)

▲ orange = pre-spike · ▼ cyan = post-spike

How it works

Each spine tracks a calcium-coincidence trace Ca(t) driven directly by scheduled pre- and post-synaptic spikes, and a head volume V that obeys the calcium-control hypothesis (Shouval, Graupner & Brunel-style reduced model). Both are integrated frame-by-frame, not scripted:

Ca(t): jumps by C_pre at t_pre+δ (NMDAR opening delay)
       jumps by C_post at t_post = t_pre + Δt (bAP/VGCC influx)
       decays as dCa/dt = −Ca/τ_Ca between jumps

Ω(Ca) = +1   Ca > θ_p            (potentiation)
         0   θ_d < Ca ≤ θ_p      (deadband)
        −1   ε < Ca ≤ θ_d        (moderate, subthreshold → depression)
         0   Ca ≤ ε               (quiescent — no active signal)

dV/dt = η·Ω(Ca)·V(1−V/Vmax) − γ·V   (Euler-integrated every frame)

When the pre spike's delayed NMDAR-mediated influx overlaps the post spike's influx — small positive Δt, pre firing shortly before post — the two calcium jumps sum supralinearly and cross θ_p, driving net growth. When Δt is negative or large, the jumps miss each other, the trace only grazes the depression band, and the spine net-shrinks. A spine that never fires simply decays passively toward its resting volume — no coincident activity, no active signal either way.

Δt (timing offset) — post-spike time minus pre-spike time. Small positive values (pre-before-post, ~+10 ms) give the strongest calcium coincidence and the strongest potentiation; negative values (post-before-pre) or large offsets miss the coincidence window.
Pairing frequency — how often a pre/post pair repeats. Higher frequency repeats the coincidence more often per second, accelerating whichever direction (growth or shrinkage) Δt selects.

Real-world relevance: this Δt-dependence is the defining signature of spike-timing-dependent plasticity (STDP) measured across cortex and hippocampus — the same "who fired first" coincidence detection that lets correlated activity during learning selectively strengthen the synapses that predicted a postsynaptic response.

t = 0.0 s