Each site along the dendrite is a candidate synapse whose head volume V (a proxy for AMPA-receptor content / synaptic strength) is driven by a calcium-threshold plasticity rule, the simplified core of the calcium-control hypothesis used in structural-plasticity models (Shouval et al.; Fauth & Tetzlaff):
Ca_i(t) = coincidence trace of correlated pre- and post-synaptic spikes
Ω(Ca) = −1 for Ca < θ_d (depression)
0 for θ_d ≤ Ca ≤ θ_p (no change)
+1 for Ca > θ_p (potentiation)
dV_i/dt = η · Ω(Ca_i) · V_i(1−V_i/Vmax) − γ·V_i
Volume above Vmax/2 counts as a stabilized "mushroom" spine (low turnover, large AMPAR pool); volume that decays past a minimum eliminates the spine outright — the site returns to bare dendrite. Empty sites stochastically sprout thin, motile filopodia at a rate set by the exploration slider; a filopodium that samples enough correlated activity converts into a real spine, otherwise it retracts within a few seconds, exactly as filopodial "sampling" behaves in two-photon imaging studies of developing and adult cortex.
- Pre/post coherence — how correlated presynaptic firing is with postsynaptic depolarization (e.g. attention, rehearsal, coincident sensory input). Higher coherence pushes more sites' calcium above θp, driving net growth.
- Plasticity threshold θp — the calcium level needed to potentiate rather than depress a synapse (a simplified stand-in for NMDA-receptor/metaplastic gating). Raising it makes potentiation harder to reach, favoring pruning.
- Exploration rate — the sprouting rate of new filopodia on empty sites, i.e. how actively the dendrite samples new potential contacts.
Real-world relevance: this is the mechanism behind learning-related spine turnover measured in vivo — motor-skill training and sensory enrichment increase new spine formation and survival, while chronic low activity or aging shifts the balance toward net pruning.