This lab models the structural side of synaptic plasticity: dendritic spines — the small actin-rich protrusions that host most excitatory synapses — physically growing, shrinking, and being formed or pruned. That is a different mechanism from spike-timing-dependent plasticity (STDP), which only changes how strongly an existing connection transmits a signal. Here, each spine's own head volume changes because of what its synapse has recently experienced.
Every spine keeps a leaky-integrator calcium trace, Ca(t), that rises with each simulated NMDA-receptor-mediated calcium influx event (driven by local synaptic input) and decays exponentially between events:
event with probability r(x,t)·dt → Ca += q
every step: dCa/dt = −Ca/τ_Ca
Spine size S then follows a real bidirectional calcium-threshold rule (the same class of rule used in calcium-based plasticity models, applied here to spine volume instead of synaptic weight): high sustained Ca drives actin polymerization and growth, low Ca lets constitutive actin turnover shrink the spine, and a spine that shrinks past a minimum size is pruned outright.
dS/dt = k_grow·σ(Ca−θ_p)·(S_max−S)
− k_shrink·σ(θ_d−Ca)·S
− turnover·S
- Local burst zone places a Gaussian-shaped patch of high input rate along the dendrite — drag it to see spines under the patch grow while spines outside it don't.
- Spontaneous background gives every spine a small non-zero baseline input rate, keeping already-grown spines alive without letting new ones form quickly.
- Deprivation pulse cuts all input to zero for 6 seconds, mimicking sensory deprivation experiments — spines without a rescuing burst shrink and prune.
- New thin filopodia sprout at random positions at a steady baseline rate — real dendrites constantly sample the surrounding neuropil this way. Most retract within seconds; only ones that land in an active zone accumulate enough calcium to stabilize into a real spine, directly illustrating the synaptotropic hypothesis of activity-dependent spine stabilization.
Real-world relevance: this activity-dependent growth/pruning of dendritic spines is believed to be how the brain physically wires and rewires itself over hours to days — the structural substrate that STDP's fast synaptic-weight changes ultimately consolidate into (or fail to, if the activity doesn't persist).