How it Works
The BCM (Bienenstock-Cooper-Munro) rule models synaptic plasticity with a sliding threshold. The modification function φ(v_post) is negative (LTD) when postsynaptic activity is below θ_M and positive (LTP) when above. The threshold θ_M itself slides with the running average of postsynaptic activity, providing homeostatic stability.
The simulation shows the time course of synaptic weight W under different pre/post firing rate combinations. The BCM curve is plotted in real time, showing where LTP/LTD transitions occur.
φ(v, θ) = v · (v − θ) [BCM modification function]
dθ_M/dt = (v_post² − θ_M) / τ_θ [sliding threshold]
v_post = W · v_pre + noise
Frequently Asked Questions
What is Long-Term Potentiation (LTP)?
LTP is a long-lasting increase in synaptic strength following high-frequency stimulation. It requires coincident pre- and postsynaptic activity (Hebbian rule), is dependent on NMDA receptor activation, and is widely considered a cellular mechanism for learning and memory formation.
What is Long-Term Depression (LTD)?
LTD is a long-lasting decrease in synaptic strength, typically induced by low-frequency stimulation or asynchronous pre/post activity. It is thought to balance LTP, preventing saturation of synaptic weights and allowing forgetting or memory refinement.
What is the Hebbian learning rule?
Hebb's rule: 'Neurons that fire together, wire together.' Formally, the synaptic weight change dW/dt ∝ v_pre · v_post. When pre- and postsynaptic neurons are simultaneously active, the synapse is strengthened. This is implemented biophysically through NMDA receptor coincidence detection.
What is the BCM rule?
The BCM rule extends Hebb: dW/dt = φ(v_post, θ_M) · v_pre, where φ changes sign at a sliding threshold θ_M. Below θ_M, activity induces LTD; above θ_M, it induces LTP. θ_M slides with mean postsynaptic activity, providing synaptic stability.
How do NMDA receptors act as coincidence detectors?
NMDA receptors require both glutamate binding (presynaptic) and postsynaptic depolarization to remove the Mg²⁺ block. This coincidence detection means only synapses active while the postsynaptic cell is depolarized become potentiated — implementing Hebbian plasticity at the molecular level.
What is spike-timing-dependent plasticity (STDP)?
STDP is a precise form of Hebbian plasticity where the direction and magnitude of synaptic change depends on the relative timing of pre- and postsynaptic spikes. If the presynaptic spike precedes postsynaptic firing by less than 20ms, LTP occurs; if it follows, LTD is induced.
What is synaptic tagging?
Synaptic tagging is a mechanism for late-LTP requiring protein synthesis. Brief stimulation sets a 'tag' at active synapses. When strong stimulation elsewhere triggers protein synthesis, those proteins are captured by tagged synapses, converting early-LTP (hours) into late-LTP (days), linking different memories.
How does LTP relate to memory?
LTP is the leading candidate for the synaptic basis of memory. Evidence includes: LTP induction uses the same protocols as learning, LTP occurs in memory areas (hippocampus), blocking NMDA receptors impairs both LTP and spatial learning, and spine enlargement during LTP mirrors changes seen in learning.
What is metaplasticity?
Metaplasticity is 'plasticity of plasticity' — the history of synaptic activity modifies the threshold for future LTP/LTD. In the BCM rule, θ_M slides upward with high average activity (making LTP harder to induce) and downward with low activity, preventing runaway potentiation.
What is the role of CaMKII in LTP?
CaMKII (Ca²⁺/calmodulin-dependent protein kinase II) is a key LTP effector. Ca²⁺ influx through NMDA receptors activates CaMKII, which phosphorylates AMPA receptors (increasing conductance), promotes AMPA receptor insertion into the synapse, and can remain active after Ca²⁺ returns to baseline (molecular memory).