`Voltage-Context` is labelled as an Episode but contains sub-episodes — it should be a Context. Same for `NMDA-Coincidence` and `Ca-Dynamics & ATP-Drain`. You have used Episode and Context interchangeably in a few places; the distinction matters for the specification: a Context sets the conditions, an Episode is a named outcome within those conditions.
`Vpost_Maximum` lists `V_bAP full OR (g_AMPA full AND V_bAP medium)` — this is correct Boolean logic and should be kept exactly as written. It captures the two ways the postsynapse can reach maximum depolarisation: the bAP alone if it is strong enough, or AMPA plus a partial bAP together.
`AMPA_Population_Increase` correctly gates on `ATP_level_post NOT empty` — LTP requires ATP for CaMKII phosphorylation and receptor trafficking. LTD does not have the same gate in your spec. This is slightly asymmetric — LTD (receptor internalisation via endocytosis) is also ATP-dependent, though less so than LTP. Worth noting.
`Plasticity_LTD` covers `Ca_post_history medium` but does not cover the case where `Ca_post_history` is empty — a completely silent synapse also weakens over time (homeostatic depression). This can be left as a gap or named explicitly.
The bAP needs new parameters and state variables in the model before it can be expressed as a fully implemented behavior. I will add those inline as `[GAP — to implement]` markers so the spec is complete even where the code is not yet written.
Short-term potentiation (STP) and short-term depression (STD) are distinct from LTP/LTD in a fundamental way: they are **temporary** changes that last seconds to minutes and leave no lasting structural trace. They do not require the postsynapse at all — they are entirely presynaptic phenomena in most cases, and they operate on a completely different mechanism.
---
**What they are and where they live**
Short-term plasticity is driven by the **history of presynaptic Ca²⁺** and **vesicle pool state**, not by postsynaptic coincidence detection. The table we just built describes long-term plasticity — structural changes to AMPA density driven by Ca_post. Short-term plasticity describes transient changes to **how much NT the presynapse releases** on the next spike, driven by what happened on the last few spikes.
There are two opposing forms:
**Short-term potentiation / facilitation** — if a spike arrives shortly after the previous one, residual Ca²⁺ from the first spike has not fully cleared. The next spike adds to this residual, producing a larger Ca_post microdomain and therefore a higher release probability. The synapse releases more NT on the second spike than the first. This is already partially captured in the presynaptic model through `Tr_Ca` — elevated calcium trace from recent activity speeds up RRP recruitment and effectively increases release efficiency.
**Short-term depression** — if spikes arrive rapidly, the RRP depletes faster than it can be refilled. Each successive spike releases fewer vesicles because there are fewer available. NT release drops with each spike in a burst. This is already the core of CASCADE 1 in the presynaptic model — RRP depletion under high firing rate.
---
**Where they fit in the model**
Both are already implicitly present in the presynaptic ms and seconds loops:
```
Short-term facilitation:
Residual Ca_micro from spike N
→ elevated Ca_micro at spike N+1
→ higher release fraction in deterministic_release (Hill curve)
→ more NT per spike
→ decays as Ca_micro clears between spikes (tau ~100-200 ms)
Short-term depression:
Rapid firing depletes N_RRP
→ fewer vesicles available per spike
→ released_NT falls
→ recovers as RP→RRP recruitment refills (seconds timescale)
```
The timescale of each depends on parameters already in the model:
The model captures both implicitly but does not name them as behaviours. Two things are genuinely absent:
**Augmentation** — a slower form of facilitation lasting 5-10 seconds, driven by residual Ca²⁺ accumulating in the presynaptic terminal across many spikes. It is distinct from spike-by-spike facilitation and would require a second, slower Ca²⁺ trace with `tau ~5000 ms`. The current `Tr_Ca` with `tau = 1000 ms` is between the two — it captures some augmentation but not cleanly.
**Post-tetanic potentiation (PTP)** — an even slower presynaptic enhancement lasting minutes after a high-frequency burst, driven by protein kinase C activation from sustained Ca²⁺ elevation. This is a presynaptic phenomenon that looks like LTP from the outside but has no postsynaptic component and no structural change. It would require a third, very slow trace variable.
---
**How they interact with the LTP/LTD table**
Short-term and long-term plasticity operate on the same synapse simultaneously but independently:
```
Spike arrives
→ short-term: how much NT releases THIS spike (presynaptic, ms-seconds)
→ long-term: does the synapse get stronger or weaker PERMANENTLY (postsynaptic, mins-hours)
```
A synapse can be undergoing LTD (slowly losing AMPA receptors over minutes) at the same time as it is showing short-term facilitation (releasing more NT per spike due to residual Ca²⁺). The two processes do not interfere — they act on different variables through different mechanisms.
The important implication for your model is that **the LTP/LTD table we built describes what happens to**`g_AMPA_baseline`**over minutes**. Short-term potentiation/depression describes what happens to `released_NT` over milliseconds to seconds. They are different outputs of the same synapse, running in parallel.
If you want to add short-term plasticity explicitly to the behaviour specification it would live entirely in the presynaptic ms and seconds loops as named episodes of existing variables:
```
— ms (presynapse, short-term plasticity):
ShortTermFacilitation: Episode
— residual Ca_micro > 0 at next spike arrival
— release_frac in deterministic_release elevated above baseline
— decays as Ca_micro clears (tau ~100-500 ms)
— more NT per spike than at rest
ShortTermDepression: Episode
— N_RRP depleted by rapid successive spikes
— release_frac unchanged but N_RRP reduced
— fewer absolute vesicles released per spike
— recovers via RP→RRP recruitment (seconds)
— seconds (presynapse, short-term plasticity):
Augmentation: Episode [GAP — not yet modelled]
— requires second slow Ca2+ trace (tau ~5000 ms)
— elevated release probability for 5-10 s after burst
— distinct from spike-by-spike facilitation
PostTetanicPotentiation: Episode [GAP — not yet modelled]
— requires very slow trace (tau ~minutes)
— elevated release probability for minutes after tetanus
This is one of the most important questions in neuroscience and it reveals a gap in the current model — the postsynapse as we have described it is a single compartment, but the real postsynapse is embedded in a spatial structure where location matters enormously.
---
**The physical structure**
The postsynapse sits at the tip of a **dendritic spine** — a tiny mushroom-shaped protrusion, roughly 1 µm across, that branches off the main dendrite shaft. The spine is connected to the dendrite by a narrow neck, which acts as both a diffusion barrier and an electrical resistor. The spine is not just a passive receptor — it is a semi-isolated compartment with its own calcium dynamics, its own molecular machinery, and its own local membrane potential that can differ from the dendrite by tens of millivolts.
From spine to soma the signal travels through three successive stages, each with its own physics:
---
**Stage 1 — Spine to dendrite shaft (µm, microseconds to milliseconds)**
After Ca²⁺ enters through NMDA, two things happen simultaneously in the spine.
The **electrical signal** — the change in V_post from AMPA and NMDA currents — spreads electrotonically from the spine head through the spine neck into the dendrite shaft. This is a passive electrical process governed by cable theory: the spine neck has resistance, which causes voltage attenuation. A strong EPSP in the spine arrives at the dendrite shaft as a smaller depolarisation. The narrower and longer the neck, the more attenuation.
The **chemical signal** — Ca²⁺ itself — diffuses much more slowly and is largely trapped in the spine by the neck geometry and by the calcium buffers and pumps in the spine head. This is deliberate: it means each spine is a private calcium compartment. What happens in one spine does not directly raise Ca²⁺ in the neighbouring spine. This compartmentalisation is what makes synapse-specific plasticity possible — only the spine that received the coincident signal gets potentiated, not all spines on the same dendrite.
---
**Stage 2 — Dendrite shaft to soma (µm to mm, milliseconds)**
Once the electrical signal enters the dendrite shaft it travels toward the soma as a graded potential — not an action potential, just a spreading wave of depolarisation that decays with distance and time. The key variables are the **length constant** (how far the signal travels before decaying to 1/e of its original amplitude, typically 100-500 µm in dendrites) and the **time constant** (how long the signal lasts, typically 10-50 ms).
Dendrites are not passive cables. They contain their own voltage-gated channels — including NMDA receptors on the dendritic shaft, voltage-gated Na⁺ and Ca²⁺ channels, and K⁺ channels that actively shape the signal as it travels. In some neurons, particularly pyramidal cells, a strong enough EPSP can trigger a **dendritic spike** — a locally regenerative event that amplifies the signal and ensures it reaches the soma with enough strength to trigger firing. Dendritic spikes are essentially local action potentials in the dendrite, and they are one of the mechanisms that give individual dendrites computational properties beyond simple summation.
Multiple EPSPs arriving at different spines within a short time window sum together in the dendrite shaft. If they arrive close enough in space and time, their summed depolarisation exceeds threshold at the soma. This spatial and temporal summation is how the neuron integrates thousands of inputs simultaneously.
The soma collects all the dendritic inputs and performs a threshold comparison. The axon hillock — the junction between the soma and the axon — has the highest density of voltage-gated Na⁺ channels in the neuron and the lowest threshold for firing. When the summed depolarisation at the axon hillock crosses roughly -55 mV (from a resting potential of about -70 mV), an action potential is triggered. This AP then propagates forward down the axon and simultaneously backward up the dendrites as the bAP.
---
**What this means for the model**
The current model has no spatial structure. V_post is a single number representing the entire postsynaptic compartment — there is no distinction between spine voltage, dendritic shaft voltage, and somatic voltage. The bAP is treated as an external input rather than the consequence of somatic threshold crossing fed back to the dendrite.
The missing components that would be needed for a spatially accurate model are:
```
Spine compartment:
V_spine — local membrane potential at the spine head
Ca_post — spine calcium (already modelled)
spine_neck_resistance — attenuation from spine to dendrite
Dendrite compartment:
V_dendrite — shaft potential (sum of attenuated spine EPSPs)
length_constant — spatial decay of signal along shaft
dendritic_spike_threshold — if V_dendrite crosses this,
local regenerative event
Soma compartment:
V_soma — integrated input from all dendrites
AP_threshold — typically ~15 mV above rest
fired — boolean, triggers bAP_train for next cycle
```
The bAP then becomes an output of the soma rather than an independent input:
```
if V_soma > AP_threshold:
fired = True
bAP_train.append(current_step) # feeds back to spine
V_soma resets via Na/K-ATPase
```
This closes the loop properly: the spine signal travels up, the soma decides whether to fire, and the firing decision travels back down as the bAP that enables NMDA coincidence detection at the very spine that contributed to triggering the somatic AP. The synapse is strengthened only if its contribution was part of what caused the neuron to fire — which is the biological definition of Hebbian learning expressed as a physical circuit.
---
**Why the spine neck is biologically critical**
The spine neck geometry is not fixed — it changes with activity. During LTP, the neck widens and shortens, reducing attenuation and making the spine electrically closer to the dendrite. During LTD, the neck narrows and the spine may retract entirely. This means the structural change of plasticity is not just the number of AMPA receptors — it is also the geometry of the spine itself, which changes how well future signals from that spine will reach the soma. Potentiation makes potentiation more likely not just through more AMPA but through better electrical coupling. This is a physical feedback loop operating at the structural level, on timescales of minutes to hours, that is entirely absent from computational models of this type and may be one of the things that cannot be captured by any purely computational description.
