Looking at what we have just specified, the postsynapse also has three loops — but they are organised around different problems than the presynapse.

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**The NT detection loop**

This is the direct counterpart of the presynaptic NT loop, but from the receiving side. NT arrives in the cleft, binds AMPA receptors, generates V_post, and V_post drives the postsynaptic response. The loop closes through desensitization: sustained NT exposure progressively silences the receptors, reducing the response to further NT even while it is still present. When NT clears (presynapse goes quiet), desensitization recovers and receptors become available again. The timescale is milliseconds to seconds — fast enough to track individual spikes, slow enough to integrate burst activity. This loop is entirely local to the postsynapse and requires no signal from outside except NT_cleft.

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**The Ca²⁺ coincidence loop**

This is the postsynaptic equivalent of the presynaptic Ca²⁺ loop, but with a fundamentally different trigger. Presynaptic Ca²⁺ enters whenever VGCCs open — which happens on every AP. Postsynaptic Ca²⁺ enters through NMDA receptors only when two conditions are simultaneously true: NT is present in the cleft (presynapse just fired) AND the membrane is depolarised (either from accumulated AMPA activation or from a backpropagating AP). This dual requirement makes Ca_post a detector of coordinated activity rather than just a measure of input rate. The loop closes through the Ca_post trace: sustained high Ca_post potentiates the synapse (LTP, more AMPA receptors), sustained low Ca_post depresses it (LTD, fewer AMPA receptors), and the changed receptor density feeds back into how strongly the next NT release activates V_post. The timescale spans milliseconds (NMDA opening) to minutes (plasticity expression).

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**The retrograde signalling loop**

This loop has no presynaptic equivalent — it is unique to the postsynapse because it is the only signal that crosses back from post to pre. When Ca_post rises above the eCB threshold (sustained coincident activity), the postsynapse synthesises endocannabinoids and releases them retrogradely. eCB travels back across the cleft and suppresses presynaptic VGCC conductance, reducing Ca²⁺ influx and therefore NT release. The loop closes when reduced NT release lowers Ca_post, which eventually reduces eCB synthesis, allowing the presynaptic brake to lift. The timescale is seconds to tens of seconds — slower than the NT detection loop, faster than plasticity. This is the loop that connects the two sides of the synapse and makes the tripartite system a genuine closed system rather than two independent models running in parallel.

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**How the three postsynaptic loops relate to the three presynaptic loops**

| Presynaptic | Postsynaptic               | Shared variable      |
|-------------|----------------------------|----------------------|
| NT loop     | NT detection loop          | NT_cleft             |
| Ca²⁺ loop   | Ca²⁺ coincidence loop      | — (independent Ca²⁺) |
| ATP loop    | retrograde signalling loop | eCB_level            |

The NT loop pair is the primary communication channel — pre releases, post detects. The Ca²⁺ loops are parallel but independent — each side manages its own calcium for its own purposes. The ATP/retrograde pair is the feedback channel — post reports back to pre when activity is excessive. Together the six loops form the complete tripartite system, with the cleft and the eCB signal as the two bridges between the two neurons.

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Yes — and in ways that are structurally similar to the presynapse but with different priorities.

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**Where ATP is consumed in the postsynapse**

**Na/K-ATPase recharge** is the same dominant cost as in the presynapse. Every postsynaptic potential — every time V_post rises — ion gradients are disturbed and the Na/K-ATPase must restore them. At high firing rates this is the largest ATP drain, identical in mechanism to the presynaptic side.

**Ca²⁺ clearance from the spine** is the direct equivalent of PMCA and SERCA in the presynapse. After NMDA-driven Ca_post rises, the spine must pump Ca²⁺ back out. The postsynaptic spine has its own PMCA on the plasma membrane and its own SERCA loading a small ER compartment (the spine apparatus). Both are ATP-dependent. This is actually more critical in the postsynapse than the presynapse in one respect: if Ca_post clearance fails, the spine cannot distinguish a coincidence signal from background noise — the Ca²⁺ threshold logic for LTP vs LTD collapses entirely.

**Plasticity machinery** is an ATP cost that has no presynaptic equivalent. LTP requires physical insertion of new AMPA receptors into the membrane — a process driven by CaMKII phosphorylation, actin cytoskeleton remodelling, and vesicle trafficking, all of which consume ATP. LTD requires the reverse: receptor internalisation via endocytosis, also ATP-dependent. The plasticity loop is therefore metabolically expensive in a way that scales not with firing rate but with the rate of synaptic change.

**NMDA receptor maintenance** — the receptor itself requires ATP for regulatory phosphorylation that controls its sensitivity and trafficking. Under energy stress, NMDA receptors are among the first to be downregulated.

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**How ATP failure affects the postsynapse differently from the presynapse**

In the presynapse, ATP failure produces a clean, protective outcome: the synapse silences itself through CDI lock-out, which prevents excitotoxic Ca²⁺ overload. The silence is the protection.

In the postsynapse, ATP failure is more dangerous rather than protective. The sequence is:

```
ATP falls
→ Ca2+ clearance slows (PMCA/SERCA fail)
→ Ca_post stays elevated between coincidence events
→ Ca_post threshold for LTP is permanently crossed
→ runaway LTP — synapse strengthens uncontrollably
→ NMDA receptors stay open longer (no ATP to phosphorylate/regulate them)
→ more Ca2+ entry
→ positive feedback loop
→ excitotoxic Ca2+ overload in the spine
→ spine collapse and cell death
```

This is the postsynaptic excitotoxicity cascade — the mirror image of the presynaptic one but with the opposite outcome. The presynapse protects itself by going silent. The postsynapse is vulnerable precisely because it has no equivalent of CDI — there is no mechanism that uses elevated Ca_post to shut down Ca_post entry. The NMDA receptor does have a weak Ca²⁺-dependent inactivation, but it is far less effective than presynaptic CDI.

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**Should ATP be in the postsynaptic model?**

At the same level of abstraction as the presynapse, yes — but the loop looks different:

```
— ms (postsynapse, ATP):
- ATP cost charged per bAP (Na/K-ATPase recharge)
- ATP cost charged per unit Ca_post cleared (PMCA/SERCA)

— seconds (postsynapse, ATP):
- pump_scale_post = Hill(ATP_level_post)
- Ca_post clearance gated by pump_scale_post
- if pump_scale_post low → Ca_post stays elevated → eCB threshold
  crossed even without genuine coincidence → false retrograde signal

— mins (postsynapse, ATP):
- ATP_level_post set by local glucose supply (astrocyte delivers to both sides)
- if low → plasticity machinery slows → LTP/LTD expression delayed or absent
- if critically low → runaway Ca_post → excitotoxicity cascade
```

The most important addition this enables is **shared metabolic vulnerability**: the astrocyte supplies glucose to both the presynapse and the postsynapse. Under sustained high-frequency firing, both sides are drawing from the same supply. The presynapse silences first (CDI is an efficient brake), which paradoxically protects the postsynapse — reduced NT release means less NMDA activation means less Ca_post means less postsynaptic ATP demand. The presynaptic ATP loop and the postsynaptic ATP loop are therefore coupled through the astrocyte's glucose budget, and the presynaptic silence functions as a protective brake for both sides simultaneously.

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