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neuron/BEH-BD.md
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# BEH-AXO.md
# BEH-BD.md
Qui comprendiamo:
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## BEH-POST: Container
The postsynapse is the receiving terminal of the neuron—typically a tiny protrusion called a **dendritic spine**. While the presynapse is a "sending" machine, the postsynapse is a "comparing" machine. Its primary job is to decide if the incoming neurotransmitter (NT) signal is significant enough to warrant a change in synaptic strength, a process it performs by intersecting local chemical signals with global electrical feedback from the cell body.
Like its presynaptic partner, the postsynapse is governed by three interlocking loops—**the $V_{post}$ loop, the $Ca^{2+}$ loop, and the ATP loop**—operating across three distinct timescales.
---
### 1. The $V_{post}$ Loop: The Fast Gatekeeper (Milliseconds)
This is the primary electrophysiological response, where chemical signals are converted back into electricity.
- **Activation:** When NT arrives in the cleft, it binds to **AMPA receptors**. These act as the primary current drivers. If `NT_cleft` is **Full** and receptors are not in a **Desensitization** state, the $Na^{+}$ influx causes the local membrane potential ($V_{post}$) to rise steeply.
- **The bAP Feedback:** The postsynapse does not work in isolation. It receives a **back-propagating Action Potential (bAP)**—an electrical "echo" sent from the cell body whenever the neuron fires.
- **Coincidence Logic:** On this millisecond scale, the loop computes a logical **AND** operation. If local AMPA-driven depolarization coincides with a somatic bAP, the total $V_{post}$ becomes **Full**. This massive depolarization is the only thing strong enough to kick the magnesium "plug" out of the **NMDA receptors**, allowing the next loop to begin.
---
### 2. The $Ca^{2+}$ Loop: The Plasticity Controller (Seconds)
This loop translates electrical timing into biological "memory."
- **The NMDA Gate:** $Ca^{2+}$ entry is strictly gated by the NMDA receptor. Unlike the presynaptic VGCCs (which open with any spike), the NMDA channel only opens if it senses both NT (from the presynapse) and high $V_{post}$ (from the bAP).
- **Signaling Fate (LTP/LTD):** The amplitude of the $Ca^{2+}$ surge determines the synapse’s fate. A **Full** surge (perfect coincidence) triggers **LTP**, signaling the astrocyte to help strengthen the synapse. A **Medium** or poorly timed surge triggers **LTD**, weakening the connection.
- **Retrograde Signaling (eCB):** If $Ca^{2+}$ levels remain high for too long, the postsynapse synthesizes **endocannabinoids (eCB)**. This signal travels backward across the cleft to tell the presynapse to stop sending NT. This is the primary safety valve that prevents the postsynapse from being overwhelmed.
---
### 3. The ATP Loop: The Metabolic Backbone (Minutes)
This is the "Hidden Master" that determines if the other two loops are allowed to function.
- **The Cost of Logic:** The postsynapse is metabolically expensive. The $Na/K$ pumps must work constantly to reset the $V_{post}$ gradient, and the **PMCA pumps** must use ATP to flush out the $Ca^{2+}$ that entered through NMDA channels.
- **The Astrocyte Bridge:** The astrocyte provides the glucose required to replenish ATP. It also performs a "janitorial" service: it clears excess Potassium ($K^{+}$) and Glutamate from the cleft. If the astrocyte is starved of glucose, the **ATP_level_post** drops to **Empty**.
- **The False Trigger (Excitotoxic Protection):** When ATP fails, the $Ca^{2+}$ pumps stop. Even without an NMDA surge, $Ca^{2+}$ begins to "leak" and accumulate in the spine. This creates a **False Trigger**: the high $Ca^{2+}$ level initiates eCB synthesis, silencing the presynapse even though there was no "real" signal. This is a desperate survival mechanism; by tricking the presynapse into silence, the postsynapse stops the influx of ions and buys time for its ATP levels to recover.
---
### The Critical Connection with the presynapse
The system is beautifully asymmetric. While the presynapse is built to **supply** signal, the postsynapse is built to **filter** it. The failure of the ATP loop in the postsynapse is arguably more dangerous; if the postsynaptic pumps fail and the eCB "False Trigger" doesn't fire, the spine will literally digest itself from $Ca^{2+}$ overload.
```Gen
container: BEH-POST
neuron/appunti/2026-03-30-behavior-POST.md
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```
BEH-AXO.md
BEH-AXO: Container
## BEH-POST-UNIFIED: The Integrated Postsynaptic Model
BEH-PRE: Container
[as previously defined]
### **ms: behaviors (Fast Kinetics & Gate Logic)**
BEH-POST: Container
#### **Voltage-Context: Episode**
ms: behaviors
*Determines the total depolarization level (Vpost​) available to clear the NMDA Mg-block.*
POST-NTContext: Context
— NT_cleft level arriving from presynapse
— Desensitization_level of receptors at this moment
— these two together determine effective NT binding
- **Vpost_Maximum: Episode**
- — `V_bAP` full OR (`g_AMPA` full AND `V_bAP` medium)
- — Result: Vpost​ is high enough for complete Mg-block removal.
- **Vpost_Attenuated: Episode**
- — `g_AMPA` medium AND `V_bAP` empty/low
- — Result: Vpost​ is sub-threshold; Mg-block partially remains.
- **Vpost_Passive: Episode**
- — `g_AMPA` empty AND `V_bAP` empty
- — Result: Vpost​ at rest; Mg-block fully intact.
NTDetection
NTDetectionMaximum: Episode
— NT_cleft full, Desensitization_level empty
— all receptors available, full NT signal
— receptor_conductance rises steeply
NTDetectionHigh: Episode
— NT_cleft full, Desensitization_level medium OR
— NT_cleft medium, Desensitization_level empty
— strong response, partially attenuated
NTDetectionMedium: Episode
— NT_cleft medium, Desensitization_level medium OR
— NT_cleft low, Desensitization_level empty
— moderate response
NTDetectionLow: Episode
— NT_cleft low, Desensitization_level medium OR
— NT_cleft medium, Desensitization_level full
— weak response, most receptors deaf
NTDetectionNone: Episode
— NT_cleft empty OR
— Desensitization_level full
— no effective binding regardless of NT
#### **NMDA-Coincidence: Context**
ReceptorDesensitization
DesensitizationRising: Episode
— NT_cleft sustained high
— receptors accumulate closed state each ms
— attenuates subsequent NTDetection episodes
DesensitizationRecovering: Episode
— NT_cleft low or empty
— receptors recover availability passively
— rate governed by tau_desensitization = 500 ms
- **NMDA_Open: Episode**
- — `NT_cleft` full AND `V_post` maximum
- — Result: Capost​ surges; triggers high ATP demand for clearance.
- **NMDA_LogicBlocked: Episode**
- — `NT_cleft` full BUT `V_post` attenuated/passive
- — Result: Mg-block prevents Ca2+ influx despite NT presence.
- **NMDA_LigandBlocked: Episode**
- — `V_post` maximum BUT `NT_cleft` empty
- — Result: No glutamate to open the channel; Ca2+ entry zero.
VpostDecay
VpostDecayActive: Episode
— receptor_conductance non-zero
— V_post sustained by ongoing NT binding
VpostDecayPassive: Episode
— receptor_conductance near zero
— V_post decays with tau_post_membrane = 20 ms
— inter-burst silence
#### **Ca-Dynamics & ATP-Drain: Context**
POST-Ca2+Context: Context
— V_post level (sets Mg block removal)
— NT_cleft level (ligand gate for NMDA)
— together these determine NMDA opening
— coincidence required: both must be non-zero for Ca_post to rise
NMDACoincidence
NMDACoincidenceMaximum: Episode
— NT_cleft full AND V_post full
— Mg block fully lifted, NMDA wide open
— Ca_post surges — LTP territory
NMDACoincidenceHigh: Episode
— NT_cleft full AND V_post medium OR
— NT_cleft medium AND V_post full
— strong Ca_post rise
NMDACoincidenceMedium: Episode
— NT_cleft medium AND V_post medium
— moderate Ca_post rise — LTP/LTD boundary zone
NMDACoincidenceLow: Episode
— NT_cleft low OR V_post low (but not both empty)
— weak Ca_post rise — LTD territory
NMDACoincidenceNone: Episode
— NT_cleft empty OR V_post empty
— one gate closed — Ca_post does not rise
— this is the hard gate: a single missing condition blocks all entry
CaPostClearance
CaPostClearanceHigh: Episode
— ATP_level_post full
— pump_scale_post near 1
— PMCA running at full rate + NCX
— Ca_post returns to baseline rapidly between events
CaPostClearanceMedium: Episode
— ATP_level_post medium
— pump_scale_post reduced
— Ca_post clears more slowly
— residual elevation between coincidence events
CaPostClearanceLow: Episode
— ATP_level_post low
— pump_scale_post near 0
— only NCX clearing (floor, not rescue)
— Ca_post accumulates across events
— eCB threshold approached without genuine coincidence
— excitotoxicity risk zone
ATPcostPost
— charged every ms:
NKA recharge proportional to V_post level
PMCA cost proportional to cleared_Ca_post_pump
— feeds ATP_demand_post accumulator
— reset in Loop 3
sec: behaviors
POST-SecContext: Context
— Ca_post history over past 2 s (mean of log)
— determines whether eCB synthesis threshold is crossed
— note: driven by Ca_post, not V_post
— ATP failure can push Ca_post above threshold
— without genuine coincidence (false retrograde signal)
eCBSynthesis
eCBSynthesisActive: Episode
— recent_Ca_post > eCB_threshold (0.7)
— eCB synthesised and released retrogradely
— eCB_level rises with tau_eCB_rise = 2000 ms
— suppresses presynaptic VGCCs via effective_conductance
— genuine trigger: sustained NMDA coincidence (overactivity)
— false trigger: Ca_post elevated by pump failure (ATP low)
eCBSynthesisInactive: Episode
— recent_Ca_post < eCB_threshold
— eCB_level decays with tau_eCB_decay = 10000 ms
— presynaptic suppression gradually lifts
min: behaviors
POST-MinContext: Context
— Glucose_level (shared with presynapse)
— ATP_demand_post accumulated since last cycle
— both sides draw from same astrocyte glucose budget
ATPreplenishment
— compute_astrocyte_metabolic_health(Glucose_level, ATP_demand_post)
— produces ATP_level_post for next metabolic window
— ATP_demand_post resets to zero
— when Glucose_level low: both ATP_level and ATP_level_post fall
— presynaptic silence (CDI lock-out) reduces NT release
— reduced NT reduces NMDA activation
— reduced Ca_post reduces ATP_demand_post
— presynaptic silence indirectly protects postsynaptic ATP
BEH-POST-RECEPTOR: Container
ms: behavior Receptors
ReceptorOccupancy
ReceptorOccupancyFull: Episode
— NT_cleft full, Desensitization_level empty
— maximum conductance, V_post rising steeply
ReceptorOccupancyReduced: Episode
— NT_cleft medium OR Desensitization_level medium
— partial conductance
ReceptorOccupancyPartial: Episode
— NT_cleft low OR Desensitization_level high
— weak conductance
ReceptorOccupancySuppressed: Episode
— NT_cleft low AND Desensitization_level high
— near-zero conductance despite NT present
ReceptorOccupancyClosed: Episode
— NT_cleft empty OR Desensitization_level full
— no conductance
BEH-POST-NMDA: Container
ms: behavior NMDA coincidence gate
NMDAgate
NMDAgateFull: Episode
— NT_cleft full AND V_post full
— Mg_block_removal near 1
— Ca_post surges maximally
NMDAgatReduced: Episode
— one condition full, other medium
— partial Mg block removal
— Ca_post rises moderately
NMDAgatPartial: Episode
— both conditions medium
— Mg block partially lifted
— Ca_post rises weakly
NMDAgateSuppressed: Episode
— one condition low, other any
— Mg block mostly intact
— Ca_post minimal rise
NMDAgateClosed: Episode
— either NT_cleft empty OR V_post empty
— hard gate closed
— Ca_post does not rise
```
- **Clearance_Optimal: Episode**
- — `ATP_level_post` full
- — Result: Pumps flush Ca2+ rapidly; `ATP_demand_post` increases.
- **Clearance_Failing: Episode**
- — `ATP_level_post` low/empty
- — Result: Ca2+ remains elevated (residual floor); creates "False Trigger" conditions.
---
Three structural notes on how this mirrors the presynaptic taxonomy.
### **sec: behaviors (Signal Integration & Fate)**
`BEH-POST-NMDA` is the postsynaptic equivalent of `BEH-PRE-VGCC`. Both are containers for a gated calcium entry mechanism. The difference is the gating logic: VGCC is gated by CDI, eCB, and mGluR (three suppressors multiplying together); NMDA is gated by a coincidence requirement (two conditions both required). VGCC can be suppressed by any one of its three brakes acting alone. NMDA can only be blocked by the absence of either NT or depolarisation — a fundamentally different logical structure, AND versus (1 - factor).
#### **Synaptic-Weight-Decision (Plasticity)**
`NMDACoincidenceNone` is a hard gate in the same sense that `N_RRP = empty` was a hard gate in the NT release table. One missing condition alone is sufficient to prevent all Ca_post entry regardless of the other variable. This makes the postsynaptic calcium system more binary than the presynaptic one — there is no equivalent of the graded suppression that CDI or eCB provide.
- **Plasticity_LTP: Episode**
- — `Ca_post_history` (recent 2s) is **Full**
- — Result: High-frequency/High-amplitude coincidence detected; tags synapse for AMPA increase.
- **Plasticity_LTD: Episode**
- — `Ca_post_history` is **Medium**
- — Result: Low-frequency or poorly timed coincidence; tags synapse for AMPA removal.
`eCBSynthesisActive` has two distinct biological meanings depending on what is driving Ca_post — genuine overactivity (NMDA coincidence) versus pump failure (ATP depleted). The episode is the same computational event but with opposite implications for whether the retrograde signal is appropriate. This is the only place in the entire model where the same behavior has two different biological interpretations, and it is worth flagging explicitly in any documentation.
#### **Retrograde-Feedback (eCB)**
- **eCB_Synthesis_Active: Episode**
- — `Ca_post_history` > threshold (0.7)
- — **Logic A (Protection):** Response to genuine NMDA over-activity.
- — **Logic B (Error):** Response to pump failure (Ca2+ accumulation due to low ATP).
- **eCB_Synthesis_Idle: Episode**
- — `Ca_post_history` < threshold; eCB level decays.
---
### **min: behaviors (Bioenergetics & Structural Change)**
#### **Metabolic-Recovery**
- **Astrocyte_Supply_Active: Episode**
- — `Glucose_level` full; `ATP_level_post` is replenished.
- **Astrocyte_Supply_Crises: Episode**
- — `Glucose_level` low; `ATP_level_post` remains empty; Ca2+ pumps fail.
#### **Structural-Update**
- **AMPA_Population_Increase: Episode**
- — Triggered by `Plasticity_LTP` AND `ATP_level_post` NOT empty.
- — Result: `g_AMPA_baseline` shifts higher for next cycle.
- **AMPA_Population_Decrease: Episode**
- — Triggered by `Plasticity_LTD`.
- — Result: `g_AMPA_baseline` shifts lower.
---
### **Key Structural Observations**
1. **The Vpost Priority:** Vpost​ is now the "sum" of local input and global feedback. This allows the model to simulate both **Hebbian learning** (needs a bAP) and **Homeostatic Scaling** (where enough local AMPA activity can eventually trigger the NMDA gate alone).
2. **The ATP Bottleneck for LTP:** Note that in the `min` behaviors, I’ve added a constraint: LTP requires `ATP_level_post` to be healthy. Moving receptors into the membrane is a physical "work" process. If the synapse is energy-starved, it might "decide" to do LTP in the `sec` loop but fail to **execute** it in the `min` loop.
3. **The Coincidence Hierarchy:**
- **LTP** = Perfect Timing (NT + bAP).
- **LTD** = Misaligned Timing (Low NT or Out-of-sync bAP).
- **False eCB** = Metabolic Failure (No NT, No bAP, just Low ATP).