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@@ -233,7 +233,7 @@ episode: NDMAOpenMaximum
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in_context: bAp AND (NaMax OR NaMedium)
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in_context: bAp AND (NaMax OR NaMedium)
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rf: ( active: 2x )
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rf: ( active: 2x )
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hypothesis: NOT (ca2+ full)
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hypothesis: NOT (Ca2+ full)
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action: [Ca2+ increase]
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action: [Ca2+ increase]
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trace:
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trace:
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```
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```
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@@ -247,7 +247,7 @@ episode: NDMAOpenMedium
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in_context: (bAp AND NaLow) OR (NOT bAP AND NaMax)
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in_context: (bAp AND NaLow) OR (NOT bAP AND NaMax)
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rf: ( active: 4x )
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rf: ( active: 4x )
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hypothesis: NOT (ca2+ full)
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hypothesis: NOT (Ca2+ full)
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action: [Ca2+ increase]
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action: [Ca2+ increase]
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trace:
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trace:
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```
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```
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@@ -261,7 +261,7 @@ episode: NDMAOpenLow
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in_context: NOT bAP AND NaMedium
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in_context: NOT bAP AND NaMedium
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rf: ( active: 12x )
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rf: ( active: 12x )
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hypothesis: NOT (ca2+ full)
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hypothesis: NOT (Ca2+ full)
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action: [Ca2+ increase]
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action: [Ca2+ increase]
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trace:
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trace:
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```
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```
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@@ -401,3 +401,86 @@ PostTetanicPotentiation: Episode [GAP — not yet modelled]
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— elevated release probability for minutes after tetanus
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— elevated release probability for minutes after tetanus
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— presynaptic only, no postsynaptic component
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— presynaptic only, no postsynaptic component
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```
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```
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---
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## Signal traveling to the dendrite and soma
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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.
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---
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**The physical structure**
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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.
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From spine to soma the signal travels through three successive stages, each with its own physics:
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---
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**Stage 1 — Spine to dendrite shaft (µm, microseconds to milliseconds)**
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After Ca²⁺ enters through NMDA, two things happen simultaneously in the spine.
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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.
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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.
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---
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**Stage 2 — Dendrite shaft to soma (µm to mm, milliseconds)**
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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).
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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.
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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.
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---
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**Stage 3 — Soma integration and axon hillock (point decision, milliseconds)**
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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.
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---
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**What this means for the model**
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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.
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The missing components that would be needed for a spatially accurate model are:
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```
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Spine compartment:
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V_spine — local membrane potential at the spine head
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Ca_post — spine calcium (already modelled)
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spine_neck_resistance — attenuation from spine to dendrite
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Dendrite compartment:
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V_dendrite — shaft potential (sum of attenuated spine EPSPs)
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length_constant — spatial decay of signal along shaft
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dendritic_spike_threshold — if V_dendrite crosses this,
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local regenerative event
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Soma compartment:
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V_soma — integrated input from all dendrites
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AP_threshold — typically ~15 mV above rest
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fired — boolean, triggers bAP_train for next cycle
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```
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The bAP then becomes an output of the soma rather than an independent input:
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```
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if V_soma > AP_threshold:
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fired = True
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bAP_train.append(current_step) # feeds back to spine
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V_soma resets via Na/K-ATPase
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```
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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.
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---
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**Why the spine neck is biologically critical**
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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.
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