**Dendritic Branch**: In questa prima fase, non consideriamo lo spike dendritico come comportamento. Questo limita molto il modello, perche' equipara tutte le Postsinapsi sui tre branch dendritici e non permette di fare in maniera che ad esempio due branch contestualizzino (base activity) e uno faccia scattare il threshold per lo spike somatico.
Qui BEH-DB espande solo i BEH-POST, e' un cavo di collegamento come l'assone
The dendrite is the receiving arm of a neuron — a long branching extension of the cell body whose job is to collect the electrical signals generated by postsynaptic spines and route their sum toward the soma, where the decision to fire is made. In this model we consider a single dendritic branch: a passive cable connecting a set of postsynaptic spines at one end to the soma at the other.
Each spine sits along the branch and generates a small electrical signal — an excitatory postsynaptic potential, or EPSP — whenever its AMPA receptors are activated by NT from the presynapse. This EPSP spreads from the spine head through the spine neck and into the dendrite shaft, where it becomes part of a shared electrical pool. The dendrite does not process each spine's signal independently — it sums them. Two spines firing close together in time produce a larger combined depolarisation than either alone. Enough spines firing close enough together can push the dendritic potential high enough to reach the soma and trigger an action potential.
The dendrite does this passively. Unlike the presynapse, which actively pumps calcium and recycles vesicles, the dendrite shaft in this model is a cable — it conducts and attenuates electrical signals according to its physical properties, with no active amplification. The key property is the membrane time constant: how long a voltage change persists before decaying back to rest. A long time constant means EPSPs last longer and are more likely to summate with the next arriving EPSP. A short time constant means only very closely timed inputs summate effectively.
The dendrite also carries the return signal. When the soma fires, a back-propagating action potential (bAP) travels from the soma back down the dendrite to every spine. In this model the bAP arrives at all spines at full amplitude — no distance-dependent attenuation. This bAP is the postsynaptic side of the coincidence gate: it tells every spine simultaneously that the neuron just fired, enabling NMDA opening in any spine that also has NT in its cleft at that moment. Without the bAP, spines can generate V_post from AMPA alone but cannot achieve the full coincidence required for LTP.
The dendrite therefore runs two interlocking loops. The summation loop collects spine EPSPs every millisecond and maintains a running dendritic potential V_dend. The bAP loop receives the external firing signal and distributes it back to all spines as the V_bAP input that the postsynaptic model reads. Together these two loops make the dendrite the spatial and temporal integrator of the synapse — it is where individual spine signals become a collective decision, and where the outcome of that decision is fed back to the very spines that contributed to it.
In this model the dendrite is already at its simplest meaningful form given the four choices. No further simplifications are applied. The only two active processes are:
