The provided code models synaptic transmission and plasticity involving AMPA and NMDA receptor-mediated responses, as well as local calcium signaling in interneuron cells of the brain. Below are the key biological components and processes that the code aims to simulate:

Synaptic Transmission

1. Receptors Modeled:

   • NMDA Receptors: These allow for calcium (Ca²⁺) and sodium (Na⁺) influx when activated. NMDA receptors are voltage-dependent and require both ligand binding and membrane depolarization to remove the magnesium (Mg²⁺) block, which is represented through the sfunc(v) function.
   • AMPA Receptors: These primarily mediate fast synaptic transmission through sodium (Na⁺) and sometimes calcium (Ca²⁺) influx when bound by glutamate. The AMPA-related parameters (e.g., gbar_ampa, Erev_ampa) simulate their kinetic properties and conductance.

2. Synaptic Currents:

   • inmda and iampa: These are the synaptic currents through NMDA and AMPA receptors, respectively. The currents are influenced by synaptic weights (W_nmda and W), which are critical for modeling synaptic plasticity.

Calcium Dynamics

• Local Calcium Pool: This is critical for activating various intracellular signaling pathways. The local calcium concentration is represented by capoolcon, which can affect synaptic strength through what appears to be modeled calcium-dependent plasticity mechanisms.
• Calcium Influx and Pumping: Calcium ions enter through activated NMDA receptors (ICan) and AMPA receptors (ICaa). The term Icatotal sums these contributions. Additionally, calcium dynamics are subject to removal or decay (-fCan*Afactor*Icatotal + (Cainf-capoolcon)/tauCa), mimicking calcium buffering and extrusion processes.

Synaptic Plasticity

• Weight Modification:

  • The synaptic weights (W) can change based on calcium concentration, representing activity-dependent plasticity akin to long-term potentiation (LTP) or depression (LTD).
  • The algorithms capture synaptic weight saturation using the Wmax and Wmin limits, ensuring physiological plausibility.

• Learning Rules:

  • Functions eta and omega describe the transition rules governing synaptic weight changes. These depend on the intracellular calcium concentration relative to predefined thresholds (threshold1, threshold2), linking activity-dependent plasticity to calcium signaling.
  • GAP Mechanism: Although not fully detailed in the description, the GAP mechanism is designed to manipulate synaptic weight changes perhaps during specific learning or developmental stages, captured by the GAP1 function.

General Properties

• Time Constants and Kinetics: Parameters such as AlphaTmax_nmda, Beta_nmda, Cdur_nmda, and their AMPA counterparts define the kinetics of receptor activation/deactivation, which are essential for modeling synaptic timing and integration.
• Electrical Properties: Parameters like reversal potentials (Erev) and initial conditions (initW) are set to match typical electrophysiological observations of synaptic activity.

In summary, this code provides a computational model that represents the dynamics of synaptic transmission mediated by AMPA and NMDA receptors, coupled with calcium signaling and synaptic plasticity, reflecting fundamental processes underlying learning and memory in the brain's neural circuits.