# Biological Basis of the AMPA and NMDA Receptor Model with Short-Term Plasticity The provided code is a computational model that simulates the dynamics of AMPA and NMDA receptor-mediated synaptic currents, incorporating essential features of synaptic transmission and plasticity seen in neurons. Here’s a breakdown of the biological concepts represented in the model: ## Synaptic Transmission ### AMPA Receptors - **AMPA receptors** are ionotropic glutamate receptors responsible for fast excitatory synaptic transmission. They mediate the passage of sodium (Na\(^+\)) and potassium (K\(^+\)) ions, leading to rapid depolarization of the postsynaptic membrane. - In the code, `sAMPA` represents a state variable that models the activation and decay of AMPA conductance over time, characterized by the `tau_sAMPA` time constant. ### NMDA Receptors - **NMDA receptors** are another class of ionotropic glutamate receptors that are voltage-dependent and have a slower kinetics compared to AMPA receptors. They conduct calcium (Ca\(^{2+}\)) and other ions, contributing to synaptic plasticity. - NMDA receptors require both glutamate binding and membrane depolarization to relieve the magnesium (Mg\(^{2+}\)) block and allow ion flow. The `mggate` variable in the code models this voltage-dependent block based on voltage `v` and extracellular magnesium concentration `MgCon`. - The state variables `sNMDA` and `xNMDA` together govern the NMDA receptor dynamics through a dual-exponential profile, modulated by time constants `tau_sNMDA` and `tau_xNMDA`. ## Synaptic Plasticity - The code describes **short-term synaptic plasticity**, focusing on synaptic depression, which was originally part of the model but later removed. - Despite the removal of synaptic depression, short-term modifications would be reflected by changes in synaptic strength or conductance over short timescales. ## Biological Relevance of Reversal Potentials and Current - The reversal potential `E_Glu` is set to 0 mV, representing a typical excitatory synapse where the net flow of charge carriers (ions) balances out. - Currents `i_AMPA` and `i_NMDA` represent the actual ionic currents flowing through AMPA and NMDA receptors, respectively. They are calculated based on the difference between the membrane potential `v` and the reversal potential. ## Calcium Dynamics - Calcium current `ica` is derived from the total synaptic current `i` with a factor, indicating the role of NMDA receptors in Ca\(^{2+}\) influx, crucial for signaling pathways involved in synaptic plasticity and neurotransmitter release modulation. The model effectively captures key aspects of excitatory synaptic transmission and highlights the role of AMPA and NMDA receptors in modulating synaptic strength and activity-dependent plasticity within neural circuits.