The provided code is a computational model of synaptic transmission, specifically focusing on the dynamics of AMPA and NMDA receptors, which are types of glutamate receptors critical for synaptic plasticity and transmission in the central nervous system. The model aims to simulate the postsynaptic conductance changes at excitatory synapses found in neurons, such as those in the striatum. ### Biological Basis #### **Types of Receptors Modeled** - **AMPA Receptors (AMPAR):** - Activated by the neurotransmitter glutamate, these receptors mediate fast synaptic transmission by allowing Na⁺ and K⁺ ions to pass through once they bind glutamate. The model describes this with parameters `tau1_ampa` and `tau2_ampa`, which correspond to the rise and decay times of AMPA receptor-mediated conductance, reflecting the fast nature of AMPA-based synaptic currents. - **NMDA Receptors (NMDAR):** - NMDA receptors also bind glutamate but possess unique characteristics, including a slower kinetic profile (`tau1_nmda`, `tau2_nmda`) and a voltage-dependent block by Mg²⁺ ions, which is captured by the `MgBlock()` function. NMDA receptors allow Ca²⁺ in addition to Na⁺ and K⁺ ions to flow into the cell, playing a key role in synaptic plasticity mechanisms like long-term potentiation (LTP). #### **Mg²⁺ Block** - The `MgBlock()` function models the voltage-dependent blockade of NMDA receptors by extracellular magnesium ions (Mg²⁺). This block is relieved upon depolarization of the postsynaptic membrane, allowing ion flow and contributing to the non-linear properties of the NMDA receptor. The parameters `mg`, `eta`, and `alpha` describe how Mg²⁺ affects the receptor's ion permeability in response to changes in membrane potential (`v`). #### **Kinetics and Conductance** - The model uses an exponential decay scheme (`cnexp` method) to compute the time course of synaptic conductance changes, reflecting the transient nature of synaptic currents. This involves solving differential equations (`A'`, `B'`, `C'`, `D'`) for the state variables of AMPA and NMDA conductances. - The model calculates synaptic currents (`i_ampa`, `i_nmda`) based on the conductance (`g_ampa`, `g_nmda`) and the driving force (the difference between the postsynaptic membrane potential `v` and the reversal potential `erev`). #### **Synaptic Modality** - It models two-state kinetic schemes that assume the binding of glutamate to receptors leads to activation (open state) and subsequent deactivation/closure (closed state), controlled by the time constants. The `factor_nmda` and `factor_ampa` ensure normalization so that a synaptic event of weight 1 generates a peak conductance of 1 unit. Overall, this computational model provides a detailed simulation of the biophysical properties of AMPA and NMDA receptor-mediated synapses, including their distinct temporal dynamics and interactions with extrinsic factors like membrane potential and magnesium ions, as related to striatal medium spiny neurons described in referenced studies.