The code provided models a synaptic conductance mechanism, specifically an extended version of the dual exponential synapse (Exp2Syn) model, to incorporate properties characteristic of NMDA (N-methyl-D-aspartate) receptor channels. ### Biological Basis **NMDA Receptors:** NMDA receptors are a subtype of glutamate receptors that play a crucial role in synaptic plasticity, memory formation, and excitatory neurotransmission in the central nervous system. They are known for their unique properties, including: 1. **Dual Gating Mechanism:** - NMDA receptors require both ligand binding (glutamate) and membrane depolarization to become fully activated. This dual gating is crucial for their role in coincidence detection in the synapse. 2. **Voltage-Dependent Magnesium Block:** - At resting membrane potentials, Mg²⁺ ions block the NMDA receptor channel. Depolarization relieves this block, allowing Ca²⁺ and other cations to enter the neuron. - This model incorporates a voltage-dependent Mg²⁺ block, mimicking how external magnesium concentration and membrane potential influence conductance. 3. **Calcium Permeability:** - NMDA receptors are highly permeable to Ca²⁺ ions, in addition to Na⁺ and K⁺. This Ca²⁺ influx is pivotal for initiating intracellular signaling cascades involved in synaptic plasticity. - Although Ca²⁺ tracking was considered in earlier versions, it has been removed in this specific implementation. ### Computational Model The code simulates the synaptic conductance using a dual exponential decay function to represent the kinetics of NMDA receptor activation and deactivation. The primary components include: - **Tau Parameters:** - `tau1` and `tau2` define the rise and decay time constants of NMDA receptor-mediated conductance. The condition `tau1 < tau2` ensures a realistic conductance time course. - **Voltage Dependence:** - The model includes a function (`vspom`) to compute the voltage-dependent Mg²⁺ block, which is critical for simulating the receptor's voltage-sensitivity and integration role in neuronal activity. - **Conductance (Gating Variables):** - `A` and `B` represent the states of the conductance channels modulated by neurotransmitter release, reflecting NMDA receptor kinetics. ### Conclusion The NMDA receptor model here extends a basic synaptic conductance model to capture the distinctive features of NMDA receptor channels, notably their dual requirement for ligand and voltage-dependent activation and their modulation by external Mg²⁺ concentrations. These features allow the model to mimic crucial aspects of synaptic integration and plasticity mechanisms attributed to NMDA receptors in the nervous system.