The provided code is a computational model of NMDA-type Glutamate Receptors, also known as GluN-R, which play a critical role in synaptic transmission and plasticity in the brain. The key biological aspects represented in the code include: ### NMDA Receptors (NMDARs): - **Receptor Functionality**: NMDA receptors are a type of ionotropic glutamate receptor that are permeable to cations, including Ca²⁺, Na⁺, and K⁺. They are crucial in mediating synaptic transmission, synaptic plasticity, and are known for their role in learning and memory. - **Voltage-Dependent Magnesium Block**: One characteristic feature of NMDARs is their voltage-dependent block by extracellular magnesium ions (Mg²⁺). When the membrane is at a resting potential, Mg²⁺ blocks the receptor's ion channel. Depolarization of the membrane reduces this block, allowing ions to flow through the channel. This property is reflected in the `mgblock(v)` function within the code, which adjusts the fraction of receptors not blocked by Mg²⁺ (`B`). ### Kinetic Model of Binding and Gating: - **Transmitter Binding**: The receptor model is based on a simplified kinetic scheme describing glutamate (the neurotransmitter) binding. Upon presynaptic activity (a spike), glutamate is released and binds to the unbound receptor (`Ru`), transitioning it to a bound state (`Rb`). This is defined by the rate constants `kon` and `koff` for the binding and unbinding of the neurotransmitter. - **Channel Gating**: The model includes states transitioning from closed bound (`Rb`) to closed cleft (`Rc`), and finally to the open state (`Ro`). This is mediated by the closing (`CC`), opening (`CO`), channel opening (`Beta`), and closing (`Alpha`) rates, reflecting the sequential conformational changes that the receptor undergoes upon binding glutamate. - **Conductance**: The maximum conductance `gmax` determines the overall strength of the ionic current flowing through open channels (`Ro`). This conductance is modulated by synaptic weight (`scale`) and the Mg²⁺ block (`B`), directly affecting the postsynaptic current `i = g * (v - Erev)`. ### Mg²⁺ Sensitivity: - **Voltage Sensitivity**: The receptor's response is also affected by the membrane voltage (`v`), and this is incorporated through the parameters `gamma` and `Kd` that define the Mg²⁺ sensitivity of the receptor's blocking state. A procedure calculates the voltage-dependent block, adding a biologically realistic feature to the model. This model attempts to simulate the kinetic behavior of NMDA receptors under physiological conditions, providing insight into how synaptic inputs might be integrated through voltage-dependent mechanisms and ligand binding. It captures dynamic transitions in receptor states triggered by neurotransmitter binding and influenced by extracellular factors such as Mg²⁺ concentration, thus representing critical aspects of synaptic transmission and its modulation in neural circuits.