# Biological Basis of the NMDA Synapse Model The provided code models a synaptic mechanism, specifically focusing on NMDA (N-methyl-D-aspartate) receptor-mediated synaptic transmission. The NMDA receptor is a type of glutamate receptor that is critical for synaptic plasticity, learning, and memory in the brain. Here's an explanation of the biological foundations of the model: ## NMDA Receptor Dynamics - **Voltage Dependence and Magnesium Block**: NMDA receptors exhibit voltage-dependent properties due to the blockade by magnesium ions. The unblock of NMDA receptors occurs with depolarization. This model incorporates voltage dependence through the term `s = 1.50265/(1+0.33*exp(-0.0625*v))`, which suggests a relation between synaptic conductance and the membrane potential `v`. The exponential factor reflects the voltage-dependent removal of the magnesium block. - **Calcium Permeability**: NMDA receptors are permeable to calcium ions, in addition to sodium and potassium. While the explicit modeling of calcium influx is not depicted in this code, the regulation of synaptic conductance (`g`) and current (`i`) demonstrates how NMDA receptor activity influences membrane potential and potentially intracellular calcium dynamics. ## Synaptic Conductance and Current - **Receptor Kinetics**: The NMDA receptor conductance change is depicted using a two-state model (`a` and `b`) with characteristic time constants (`tcon` and `tcoff`). These can be thought to represent the transition between bound and unbound states of the receptor complex as neurotransmitter glutamate binds and unbinds. - **Synaptic Current**: The current (`i`) flowing through the NMDA receptor is computed as the product of the maximum conductance (`gNMDAmax`), the synaptic gating variable difference (`g = b-a`), and the voltage-dependent term `s`, all modulated by the difference between the membrane potential and the NMDA reversal potential (`v-enmda`). ## Short-Term Synaptic Plasticity - **Facilitation and Depression**: The implementation of `tauD` and `tauF` represents short-term synaptic depression and facilitation, respectively. These phenomena are critical in synaptic transmission, where repeated stimuli can lead to either a decreased or increased synaptic response. The `NET_RECEIVE` block in the code updates states (`R` for the synaptic resource, `u` for the utilization of that resource) which reflect these dynamic changes in synaptic strength due to patterns of presynaptic activity. ## Cited Background and Context - **Reference**: The citation of Durstewitz & Gabriel (2006) implies a basis in established literature, indicating that the parameters and mathematical formulations are likely derived from empirical observations and prior computational studies pertinent to the role of NMDA receptors in cortical dynamics. This model highlights crucial neurophysiological properties of NMDA receptors, reflecting their complex role in mediating synaptic responses and their activity-dependent modulation critical for computational functions in neural circuits.