The provided code models the activity of an NMDA (N-methyl-D-aspartate) receptor synapse, focusing specifically on the synaptic conductance dynamics that are mediated by NMDA receptors. This model includes key features of NMDA receptor function, including the time-dependent dynamics of synaptic currents and the effects of magnesium (Mg²⁺) block on voltage-dependent receptor activity. ### Biological Basis #### NMDA Receptors NMDA receptors are a type of glutamate receptor found in the central nervous system. They play a critical role in synaptic plasticity, which is essential for learning and memory. Unlike other ionotropic glutamate receptors, NMDA receptors are both ligand-gated and voltage-dependent. - **Dual Gating Mechanism**: For NMDA receptors to conduct ions, they require the binding of glutamate (a neurotransmitter) and a simultaneous depolarization of the postsynaptic membrane to relieve a voltage-dependent block by Mg²⁺ ions. This "mgBlock" is modeled using a function that adjusts conductance based on membrane voltage. - **Calcium Permeability**: NMDA receptors are permeable to Calcium (Ca²⁺) as well as Na⁺ and K⁺ ions. The influx of Ca²⁺ plays a crucial role in signaling pathways that lead to synaptic strengthening or weakening. #### Dynamics Modeled in the Code - **Open (o) and Closed (c) States**: The code tracks the proportion of receptors in open and closed states. This reflects the time course of receptor activation and deactivation upon synaptic input, governed by exponential decay functions ("cnexp" method) with time constants `tau_o` (open state) and `tau_c` (closed state). - **Saturation and Synaptic Weight**: The code includes a model of receptor saturation (parameter `nmda_sat`) which limits the extent to which the synaptic response can grow with repeated activation. Moreover, the receptor conductance is modulated by synaptic weight and the number of stimuli received, adapting in response to synaptic input history. - **Reversal Potential (erev)**: This parameter represents the equilibrium potential for the ions conducted by the receptor, influencing the direction and magnitude of ionic currents when the receptor channels are open. #### Magnesium Block Modeling - **Voltage Dependence**: The function `mgBlock(v)` captures the Mg²⁺ block, reflecting its alleviation as membrane potential depolarizes. Parameters `c1` and `c2` define the strength and sensitivity of the voltage-dependent block. ### Conclusion Overall, this model encapsulates key physiological processes that occur at NMDA synapses, capturing the complex interplay of temporal dynamics, membrane voltage, and ion fluxes that characterize NMDA receptor functionality and synaptic signaling. This model is valuable for simulating how synaptic efficacy changes in response to patterns of neural activity, informing our understanding of mechanisms underpinning synaptic plasticity.