# Biological Basis of the Code: NMDA and AMPA Receptors ## Overview The provided code models synaptic transmission mediated by AMPA and NMDA glutamate receptors, key types of ionotropic receptors involved in excitatory neurotransmission in the central nervous system. These receptors play crucial roles in synaptic plasticity, development, and numerous neurophysiological processes. ## AMPA Receptors - **Function**: AMPA receptors mediate fast synaptic transmission in the brain. They are activated by glutamate, the primary excitatory neurotransmitter. - **Kinetics**: The code uses a simplified kinetic model with parameters such as `Alpha` (binding rate) and `Beta` (unbinding rate) to describe the dynamics of receptor binding and unbinding. - **Conductance**: The `gampa` variable represents the conductance of the AMPA receptors, contributing to the current (`iampa`) through the receptor when glutamate is bound. ## NMDA Receptors - **Function**: NMDA receptors contribute to synaptic plasticity and are permeable to calcium ions, playing a critical role in long-term potentiation (LTP) and depression (LTD). - **Magnesium Block**: The function `mgblock(v)` models the voltage-dependent block of the NMDA receptor channel by Mg²⁺ ions, a key feature that makes NMDA receptor activity contingent on postsynaptic depolarization. In the presence of Mg²⁺, NMDA receptors do not conduct ions unless the postsynaptic membrane is depolarized. - **Kinetics**: The variable `gnmda` represents the conductance of NMDA receptors, factoring in the magnesium block and the bound state of the receptor. Like AMPA receptors, `gnmda` contributes to the total synaptic current (`inmda`). ## Synaptic Plasticity - **Spike-Timing-Dependent Plasticity (STDP)**: The model incorporates mechanisms for LTP and LTD based on the timing of spikes relative to recent synaptic activity, adjusted through parameters like `ltpinvl` and `ltdinvl`. - **Plasticity Scaling**: The `plast` function models a sigmoidal function to capture synaptic weight changes depending on the variable `s`, which accumulates spike activity and modifies synaptic efficacy over time. ## Parameters - **Reversal Potential (E)**: Set to 0 mV, representing the equilibrium potential for the conductance mediated by these channels. - **Magnesium Concentration**: External magnesium concentration (`mg`) is modeled to assess its role in blocking the NMDA receptor channel. - **Synapse Location**: Variables such as `x`, `mgid`, and `ggid` are used for organizing spatial and network connections, emphasizing the synapse's placement within a larger neuronal network. ## Integration in Computational Models - The code uses a kinetic scheme to transition between bound and unbound states, enabling fast computational simulations without solving complex differential equations dynamically. - `NET_RECEIVE` and `BREAKPOINT` blocks facilitate the synaptic event handling, ensuring proper integration with a realistic temporal sequence of neurotransmitter release and receptor binding, mimicking biological synaptic responses. In summary, the code provides a computational framework to study the biophysical properties of NMDA and AMPA receptors within synaptic models, emphasizing their roles in neurotransmission and plasticity.