# Biological Basis of the NMDA and AMPA Synapse Model The provided code is part of a computational model that simulates the dynamics of synaptic transmission mediated by NMDA (N-methyl-D-aspartate) and AMPA (α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid) receptors, two major types of glutamate receptors in the central nervous system. ## Synaptic Transmission ### NMDA and AMPA Receptors: 1. **AMPA Receptors:** - **Fast excitatory transmission:** AMPA receptors are responsible for mediating rapid excitatory synaptic transmission. - **Kinetics:** The model specifies fast activation (`tau4`) and inactivation (`tau3`) kinetics, reflecting how AMPA receptors quickly respond to glutamate influx. - **Parameters and Modulation:** The facilitation (`fampa`) and depression (`dampa`) variables model short-term synaptic plasticity, affecting the amplitude of successive excitatory postsynaptic currents (EPSCs). 2. **NMDA Receptors:** - **Voltage-dependent properties:** These receptors require both ligand binding (glutamate) and depolarization to relieve the Mg²⁺ block, which is reflected in the voltage-dependent term using the constants `n` and `gama`. - **Slow excitatory transmission:** They exhibit slower kinetics with longer activation (`tau2`) and inactivation (`tau1`) phases compared to AMPA receptors, contributing to synaptic integration over longer time scales. - **Calcium Permeability:** NMDA receptors allow calcium influx, crucial for synaptic plasticity, although not explicitly modeled here. - **Parameters and Modulation:** Depression (`dnmda`) and facilitation (`fnmda`) variables modify synaptic strength over time, incorporating dynamic changes akin to synaptic plasticity. ## Plasticity Mechanisms - **Short-term Synaptic Plasticity:** This model includes short-term depression and facilitation, which are forms of temporary changes in synaptic strength. Depression generally results from neurotransmitter depletion, while facilitation can enhance neurotransmitter release probability. ## Mathematical Representation - **Normalization Factors:** `factor1` and `factor2` are calculated for NMDA and AMPA receptor components, respectively, ensuring the receptor conductance dynamics are normalized over time. - **Dynamic Conductance Changes:** `gnmda` and `gampa` represent the conductance through NMDA and AMPA receptors, reflecting how synaptic current varies with voltage and receptor state changes. The model is based on foundational synaptic transmission properties and extends them to simulate not just the receptor kinetics but also their modulation through synaptic plasticity, modeled after key studies like those by Schiller and Larkum, and Varela et al. These mechanisms are fundamental for understanding synaptic integration and plasticity, critical processes for learning, memory, and neural computation in the brain.