# Biological Basis of the AMPA and NMDA Receptor Model with Short-term Plasticity The provided code models synaptic currents mediated by AMPA and NMDA receptors, key components in synaptic transmission and plasticity in the central nervous system. These receptors are involved in excitatory neurotransmission, primarily utilizing the neurotransmitter glutamate. ## AMPA Receptors ### Function AMPA receptors are ionotropic receptors that mediate fast excitatory synaptic transmission in the brain. They are permeable primarily to Na⁺ and K⁺ ions, and their activation rapidly depolarizes the post-synaptic neuron. ### Key Aspects in Code - **State Variable (`sAMPA`)**: Represents the conductance state of the AMPA receptor, which follows a single-exponential decay. - **Maximal Conductance (`gAMPAmax`)**: A parameter representing the maximal synaptic conductance through AMPA receptors. - **Reversal Potential (`E_Glu`)**: The reversal potential for the AMPA receptor, typically reflecting the equilibrium potential for Na⁺ and K⁺ ions. ## NMDA Receptors ### Function NMDA receptors are also ionotropic but have unique gating properties. They require both presynaptic glutamate release and postsynaptic depolarization to become fully active. They have a slower kinetics compared to AMPA receptors and are permeable to Na⁺, K⁺, and Ca²⁺ ions. ### Key Aspects in Code - **State Variables (`sNMDA`, `xNMDA`)**: Represent the NMDA conductance. The NMDA receptor model includes dual-exponential decay to capture its slower kinetics. - **Voltage-dependency (`mggate`)**: A variable affected by the extracellular magnesium concentration (`MgCon`), which influences the receptor's voltage-dependent block, characterized by a computational model following Jahr & Stevens (1990). - **Maximal Conductance (`gNMDAmax`)**: Represents the maximal synaptic conductance through NMDA receptors. ## Short-term Plasticity The model captures synaptic dynamics without the short-term depression component, reflecting changes in synaptic strength that occur on a fast timescale. The code includes mechanisms to ensure state variables representing receptor activation do not exceed physiological limits. ## Biological Relevance This model reflects the integration of AMPA and NMDA receptor currents in response to glutamatergic synaptic input. AMPA receptors contribute to fast synaptic transmission, while NMDA receptors are important for synaptic plasticity and are integral for processes such as synaptic strengthening associated with learning and memory. The inclusion of voltage-dependent properties and dual-exponential conductance profiles highlights crucial aspects of how synaptic integration and plasticity are modeled computationally, reflecting biological reality. In summary, this code provides a model of synaptic currents using computational representations of biophysical parameters and kinetics reflective of AMPA and NMDA receptors. The design emphasizes behaviors around excitatory synaptic transmission and plasticity pivotal in neuron communication and network dynamics.