The provided code is a computational model of synaptic transmission at excitatory synapses in the brain, specifically focusing on AMPA and NMDA receptor dynamics complemented by presynaptic short-term plasticity mechanisms. Below is the biological context and basis of the model: ### AMPA and NMDA Receptors - **AMPA Receptors**: These are ionotropic receptors that mediate fast synaptic transmission in the central nervous system. Upon binding of glutamate, these receptors allow the influx of Na+ ions, leading to rapid depolarization of the postsynaptic membrane. In the code, the AMPA receptor dynamics are modeled using a dual-exponential function characterized by rise (`tau_r_AMPA`) and decay (`tau_d_AMPA`) times to represent the receptor's conductance profile. - **NMDA Receptors**: These are also ionotropic receptors but with distinct properties. They require not only the binding of glutamate but also depolarization of the postsynaptic membrane to relieve a Mg²⁺ block. This feature makes them important for synaptic plasticity. In the code, NMDA receptor conductance is also modeled with a dual-exponential profile, and the effect of Mg²⁺ is modeled via the `mggate` function, which represents the voltage-dependent blockade by Mg²⁺. ### Short-term Synaptic Plasticity - **Utilization of Synaptic Efficacy (Use)**: This parameter represents the probability of vesicle release upon an action potential. In biological terms, it relates to how effectively a synaptic input can elicit a postsynaptic response. - **Facilitation (Fac)** and **Depression (Dep)**: These elements of presynaptic short-term plasticity describe how recent activity at a synapse affects neurotransmitter release. Facilitation (`Fac`) enhances release probability if synaptic events occur closely in time, often due to residual calcium accumulation. Depression (`Dep`), conversely, reduces release probability due to depletion of readily releasable vesicle pools. - **Probability of Vesicle Release (Pr)**: This is calculated as a product of `u` (running value of Use) and `Pv` (probability of vesicle availability), dynamically adjusting based on synaptic history, and contributes to the decision-making mechanism regarding whether the synapse is activated during an event. ### Conductance and Current Calculations - **Conductance Variables**: The model computes conductances for both AMPA (`g_AMPA`) and NMDA (`g_NMDA`) receptors. These are influenced by state variables A and B (for both AMPA and NMDA), which capture the temporal dynamics of receptor activity. - **Current Calculations**: Ionic currents through AMPA and NMDA receptors (`i_AMPA`, `i_NMDA`) are determined by their respective conductances and driving force (difference between membrane potential `v` and reversal potential `e`). ### Randomization for Synaptic Event Probability - **Random Number Generation**: The use of random numbers to simulate the likelihood of synaptic events mirrors the stochastic nature of neurotransmitter release and synaptic transmission, crucial for encoding variability and probabilistic behavior in synapses. Overall, this model seeks to represent the complex interplay between fast excitatory synaptic currents through AMPA and NMDA receptors and presynaptic modifications due to short-term plasticity, crucial for understanding synaptic integration and plasticity in neural circuits.