The given code models two types of glutamatergic synaptic inputs observed in the central nervous system: **AMPAR (AMPA receptor)** and **NMDAR (NMDA receptor)** mediated synaptic transmission, combined with a mechanism for **presynaptic short-term plasticity**. These models are commonly used to simulate synaptic inputs in neuronal models, particularly in the context of learning and memory-related processes. ### AMPA and NMDA Receptors - **AMPA Receptors (AMPARs):** These receptors are ionotropic and mediate fast synaptic transmission. They allow Na+ ions to enter the postsynaptic neuron upon glutamate binding, leading to a depolarizing synaptic current. The code represents AMPAR dynamics using dual-exponential profiles (with rise (`tau_r_AMPA`) and decay (`tau_d_AMPA`) time constants). The reversal potential is denoted by `e`. - **NMDA Receptors (NMDARs):** These receptors are also ionotropic but have more complex properties. They pass Na+, K+, and Ca2+ ions, and their activation depends on both glutamate binding and membrane depolarization (voltage-dependence). This is modeled by the `mggate` parameter in the code, representing magnesium block modulation. The NMDAR contains slower dynamics with distinct rise (`tau_r_NMDA`) and decay (`tau_d_NMDA`) time constants compared to AMPARs. ### Presynaptic Short-term Plasticity Presynaptic short-term plasticity is reflected in the code by dynamic changes in neurotransmitter release probability based on recent activity, chiefly through: - **Facilitation (`Fac`):** Short-term increase in synaptic strength, where `u` captures the effective neurotransmitter release probability. Its evolution depends on the parameter `Fac`. - **Depression (`Dep`):** Use-dependent decrease in synaptic strength as neurotransmitter resources deplete over repeated stimulation events. `Pv` (probability of vesicle availability) and `Pr` (release probability) are dynamically modulated to capture depression. Short-term plasticity is mathematically modeled using principles derived from Fuhrmann et al. 2002 which describe how synaptic efficacy (`Use`) and availability of synaptic resources (`Pv` and `Pr`) adjust based on inter-spike intervals. ### Biological Significance By capturing both the distinct kinetics of AMPAR and NMDAR responses and the dynamics of short-term synaptic plasticity, this model mimics the complexity of synaptic transmission in real neurons. This level of detail is crucial for understanding synaptic integration, which underlies neural computation and information processing during physiological functions such as learning and memory.