The provided code models synaptic transmission and plasticity mechanisms involving AMPA and NMDA receptors, key components of excitatory neurotransmission in the central nervous system (CNS). Specifically, it aims to simulate postsynaptic conductance changes mediated by these receptors and presynaptic short-term plasticity. ### Key Biological Concepts 1. **AMPA and NMDA Receptors**: - **AMPA Receptors**: Responsible for fast excitatory synaptic transmission. Upon glutamate binding, they allow Na\(^+\) and, to a lesser extent, Ca\(^2+\) ions to flow, causing a rapid depolarization of the postsynaptic cell. These receptors follow a dual-exponential decay characterized by rise (`tau_r_AMPA`) and decay (`tau_d_AMPA`) time constants, reflecting the rapid onset and offset of AMPA-mediated currents. - **NMDA Receptors**: Characterized by slower kinetics due to dual-exponential rise (`tau_r_NMDA`) and decay (`tau_d_NMDA`) profiles, these receptors are permeable to Na\(^+\), K\(^+\), and importantly Ca\(^2+\). NMDA receptor activation is both ligand and voltage-dependent, as modeled by the `mggate` variable, which accounts for Mg\(^{2+}\) blockade relieved during depolarization. 2. **Synaptic Plasticity**: - **Short-term Plasticity**: This refers to rapid, transient changes in synaptic strength due to presynaptic mechanisms. The model incorporates both facilitation (`Fac`) and depression (`Dep`). Facilitation increases synaptic efficacy with repetitive stimulation, while depression reduces it. These are modeled using `Use`, `u`, and probabilities `Pv` and `Pr`, which dictate vesicle release likelihood and hence synaptic efficacy. 3. **Voltage Dependence and Mg\(^{2+}\) Block**: - The NMDA receptor is voltage-dependent, a property derived from the Mg\(^{2+}\) block, which is modeled in the code through `mgVoltageCoeff`. This block prevents ion flow at resting potentials and is removed during depolarization, allowing Ca\(^{2+}\) influx, which is crucial for synaptic plasticity signaling cascades. ### Importance in Neuroscience These receptor dynamics and the inclusion of short-term plasticity mechanisms are critical for understanding synaptic integration and the strength of synaptic transmission, which underlies learning and memory processes. AMPA receptors rapidly mediate synaptic responses, while NMDA receptors contribute to synaptic plasticity and signal transduction pathways due to Ca\(^{2+}\) influx. This model reflects how synaptic strength and efficacy are dynamically regulated by activity and presynaptic factors, providing a mechanistic insight into synaptic communication and its alteration under various physiological and pathological conditions.