The provided code models synaptic transmission in pyramidal neurons, focusing on the integration of excitatory inputs mediated by AMPA and NMDA receptors. These two receptor types play critical roles in synaptic plasticity and neurotransmission in the central nervous system, particularly in the context of excitatory synapses. ### Biological Basis #### Pyramidal Neurons Pyramidal cells are excitatory neurons found in several brain regions, including the cortex and hippocampus. They are characterized by their pyramid-shaped soma, long apical dendrite, and numerous basal dendrites, allowing them to integrate synaptic input from large numbers of presynaptic neurons. #### AMPA and NMDA Receptors - **AMPA Receptors (AMPARs):** - AMPARs are ionotropic glutamate receptors that mediate fast synaptic transmission. When glutamate binds to AMPARs, they allow the influx of Na⁺ ions, resulting in depolarization of the postsynaptic membrane. - The parameters `Cdur_ampa`, `AlphaTmax_ampa`, `Beta_ampa`, `Erev_ampa`, and `gbar_ampa` represent AMPA receptor kinetics, reversal potential, and conductance respectively. - **NMDA Receptors (NMDARs):** - NMDARs are also ionotropic glutamate receptors but exhibit a slower response compared to AMPARs. They are unique due to their voltage-dependent block by Mg²⁺ ions and permeability to Ca²⁺, Na⁺, and K⁺ ions. - Key parameters include `Cdur_nmda`, `AlphaTmax_nmda`, `Beta_nmda`, `Erev_nmda`, and `gbar_nmda`. The receptor's conductance also depends on the membrane potential, which is illustrated by the `sfunc(v)` function to model Mg²⁺ block relief as the membrane depolarizes. #### Synaptic Transmission Model - **Timing and Dynamics:** The `t0` variable tracks the timing of synaptic events, and the kinetic scheme described by `r_nmda'` and `r_ampa'` represents the fraction of receptor occupancy and gating kinetics in a simplified manner. - **Synaptic Conductance and Currents:** The conductance (`g_nmda`, `g_ampa`) and currents (`inmda`, `iampa`) are calculated based on the number of open receptors, which are modulated by parameters like `W_nmda` and `W_ampa`. These might represent the initial synaptic weight or strength impacting the potential amplitudes. ### Local Ca²⁺ Pool and Plasticity Though not explicitly modeled in the provided code, NMDA receptor's permeability to Ca²⁺ is crucial for synaptic plasticity mechanisms such as long-term potentiation (LTP). This process is vital for learning and memory, where increased intracellular Ca²⁺ can trigger various intracellular signaling pathways. ### Summary This code models the integration of synaptic inputs via AMPA and NMDA receptors in pyramidal neurons, crucial for understanding excitatory neurotransmission and synaptic plasticity. The parameters reflect the kinetics and dynamics of these receptors, providing insight into their roles in neuronal communication and computational aspects of brain function.