The provided code snippet models the synaptic transmission and plasticity at a synapse between a tone (auditory stimulus) and pyramidal neurons, focusing on AMPA and NMDA receptor dynamics as well as calcium (Ca²⁺) signaling. The model represents a set of biological mechanisms that are crucial for synaptic signaling and plasticity, which underlie functions like learning and memory. ### Key Biological Components Modeled: #### 1. **Synaptic Receptors:** - **AMPA Receptors:** These are fast excitatory ionotropic receptors that mediate synaptic transmission. The code models AMPA conductance with `g_ampa`, where parameters like `Cdur_ampa`, `AlphaTmax_ampa`, and `Beta_ampa` represent the kinetics of AMPA receptor opening and closing in response to neurotransmitter binding. - **NMDA Receptors:** These are slower ionotropic receptors that play a crucial role in synaptic plasticity. They are voltage-dependent due to a magnesium block relieved by depolarization. The NMDA conductance is modeled with `g_nmda`, and parameters such as `Cdur_nmda`, `AlphaTmax_nmda`, and `Beta_nmda` govern the kinetics of NMDA receptor activity. The NMDA component is sensitive to calcium (Ca²⁺) influx, which is critical for downstream signaling and plasticity mechanisms. #### 2. **Calcium Dynamics:** - Calcium influx through NMDA receptors is a pivotal signal for synaptic plasticity. The model includes a local calcium pool (`capoolcon`) that governs synaptic weight changes via a calcium-dependent signaling mechanism. Parameters `eca`, `P0`, and `ICa` control calcium influx and its effect on the synapse. #### 3. **Calcium-based Plasticity:** - **Synaptic Weight Modulation:** The code includes functions to update synaptic weights (`W`), which are adjusted based on calcium concentration. It utilizes functions `eta()` and `omega()` to model plasticity rules. `eta` is a learning rate function influenced by local calcium concentration, while `omega` represents the bidirectional plasticity (LTP/LTD) governed by calcium thresholds (`threshold1`, `threshold2`). - **Weight Constraints:** The model includes mechanisms to constrain synaptic weight within biologically relevant limits (`Wmax` and `Wmin`), factoring in the maximum (`fmax`) and minimum (`fmin`) possible synaptic strengths. #### 4. **Membrane Voltage Dynamics:** - The model includes expressions that regulate how NMDA and AMPA currents (`inmda`, `iampa`) contribute to the postsynaptic neuron's voltage change (`v`), impacting downstream neural computation. ### Biological Significance: This model emphasizes the role of NMDA and AMPA receptors in synaptic transmission and plasticity, specifically how calcium dynamics mediated through these receptors lead to changes in synaptic strength. The interplay between calcium signaling and synaptic weight adaptation is crucial for understanding mechanisms of learning and memory, where synaptic connections are strengthened or weakened in response to activity patterns. Overall, the model portrays a biochemical and electrical synaptic environment where the interaction between neurotransmitter release, receptor activation, ion flow (especially Ca²⁺), and synaptic weight changes collectively contribute to the adaptive behavior of neural circuits critical for auditory processing and other higher-level brain functions.