The provided code snippet models synaptic plasticity through a four-pathway phenomenological rule based on the work of Ebner et al. (2019). This model is designed to capture the complex interactions governing changes in synaptic weights, indicative of learning and memory processes in the brain. ### Biological Basis The model aims to represent several key biological mechanisms underlying synaptic plasticity, particularly long-term potentiation (LTP) and long-term depression (LTD), which are critical for memory formation and learning: 1. **Synaptic Transmission**: - **AMPAR and NMDAR Currents**: The synaptic transmission is mediated by AMPA receptors (AMPAR) and NMDA receptors (NMDAR). The `g_ampa` and `g_nmda` represent conductances attributable to AMPAR and NMDAR, respectively. NMDARs are crucial for synaptic plasticity as they allow Ca²⁺ influx when depolarized and are not blocked by Mg²⁺ (modeled by `mgblock`), a voltage-dependent phenomenon. 2. **Plasticity Pathways**: - **Pre-synaptic Plasticity**: Involvement of variables such as `w_pre`, `G`, and `Z` to simulate pre-synaptic mechanisms. This includes processes that are dependent on presynaptic spikes and neurotransmitter release. - **Post-synaptic Plasticity**: Post-synaptic events are represented using the variables `w_post`, `C`, `P`, `K_alpha`, and `Rho`, reflecting the cellular responses to neurotransmitters and intracellular signaling cascades following receptor activation. 3. **Calcium Dynamics**: - **Voltage Thresholds**: The dynamics involving `theta_u_T`, `theta_u_N`, and `theta_u_C` are used to calculate post-synaptic responses based on voltage thresholds, which might be tied to calcium signaling since calcium influx is critical in activating downstream pathways for synaptic plasticity. 4. **Activity-Dependent Modulation**: - **Saturation Functions**: Functions like `sigmoid_sat` are employed to simulate the non-linear and saturating response of intracellular activities like second messenger cascades and synaptic modulation based on the frequency and pattern of synaptic activity. 5. **Glutamatergic Signaling**: - Both AMPA and NMDA receptors are glutamate receptors. The model captures how glutamate-mediated excitatory postsynaptic potentials (EPSPs) can lead to LTP and LTD, influenced by the balance between AMPA and NMDA currents (`s_ampa`, `s_nmda`). By simulating biophysical dynamics around these aspects, the code provides a computational framework to understand how synaptic strengths change in response to neuronal activity patterns, providing insights into adaptive neural processes similar to those observed in biological systems.