The code provided models synaptic transmission and plasticity between pyramidal neurons in the brain, focusing on the dynamic processes that regulate synaptic strength through AMPA and NMDA receptor interactions along with the influence of local calcium ion (Ca²⁺) concentrations. ### Biological Basis of the Code #### Synaptic Transmission - **AMPA and NMDA Receptors**: The code describes two types of glutamatergic receptors known to be involved in synaptic transmission—AMPA receptors (AMPARs) and NMDA receptors (NMDARs). - **AMPA Receptors**: Responsible for fast synaptic transmission. Their conductance is calculated using parameters such as `Cdur_ampa`, `AlphaTmax_ampa`, `Beta_ampa`, and `Erev_ampa`, reflecting the kinetics and reversal potential of AMPAR-mediated currents. - **NMDA Receptors**: Provide slow and lasting synaptic currents, allowing Ca²⁺ influx, which is crucial for synaptic plasticity. The NMDA component is modeled with parameters like `Cdur_nmda`, `AlphaTmax_nmda`, `Beta_nmda`, and `Erev_nmda`. #### Calcium Dynamics - **Calcium Influx and Pool**: The influx of Ca²⁺ through NMDA receptors, driven by the `ICa` term, is modeled as a key signal for synaptic plasticity. This is influenced by the local Ca²⁺ pool (`capoolcon`) and related parameters such as `Cainf`, `tauCa` (time constant for Ca²⁺ decay), and `Afactor` (a scaling coefficient for Ca²⁺ entry). #### Synaptic Plasticity - **Short-term Plasticity**: Factors such as facilitation (`F`, `facfactor`) and depression (`D1`, `D2`) are used to model the short-term plastic changes that affect synaptic strength. These variables account for transient changes in synapse responsiveness due to recent activity, resulting from interactions between molecular constituents like presynaptic vesicles. - **Long-term Plasticity**: This involves weight changes through long-term potentiation (LTP) and long-term depression (LTD). The model simulates this using variables such as `W`, `initW`, and functions `eta` and `omega` to model synaptic weight change (`dW_ampa`) based on Ca²⁺ levels and thresholds (`threshold1`, `threshold2`), reflecting the complex interplay of signaling cascades leading to LTP/LTD. #### Spike-timing Dependent Plasticity - **Timing Dependence**: The spike-timing dependency is connected to synaptic efficacy changes mediated by NMDA receptor activity and subsequent calcium entry, influencing the parameters controlling the synaptic conductance and plasticity rules (`rp`, `thr_rp`). ### Neurophysiological Relevance This model reflects key physiological processes in the brain's excitatory synapses, specifically involving pyramidal neurons, which are crucial for various cognitive functions and neural circuit computations. The model captures the interactions between fast synaptic signaling and slower postsynaptic calcium-dependent plasticity, which are foundational for learning and memory mechanisms. The involvement of facilitation and depression also indicates a dynamic regulation of synaptic efficacy, sensitive to recent histories of synaptic activity. These mechanisms lay the groundwork for understanding how synaptic connections can change and strengthen over time in response to activity patterns, underpinning learning processes and memory formation in neural networks.