# Biological Basis of the Model Code The provided code is a computational model of synaptic interactions between pyramidal neurons, capturing the dynamics of synaptic plasticity and ion channel activity, specifically focusing on AMPA and NMDA receptor-mediated synaptic transmission, as well as calcium dynamics. ## Synaptic Transmission ### AMPA and NMDA Receptors - **AMPA Receptors**: These are ionotropic glutamate receptors that mediate fast synaptic transmission in the central nervous system. The model includes parameters for AMPA receptor conductance (`gbar_ampa`), dynamics of gating (`AlphaTmax_ampa`, `Beta_ampa`), and reversal potential (`Erev_ampa`). - **NMDA Receptors**: These are also glutamate receptors, but they have distinct biophysical properties requiring both ligand binding and membrane depolarization for activation. NMDA receptors are crucial for synaptic plasticity and are modeled with similar parameters to AMPA receptors (`gbar_nmda`, `AlphaTmax_nmda`, `Beta_nmda`, `Erev_nmda`), with additional voltage-dependent term `sfunc(v)` which models the magnesium block present in NMDA receptors. ## Calcium Dynamics - **Calcium Influx**: NMDA receptors allow calcium ions (Ca²⁺) to enter the cell, which is critical for synaptic plasticity mechanisms like long-term potentiation (LTP) and long-term depression (LTD). The model calculates calcium current (`ICa`) and changes in calcium concentration (`capoolcon`). - **Calcium Buffering and Dynamics**: The model uses a local calcium pool to simulate the intracellular concentration of calcium ions, with parameters governing the calcium dynamics such as `tauCa` (time constant for calcium decay) and `Afactor` (affects the conversion of ionic current into concentration change). ## Synaptic Plasticity - **Plasticity Rules**: The model incorporates a learning rule based on calcium levels, representing synaptic plasticity. The function `eta` calculates the synaptic modification rate based on calcium concentration. The `omega` function describes the modification direction (potentiation vs. depression) depending on calcium thresholds (`threshold1`, `threshold2`). - **Weight Dynamics**: Synaptic weight (`W` and `W_nmda`) changes are governed by differential equations that consider the current calcium concentration (`capoolcon`). Constraints are placed on weight changes (`Wmax`, `Wmin`) to prevent unstable synaptic scaling. ## Short-term Synaptic Plasticity - **Facilitation and Depression**: The model includes short-term synaptic plasticity features like facilitation (`f`) and depression (fast `D1` and slow `D2`), which modify the effectiveness of synaptic transmission. These are managed through `facfactor` representing the multiplicative effect of facilitation and depression on synaptic conductance. ## Additional Dynamics - **Randomness in Synaptic Activity**: The `rp` variable, set by `unirand()`, introduces randomness in synaptic activity to reflect stochastic aspects of synaptic transmission. - **Use of Ions**: The `USEION` statement with `ca` refers to the read of equilibrium potential for calcium ions (`eca`), linking ion dynamics to synaptic changes. This model is designed to simulate complex interactions at synapses that depend on both synaptic inputs and intrinsic ionic mechanisms, providing insights into how pyramidal cells communicate and adapt in response to activity.