# Biological Basis of the Code The provided code models the synaptic dynamics of AMPA and NMDA receptors, with a focus on simulating presynaptic short-term plasticity. Here's an overview of the biological phenomena being modeled: ## AMPA and NMDA Receptors AMPA and NMDA receptors are two types of ionotropic glutamate receptors. - **AMPA Receptors**: These receptors mediate fast synaptic transmission in the central nervous system. When activated by glutamate, they allow the flow of Na⁺ (and to a lesser extent, K⁺) ions, leading to a rapid depolarization of the postsynaptic neuron. The code uses dual-exponential functions to model the conductance profile (with parameters `tau_r` and `tau_d`), reflecting the fast kinetics of the AMPA receptor currents. - **NMDA Receptors**: These receptors are also activated by glutamate but have a distinct mechanism involving Mg²⁺ block that is voltage-dependent. When the postsynaptic neuron is sufficiently depolarized, the Mg²⁺ block is relieved, allowing Ca²⁺ (along with Na⁺ and K⁺) to enter the cell. This provides a slower, longer-lasting current. While the detailed Mg²⁺ block mechanism is not explicitly included in this code, the NMDA conductance is integrated into the overall synaptic weight, which is made equal to AMPA, suggesting a focus on postsynaptic coactivation dynamics. ## Presynaptic Short-Term Plasticity The code implements models of short-term plasticity as described by Fuhrmann et al. (2002). This involves two main processes: - **Facilitation**: The increase in synaptic strength following a presynaptic action potential. In the code, `Fac` and the running variable `u` represent this mechanism, allowing for an increased probability of neurotransmitter release for subsequent action potentials if the facilitation time constant (`Fac`) is significant. - **Depression**: The decrease in synaptic strength following repeated presynaptic activity, due to depletion of readily releasable vesicles. This is captured in the code through the parameter `Dep` and the probability variable `Pv`, which represents the availability of vesicles for release. The code calculates these dynamics during synaptic events and updates variables such as the utilization of synaptic efficacy (`u`) and the probability of vesicle availability (`Pv`) to determine the immediate likelihood of neurotransmitter release. ## Synaptic Conductance and Dynamics This model calculates synaptic conductance (`g`) as a function of the state variables `A` and `B`, which embody the rise and decay phases of synaptic conductance changes following neurotransmitter release. The synaptic current (`i`) is derived from this conductance and the difference between the membrane potential (`v`) and the reversal potential (`e`), which is set to 0 mV, a common approximation for glutamatergic synapses under certain conditions. ## Modulation and Stochasticity The `rng` and related functions (e.g., `erand`) introduce stochasticity into the synaptic release process, reflecting the inherent randomness in vesicle release and neurotransmitter binding at synapses. In summary, the code models the dynamic interplay of AMPA and NMDA receptor-mediated postsynaptic currents with presynaptic short-term plasticity mechanisms, capturing essential features of synaptic transmission and plasticity observed in neuronal circuits.