### Biological Basis of the Model The provided code models synaptic transmission with a focus on glutamatergic synapses involving AMPA and NMDA receptors, incorporating mechanisms of presynaptic short-term plasticity. Here's how it relates to relevant biological phenomena: #### AMPA and NMDA Receptors - **AMPA Receptors**: These receptors are glutamate-gated ion channels that primarily mediate fast synaptic transmission in the central nervous system. They have rapid kinetics, characterized by dual-exponential profiles for their conductance, reflecting fast rise and decay times. In the code, this is represented by the variables `tau_r` and `tau_d`, which control the rise and decay time constants, ensuring `tau_r < tau_d` to simulate realistic synaptic currents. - **NMDA Receptors**: These receptors are both ligand- and voltage-gated, contributing to synaptic plasticity and memory functions. They are slower to activate and deactivate compared to AMPA receptors and are permeable to Ca²⁺ ions in addition to Na⁺ and K⁺. Although specific NMDA receptor kinetics are not expanded in this code, the code framework allows for modeling both receptor types using a shared weight factor (`gmax`) indicating the conductance level. #### Short-term Synaptic Plasticity - **Facilitation and Depression**: The code implements short-term synaptic plasticity based on the work of Fuhrmann et al., 2002. This includes facilitation and depression mechanisms that adjust synaptic efficacy on a short timescale. - **Facilitation**: Represented by the parameter `Fac`, facilitation increases synaptic strength following recent activity. The variable `u` is dynamically updated during synaptic events to represent the probability of neurotransmitter release as it adapts to previous synaptic activity. - **Depression**: Given by the parameter `Dep`, depression reduces synaptic efficacy following repeated stimulation. This reflects the depletion of available synaptic resources, represented by the variable `Pv`, which adjusts the probability of vesicle availability for subsequent neurotransmitter release. - **Utilization of Synaptic Efficacy**: The parameter `Use` dictates the initial utilization of synaptic efficacy. It represents the basal probability of neurotransmitter release in response to an action potential. #### Randomness and Synaptic Transmission - **Probabilistic Release**: Synaptic transmission is inherently stochastic. The code uses random number generation to model this aspect, reflected in the use of `rng` to decide if a synaptic release event occurs, similar to biological processes where release is not deterministically guaranteed. #### Synaptic Conductance and Driving Force - **Conductance Dynamics**: The code calculates synaptic conductance (`g`) and the corresponding synaptic current (`i`) using the difference between state variables `A` and `B`, representing the dynamics of AMPA receptor activation following synaptic events. - **Reversal Potential**: The reversal potential (`e`) is set to 0 mV, typical for glutamatergic synapses, where the excitatory nature of glutamate causes a depolarizing effect on postsynaptic membranes. In summary, the code simulates the dual-exponential kinetics of AMPA receptor-mediated transmission, NMDA receptor co-activation, and dynamic presynaptic short-term plasticity mechanisms. These elements are critical for understanding synaptic communication, learning, and memory at the cellular level in neurobiological systems.