The provided code models synaptic transmission in neurons, focusing on AMPA and NMDA receptors and presynaptic short-term plasticity. Here’s a concise breakdown of the biological basis: ### Synaptic Transmission 1. **Receptor Types:** - **AMPA Receptors (AMPARs):** These ionotropic glutamate receptors mediate fast synaptic transmission in the central nervous system. When glutamate binds to AMPA receptors, they allow Na⁺ and K⁺ ions to pass through, resulting in excitatory postsynaptic potentials. - **NMDA Receptors (NMDARs):** These receptors are also ionotropic glutamate receptors but have slower kinetics than AMPARs. NMDA receptors allow Ca²⁺, Na⁺, and K⁺ to flow through the channel, and are voltage-dependent due to the Mg²⁺ block, which is relieved upon depolarization. They are crucial for synaptic plasticity and memory functions. 2. **Dual-exponential Conductance:** - The code employs a dual-exponential model for receptor conductance, which captures the kinetics of synaptic transmission: a rapid rise (tau_r) followed by a slower decay (tau_d). This reflects the biological reality of how AMPA and NMDA receptors activate and deactivate in response to glutamate. ### Short-term Synaptic Plasticity 1. **Facilitation and Depression:** - **Facilitation (Fac):** An increase in synaptic strength that occurs when two or more action potentials invade a terminal in quick succession. The residual calcium hypothesis underlies this: calcium remaining in the presynaptic terminal after the first spike facilitates neurotransmitter release upon subsequent spikes. - **Depression (Dep):** A decrease in synaptic strength following a high-frequency train of action potentials. This is typically due to depletion of the readily releasable pool of synaptic vesicles. 2. **Utilization of Synaptic Efficacy (Use):** - Represents the probability that a presynaptic action potential will trigger neurotransmitter release, influenced by factors such as previous activity which affects facilitation and depression dynamics. ### Stochastic and Computational Elements - **Stochastic Release:** The code includes probabilistic elements to simulate realistic synaptic behavior. The parameter "Pr" represents the probability of neurotransmitter release, incorporating both the state of vesicle availability (Pv) and utilization factor (u). - **Random Number Generation:** Used to simulate the probabilistic nature of synaptic transmission. The function `erand` provides randomness, essential for capturing the inherent variability in neurotransmitter release. Overall, the code represents a model of synaptic behavior mimicking biological processes such as synaptic conductance dynamics and plasticity, providing insights into how neurons communicate under various conditions.