### Biological Basis of the Model The provided code models the stochastic release probability of neurotransmitters at a synapse, incorporating mechanisms of short-term synaptic plasticity, primarily focusing on facilitation and depression dynamics. The biological significance of this model lies in its attempt to capture the probabilistic nature of synaptic vesicle release and the dynamic changes in synaptic strength over short timescales due to recent synaptic activity. #### Stochastic Neurotransmitter Release At synaptic terminals, the release of neurotransmitters into the synaptic cleft is not deterministic; rather, it occurs with a certain probability that can vary with recent synaptic activity. This code implements a stochastic model where neurotransmitter release is probabilistically determined upon receiving a presynaptic spike. The release probability, `P`, is compared against a random number to decide if a vesicle is released. #### Short-term Synaptic Plasticity **Facilitation and Depression:** 1. **Facilitation:** - **Biological Background:** After a presynaptic neuron fires, the probability of neurotransmitter release increases for subsequent spikes. This is due to the residual calcium ions in the presynaptic terminal, which enhances the likelihood of vesicle release. - **Model Implementation:** The variable `F` represents the facilitation level, which increases with each spike and decays back to baseline over time, controlled by `tau_F`, the time constant for facilitation decay. The parameter `f` denotes the additive increase in facilitation with each spike. 2. **Depression:** - **Biological Background:** Synaptic depression refers to the reduction in neurotransmitter release probability following repeated stimulation, typically due to the depletion of readily releasable vesicle pools. - **Model Implementation:** This is represented by the variable `D1`, modeling fast depression which multiplicatively decreases with each spike. The recovery from depression is controlled by the time constant `tau_D1`. The parameter `d1` governs the extent of fast depression. Additional variables for slow depression (`D2`, `tau_D2`) are commented out in the code but suggest an intention to model slower forms of synaptic depression, indicating recognition of multiple temporal regimes in synaptic depression. #### Basal Release Probability - **Biological Background:** Each synapse has a baseline probability of releasing neurotransmitter vesicles in response to an action potential, known as the basal release probability. - **Model Implementation:** This is captured by the parameter `P0`, which is the base or initial release probability before any spikes have influenced the synapse's state. By modeling these processes, the code aims to replicate the complex and dynamic behavior observed in synapses, specifically in environments such as the layer 2/3 excitatory synapses of the rat primary visual cortex, as detailed by Varela et al. This study is foundational for understanding how synaptic behaviors change rapidly in response to neuronal activity, impacting circuit computations and overall brain functionality.