The provided code models synaptic dynamics using the Tsodyks-Markram (TM) synapse model, which addresses the short-term plasticity mechanisms observed at excitatory synapses. This type of computational model captures the dynamic changes in synaptic strength that occur on timescales from milliseconds to seconds, resulting from presynaptic neuronal activity. ### Biological Basis 1. **Synaptic Transmission and Plasticity:** - **Facilitation (F), Depression (D), and P Synapses:** - The model considers three types of synapses: facilitating (F), depressing (D), and presumably a baseline pattern (P), reflecting their respective synaptic plasticity behaviors. - **Facilitation** involves an increase in synaptic strength due to successive spikes, characterized by an increased release probability of neurotransmitters. - **Depression** captures a decrease in synaptic strength, typically due to the depletion of neurotransmitter vesicles or receptor desensitization following repeated stimulation. 2. **Key Variables:** - **r (Release probability):** This variable represents the probability that a neurotransmitter is released from presynaptic terminals upon the arrival of an action potential. It is dynamically adjusted for each synapse. - **x (Fraction of available resources):** This tracks the proportion of neurotransmitter resources available for release. Values decrease with neurotransmitter release and recover over time. - **Is (Synaptic current contribution):** Represents the synaptic current's contribution to the postsynaptic neuron, integrated over time. 3. **Parameters:** - **tauf and taud:** Time constants representing the timescales of facilitation (tauf) and depression (taud), unique to each synapse type. They determine how quickly these processes decay back to baseline following synaptic activity. - **U (Utilization parameter):** Represents the fraction of available resources used per action potential, differing among synapses. It modulates how much neurotransmitter can be released during synapse activation. - **A (Synaptic efficacy):** This factor reflects the maximum potential impact on the postsynaptic neuron. It incorporates the effect of synaptic dynamics on observed postsynaptic responses. 4. **Integration of Synaptic Dynamics:** - The code uses differential equations to simulate the evolution of synaptic state variables (r, x, Is) using biologically relevant time constants and parameters. The variables are updated based on this dynamic interplay, modeling how synaptic efficacy changes over short time periods in response to spike events (`sp_event`). ### Conclusion This computational implementation of the Tsodyks-Markram model provides insights into how synaptic interactions dynamically regulate neurotransmission through facilitation and depression within neural circuits. Used extensively in computational neuroscience, such models help elucidate how short-term synaptic plasticity can influence information processing and network behavior.