The `tsodyks_connection.cpp` file models synaptic dynamics based on the Tsodyks-Markram model, which describes synaptic transmission with short-term plasticity mechanisms. This model focuses on two main phenomena: synaptic facilitation and synaptic depression, both of which are essential for understanding the transient behavior of synapses in response to action potential firing. ### Key Biological Concepts 1. **Synaptic Facilitation and Depression**: - **Facilitation** refers to a temporary increase in synaptic strength, often due to the residual calcium effect that increases neurotransmitter release probability with successive action potentials. - **Depression** is a temporary reduction in synaptic efficacy, occurring when the readily releasable pool of vesicles is depleted due to sustained firing. 2. **Dynamic Synaptic Variables**: - `U_`: Represents the utilization of synaptic efficacy (neurotransmitter release probability). It corresponds to how readily neurotransmitters are released in response to an action potential, a key factor in synaptic facilitation. - `x_` and `y_`: Represent dynamic states of available synaptic resources. `x_` indicates the fraction of available resources, while `y_` accounts for the fraction of resources currently engaged in transmission. These variables capture the balance of vesicle depletion and recovery, essential for modeling depression. - `u_`: Reflects the temporal change in `U_`, adding a dynamic aspect to facilitation where the release probability can change over time based on neural activity. 3. **Time Constants**: - `tau_psc_`: The decay time constant of the synaptic current. This determines how quickly the synaptic current attenuates over time. - `tau_fac_`: The facilitation time constant, dictating how quickly the synaptic efficacy increases with repeated stimulation. - `tau_rec_`: The recovery time constant, which describes the time it takes for synaptic resources to replenish after being depleted, crucial for the dynamics of synaptic depression. ### Biological Modeling Collectively, the parameters and dynamic variables create a model of synaptic behavior that reflects the transient periods of synaptic strengthening or weakening in response to neural activity. This model helps to capture the complex interplay between vesicle release, the probability of synaptic release, and the replenishment dynamics of synaptic resources. It provides insights into how neurons communicate and adapt through changes in synaptic strength, which can be influenced by various factors such as spiking history and synaptic resource availability. The Tsodyks-Markram model is fundamental in computational neuroscience for simulating and understanding how synapses behave under different stimulation patterns, reflecting both facilitation and depression phenomena observed in biological synapses. This file thus represents a critical component of modeling short-term synaptic plasticity in neuronal networks.