The provided code models a synaptic mechanism with graded synapse dynamics using first-order binding kinetics, focusing specifically on the synaptic conductance changes associated with neurotransmitter release and receptor activation. Here are the key biological aspects addressed in the code: ### Biological Basis 1. **Graded Synaptic Transmission:** - The model implements graded synaptic transmission, which differs from the all-or-none action potential responses typically seen in neurons. Instead, it reflects the continuous nature of neurotransmitter release and receptor activation, allowing for varying levels of postsynaptic response based on the presynaptic voltage (`V_pre`). 2. **Synaptic Receptor Kinetics:** - The kinetic scheme assumes first-order binding kinetics, suggesting a linear relationship between neurotransmitter release and receptor activation. The code uses a time constant (`tau`) to model the rate of change in synaptic conductance. 3. **Voltage Dependence:** - The model incorporates voltage dependence using a threshold potential (`V_thr`) and a slope factor (`V_slope`). This simulates how the likelihood of neurotransmitter binding to its receptor changes with the presynaptic membrane potential (`V_pre`), described by a hyperbolic tangent function (`tanh`), which smooths the transition from inactive to fully active states based on threshold crossing. 4. **Synaptic Current and Conductance:** - The code calculates synaptic current (`i`) based on the synaptic conductance (`g`) and the reversal potential (`e`). The conductance is maximal (`g_max`) when the supply of neurotransmitters completely saturates the receptors, leading to full activation of the synapse. 5. **Saturation and Lower Bounds:** - The conductance state (`s`) is bounded between a lower limit (preventing conductance from falling below a small value) and saturation at `1`, ensuring biological plausibility by preventing excessively small or large conductance values that are not typically observed in physiological conditions. ### Summary Overall, the code models the dynamics of a synapse with continuous, graded responses to presynaptic voltage changes. This model is particularly suitable for simulating synapses where neurotransmitter release and receptor activation vary continuously rather than being tightly coupled to action potentials. The use of a hyperbolic tangent function and first-order kinetics captures the biophysical properties of graded synaptic responses in neurobiological systems.