The provided code models synaptic transmission and neuronal dynamics using computational principles. Below is an explanation of the biological basis underlying key aspects of the code: ### Biological Basis 1. **Synaptic Dynamics and Short-Term Plasticity:** - **Synaptic Release Probability (U):** In synapses, neurotransmitter release is probabilistic and can vary over time. The code uses `U` as the baseline probability of synaptic release. This captures synaptic plasticity behaviors like facilitation and depression. - **Depression Recovery Time Constant (tau_rec):** This parameter (`tau_rec`) models the time constant for synaptic resource recovery post-transmission. In neurophysiology, synaptic depression occurs when neurotransmitter resources are temporarily depleted after repeated transmission. `tau_rec` reflects the time required to replenish these resources. - **Facilitation Time Constant (tau_fac):** Facilitation refers to the increased probability of neurotransmitter release following prior activity. The `tau_fac` parameter dictates how quickly this facilitative effect decays over time. - **Instantaneous Release Probability (u) and Recovered Resources (x):** Variables `u` and `x` represent dynamic changes in synaptic transmission probability and resource availability. They model the fluctuating states of synaptic resources and release probability due to depression and facilitation mechanisms. 2. **Neuronal Dynamics:** - **Membrane Time Constant (tau_V):** The `tau_V` parameter represents the time constant of neuronal membrane potential. It reflects how quickly a neuron's membrane potential returns to baseline following inputs, influenced by membrane capacitance and conductance. - **Neuronal Response Function (PHI):** The function `PHI(V, threshold, alpha)` likely represents a neuronal response or firing rate function, dependent on the membrane potential `V`. This captures the neuron's firing probability or rate as influenced by synaptic input, threshold, and gain (`alpha`). - **Noise in Neuronal Activity:** The `noise` variable in the simulation introduces stochasticity to the model, mimicking the intrinsic and extrinsic variability in neuronal firing due to factors like ion channel fluctuations. 3. **External and Internal Inputs:** - **Recurrent Synaptic Coupling Efficacy (J):** This parameter simulates the strength of synaptic coupling among neurons, capturing how strongly output from one neuron influences another. - **External Input (I):** The term `I` is used to represent any external inputs to the neuron, such as stimulus or other modulatory signals in a biological context. ### Summary The script simulates a single-neuron or a network's response dynamics capturing biologically plausible synaptic and neuronal properties. This model explores synaptic transmission variability, including short-term plasticity (depression and facilitation) and neuronal integration influenced by synaptic inputs and inherent noise, central to understanding neural circuit behavior in the cortex.