The provided code is a computational model that attempts to simulate the dynamics of a neuronal action potential in response to external stimuli. Here's a breakdown of the biological aspects that the code captures: ### Neuronal Model - **AdEx Neuron Model**: The code implements an adaptive exponential integrate-and-fire (AdEx) model. This type of model accurately mimics neuronal firing properties, particularly the adaptation seen in real neurons as they produce action potentials. - **Parameters**: These parameters (`gl`, `el`, `vt`, `delta`, `vreset`, `a`, `tauw`, `b`) represent various biological properties: - `gl`: Leak conductance, which models the passive flow of ions across the cell membrane. - `el`: Leak reversal potential, representing the resting membrane potential. - `vt`: Spike threshold that determines when an action potential is initiated. - `delta`: Spike slope factor, a parameter indicative of how sharp the membrane potential rises. - `vreset`: Reset potential after a spike, emulating the after-hyperpolarization phase. - `a`, `tauw`, `b`: Parameters related to adaptation currents responsible for encoding slow changes in firing rates over time. ### External Stimuli and Biexponential Input - **Input Current (`Am`)**: Represents the amplitude of an external stimulus, often mimicking synaptic input. The current changes in discrete steps across multiple simulations, simulating varying strengths of external stimuli, from low to high amplitude. - **Biexponential Synaptic Current**: The model incorporates rise and decay constants (`taus1`, `taus2`) to simulate how synaptic currents dynamically change over time, closely paralleling the neurotransmitter kinetics at synapses in the brain. ### Basins of Attraction - **State Space (Voltage `v` and Adaptation `w`)**: The simulation checks whether the neuronal state `(v, w)` is within the basin of attraction—a region in phase space where trajectories tend to converge. This mirrors the biological stability regions that define neuron behavior under different input conditions. ### Adaptation Mechanisms - **Adaptive Current (`w`)**: Influenced by the parameters `a` and `tauw`, it reflects the slow recovery of the neuron back to resting state, capturing spike-frequency adaptation where successive action potentials become less probable over time with constant input. ### Noise and Fluctuations - **Stochasticity (`temp`)**: Gaussian noise is added to simulate the random fluctuations generally present in ion channel activity and neurotransmitter release, mimicking real neuronal environments filled with inherent variability. ### Overall Biological Objective The primary biological objective of this code is to understand how neurons integrate external input to produce output (action potentials), taking into account key physiological processes such as synaptic kinetics, ion conductance, adaptation, and noise. By doing so, it seeks to replicate real neuronal behavior and predict how neurons might respond to varying synaptic inputs, potentially aiding in understanding neural information processing in the brain.