The code provided models a simplified neural network in computational neuroscience, focusing on the interplay between excitatory and inhibitory neurons in a network. This kind of model aims to simulate the dynamics and connectivity patterns observed in biological neural circuits in the brain. Below are the biological concepts that the code captures and how they are represented: ### Neuron Types - **Excitatory Neurons:** These neurons increase the likelihood of the post-synaptic neuron firing an action potential. In the model, they have specific parameters and connections, such as `TAU_EX` for their time constant and `THETA_EX` for their firing threshold. - **Inhibitory Neurons:** In contrast, inhibitory neurons decrease the likelihood of action potential firing in post-synaptic neurons. They are modeled with their own time constant (`TAU_INH`) and firing threshold (`THETA_INH`). ### Synaptic Connections - **Excitatory to Excitatory (`w_exex`):** Although the specific connectivity and weight values are read from an input file (`w.in`), this connection type represents the direct transmission of excitatory signals between neurons. - **Inhibitory to Excitatory (`w_exinh`):** This connection typically represents feedback inhibition in real neural circuits, ensuring excitatory activity does not spiral out of control. The code initializes these connections mostly as self-inhibitory loops (`w_exinh[id(i,i)] = C_EXINH`). - **Excitatory to Inhibitory (`w_inhex`):** These connections in the model facilitate the modulation of inhibitory neurons by excitatory neuron activity. They are set with random sparse connections in the model. - **Inhibitory to Inhibitory (`w_inhinh`):** This models the direct inhibitory feedback within the inhibitory population, affecting overall network stability. ### Neuron Dynamics - **Integration and Firing:** The dynamics of each neuron are modeled using a simple differential equation (`dudt`) which approximates how membrane potentials change over time due to synaptic input (both excitatory and inhibitory). - **Firing Behavior:** Neurons "fire" or output an activity based on whether their potential exceeds a threshold value (`THETA_EX` or `THETA_INH`). This binary event (spike or no spike) connects directly back to the biological all-or-nothing principle observed in real neurons. ### Noise and Input - **Random Noise (`ETA`):** The model includes a stochastic component to simulate the inherent noise in real neural communication and variability in synaptic strength. - **Input Signals (`I_CS`):** These represent external stimuli applied to a subset of neurons (`N_CS`), simulating input from external sources as occurs in sensory or task-driven neural circuits. ### Plasticity - **Learning and Adaptation:** The model implements a simple form of synaptic plasticity in the update of excitatory-excitatory connections (`update_connections`). This reflects Hebbian learning principles, where synaptic weights are updated based on the activity correlation between neurons over time, modulated by `ALPHA` (learning rate). ### Summary This model represents a simplified but biologically inspired system of excitatory and inhibitory interactions critical for understanding fundamental cortical processes. It abstracts the complexity of real neural systems into manageable computational rules to investigate the emergent behaviors of neural networks, such as oscillations, synchronization, and spiking patterns, which are foundational to brain function.