The provided code is a computational model designed to simulate a neuronal network based on the principles laid out in the seminal paper by Brunel (2000) in the Journal of Computational Neuroscience. This model represents a simplified version of a random, balanced network of spiking neurons, with specific attention to excitatory and inhibitory interactions and synaptic plasticity mechanisms. Here’s a breakdown of the biological basis of the different aspects of the code: ### Neuronal Dynamics - **Neuronal Types:** The model includes two primary types of neurons: excitatory (N_E) and inhibitory (N_I). This dichotomy reflects the fundamental classification of neurons based on their effects on other neurons in the brain. - **Neuron Model:** The neurons are modeled using the `iaf_psc_delta`, an integrate-and-fire neuron model with delta-shaped post-synaptic currents, commonly used to simulate the membrane potential dynamics of real neurons. Key parameters like the membrane time constant (`tau_m`), spike threshold (`V_th`), and reset potential contribute to the firing behavior. ### Synaptic Connections and Plasticity - **Excitatory and Inhibitory Synapses:** The code defines a ratio (`g`) to model the relative strength of inhibitory post-synaptic potentials (IPSPs) to excitatory post-synaptic potentials (EPSPs). This reflects the balance between excitation and inhibition, crucial for maintaining stable network activity and preventing runaway excitation. - **STDP (Spike-Timing-Dependent Plasticity):** Synaptic plasticity is introduced through a Hebbian learning rule (`stdp_synapse_hom`). The parameter `STDP_alpha` dictates the relative strength of synaptic depression versus potentiation, based on the timing of spikes between pre- and post-synaptic neurons. This mechanism is key for learning and memory in biological neuronal networks. ### Network and Simulation Setup - **Network Architecture:** The model creates a random network where each neuron connects to a subset of other neurons, mimicking the sparse connectivity observed in cortical networks. The excitatory population is connected with plastic synapses, while static synapses are used for inhibitory connections and external input. - **External Drive:** A Poisson generator models external random input, representing noisy background activity from other brain regions. ### Measurements and Observations - **Membrane Potential and Synaptic Weights:** Initial conditions for membrane potentials are randomized to reflect physiological diversity. The initial distribution of synaptic weights among excitatory-excitatory synapses is also explored, showing how variability impacts activity patterns. - **Spike Detection and Firing Rates:** The code measures firing rates for excitatory and inhibitory neurons, providing insight into the network’s dynamic behavior. This metric parallels how firing rates encode information in real neural tissue. ### Visualization and Output - **Histograms and Raster Plots:** Visualization tools, like histograms and raster plots, help display distributions of membrane potentials and synaptic weights, as well as firing patterns over time. This visual representation is crucial for understanding the emergent properties of the modeled network's activity. Overall, the code presents a model that captures key neuronal dynamics and plasticity mechanisms to study network behavior and the balance between excitatory and inhibitory interactions, reflecting the fundamental properties of computational neuroscience.