The provided code is a simulation of a network model of spiking neurons inspired by the work of Nicolas Brunel, designed to study asynchronous irregular activity in large-scale networks of excitatory and inhibitory neurons. The model aims to replicate certain features observed in cortical networks, specifically the high variability of neuronal firing and the approximate balance between excitatory and inhibitory inputs. ### Key Biological Features Modeled #### Neuron Model - **Integrate-and-Fire Model**: The code uses a leaky integrate-and-fire (LIF) neuron model (`iaf_psc_alpha` in NEST), which is a simplification of neuronal behavior focusing on the membrane potential dynamics. The neurons integrate incoming post-synaptic potentials until a threshold is reached, at which point they produce a spike and reset their potential. This model captures essential features of real neuron electrical activity without the complexity of detailed ion channel dynamics. - **Alpha-Function Synapses**: Synaptic currents are modeled with an alpha function (`psc_alpha`), which shapes post-synaptic potentials (PSPs) to rise and decay exponentially, mimicking the synaptic influence on neurons in terms of temporal dynamics. #### Network Structure - **Excitatory and Inhibitory Neurons**: The network consists of excitatory and inhibitory neurons, consistent with the division found in biological neural circuits. The parameters (`NE` and `NI`) define the relative proportions found in the cortex, with more excitatory than inhibitory neurons. - **Random Connectivity**: The neurons are connected probabilistically, representing the sparse and random character of real cortical connectivity. This randomness is implemented using numpy to draw connections between neurons. #### Synaptic Dynamics - **Weight Normalization**: The synaptic weights (`J_ex` and `J_in`) are adjusted to ensure that the post-synaptic potentials produce a specified change in membrane potential, mirroring synaptic strength and efficacy. The excitatory and inhibitory synaptic weights differ in sign and magnitude to reflect the opposing roles these inputs play in neural activity. #### Activity Dynamics - **Poisson Input**: Neurons receive external input modeled as a Poisson process. This stochastic input simulates the background synaptic noise typical in cortical areas due to continuous signaling from other brain regions. - **Balancing Excitation and Inhibition**: The model exhibits a balance between excitatory and inhibitory inputs (`g` and `eta` parameters), a critical feature for maintaining stability and irregular activity characteristic of cortical networks. ### Biological Phenomena Studied This model investigates asynchronous irregular activity, which is a fundamental property of in-vivo cortical networks. The high variability in neuronal firing is believed to result from a delicate balance between excitation and inhibition, a critical aspect captured in the model's design. The code evaluates network dynamics by measuring firing rates, synaptic connectivity, and simulating neuronal responses over time, thus providing insights into how biological neural networks might function under similar conditions. Overall, the code provides a framework to explore the dynamics of large networks of simple model neurons, capturing key features of cortical circuitry, particularly the balance of excitation and inhibition and the resultant irregular spiking activity.