The provided code is a computational implementation of a spiking neural network model based on the work by Nicolas Brunel (Brunel, 2000). The model is designed to simulate the dynamics of a large network of neurons, specifically focusing on the balance between excitatory and inhibitory synaptic inputs and their role in neuronal firing rates and network activity. Below is a description of the biological basis of the model being represented by the code: ### Biological Basis 1. **Neuron Types:** - The code simulates two primary types of neurons: excitatory and inhibitory. - **Excitatory Neurons (N_E=8000):** These neurons increase the likelihood of firing in their target neurons via excitatory postsynaptic potentials (EPSPs). This is reflected in the positive synaptic weight parameter (`J_E=0.1`). - **Inhibitory Neurons (N_I=2000):** These neurons decrease the likelihood of firing in their target neurons via inhibitory postsynaptic potentials (IPSPs). In the model, the strength of the inhibitory input is five times that of the excitatory input (`g = 5.0`), represented by the synaptic weight (`J_I = -g*J_E`). 2. **Membrane and Synaptic Properties:** - **Membrane Time Constant (`tau_m=20.0 ms`):** This parameter represents how quickly the membrane potential decays back to rest after being depolarized. It is key for determining the temporal integration of synaptic inputs. - **Spike Generation:** A neuron generates a spike when its membrane potential exceeds a threshold (`V_th=20.0 mV`), and after a spike, the membrane potential is reset to `10.0 mV`. 3. **Synaptic Dynamics:** - **Synaptic Delay (`delay=1.5 ms`):** This mimics the time it takes for a synaptic input to affect the postsynaptic neuron, crucial for temporal processing in neural networks. - **Connectivity:** Each neuron receives excitatory and inhibitory inputs reflecting biological connectivity rates: these are 800 and 200 on average for each neuron, respectively. 4. **External Inputs:** - **Poisson Noise (`poisson_generator`):** Represents the background synaptic input that neurons receive, which is crucial for maintaining ongoing activity similar to the stochastic nature of biological synaptic input. - **Input Rate Control (`eta=2.0`):** Controls the rate of external inputs relative to a threshold firing rate, influencing the overall excitatory drive to the network. 5. **Population Dynamics:** - **Balanced Network:** The model focuses on the concept of balanced excitatory and inhibitory input, which is essential for maintaining stable activity and is a hallmark of cortical networks. - **Global Activity Patterns:** The code measures the firing rates of excitatory and inhibitory populations, capturing essential aspects of how these populations interact and stabilize within a neural circuit. ### Conclusion This model encapsulates fundamental features of cortical microcircuits by balancing excitatory and inhibitory dynamics, thereby providing insights into how networks of spiking neurons can generate and maintain activity patterns observed in the brain. Through parameters such as synaptic weights, delays, and external noise, the model captures key biological characteristics critical for understanding neural computation.