The code provided models a sensory circuit as a spiking neural network, capturing key aspects of neural activity and population dynamics observed in biological systems. This model specifically represents interactions between excitatory and inhibitory neurons, inspired by realistic cortical structures found in the brain. ### Key Biological Concepts 1. **Populations of Neurons:** - **Excitatory Neurons (E):** These neurons increase the likelihood that the target neuron will produce an action potential (spike). In the model, there are 1600 excitatory neurons, divided into two populations (E1 and E2), each comprising 800 neurons. This division allows simulation of local and cross-population dynamics, reflecting the organization of neurons in cortical columns. - **Inhibitory Neurons (I):** In contrast to excitatory neurons, inhibitory neurons reduce the likelihood of action potentials in target neurons. The model includes 400 inhibitory neurons influencing excitatory populations, capturing the balance of excitation and inhibition vital for cortical function. - **External Population (X):** Represents external input to the sensory circuit, modeled as a Poisson process. This reflects constant external sensory input into cortical areas. 2. **Synaptic Dynamics:** - **Connection Strength and Probability:** The code incorporates both AMPA and GABA synaptic dynamics, linking neurons within and between populations with specific probabilities and synaptic weights. These synapses allow for both excitation (AMPA-type) and inhibition (GABA-type) between neurons, crucial for simulating cortical microcircuits. - **Transmission Delays:** Introduced into the connections, these emulate the time delays in signal transmission across synapses due to axonal and synaptic conductance times. 3. **Neuronal Properties:** - **Membrane Potential Dynamics:** Modeled using differential equations that govern the change in membrane potential due to synaptic inputs and intrinsic properties like leak conductance. The excitatory and inhibitory neurons have distinct capacitance and leak conductances, indicative of differences seen biologically in cortical neurons. - **Refractory Periods and Thresholds:** These parameters model the refractory period and spiking threshold of neurons, essential for realistic neuronal firing behavior post-action potential. 4. **External Inputs and Gating Variables:** - The circuit receives external inputs from a Poisson generator, mimicking stochastic sensory input to the neural populations, a common approach in modeling the bombardment of sensory inputs to cortical neurons. - **Synapse Kinetics and Gating Variables (`xe`, `xi`):** These represent excitatory and inhibitory conductance changes over time, capturing fast synaptic dynamics essential for transient information processing in the brain. ### Biological Implications The simulated sensory circuit is designed to reflect the structured connectivity and dynamics of cortical sensory processing areas. By including both excitatory and inhibitory populations, the model demonstrates the balance and interplay necessary for network stability and function, akin to real cortical circuits involved in sensory perception. Additionally, the model can facilitate the study of phenomena such as oscillations, plasticity, and collective neural dynamics, offering insights into how sensory information is processed at the network level in biological systems.