The provided code is part of a computational model aiming to simulate the dynamics of neuronal networks, likely focusing on networks of fast-spiking inhibitory neurons (FSIN), as suggested by the module name `FSIN` used in the code. Here's a breakdown of the biological basis underlying this model: ### Neuronal Networks and Dynamics 1. **Neuron Types**: - The code appears to simulate two configurations of neuronal networks: homogeneous and heterogeneous. Homogeneous networks likely consist of neurons with similar intrinsic properties, while heterogeneous networks introduce variability in either neuron properties or synaptic connections. 2. **Synaptic Properties**: - The synaptic reversal potentials (Esyn) are set to two different values, `-75 mV` and `-55 mV`. These are critical parameters that affect how excitatory or inhibitory inputs influence the postsynaptic neuron. Typically, Esyn near -75 mV suggests inhibitory GABAergic transmission, while less negative potentials might imply a mix or varied synaptic roles. 3. **Theta Rhythms**: - The model simulates theta frequency, which is a prominent oscillatory activity in the brain typically occurring at 4-12 Hz. The specific setting here is around 8 Hz. Theta rhythms are crucial for memory processing and navigation, and studying their modulation can be critical for understanding cognitive and emotional processing. 4. **Network Heterogeneity**: - Various types of heterogeneity are considered: - **Intrinsic Heterogeneity**: Variability in the intrinsic properties of neurons, possibly including differences in ion channel densities, membrane properties, or firing thresholds. - **Synaptic Heterogeneity**: Variability in the strength or configuration of synaptic connections, which can influence the overall dynamics and plasticity of the network. 5. **Simulation Techniques**: - The code uses different numerical methods (`euler`, `rk4`, etc.) for differential equation integration, which are crucial for capturing the dynamics of action potentials and oscillatory behavior in biophysical models of neurons. 6. **Parameters**: - The gating variables and conductances (e.g., `gmsSim` and `gsin`) control the dynamics of synaptic input and intrinsic membrane properties. - `kneu` and `dt` are important for setting the spatial and temporal resolution of the simulations, allowing detailed capturing of fast-paced neuronal dynamics. 7. **Temporal Dynamics**: - The use of sinusoidal inputs replicates oscillatory drive which might mimic input from other brain regions or network subgroups that are coherent with theta wave oscillations. This allows investigation of how the network entrains to or modulates these rhythms. The model essentially explores how different levels of neuronal and synaptic heterogeneity influence network dynamics, particularly in terms of spike timing and network rhythms, key factors in understanding neuronal computation and information processing in the brain.