The provided code is a simulation of a biophysical model of neural circuitry in the hippocampus, focusing on interactions between distinct neuronal populations and their contributions to specific brain rhythms, namely gamma and theta rhythms. Here's the biological background: ### **Neuronal Populations and Synapses** 1. **Neuronal Types:** - **Pyramidal Cells (E):** These are excitatory neurons, which are typically responsible for long-range connections within the hippocampus and to other brain areas. They primarily use glutamatergic synapses. - **Parvalbumin-Expressing Interneurons (I, PV):** These are fast-spiking inhibitory neurons that use GABA as a neurotransmitter. They are crucial for synchronizing local neural activity and contribute to gamma rhythms. - **Cholecystokinin-Expressing Interneurons (I2, CCK):** These are another type of inhibitory neurons. Unlike PV interneurons, CCK interneurons are involved in different modulatory roles and contribute to theta rhythms. 2. **Synaptic Interactions:** - The `g_ee`, `g_ei`, `g_ie`, `g_ii` variables in the code represent synaptic conductance matrices that model connections among these neurons. These matrices incorporate the coupling probabilities (e.g., `p_ee` for E-to-E coupling) and maximum conductances (e.g., `g_hat_ee`) to simulate how these neurons influence each other through synaptic interactions. ### **Neuronal Dynamics** 1. **Hodgkin-Huxley Framework:** - The model is built on Hodgkin-Huxley-like equations, describing the dynamics of the membrane potential and ionic currents. The code uses parameters like `v_e`, `v_i`, `v_i2` for membrane potentials of the different cell types and includes variables for gating dynamics of ion channels: - **Sodium (Na⁺) Channels:** The gates `m_e`, `m_i`, `m_i2` and related variables (e.g., `h_e`, `h_i`, `h_i2`) represent the activation and inactivation of sodium channels, crucial for action potentials. - **Potassium (K⁺) Channels:** The `n_e`, `n_i`, `n_i2` gates are related to potassium channel activation, which is significant for repolarization of the neuron following an action potential. 2. **Stochastic Inputs:** - The variables `s_stoch_e`, `s_stoch_i`, and `s_stoch_i2` model stochastic (random) synaptic inputs that mimic the unpredictable nature of synaptic bombardment neurons receive in vivo, contributing to variability in neuronal firing. ### **Biological Rhythm Modeling** 1. **Gamma and Theta Rhythms:** - **Gamma Rhythm (30-80 Hz):** Typically arises from the interactions between excitatory pyramidal neurons and fast-spiking inhibitory PV interneurons. This rhythm is crucial for attention, perception, and memory processes. - **Theta Rhythm (4-12 Hz):** Often generated by the activity of excitatory neurons and rhythmically active CCK interneurons. Theta rhythms are linked to navigation, memory encoding, and retrieval processes. ### **Notable Features** - **Spike Detection and Raster Plotting:** - The code includes routines for detecting neuronal spikes, which is integral for analyzing and visualizing network activity patterns, such as the spike raster plot commonly used in electrophysiological studies. Through these mechanisms, the code simulates the complex interplay of excitation and inhibition in hippocampal microcircuits, providing insights into how such networks can give rise to collective neural rhythms. This model is fundamental for understanding how different types of neurons contribute to the emergent properties of brain networks, particularly within the context of the hippocampus.