The provided code models the interaction between hippocampal place cells (excitatory neurons) and local inhibitory interneurons to simulate a neurophysiological phenomenon known as "phase precession." This phenomenon involves the systematic shift of a neuron's firing phase in relation to the local theta rhythm as an animal traverses a spatial location. ### Biological Concepts Modeled 1. **Place Cells and Inhibitory Interneurons:** - **Place Cells:** These are hippocampal pyramidal neurons that become active when an animal is in or is thinking about a specific location in its environment. Place cells form a cognitive map of the space. - **Interneurons:** These are local inhibitory neurons that modulate the activity of place cells through synaptic inhibition. 2. **Theta Rhythm:** - The theta rhythm is a regular oscillation in the range of 4-10 Hz observed in the local field potential of the hippocampus. It is associated with activities such as spatial navigation and memory encoding. - The code models theta rhythm changes through acceleration, impacting the excitatory neurons’ phase precession. 3. **Phase Precession:** - Phase precession refers to the correlation found in place cells, where their spikes occur at progressively earlier phases of the theta cycle as an animal moves through the cell's place field. - The code calculates phases based on theta periods, adjusting phases so that first spikes align with a complete theta cycle (2π). 4. **Synaptic Currents and Membrane Potentials:** - The code calculates synaptic currents (excitatory and inhibitory) impacting the membrane potential of both inhibitory and excitatory neurons. Synaptic conductances are modified based on exponential decay formulations typical of biophysical models of synaptic transmission. - Parameters such as `V_i` and `V_e` represent the membrane potentials of inhibitory and excitatory neurons, influenced by synaptic inputs (`Isyn_ti`, `Isyn_te`, `Isyn_ie`). 5. **Neuronal Firing Thresholds and Resets:** - Neurons fire action potentials when their membrane potentials (`V_i` or `V_e`) exceed a threshold, prompting a reset to a baseline potential. - `FIRINGS_OUT_i` and `FIRINGS_OUT_e` store the firing times of inhibitory and excitatory neurons, respectively, indicating the temporal pattern of neuronal spiking. 6. **Interspike Intervals (ISIs):** - The code computes interspike intervals for both neuron types, highlighting the temporal dynamics of neuronal spiking. ### Biophysical Model Components - **Synaptic Conductance Parameters:** - Parameters such as `g_ti`, `g_te`, and `g_ie` denote synaptic conductances for different neurotransmitter receptor types, reflecting synaptic strength. - **Membrane Time Constants (`Taum_i`, `Taum_e`):** - These derive from the passive properties of neuronal membranes, impacting the integration of synaptic inputs over time. - **Input Parameters:** - Variables such as `fmin`, `fmax`, and parameters related to excitation and inhibition strengths are modeled to simulate biological conditions effectively. ### Plotting and Output The graphical outputs represent various phenomena: - **Phase Precession Curves:** Graphs show how place cells' spike timing advances with respect to ongoing theta cycles. - **Intensity Functions:** These illustrate variations in input stimulus or signal strength over time. - **Membrane Potentials and Currents:** These plots depict voltage and current changes during simulations, critical for understanding the modeled neuronal dynamics. Overall, the code encapsulates the intricate dynamics between place cells and local interneurons within the hippocampus, focusing on how acceleration of the local theta rhythm can facilitate phase precession. This closely mimics physiological processes involved in spatial navigation and memory encoding.