The provided code models the neural basis for spatial navigation in the mammalian brain, focusing specifically on the role of theta oscillations and grid cells in the entorhinal cortex. Here's an explanation of the biological concepts represented in the code: ### Theta Rhythms and Ring Oscillators - **Theta Oscillations:** These are low-frequency brain waves, typically in the 4-10 Hz range, that are crucial for navigation and memory. The code uses a **Central Pattern Generator (CPG)** framework to simulate theta oscillations. Each "ring oscillator" in the code represents this generator, modeling a cyclic activity pattern of neurons. - **VCO (Velocity-Controlled Oscillators):** The code represents cells in a ring, each assigned a phase using the `phz` matrix. Each position in the ring is a potential input to a target neuron, mimicking inputs from specialized neurons affected by speed and direction, correlating to `theta cells`. ### Grid Cells and Spatial Encoding - **Grid Cells:** In the rodent's medial entorhinal cortex, grid cells form a hexagonal spatial pattern when an animal navigates. Cells fire in a periodic pattern across the environment. This code assigns grid cell properties by modulating the input to these cells through the `phz` array where specific grid cells receive input from theta cells at various positions. - **Spatial Modules:** The `phz` matrix configurations in different sections suggest different spatial patterns, like large-spacing and small-spacing grid cells reflecting different physical environments or scales within an environment. ### Computational Parameters and Biological Implications - **`cells_per_ring` and `cell_phases`:** These determine the number of neurons within each ring and their respective phases, simulating how neural populations synchronize and diverse phases to encode spatial positions. - **`phz` Matrix:** The matrix entries that are non-NaN dictate which specific phase-contributing neurons (theta cells) provide input to the grid cells, akin to connecting distinct neural properties in the spatial navigation network. - **Gain Modulation:** The parameter `q` acts as a threshold for neuronal spiking, akin to how biological neurons have firing thresholds dependent on input strength. - **Afferent Inputs:** The weight calculations, set to `1` when a phase is assigned, model the uniform contribution each input neuron imparts toward the spatial map representation by grid cells. In real biological systems, such input weighting could vary, impacting spatial resolutions. ### Output Visuals - **Spatial Firing Patterns:** The figure generation part of the code models how spatial representations (e.g., grid patterns) might appear for grid cells. The figures display potential grid cell activity maps that emerge from the combined oscillatory inputs, mirroring real spatial firing patterns. Overall, the code explores the interplay of synaptic inputs, theta oscillations, and spatial modulation to simulate entorhinal cortex dynamics, particularly how grid cells might encode environmental geometry through varying oscillatory inputs. This understanding assists in deciphering cognitive maps involved in navigation and memory.