The code represents a computational model inspired by work from Kropff and Treves in 2008, which attempts to elucidate the developmental process of grid cell formation in the mammalian brain. Grid cells, primarily found in the medial entorhinal cortex (mEC) of the brain, are crucial for spatial navigation, mapping environments, and forming a metric system that helps track an animal’s position in space. This model provides insights into how grid cells might develop their characteristic hexagonal firing patterns, leveraging input from place cells through a learning process. ### Biological Basis of the Model #### Grid Cells - **Hexagonal Firing Patterns:** Grid cells exhibit periodic firing at vertexes of a tessellating hexagonal grid when the animal navigates an open environment. This spatial pattern helps in mapping relative positions consistently. #### Place Cells - **Input to Grid Cells:** Place cells, located in the hippocampus, become active when an animal visits specific locations in an environment, known as place fields. This model assumes grid cells receive input from place cells, whose fields are arranged in a grid-like pattern. #### Learning and Adaptation - **Initial Random Firing:** The model starts with grid cells developing fields at random locations based on initially random synaptic connections from place cells. - **Field Drift and Stabilization:** Over time, grid cells adjust these fields through a process called drift, moving towards stable hexagonal formations. This drift occurs via an adaptation mechanism where firing lessens as a grid cell becomes active, leading to a decrease in the influence from the place cells. #### Plasticity and Synaptic Weight Adjustment - **Synaptic Plasticity:** The learning mechanism involves adjusting the synaptic weights between place cells and grid cells, guided by synaptic plasticity rules. This allows the system to stabilize and maintain the fields once the adaptation effect decreases. - **Adaptation Current:** When a grid cell fires, an adaptation current reduces its firing rate, impacting the strengthening or weakening of synaptic inputs according to the firing dynamics. #### Movement and External Influences - **Environment Exploration:** The model simulates an animal randomly exploring a 20x20 unit square environment. This mimics natural behavior necessary for the grid cell network to capture and learn spatial patterns. #### Computational Aspects related to Biology - **Dynamic Normalization:** The code adjusts certain parameters to aim for a target mean activity and sparseness, reflecting homeostatic mechanisms in biological systems to maintain stability. - **Random Walk Simulation:** The code uses a random walk to simulate environmental exploration, capturing the intrinsic stochastic nature of animal movement in an unfamiliar environment. Overall, this computational approach uses known principles of synaptic plasticity, biological adaptation, and neuronal firing dynamics to model the development of grid cell spatial firing patterns. The model focuses on bridging cellular-level plasticity mechanisms with broader network-level spatial mapping functions.