eMB: Axiomatic Framework Underpinning the Emergence of Geometric Patterns in the Coding of Space by Grid Cells

Grid cells, a type of nerve cell in the brain, are important for spatial navigation and create a grid-like map of the environment by being active at specific locations in space that fall on a hexagonal lattice. Furthermore, grid cells are organized in a modular way, so that the grids of the next module span a larger area than the grids of the previous module.

Intriguingly, the sizes of grids increase from module to module by the square root of 2. Yet, no mathematical framework exists to date that explains the emergence of geometric patterns in the activity of grid cells from a set of simple rules governing brain activity, applied to the special case of navigating physical and abstract space. The project will identify the set of rules from which grid cells emerge during navigation, how the activity of grid cells on the single cell level gives rise to grid-like activity on the population level, how the identified set of rules predict distortions of grids in multi-dimensional space, and how the rules can be implemented in a biologically plausible simulation.

The expected outcomes will help develop computationally efficient and interpretable algorithms for use in artificial intelligence systems. The engagement of local high school students and undergraduate students in the project's activities will foster awareness of and interest in STEM fields. Recruitment efforts by the investigators will focus on female students and first-generation students that constitute almost 40% of the student population at George Mason University.

Despite research on the mechanisms underlying the firing patterns of grid cells in the medial entorhinal cortex, no mathematical framework or theory exists to date that sufficiently explains the experimentally observed geometric patterns in grid cell activity and the specific ways these patterns are distorted in asymmetric and multidimensional environments, such as those found in nature. As a result, our understanding of grid cell firing patterns and their computational function in the context of spatial navigation and episodic memory remains superficial.

The project will be significant because it will develop an axiomatic framework for sequence coding of trajectories in multidimensional space that will explain geometric patterns in the firing patterns of grid cells as emergent properties. Moreover, the same axiomatic framework will explain the emergence of grid-like activity in humans. This is a significant contribution because it is not known to date how grid-like activity on the population level emerges from the activity of grid cells on the single cell level.

The developed framework will thereby bridge a gap between animal experiments and human relevance. Furthermore, the framework will make it possible to develop algorithmic implementations of a brain-inspired sequence code of trajectories for artificial agents. Finally, a unifying framework explaining geometric organization in the grid cell system and its implementation in biologically plausible spiking neural networks will advance our understanding of how the mammalian brain performs navigational computations and higher cognitive functions such as episodic memory.

This project is jointly funded by the Mathematical Biology Program in the Division of Mathematical Sciences and the Neural Systems Cluster in the Division of Integrative Organismal Systems in the Directorate for Biological Sciences.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.