Spontaneous emergence of topologically robust grid cell modules: A multiscale instability theory

Modular structure and function are ubiquitous in biology, from the organization of animal bodies and brains to the scale of ecosystems. However, the mechanisms of modularity emergence remain unclear. Here we introduce the principle of peak selection, a process by which purely local interactions and smooth gradients can result in global modular organization. It can lead to the self-organization of discontinuous module boundaries from a smooth global gradient, unifying the positional hypothesis and the Turing pattern formation hypothesis for morphogenesis. Applied to the brain's grid cell networks, peak selection results in the spontaneous emergence of functionally distinct modules with discretely spaced spatial periods. Applied to ecological systems, a generalization of the process results in discrete systems-level niches. The dynamics exhibits emergent self-scaling to variations in system size and "topological robustness" that renders module emergence and module properties insensitive to most parameters. Further, peak selection confers robustness within modules. It ameliorates the fine-tuning requirement of continuous attractor dynamics even in single grid cell modules. It makes a detail-independent prediction that grid module period ratios should approximate adjacent integer ratios, furnishing the most accurate match to data to date. Additional testable predictions promise to bridge physiology, connectomics, and transcriptomics. In sum, our results indicate that local interactions combined with low-information global gradients can drive robust global module emergence.