A Model of Brain Folding Based on Strong Local and Weak Long-Range Connectivity Requirements.

Throughout the animal kingdom, the structure of the central nervous system varies widely from distributed ganglia in worms to compact brains with varying degrees of folding in mammals. The differences in structure may indicate a fundamentally different circuit organization. However, the folded brain most likely is a direct result of mechanical forces when considering that a larger surface area of cortex packs into the restricted volume provided by the skull. Here, we introduce a computational model that instead of modeling mechanical forces relies on dimension reduction methods to place neurons according to specific connectivity requirements. For a simplified connectivity with strong local and weak long-range connections, our model predicts a transition from separate ganglia through smooth brain structures to heavily folded brains as the number of cortical columns increases. The model reproduces experimentally determined relationships between metrics of cortical folding and its pathological phenotypes in lissencephaly, polymicrogyria, microcephaly, autism, and schizophrenia. This suggests that mechanical forces that are known to lead to cortical folding may synergistically contribute to arrangements that reduce wiring. Our model provides a unified conceptual understanding of gyrification linking cellular connectivity and macroscopic structures in large-scale neural network models of the brain.

Universal transition from unstructured to structured neural maps.

Neurons sharing similar features are often selectively connected with a higher probability and should be located in close vicinity to save wiring. Selective connectivity has, therefore, been proposed to be the cause for spatial organization in cortical maps. Interestingly, orientation preference (OP) maps in the visual cortex are found in carnivores, ungulates, and primates but are not found in rodents, indicating fundamental differences in selective connectivity that seem unexpected for closely related species. Here, we investigate this finding by using multidimensional scaling to predict the locations of neurons based on minimizing wiring costs for any given connectivity. Our model shows a transition from an unstructured salt-and-pepper organization to a pinwheel arrangement when increasing the number of neurons, even without changing the selectivity of the connections. Increasing neuronal numbers also leads to the emergence of layers, retinotopy, or ocular dominance columns for the selective connectivity corresponding to each arrangement. We further show that neuron numbers impact overall interconnectivity as the primary reason for the appearance of neural maps, which we link to a known phase transition in an Ising-like model from statistical mechanics. Finally, we curated biological data from the literature to show that neural maps appear as the number of neurons in visual cortex increases over a wide range of mammalian species. Our results provide a simple explanation for the existence of salt-and-pepper arrangements in rodents and pinwheel arrangements in the visual cortex of primates, carnivores, and ungulates without assuming differences in the general visual cortex architecture and connectivity.