Connectivity-driven white matter scaling and folding in primate cerebral cortex

Larger brains have an increasingly folded cerebral cortex whose white matter scales up faster than the gray matter. Here we analyze the cellular composition of the subcortical white matter in 11 primate species, including humans, and one Scandentia, and show that the mass of the white matter scales linearly across species with its number of nonneuronal cells, which is expected to be proportional to the total length of myelinated axons in the white matter. This result implies that the average axonal cross-section area in the white matter, a, does not scale significantly with the number of neurons in the gray matter, N. The surface area of the white matter increases with N(0.87), not N(1.0). Because this surface can be defined as the product of N, a, and the fraction n of cortical neurons connected through the white matter, we deduce that connectivity decreases in larger cerebral cortices as a slowly diminishing fraction of neurons, which varies with N(-0.16), sends myelinated axons into the white matter. Decreased connectivity is compatible with previous suggestions that neurons in the cerebral cortex are connected as a small-world network and should slow down the increase in global conduction delay in cortices with larger numbers of neurons. Further, a simple model shows that connectivity and cortical folding are directly related across species. We offer a white matter-based mechanism to account for increased cortical folding across species, which we propose to be driven by connectivity-related tension in the white matter, pulling down on the gray matter.