Cortical folding scales universally with surface area and thickness, not number of neurons

The best way to fold a mammalian brain As mammalian brains grew larger through evolution, the organization and folding of brains changed too. In a series of statistical analyses comparing a large number of mammalian species, Mota and Herculano-Houzel found that brain folding is not simply a phylogenetic consequence of brain mass increase (see the Perspective by Striedter and Srinivasan). The exposed surface of the cortex scales across all mammals and across individuals as a single power law of the product of total cortical surface and the square root of cortical thickness. Science, this issue p. 74; see also p. 31 A general physical rule governs brain folding across species and even individuals. [Also see Perspective by Striedter and Srinivasan] Larger brains tend to have more folded cortices, but what makes the cortex fold has remained unknown. We show that the degree of cortical folding scales uniformly across lissencephalic and gyrencephalic species, across individuals, and within individual cortices as a function of the product of cortical surface area and the square root of cortical thickness. This relation is derived from the minimization of the effective free energy associated with cortical shape according to a simple physical model, based on known mechanisms of axonal elongation. This model also explains the scaling of the folding index of crumpled paper balls. We discuss the implications of this finding for the evolutionary and developmental origin of folding, including the newfound continuum between lissencephaly and gyrencephaly, and for pathologies such as human lissencephaly.