The remarkable ability of the cortex to form its complex folds does not depend upon how many neurons it has or the intelligence of its bearer, but instead is governed by the same simple rules that dictate how a piece of paper crumples. A study published July 3 in Science reported that the degree to which the cortex forms its winding gyri and sulci is a function of the cortical surface area and its thickness. Thus, cortical folds are not a specialized trait acquired through evolution, suggest first author Bruno Mota and senior author Suzana Herculano-Houzel of the Federal University of Rio de Janeiro in Brazil. They found that this simple relationship, which also determines the shape of the paper basketballs in your trash can, endured across mammals.

Cortical Folding, on Paper. A series of crumpled paper balls made of stacks of (from right to left) one, two, three, four, six, or eight sheets of A4 paper. Increasing thickness of the paper stacks results in progressively fewer folds. [Courtesy of Suzana and Luiza Herculano-Houzel.]

Researchers have long known that bigger brains tend to have more folds than smaller brains. However, the relationship between brain volume and cortical folding varies across mammalian orders, indicating that folds are governed by other forces as well. Furthermore, little is known about the developmental mechanism that governs the degree of folding.

To clarify the relationships between folding and the brain’s physical attributes, Mota and Herculano-Houzel scoured vast datasets containing information about brains across mammalian orders and clades to see what predicted the folding index, or the ratio of the total cortical surface area (which includes the portions concealed within the folds) to the exposed surface area. This included their own data (which charted numbers of cortical neurons and cortical surface area) as well as several published reports about cortical surface area, thickness, brain volume, and folding index across diverse animal orders. Putting these datasets together, the researchers found that while brain volume correlated with the degree of cortical folding, several species—most notably cetaceans (whales), manatees, and humans—fell far outside of the confidence interval for that relationship.

The same was true for number of neurons. Although all species with less than 30 million cortical neurons were lissencephalic (smooth-brained, without folds), among gyrencephalic species (those with folded cortices) the relationship between neuron number and folding index varied within each animal order. For example, the folding index for a given number of neurons is larger among artriodactyls (even-toed ungulates such as giraffes, sheep, and pigs) than among primate species. Furthermore, the folding index in the elephant cortex is twice that in the human cortex, despite the fact that the elephant cortex houses only a third as many neurons as the human (see Herculano-Houzel et al., 2014). The relationship between total cortical surface area and folding was more consistent across orders, but still varied.

The researchers ultimately discovered that cortical thickness was the missing unifying factor. They found that the degree of folding was a function of the total cortical area multiplied by the square root of cortical thickness. Interestingly, this relationship also governs the folds formed when a piece of paper is crumpled: The larger the surface area, the more folds formed; the thicker the paper is, the harder it is to fold. The researchers found that this relationship held up surprisingly well for cortices across all mammalian orders, even among lissencephalic species, which have a folding index of 1 and contain no folds.

While paper mills determine the surface area and thickness of a piece of paper, what dictates these parameters in the cerebral cortex? Researchers have reported that many factors govern cortical surface area, including how far neural progenitors spread laterally during development (see Lui et al., 2011). Thickness is another matter, driven by how many neurons differentiate from each progenitor cell, Herculano-Houzel told Alzforum. Surface area and thickness vary across animal species, but the relationship between them and cortical folding endures.

The findings help explain lissencephaly, a disorder in which the brain fails to form folds. Mutations that prevent the migration of neural progenitor cells—which would reduce cortical surface area and potentially increase thickness—cause the disorder (see Hong et al., 2000). The surface area/thickness relationship also explains some striking differences among species. For example, the manatee brain is relatively smooth for its large size. Herculano-Houzel speculated that this could be due to decreased lateral mobility of neural progenitor cells and/or robust production of neurons from a given progenitor cell.

Lastly, while pieces of paper crumple into random shapes, brains form a consistent pattern of folds within each species. Where does this specificity come from? According to Herculano-Houzel, white-matter fibers, which form prior to gray-matter folds during development, dictate where the folds take place. White-matter tracts are conserved among different orders of mammals, so that rodents, for example, have similar cortical folding pattern, as do primates.—Jessica Shugart


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Paper Citations

  1. . The elephant brain in numbers. Front Neuroanat. 2014;8:46. Epub 2014 Jun 12 PubMed.
  2. . Development and evolution of the human neocortex. Cell. 2011 Jul 8;146(1):18-36. PubMed.
  3. . Autosomal recessive lissencephaly with cerebellar hypoplasia is associated with human RELN mutations. Nat Genet. 2000 Sep;26(1):93-6. PubMed.

Further Reading


  1. . The human cerebral cortex is neither one nor many: neuronal distribution reveals two quantitatively different zones in the gray matter, three in the white matter, and explains local variations in cortical folding. Front Neuroanat. 2013;7:28. Epub 2013 Sep 2 PubMed.
  2. . How the cortex gets its folds: an inside-out, connectivity-driven model for the scaling of Mammalian cortical folding. Front Neuroanat. 2012;6:3. Epub 2012 Feb 2 PubMed.

Primary Papers

  1. . BRAIN STRUCTURE. Cortical folding scales universally with surface area and thickness, not number of neurons. Science. 2015 Jul 3;349(6243):74-7. PubMed.