Wrinkled brain mimics crumpled paper

Power law relationship for folding applies across species

PAPER TOSS  When sheets of paper were scrunched, variations in surface area (larger on the left) led to balls with different levels of crumpled folding. Surface area is one part of a new equation that may help describe how brains fold.

Suzana and Luiza Herculano-Houzel 

Cramming a big brain into a skull may be as easy as just wadding it up. The same physical rules that dictate how a paper ball crumples also describe how brains get their wrinkles, scientists suggest July 3 in Science.

That insight, arrived at in part by balling up sheets of standard-sized A4 office paper, offers a simple explanation for the ridges and valleys that give rise to thoughts, memories and emotions. The results also explain the shapes of a multitude of mammal brains ranging from the ultrawrinkled dolphin brain to the smooth brain of manatees, says study coauthor Suzana Herculano-Houzel. “There are no outliers.”

Other researchers argue that the simple physical explanation ignores clear evidence of other factors involved, such as nerve cell production and the behavior of genes. How the brain folds is still very much up for debate, they say. “It could very well be that aspects of the paper are true,” says cell biologist and neurobiologist Wieland Huttner of the Max Planck Institute of Molecular Cell Biology and Genetics in Dresden, Germany. “But I think it is overstated to say that this is the only explanation and that it is universal.”

Herculano-Houzel and Bruno Mota of Universidade Federal do Rio de Janeiro examined brains from 74 species. By studying properties including thickness and surface area of the brains’ cortices, the outermost layers, the researchers uncovered a simple mathematical relationship known as a power law. Brain wrinkledness depended on the relationship between two physical properties: Surface area and the thickness of the cortex. Brains fold more when the cortex is thin and has a large surface area. The researchers measured brain folding for each species by finding how much of the cortex was buried underneath its surface. The equation linking surface area and thickness predicted folding amounts, the team found. “We were both bug-eyed, just looking at that and thinking, ‘Whoa, this actually worked!’” Herculano-Houzel says.

By crumpling up papers of different dimensions and stacked to create different thicknesses, the researchers found that the same mathematical relationship also describes how a paper ball crumples.

The new description of brain folding is unexpected in part because of what it leaves out. The number of nerve cells has nothing to do with brain folding, an idea that other research had suggested. “Numbers of neurons do not matter,” Herculano-Houzel says.

Not everyone is convinced. “I absolutely disagree with that,” Huttner says. Other studies have clearly shown that the birth of new neurons can have a profound effect on brain folding, he says. Many of those studies focus on how the brain folds as it grows, and not the final folded product as in the new study.

It’s possible that the mathematical relationship described in the paper may contribute to folding, Huttner says. But it probably isn’t alone.

“The model that they proposed is intriguing and debatable,” says neuroscientist Tao Sun of Weill Cornell Medical College in New York City. “While I like the model myself, one needs to be cautious as well.” The results are based on existing data, not experiments, he says. Insight will come from testing how the size and thickness of the cortex as well as numbers of neurons influence folding, he says. 

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