2015
DOI: 10.1126/science.aaa9101
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Cortical folding scales universally with surface area and thickness, not number of neurons

Abstract: 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 k… Show more

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Cited by 253 publications
(264 citation statements)
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“…When one does, it is indicative of a constraint at the physical (mechanical properties of tissue), biochemical (binding site constancy), or biological level (physiology). The degree of folding of any cerebral cortex, for instance, is strictly tied to the combination of cortical surface area and thickness-even though these are free to vary-according to physical minimization of free energy as the tissue forms under uneven pressures [102]. The genetic code is possibly fixed by the matching of the spatial conformation of dinucleotides and amino acid precursors [103].…”
Section: Why Should Glial Cell Size Be Constrained?mentioning
confidence: 99%
“…When one does, it is indicative of a constraint at the physical (mechanical properties of tissue), biochemical (binding site constancy), or biological level (physiology). The degree of folding of any cerebral cortex, for instance, is strictly tied to the combination of cortical surface area and thickness-even though these are free to vary-according to physical minimization of free energy as the tissue forms under uneven pressures [102]. The genetic code is possibly fixed by the matching of the spatial conformation of dinucleotides and amino acid precursors [103].…”
Section: Why Should Glial Cell Size Be Constrained?mentioning
confidence: 99%
“…Most such studies have focused on human cortices, using detailed MRI data to postulate folding as driven by the [possibly differential (5) or multilayered (6)] expansion of the cortical surface. In contrast, we have recently proposed a model (7), in which folding is a consequence of the dynamics of surface expansion and self-avoidance coupled with a negative tension term. This model was partly inspired by the axonal tension hypothesis by Van Essen (8) and the statistical physics of membranes (9).…”
mentioning
confidence: 99%
“…7). In geometric terms, the variables T, A t , and A e associated with each cortex define a point in the log T × log A t × log A e space, and Eq.…”
mentioning
confidence: 99%
“…Although there have been studies suggesting that the brain complexity keeps increasing until teenage 32 and certain brain regions such as entorhinal cortex may have increased thickness until the age of 30 33 , our study suggests that the GI starts to decrease already around the age of four. The cellular mechanisms underlying the gyrification are still unclear 34 , although theories have been raised based on mechanical tension 35 , stress-dependent folding and differential growth 36,37 , regulated radial and tangential expansion 38 , axonal pushing 39 and minimization of effective free energy associated with cortical shape 3,30 . Most of these theories focused on the brain development during the young age, and the trajectory observed in the present study may be associated with different mechanisms.…”
Section: Discussionmentioning
confidence: 99%