Why cortex is folded

As we have seen, this results in average propagation times increasing more slowly with the addition of more axons in WM. This leads to the interesting realization that decreasing the fraction of cortical neurons connected through the WM that is, more negative values of c minimizes the upscaling of propagation times in larger cortices. There are two main ways in which our model can be tested: by designing experiments to address the prediction that cortical connectivity through the WM affects the establishment of cortical folds; and by testing the quantitative relationships predicted by the model.

While we have not yet had the opportunity to design experiments specifically to test this model, earlier experiments showing that cortical folding is altered after disrupting cortical connectivity but not after partial removal of the skull during development reviewed in Kaas, do support our proposal that cortical folding is driven by pulling on the inside of the cortex, rather than from the cortex pushing inward.

Testing the numerical relationships predicted by the current model requires quantifying, across different mammalian species, their numbers of neurons in the GM, numbers of other cells in the WM; obtaining surface and volume measurements for the GM and WM; and determining, from the scaling across these parameters, whether the exponents thus calculated match the predictions from the model.

The exponent c can next be calculated simply from the scaling relationship above between A W and N , now that has been determined. If these quantities are equal, then the WM should scale isometrically.

This model has so far been applied to a primate dataset containing 11 species, including humans Herculano-Houzel et al. Experimentally, we find that the average cross-section area remains nearly invariant in primates as a function of N , while it increases sharply with N across rodents.

This is qualitatively very similar to what happens with average neuron size in both orders: It increases significantly with N in rodents, but increases very slowly with N across primate species Herculano-Houzel, , suggesting there is a connection between average neuron size and axon caliber.

As for the fraction of GM neurons projecting axons through the WM, we find that it decreases with N in both orders, but at a rate that is more pronounced in primates than in rodents. As a result, the WM becomes increasingly folded in larger primate brains, but less rapidly in larger rodent brains. Using the experimental method described above to determine the values of the scaling exponents that appear in the model, we obtained, in rodents and in primates, the values listed in Table 1.

Table 1. Experimentally determined exponents for, respectively, the scaling of average axonal length in the WM l , average axonal cross-sectional area in the WM a , fraction of GM neurons connected through the WM n , average GM thickness t , and neuronal density in the GM d as power functions of the number of cortical neurons N. In both orders, l scales sublinearly with N , which is a significant finding given that any increase in average axon length implies an increase in volumetric and propagation time costs.

This is a strong indication that in primates, the increase in distance between interconnected cortical regions is minimized by effective shortening of the axons, as would be expected to happen if they grew under longitudinal tension Van Essen, As a consequence of these exponents, the folding of the WM is predicted to scale as the cortex gains neurons with N 0.

Notice that this prediction apparently contradicts the finding that large rodent cortices, such as those of the agouti and capybara, are indeed folded. We believe, however, that the apparent failure of the model to predict the folding of large rodent cortices is due to the fact that in our sample, three of the five species mouse, rat, and guinea pig are small-brained and practically lissencephalic.

Thus, rodent cortices seem to scale without becoming folded only up to a certain point, beyond which larger cortices do become increasingly folded. This is actually circumstantial evidence in favor of the push—pull model that we propose, in which the WM only begins to fold once the traction that it exerts upon the GM exceeds the resistance of the latter to becoming folded inward.

Although we do not dispose of estimates of the actual number of cortical neurons connected through the WM, it is illuminating to consider the following exercise scenario. In the exercise scenario above, the total number of axons in the WM would increase from about million in the marmoset, to million in the macaque, to 3.

Larger primate cortices, therefore, increase in size proportionally to N 1 neurons in the GM, of which a number proportional to N 0.

It has been proposed that larger cortices scale with a ratio between the volumes of the WM and GM that increases homogeneously across all mammalian species, with V W scaling with V G 1. We find that V W scales with V G 1. Thus, V W appears to scale as not significantly different functions of V G across the two orders. This suggests that average signal propagation time through the WM increases far more steeply with N in rodent brains than in primate brains.

Indeed, a recent study of the corpus callosum in primates suggested that the expected conduction delays between the hemispheres for different cortical areas doubles from macaque to man Caminiti et al. Interestingly, although propagation time could in theory scale similarly across orders which would offer evidence of a common trend toward minimization of propagation time in brain evolution , our initial results suggest that it not only increases in larger primate cortices, but it also increases faster in rodents than in primates.

The faster scaling of WM folding in primate than in rodent brains, which we propose to result from the stronger minimization of axonal lengths under tension in the former, thus bestows upon primate cortices the advantage over rodents of gaining neurons without having signal propagation through the WM slowed down as much.

As described above, the computational capacity of the WM the number of operations involving WM axons that a cortex would be able to perform per unit time is proportional to the number of axons in the WM, and inversely proportional to the average propagation time.

Like for propagation times, we find that the total computational capacity of the cortex through the WM also scales faster in primates than in rodents, although increasing more slowly than the rate at which the cortex gains neurons.

In both orders, thus, the increase in number of cerebral cortical neurons is accompanied by a decrease in the computational efficiency of the WM — a decrease that is faster in rodents than in primates. One influential hypothesis for the formation of cortical folds is the differential growth hypothesis, which considers that the faster growth of the outer cortical layers compared to the inner layers cause the cortical GM to fold Richman et al.

That hypothesis, however, assumes that cortical GM is much stiffer by an unrealistic factor of 10 than the underlying WM. Our model, in contrast, is aligned with the opposite view that cortical folding is driven by tension generated by axonal connectivity in the WM Van Essen, , which posits that differences in cortical growth might be a result, and not the cause of cortical folding Hilgetag and Barbas, Another previous model of cortical folding acknowledged a radial pull on the cortical GM by elastic axonal fibers in the WM Toro and Burnod, That model, however, attributed the source of cortical folding to a growing cortical surface, depending simply on cortical thickness and mechanical properties of the cortical GM.

Although the model showed cortical convolutions to form as a natural consequence of cortical growth, it was largely descriptive, not predictive, since cortical thickness does not appear as an independent parameter; did not take numbers of neurons, of fibers in the WM, nor neuronal size into consideration; nor did it acknowledge that the cerebral cortex may scale as different functions of its number of neurons and connectivity across mammalian groups.

Recently, a study of the distribution of stress in the subcortical WM of the developing ferret brain found that axons are indeed under tension, although the majority of them are located circumferentially in the WM, radially in the subplate, and in the cores of outward folds Xu et al. Evidence that induced, abnormal cortical growth induces convolutions in the normally lissencephalic mouse brain Haydar et al.

However, our model, which attributes no major determinant role to the thickness of the WM, also predicts increased folding as a consequence of a larger number of cortical neurons, depending simply on there being enough internal tension in the WM, even if cortical connectivity remains unchanged. One of the key features of our connectivity-based model, then, is that it shows that changes in the properties of the GM are not necessarily a factor driving cortical folding; rather, they may occur as a consequence of WM folding, depending on other, possibly unrelated factors such as the average neuronal size, number of neurons in the GM and the fraction connected through the WM, determining for instance the resulting average cortical thickness.

Note that, according to our model, local variations in cortical thickness do not affect the WM volume and folding index. Such variations in thickness across the cortical surface, which are known to be exist, may however in some cases create discrepancies between our expected and observed values of the GM folding. Notice that our model does not predict where cortical folds should occur. Our model does not deny the influence of differential growth in cortical patterning; it simply predicts that the extent of these folds should scale as the cortex gains neurons depending on the connectivity fraction, the average cross-sectional area of the axons in the WM, and their tension.

In the end, we envision cortical patterning as the result of a mechanical phenomenon, probably involving a tug-of-war or push—pull effect of GM and WM on each other during development — maybe as the GM is nudged into curving by its expanding outer layers, at the same time as the WM pulls onto it. The organization anisotropy of the WM seems to come into being via stretch growth, in which it is pulled outward as the diameter of the growing cortex increases Smith, — and, therefore, as it necessarily resists this outward pull, due to intrinsic tension or axons would continue to grow in a disorganized fashion.

In culture, stretch growth transforms random axonal projections formed via outgrowth from central nervous system explants into uniform parallel fascicles Smith et al. The same process is likely to occur in the brain, as the expanding ensemble of the growing cortex physically pulls the WM into long organized tracts during development. Our finding that the volume of the WM grows hypometrically relative to its surface Herculano-Houzel et al.

Qualitatively, thinner cerebral cortices are usually found in more convoluted brains, whether across species or in pathological conditions. In schizophrenia, for example, the cortex may be found to be thinner than usual, with a reduced volume of the superficial layers, and also more folded Sallet et al. These findings are often interpreted as evidence of a thicker cortex resisting buckling. Our model, however, offers an alternative interpretation: that cortical thickness increases as a consequence of a smaller fraction of neurons connected through the WM, in combination or not to an increased average neuronal size in the WM.

Similarly, the thicker lissencephalic cortex is predicted to be a result of abnormal insufficient cortical connectivity through the WM, possibly due to abnormal neuronal migration Olson and Walsh, , and not simply a cortex that became too thick to be folded. One last and very important aspect of cortical folding is that is has often been considered a means of making more neurons fit into a space-limited brain, as the larger-than-expected cortical surface supposedly allows a larger-than-expected number of neurons for a given cranial volume.

However, this would only be the case if cortical expansion occurred mostly laterally, and with a homogeneous number of neurons per surface area. In contrast, as we have shown previously, cortical expansion can no longer be considered to occur homogeneously across species, nor with a homogeneous number of neurons beneath a unit surface area.

This means that it is no longer necessarily true that more convoluted cortices have more neurons than less convoluted cortices. Indeed, the elephant cortex, which has a larger surface area and is more convoluted than the human brain, has been estimated to have fewer neurons than the letter Roth and Dicke, ; Herculano-Houzel, Here we show that cortical folding in mammals can be predicted to happen as a consequence of the folding of the underlying WM under tension of its axons, and not as a simple, linear function of its number of neurons.

Moreover, we show that the scaling of cortical folding with larger numbers of cortical neurons can be predicted, and possibly determined, in different groups of mammals by the scaling of a small number of parameters: 1 the fraction of cortical neurons connected through the WM; 2 the average cross-sectional area of axons in the WM; and 3 the shrinkage, under tension, of average axonal length relative to isometry.

Just one further parameter, the scaling of 4 neuronal density, is required next to predict, or determine, both how the thickness of the GM varies, and how the folding of the GM itself scales.

This of course assumes near perpendicular or at least invariant across species incidence of axonal fibers at the WM—GM interface. This is a plausible hypothesis for fibers under longitudinal tension; but the lack of actual systematic measurement of incidence angles that could confirm this hypothesis must be takes as a limitation of the present work.

Such a measurement would be most welcome, allowing us extend our model by introducing another measured coefficient relating the average incidence angle as a power law of N , to recalculate the values of the various coefficients with a source of uncertainty removed, and to independently test our underlying hypothesis since we expect a cortex grown subject to axonal longitudinal tensions to show a marked tendency toward orthogonal incidence.

Importantly, while the model is potentially universal, applying across the different orders of mammals, it does not at all imply that there is a single way for the cortex to scale. Again, our model predicts that cortical thickness is not a determinant of cortical folding, but rather a consequence, depending on the scaling of neuronal density as well as of the connectivity fraction and average cross-sectional area of the axons in the WM.

Even in the case that experimental testing eventually shows that causality in cortical folding is not as proposed in our model without the introduction of further variables, the latter has the enormous advantage of allowing one to deduce the scaling of cortical connectivity, axonal length, cross-sectional area, and thus to infer propagation time and computational capability and efficacy, from readily measurable values of A W , V W , N , O W , and D N.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Barres, B. Control of oligodendrocyte number in the developing rat optic nerve.

Neuron 12, — Axonal control of oligodendrocyte development. Cell Biol. Braitenberg, V. Berlin: Springer Verlag.

Fry, A. De novo mutations in GRIN1 cause extensive bilateral polymicrogyria. Piao, X. An autosomal recessive form of bilateral frontoparietal polymicrogyria maps to chromosome 16q Genotype-phenotype analysis of human frontoparietal polymicrogyria syndromes. Bahi-Buisson, N. GPR56 -related bilateral frontoparietal polymicrogyria: further evidence for an overlap with the cobblestone complex. Faisst, A. Rotatin is a novel gene required for axial rotation and left-right specification in mouse embryos.

Kheradmand Kia, S. RTTN mutations link primary cilia function to organization of the human cerebral cortex. Cantagrel, V. Truncation of NHEJ1 in a patient with polymicrogyria. Squier, W. Polymicrogyria: pathology, fetal origins and mechanisms. Acta Neuropathol. Poirier, K. Valence, S. Neurogenetics 14 , — Barak, T. Recessive LAMC3 mutations cause malformations of occipital cortical development.

Mishra-Gorur, K. Mutations in KATNB1 cause complex cerebral malformations by disrupting asymmetrically dividing neural progenitors. Neuron 84 , — Cellular and clinical impact of haploinsufficiency for genes involved in ATR signaling. Yu, T. Mutations in WDR62 , encoding a centrosome-associated protein, cause microcephaly with simplified gyri and abnormal cortical architecture. Battaglia, A. Further delineation of deletion 1p36 syndrome in 60 patients: a recognizable phenotype and common cause of developmental delay and mental retardation.

Pediatrics , — Mazzarella, R. Pathological consequences of sequence duplications in the human genome. Genome Res. Shiba, N.

Neuropathology of brain and spinal malformations in a case of monosomy 1p Jansen, A. Genetics of the polymicrogyria syndromes. Bingham, P. Polymicrogyria in chromosome 22 delection syndrome. Neurology 51 , — Mirzaa, G. Megalencephaly and perisylvian polymicrogyria with postaxial polydactyly and hydrocephalus: a rare brain malformation syndrome associated with mental retardation and seizures.

Neuropediatrics 35 , — A protein related to extracellular matrix proteins deleted in the mouse mutant reeler. Dulabon, L. Neuron 27 , 33—44 Kumar, R. TUBA1A mutations cause wide spectrum lissencephaly smooth brain and suggest that multiple neuronal migration pathways converge on alpha tubulins. Morris-Rosendahl, D. Verloes, A. Genetic and clinical aspects of lissencephaly [French]. Sapir, T. Reduction of microtubule catastrophe events by LIS1, platelet-activating factor acetylhydrolase subunit.

TUBA1A mutations: from isolated lissencephaly to familial polymicrogyria. Neurology 76 , — Di Donato, N. Tubulinopathies overview. Hertecant, J. A novel de novo mutation in DYNC1H1 gene underlying malformation of cortical development and cataract. Meta Gene 9 , — Parrini, E. Genetic basis of brain malformations. Tian, G. A patient with lissencephaly, developmental delay, and infantile spasms, due to de novo heterozygous mutation of KIF2A.

Uyanik, G. ARX mutations in X-linked lissencephaly with abnormal genitalia. Neurology 61 , — Kitamura, K. Mutation of ARX causes abnormal development of forebrain and testes in mice and X-linked lissencephaly with abnormal genitalia in humans. Derewenda, U. The structure of the coiled-coil domain of Ndel1 and the basis of its interaction with Lis1, the causal protein of Miller-Dieker lissencephaly. Structure 15 , — Download references.

The authors thank members of the Borrell laboratory, P. Bayly, R. Toro, M. Huttner, for insightful discussions. The authors apologize to colleagues whose research was not cited owing to the broad scope and space limitations of this Review.

Nature Reviews Neuroscience thanks H. Kawasaki and the other anonymous reviewer s for their contribution to the peer review of this work. You can also search for this author in PubMed Google Scholar. Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rounded elevations of cortical tissue between two sulci that contain all six neuronal layers bending outwards, such that the deep layers on either side of a gyrus come close together. Depressions or grooves of cortical tissue that contain all six neuronal layers bending inwards, such that the superficial cortical layers come close together on either side of a sulcus. The characteristic of a brain presenting cortical folds, giving a convoluted or wrinkled appearance.

Measure of a mechanical property of a material. The elastic modulus is the measure of the resistance of an object to being deformed elastically after stress is applied. Property of a material that defines its resistance to being deformed after force is applied to it.

Transient layer of the developing cortex, located beneath the marginal zone and containing the neurons that most recently finished radial migration.

Property of nearly inertia-less, non-Newtonian, flowing, complex fluids, such as polymer melts and solutions. The characteristic of materials of having different physical or mechanical properties when measured along different axes. Detachment from the apical adherens junction belt, followed by basal movement, away from the ventricular zone.

Germinal cells born from apical radial glial cells that populate the subventricular zone basal from the ventricular zone and produce neurons. Phase of early embryonic development during which the single-layered blastula is reorganized into a multilayered gastrula. Regions in the genome that exhibit elevated rates of a specific event.

In evolutionary hot spots, the local sequence of DNA has changed rapidly during evolution. Reprints and Permissions. Llinares-Benadero, C. Deconstructing cortical folding: genetic, cellular and mechanical determinants. Nat Rev Neurosci 20, — Download citation. Published : 04 January Issue Date : March Anyone you share the following link with will be able to read this content:.

Sorry, a shareable link is not currently available for this article. Provided by the Springer Nature SharedIt content-sharing initiative. Nature Reviews Neuroscience Nature Reviews Molecular Cell Biology Neuropsychopharmacology Integrative Psychological and Behavioral Science Neuropsychology Review Advanced search. Skip to main content Thank you for visiting nature. Subjects Brain Development of the nervous system Developmental disorders Developmental neurogenesis Evolutionary developmental biology.

Abstract Folding of the cerebral cortex is a fundamental milestone of mammalian brain evolution and is associated with dramatic increases in size and complexity. Access through your institution. Buy or subscribe. Rent or Buy article Get time limited or full article access on ReadCube. References 1. PubMed Google Scholar 4. PubMed Google Scholar 5. CAS Google Scholar 8. PubMed Google Scholar Google Scholar CAS Google Scholar Acknowledgements The authors thank members of the Borrell laboratory, P.

Reviewer information Nature Reviews Neuroscience thanks H. View author publications. Ethics declarations Competing interests The authors declare no competing interests. Gyrencephalic The characteristic of a brain presenting cortical folds, giving a convoluted or wrinkled appearance. The top or outermost part of a gyrus.

The bottom or deepest part of a sulcus. Lateral walls Portions of cortex between gyral crowns and sulcal fundi. Cells positioned in an abnormal location. Hydraulic pressure Force exerted by a fluid onto the surrounding tissue that contains it under pressure.

Cranial sutures Fibrous joints between the cranial bones. Modulus Measure of a mechanical property of a material. Stiffness Property of a material that defines its resistance to being deformed after force is applied to it. The cortex, or the outer surface of the brain — what's colloquially referred to as "gray matter" — expands and subsequently folds as our brains develop in the womb, said Lisa Ronan, a research fellow in the Department of Psychiatry at the University of Cambridge in England.

In essence, this expansion causes pressure to increase in that outer surface, which is then mitigated by folding, Ronan, told Live Science. Basically, imagine pushing at either end of a piece of rubber — at some point, the surface will bend in response to the increasing pressure.

Or, if you're into geology, think of it like two tectonic plates crashing into each other: The pressure during the collision eventually becomes so great that those plates experience a geological fold. It is one of the most important regions of the brain and attracts much attention in brain research. A higher mammal akin to the weasel.

The ferret has a more developed brain than the mouse and has gyri. Hence, the ferret is used as a model animal in this study. Few studies have been done on ferret genetics and our research group is the world leader in this field.

One of techniques to selectively 'edit' a target portion of a genome, including knocking out genes. Materials provided by Kanazawa University. Note: Content may be edited for style and length. Science News. Gyrus impairment by knocking out the gene Cdk5 We have applied the above-mentioned technique to knocking out a gene called Cdk5 in the ferret cerebral cortex and found that gyrus formation was impaired.

Important neurons for gyrus formation advertisement. Story Source: Materials provided by Kanazawa University. Cell Reports , ; 20 9 : DOI: