Folding of the Cerebral Cortex in Mammals

Prothero, John; Sundsten, John W.

doi:10.1159/000121313

Cited by 112 publications

(91 citation statements)

References 3 publications

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“…4, 5, and [13][14][15][16]. This is very close to the exponent of 1.138 for the total number of highway exits (Table 1b), suggesting perhaps that 9/8 may be the theoretical exponent for exits (as well as for number of zip codes and number of public high schools).…”

Section: Number Of Highway Exits and Number Of Neuronal Synapsessupporting

confidence: 64%

“…This is very close to the exponent of 1.138 for the total number of highway exits (Table 1b), suggesting perhaps that 9/8 may be the theoretical exponent for exits (as well as for number of zip codes and number of public high schools). As was the case for city highway networks, the surface density of synapses rises approximately as the 1/8 power of neocortex surface area, and this is entirely accommodated by the thickness of gray matter increasing as the 1/8 power [4,5,[13][14][15][16], amounting to a slow increase from about half a millimeter in the smallest mammals to a couple millimeters in man. Gray matter thickness may, then, be akin to the surface density of a city (some of this surface density increase in cities which may literally be due to increasing ''thickness,'' i.e., to cities growing in the third dimension).…”

Section: Number Of Highway Exits and Number Of Neuronal Synapsesmentioning

confidence: 99%

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Common scaling laws for city highway systems and the mammalian neocortex

Changizi

Destefano

2009

Complexity

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A variety of scaling laws are known for the mammalian neocortex relating gray matter volume, total number of synapses [1,2], white matter volume [3][4][5][6][7][8][9], number of neurons [6,[10][11][12], surface area [4,5,[13][14][15][16], axon caliber [1,17], and number of cortical areas or compartments [18]. These neocortical scaling laws appear to be a consequence of selection pressure for a sheet-like structure (namely, gray matter) to economically maintain a high level of interconnectedness [1,2,19,20]. We might therefore expect to find similar scaling laws for any sheetlike structure under similar selection pressures, in which case the neocortex would be just an instance of a more general kind of structure.Here, we investigate city highway systems as a potential kind of network which may be driven by similar principles as the neocortex. In contrast to neurons, which are conduits for information-related signals on which brain computations rely, highways are conduits for physical materials and people. But from the perspective of the city as a whole, the materials and people that highways transport are crucial to the large-scale function carried out by the city, and are, in a sense, signals-that one signal is electric and the other physical may not matter in regards to the fundamental principles governing them. In addition to the prima facie analogy between city highway networks and the brain's neural connections, there are several other reasons we chose to examine city highway networks. First, the organization of city highway networks tends to be driven by political and economic forces over decades, rather than being planned in advanced following known principles of highway engineering [21]-i.e., city highways systems are a result of an evolution-like mechanism. Second, cities are under selection pressure to efficiently interconnect via highways and roads. Third, because cities lie on the land they are approximately a surface, or a sheet. Fourth, highway network data are readily available (and our data set consists of 60 U.S. cities varying in population from 10 4 to nearly 10 7 , see Table 2 for raw data). Finally, the organization of city highway systems is interesting in and of itself: nearly half of Earth's 6.6 billion people now live in cities, and cities are becoming ever larger and densely populated. The proper functioning of a city requires that people and materials be quickly moved throughout it. This is a very difficult design problem, one that is magnified by the fact that city population tends to grow much faster than city surface area, and cities tend to increase in population over time, so that the efficient highway network must constantly evolve from the pre-existing one. Identification of scaling laws governing how highway organization scales with city size could potentially lead to better highway systems, and more efficiently running cities.

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Section: Number Of Highway Exits and Number Of Neuronal Synapsessupporting

confidence: 64%

Section: Number Of Highway Exits and Number Of Neuronal Synapsesmentioning

confidence: 99%

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Common scaling laws for city highway systems and the mammalian neocortex

Changizi

Destefano

2009

Complexity

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“…One possible explanation is that involution of the ventricular surface would make it more difficult for axons to cross from one side of a gyrus to the other (43). It would also obstruct the path of long-range axons that normally pass down the center of individual cortical gyri (44). Alternatively, the downside of the natural mode of cortical foliation is that it requires an enormous expansion of the pial surface because, without it, gyral growth would likely rupture the pia and disrupt lamination.…”

Section: Resultsmentioning

confidence: 99%

Expansion, folding, and abnormal lamination of the chick optic tectum after intraventricular injections of FGF2

McGowan

Alaama

Freise

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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Comparative research has shown that evolutionary increases in brain region volumes often involve delays in neurogenesis. However, little is known about the influence of such changes on subsequent development. To get at this question, we injected FGF2-which delays cell cycle exit in mammalian neocortex-into the cerebral ventricles of chicks at embryonic day (ED) 4. This manipulation alters the development of the optic tectum dramatically. By ED7, the tectum of FGF2-treated birds is abnormally thin and has a reduced postmitotic layer, consistent with a delay in neurogenesis. FGF2 treatment also increases tectal volume and ventricular surface area, disturbs tectal lamination, and creates small discontinuities in the pia mater overlying the tectum. On ED12, the tectum is still larger in FGF2-treated embryos than in controls. However, lateral portions of the FGF2-treated tectum now exhibit volcano-like laminar disturbances that coincide with holes in the pia, and the caudomedial tectum exhibits prominent folds. To explain these observations, we propose that the tangential expansion of the ventricular surface in FGF2-treated tecta outpaces the expansion of the pial surface, creating abnormal mechanical stresses. Two alternative means of alleviating these stresses are tectal foliation and the formation of pial holes. The latter probably alter signaling gradients required for normal cell migration and may generate abnormal patterns of cerebrospinal fluid flow; both abnormalities would generate disturbances in tectal lamination. Overall, our findings suggest that evolutionary expansion of sheet-like, laminated brain regions requires a concomitant expansion of the pia mater.brain evolution | evolutionary developmental biology | proliferation | meninges | cortical folding E volutionary increases in brain region volumes are common (1).For example, the neocortex is disproportionately enlarged in primates relative to other mammals, and the telencephalon is disproportionately enlarged in parrots and songbirds relative to other birds (1-4). Recent work in evolutionary developmental neurobiology has shown that these evolutionary increases in brain region volumes are often caused by delays in cell cycle exit of neuronal precursors (5, 6). Among birds, for example, parrots and songbirds exhibit delayed telencephalic neurogenesis relative to chicken-like birds (7-9). Among mammals, cell cycle exit in the neocortex is similarly delayed in primates, which have a disproportionately enlarged neocortex (5, 10-12).Unfortunately, the downstream effects of delayed cell cycle exit on subsequent developmental processes and adult morphology remain poorly understood. One way to fill this gap in our knowledge is to experimentally recreate the key species differences in the laboratory by means of carefully selected developmental manipulations. A good example of this phenocopy approach was the creation of transgenic mice with a constitutively active form of β-catenin that prolongs proliferation, increases neocortical volume, and generates cortica...

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“…The slow thickening of cortex for larger brains can be fitted by power laws against various variables (8,12,19,28,29). Consistent with previous results, direct power law regression of cortical thickness against gray matter volume yielded T ϳ G 0.10Ϯ0.02 , with a moderate correlation coefficient r ϭ 0.81 in log-log space, based on 22 species from the data in table 1 in ref.…”

Section: Cortical Thicknessmentioning

confidence: 99%

A universal scaling law between gray matter and white matter of cerebral cortex

Zhang

Sejnowski

2000

Proc. Natl. Acad. Sci. U.S.A.

637

450

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Neocortex, a new and rapidly evolving brain structure in mammals, has a similar layered architecture in species over a wide range of brain sizes. Larger brains require longer fibers to communicate between distant cortical areas; the volume of the white matter that contains long axons increases disproportionally faster than the volume of the gray matter that contains cell bodies, dendrites, and axons for local information processing, according to a power law. The theoretical analysis presented here shows how this remarkable anatomical regularity might arise naturally as a consequence of the local uniformity of the cortex and the requirement for compact arrangement of long axonal fibers. The predicted power law with an exponent of 4͞3 minus a small correction for the thickness of the cortex accurately accounts for empirical data spanning several orders of magnitude in brain sizes for various mammalian species, including human and nonhuman primates.

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Folding of the Cerebral Cortex in Mammals

Cited by 112 publications

References 3 publications

Common scaling laws for city highway systems and the mammalian neocortex

Common scaling laws for city highway systems and the mammalian neocortex

Expansion, folding, and abnormal lamination of the chick optic tectum after intraventricular injections of FGF2

A universal scaling law between gray matter and white matter of cerebral cortex

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