How do cell number and size determine brain size? Here, we show that, in the order Rodentia, increased size of the cerebral cortex, cerebellum, and remaining areas across six species is achieved through greater numbers of neurons of larger size, and much greater numbers of nonneuronal cells of roughly invariant size, such that the ratio between total neuronal and nonneuronal mass remains constant across species. Although relative cerebellar size remains stable among rodents, the number of cerebellar neurons increases with brain size more rapidly than in the cortex, such that the cerebellar fraction of total brain neurons increases with brain size. In contrast, although the relative cortical size increases with total brain size, the cortical fraction of total brain neurons remains constant. We propose that the faster increase in average neuronal size in the cerebral cortex than in the cerebellum as these structures gain neurons and the rapidly increasing glial numbers that generate glial mass to match total neuronal mass at a fixed glia͞neuron total mass ratio are fundamental cellular constraints that lead to the relative expansion of cerebral cortical volume across species.allometry ͉ brain size ͉ comparative neuroanatomy ͉ number of glia ͉ number of neurons B rain size varies by a factor of Ϸ100,000 across mammalian species (1, 2), and, although the cellular composition of the brain is one of the major determinants of its computational capacities (3), little is known about how the cellular composition varies with brain size. What are the cellular scaling rules that determine brain allometry? How do numbers of neuronal and nonneuronal cells contribute to structure size? What are the relative contributions of these cells across species of different brain sizes?Glia are said to be the most numerous cell type in the brain (4, 5) and to be 10-50 times more numerous than neurons in humans (6). Evidence for this assertion, however, is scant. The ratio between the total number of glial and neuronal cells (glia͞neuron ratio) in the cerebral cortex has been shown to increase with brain size (1, 7). However, the numeric expansion of glial cells relative to neurons seems to contradict the observation that the neuronal need for metabolic support remains similar across species (8). Data on how neuronal and glial cell sizes scale with brain size might help solve this discrepancy, but such data are lacking in the literature.Not much is known, either, about the total numbers of neuronal and nonneuronal cells in the brains of different species, because methodological limitations have largely restricted comparative studies of brain anatomy to analyses of volumetric data published by a small number of laboratories. Strikingly, analyses of the same data yield conflicting conclusions. For instance, although the neocortical fraction of brain volume increases from 14% in basal insectivores to 80% in humans (9), the cerebellar fraction varies little across individuals of different mammalian orders (10), a discrepancy that the latter au...

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 known mechanisms of axonal elongation. This model also explains the scaling of the folding index of crumpled paper balls. We discuss the implications of this finding for the evolutionary and developmental origin of folding, including the newfound continuum between lissencephaly and gyrencephaly, and for pathologies such as human lissencephaly.

Larger brains have an increasingly folded cerebral cortex whose white matter scales up faster than the gray matter. Here we analyze the cellular composition of the subcortical white matter in 11 primate species, including humans, and one Scandentia, and show that the mass of the white matter scales linearly across species with its number of nonneuronal cells, which is expected to be proportional to the total length of myelinated axons in the white matter. This result implies that the average axonal cross-section area in the white matter, a, does not scale significantly with the number of neurons in the gray matter, N. The surface area of the white matter increases with N 0.87. Because this surface can be defined as the product of N, a, and the fraction n of cortical neurons connected through the white matter, we deduce that connectivity decreases in larger cerebral cortices as a slowly diminishing fraction of neurons, which varies with N −0.16 , sends myelinated axons into the white matter. Decreased connectivity is compatible with previous suggestions that neurons in the cerebral cortex are connected as a small-world network and should slow down the increase in global conduction delay in cortices with larger numbers of neurons. Further, a simple model shows that connectivity and cortical folding are directly related across species. We offer a white matter-based mechanism to account for increased cortical folding across species, which we propose to be driven by connectivity-related tension in the white matter, pulling down on the gray matter.brain size | number of neurons | small-world networks | evolution L arger mammalian brains have relatively larger cerebral cortices that become increasingly folded, such that the overall cortical surface increases more quickly than the exposed cortical surface, presumably as a result of fast expansion of the gray matter (1). The fastest expanding structure, however, is not the cortical gray matter (GM), but the subcortical white matter (WM), which contains the axons that interconnect nearby as well as distant areas in the GM and their subcortical targets. Across mammalian species, the WM comprises as little as 5% of the cerebral cortex in the smallest insectivores, but >40% of the cerebral cortex of dolphins, whales, elephants, and humans (2). The faster increase in WM volume V W than in GM volume V G is to be expected from their spatial characteristics, one as the core, and the other as the shell, of the cortex; if the WM were a perfect sphere surrounded by a spherical shell of GM of constant thickness, V W should increase with V G 3/2 or V G 1.5. However, WM has been found to increase more slowly than expected across mammalian species, with V G 1.22 (3), V G 1.24 (4), V G 1.33 (2), or V G 1.23 (5), which raises the possibility that connectivity through the WM does not increase proportionally with increases in GM.It has been argued that an exponent of 1.23 would follow naturally once the exponent of 1.33, or 4/3, consequence of the local uniformity of the cortex (in number ...

Aims. Analyses of recent cosmic microwave background (CMB) observations have provided increasing hints that there are deviations in the universe from statistical isotropy on large scales. Given the far reaching consequences of such an anisotropy for our understanding of the universe, it is important to employ alternative indicators in order to determine whether the reported anisotropy is cosmological in origin and, if so, extract information that may be helpful for identifying its causes. Methods. Here we propose a new directional indicator, based on separation histograms of pairs of pixels, which provides a measure of departure from statistical isotropy. The main advantage of this indicator is that it generates a sky map of large-scale anisotropies in the CMB temperature map, thus allowing a possible additional window into their causes. Results. Using this indicator, we find statistically significant excess of large-scale anisotropy at well over the 95% confidence level. This anisotropy defines a preferred direction in the CMB data. We discuss the statistical significance of this direction compared to Monte Carlo data obtained under the statistical isotropy hypothesis, and also compare it with other such axes recently reported in the literature. In addition we show that our findings are robust with respect to the details of the method used, so long as the statistical noise is kept under control; and they remain unchanged compared to the foreground cleaning algorithms used in CMB maps. We also find that the application of our method to the first and three-year WMAP data produces similar results.