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1.  Cellular scaling rules for the brain of afrotherians 
Quantitative analysis of the cellular composition of rodent, primate and eulipotyphlan brains has shown that non-neuronal scaling rules are similar across these mammalian orders that diverged about 95 million years ago, and therefore appear to be conserved in evolution, while neuronal scaling rules appear to be free to vary in evolution in a clade-specific manner. Here we analyze the cellular scaling rules that apply to the brain of afrotherians, believed to be the first clade to radiate from the common eutherian ancestor. We find that afrotherians share non-neuronal scaling rules with rodents, primates and eulipotyphlans, as well as the coordinated scaling of numbers of neurons in the cerebral cortex and cerebellum. Afrotherians share with rodents and eulipotyphlans, but not with primates, the scaling of number of neurons in the cortex and in the cerebellum as a function of the number of neurons in the rest of the brain. Afrotheria also share with rodents and eulipotyphlans the neuronal scaling rules that apply to the cerebral cortex. Afrotherians share with rodents, but not with eulipotyphlans nor primates, the neuronal scaling rules that apply to the cerebellum. Importantly, the scaling of the folding index of the cerebral cortex with the number of neurons in the cerebral cortex is not shared by either afrotherians, rodents, or primates. The sharing of some neuronal scaling rules between afrotherians and rodents, and of some additional features with eulipotyphlans and primates, raise the interesting possibility that these shared characteristics applied to the common eutherian ancestor. In turn, the clade-specific characteristics that relate to the distribution of neurons along the surface of the cerebral cortex and to its degree of gyrification suggest that these characteristics compose an evolutionarily plastic suite of features that may have defined and distinguished mammalian groups in evolution.
doi:10.3389/fnana.2014.00005
PMCID: PMC3925844  PMID: 24596544
evolution; glia-neuron ratio; numbers of neurons; cortical expansion; gyrification
2.  Faster scaling of visual neurons in cortical areas relative to subcortical structures in non-human primate brains 
Brain structure & function  2012;218(3):805-816.
Cortical expansion, both in absolute terms and in relation to subcortical structures, is considered a major trend in mammalian brain evolution with important functional implications, given that cortical computations should add complexity and flexibility to information processing. Here, we investigate the numbers of neurons that compose 4 structures in the visual pathway across 11 non-human primate species to determine the scaling relationships that apply to these structures and among them. We find that primary visual cortex, area V1, as well as the superior colliculus (SC) and lateral geniculate nucleus scale in mass faster than they gain neurons. Areas V1 and MT gain neurons proportionately to the entire cerebral cortex, and represent fairly constant proportions of all cortical neurons (36 and 3 %, respectively), while V1 gains neurons much faster than both subcortical structures examined. Larger primate brains therefore have increased ratios of cortical to subcortical neurons involved in processing visual information, as observed in the auditory pathway, but have a constant proportion of cortical neurons dedicated to the primary visual representation, and a fairly constant ratio of about 45 times more neurons in primary visual than in primary auditory cortical areas.
doi:10.1007/s00429-012-0430-5
PMCID: PMC3727908  PMID: 22684638
Superior colliculus; Visual cortex; Lateral geniculate nucleus; V1; Area MT; Thalamus; Allometry; Brain size; Evolution
3.  Different scaling of white matter volume, cortical connectivity, and gyrification across rodent and primate brains 
Expansion of the cortical gray matter in evolution has been accompanied by an even faster expansion of the subcortical white matter volume and by folding of the gray matter surface, events traditionally considered to occur homogeneously across mammalian species. Here we investigate how white matter expansion and cortical folding scale across species of rodents and primates as the gray matter gains neurons. We find very different scaling rules of white matter expansion across the two orders, favoring volume conservation and smaller propagation times in primates. For a similar number of cortical neurons, primates have a smaller connectivity fraction and less white matter volume than rodents; moreover, as the cortex gains neurons, there is a much faster increase in white matter volume and in its ratio to gray matter volume in rodents than in primates. Order-specific scaling of the white matter can be attributed to different scaling of average fiber caliber and neuronal connectivity in rodents and primates. Finally, cortical folding increases as different functions of the number of cortical neurons in rodents and primates, scaling faster in the latter than in the former. While the neuronal rules that govern gray and white matter scaling are different across rodents and primates, we find that they can be explained by the same unifying model, with order-specific exponents. The different scaling of the white matter has implications for the scaling of propagation time and computational capacity in evolution, and calls for a reappraisal of developmental models of cortical expansion in evolution.
doi:10.3389/fnana.2013.00003
PMCID: PMC3620553  PMID: 23576961
white matter; number of neurons; allometry; brain size; cortical expansion; gyrification
4.  The human cerebral cortex is neither one nor many: neuronal distribution reveals two quantitatively different zones in the gray matter, three in the white matter, and explains local variations in cortical folding 
The human prefrontal cortex has been considered different in several aspects and relatively enlarged compared to the rest of the cortical areas. Here we determine whether the white and gray matter of the prefrontal portion of the human cerebral cortex have similar or different cellular compositions relative to the rest of the cortical regions by applying the Isotropic Fractionator to analyze the distribution of neurons along the entire anteroposterior axis of the cortex, and its relationship with the degree of gyrification, number of neurons under the cortical surface, and other parameters. The prefrontal region shares with the remainder of the cerebral cortex (except for occipital cortex) the same relationship between cortical volume and number of neurons. In contrast, both occipital and prefrontal areas vary from other cortical areas in their connectivity through the white matter, with a systematic reduction of cortical connectivity through the white matter and an increase of the mean axon caliber along the anteroposterior axis. These two parameters explain local differences in the distribution of neurons underneath the cortical surface. We also show that local variations in cortical folding are neither a function of local numbers of neurons nor of cortical thickness, but correlate with properties of the white matter, and are best explained by the folding of the white matter surface. Our results suggest that the human cerebral cortex is divided in two zones (occipital and non-occipital) that differ in how neurons are distributed across their gray matter volume and in three zones (prefrontal, occipital, and non-occipital) that differ in how neurons are connected through the white matter. Thus, the human prefrontal cortex has the largest fraction of neuronal connectivity through the white matter and the smallest average axonal caliber in the white matter within the cortex, although its neuronal composition fits the pattern found for other, non-occipital areas.
doi:10.3389/fnana.2013.00028
PMCID: PMC3759024  PMID: 24032005
human; prefrontal cortex; occipital cortex; evolution; cortical expansion
5.  Distribution of neurons in functional areas of the mouse cerebral cortex reveals quantitatively different cortical zones 
How are neurons distributed along the cortical surface and across functional areas? Here we use the isotropic fractionator (Herculano-Houzel and Lent, 2005) to analyze the distribution of neurons across the entire isocortex of the mouse, divided into 18 functional areas defined anatomically. We find that the number of neurons underneath a surface area (the N/A ratio) varies 4.5-fold across functional areas and neuronal density varies 3.2-fold. The face area of S1 contains the most neurons, followed by motor cortex and the primary visual cortex. Remarkably, while the distribution of neurons across functional areas does not accompany the distribution of surface area, it mirrors closely the distribution of cortical volumes—with the exception of the visual areas, which hold more neurons than expected for their volume. Across the non-visual cortex, the volume of individual functional areas is a shared linear function of their number of neurons, while in the visual areas, neuronal densities are much higher than in all other areas. In contrast, the 18 functional areas cluster into three different zones according to the relationship between the N/A ratio and cortical thickness and neuronal density: these three clusters can be called visual, sensory, and, possibly, associative. These findings are remarkably similar to those in the human cerebral cortex (Ribeiro et al., 2013) and suggest that, like the human cerebral cortex, the mouse cerebral cortex comprises two zones that differ in how neurons form the cortical volume, and three zones that differ in how neurons are distributed underneath the cortical surface, possibly in relation to local differences in connectivity through the white matter. Our results suggest that beyond the developmental divide into visual and non-visual cortex, functional areas initially share a common distribution of neurons along the parenchyma that become delimited into functional areas according to the pattern of connectivity established later.
doi:10.3389/fnana.2013.00035
PMCID: PMC3800983  PMID: 24155697
mouse; visual cortex; occipital cortex; cortical development; neuronal density; numbers of neurons
6.  Updated Neuronal Scaling Rules for the Brains of Glires (Rodents/Lagomorphs) 
Brain, Behavior and Evolution  2011;78(4):302-314.
Brain size scales as different functions of its number of neurons across mammalian orders such as rodents, primates, and insectivores. In rodents, we have previously shown that, across a sample of 6 species, from mouse to capybara, the cerebral cortex, cerebellum and the remaining brain structures increase in size faster than they gain neurons, with an accompanying decrease in neuronal density in these structures [Herculano-Houzel et al.: Proc Natl Acad Sci USA 2006;103:12138–12143]. Important remaining questions are whether such neuronal scaling rules within an order apply equally to all pertaining species, and whether they extend to closely related taxa. Here, we examine whether 4 other species of Rodentia, as well as the closely related rabbit (Lagomorpha), conform to the scaling rules identified previously for rodents. We report the updated neuronal scaling rules obtained for the average values of each species in a way that is directly comparable to the scaling rules that apply to primates [Gabi et al.: Brain Behav Evol 2010;76:32–44], and examine whether the scaling relationships are affected when phylogenetic relatedness in the dataset is accounted for. We have found that the brains of the spiny rat, squirrel, prairie dog and rabbit conform to the neuronal scaling rules that apply to the previous sample of rodents. The conformity to the previous rules of the new set of species, which includes the rabbit, suggests that the cellular scaling rules we have identified apply to rodents in general, and probably to Glires as a whole (rodents/lagomorphs), with one notable exception: the naked mole-rat brain is apparently an outlier, with only about half of the neurons expected from its brain size in its cerebral cortex and cerebellum.
doi:10.1159/000330825
PMCID: PMC3237106  PMID: 21985803
Rodents; Brain size; Evolution; Neurons; Glia; Glires
7.  Gorilla and Orangutan Brains Conform to the Primate Cellular Scaling Rules: Implications for Human Evolution 
Brain, Behavior and Evolution  2011;77(1):33-44.
Gorillas and orangutans are primates at least as large as humans, but their brains amount to about one third of the size of the human brain. This discrepancy has been used as evidence that the human brain is about 3 times larger than it should be for a primate species of its body size. In contrast to the view that the human brain is special in its size, we have suggested that it is the great apes that might have evolved bodies that are unusually large, on the basis of our recent finding that the cellular composition of the human brain matches that expected for a primate brain of its size, making the human brain a linearly scaled-up primate brain in its number of cells. To investigate whether the brain of great apes also conforms to the primate cellular scaling rules identified previously, we determine the numbers of neuronal and other cells that compose the orangutan and gorilla cerebella, use these numbers to calculate the size of the brain and of the cerebral cortex expected for these species, and show that these match the sizes described in the literature. Our results suggest that the brains of great apes also scale linearly in their numbers of neurons like other primate brains, including humans. The conformity of great apes and humans to the linear cellular scaling rules that apply to other primates that diverged earlier in primate evolution indicates that prehistoric Homo species as well as other hominins must have had brains that conformed to the same scaling rules, irrespective of their body size. We then used those scaling rules and published estimated brain volumes for various hominin species to predict the numbers of neurons that composed their brains. We predict that Homo heidelbergensis and Homo neanderthalensis had brains with approximately 80 billion neurons, within the range of variation found in modern Homo sapiens. We propose that while the cellular scaling rules that apply to the primate brain have remained stable in hominin evolution (since they apply to simians, great apes and modern humans alike), the Colobinae and Pongidae lineages favored marked increases in body size rather than brain size from the common ancestor with the Homo lineage, while the Homo lineage seems to have favored a large brain instead of a large body, possibly due to the metabolic limitations to having both.
doi:10.1159/000322729
PMCID: PMC3064932  PMID: 21228547
Allometry; Brain size; Great apes; Human; Evolution, human; Neurons, number
8.  How the Cortex Gets Its Folds: An Inside-Out, Connectivity-Driven Model for the Scaling of Mammalian Cortical Folding 
Larger mammalian cerebral cortices tend to have increasingly folded surfaces, often considered to result from the lateral expansion of the gray matter (GM), which, in a volume constrained by the cranium, causes mechanical compression that is relieved by inward folding of the white matter (WM), or to result from differential expansion of cortical layers. Across species, thinner cortices, presumably more pliable, would offer less resistance and hence become more folded than thicker cortices of a same size. However, such models do not acknowledge evidence in favor of a tension-based pull onto the GM from the inside, holding it in place even when the constraint imposed by the cranium is removed. Here we propose a testable, quantitative model of cortical folding driven by tension along the length of axons in the WM that assumes that connections through the WM are formed early in development, at the same time as the GM becomes folded, and considers that axonal connections through the WM generate tension that leads to inward folding of the WM surface, which pulls the GM surface inward. As an important necessary simplifying hypothesis, we assume that axons leaving or entering the WM do so approximately perpendicularly to the WM–GM interface. Cortical folding is thus driven by WM connectivity, and is a function of the fraction of cortical neurons connected through the WM, the average length, and the average cross-sectional area of the axons in the WM. Our model predicts that the different scaling of cortical folding across mammalian orders corresponds to different combinations of scaling of connectivity, axonal cross-sectional area, and tension along WM axons, instead of being a simple function of the number of GM neurons. Our model also explains variations in average cortical thickness as a result of the factors that lead to cortical folding, rather than as a determinant of folding; predicts that for a same tension, folding increases with connectivity through the WM and increased axonal cross-section; and that, for a same number of neurons, higher connectivity through the WM leads to a higher degree of folding as well as an on average thinner GM across species.
doi:10.3389/fnana.2012.00003
PMCID: PMC3270328  PMID: 22347170
allometry; brain size; evolution; white matter; cortical folding; connectivity; axon caliber; cortical thickness
9.  Age-related neuronal loss in the rat brain starts at the end of adolescence 
Aging-related changes in the brain have been mostly studied through the comparison of young adult and very old animals. However, aging must be considered a lifelong process of cumulative changes that ultimately become evident at old age. To determine when this process of decline begins, we studied how the cellular composition of the rat brain changes from infancy to adolescence, early adulthood, and old age. Using the isotropic fractionator to determine total numbers of neuronal and non-neuronal cells in different brain areas, we find that a major increase in number of neurons occurs during adolescence, between 1 and 2–3 months of age, followed by a significant trend of widespread and progressive neuronal loss that begins as early as 3 months of age, when neuronal numbers are maximal in all structures, until decreases in numbers of neurons become evident at 12 or 22 months of age. Our findings indicate that age-related decline in the brain begins as soon as the end of adolescence, a novel finding has important clinical and social implications for public health and welfare.
doi:10.3389/fnana.2012.00045
PMCID: PMC3481355  PMID: 23112765
aging; number of neurons; brain size; atrophy; neuronal loss
10.  Cellular Scaling Rules for the Brains of an Extended Number of Primate Species 
Brain, Behavior and Evolution  2010;76(1):32-44.
What are the rules relating the size of the brain and its structures to the number of cells that compose them and their average sizes? We have shown previously that the cerebral cortex, cerebellum and the remaining brain structures increase in size as a linear function of their numbers of neurons and non-neuronal cells across 6 species of primates. Here we describe that the cellular composition of the same brain structures of 5 other primate species, as well as humans, conform to the scaling rules identified previously, and that the updated power functions for the extended sample are similar to those determined earlier. Accounting for phylogenetic relatedness in the combined dataset does not affect the scaling slopes that apply to the cerebral cortex and cerebellum, but alters the slope for the remaining brain structures to a value that is similar to that observed in rodents, which raises the possibility that the neuronal scaling rules for these structures are shared among rodents and primates. The conformity of the new set of primate species to the previous rules strongly suggests that the cellular scaling rules we have identified apply to primates in general, including humans, and not only to particular subgroups of primate species. In contrast, the allometric rules relating body and brain size are highly sensitive to the particular species sampled, suggesting that brain size is neither determined by body size nor together with it, but is rather only loosely correlated with body size.
doi:10.1159/000319872
PMCID: PMC2980814  PMID: 20926854
Allometry; Brain size; Evolution; Glia, number; Neurons, number; Primates
11.  Cellular Scaling Rules for Primate Spinal Cords 
Brain, Behavior and Evolution  2010;76(1):45-59.
The spinal cord can be considered a major sensorimotor interface between the body and the brain. How does the spinal cord scale with body and brain mass, and how are its numbers of neurons related to the number of neurons in the brain across species of different body and brain sizes? Here we determine the cellular composition of the spinal cord in eight primate species and find that its number of neurons varies as a linear function of cord length, and accompanies body mass raised to an exponent close to 1/3. This relationship suggests that the extension, mass and number of neurons that compose the spinal cord are related to body length, rather than to body mass or surface. Moreover, we show that although brain mass increases linearly with cord mass, the number of neurons in the brain increases with the number of neurons in the spinal cord raised to the power of 1.7. This faster addition of neurons to the brain than to the spinal cord is consistent with current views on how larger brains add complexity to the processing of environmental and somatic information.
doi:10.1159/000319019
PMCID: PMC2980815  PMID: 20926855
Allometry; Number of neurons; Evolution; Connectivity
12.  Scaling of Brain Metabolism with a Fixed Energy Budget per Neuron: Implications for Neuronal Activity, Plasticity and Evolution 
PLoS ONE  2011;6(3):e17514.
It is usually considered that larger brains have larger neurons, which consume more energy individually, and are therefore accompanied by a larger number of glial cells per neuron. These notions, however, have never been tested. Based on glucose and oxygen metabolic rates in awake animals and their recently determined numbers of neurons, here I show that, contrary to the expected, the estimated glucose use per neuron is remarkably constant, varying only by 40% across the six species of rodents and primates (including humans). The estimated average glucose use per neuron does not correlate with neuronal density in any structure. This suggests that the energy budget of the whole brain per neuron is fixed across species and brain sizes, such that total glucose use by the brain as a whole, by the cerebral cortex and also by the cerebellum alone are linear functions of the number of neurons in the structures across the species (although the average glucose consumption per neuron is at least 10× higher in the cerebral cortex than in the cerebellum). These results indicate that the apparently remarkable use in humans of 20% of the whole body energy budget by a brain that represents only 2% of body mass is explained simply by its large number of neurons. Because synaptic activity is considered the major determinant of metabolic cost, a conserved energy budget per neuron has several profound implications for synaptic homeostasis and the regulation of firing rates, synaptic plasticity, brain imaging, pathologies, and for brain scaling in evolution.
doi:10.1371/journal.pone.0017514
PMCID: PMC3046985  PMID: 21390261
13.  Coordinated Scaling of Cortical and Cerebellar Numbers of Neurons 
While larger brains possess concertedly larger cerebral cortices and cerebella, the relative size of the cerebral cortex increases with brain size, but relative cerebellar size does not. In the absence of data on numbers of neurons in these structures, this discrepancy has been used to dispute the hypothesis that the cerebral cortex and cerebellum function and have evolved in concert and to support a trend towards neocorticalization in evolution. However, the rationale for interpreting changes in absolute and relative size of the cerebral cortex and cerebellum relies on the assumption that they reflect absolute and relative numbers of neurons in these structures across all species – an assumption that our recent studies have shown to be flawed. Here I show for the first time that the numbers of neurons in the cerebral cortex and cerebellum are directly correlated across 19 mammalian species of four different orders, including humans, and increase concertedly in a similar fashion both within and across the orders Eulipotyphla (Insectivora), Rodentia, Scandentia and Primata, such that on average a ratio of 3.6 neurons in the cerebellum to every neuron in the cerebral cortex is maintained across species. This coordinated scaling of cortical and cerebellar numbers of neurons provides direct evidence in favor of concerted function, scaling and evolution of these brain structures, and suggests that the common notion that equates cognitive advancement with neocortical expansion should be revisited to consider in its stead the coordinated scaling of neocortex and cerebellum as a functional ensemble.
doi:10.3389/fnana.2010.00012
PMCID: PMC2839851  PMID: 20300467
brain size; brain scaling; mosaic evolution; numbers of neurons; cerebral cortex; cerebellum
14.  Cellular Scaling Rules of Insectivore Brains 
Insectivores represent extremes in mammalian body size and brain size, retaining various “primitive” morphological characteristics, and some species of Insectivora are thought to share similarities with small-bodied ancestral eutherians. This raises the possibility that insectivore brains differ from other taxa, including rodents and primates, in cellular scaling properties. Here we examine the cellular scaling rules for insectivore brains and demonstrate that insectivore scaling rules overlap somewhat with those for rodents and primates such that the insectivore cortex shares scaling rules with rodents (increasing faster in size than in numbers of neurons), but the insectivore cerebellum shares scaling rules with primates (increasing isometrically). Brain structures pooled as “remaining areas” appear to scale similarly across all three mammalian orders with respect to numbers of neurons, and the numbers of non-neurons appear to scale similarly across all brain structures for all three orders. Therefore, common scaling rules exist, to different extents, between insectivore, rodent, and primate brain regions, and it is hypothesized that insectivores represent the common aspects of each order. The olfactory bulbs of insectivores, however, offer a noteworthy exception in that neuronal density increases linearly with increasing structure mass. This implies that the average neuronal cell size decreases with increasing olfactory bulb mass in order to accommodate greater neuronal density, and represents the first documentation of a brain structure gaining neurons at a greater rate than mass. This might allow insectivore brains to concentrate more neurons within the olfactory bulbs without a prohibitively large and metabolically costly increase in structure mass.
doi:10.3389/neuro.05.008.2009
PMCID: PMC2713736  PMID: 19636383
allometry; brain size; comparative neuroanatomy; glia; neurons; evolution; olfactory bulb
15.  The Human Brain in Numbers: A Linearly Scaled-up Primate Brain  
The human brain has often been viewed as outstanding among mammalian brains: the most cognitively able, the largest-than-expected from body size, endowed with an overdeveloped cerebral cortex that represents over 80% of brain mass, and purportedly containing 100 billion neurons and 10× more glial cells. Such uniqueness was seemingly necessary to justify the superior cognitive abilities of humans over larger-brained mammals such as elephants and whales. However, our recent studies using a novel method to determine the cellular composition of the brain of humans and other primates as well as of rodents and insectivores show that, since different cellular scaling rules apply to the brains within these orders, brain size can no longer be considered a proxy for the number of neurons in the brain. These studies also showed that the human brain is not exceptional in its cellular composition, as it was found to contain as many neuronal and non-neuronal cells as would be expected of a primate brain of its size. Additionally, the so-called overdeveloped human cerebral cortex holds only 19% of all brain neurons, a fraction that is similar to that found in other mammals. In what regards absolute numbers of neurons, however, the human brain does have two advantages compared to other mammalian brains: compared to rodents, and probably to whales and elephants as well, it is built according to the very economical, space-saving scaling rules that apply to other primates; and, among economically built primate brains, it is the largest, hence containing the most neurons. These findings argue in favor of a view of cognitive abilities that is centered on absolute numbers of neurons, rather than on body size or encephalization, and call for a re-examination of several concepts related to the exceptionality of the human brain.
doi:10.3389/neuro.09.031.2009
PMCID: PMC2776484  PMID: 19915731
brain scaling; number of neurons; human; encephalization

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