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1.  Cellular scaling rules for the brain of Artiodactyla include a highly folded cortex with few neurons 
Quantitative analysis of the cellular composition of rodent, primate, insectivore, and afrotherian 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 a clade-specific manner. Here we analyze the cellular scaling rules that apply to the brain of artiodactyls, a group within the order Cetartiodactyla, believed to be a relatively recent radiation from the common Eutherian ancestor. We find that artiodactyls share non-neuronal scaling rules with all groups analyzed previously. Artiodactyls share with afrotherians and rodents, but not with primates, the neuronal scaling rules that apply to the cerebral cortex and cerebellum. The neuronal scaling rules that apply to the remaining brain areas are, however, distinct in artiodactyls. Importantly, we show that the folding index of the cerebral cortex scales with the number of neurons in the cerebral cortex in distinct fashions across artiodactyls, afrotherians, rodents, and primates, such that the artiodactyl cerebral cortex is more convoluted than primate cortices of similar numbers of neurons. Our findings suggest that the scaling rules found to be shared across modern afrotherians, glires, and artiodactyls applied to the common Eutherian ancestor, such as the relationship between the mass of the cerebral cortex as a whole and its number of neurons. In turn, the distribution of neurons along the surface of the cerebral cortex, which is related to its degree of gyrification, appears to be a clade-specific characteristic. If the neuronal scaling rules for artiodactyls extend to all cetartiodactyls, we predict that the large cerebral cortex of cetaceans will still have fewer neurons than the human cerebral cortex.
PMCID: PMC4228855  PMID: 25429261
evolution; cortical expansion; numbers of neurons; gyrification; brain size
2.  All brains are made of this: a fundamental building block of brain matter with matching neuronal and glial masses 
How does the size of the glial and neuronal cells that compose brain tissue vary across brain structures and species? Our previous studies indicate that average neuronal size is highly variable, while average glial cell size is more constant. Measuring whole cell sizes in vivo, however, is a daunting task. Here we use chi-square minimization of the relationship between measured neuronal and glial cell densities in the cerebral cortex, cerebellum, and rest of brain in 27 mammalian species to model neuronal and glial cell mass, as well as the neuronal mass fraction of the tissue (the fraction of tissue mass composed by neurons). Our model shows that while average neuronal cell mass varies by over 500-fold across brain structures and species, average glial cell mass varies only 1.4-fold. Neuronal mass fraction varies typically between 0.6 and 0.8 in all structures. Remarkably, we show that two fundamental, universal relationships apply across all brain structures and species: (1) the glia/neuron ratio varies with the total neuronal mass in the tissue (which in turn depends on variations in average neuronal cell mass), and (2) the neuronal mass per glial cell, and with it the neuronal mass fraction and neuron/glia mass ratio, varies with average glial cell mass in the tissue. We propose that there is a fundamental building block of brain tissue: the glial mass that accompanies a unit of neuronal mass. We argue that the scaling of this glial mass is a consequence of a universal mechanism whereby numbers of glial cells are added to the neuronal parenchyma during development, irrespective of whether the neurons composing it are large or small, but depending on the average mass of the glial cells being added. We also show how evolutionary variations in neuronal cell mass, glial cell mass and number of neurons suffice to determine the most basic characteristics of brain structures, such as mass, glia/neuron ratio, neuron/glia mass ratio, and cell densities.
PMCID: PMC4228857  PMID: 25429260
allometry; glia/neuron ratio; number of neurons; number of glial cells; cell size; brain size
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.
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.
PMCID: PMC3759024  PMID: 24032005
human; prefrontal cortex; occipital cortex; evolution; cortical expansion
5.  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.
PMCID: PMC3270328  PMID: 22347170
allometry; brain size; evolution; white matter; cortical folding; connectivity; axon caliber; cortical thickness

Results 1-5 (5)