Bruno Mota

Cellular scaling rules for rodent brains

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 glia/neuron total mass ratio are fundamental cellular constraints that lead to the relative expansion of cerebral cortical volume across species.

Connectivity-driven white matter scaling and folding in primate cerebral cortex

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 N0.87, not N1.0. 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.

Cortical folding scales universally with surface area and thickness, not number of neurons

The best way to fold a mammalian brain As mammalian brains grew larger through evolution, the organization and folding of brains changed too. In a series of statistical analyses comparing a large number of mammalian species, Mota and Herculano-Houzel found that brain folding is not simply a phylogenetic consequence of brain mass increase (see the Perspective by Striedter and Srinivasan). The exposed surface of the cortex scales across all mammals and across individuals as a single power law of the product of total cortical surface and the square root of cortical thickness. Science, this issue p. 74; see also p. 31 A general physical rule governs brain folding across species and even individuals. [Also see Perspective by Striedter and Srinivasan] 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.

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.

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.

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.

No relative expansion of the number of prefrontal neurons in primate and human evolution

Significance Human brain evolution is often considered synonymous with cortical expansion, in particular of the prefrontal cortex, a cortical region required for our remarkable cognitive abilities such as personality expression, planning, and decision making. In this study, we show that the expansion of numbers of cortical neurons in human and nonhuman primate evolution occurred in a similar manner across the cortex, without an increase in the relative number of neurons in the prefrontal region, and without a relative increase in the number of cells in the prefrontal white matter. One thing that distinguishes the human brain from other primate brains is thus not the relative size of its prefrontal cortex but its absolute number of neurons. Human evolution is widely thought to have involved a particular expansion of prefrontal cortex. This popular notion has recently been challenged, although controversies remain. Here we show that the prefrontal region of both human and nonhuman primates holds about 8% of cortical neurons, with no clear difference across humans and other primates in the distribution of cortical neurons or white matter cells along the anteroposterior axis. Further, we find that the volumes of human prefrontal gray and white matter match the expected volumes for the number of neurons in the gray matter and for the number of other cells in the white matter compared with other primate species. These results indicate that prefrontal cortical expansion in human evolution happened along the same allometric trajectory as for other primate species, without modification of the distribution of neurons across its surface or of the volume of the underlying white matter. We thus propose that the most distinctive feature of the human prefrontal cortex is its absolute number of neurons, not its relative volume.

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.

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.

Universality in human cortical folding in health and disease

Significance Despite of the enormous diversity in size and function of the mammalian cerebral cortex, it has been shown that the cortices of different species fold according to a simple universal law. In this study, we investigate if this law also applies to variation within a single species—our own. Specifically, we examine how the law is affected by sex, age, or the presence of Alzheimer’s disease. By investigating and quantifying what remains invariant and what changes in each case, we shed some light on the underlying mechanisms through which the cortex changes in health and disease and argue that morphological complexity could emerge from a few simple rules. The folding of the cortex in mammalian brains across species has recently been shown to follow a universal scaling law that can be derived from a simple physics model. However, it was yet to be determined whether this law also applies to the morphological diversity of different individuals in a single species, in particular with respect to factors, such as age, sex, and disease. To this end, we derived and investigated the cortical morphology from magnetic resonance images (MRIs) of over 1,000 healthy human subjects from three independent public databases. Our results show that all three MRI datasets follow the scaling law obtained from the comparative neuroanatomical data, which strengthens the case for the existence of a common mechanism for cortical folding. Additionally, for comparable age groups, both male and female brains scale in exactly the same way, despite systematic differences in size and folding. Furthermore, age introduces a systematic shift in the offset of the scaling law. In the model, this shift can be interpreted as changes in the mechanical forces acting on the cortex. We also applied this analysis to a dataset derived from comparable cohorts of Alzheimer’s disease patients and healthy subjects of similar age. We show a systematically lower offset and a possible change in the exponent for Alzheimer’s disease subjects compared with the control cohort. Finally, we discuss implications of the changes in offset and exponent in the data and relate it to existing literature. We, thus, provide a possible mechanistic link between previously independent observations.