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. 2014 Dec 9;111(49):17642-7.
doi: 10.1073/pnas.1409271111. Epub 2014 Nov 24.

Modeling local and cross-species neuron number variations in the cerebral cortex as arising from a common mechanism

Diarmuid J Cahalane  1 , Christine J Charvet  2 , Barbara L Finlay  3
Affiliations

Modeling local and cross-species neuron number variations in the cerebral cortex as arising from a common mechanism

Diarmuid J Cahalane et al. Proc Natl Acad Sci U S A. .

Abstract

A massive increase in the number of neurons in the cerebral cortex, driving its size to increase by five orders of magnitude, is a key feature of mammalian evolution. Not only are there systematic variations in cerebral cortical architecture across species, but also across spatial axes within a given cortex. In this article we present a computational model that accounts for both types of variation as arising from the same developmental mechanism. The model employs empirically measured parameters from over a dozen species to demonstrate that changes to the kinetics of neurogenesis (the cell-cycle rate, the progenitor death rate, and the "quit rate," i.e., the ratio of terminal cell divisions) are sufficient to explain the great diversity in the number of cortical neurons across mammals. Moreover, spatiotemporal gradients in those same parameters in the embryonic cortex can account for cortex-wide, graded variations in the mature neural architecture. Consistent with emerging anatomical data in several species, the model predicts (i) a greater complement of neurons per cortical column in the later-developing, posterior regions of intermediate and large cortices, (ii) that the extent of variation across a cortex increases with cortex size, reaching fivefold or greater in primates, and (iii) that when the number of neurons per cortical column increases, whether across species or within a given cortex, it is the later-developing superficial layers of the cortex which accommodate those additional neurons. We posit that these graded features of the cortex have computational and functional significance, and so must be subject to evolutionary selection.

Keywords: cerebral cortex; development; evolution; mathematical modeling; neurogenesis.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Fig. 1.
Fig. 1.
(A) Estimates for the founder population (dashed line) and total neuronal output of the ventricular zone (solid line) as a function of cortex score sc. The solid symbols represent adult cortical neuron counts in rodents (blue disks) and primates (red squares), each multiplied by a factor of 1.5 to allow for the large fraction of neurons that dies after reaching the cortex. The open symbols represent empirical counts of cells in the precursor pools of rodents (blue circles), carnivores (green triangles), and a sheep (orange diamond). The ratio of the two fitted functions gives an estimate of the amplification factor for a given cortex score. See SI Appendix, Tables S1 and S2 for data and sources. (B) To estimate the proportion of neurons whose adult location is in the upper layers (II–IV) versus lower layers (V and VI) of the cortex, a linear regression of the proportion as assessed in six rodents (blue disks), three carnivores (green triangles), and five primates (red squares) against cortex score sc is carried out. For species and sources, see SI Appendix, Table S3.
Fig. 2.
Fig. 2.
Model neuronal output over embryonic days, across the cortex for mouse (Left) cortex score 0.701, ferret (Middle) cortex score 1.714, and macaque (Right) cortex score 2.472. Model parameters for (A) the quit fraction, (B) the cell-cycle duration in hours, and (C) the death rate in the ventricular zone result in trajectories for the precursor pool (D) and the total neuronal population (E) given on a log scale as a multiple of the initial precursor populations for each species. The thick red line in each case corresponds to the later-developing (typically posterior) regions, compared with the earlier progressing (typically anterior) cortex, represented by the thinner yellow line. The cross-cortex gradient in neuronal output is predicted to be more pronounced in those species with a larger cortex. An alternative set of parameters, represented by dashed lines in A and B, is tested for macaque only; the resultant populations are given by the dashed lines in D and E. Empirical evidence suggests a nonmonotonic trajectory for q(t) and c(t) in macaque, although the persistence of a large precursor pool in late neurogenesis, as implied by the present model, is not expected; see Discussion.
Fig. 3.
Fig. 3.
Model-predicted interspecies and intracortex differences in the timing, extent, and layer assignment of cortical neuron output. Shown here are the predicted amounts of neuronal output (in terms of amplification of a unit precursor pool) across the anterior–posterior (spatial) axis of the cortex over the course of embryonic neurogenesis (time axis) for three different cortex scores (1.0, similar to a rat; 1.75, similar to a ferret; 2.5, similar to a macaque monkey). The larger cortices have a longer developmental interval, produce orders of magnitude more neurons in total and, in particular, have a greater complement of upper layer neurons. The anterior–posterior gradient in neuron number becomes more pronounced in larger cortices and it is the upper layers which accommodate the greater proportion of the increasing quantities of neurons. Rat and ferret images courtesy of iStockphoto/GlobalP. Macaque image courtesy of iStockphoto/JackF.
Fig. 4.
Fig. 4.
Using a two-factor model (location and an indicator for primary or nonprimary area) of neuronal density is better than a location-only model. In the two-factor model, primary sensory areas have a neuronal density 26% higher than would a nonprimary sensory area at the same location (the dashed line is 1.26× the base level density indicated by the solid line). The origin of the spatial “principal” axis is at the posterior medial pole of the flattened cortex and it extends toward the anterior lateral pole.
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