Morphogenesis and morphometry of brain folding patterns across species
- School of Engineering and Applied Sciences, Harvard University, United States
- Department of Mathematics, The Chinese University of Hong Kong, Hong Kong
- Institut Pasteur, Université Paris Cité, Unité de Neuroanatomie Appliquée et Théorique, France
- Department of Physics, Harvard University, United States
- Department of Organismic and Evolutionary Biology, Harvard University, United States
Figures
Figure 1
The diversity of the cortical morphologies and developmental processes across species.
(a) Phylogenetic relationship of species. Adapted from Takahata et al., 2012; Heuer et al., 2019. Typical real brain surfaces of ferrets and primates are presented. Color represents mean curvature. Scale bars: 1 cm (estimated from Herculano-Houzel, 2009). (b) Stained sections of mature brain tissue from ferret, rhesus macaque, and human. Scale bar: 10 mm. Adapted from Noctor, 2016. (c–e) 3D reconstruction of cortical surfaces of ferret, macaque, and human brains from fetal to adult. (c) Ferret: postnatal day 4, 10, 17, and adult maturation (Barnette et al., 2009). Scale bar: 1 cm; (d) Macaque: gestation day 85, 110, 135 (Liu et al., 2020), and adult maturation (Calabrese et al., 2015). Scale bar: 1 cm; (e) Human: gestation day 175 (week 25), 210 (week 30), 231 (week 33), 273 (week 39), and adult maturation (Barnette et al., 2009). Scale bar: 5 cm.
© 2009, Springer Nature. This figure1/Panel C,E was reprinted with permission from Figure 6 in Barnette et al., 2009. It is not covered by the CC-BY 4.0 license and further reproduction of this panel would need permission from the copyright holder.
Figure 2
Physical gel model that recapitulates the growth-driven morphogenesis mechanism across phylogeny and developmental stages.
(a) A time-lapse of the physical gel brain mimicking macaque brain development starting from G110. (b) Left views of three physical gels mimicking macaque post-gestation day 85, day 110, and day 135 before and after hexane swelling. Scale bar: 1 cm. (c) Comparison of fetal/newborn brain scans and the reconstructed surfaces of swollen physical gels for various species. Scale bars: 1 cm.
Figure 3
Simulations of growing brains of (a) ferret, (b) rhesus macaque, and (c) human.
Starting from smooth fetal/newborn brains, simulations show different gyrification patterns across species. The brains are modeled as soft elastic solids with tangential growth in the gray matter (see Simulations of growing brains for details). Initial 3D geometries are taken from the reconstruction of MRI (see Methods, 3D model reconstruction). Mechanical parameters of growth ratio and cortical thickness are provided in Table 2. Color from dark to light blue represents shape index (as defined in Equation 2) from −1 to 1.
Figure 4
Comparison among real (), simulated (), and gel brains () of ferret, rhesus macaque, and human via morphometric analysis.
(a) 3D cortical surfaces of in vivo, in vitro, and in silico models. Left brain surfaces are provided here. The symmetry of the left and right halves of the brain surfaces is discussed in Videos 2–4, Appendix 1—figures 3 and 4. Three or four major folds of each brain model are highlighted and serve as landmarks. The occipital pole region of macaque brains remains smooth in real and simulated brains. (b) The quasi-conformal disk mapping with landmark matching of cortical surfaces on disk (see Sec Morphometric analysis for details). Blue or red curves represent corresponding landmarks. Color represents shape index (SI, as defined in Equation 2). Similarity indices of each simulated and gel brain surfaces are presented in Table 1. (c) Histogram of shape index of ferret, macaque, and human. Black, red, and blue dots represent the probability of shape index of real, gel, and simulated surfaces, respectively.
Appendix 1—figure 1
Human brain malformation.
(a) MRI scans showing common malformations of cortical development of human brains. Adapted from Oegema et al., 2020 with permission. Left: normal brain. Middle: lissencephaly spectrum with agyria–severe pachygyria (arrows). Right: bilateral frontoparietal polymicrogyria with abnormally small gyri and shallow sulci (arrows). Scale bars: 3 cm (estimated from Mochida, 2009). (b) A non-coding mutation in the GPR56 gene disrupts perisylvian gyri. MRI shows polymicrogyria in the perisylvian area, resulting in a characteristic, thickened appearance. Adapted from Bae et al., 2014 with permission.
Appendix 1—figure 2
Illustration of shape index scale divided into nine categories: spherical cup, trough rut, saddle rut, saddle, saddle ridge, ridge, dome, and spherical cap.
The insets are schematics of local curved surfaces. All outward normals pointing upwards.
Appendix 1—figure 3
The histogram of shape index SI (top two rows) and rescaled mean curvature (bottom two rows) of adult cortical surfaces of ferret, macaque and human.
Insets are real brain surfaces. Colors represent shape index SI (Equation 2 in the main text) or rescaled mean curvature (Equation 3 in the main text).
Appendix 1—figure 4
Comparison among real (), simulated (), and gel brains () of ferret, rhesus macaque, and human via morphometric analysis.
(a) 3D cortical surfaces of in vivo, in silico, and in vitro models. Both left and right cortical surfaces are provided to present the left-right symmetry. (b) The quasi-conformal disk mapping with landmark matching of cortical surfaces on disk. Blue or red curves represent corresponding landmarks. Color represents shape index (SI). Similarity indices of each simulated and gel brain surfaces are presented in Appendix 1—table 2.
Appendix 1—figure 5
Comparison across 10 primate species.
Each species is listed by its common name and scientific name, and accompanied by a picture. Scale bar: 1 cm. Color represents the shape index. Pictures are taken from Wikipedia.
Author response image 1
Left-right similarity index of ferret brains.
Videos
Video 1
Part 1: The swelling processes of physical gel brains of ferret, macaque, and human brains; Part 2: The simulations mimicking the developmental processes of fetal brains of ferret, macaque, and human from smooth surface to the convoluted pattern.
Video 2
Comparison of the real (gray), gel (pink), and simulated (blue) ferret brains.
Color represents shape index.
Video 3
Comparison of the real (gray), gel (pink), and simulated (blue) macaque brains.
Color represents shape index.
Video 4
Comparison of the real (gray), gel (pink), and simulated (blue) human brains.
Color represents shape index.
Tables
Table 1
Similarity index evaluated by comparing the shape index of simulated brains (S), swollen gel brain simulacrums (G), and real brain surfaces (R), calculated with vector p-norm , as described in Equation 4.
| Similarity Index | Simulation-reaGl | Gel-real | Simulation-gel |
|---|---|---|---|
| Ferret (left) | 0.7632 | 0.7307 | 0.7117 |
| Ferret (right) | 0.7339 | 0.7222 | 0.7019 |
| Macaque (left) | 0.7624 | 0.7608 | 0.7512 |
| Macaque (right) | 0.7559 | 0.7632 | 0.7463 |
| Human (left) | 0.6947 | 0.7425 | 0.7000 |
| Human (right) | 0.6909 | 0.7325 | 0.7001 |
Table 2
Parameters for numerical simulations.
| Species | Model | Growth ratio | Stiffness ratio | Normalized cortical thickness |
|---|---|---|---|---|
| Ferret | step-wise | 1.8 | 1 | 0.1−0.005t |
| Macaque | step-wise | 1.8 | 1 | 0.1−0.05t, 0.1−0.1t |
| Human | continuous | 1.8 | 1 | 0.05−0.03t |
Appendix 1—table 1
Gene-related brain properties and malformation.
| Gene | Change in geometry or physical properties | Malformations and dysfunctions |
|---|---|---|
| foxp2 Barresi et al., 2024; Lai et al., 2003 | Reduced gray matter density (thinner cortex) in Broca’s area | Polymicrogyria, speech, and language disorder |
| SP0535 Qi et al., 2023 | Increased expansion of neural progenitors | improved cognitive ability and working memory |
| Cdk5 Magen et al., 2015; Shinmyo et al., 2017 | Abnormalities in neuronal migration and organization | Lissencephaly with cerebellar hypoplasia (LCH) |
| GPR56 Bae et al., 2014; Luo et al., 2011 | Neural progenitors migration | Bilateral frontoparietal polymicrogyria |
| PAFAH1B1, RELN, TUB1A1, DCX, ARX, NDE1 Koenig et al., 2021; Verrotti et al., 2010 | Increased cortical thickness | Lissencephaly |
Appendix 1—table 2
Similarity index (main text, Equation 4) evaluated by rescaled mean curvature of simulated and gel brain surfaces with comparison to the real brain surfaces, calculated with different vector p-norm: , and .
| Similarity index | Simulated | Gel | ||||
|---|---|---|---|---|---|---|
| 1 | 2 | ∞ | 1 | 2 | ∞ | |
| Ferret (left) | 0.8188 | 0.7541 | 1 | 0.7448 | 0.6746 | 1 |
| Ferret (right) | 0.7733 | 0.7005 | 1 | 0.7533 | 0.6887 | 1 |
| Macaque (left) | 0.6886 | 0.6039 | 1 | 0.7658 | 0.7086 | 1 |
| Macaque (right) | 0.6832 | 0.5994 | 1 | 0.7578 | 0.6989 | 1 |
| Human (left) | 0.6056 | 0.5090 | 1 | 0.7037 | 0.6540 | 1 |
| Human (right) | 0.5911 | 0.4909 | 1 | 0.7028 | 0.6525 | 1 |
Author response table 1
Left-right similarity index evaluated by comparing the shape index of ferret brains, calculated with vector P-NORM p=2,.
| real | gel | simu |
|---|---|---|
| 0.5754 | 0.7014 | 0.5868 |
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Morphogenesis and morphometry of brain folding patterns across species
eLife 14:RP107138.
https://doi.org/10.7554/eLife.107138.3
