Mathematical Modeling of Cortical Neurogenesis Reveals that the Founder Population does not Necessarily Scale with Neurogenic Output

The Principle of Cortical Development and Evolution

Human's robust cognitive abilities, including creativity and language, are made possible, at least in large part, by evolutionary changes made to the cerebral cortex. This paper reviews the biology and evolution of mammalian cortical radial glial cells (primary neural stem cells) and introduces the concept that a genetically step wise process, based on a core molecular pathway already in use, is the evolutionary process that has molded cortical neurogenesis. The core mechanism, which has been identified in our recent studies, is the extracellular signal-regulated kinase (ERK)-bone morphogenic protein 7 (BMP7)-GLI3 repressor form (GLI3R)-sonic hedgehog (SHH) positive feedback loop. Additionally, I propose that the molecular basis for cortical evolutionary dwarfism, exemplified by the lissencephalic mouse which originated from a larger gyrencephalic ancestor, is an increase in SHH signaling in radial glia, that antagonizes ERK-BMP7 signaling. Finally, I propose that: (1) SHH signaling is not a key regulator of primate cortical expansion and folding; (2) human cortical radial glial cells do not generate neocortical interneurons; (3) human-specific genes may not be essential for most cortical expansion. I hope this review assists colleagues in the field, guiding research to address gaps in our understanding of cortical development and evolution.

Approaches to embryonic neurodevelopment: from neural cell to neural tube formation through mathematical models

The development of the human central nervous system initiates in the early embryonic period until long after delivery. It has been shown that several neurological and neuropsychiatric diseases originate from prenatal incidents. Mathematical models offer a direct way to understand neurodevelopmental processes better. Mathematical modelling of neurodevelopment during the embryonic period is challenging in terms of how to 'Approach', how to initiate modelling and how to propose the appropriate equations that fit the underlying dynamics of neurodevelopment during the embryonic period while including the variety of elements that are built-in naturally during the process of neurodevelopment. It is imperative to answer where and how to start modelling; in other words, what is the appropriate 'Approach'? Therefore, one objective of this study was to tackle the mathematical issue broadly from different aspects and approaches. The approaches were divided into three embryonic categories: cell division, neural tube growth and neural plate growth. We concluded that the neural plate growth approach provides a suitable platform for simulation of brain formation/neurodevelopment compared to cell division and neural tube growth. We devised a novel equation and designed algorithms that include geometrical and topological algorithms that could fit most of the necessary elements of the neurodevelopmental process during the embryonic period. Hence, the proposed equations and defined mathematical structure would be a platform to generate an artificial neural network that autonomously grows and develops.

ERK signaling expands mammalian cortical radial glial cells and extends the neurogenic period

The molecular basis for cortical expansion during evolution remains largely unknown. Here, we report that fibroblast growth factor (FGF)-extracellular signal-regulated kinase (ERK) signaling promotes the self-renewal and expansion of cortical radial glial (RG) cells. Furthermore, FGF-ERK signaling induces bone morphogenic protein 7 (Bmp7) expression in cortical RG cells, which increases the length of the neurogenic period. We demonstrate that ERK signaling and Sonic Hedgehog (SHH) signaling mutually inhibit each other in cortical RG cells. We provide evidence that ERK signaling is elevated in cortical RG cells during development and evolution. We propose that the expansion of the mammalian cortex, notably in human, is driven by the ERK-BMP7-GLI3R signaling pathway in cortical RG cells, which participates in a positive feedback loop through antagonizing SHH signaling. We also propose that the relatively short cortical neurogenic period in mice is partly due to mouse cortical RG cells receiving higher SHH signaling that antagonizes ERK signaling.

The Phylotypic Brain of Vertebrates, from Neural Tube Closure to Brain Diversification

BACKGROUND

The phylotypic or intermediate stages are thought to be the most evolutionary conserved stages throughout embryonic development. The contrast with divergent early and later stages derived from the concept of the evo-devo hourglass model. Nonetheless, this developmental constraint has been studied as a whole embryo process, not at organ level. In this review, we explore brain development to assess the existence of an equivalent brain developmental hourglass. In the specific case of vertebrates, we propose to split the brain developmental stages into: (1) Early: Neurulation, when the neural tube arises after gastrulation. (2) Intermediate: Brain patterning and segmentation, when the neuromere identities are established. (3) Late: Neurogenesis and maturation, the stages when the neurons acquire their functionality. Moreover, we extend this analysis to other chordates brain development to unravel the evolutionary origin of this evo-devo constraint.

SUMMARY

Based on the existing literature, we hypothesise that a major conservation of the phylotypic brain might be due to the pleiotropy of the inductive regulatory networks, which are predominantly expressed at this stage. In turn, earlier stages such as neurulation are rather mechanical processes, whose regulatory networks seem to adapt to environment or maternal geometries. The later stages are also controlled by inductive regulatory networks, but their effector genes are mostly tissue-specific and functional, allowing diverse developmental programs to generate current brain diversity. Nonetheless, all stages of the hourglass are highly interconnected: divergent neurulation must have a vertebrate shared end product to reproduce the vertebrate phylotypic brain, and the boundaries and transcription factor code established during the highly conserved patterning will set the bauplan for the specialised and diversified adult brain.

KEY MESSAGES

The vertebrate brain is conserved at phylotypic stages, but the highly conserved mechanisms that occur during these brain mid-development stages (Inducing Regulatory Networks) are also present during other stages. Oppositely, other processes as cell interactions and functional neuronal genes are more diverse and majoritarian in early and late stages of development, respectively. These phenomena create an hourglass of transcriptomic diversity during embryonic development and evolution, with a really conserved bottleneck that set the bauplan for the adult brain around the phylotypic stage.

Toward a better understanding of how a gyrified brain develops

The size and shape of the cerebral cortex have changed dramatically across evolution. For some species, the cortex remains smooth (lissencephalic) throughout their lifetime, while for other species, including humans and other primates, the cortex increases substantially in size and becomes folded (gyrencephalic). A folded cortex boasts substantially increased surface area, cortical thickness, and neuronal density, and it is therefore associated with higher-order cognitive abilities. The mechanisms that drive gyrification in some species, while others remain lissencephalic despite many shared neurodevelopmental features, have been a topic of investigation for many decades, giving rise to multiple perspectives of how the gyrified cerebral cortex acquires its unique shape. Recently, a structurally unique germinal layer, known as the outer subventricular zone, and the specialized cell type that populates it, called basal radial glial cells, were identified, and these have been shown to be indispensable for cortical expansion and folding. Transcriptional analyses and gene manipulation models have provided an invaluable insight into many of the key cellular and genetic drivers of gyrification. However, the degree to which certain biomechanical, genetic, and cellular processes drive gyrification remains under investigation. This review considers the key aspects of cerebral expansion and folding that have been identified to date and how theories of gyrification have evolved to incorporate this new knowledge.

BMP7 expression in mammalian cortical radial glial cells increases the length of the neurogenic period

The seat of human intelligence is the human cerebral cortex, which is responsible for our exceptional cognitive abilities. Identifying principles that lead to the development of the large-sized human cerebral cortex will shed light on what makes the human brain and species so special. The remarkable increase in the number of human cortical pyramidal neurons and the size of the human cerebral cortex is mainly because human cortical radial glial cells, primary neural stem cells in the cortex, generate cortical pyramidal neurons for more than 130 days, whereas the same process takes only about 7 days in mice. The molecular mechanisms underlying this difference are largely unknown. Here, we found that bone morphogenic protein 7 (BMP7) is expressed by increasing the number of cortical radial glial cells during mammalian evolution (mouse, ferret, monkey, and human). BMP7 expression in cortical radial glial cells promotes neurogenesis, inhibits gliogenesis, and thereby increases the length of the neurogenic period, whereas Sonic Hedgehog (SHH) signaling promotes cortical gliogenesis. We demonstrate that BMP7 signaling and SHH signaling mutually inhibit each other through regulation of GLI3 repressor formation. We propose that BMP7 drives the evolutionary expansion of the mammalian cortex by increasing the length of the neurogenic period.

Non-uniform temporal scaling of developmental processes in the mammalian cortex

The time that it takes the brain to develop is highly variable across animals. Although staging systems equate major developmental milestones between mammalian species, it remains unclear how distinct processes of cortical development scale within these timeframes. Here, we compare the timing of cortical development in two mammals of similar size but different developmental pace: eutherian mice and marsupial fat-tailed dunnarts. Our results reveal that the temporal relationship between cell birth and laminar specification aligns to equivalent stages between these species, but that migration and axon extension do not scale uniformly according to the developmental stages, and are relatively more advanced in dunnarts. We identify a lack of basal intermediate progenitor cells in dunnarts that likely contributes in part to this timing difference. These findings demonstrate temporal limitations and differential plasticity of cortical developmental processes between similarly sized Therians and provide insight into subtle temporal changes that may have contributed to the early diversification of the mammalian brain.

Ubiquitous lognormal distribution of neuron densities in mammalian cerebral cortex

Numbers of neurons and their spatial variation are fundamental organizational features of the brain. Despite the large corpus of cytoarchitectonic data available in the literature, the statistical distributions of neuron densities within and across brain areas remain largely uncharacterized. Here, we show that neuron densities are compatible with a lognormal distribution across cortical areas in several mammalian species, and find that this also holds true within cortical areas. A minimal model of noisy cell division, in combination with distributed proliferation times, can account for the coexistence of lognormal distributions within and across cortical areas. Our findings uncover a new organizational principle of cortical cytoarchitecture: the ubiquitous lognormal distribution of neuron densities, which adds to a long list of lognormal variables in the brain.

Accounting for dimensional differences in stochastic domain invasion with applications to precancerous cell removal

We consider a specific form of domain invasion that is an abstraction of pancreatic tissue eliminating precancerous mutant cells through juxtacrine signalling. The model is explored discretely, continuously, stochastically and deterministically, highlighting unforeseen nonlinear dependencies on the dimension of the solution domain. Specifically, stochastically simulated populations invade with a dimension dependent wave speed that can be over twice as fast as their deterministic analogues. Although the wave speed can be analytically derived in the cases of small domains, the probabilistic state space grows exponentially and, thus, we use numeric simulation and curve fitting to predict limiting dynamics.

Maximum Entropy Principle Underlies Wiring Length Distribution in Brain Networks

A brain network comprises a substantial amount of short-range connections with an admixture of long-range connections. The portion of long-range connections in brain networks is observed to be quantitatively dissimilar across species. It is hypothesized that the length of connections is constrained by the spatial embedding of brain networks, yet fundamental principles that underlie the wiring length distribution remain unclear. By quantifying the structural diversity of a brain network using Shannon's entropy, here we show that the wiring length distribution across multiple species-including Drosophila, mouse, macaque, human, and C. elegans-follows the maximum entropy principle (MAP) under the constraints of limited wiring material and the spatial locations of brain areas or neurons. In addition, by considering stochastic axonal growth, we propose a network formation process capable of reproducing wiring length distributions of the 5 species, thereby implementing MAP in a biologically plausible manner. We further develop a generative model incorporating MAP, and show that, for the 5 species, the generated network exhibits high similarity to the real network. Our work indicates that the brain connectivity evolves to be structurally diversified by maximizing entropy to support efficient interareal communication, providing a potential organizational principle of brain networks.

Evolution: Does More Time Buy More Neurons?

Brain expansion and increased neuronal number are hallmarks of cortical evolution, particularly in humans. A new study establishes a link between the length of gestation, neurogenesis, the maternal environment, and key features associated with more complex brains.

Length of the Neurogenic Period-A Key Determinant for the Generation of Upper-Layer Neurons During Neocortex Development and Evolution

The neocortex, a six-layer neuronal brain structure that arose during the evolution of, and is unique to, mammals, is the seat of higher order brain functions responsible for human cognitive abilities. Despite its recent evolutionary origin, it shows a striking variability in size and folding complexity even among closely related mammalian species. In most mammals, cortical neurogenesis occurs prenatally, and its length correlates with the length of gestation. The evolutionary expansion of the neocortex, notably in human, is associated with an increase in the number of neurons, particularly within its upper layers. Various mechanisms have been proposed and investigated to explain the evolutionary enlargement of the human neocortex, focussing in particular on changes pertaining to neural progenitor types and their division modes, driven in part by the emergence of human-specific genes with novel functions. These led to an amplification of the progenitor pool size, which affects the rate and timing of neuron production. In addition, in early theoretical studies, another mechanism of neocortex expansion was proposed—the lengthening of the neurogenic period. A critical role of neurogenic period length in determining neocortical neuron number was subsequently supported by mathematical modeling studies. Recently, we have provided experimental evidence in rodents directly supporting the mechanism of extending neurogenesis to specifically increase the number of upper-layer cortical neurons. Moreover, our study examined the relationship between cortical neurogenesis and gestation, linking the extension of the neurogenic period to the maternal environment. As the exact nature of factors promoting neurogenic period prolongation, as well as the generalization of this mechanism for evolutionary distinct lineages, remain elusive, the directions for future studies are outlined and discussed.

A Connectomic Hypothesis for the Hominization of the Brain

Cognitive abilities of the human brain, including language, have expanded dramatically in the course of our recent evolution from nonhuman primates, despite only minor apparent changes at the gene level. The hypothesis we propose for this paradox relies upon fundamental features of human brain connectivity, which contribute to a characteristic anatomical, functional, and computational neural phenotype, offering a parsimonious framework for connectomic changes taking place upon the human-specific evolution of the genome. Many human connectomic features might be accounted for by substantially increased brain size within the global neural architecture of the primate brain, resulting in a larger number of neurons and areas and the sparsification, increased modularity, and laminar differentiation of cortical connections. The combination of these features with the developmental expansion of upper cortical layers, prolonged postnatal brain development, and multiplied nongenetic interactions with the physical, social, and cultural environment gives rise to categorically human-specific cognitive abilities including the recursivity of language. Thus, a small set of genetic regulatory events affecting quantitative gene expression may plausibly account for the origins of human brain connectivity and cognition.

Fate restrictions in embryonic neural progenitors

The vertebrate central nervous system (CNS) is a fantastically complex organ composed of dozens of cell types within the neural and glial lineages. Its organization is laid down during development, through the localized and sequential production of subsets of neurons with specific identities. The principles and mechanisms that underlie the timely production of adequate classes of cells are only partially understood. Recent advances in molecular profiling describe the developmental trajectories leading to this amazing cellular diversity and provide us with cell atlases of an unprecedented level of precision. Yet, some long-standing questions pertaining to lineage relationships between neural progenitor cells and their differentiated progeny remain unanswered. Here, we discuss questions related to proliferation potential, timing of fate choices and restriction of neuronal output potential of individual CNS progenitors through the lens of lineage relationship. Unlocking methodological barriers will be essential to accurately describe CNS development at a cellular resolution.

Population Dynamics and Neuronal Polyploidy in the Developing Neocortex

The mammalian neocortex is composed of different subtypes of projection neurons that are generated sequentially during embryogenesis by differentiation of neural progenitors. While molecular mechanisms that control neuronal production in the developing neocortex have been extensively studied, the dynamics and absolute numbers of the different progenitor and neuronal populations are still poorly characterized. Here, we describe a medium throughput approach based on flow cytometry and well-known identity markers of cortical subpopulations to collect quantitative data over the course of mouse neocortex development. We collected a complete dataset in a physiological developmental context on two progenitor and two neuron populations, including relative proportions and absolute numbers. Our study reveals unexpected total numbers of Tbr2+ progenitors. In addition, we show that polyploid neurons are present throughout neocortex development.

A common rule governing differentiation kinetics of mouse cortical progenitors

The balance between proliferation and differentiation of stem cells and progenitors determines the size of an adult brain region. While the molecular mechanisms regulating proliferation and differentiation of cortical progenitors have been intensively studied, an analysis of the kinetics of progenitor choice between self-renewal and differentiation in vivo is, due to the technical difficulties, still unknown. Here we established a descriptive mathematical model to estimate the probability of self-renewal or differentiation of cortical progenitor behaviors in vivo, a variable we have termed the expansion coefficient. We have applied the model, one which depends only on experimentally measured parameters, to the developing mouse cortex where the expansive neuroepithelial cells and neurogenic radial glial progenitors are coexisting. Surprisingly, we found that the expansion coefficients of both neuroepithelium cells and radial glial progenitors follow the same developmental trajectory during cortical development, suggesting a common rule governing self-renewal/differentiation behaviors in mouse cortical progenitor differentiation.

A Primate-Specific Isoform of PLEKHG6 Regulates Neurogenesis and Neuronal Migration

The mammalian neocortex has undergone remarkable changes through evolution. A consequence of such rapid evolutionary events could be a trade-off that has rendered the brain susceptible to certain neurodevelopmental and neuropsychiatric conditions. We analyzed the exomes of 65 patients with the structural brain malformation periventricular nodular heterotopia (PH). De novo coding variants were observed in excess in genes defining a transcriptomic signature of basal radial glia, a cell type linked to brain evolution. In addition, we located two variants in human isoforms of two genes that have no ortholog in mice. Modulating the levels of one of these isoforms for the gene PLEKHG6 demonstrated its role in regulating neuroprogenitor differentiation and neuronal migration via RhoA, with phenotypic recapitulation of PH in human cerebral organoids. This suggests that this PLEKHG6 isoform is an example of a primate-specific genomic element supporting brain development.

A multiscale mathematical model of cell dynamics during neurogenesis in the mouse cerebral cortex

Background

Neurogenesis in the murine cerebral cortex involves the coordinated divisions of two main types of progenitor cells, whose numbers, division modes and cell cycle durations set up the final neuronal output. To understand the respective roles of these factors in the neurogenesis process, we combine experimental in vivo studies with mathematical modeling and numerical simulations of the dynamics of neural progenitor cells. A special focus is put on the population of intermediate progenitors (IPs), a transit amplifying progenitor type critically involved in the size of the final neuron pool.

Results

A multiscale formalism describing IP dynamics allows one to track the progression of cells along the subsequent phases of the cell cycle, as well as the temporal evolution of the different cell numbers. Our model takes into account the dividing apical progenitors (AP) engaged into neurogenesis, both neurogenic and proliferative IPs, and the newborn neurons. The transfer rates from one population to another are subject to the mode of division (proliferative, or neurogenic) and may be time-varying. The model outputs are successfully fitted to experimental cell numbers from mouse embryos at different stages of cortical development, taking into account IPs and neurons, in order to adjust the numerical parameters. We provide additional information on cell kinetics, such as the mitotic and S phase indexes, and neurogenic fraction.

Conclusions

Applying the model to a mouse mutant for Ftm/Rpgrip1l, a gene involved in human ciliopathies with severe brain abnormalities, reveals a shortening of the neurogenic period associated with an increased influx of newborn IPs from apical progenitors at mid-neurogenesis. Our model can be used to study other mouse mutants with cortical neurogenesis defects and can be adapted to study the importance of progenitor dynamics in cortical evolution and human diseases.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-3018-8) contains supplementary material, which is available to authorized users.

New insights into the development of the human cerebral cortex

The cerebral cortex constitutes more than half the volume of the human brain and is presumed to be responsible for the neuronal computations underlying complex phenomena, such as perception, thought, language, attention, episodic memory and voluntary movement. Rodent models are extremely valuable for the investigation of brain development, but cannot provide insight into aspects that are unique or highly derived in humans. Many human psychiatric and neurological conditions have developmental origins but cannot be studied adequately in animal models. The human cerebral cortex has some unique genetic, molecular, cellular and anatomical features, which need to be further explored. The Anatomical Society devoted its summer meeting to the topic of Human Brain Development in June 2018 to tackle these important issues. The meeting was organized by Gavin Clowry (Newcastle University) and Zoltán Molnár (University of Oxford), and held at St John's College, Oxford. The participants provided a broad overview of the structure of the human brain in the context of scaling relationships across the brains of mammals, conserved principles and recent changes in the human lineage. Speakers considered how neuronal progenitors diversified in human to generate an increasing variety of cortical neurons. The formation of the earliest cortical circuits of the earliest generated neurons in the subplate was discussed together with their involvement in neurodevelopmental pathologies. Gene expression networks and susceptibility genes associated to neurodevelopmental diseases were discussed and compared with the networks that can be identified in organoids developed from induced pluripotent stem cells that recapitulate some aspects of in vivo development. New views were discussed on the specification of glutamatergic pyramidal and γ-aminobutyric acid (GABA)ergic interneurons. With the advancement of various in vivo imaging methods, the histopathological observations can be now linked to in vivo normal conditions and to various diseases. Our review gives a general evaluation of the exciting new developments in these areas. The human cortex has a much enlarged association cortex with greater interconnectivity of cortical areas with each other and with an expanded thalamus. The human cortex has relative enlargement of the upper layers, enhanced diversity and function of inhibitory interneurons and a highly expanded transient subplate layer during development. Here we highlight recent studies that address how these differences emerge during development focusing on diverse facets of our evolution.

A mathematical insight into cell labelling experiments for clonal analysis

Studying the progression of the proliferative and differentiative patterns of neural stem cells at the individual cell level is crucial to the understanding of cortex development and how the disruption of such patterns can lead to malformations and neurodevelopmental diseases. However, our understanding of the precise lineage progression programme at single-cell resolution is still incomplete due to the technical variations in lineage-tracing approaches. One of the key challenges involves developing a robust theoretical framework in which we can integrate experimental observations and introduce correction factors to obtain a reliable and representative description of the temporal modulation of proliferation and differentiation. In order to obtain more conclusive insights, we carry out virtual clonal analysis using mathematical modelling and compare our results against experimental data. Using a dataset obtained with Mosaic Analysis with Double Markers, we illustrate how the theoretical description can be exploited to interpret and reconcile the disparity between virtual and experimental results.

Theoretical Models of Neural Development

Constructing a functioning nervous system requires the precise orchestration of a vast array of mechanical, molecular, and neural-activity-dependent cues. Theoretical models can play a vital role in helping to frame quantitative issues, reveal mathematical commonalities between apparently diverse systems, identify what is and what is not possible in principle, and test the abilities of specific mechanisms to explain the data. This review focuses on the progress that has been made over the last decade in our theoretical understanding of neural development.

Time to change your mind? Modelling transient properties of cortex formation highlights the importance of evolving cell division strategies

The successful development of the mammalian cerebral neocortex is linked to numerous cognitive functions such as language, voluntary movement, and episodic memory. Neocortex development occurs when neural progenitor cells divide and produce neurons. Critically, although the progenitor cells are able to self-renew they do not reproduce themselves endlessly. Hence, to fully understand the development of the neocortex we are faced with the challenge of understanding temporal changes in cell division strategy. Our approach to modelling neuronal production uses non-autonomous ordinary differential equations and allows us to use a ternary coordinate system in order to define a strategy space, through which we can visualise evolving cell division strategies. Using this strategy space, we fit the known data and use approximate Bayesian computation to predict the founding progenitor population sizes, currently unavailable in the experimental literature. Counter-intuitively, we show that humans can generate a larger number of neurons than a macaque's even when starting with a smaller number of progenitor cells. Accompanying the article is a self-contained piece of software, which provides the reader with immediate simulated results that will aid their intuition. The software can be found at www.dpag.ox.ac.uk/team/noemi-picco.