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

A stochastic model for neural progenitor dynamics in the mouse cerebral cortex

We have designed a stochastic model of embryonic neurogenesis in the mouse cerebral cortex, using the formalism of compound Poisson processes. The model accounts for the dynamics of different progenitor cell types and neurons. The expectation and variance of the cell number of each type are derived analytically and illustrated through numerical simulations. The effects of stochastic transition rates between cell types, and stochastic duration of the cell division cycle have been investigated sequentially. The model does not only predict the number of neurons, but also their spatial distribution into deeper and upper cortical layers. The model outputs are consistent with experimental data providing the number of neurons and intermediate progenitors according to embryonic age in control and mutant situations.

Mathematics of neural stem cells: Linking data and processes

Adult stem cells are described as a discrete population of cells that stand at the top of a hierarchy of progressively differentiating cells. Through their unique ability to self-renew and differentiate, they regulate the number of end-differentiated cells that contribute to tissue physiology. The question of how discrete, continuous, or reversible the transitions through these hierarchies are and the precise parameters that determine the ultimate performance of stem cells in adulthood are the subject of intense research. In this review, we explain how mathematical modelling has improved the mechanistic understanding of stem cell dynamics in the adult brain. We also discuss how single-cell sequencing has influenced the understanding of cell states or cell types. Finally, we discuss how the combination of single-cell sequencing technologies and mathematical modelling provides a unique opportunity to answer some burning questions in the field of stem cell biology.

Mechanical constraints to cell-cycle progression in a pseudostratified epithelium

As organs and tissues approach their normal size during development or regeneration, growth slows down, and cell proliferation progressively comes to a halt. Among the various processes suggested to contribute to growth termination,1-10 mechanical feedback, perhaps via adherens junctions, has been suggested to play a role.11-14 However, since adherens junctions are only present in a narrow plane of the subapical region, other structures are likely needed to sense mechanical stresses along the apical-basal (A-B) axis, especially in a thick pseudostratified epithelium. This could be achieved by nuclei, which have been implicated in mechanotransduction in tissue culture.15 In addition, mechanical constraints imposed by nuclear crowding and spatial confinement could affect interkinetic nuclear migration (IKNM),16 which allows G2 nuclei to reach the apical surface, where they normally undergo mitosis.17-25 To explore how mechanical constraints affect IKNM, we devised an individual-based model that treats nuclei as deformable objects constrained by the cell cortex and the presence of other nuclei. The model predicts changes in the proportion of cell-cycle phases during growth, which we validate with the cell-cycle phase reporter FUCCI (Fluorescent Ubiquitination-based Cell Cycle Indicator).26 However, this model does not preclude indefinite growth, leading us to postulate that nuclei must migrate basally to access a putative basal signal required for S phase entry. With this refinement, our updated model accounts for the observed progressive slowing down of growth and explains how pseudostratified epithelia reach a stereotypical thickness upon completion of growth.

Modeling viral dynamics in SARS-CoV-2 infection based on differential equations and numerical analysis

Computational modeling and simulation of viral dynamics would explain the pathogenesis for any virus. Such computational attempts have been successfully made to predict and control HIV-1 or hepatitis B virus. However, the dynamics for SARS-CoV-2 has not been adequately investigated. The purpose of this research is to propose different SARS-CoV-2 dynamics models based on differential equations and numerical analysis towards distilling the models to explain the mechanism of SARS-CoV-2 pathogenesis. The proposed four models formalize the dynamical system of SARS-CoV-2 infection, which consists of host cells and viral particles. These models undergo numerical analysis, including sensitivity analysis and stability analysis. Based on the sensitivity indices of the four models' parameters, the four models are simplified into two models. In advance of the following calibration experiments, the eigenvalues of the Jacobian matrices of these two models are calculated, thereby guaranteeing that any solutions are stable. Then, the calibration experiments fit the simulated data sequences of the two models to two observed data sequences, SARS-CoV-2 viral load in mild cases and that in severe cases. Comparing the estimated parameters in mild cases and severe cases indicates that cell-to-cell transmission would significantly correlate to the COVID-19 severity. These experiments for modeling and simulation provide plausible computational models for the SARS-CoV-2 dynamics, leading to further investigation for identifying the essential factors in severe cases.

The Multifaceted Roles of Primary Cilia in the Development of the Cerebral Cortex

The primary cilium, a microtubule based organelle protruding from the cell surface and acting as an antenna in multiple signaling pathways, takes center stage in the formation of the cerebral cortex, the part of the brain that performs highly complex neural tasks and confers humans with their unique cognitive capabilities. These activities require dozens of different types of neurons that are interconnected in complex ways. Due to this complexity, corticogenesis has been regarded as one of the most complex developmental processes and cortical malformations underlie a number of neurodevelopmental disorders such as intellectual disability, autism spectrum disorders, and epilepsy. Cortical development involves several steps controlled by cell–cell signaling. In fact, recent findings have implicated cilia in diverse processes such as neurogenesis, neuronal migration, axon pathfinding, and circuit formation in the developing cortex. Here, we will review recent advances on the multiple roles of cilia during cortex formation and will discuss the implications for a better understanding of the disease mechanisms underlying neurodevelopmental disorders.

Cilia, ciliopathies and hedgehog-related forebrain developmental disorders

Development of the forebrain critically depends on the Sonic Hedgehog (Shh) signaling pathway, as illustrated in humans by the frequent perturbation of this pathway in holoprosencephaly, a condition defined as a defect in the formation of midline structures of the forebrain and face. The Shh pathway requires functional primary cilia, microtubule-based organelles present on virtually every cell and acting as cellular antennae to receive and transduce diverse chemical, mechanical or light signals. The dysfunction of cilia in humans leads to inherited diseases called ciliopathies, which often affect many organs and show diverse manifestations including forebrain malformations for the most severe forms. The purpose of this review is to provide the reader with a framework to understand the developmental origin of the forebrain defects observed in severe ciliopathies with respect to perturbations of the Shh pathway. We propose that many of these defects can be interpreted as an imbalance in the ratio of activator to repressor forms of the Gli transcription factors, which are effectors of the Shh pathway. We also discuss the complexity of ciliopathies and their relationships with forebrain disorders such as holoprosencephaly or malformations of cortical development, and emphasize the need for a closer examination of forebrain defects in ciliopathies, not only through the lens of animal models but also taking advantage of the increasing potential of the research on human tissues and organoids.

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 transient role of the ciliary gene Inpp5e in controlling direct versus indirect neurogenesis in cortical development

During the development of the cerebral cortex, neurons are generated directly from radial glial cells or indirectly via basal progenitors. The balance between these division modes determines the number and types of neurons formed in the cortex thereby affecting cortical functioning. Here, we investigate the role of primary cilia in controlling the decision between forming neurons directly or indirectly. We show that a mutation in the ciliary gene Inpp5e leads to a transient increase in direct neurogenesis and subsequently to an overproduction of layer V neurons in newborn mice. Loss of Inpp5e also affects ciliary structure coinciding with reduced Gli3 repressor levels. Genetically restoring Gli3 repressor rescues the decreased indirect neurogenesis in Inpp5e mutants. Overall, our analyses reveal how primary cilia determine neuronal subtype composition of the cortex by controlling direct versus indirect neurogenesis. These findings have implications for understanding cortical malformations in ciliopathies with INPP5E mutations.