During epithelial tissue morphogenesis, developmental progenitor cells undergo dynamic adhesive and cytoskeletal remodeling to trigger proliferation and migration. Transcriptional mechanisms that restrict such mild form of epithelial plasticity to maintain lineage-restricted differentiation in committed epithelial tissues are poorly understood. Here we report that simultaneous ablation of transcriptional repressor-encoding Ovol1 and Ovol2 results in expansion and blocked terminal differentiation of embryonic epidermal progenitor cells. Conversely, mice overexpressing Ovol2 in their skin epithelia exhibit precocious differentiation accompanied by smaller progenitor cell compartments. We show that Ovol1/2-deficient epidermal cells fail to undertake α-catenin–driven actin cytoskeletal reorganization and adhesive maturation, and exhibit changes that resemble epithelial-to-mesenchymal transition (EMT). Remarkably, these alterations as well as defective terminal differentiation are reversed upon depletion of EMT-promoting transcriptional factor Zeb1. Collectively, our findings reveal Ovol-Zeb1-α-catenin sequential repression and highlight functions of Ovol as gatekeepers of epithelial adhesion and differentiation by inhibiting progenitor-like traits and epithelial plasticity.

For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. For reaction-diffusion systems with both stiff reaction and diffusion terms, implicit integration factor (IIF) method and its higher dimensional analog compact IIF (cIIF) serve as an efficient class of time-stepping methods, and their second order version is linearly unconditionally stable. For nonlinear hyperbolic equations, weighted essentially non-oscillatory (WENO) methods are a class of schemes with a uniformly high-order of accuracy in smooth regions of the solution, which can also resolve the sharp gradient in an accurate and essentially non-oscillatory fashion. In this paper, we couple IIF/cIIF with WENO methods using the operator splitting approach to solve reaction-diffusion-advection equations. In particular, we apply the IIF/cIIF method to the stiff reaction and diffusion terms and the WENO method to the advection term in two different splitting sequences. Calculation of local truncation error and direct numerical simulations for both splitting approaches show the second order accuracy of the splitting method, and linear stability analysis and direct comparison with other approaches reveals excellent efficiency and stability properties. Applications of the splitting approach to two biological systems demonstrate that the overall method is accurate and efficient, and the splitting sequence consisting of two reaction-diffusion steps is more desirable than the one consisting of two advection steps, because CWC exhibits better accuracy and stability.

The spatial organization of stem cells into a niche is a key factor for growth and continual tissue renewal during development, sustenance, and regeneration. Stratified epithelia serve as a great context to study the spatial aspects of the stem cell niche and cell lineages by organizing into layers of different cell types. Several types of stratified epithelia develop morphologies with advantageous, protruding structures where stem cells reside, such as rete pegs and palisades of Vogt. Here, multistage, spatial cell lineage models for epithelial stratification are used to study how the stem cell niche influences epithelial morphologies. When the stem cell niche forms along a rigid basal lamina, relatively regular morphologies are maintained. In contrast, stem cell niche formation along a free-moving basal lamina may prompt distorted epithelial morphologies with stem cells accumulating at the tips of fingerlike structures that form. The correspondence between our simulated morphologies and developmental stages of the human epidermis is also explored. Overall, our work provides an understanding of how stratified epithelia may attain distorted morphologies and sheds light on the importance of the spatial aspects of the stem cell niche.

Growth of developing and regenerative biological tissues of different cell types is usually driven by stem cells and their local environment. Here, we present a computational framework for continuum tissue growth models consisting of stem cells, cell lineages, and diffusive molecules that regulate proliferation and differentiation through feedback. To deal with the moving boundaries of the models in both open geometries and closed geometries (through polar coordinates) in two dimensions, we transform the dynamic domains and governing equations to fixed domains, followed by solving for the transformation functions to track the interface explicitly. Clustering grid points in local regions for better efficiency and accuracy can be achieved by appropriate choices of the transformation. The equations resulting from the incompressibility of the tissue is approximated by high-order finite difference schemes and is solved using the multigrid algorithms. The numerical tests demonstrate an overall spatiotemporal second-order accuracy of the methods and their capability in capturing large deformations of the tissue boundaries. The methods are applied to two biological systems: stratified epithelia for studying the effects of two different types of stem cell niches and the scaling of a morphogen gradient with the size of the Drosophila imaginal wing disc during growth. Direct simulations of both systems suggest that that the computational framework is robust and accurate, and it can incorporate various biological processes critical to stem cell dynamics and tissue growth.

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