Statistical theory of branching morphogenesis

Convective stability of the critical waves of an FKPP-type model for self-organized growth

We construct the traveling wave solutions of an FKPP growth process of two densities of particles, and prove that the critical traveling waves are locally stable in a space where the perturbations can grow exponentially at the back of the wave. The considered reaction-diffusion system was introduced by Hannezo et al. (Cell 171(1):242-255, 2017) in the context of branching morphogenesis: active, branching particles accumulate inactive particles, which do not react. Thus, the system features a continuum of steady state solutions, complicating the analysis. We adopt a result by Faye and Holzer (J Differ Equ 269(9):6559-6601, 2020) for proving the stability of the critical traveling waves, and modify the semi-group estimates to spaces with unbounded weights. We use a Feynman-Kac formula to get an exponential a priori estimate for the tail of the PDE, a novel and simple approach.

PDX1 as a Marker of Early Differentiation of Human Pancreatic Duct Cells

Epithelial progenitor cells of the primitive pancreatic ducts differentiate in 3 directions, which is accompanied by changes in cell phenotype. We analyze the distribution of the pancreatic and duodenal homeobox 1 (PDX1) in the epithelial cells of pancreatic ducts during the prenatal development in order to determine the potential use of this marker as an indicator of pancreatic cell maturation. Pancreatic autopsies from human fetuses (gestation weeks 17-23) were examined by immunohistochemical methods. In general, PDX1 was detected in the epithelial cells that are involved in various morphogenetic processes related to the growth and branching of the fetal pancreatic ducts. The intensive positive reaction to PDX1/cytokeratin 19 indicates immature (progenitor) polypotent ductal cells.

Tumor architecture and emergence of strong genetic alterations are bottlenecks for clonal evolution in primary prostate cancer

Prostate cancer (PCA) exhibits high levels of intratumoral heterogeneity. In this study, we developed a mathematical model to study the growth and genetic evolution of PCA. We explored the possible evolutionary patterns and demonstrated that tumor architecture represents a major bottleneck for divergent clonal evolution. Early consecutive acquisition of strong genetic alterations serves as a proxy for the formation of aggressive tumors. A limited number of clonal hierarchy patterns were identified. A biopsy study of synthetic tumors shows complex spatial intermixing of clones and delineates the importance of biopsy extent. Deep whole-exome multiregional next-generation DNA sequencing of the primary tumors from five patients was performed to validate the results, supporting our main findings from mathematical modeling. In conclusion, our model provides qualitatively realistic predictions of PCA genomic evolution, closely aligned with the evidence available from patient samples. We share the code of the model for further studies. A record of this paper's transparent peer review process is included in the supplemental information.

Cancer invasion and metastasis: Insights from murine pubertal mammary gland morphogenesis

Cancer invasion and metastasis accounts for the majority of cancer related mortality. A better understanding of the players that drive the aberrant invasion and migration of tumors cells will provide critical targets to inhibit metastasis. Postnatal pubertal mammary gland morphogenesis is characterized by highly proliferative, invasive, and migratory normal epithelial cells. Identifying the molecular regulators of pubertal gland development is a promising strategy since tumorigenesis and metastasis is postulated to be a consequence of aberrant reactivation of developmental stages. In this review, we summarize the pubertal morphogenesis regulators that are involved in cancer metastasis and revisit pubertal mammary gland transcriptome profiling to uncover both known and unknown metastasis genes. Our updated list of pubertal morphogenesis regulators shows that most are implicated in invasion and metastasis. This review highlights molecular linkages between development and metastasis and provides a guide for exploring novel metastatic drivers.

Lineage tracing reveals the dynamic contribution of Id2+ progenitor cells to branching morphogenesis

Branching morphogenesis is an important process in shaping the arborized structures of several organs. However, the driving force that directs this process from progenitor pools remains incompletely understood. In this lineage tracing study, we investigated the role of Id2+ embryonic progenitor cells in branching organs such as the pancreas, kidney, mammary gland, thyroid gland, and salivary gland. We found that a subset of Id2+ distal progenitor cells in the embryonic pancreas and kidney can give rise to multiple lineages of progeny cells during branching morphogenesis. Id2-labelled cells also supported the postnatal development of the mammary glands. However, Id2+ cells did not contribute to the development of the salivary and thyroid glands. We found the Id2+ cells located in the tip progenitor pools of pancreas and kidney have self-renewal potential and contribute descendents to multiple epithelial cell lineages. Our findings enrich the current model of distal progenitor pools driving branching morphogenesis and provide a new marker to investigate the regularity of branching in these organs.

Active flows and deformable surfaces in development

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients- active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

Multi-scale simulation of early kidney branching morphogenesis

An important feature of the branch morphogenesis during kidney development is the termination of the tips on the outer surface of a kidney. This feature requires the avoidance of the intersection between the tips and existing ducts inside the kidney. Here, we started from a continuous model and implemented the coarse grained rules into a fast and discrete simulations. The ligand-receptor-based Turing mechanism suggests a repulsion that decreases exponentially with distance between interacting branches, preventing the intersection between neighboring branches. We considered this repulsive effect in numerical simulations and successfully reproduce the key features of the experimentally observed branch morphology for an E15.5 kidney. We examine the similarity of several geometrical parameters between the simulation results and experimental observations. The good agreement between the simulations and experiments suggests that the concentration decay caused by the absorption of glial cell line derived neurotrophic factor might be the key factor to affect the geometry in early kidney development.

Inductive signals in branching morphogenesis - lessons from mammary and salivary glands

Branching morphogenesis is a fundamental developmental program that generates large epithelial surfaces in a limited three-dimensional space. It is regulated by inductive tissue interactions whose effects are mediated by soluble signaling molecules, and cell-cell and cell-extracellular matrix interactions. Here, we will review recent studies on inductive signaling interactions governing branching morphogenesis in light of phenotypes of mouse mutants and ex vivo organ culture studies with emphasis on developing mammary and salivary glands. We will highlight advances in understanding how cell fate decisions are intimately linked with branching morphogenesis. We will also discuss novel insights into the molecular control of cellular mechanisms driving the formation of these arborized ductal structures and reflect upon how distinct spatial patterns are generated.

Statistical theory of branching morphogenesis

Branching morphogenesis remains a subject of abiding interest. Although much is known about the gene regulatory programs and signaling pathways that operate at the cellular scale, it has remained unclear how the macroscopic features of branched organs, including their size, network topology and spatial patterning, are encoded. Lately, it has been proposed that, these features can be explained quantitatively in several organs within a single unifying framework. Based on large-scale organ reconstructions and cell lineage tracing, it has been argued that morphogenesis follows from the collective dynamics of sublineage-restricted self-renewing progenitor cells, localized at ductal tips, that act cooperatively to drive a serial process of ductal elongation and stochastic tip bifurcation. By correlating differentiation or cell cycle exit with proximity to maturing ducts, this dynamic results in the specification of a complex network of defined density and statistical organization. These results suggest that, for several mammalian tissues, branched epithelial structures develop as a self-organized process, reliant upon a strikingly simple, but generic, set of local rules, without recourse to a rigid and deterministic sequence of genetically programmed events. Here, we review the basis of these findings and discuss their implications.