Defining the contribution of Troy-positive progenitor cells to the mouse esophageal epithelium.

Progenitor cells adapt their behavior in response to tissue demands. However, the molecular mechanisms controlling esophageal progenitor decisions remain largely unknown. Here, we demonstrate the presence of a Troy (Tnfrsf19)-expressing progenitor subpopulation localized to defined regions along the mouse esophageal axis. Lineage tracing and mathematical modeling demonstrate that Troy-positive progenitor cells are prone to undergoing symmetrical fate choices and contribute to esophageal tissue homeostasis long term. Functionally, TROY inhibits progenitor proliferation and enables commitment to differentiation without affecting fate symmetry. Whereas Troy expression is stable during esophageal homeostasis, progenitor cells downregulate Troy in response to tissue stress, enabling proliferative expansion of basal cells refractory to differentiation and reestablishment of tissue homeostasis. Our results demonstrate functional, spatially restricted progenitor heterogeneity in the esophageal epithelium and identify how dynamic regulation of Troy coordinates tissue generation.

On compositions of special cases of Lipschitz continuous operators.

Many iterative optimization algorithms involve compositions of special cases of Lipschitz continuous operators, namely firmly nonexpansive, averaged, and nonexpansive operators. The structure and properties of the compositions are of particular importance in the proofs of convergence of such algorithms. In this paper, we systematically study the compositions of further special cases of Lipschitz continuous operators. Applications of our results include compositions of scaled conically nonexpansive mappings, as well as the Douglas-Rachford and forward-backward operators, when applied to solve certain structured monotone inclusion and optimization problems. Several examples illustrate and tighten our conclusions.