Equivariant compactifications of reductive groups

We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under the action of the doubled group by left/right multiplications, the local structure in a neighborhood of a closed orbit, and obtain some conditions of normality and smoothness of a compactification. Our methods of research use the theory of equivariant embeddings of spherical homogeneous spaces and of reductive algebraic semigroups.Comment: 30 pages, AmSLaTeX. Bibliography: 36 item

Cellulose-based scaffolds for fluorescence lifetime imaging-assisted tissue engineering

Quantitative measurement of pH and metabolite gradients by microscopy is one of the challenges in the production of scaffold-grown organoids and multicellular aggregates. Herein, we used the cellulose-binding domain (CBD) of the Cellulomonas fimi CenA protein for designing biosensor scaffolds that allow measurement of pH and Ca2+ gradients by fluorescence intensity and lifetime imaging (FLIM) detection modes. By fusing CBD with pH-sensitive enhanced cyan fluorescent protein (CBD-ECFP), we achieved efficient labeling of cellulose-based scaffolds based on nanofibrillar, bacterial cellulose, and decellularized plant materials. CBD-ECFP bound to the cellulose matrices demonstrated pH sensitivity comparable to untagged ECFP (1.9–2.3 ns for pH 6–8), thus making it compatible with FLIM-based analysis of extracellular pH. By using 3D culture of human colon cancer cells (HCT116) and adult stem cell-derived mouse intestinal organoids, we evaluated the utility of the produced biosensor scaffold. CBD-ECFP was sensitive to increases in extracellular acidification: the results showed a decline in 0.2–0.4 pH units in response to membrane depolarization by the protonophore FCCP. With the intestinal organoid model, we demonstrated multiparametric imaging by combining extracellular acidification (FLIM) with phosphorescent probe-based monitoring of cell oxygenation. The described labeling strategy allows for the design of extracellular pH-sensitive scaffolds for multiparametric FLIM assays and their use in engineered live cancer and stem cell-derived tissues. Collectively, this research can help in achieving the controlled biofabrication of 3D tissue models with known metabolic characteristics. Statement of Significance: We designed biosensors consisting of a cellulose-binding domain (CBD) and pH- and Ca2+-sensitive fluorescent proteins. CBD-tagged biosensors efficiently label various types of cellulose matrices including nanofibrillar cellulose and decellularized plant materials. Hybrid biosensing cellulose scaffolds designed in this study were successfully tested by multiparameter FLIM microscopy in 3D cultures of cancer cells and mouse intestinal organoids