Reflexive functors of modules in Commutative Algebra

Reflexive functors of modules naturally appear in Algebraic Geometry, mainly in the theory of linear representations of group schemes, and in "duality theories". In this paper we study and determine reflexive functors and we give many properties of reflexive functors

Function of Bmpr1a in ES cell differentiation and cell competition

Bone morphogenetic protein (BMP) 4 signalling via BMPR1A is required for the maintenance of the epiblast in the early embryo, and for self-renewal of pluripotent mouse embryonic stem (ES) cells by inhibiting neural differentiation. In this study, the self-renewal and differentiation abilities of ES cells lacking BMPR1A were investigated. Bmpr1a-null ES cells did not respond to BMP4 but retained a degree of SMAD1/5/8 activation and Id1 expression. This activation was likely due to BMP7 signalling via ACVR1. The observation that Bmpr1a-/- ES cells showed no selfrenewal or pluripotency defects suggested that signalling by BMPs of the 60a subgroup (such as BMP7) can also maintain pluripotency. When Bmpr1a-/- ES cells were differentiated, although they did form derivatives of the three germ layers, they displayed a higher propensity to undergo neurectodermal specification than control cells, likely due to their lower levels of BMP signalling. Cell Competition is the process by which viable cells are eliminated in the presence of metabolically more active or fitter cells. In Drosophila this process depends on dMyc levels and on limiting amounts of the survival factor Decapentaplegic (homologous to the mammalian BMPs). When Bmpr1a-/- ES cells were co-cultured with wild-type cells, they gradually disappeared from the culture and were therefore out-competed. This cell competition was enhanced by limiting the amounts of survival and growth factors and could be rescued by restoring BMP4 signalling in Bmpr1a-/- cells. In co-culture, Bmpr1a-/- ES cells showed no significant changes in apoptosis but had a decreased cell cycle rate and increased levels of differentiation. Concomitantly, higher c-MYC levels were observed in wild-type cells due to increased protein stability. The out-competition of Bmpr1a-/- cells was dependent on differentiation as it could be prevented by inhibiting this process. These results suggest that during development cell competition may be an important mechanism controlling cell fate and survival