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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
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