Summary
The Wnt inhibitor Dickkopf-1 (DKK1) is a negative regulator of bone formation and bone mass and is dysregulated in various bone diseases. How DKK1 contributes to postmenopausal osteoporosis, however, remains poorly understood. Here, we show that mice lacking DKK1 in T cells are protected from ovariectomy-induced bone loss. Ovariectomy activated CD4+ and CD8+ T cells and increased their production of DKK1. Co-culture of activated T cells with osteoblasts inhibited Wnt signaling in osteoblasts, leading to impaired differentiation. Importantly, DKK1 expression in T cells also controlled physiological bone remodeling. T-cell-deficient
Dkk1
knock-out mice had a higher bone mass with an increased bone formation rate and decreased numbers of osteoclasts compared with controls, a phenotype that was rescued by adoptive transfer of wild-type T cells. Thus, these findings highlight that T cells control bone remodeling in health and disease via their expression of DKK1.
Some new necessary conditions for the existence of vector space partitions are derived. They are applied to the problem of finding the maximum number of spaces of dimension t in a vector space partition of V (2t, q) that contains m d spaces of dimension d, where t/2 < d < t, and also spaces of other dimensions. It is also discussed how this problem is related to maximal partial t-spreads in V (2t, q). We also give a lower bound for the number of spaces in a vector space partition and verify that this bound is tight.
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