Differential involvement of Wnt signaling in Bmp regulation of cancellous versus periosteal bone growth

Bone morphogenetic proteins (Bmp) are well-known to induce bone formation following chondrogenesis, but the direct role of Bmp signaling in the osteoblast lineage is not completely understood. We have recently shown that deletion of the receptor Bmpr1a in the osteoblast lineage with Dmp1-Cre reduces osteoblast activity in general but stimulates proliferation of preosteoblasts specifically in the cancellous bone region, resulting in diminished periosteal bone growth juxtaposed with excessive cancellous bone formation. Because expression of sclerostin (SOST), a secreted Wnt antagonist, is notably reduced in the Bmpr1a-deficient osteocytes, we have genetically tested the hypothesis that increased Wnt signaling might mediate the increase in cancellous bone formation in response to Bmpr1a deletion. Forced expression of human SOST from a Dmp1 promoter fragment partially rescues preosteoblast hyperproliferation and cancellous bone overgrowth in the Bmpr1a mutant mice, demonstrating functional interaction between Bmp and Wnt signaling in the cancellous bone compartment. To test whether increased Wnt signaling can compensate for the defect in periosteal growth caused by Bmpr1a deletion, we have generated compound mutants harboring a hyperactive mutation (A214V) in the Wnt receptor Lrp5. However, the mutant Lrp5 does not restore periosteal bone growth in the Bmpr1a-deficient mice. Thus, Bmp signaling restricts cancellous bone accrual partly through induction of SOST that limits preosteoblast proliferation, but promotes periosteal bone growth apparently independently of Wnt activation

Quantitative global well-posedness of Boltzmann-Bose-Einstein equation and incompressible Navier-Stokes-Fourier limit

In the diffusive scaling and in the whole space, we prove the global well-posedness of the scaled Boltzmann-Bose-Einstein (briefly, BBE) equation with high temperature in the low regularity space $H^2_xL^2$. In particular, we quantify the fluctuation around the Bose-Einstein equilibrium $\mathcal{M}_{\lambda,T}(v)$ with respect to the parameters $\lambda$ and temperature $T$. Furthermore, the estimate for the diffusively scaled BBE equation is uniform to the Knudsen number $\epsilon$. As a consequence, we rigorously justify the hydrodynamic limit to the incompressible Navier-Stokes-Fourier equations. This is the first rigorous fluid limit result for BBE.Comment: 42 page