Tumor necrosis factor (TNF) superfamily member 11 (TNFSF11, also known as RANKL) regulates multiple physiological or pathological functions, including osteoclast differentiation and osteoporosis. TNFRSF11A (also called RANK) is considered to be the sole receptor for RANKL. Herein we report that leucine-rich repeat-containing G-protein-coupled receptor 4 (LGR4, also called GPR48) is another receptor for RANKL. LGR4 competes with RANK to bind RANKL and suppresses canonical RANK signaling during osteoclast differentiation. RANKL binding to LGR4 activates the Gαq and GSK3-β signaling pathway, an action that suppresses the expression and activity of nuclear factor of activated T cells, cytoplasmic, calcineurin-dependent 1 (NFATC1) during osteoclastogenesis. Both whole-body (Lgr4(-/-)) and monocyte conditional knockout mice of Lgr4 (Lgr4 CKO) exhibit osteoclast hyperactivation (including elevation of osteoclast number, surface area, and size) and increased bone erosion. The soluble LGR4 extracellular domain (ECD) binds RANKL and inhibits osteoclast differentiation in vivo. Moreover, LGR4-ECD therapeutically abrogated RANKL-induced bone loss in three mouse models of osteoporosis. Therefore, LGR4 acts as a second RANKL receptor that negatively regulates osteoclast differentiation and bone resorption.

Activation of NF-kB and MAPK/activator protein 1 (AP-1) signaling pathways by receptor activator NF-kB ligand (RANKL) is essential for osteoclast activity. Targeting NF-kB and MAPK/AP-1 signaling to modulate osteoclast activity has been a promising strategy for osteoclast-related diseases. In this study we examined the effects of maslinic acid (MA), a pentacyclic triterpene acid that is widely present in dietary plants, on RANKL-induced osteoclastogenesis, osteoclast function, and signaling pathways by in vitro and in vivo assay systems. In mouse bone marrow monocytes (BMMs) and RAW264.7 cells, MA inhibited RANKL-induced osteoclastogenesis in a dosedependent manner within nongrowth inhibitory concentration, and MA decreased osteoclastogenesis-related marker gene expression, including TRACP, MMP9, c-Src, CTR, and cathepsin K. Specifically, MA suppressed osteoclastogenesis and actin ring formation at early stage. In ovariectomized mice, administration of MA prevented ovariectomy-induced bone loss by inhibiting osteoclast activity. At molecular levels, MA abrogated the phosphorylation of MAPKs and AP-1 activity, inhibited the IkBa phosphorylation and degradation, blocked NF-kB/p65 phosphorylation, nuclear translocation, and DNA-binding activity by downregulating RANK expression and blocking RANK interaction with TRAF6. Together our data demonstrate that MA suppresses RANKL-induced osteoclastogenesis through NF-kB and MAPK/AP-1 signaling pathways and that MA is a promising agent in the treatment of osteoclast-related diseases such as osteoporosis. ß

D’Amico et al. show that Dkk1 exerts immune-suppressive effects by directly targeting β-catenin in murine and human MDSCs and promoting their activation in cancer.

Abstract. The task of determining the approximate greatest common divisor (GCD) of univariate polynomials with inexact coefficients can be formulated as computing for a given Sylvester matrix a new Sylvester matrix of lower rank whose entries are near the corresponding entries of that input matrix. We solve the approximate GCD problem by a new method based on structured total least norm (STLN) algorithms, in our case for matrices with Sylvester structure. We present iterative algorithms that compute an approximate GCD and that can certify an approximate ǫ-GCD when a tolerance ǫ is given on input. Each single iteration is carried out with a number of floating point operations that is of cubic order in the input degrees. We also demonstrate the practical performance of our algorithms on a diverse set of univariate pairs of polynomials. Mathematics Subject Classification (2000). Primary 68W30; Secondary 65K10.Keywords. Sylvester matrix, approximate greatest common divisor, structured total least norm, hybrid symbolic/numeric algorithm.

Receptor activator of NF-kB ligand (RANKL) stimulation leads to the activation of mitogen-activated protein kinase (MAPK)/AP-1 and Ca 2þ -nuclear factor of activated T-cells cytoplasmic 1 (NFATc1) signaling pathways in osteoclastogenesis. Targeting these pathways has been an encouraging strategy for bone-related diseases, such as postmenopausal osteoporosis. In this study, we examined the effects of caffeic acid 3,4-dihydroxy-phenethyl ester (CADPE) on osteoclastogenesis. In mouse bone marrow monocytes (BMMs) and RAW264.7 cells, CADPE suppressed RANKL-induced osteoclast differentiation and actin-ring formation in a dose-dependent manner within non-growth inhibitory concentrations at the early stage, while CADPE had no effect on macrophage colony-stimulating factor (M-CSF)-induced proliferation and differentiation. At the molecular level, CADPE inhibited RANKL-induced phosphorylation of MAPKs, including extracellular signal-regulated kinases 1/2 (ERK1/2), p38, and c-Jun N-terminal kinase (JNK), without significantly affecting the NF-kB signaling pathway. CADPE abrogated RANKL-induced activator protein 1 (AP-1)/FBJ murine osteosarcoma viral oncogene homolog (c-Fos) nuclear translocation and activation. Overexpression of c-Fos prevented the inhibition by CADPE of osteoclast differentiation. Furthermore, CADPE suppressed RANKL-induced the tumor necrosis factor receptor associated factor 6 (TRAF6) interaction with c-src tyrosine kinase (c-Src), blocked RANKL-induced the phosphorylation of protein kinase B (AKT), and inhibited RANKL-induced Ca 2þ oscillation. As a result, CADPE decreased osteoclastogenesis-related marker gene expression, including NFATc1, TRAP, cathepsin K, and c-Src. To test the effects of CADPE on osteoclast activity in vivo, we showed that CADPE prevented ovariectomyinduced bone loss by inhibiting osteoclast activity. Together, our data demonstrate that CADPE suppresses osteoclastogenesis and bone loss through inhibiting RANKL-induced MAPKs and Ca 2þ -NFATc1 signaling pathways. CADPE is a novel agent in the treatment of osteoclast-related diseases, such as osteoporosis. ß