Mitogen-activated protein kinase (MAPK)-regulated interactions between Osterix and Runx2 are critical for the transcriptional osteogenic program.

The transcription factors Runx2 and Osx (Osterix) are required for osteoblast differentiation and bone formation. Runx2 expression occurs at early stages of osteochondroprogenitor determination, followed by Osx induction during osteoblast maturation. We demonstrate that coexpression of Osx and Runx2 leads to cooperative induction of expression of the osteogenic genes Col1a1, Fmod, and Ibsp. Functional interaction of Osx and Runx2 in the regulation of these promoters is mediated by enhancer regions with adjacent Sp1 and Runx2 DNA-binding sites. These enhancers allow formation of a cooperative transcriptional complex, mediated by the binding of Osx and Runx2 to their specific DNA promoter sequences and by the protein-protein interactions between them. We also identified the domains involved in the interaction between Osx and Runx2. These regions contain the amino acids in Osx and Runx2 known to be phosphorylated by p38 and ERK MAPKs. Inhibition of p38 and ERK kinase activities or mutation of their known phosphorylation sites in Osx or Runx2 strongly disrupts their physical interaction and cooperative transcriptional effects. Altogether, our results provide a molecular description of a mechanism for Osx and Runx2 transcriptional cooperation that is subject to further regulation by MAPK-activating signals during osteogenesis.

Overestimation and Underestimation Biases in Photon Mapping with Non-Constant Kernels.

This paper presents an analysis of the overestimation bias in common used filtering kernels in the context of photon mapping density estimation. We use the joint distribution of order statistics to calculate the expected value of the estimators of irradiance, and show that the estimator provided by the cone filter is not consistent unless the slope is one (yielding the triangular kernel), and that the Epanechnikov and Silverman kernels are consistent. The Gaussian filter has two different estimation biases: the original normalization constant α underestimates radiance by 46.9 percent, and the use of the kth nearest photon reduces this underestimation slightly. We also show that a new normalization constant for the Gaussian filter together with discarding the contribution of the kth nearest photon in the Gaussian and cone filter estimators produces new, consistent estimators. The specialized differential filter also benefits from the new estimate.