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Vitamin A metabolites such as all-trans-retinoic acid (all-trans-RA) affect several steps of metabolic processes in vertebrates. In the last few years, several studies have shown the effect of RA on bone formation and metabolism. However, mechanisms of its action still remain unclear, especially with respect to the regulation of bone cells. Therefore, this study was carried out to clarify how RA regulates the activity of osteoclasts. Using a pit assay involving unfractionated bone cells, including osteoclasts obtained from rabbits, we found that RA stimulated an increase in the bone-resorbing activity in a dose- and time-dependent manner. Furthermore, this effect occurred more rapidly than that of treatments with 1 alpha,25-dihydroxyvitamin D3. However, this effect of RA may be partly related to cross-talk between osteoclasts and other types of cells. Therefore we studied the effect of RA on isolated osteoclasts. We found that all-trans-RA regulates the gene expression of cathepsin K/OC-2, a dominant cysteine proteinase, at the transcriptional level in mature osteoclasts isolated from rabbits. Moreover, retinoic acid-receptor alpha mRNA and retinoid X-receptor beta mRNA were expressed in these mature osteoclasts. Our results indicate that osteoclasts are target cells for RA and that RA might regulate a part of bone formation and metabolism through osteoclasts.

Prostaglandins (PGs) are well known to be important local factors in regulating bone formation and resorption. PGE2 is a potent stimulator of bone resorption because of enhancing osteoclast formation by its indirect action through stromal cells. However, the direct action of PGE2 on functionally mature osteoclasts is still controversial. In this study using highly purified rabbit mature osteoclasts, we examined the direct effect of PGE2 on osteoclastic bone-resorbing activity and its mechanism. PGE2 inhibited resorption pit formation on a dentine slice by the purified osteoclasts in a dose- and time-dependent manner. The inhibitory effect appeared as early as 4 hours after the PGE2 addition. Forskolin and 12-0-tetradecanoyl phorbol-13-acetate (TPA), respective activators of adenylate cyclase and protein kinase C, also decreased the osteoclastic bone-resorbing activity. PGE2 increased the content of intracellular cAMP in a dose range effective for the inhibition of bone resorption, whereas the prostanoid did not alter the intracellular level of inositol triphosphate. The inhibition of osteoclastic bone resorption by PGE2 was amplified and diminished by a cAMP phosphodiesterase inhibitor (isobutyl methylxanthine) and a protein kinase A inhibitor (Rp-cAMP), respectively. Of four different subtypes of PGE2 receptors (EPs), EP4 mRNA was predominantly expressed in isolated osteoclasts, whereas the other types of EP mRNA were detected in only small amounts. These results suggest that the PGE2 inhibitory effect was mediated by an adenylate cyclase system coupled with EP4. This possible association of PGE2 with EP4 in mature osteoclasts was supported by the finding that a specific agonist of EP4 (AE-604) inhibited the bone-resorbing activity and elevated the intracellular cAMP content. However, butaprost, a selective EP2 agonist, also mimicked the PGE2 effects on isolated osteoclasts although EP2 mRNA expression was minimal. In conclusion, PGE2 directly inhibits bone-resorbing activity of functionally mature osteoclasts by activation of the adenylate cyclase system, perhaps mainly through EP4.

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The knapsack problem and the minimum spanning tree problem are both fundamental in operations research and computer science. We are concerned with a combination of these two problems. That is, we are given a knapsack of a fixed capacity, as well as an undirected graph where each edge is associated with profit and weight. The problem is to fill the knapsack with a feasible spanning tree such that the tree profit is maximized. We prove this problem NP-hard, present upper and lower bounds, develop a branch-and-bound algorithm to solve the problem to optimality and propose a shooting method to accelerate computation. We evaluate the developed algorithm through a series of numerical experiments for various types of test problems.

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