A logarithmically completely monotonic function is completely monotonic. The function 1 − ln x + 1x ln Γ (x + 1) is strictly completely monotonic on (0, ∞). The function x √ Γ (x + 1)/x is strictly logarithmically completely monotonic on (0, ∞).

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Peptidoglycan (PGN), the major component of the cell wall of Gram-positive bacteria, activates the innate immune system of the host and induces the release of cytokines and chemokines. We investigated the signaling pathway involved in IL-6 production stimulated by PGN in rheumatoid arthritis synovial fibroblasts. PGN caused concentration- and time-dependent increases in IL-6 production. PGN-mediated IL-6 production was attenuated by TLR2 small interfering RNA and nucleotide-binding oligomerization domain 2 small interfering RNA. Pretreatment with PI3K inhibitor (Ly294002 and wortmannin), Akt inhibitor, and AP-1 inhibitor (tanshinone IIA) also inhibited the potentiating action of PGN. PGN increased the focal adhesion kinase (FAK), PI3K, and Akt phosphorylation. Stimulation of rheumatoid arthritis synovial fibroblast cells with PGN increased the accumulation of phosphorylated c-Jun in the nucleus, AP-1-luciferase activity, and c-Jun binding to the AP-1 element on the IL-6 promoter. PGN mediated an increase in the accumulation of phosphorylated c-Jun in the nucleus, AP-1-luciferase activity, and c-Jun binding to AP-1 element was inhibited by Ly294002, Akt inhibitor, and FAK mutant. Our results suggest that PGN increased IL-6 production in human synovial fibroblasts via the TLR2 receptor/FAK/PI3K/Akt and AP-1 signaling pathway.

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