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In this paper, we study minimal submanifolds in some general ( α , β ) -spaces. We firstly establish the equations for minimal submanifolds in a general ( α , β ) -space. Then we construct some kinds of minimal surfaces in some 4-dimensional general ( α , β ) -space. [ABSTRACT FROM AUTHOR]

Highlights • The TOR pathway regulates cell wall integrity (CWI) in G. lucidum. • Inhibition of TOR increased cell wall thickness, components contents in G. lucidum. • Inhibition of TOR increased the Slt2 relative phosphorylation level in G. lucidum. • TOR regulates synthesis of cell wall components through Slt2-MAPK in G. lucidum. Abstract The fungal cell wall is very important for cell growth and survival during stress, and the target of rapamycin (TOR) pathway plays a major role in regulating cell growth in response to environmental cues. Ganoderma lucidum is an important edible and medicinal fungus, and the function of TOR in this organism remains unclear. As shown in the present study, the TOR pathway regulates cell wall integrity (CWI) in G. lucidum. Inhibition of TOR signaling by RNA interference (RNAi) or rapamycin treatment reduced the growth of G. lucidum mycelia, increased contents of the cell wall components chitin and β-1,3-glucan, and increased cell wall thickness. Furthermore, inhibition of TOR signaling enhanced the relative level of phosphorylated Slt2, a member of the MAPK cascade involved in CWI signaling. Moreover, when treated with rapamycin, significantly lower chitin and β-1,3-glucan contents were observed in Slt2-silenced strains than in WT strains, indicating that TOR regulates the synthesis of these cell wall components through the Slt2-MAPK pathway. These results indicate a potential relationship between TOR signaling and CWI signaling. Additionally, participation of Slt2-MAPK in TOR-mediated regulation of cell wall component production has not previously been reported in a microorganism. [ABSTRACT FROM AUTHOR]