• Molecules and Cells
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• v.25 no.2
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• pp.289-293
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• 2008

The role of SPOP in the ubiquitination of $ER{\alpha}$ by the Cullin3-based E3 ubiquitin ligase complex was investigated. We showed that the N-terminal region of SPOP containing the MATH domain interacts with the AF-2 domain of $ER{\alpha}$ in cultured human embryonic 293 cells. SPOP was required for coimmunoprecipitation of $ER{\alpha}$ with Cullin3. This is the first report of the essential role of SPOP in $ER{\alpha}$ ubiquitination by the Cullin3-based E3 ubiquitin ligase complex. We also demonstrated repression of the transactivation capability of $ER{\alpha}$ in cultured mammalian cells.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1841-1850
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• 2014

It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.