• 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.

• The Korean Journal of Physiology and Pharmacology
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• v.16 no.5
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• pp.327-332
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• 2012

Sertraline is a commonly used antidepressant of the selective serotonin reuptake inhibitors (SSRIs) class. In these experiments, we have used the whole cell patch clamp technique to examine the effects of sertraline on the major cardiac ion channels expressed in HEK293 cells and the native voltage-gated $Ca^{2+}$ channels in rat ventricular myocytes. According to the results, sertraline is a potent blocker of cardiac $K^+$ channels, such as hERG, $I_{Ks}$ and $I_{K1}$. The rank order of inhibitory potency was hERG > $I_{K1}$ > $I_{Ks}$ with $IC_{50}$ values of 0.7, 10.5, and 15.2 ${\mu}M$, respectively. In addition to $K^+$ channels, sertraline also inhibited $I_{Na}$ and $I_{Ca}$, and the $IC_{50}$ values are 6.1 and 2.6 ${\mu}M$, respectively. Modification of these ion channels by sertraline could induce changes of the cardiac action potential duration and QT interval, and might result in cardiac arrhythmia.

• Archives of Pharmacal Research
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• v.28 no.1
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• pp.61-67
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• 2005

We evaluated the antiplatelet effects of two classes of ATP-sensitive potassium channel openers $(K_{ATP}\;openers)$ on washed human platelets, and the study's emphasis was on the role of mitochondrial $K_{ATP}$ in platelet aggregation. Collagen-induced platelet aggregation was inhibited in a dose dependent manner by lemakalim and SKP-450, which are potent cardio-nonselective $K_{ATP}$ openers, and also by cardioselective BMS-180448 and BMS-191095 $(IC_{50}\;:\;1,130,\;>\;1,500,\;305.3\;and\;63.9\;{\mu}M,\;respectively)$, but a significantly greater potency was noted for the cardioselective $K_{ATP}$ openers. The latter two $K_{ATP}$ openers also inhibited platelet aggregation induced by thrombin, another important blood-borne platelet activator, with similar rank order of potency $(IC_{50}\;:\;498.0\;and\;104.8{\mu}M\; for\;BMS-180448\;and\;BMS-191095,\;respectively)$. The inhibitory effects of BMS-191095 on collagen-induced platelet aggregation were significantly blocked by a 30-min pretreatment of platelets with glyburide $(1{\mu}M)$ or sodium 5-hydroxyde­canoate$(5-HD,\;100{\mu}M)$, a nonselective and selective mitochondrial $K_{ATP}$ antagonist, respectively, at similar magnitudes; this indicates the role of mitochondrial $K_{ATP}$ in the antiplatelet activity of BMS-191095. However, glyburide and 5-HD had no effect when they were added to the platelet cuvette immediately prior to the addition of BMS-191095. These findings indicate that cardioselective mitochondrial $K_{ATP}$ openers like BMS-191095 are able to exert cardioprotective effects in cardiac ischemia/reperfusion injury via dual mechanisms directed at the inhibition of platelet aggregation and the protection of cardiomyocytes, and both these mechanisms are mediated by mitochondrial$K_{ATP}$.

• The Korean Journal of Pharmacology
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• v.28 no.2
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• pp.147-162
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• 1992

The objectives of the present experiments were to characterize the effects of the peptides belonging to the pancreatic polypeptide family on the contractility of cerebral arteries and to observe the interactions of these peptides with the cyclic nucleotide activators and the potassium channel openers. Dogs of either sex, $20{\sim}30\;Kg$ in weight, were sacrificed. Basilar and middle cerebral arteries from brain were isolated and prepared for myography in the PSS equilibrated with 95% $O_2$ and 5% $CO_2$ at $37^{\circ}C$. The endothelial cells of the spiral strips were removed by CHAPS solution (0.3% w/v, 15 seconds). 1. PP, PYY and NPY contracted the arterial strips concentration-dependently with a rank order of potency of PYY>NPY>PP. These peptides were 20 to 200 times more potent than norepinephrine, and only PYY showed a greater potency than 5-HT. 2. Cyclic nucleotide activators, forskolin (for cAMP) and sodium nitroprusside (for cGMP) reduced the basal tone and inhibited the PP-, PYY- and NPY- induced contractions by concentration-dependent manners. Forskolin was more potent in reducing basal tone than sodium nitroprusside. 3. Potassium channel openers, RP 49356, P 1060 and BRL 38227 reduced the basal tone concentration-dependently and tended to inhibit the PP-, PYY- and NPY- induced contractions. Notably, BRL 38227 with low concentration $(0.1\;{\mu}M)$ enhanced the contractions induced by those peptides while P 1060 inhibited the contractions concentration-dependently. 4. The combinations of the cyclic nucleotide activators and the potassium channel openers were slightly additive in reducing the basal tone. P 1060 and BRL 38227 enhanced the relaxant effect of sodium nitroprusside significantly. On the PYY-induced contration $(0.1\;{\mu}M)$, $K^+$ channel openers tended to inhibit the inhibitory actions of forskolin and sodium nitroprusside. P 1060 and BRL 38227 antagonized the inhibitory action of sodium nitroprusside significantly. The results of the present study may be summarized that in canine cerebral arteries, not only NPY but also PYY may play a role in a cerebrovascular spasm, and intracellular concentration of either cAMP or cGMP may be involved in the mechanism of vasoconstrictive actions of these peptides, which may be affected either positively or negatively by a $K^+$ channel opener.