On the graph condition regarding the FF-inverse cover problem

In their paper titled "On $F$-inverse covers of inverse monoids", Auinger and Szendrei have shown that every finite inverse monoid has an $F$-inverse cover if and only if each finite graph admits a locally finite group variety with a certain property. We study this property and prove that the class of graphs for which a given group variety has the required property is closed downwards in the minor ordering, and can therefore be described by forbidden minors. We find these forbidden minors for all varieties of Abelian groups, thus describing the graphs for which such a group variety satisfies the above mentioned condition

Inverse monoids of partial graph automorphisms

A partial automorphism of a finite graph is an isomorphism between its vertex induced subgraphs. The set of all partial automorphisms of a given finite graph forms an inverse monoid under composition (of partial maps). We describe the algebraic structure of such inverse monoids by the means of the standard tools of inverse semigroup theory, namely Green's relations and some properties of the natural partial order, and give a characterization of inverse monoids which arise as inverse monoids of partial graph automorphisms. We extend our results to digraphs and edge-colored digraphs as well

Algorithmic properties of inverse monoids with hyperbolic and tree-like Sch\"utzenberger graphs

We prove that the class of finitely presented inverse monoids whose Sch\"utzenberger graphs are quasi-isometric to trees has a uniformly solvable word problem, furthermore, the languages of their Sch\"utzenberger automata are context-free. On the other hand, we show that there is a finitely presented inverse monoid with hyperbolic Sch\"utzenberger graphs and an unsolvable word problem

Impact of copper and iron binding properties on the anticancer activity of 8-hydroxyquinoline derived Mannich bases.

The anticancer activity of 8-hydroxyquinolines relies on complex formation with redox active copper and iron ions. Here we employ UV-visible spectrophotometry and EPR spectroscopy to compare proton dissociation and complex formation processes of the reference compound 8-hydroxyquinoline (Q-1) and three related Mannich bases to reveal possible correlations with biological activity. The studied derivatives harbor a CH2-N moiety at position 7 linked to morpholine (Q-2), piperidine (Q-3), and chlorine and fluorobenzylamino (Q-4) substituents. Solid phase structures of Q-3, Q-4·HCl·H2O, [(Cu(HQ-2)2)2]·(CH3OH)2·Cl4·(H2O)2, [Cu(Q-3)2]·Cl2 and [Cu(HQ-4)2(CH3OH)]·ZnCl4·CH3OH were characterized by single-crystal X-ray diffraction analysis. In addition, the redox properties of the copper and iron complexes were studied by cyclic voltammetry, and the direct reaction with physiologically relevant reductants (glutathione and ascorbic acid) was monitored. In vitro cytotoxicity studies conducted with the human uterine sarcoma MES-SA/Dx5 cell line reveal the significant cytotoxicity of Q-2, Q-3, and Q-4 in the sub- to low micromolar range (IC50 values 0.2-3.3 μM). Correlation analysis of the anticancer activity and the metal binding properties of the compound series indicates that, at physiological pH, weaker copper(ii) and iron(iii) binding results in elevated toxicity (e.g.Q4: pCu = 13.0, pFe = 6.8, IC50 = 0.2 μM vs.Q1: pCu = 15.1, pFe = 13.0 IC50 = 2.5 μM). Although the studied 8-hydroxyquinolines preferentially bind copper(ii) over iron(iii), the cyclic voltammetry data revealed that the more cytotoxic ligands preferentially stabilize the lower oxidation state of the metal ions. A linear relationship between the pKa (OH) and IC50 values of the studied 8-hydroxyquinolines was found. In summary, we identify Q-4 as a potent and selective anticancer candidate with significant toxicity in drug resistant cells

Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex

Identification of novel cell-impermeant fluorescent substrates for testing the function and drug interaction of Organic Anion-Transporting Polypeptides, OATP1B1/1B3 and 2B1.

Organic Anion-Transporting Polypeptides are multispecific membrane proteins that regulate the passage of crucial endobiotics and drugs across pharmacological barriers. OATP1B1 and OATP1B3 have been described to play a major role in the hepatic uptake of statins, antivirals and various chemotherapeutics; whereas the pharmacological role of the ubiquitously expressed OATP2B1 is less well characterized. According to current industry standards, in vitro testing for susceptibility to OATP1B1 and 1B3 mediated transport is recommended for drug candidates that are eliminated in part via the liver. Here we show that human OATP1B1, 1B3 and 2B1 transport a series of commercially available viability dyes that are generally believed to be impermeable to intact cells. We demonstrate that the intracellular accumulation of Zombie Violet, Live/Dead Green, Cascade Blue and Alexa Fluor 405 is specifically increased by OATPs. Inhibition of Cascade Blue or Alexa Fluor 405 uptake by known OATP substrates/inhibitors yielded IC50 values in agreement with gold-standard radioligand assays. The fluorescence-based assays described in this study provide a new tool for testing OATP1B/2B1 drug interactions

Identification of novel cell-impermeant fluorescent substrates for testing the function and drug interaction of Organic Anion-Transporting Polypeptides, OATP1B1/1B3 and 2B1.

Organic Anion-Transporting Polypeptides are multispecific membrane proteins that regulate the passage of crucial endobiotics and drugs across pharmacological barriers. OATP1B1 and OATP1B3 have been described to play a major role in the hepatic uptake of statins, antivirals and various chemotherapeutics; whereas the pharmacological role of the ubiquitously expressed OATP2B1 is less well characterized. According to current industry standards, in vitro testing for susceptibility to OATP1B1 and 1B3 mediated transport is recommended for drug candidates that are eliminated in part via the liver. Here we show that human OATP1B1, 1B3 and 2B1 transport a series of commercially available viability dyes that are generally believed to be impermeable to intact cells. We demonstrate that the intracellular accumulation of Zombie Violet, Live/Dead Green, Cascade Blue and Alexa Fluor 405 is specifically increased by OATPs. Inhibition of Cascade Blue or Alexa Fluor 405 uptake by known OATP substrates/inhibitors yielded IC50 values in agreement with gold-standard radioligand assays. The fluorescence-based assays described in this study provide a new tool for testing OATP1B/2B1 drug interactions