Further results on the inverse along an element in semigroups and rings

In this paper, we introduce a new notion in a semigroup $S$ as an extension of Mary's inverse. Let $a,d\in S$. An element $a$ is called left (resp. right) invertible along $d$ if there exists $b\in S$ such that $bad=d$ (resp. $dab=b$) and $b\leq_\mathcal{L}d$ (resp. $b\leq_\mathcal{R}d$). An existence criterion of this type inverse is derived. Moreover, several characterizations of left (right) regularity, left (right) $\pi$-regularity and left (right) $*$-regularity are given in a semigroup. Further, another existence criterion of this type inverse is given by means of a left (right) invertibility of certain elements in a ring. Finally we study the (left, right) inverse along a product in a ring, and, as an application, Mary's inverse along a matrix is expressed.

Green's relations, regularity and abundancy for semigroups of quasi-onto transformations

Let V be an infinite-dimensional vector space and for every infinite cardinal n such that n≤dimV, let AE(V,n) denote the semigroup of all linear transformations of V whose defect is less than n. In 2009, Mendes-Gonçalves and Sullivan studied the ideal structure of AE(V,n). Here, we consider a similarly-defined semigroup AE(X,q) of transformations defined on an infinite set X. Quite surprisingly, the results obtained for sets differ substantially from the results obtained in the linear setting.

A novel hanging spherical drop system for the generation of cellular spheroids and high throughput combinatorial drug screening

We propose a novel hanging spherical drop system for anchoring arrays of droplets of cell suspension based on the use of biomimetic superhydrophobic flat substrates, with controlled positional adhesion and minimum contact with a solid substrate. By facing down the platform, it was possible to generate independent spheroid bodies in a high throughput manner, in order to mimic in vivo tumour models on the lab-on-chip scale. To validate this system for drug screening purposes, the toxicity of the anti-cancer drug doxorubicin in cell spheroids was tested and compared to cells in 2D culture. The advantages presented by this platform, such as feasibility of the system and the ability to control the size uniformity of the spheroid, emphasize its potential to be used as a new low cost toolbox for high-throughput drug screening and in cell or tissue engineering.

Extended formulations for combinatorial polytopes

Magdeburg, Univ., Fak. für Mathematik, Diss., 2012

Polyhedral and combinatorial aspects in optimization

Magdeburg, Univ., Fak. für Mathematik, Habil.-Schr., 2012

Sizes of linear descriptions in combinatorial optimization

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Combinatorial and metric properties of Thompson's group T

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word length, that F is undistorted in T, and that cyclic subgroups of T are undistorted. We show that every element of T has a power which is conjugate to an element of F and describe how to recognize torsion elements in T.

Combinatorial Synthesis and Biological Evaluation of Inhibitors of D-Ala-D-Ala-Ligase

Report for the scientific sojourn carried out at the Max Planck Institut of Molecular Phisiology, Germany, from 2006 to 2008.The work carried out during this postdoctoral stage was focused on two different projects. Firstly, identification of D-Ala D-Ala Inhibitors and the development of new synthethic approaches to obtain lipidated peptides and proteins and the use of these lipidated proteins in biological and biophysical studies. In the first project, new D-Ala D-Ala inhibitors were identified by using structural alignments of the ATP binding sites of the bacterial ligase DDl and protein and lipid kinases in complex with ATP analogs. We tested a series of commercially available kinase inhibitors and found LFM-A13 and Tyrphostine derivatives to inhibit DDl enzyme activity. Based on the initial screening results we synthesized a series of malononitrilamide and salicylamide derivatives and were able to confirm the validity of these scaffolds as inhibitors of DDl. From this investigation we gained a better understanding of the structural requirements and limitations necessary for the preparation of ATP competitive DDl inhibitors. The compounds in this study may serve as starting points for the development of bi-substrate inhibitors that incorporate both, an ATP competitive and a substrate competitive moiety. Bisubstrate inhibitors that block the ATP and D-Ala binding sites should exhibit enhanced selectivity and potency profiles by preferentially inhibiting DDl over kinases. In the second project, an optimized synthesis for tha alkylation of cysteins using the thiol ene reaction was establisehd. This new protocol allowed us to obtain large amounts of hexadecylated cysteine that was required for the synthesis of differently lipidated peptides. Afterwards the synthesis of various N-ras peptides bearing different lipid anchors was performed and the peptides were ligated to a truncated N-ras protein. The influence of this differently lipidated N-ras proteins on the partioning and association of N-Ras in model membrane subdomains was studied using Atomic Force Microscopy.

Rapid, combinatorial analysis of membrane compartments in intact plants with a multicolor marker set.

Plant membrane compartments and trafficking pathways are highly complex, and are often distinct from those of animals and fungi. Progress has been made in defining trafficking in plants using transient expression systems. However, many processes require a precise understanding of plant membrane trafficking in a developmental context, and in diverse, specialized cell types. These include defense responses to pathogens, regulation of transporter accumulation in plant nutrition or polar auxin transport in development. In all of these cases a central role is played by the endosomal membrane system, which, however, is the most divergent and ill-defined aspect of plant cell compartmentation. We have designed a new vector series, and have generated a large number of stably transformed plants expressing membrane protein fusions to spectrally distinct, fluorescent tags. We selected lines with distinct subcellular localization patterns, and stable, non-toxic expression. We demonstrate the power of this multicolor 'Wave' marker set for rapid, combinatorial analysis of plant cell membrane compartments, both in live-imaging and immunoelectron microscopy. Among other findings, our systematic co-localization analysis revealed that a class of plant Rab1-homologs has a much more extended localization than was previously assumed, and also localizes to trans-Golgi/endosomal compartments. Constructs that can be transformed into any genetic background or species, as well as seeds from transgenic Arabidopsis plants, will be freely available, and will promote rapid progress in diverse areas of plant cell biology.

A parameter-free approach for solving combinatorial optimization problems through biased randomization of efficient heuristics

This paper discusses the use of probabilistic or randomized algorithms for solving combinatorial optimization problems. Our approach employs non-uniform probability distributions to add a biased random behavior to classical heuristics so a large set of alternative good solutions can be quickly obtained in a natural way and without complex conguration processes. This procedure is especially useful in problems where properties such as non-smoothness or non-convexity lead to a highly irregular solution space, for which the traditional optimization methods, both of exact and approximate nature, may fail to reach their full potential. The results obtained are promising enough to suggest that randomizing classical heuristics is a powerful method that can be successfully applied in a variety of cases.

Combinatorial Anti-arenaviral Therapy with the Small Molecule SKI-1/S1P Inhibitor PF-429242 and Ribavirin

Arenaviruses are enveloped negative strand viruses that cause acute and chronic infections. Several Arenaviruses can cause severe hemorrhagic fever in humans. In West Africa Lassa virus causes several hundred thousand infections per year, while Junin, Machupo, Guanarito, and Sabia virus have emerged in South America. So far, only one drug is licensed against arenaviruses, the nucleoside analogue Ribavirin (Rib), which is effective when given early in disease, but shows only minor therapeutic effects in late stages of the infection. Previous works demonstrated that processing of the arenavirus glycoprotein precursor (GPC) by the cellular proprotein convertase site 1 protease (S1P), also known as subtilisin-kexinisozyme 1 (SKI-1), is crucial for cell-to-cell propagation of infectionand production of infectious virus. Recently, the SKI-1/S1P inhibitor PF-429242wasshownto inhibit Old World arenavirusGPCprocessing, cell-to-cell propagation, and infectious virus production. In the present study, we assessed the activity of PF-429242 against processing of the GPCs of the genetically and structurally more distant New World arenaviruses and found potent inhibition of processing of the GPCs of Junin, Machupo, and Guanarito virus. Using the prototypic arenavirus lymphocytic choriomeningitis virus (LCMV), we studied the potency of PF-429242 in the context of acute and chronic infection. In line with published data, PF-429242 potently inhibited acute LCMV infection. PF-429242 was also highly active against chronic infection and drug treatment resulted in rapid extinction of the virus without emergence of drug-resistant variants. In a combinatorial drug approach, we found that PF-429242 potentiated the anti-viral effect of Rib in treatment of acute andchronic infection. Taken together, we showed that the SKI-1/S1P inhibitor PF-429242 is broadly active against GPC processing of all major human pathogenic arenaviruses. Apart from being potent in acute infection, the drug is remarkably active in clearing chronic infection and potentiated the anti-arenaviral activity of Rib.

Combinatorial effects of splice variants modulate function of Aiolos

The transcription factor Aiolos (also known as IKZF3), a member of the Ikaros family of zinc-finger proteins, plays an important role in the control of B lymphocyte differentiation and proliferation. Previously, multiple isoforms of Ikaros family members arising from differential splicing have been described and we now report a number of novel isoforms of Aiolos. It has been demonstrated that full-length Ikaros family isoforms localize to heterochromatin and that they can associate with complexes containing histone deacetylase (HDAC). In this study, for the first time we directly investigate the cellular localization of various Aiolos isoforms, their ability to heterodimerize with Ikaros and associate with HDAC-containing complexes, and the effects on histone modification and binding to putative targets. Our work demonstrates that the cellular activities of Aiolos isoforms are dependent on combinations of various functional domains arising from the differential splicing of mRNA transcripts. These data support the general principle that the function of an individual protein is modulated through alternative splicing, and highlight a number of potential implications for Aiolos in normal and aberrant lymphocyte function.

Toward synthetic combinatorial peptide libraries in positional scanning format (PS-SCL)-based identification of CD8+ Tumor-reactive T-Cell Ligands: a comparative analysis of PS-SCL recognition by a single tumor-reactive CD8+ cytolytic T-lymphocyte clone.

The use of synthetic combinatorial peptide libraries in positional scanning format (PS-SCL) has emerged recently as an alternative approach for the identification of peptides recognized by T lymphocytes. The choice of both the PS-SCL used for screening experiments and the method used for data analysis are crucial for implementing this approach. With this aim, we tested the recognition of different PS-SCL by a tyrosinase 368-376-specific CTL clone and analyzed the data obtained with a recently developed biometric data analysis based on a model of independent and additive contribution of individual amino acids to peptide antigen recognition. Mixtures defined with amino acids present at the corresponding positions in the native sequence were among the most active for all of the libraries. Somewhat surprisingly, a higher number of native amino acids were identifiable by using amidated COOH-terminal rather than free COOH-terminal PS-SCL. Also, our data clearly indicate that when using PS-SCL longer than optimal, frame shifts occur frequently and should be taken into account. Biometric analysis of the data obtained with the amidated COOH-terminal nonapeptide library allowed the identification of the native ligand as the sequence with the highest score in a public human protein database. However, the adequacy of the PS-SCL data for the identification for the peptide ligand varied depending on the PS-SCL used. Altogether these results provide insight into the potential of PS-SCL for the identification of CTL-defined tumor-derived antigenic sequences and may significantly implement our ability to interpret the results of these analyses.