Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $\Theta(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.Comment: To appear in the proceedings of WORDS 201

T-2 toksin - pojavnost i toksičnost u peradi

T-2 toxin is the most toxic type A trichothecene mycotoxin. It is the secondary metabolite of the Fusarium fungi, and is common in grain and animal feed. Toxic effects have been shown both in experimental animals and in livestock. It has been implicated in several outbreaks of human mycotoxicoses. Toxic effects in poultry include inhibition of protein, DNA, and RNA synthesis, cytotoxicity, immunomodulation, cell lesions in the digestive tract, organs and skin, neural disturbances and low performance in poultry production (decreased weight gain, egg production, and hatchability). Concentrations of T-2 toxin in feed are usually low, and its immunosuppressive effects and secondary infections often make diagnosis difficult. If at the onset of the disease, a change in diet leads to health and performance improvements in animals, this may point to mycotoxin poisoning. Regular control of grain and feed samples is a valuable preventive measure, and it is accurate only if representative samples are tested. This article reviews the incidence and toxic effects of T-2 toxin in poultry.T-2 toksin je najtoksičniji predstavnik trikotecenskih mikotoksina tipa A. On je sekundarni produkt metabolizma plijesni roda Fusarium i često je prisutan u žitaricama i hrani za životinje. Štetni učinci uočeni su u eksperimentalnih životinja i životinja u uzgoju. On se povezuje s pojavom bolesti ljudi od mikotoksikoza. Učinci toksina u peradi su višestruki: inhibicija sinteze proteina, DNA i RNA, citotoksični učinak, imunomodulatorni učinak, oštećenje stanica probavnog sustava, organa i kože, živčani poremećaji te pad proizvodnih karakteristika u uzgoju peradi (slabiji prirast, pad nesivosti i valivosti). Koncentracije T-2 toksina u hrani redovito su vrlo malene, a zbog imunosupresivnog djelovanja toksina te istodobne sekundarne infekcije bolest se često teško dijagnosticira. Pri pojavi bolesti promjenom hrane može doći do poboljšanja zdravstvenog stanja, što tako|er upućuje na moguće trovanje mikotoksinima. Redovita kontrola uzoraka žitarica i hrane za životinje jedna je od preventivnih mjera, a detekcija mikotoksina u žitaricama i hrani pouzdana je samo ako se ispituje reprezentativan uzorak. U radu su opisani učestalost i toksični učinci T-2 toksina u peradi

Another Generalization of Abelian Equivalence: Binomial Complexity of Infinite Words

peer reviewedThe binomial coefficient of two words u and v is the number of times v occurs as a subsequence of u. Based on this classical notion, we introduce the m-binomial equivalence of two words refining the abelian equivalence. The m-binomial complexity of an infinite word x maps an integer n to the number of m-binomial equivalence classes of factors of length n occurring in x. We study the first properties of m-binomial equivalence. We compute the m-binomial complexity of the Sturmian words and of the Thue-Morse word. We also mention the possible avoidance of 2-binomial squares

Synthesis of DNA‐encoded disulfide‐ and thioether‐cyclized peptides

DNA-encoded chemical library technologies enable the screening of large combinatorial libraries of chemically and structurally diverse molecules, including short cyclic peptides. A challenge in the combinatorial synthesis of cyclic peptides is the final step, the cyclization of linear peptides that typically suffers from incomplete reactions and large variability between substrates. Several efficient peptide cyclization strategies rely on the modification of thiol groups, such as the formation of disulfide or thioether bonds between cysteines. In this work, we established a strategy and reaction conditions for the efficient chemical synthesis of cyclic peptide-DNA conjugates based on linking the side chains of cysteines. We tested two different thiol-protecting groups and found that tert-butylthio (S-tBu) works best for incorporating a pair of cysteines, and we show that the DNA-linked peptides can be efficiently cyclized through disulfide and thioether bond formation. In combination with established procedures for DNA encoding, the strategy for incorporation of cysteines may be readily applied for the generation and screening of disulfide- and thioether-cyclized peptide libraries

Arithmetic discrete planes are quasicrystals

Abstract. Arithmetic discrete planes can be considered as liftings in the space of quasicrystals and tilings of the plane generated by a cut and project construction. We first give an overview of methods and properties that can be deduced from this viewpoint. Substitution rules are known to be an efficient construction process for tilings. We then introduce a substitution rule acting on discrete planes, which maps faces of unit cubes to unions of faces, and we discuss some applications to discrete geometry

Thiol-to-amine cyclization reaction enables screening of large libraries of macrocyclic compounds and the generation of sub-kilodalton ligands

Macrocyclic compounds are an attractive modality for drug development, but the limited availability of large, structurally diverse macrocyclic libraries hampers the discovery of leads. Here, we describe the discovery of efficient macrocyclization reactions based on thiol-to-amine ligations using bis-electrophiles, their application to synthesize and screen large libraries of macrocyclic compounds, and the identification of potent small macrocyclic ligands. The thiol-to-amine cyclization reactions showed unexpectedly high yields for a wide substrate range, which obviated product purification and enabled the generation and screening of an 8988 macrocycle library with a comparatively small effort. X-ray structure analysis of an identified thrombin inhibitor (Ki = 42 ± 5 nM) revealed a snug fit with the target, validating the strategy of screening large libraries with a high skeletal diversity. The approach provides a route for screening large sub-kilodalton macrocyclic libraries and may be applied to many challenging drug targets