Theoretical optimization of Irinotecan-based anticancer strategies in the case of drug-induced efflux

The anticancer drug Irinotecan (CPT11) is known to trigger the induction of ATP-Binding Cassette (ABC) transporters, responsible for the efflux of the drug and its metabolites outside of the cells. The drug-modulated overexpression of those transporters prevents its accumulation in the intracellular medium, therefore decreasing its efficacy. A critical clinical concern lies in the design of CPT11-based therapeutic strategies which eradicate a maximum number of cancer cells despite their ability to become resistant. In order to address this issue, we supplemented an existing mathematical model of CPT11 molecular pharmacokinetics–pharmacodynamics (PK–PD) with a new model of CPT11-induced overexpression of ABC transporters. We then theoretically optimized exposure to CPT11 given as a single agent or combined either with ABC transporter inhibitors, or with inhibitors of nuclear factors whose activation is responsible for transporter overexpression. We firstly considered a cancer cell population endowed with the ability of inducing their transporters. For any drug combination, we concluded that the highest concentration of CPT11 should be administered in order to kill a maximum number of cancer cells, despite the triggering of resistance. We then considered a population of healthy cells which were assumed to be identical to cancer cells except that they were not able to become resistant. Optimal schemes were defined as the ones which maximized DNA damage in cancer cells under the constraint of DNA damage in healthy cells not exceeding a tolerability threshold. The optimal therapeutic strategy consisted in combining CPT11 with ABC transporter inhibitors as it achieved a complete reversal of resistance by means of the lowest concentrations of CPT11.     

On congruences of-normal semigroups-normal semigroups

Communicated by G. Lallement     

Experimental determination of rheological properties of polydimethylsiloxane

A series of linear polydimethylsiloxane of different molecular weight and with reduced polydispersity were prepared by partial fractionation of commercial products. The rheological functions, i.e. zero shear viscosity (η₀), first and second normal stress coefficients (Ψ₁₀ and Ψ₂₀), of the materials were experimentally measured by conventional rotational rheometers and by a rotation rod apparatus. The relationships between molecular structure (molecular weight and polydispersity index) and rheological functions are presented and discussed on the basis of equations proposed in the literature. Zero shear viscosity data conform to the well-known dependence on a power 3.5 of molecular weight. However, a consistently stronger influence of molecular weight over Ψ₁₀ and Ψ₂₀ is found. The influence of polydispersity over Ψ₁₀ is also analyzed.     

Nilpotent Ranks of Semigroups of Partial Transformations

A subset U of a semigroup S is a generating set for S if every element of S may be written as a finite product of elements of U. The rank of a finite semigroup S is the size of a minimal generating set of S, and the nilpotent rank of S is the size of a minimal generating set of S consisting of nilpotents in S. A partition of a q-element subset of the set X_n = {1,2,..., n} is said to be of type τ if the sizes of its classes form the partition τ of the positive integer q ≤ n. A non-trivial partition τ of q consists of k < q elements. For a non-trivial partition τ of q < n, the semigroup S(τ), generated by all the transformations with kernels of type τ, is nilpotent-generated. We prove that if τ is a non-trivial partition of q < n, then the rank and the nilpotent rank of S(τ) are both equal to the number of partitions X_n of type τ.     

A Direct Construction of Nontransitive Dice Sets

In this paper, we give a direct construction for a set of dice realizing any given tournament T. The construction for a tournament with n vertices requires dice with n sides if n is odd, sides if n is divisible by 4, and sides if mod 4. This appears to be the most efficient general construction to date. Our construction relies only on a standard construction from graph theory.     

Bronze Age pottery from the Aeolian Islands: definition of Temper Compositional Reference Units by an integrated mineralogical and microchemical approach

An integrated microchemical–petrographic approach is here proposed to discriminate the provenance of archaeological pottery artefacts from distinct production centres. Our study focuses on a statistically significant sampling (n=186) of volcanic temper-bearing potteries representative of the manufacturing and dispersion among the islands of the Aeolian Archipelago during the Bronze Age. The widespread establishment of new settlements and the abundant recovery of Aeolian-made ceramic in southern Italy attest for the increased vitality of the Archipelago during the Capo Graziano culture (Early Bronze Age–Middle Bronze Age 2; 2300–1430 BC). Potteries from three of the main known ancient communities (Lipari, Filicudi and Stromboli) have been studied integrating old collections and newly excavated material. Volcanic tempers have been first investigated through multivariate analyses of relative abundances of mineral and rock clasts along with petrographic characters. In addition, we performed in-situ mineral chemistry microanalyses by Electron Microprobe and Laser Ablation—Inductively Coupled Plasma Mass Spectrometry to assess major and trace element composition of the most common mineral phases. Four Temper Compositional Reference Units have been recognised based on compositional trends. Two units (AI and AX) are unequivocally distinct by their peculiar trace element enrichment and petrographic composition; they mostly contain samples from the sites of Lipari and Stromboli, respectively. Units AIV and AVIII, restricted to the sites of Filicudi and Stromboli, show distinct petrographic characters but overlapped geochemical fingerprints.