Search

The Oberwolfach Problem $OP(F)$ -- posed by Gerhard Ringel in 1967 -- is a paradigmatic Combinatorial Design problem asking whether the complete graph $K_v$ decomposes into edge-disjoint copies of a $2$-regular graph $F$ of order $v$. In this paper, we provide all the necessary equipment to generate solutions to $OP(F)$ for relatively small orders by using the so-called difference methods. From the theoretical standpoint, we present new insights on the combinatorial structures involved in the solution of the problem. Computationally, we provide a full recipe whose base ingredients are advanced optimization models and tailored algorithms. This algorithmic arsenal can solve the $OP(F)$ for all possible orders up to $60$ with the modest computing resources of a personal computer. The new $20$ orders, from $41$ to $60$, encompass $241200$ instances of the Oberwolfach Problem, which is 22 times greater than those solved in previous contributions., Pre-print: 31 pages, 6 figures. Code available on gitHub

GI inflammation involves pathological processes affecting the gut epithelial barrier that are poorly reversible. A direct target of such processes is the enterocyte monolayer, which absorptive function is challenged by inflammation-induced cytoskeleton dynamics. Here, we evaluate the proinflammatory effects of PMA (phorbol-12-myristate-13-acetate) on Caco-2 intestinal cells at two different stages of spontaneous differentiation i.e. undifferentiated (7 dps, days post seeding) and differentiated enterocyte-like cells (>21 dps) in the presence/absence of the natural dipeptide carnosine (CAR) as potential anti-inflammatory molecule. By analysing actin cytoskeleton in 7 dps Caco-2 monolayers versus 21 dps monolayers, we revealed opposite effects of PMA which respectively induced disruption vs. intensification of actin rings and fibers; in both cases, simultaneous administration of PMA and CAR showed counteracting effects. Remarkably, the mRNA expression analysis of the ACTB (actin b) gene mirrored the morphological evidences and the counteraction of CAR. Moreover, the mRNA expression analysis of the AIF-1 gene (Allograft Inflammatory Factor 1) revealed opposite trends in 7 dps- versus 21 dps-grown Caco-2 with respect to PMA effects, and the same holds true for the SLC15A4/PHT1 gene involved both in intestinal peptide absorption and inflammatory responses; nevertheless, AIF-1 mRNA were not affected by CAR, whilst SLC15A4/PHT1 mRNA showed CAR-dependent up-regulation regardless of the differentiation stage. Overall, our results describe cytoskeletal and gene expression modulations which hint a model to distinguish physiological and inflammatory responses based on the differentiation stage of the Caco-2 monolayer and on the effects of CAR as differentially protective substrate.

Programme and Abstracts of the 68th National Congress of the Italian Physiological Society (Società Italiana di Fisiologia) (Abstract) Carnosine (β-Ala-L-his, CAR) is an endogenous dipeptide acknowledged to contribute to maintenance of intracellular homeostasis in vertebrate excitable tissues. CAR biochemical properties (e.g. antioxidant and antiglycating activity) account for CAR homeostatic function(s) in many dysregulated states, such as hyperglycaemia upsetting diabetes-targeted tissue/organ districts. In this view, CAR hypoglycaemic effects have been shown to be physiologically regulated in the peripheral nervous system. Previously, we reported responsiveness of CAR-regulating genes in peripheral nerves of hyperglycaemic mice; remarkably, this responsiveness is strongly enhanced in the nerve’s fibroblast component. Here, we identify variations in expression of genes responsible for biosynthesis, degradation and transmembrane transport of CAR in the NIH/3T3 model of murine fibroblasts exposed to a hyperglycaemic stress, in the presence or absence of extracellular CAR. In parallel, we detect functional protection against the stress induced by glucose excess due to CAR, which inhibits ROS production and apoptotic events, and preserves fibroblast proliferation. Overall, the in vitro cellular model mirrors the ex vivo evidence in the peripheral nerves of hyperglycaemic mice, highlighting the (patho)physiological impact of CAR homeostatic variations in diabetes-targeted tissues and, remarkably, in fibroblasts, for which a functional role of ‘sensors’ of hyperglycaemic impairment in tissues could be reckoned.