The endocannabinoidome (eCBome) and the gut microbiota have been implicated in diet-induced obesity and impaired metabolism. While the eCBome and the gut microbiome are known to respond to diet macronutrient composition, interaction with micronutrient intake has been relatively unexplored. Iron (Fe) is an essential micronutrient for the function of enzymes involved in energy and lipid metabolism. Here, we evaluated how 28 days of Fe depletion and enrichment, in interaction with Low Fat-Low Sucrose (LFLS) or High Fat-High Sucrose (HFHS) diets, affect the host via the eCBome, and modulate intestinal gut microbial communities. Circulating levels of N-oleoyl-ethanolamine (OEA) showed an elevation associated with Fe-enriched LFLS diet, while the Fe-depleted HFHS diet showed an elevation of N-arachidonoyl-ethanolamine (anandamide, AEA) and a decrease of circulating linoleic acid. In parallel, the response of intestinal inflammatory mediators to Fe in the diet showed decreased levels of prostaglandins PGE1, PGE3, and 1a,1b-dihomo PGF2α in the caecum. Individual differences in microbial taxa were less pronounced in the ileum than in the caecum, where Eubacterium coprostanoligenes group showed an increase in relative abundance associated with Fe-depleted LFLS diets. In conclusion, our study shows that Fe intake modulates the response to the macronutrient composition of the diet in mice.

In this note, we discuss a representation of the class of polynomials with real coefficients having all zeros in a given disk of the complex plane C, in terms of convex combinations of certain extremal polynomials of this class. The result stated in the theorem is known [1] for polynomials having n real zeros in the interval [a.b.]. In the following z will be a complex number and D[(a + b)/2, (b-a)/2] the closed disk of the complex plane centered at the real point (a + b)/2 and having radius (b-a)/2.

Dans cette note, nous employons la terminologie et les définitions de [1] et [3].A un sous-espace vectoriel W d'un espace vectoriel V pré-ordonné par un cône convexe pointé V + avec élément unité e, nous associons la semi-norme suivante: pour x ϵ V, pw (x)=inf{ε>0|∃ωε ϵ W tel que -ωε-εe≤x≤ωε+εe}. Posons J(W)={x|pw(x)=0}={x ϵ V|∀ε > 0, ∃ωε ϵ W, -ωε-εe≤x≤ωε+εe}. J(W) est un idéal.

En étudiant certains cônes de fonctionnelles affines positives, nous avons été amenés à considérer les polynômes qui sont positifs sur l'intervalle [-1, 1]. En fait, la fonctionnelle affine