Asymptotic behavior of mean fixation times in the Moran process with frequency-independent fitnesses

We derive asymptotic formulae in the limit when population size N tends to infinity for mean fixation times (conditional and unconditional) in a population with two types of individuals, A and B, governed by the Moran process. We consider only the case in which the fitness of the two types do not depend on the population frequencies. Our results start with the important cases in which the initial condition is a single individual of any type, but we also consider the initial condition of a fraction x, 0<x<1, of A individuals, where x is kept fixed and the total population size tends to infinity. In the cases covered by Antal and Scheuring (Bull Math Biol 68(8):1923-1944, 2006), i.e. conditional fixation times for a single individual of any type, it will turn out that our formulae are much more accurate than the ones they found. As quoted, our results include other situations not treated by them.Comment: 29 pages, 6 figure

Biomatemática: que mistura é essa?

Explicamos de maneira bastante introdutória alguns modelos matemáticos para fenômenos da Biologia, mostrando a importância que a Matemática pode ter para o entendimento de algumas questões biológicas. Falamos em particular de modelos para epidemias, crescimento populacional, interações ecológicas e a evolução da espécie humana. Na maior parte do artigo os modelos ilustrados são determinísticos, mas também falamos um pouco sobre modelos estocásticos

Anti-inflammatory and antioxidant nanostructured cellulose membranes loaded with phenolic-based ionic liquids for cutaneous application

The utilization of natural compounds, such as phenolic acids and biopolymers, in the healthcare domain is gaining increasing attention. In this study, bacterial nanocellulose (BC) membranes were loaded with ionic liquids (ILs) based on phenolic acids. These ionic compounds, with improved solubility and bioavailability, were prepared by combining the cholinium cation with anions derived from caffeic, ellagic and gallic acids. The obtained BC-ILs membranes were homogeneous, conformable and their swelling ability agreed with the solubility of each IL. These membranes revealed a controlled ILs dissolution rate in the wet state and high antioxidant activity. In vitro assays performed with Raw 264.7 macrophages and HaCaT keratinocytes revealed that these novel BC-ILs membranes are non-cytotoxic and present relevant anti-inflammatory properties. Diffusion studies with Hanson vertical diffusion cells showed a prolonged release profile of the ILs from the BC membranes. Thus, this work, successfully demonstrates the potential of BC-ILs membranes for skin treatment.publishe

Surface hydrophobization of bacterial and vegetable cellulose fibers using ionic liquids as solvent media and catalysts

The surface hydrophobization through heterogeneous chemical modification of bacterial (and vegetable) cellulose fibers with several anhydrides (acetic, butyric, hexanoic and alkenyl succinic anhydrides) and hexanoyl chloride suspended in an ionic liquid, tetradecyltrihexylphosphonium bis(trifluoromethylsulfonyl) imide, [TDTHP][NTf(2)], was studied. Furthermore, in the reaction with hexanoyl chloride, another ionic liquid, N-hexyl-4-(dimethylamino)pyridinium bis(trifluoromethylsulfonyl) imide, [C(6)N(CH(3))(2)py][NTf(2)], was used instead of common organic bases as catalyst and to trap the released HCl. The analysis of the ensuing modified fibers by FTIR, XRD and SEM clearly showed that the esterification reactions occurred essentially at the fibers' outmost layers, not affecting their ultrastructure. The degree of substitution (DS) of the ensuing esterified fibers ranged from less than 0.002 to 0.41; and in all instances, the fibers' surface acquired a high hydrophobicity. This novel approach constitutes an important strategy in the preparation of modified fibers under greener conditions relaying in the use of non-volatile solvents.FCT - SFRH/BD/72830/2010SFRH/BPD/41781/2007PTDC/QUI/68472/2006PTDC/QUI/72903/200