Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay

We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of time ago. In the biological-type model, new players are born from parents who played in the past. We consider two-player games with two strategies and a unique mixed evolutionarily stable strategy. We show that in the first type of dynamics, it is asymptotically stable for small time delays and becomes unstable for big ones when the population oscillates around its stationary state. In the second type of dynamics, however, evolutionarily stable strategy is asymptotically stable for any size of a time delay.     

Force-extension formula for the worm-like chain model from a variational principle

Stiff polymers, such as single-stranded DNA, unstructured RNA and cellulose, are all basically extremely long rods with relatively short repeating monomers. The simplest model for describing such stiff polymers is called the freely jointed chain model, which treats a molecule as a chain of perfectly rigid subunits of orientationally independent statistical segments, joined together by perfectly flexible hinges. A more realistic model that incorporates the entropic elasticity of a molecule, called the worm-like chain model, has been proposed by assuming that each monomer resists the bending force. Some force-extension formulae for the worm-like chain model have been previously found in terms of interpolation and numerical solutions resulting from statistical mechanics. In this paper, however, we adopt a variational principle to seek the minimum energy configuration of a stretched molecule by incorporating all the possible orientations of each monomer under thermal equilibrium, i.e., constant temperature. We determine a force-extension formula for the worm-like chain model analytically. We find that our formula suggests new terms such as the free energy and the cut-off force of a molecule, which define a clear transition from the entropic regime to the enthalpic regime and the fracture of the molecule, respectively. In addition, we predict two possible phase changes for a stretched molecule, i.e., from a super-helix to a soliton and then from a soliton to a vertical twisted line. We show theoretically that a molecule must undergo at least one phase change before it is fully stretched into its total contour length. This new formula is used to fit recent experimental data and shows a good agreement with some current literature that uses a statistical approach. Finally, an instability analysis is adopted to investigate the sensitivity of the new formula subject to small changes in temperature.     

Convection Effects in the BIAcore Dextran Layer: Surface Reaction Model

The BIAcore is a surface plasmon resonance (SPR) device used to measure rate constants, primarily for biochemical reactions. It consists of a flow channel containing one reactant adjoining a dextran gel containing the other. In order to explain anomalous measurements from the device, it has been proposed that some flow penetrates into the dextran layer, thus enhancing transport. A model is presented that accounts for such behavior, and typical velocity fields in the dextran are constructed. The system is analyzed in the limit of the surface reaction model, which corresponds to the limit of thin dextran layers. Asymptotic and singular perturbation techniques are used to analyze association and dissociation kinetics. Linear and nonlinear integral equations result from the analysis; explicit and asymptotic solutions are constructed for physically realizable cases. The results indicate that the effects of such penetration are bound to be small, regardless of the flow model used.     

Bioavailability of zinc and its binding to casein in milks and formulas

Differences in zinc bioavailability among milk and formulas may be attributed to binding of zinc to various ligands. We determined the distribution of zinc and protein at different pHs and zinc and calcium concentrations. We used radiolabelled cow's milk, human milk, whey-predominant (WPF) and casein-predominant (CPF) infant formula. Lowering the pH changed zinc and protein distribution: zinc shifted from pellet (casein) to whey in cow's milk, from fat to whey in human milk and from fat and pellet to whey in formulas. Protein shifted from whey to pellet in human milk and from whey and pellet to fat in formulas. Increasing zinc and calcium concentrations shifted protein and zinc from pellet to whey for cow's milk and from whey and pellet to fat for the formulas. Protein distribution was not affected by calcium or zinc addition in human milk or CPF, while zinc shifted from whey to fat in human milk and from fat and pellet to whey in CPF. Zinc and calcium binding to isolated bovine or human casein increased with pH. At 500 mg/L of zinc, bovine casein bound 32.0 +/- 1.8 and human casein 10.0 +/- 0.9 mg zinc/g protein. At 500 mg/L of calcium, calcium was preferentially bound over zinc. Adding calcium and zinc resulted in 32.0 +/- 1.8 mg zinc/g bound to bovine casein and 17.0 +/- 0.8 mg zinc/g to human casein, while calcium binding was low. Suckling rat pups dosed with 65Zn labelled infant diets were killed and individual tissues were gamma counted. Lower zinc bioavailability was found for bovine milk at pH = 4.0 (%65Zn in liver = 18.7+1.4) when compared to WPF (22.8 +/- 1.6) or human milk (26.9 +/- 0.8). Lowering the pH further decreased zinc bioavailability from human milk, but not from cow's milk or WPF. Knowledge of the compounds binding minerals and trace elements in infant formulas is essential for optimizing zinc bioavailability.     

鳄梨油在化妆品中的应用及配方

本文对鳄梨油的化学成分、生物活性及美容化妆品配方进行概述。     

Effect of dietary docosahexaenoic acid on biosynthesis of docosahexaenoic acid from alpha-linolenic acid in young rats

Docosahexaenoic acid (DHA), a crucial nervous system n-3 PUFA, may be obtained in the diet or synthesized in vivo from dietary alpha-linolenic acid (LNA). We addressed whether DHA synthesis is regulated by the availability of dietary DHA in artificially reared rat pups, during p8 to p28 development. Over 20 days, one group of rat pups was continuously fed deuterium-labeled LNA (d5-LNA) and no other n-3 PUFA (d5-LNA diet), and a second group of rat pups was fed a d5-LNA diet with unlabeled DHA (d5-LNA + DHA diet). The rat pups were then euthanized, and the total amount of deuterium-labeled docosahexaenoic acid (d5-DHA) (synthesized DHA) as well as other n-3 fatty acids present in various body tissues, was quantified. In the d5-LNA + DHA group, the presence of dietary DHA led to a marked decrease (3- to 5-fold) in the total amount of d5-DHA that accumulated in all tissues that we examined, except in adipose. Overall, DHA accretion from d5-DHA was generally diminished by availability of dietary preformed DHA, inasmuch as this was found to be the predominant source of tissue DHA. When preformed DHA was unavailable, d5-DHA and unlabeled DHA were preferentially accreted in some tissues along with a net loss of unlabeled DHA from other organs.     

Effect of environmental stresses on the sensitivity of Enterobacter sakazakii in powdered infant milk formula to gamma radiation

Aim:  To evaluate the effect of starvation, heat, cold, acid, alkaline, chlorine and ethanol stresses on the resistance of Enterobacter sakazakii in powdered infant milk formula (PIMF) towards gamma radiation.
Methods and Results:  Stressed cells of E. sakazakii ATCC 51329 and four other food isolate strains were mixed individually with PIMF, kept overnight at room temperature, and then exposed to gamma radiation up to 7·5 kGy. The D ₁₀-values were determined using linear regression and for the stressed E. sakazakii strains these values ranged from 0·82 to 1·95 kGy.
Conclusions:  Environmental stresses did not significantly change the sensitivity of most E. sakazakii strains to ionizing radiation.
Significance and Impact of the Study:  Data obtained established that most forms of environmental stress are unlikely to significantly enhance the resistance of E. sakazakii strains to lethal, low dose irradiation treatment.     

一类含分布时滞革新传播模型的稳定性

建立了一类含分布时滞的革新传播模型dU（t）/dt=-（α＋βA（t））U（t）-pU（t）＋p,dA（t）/dt=∫＋∞ 0 αE（τ）U（t-τ）dτ＋βU（t）A（t）-（p＋k）A（t）。研究了分布时滞对传播过程的影响,讨论了正平衡点的存在性和唯一性及其局部与全局的渐近稳定性,当分布时滞的核函数取δe^-δτ时,证明了正平衡点是绝对渐近稳定的。