Modelling HIV immune response and validation with clinical data

A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria. We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+T-cell help in the generation of CD8+memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients.     

The dynamics of two-species allelopathic competition with optimal harvesting

This paper analyses a bionomic model of two competitive species in the presence of toxicity with different harvesting efforts. An interesting dynamics in the first quadrant is analysed and two saddle-node bifurcations are detected for different bifurcation parameters. It is noted that under certain parametric restrictions, the model has a unique positive equilibrium point that is globally asymptotically stable whenever it is locally stable. It is also noted that the model can have zero, one or two feasible equilibria appearing through saddle-node bifurcations. The non-existence of a limit cycle in the interior of the first quadrant is also discussed using the Poincare–Dulac criteria. The saddle-node bifurcations are studied using Sotomayor's theorem. Numerical simulations are carried out to validate the analytical findings. The conditions for the existence of bionomic equilibria are discussed and an optimal harvesting policy is derived using Pontryagin's maximum principle.     

Between cheap and costly signals: the evolution of partially honest communication

Costly signalling theory has become a common explanation for honest communication when interests conflict. In this paper, we provide an alternative explanation for partially honest communication that does not require significant signal costs. We show that this alternative is at least as plausible as traditional costly signalling, and we suggest a number of experiments that might be used to distinguish the two theories.     

Patterns of variation in tail ornament size in birds

In recent years several different kinds of sexual selection models have been developed, and tail ornaments in birds have frequently been used as an example of a sexually selected character where the models might apply. However, very little is known about intra- and interpopulation variation in ornament size. We have studied the elongated tail ornaments in four species of whydahs Vidua , the forktailed flycatcher Tyrannus savana and the Asian paradise flycatcher Terpsiphone paradisi. Ornaments were relatively longer in males with the longest tarsi ('heterogony' with positive allometry). Also, tail lengths were remarkably variable within each geographical area, the coefficient of variation (average = 11%) being three times as high as for body size characters. Models, with female preference of ornaments bearing no relation to male viability, usually generate lines of neutral equilibria. Thus, they predict extraordinary variation in ornaments between populations. However, elongated tail ornaments did not show higher geographical variation than the body size characters, suggesting that there is no line of equilibria for these ornaments.     

Aluminium,boron and molybdenum availability and uptake by rice in acid sulfate soils

Although Al toxicity is believed to be a problem in acid sulfate soils cropped to rice (Oryza, sativa L.), little is known about the behavior of other trace metals such as B and Mo in these soils. The objectives of this study were to measure the availability of Al, B, and Mo in these soils, to determine what governs the availability of these metals and to investigate the relationships between metal availability and uptake by rice. Metal availability and uptake by rice were evaluated in 134 flooded acid sulfate soils in the Central Plains region of Thailand and in a growth chamber study using 50 of the same soils. Soil and plant metal analyses were conducted at the panicle differentiation stage of growth in both studies and in the soil prior to transplanting in the growth chamber study. Metal activities were determined with GEOCHEM. The mineral phases believed to be governing Al³⁺ activities were jurbanite under low pH conditions and amorphous Al(OH)₃ at high pH. The Al chemistry is believed to be intimately linked to the redox-pH cycle, which is driven by the monsoonal climate. Mortality of rice associated with Al toxicity was observed under field and growth chamber conditions. Interference in P uptake and/or assimilation was believed to be the mechanism of Al toxicity. Activities of B(OH) ₄ ^– and B(OH) ₃ ⁰ were found to be highly correlated to pH and ionic strength, respectively, with the latter being the dominant B ion found in these soils. Activities of MoO ₄ ^2– were positively correlated to pH and appeared to be controlled by wulfenite. Leaf Mo contents were found to be positively correlated with MoO ₄ ^2– activity.     

Equilibria of polyoxometalates in aqueous solution

In most aqueous polyoxometalate systems, numerous, often highly negatively charged species, are formed. To establish the speciation in such complex polyanion systems, many experimental methods and techniques must be used. Moreover, it is of vital importance that the experimental data are of the highest accuracy and that the data collected from different methods are treated simultaneously with an appropriate computer program. In systems containing one or more sensitive NMR nuclei, a combined EMF-NMR method has been shown to be extremely powerful.This article firstly gives some general comments on equilibria in aqueous polyoxometalate systems including ionic medium effects, and then describes an equilibrium EMF-NMR (³¹P and⁵¹V) study of the five component system H⁺-Mo(VI)-V(V)-P(V)-e^–. The study has been focused on so-called Keggin ratio solutions, Mo+V):P=12:1, since these are commonly used in selective oxidation processes. Special attention has been given to Mo₁₀V₂P and Mo₉V₃P solutions, where positional isomers occur. We have been able to identify and characterize all the five possible isomers of -Mo₁₀V₂PO ₄₀ ^5– at 25 and 90 °C. Besides the results from the five component system, some interesting findings from the binary, ternary and quarternary sybsystems are also reported.     

The cyanobacterium Synechococcus R-2 (Anacystis nidulans, S. leopoliensis) PCC 7942 has a sodium-dependent chloride transporter

Synechococcus R-2 (PCC 7942) actively accumulated Cl^? in the light and dark, under control conditions (BG-11 media: pH_o, 7·5; [Na⁺]_o, 18 mol m^?3; [Cl^?]_o, 0·508 molm^?3). In BG-11 medium [Cl^?], was 17·2±0·848 mol m^?3 (light), electrochemical potential of Cl^? (ΔμCl^?_i,o) =+211±2mV; [Cl^?]_i= 1·24±0·11 mol m^?3(dark), ΔμCl^?_i,o=+133±4mV. Cl^? fluxes, but not permeabilities, were much higher in the light: ?Cl^?_i,o= 4·01±5·4 nmol m^?2 s^?1, ^PCl^?_i,o= 47±5pm s^?1 (light); ?Cl^?_i,o= 0·395±0·071 nmol m^?2 s^?1, _PCl^?_i,o= 69±14 pm s^?1 (dark). Chloride fluxes are inhibited by acid pH_o (pH_o 5; ?Cl^?_i,o= 0·14±0·04 nmol m^?2 s^?1); optimal at pH_o 7·5 and not strongly inhibited by alkaline pH_o (pH_o 10; ?Cl^?1_i,o= 1·7±0·14 nmol m^?2 s^?1). A Cl^?_in/2H⁺_in coporter could not account for the accumulation of Cl^? alkaline pH_o. Permeability of Cl^? is very low, below 100pm s^?1 under all conditions used, and appears to be maximal at pH_o 7·5 (50–70 pm s^?1) and minimal in acid pH_o (20pm s^?1). DCCD (dicyclohexyl-carbodiimide) inhibited ?Cl^?_i,o in the light about 75% and [Cl^?]_i fell to 2·2±0·26 (4) mol m^?3. Valinomycin had no effect but monensin severely inhibited Cl^? uptake ([Cl^?]_i= 1·02±0·32 mol m^?3; ?Cl^?_i,o= 0·20±0·1 nmol m^?2 s^?1). Vanadate (200 mmol m^?3) accelerated the Cl^? flux (?Cl^?_i,o= 5·28±0·64 nmol m^?2 s^?1) but slightly decreased accumulation of Cl^? ([Cl^?], = 13·9±1·3 mol m^?3) in BG-11 medium but had no significant effect in Na⁺-free media. DCMU (dichlorophenyldimethylurea) did not reduce [Cl^?], or ?Cl^?_i,o to that found in the dark ([Cl^?]_i= 8·41±0·76 mol m^?3; ?Cl^?_i,o= 2·06±0·36 nmol m^?2 s^?1). Synechococcus also actively accumulated Cl^? in Na⁺-free media, [Cl^?]_i was lower but ΔΨ_i,o hyperpolarized in Na⁺-free media and so the ΔμCl^?_i,o was little changed ([Cl^?]_i= 7·98±0·698 mol m^?3; ΔμCl^?_i,o=+203±3 mV). Net Cl^? uptake was stimulated by Na⁺; Li⁺ acted as a partial analogue for Na⁺. Synechococcus has a Na⁺ activated Cl^? transporter which is probably a primary 2Cl^?/ATP pump. The Cl^? pump is voltage sensitive. ΔμCl^?_i,o is directly proportional to ΔΨ_i,o(P»0·01%): ΔμCl^?_i,o= -1·487 (±0·102) ×ΔΨ_i,o, r= -0·983, n= 31. The ΔμCl^?_i,o increased (more positive) as the Δμ_i,o became more negative. The ΔμCl^?_i,o has no known function, but might provide a driving force for the uptake of micronutrients.     

Vapour-Liquid Phase Equilibria of n-alkanes by Direct Monte Carlo Simulations

Abstract

We report results of direct Monte Carlo simulations of n-pentane and n-decane at the liquidvapour interface for a number of temperatures. The intermolecular interactions are modeled using the last version of the anisotropic united atom model (AUA4). We have used the local long range correction energy and an algorithm allowing to select randomly with equal probability two different displacements. The liquid and vapour densities are in excellent agreement with experimental data and with those previously calculated using the GEMC method.     

Direct Evaluation of Vapour-Liquid Equilibria of Mixtures by Molecular Dynamics Using Gibbs-Duhem Integration

Abstract

We present an extension of the Gibbs-Duhem integration method that permits direct evaluation of vapour-liquid equilibria of mixtures by molecular dynamics. The Gibbs-Duhem integration combines the best elements of the Gibbs ensemble Monte Carlo technique and thermodynamic integration. Given conditions of coexistence of pure substances, simultaneous but independent molecular dynamics simulations of each phase at constant number of particles, constant pressure, constant temperature and constant fugacity fraction of species 2 are carried out in succession along coexistence lines. In each simulation, the coexistence pressure is adjusted to satisfy the Clapeyron-type equation. The Clapeyron-type equation is a first-order nonlinear differential equation that prescribes how the pressure must change with the fugacity fraction of species 2 to maintain coexistence at constant temperature. The Clapeyron-type equation is solved by the predictor-corrector method. Running averages of mole fraction and compressibility factor for the two phases are used to evaluate the right-hand side of the Clapeyron-type equation. The Gibbs-Duhem integration method is applied to three prototypes of binary mixtures of the two-centre Lennard-Jones fluid having various elongations. The starting points on the coexistence curve were taken from published data.