The effect of intrinsic stochasticity on transmitted HIV drug resistance patterns.

Estimates of transmitted HIV drug-resistance prevalence vary widely among and within epidemiological surveys. Interpretation of trends from available survey data is therefore difficult. Because the emergence of drug-resistance involves small populations of infected drug-resistant individuals, the role of stochasticity (chance events) is likely to be important. The question addressed here is: how much variability in transmitted HIV drug-resistance prevalence patterns arises due to intrinsic stochasticity alone, i.e., if all starting conditions in the different epidemics surveyed were identical? This 'thought experiment' gives insight into the minimum expected variabilities within and among epidemics. A simple stochastic mathematical model was implemented. Our results show that stochasticity alone can generate a significant degree of variability and that this depends on the size and variation of the pool of new infections when drug treatment is first introduced. The variability in transmitted drug-resistance prevalence within an epidemic (i.e., the temporal variability) is large when the annual pool of all new infections is small (fewer than 200, typical of the HIV epidemics in Central European and Scandinavian countries) but diminishes rapidly as that pool grows. Epidemiological surveys involving hundreds of new infections annually are therefore needed to allow meaningful interpretation of temporal trends in transmitted drug-resistance prevalence within individual epidemics. The stochastic variability among epidemics shows a similar dependence on the pool of new infections if treatment is introduced after endemic equilibrium is established, but can persist even when there are more than 10,000 new infections annually if drug therapy is introduced earlier. Stochastic models may therefore have an important role to play in interpreting differences in transmitted drug-resistance prevalence trends among epidemiological surveys.

Electron delocalization patterns in models of distorted (D2d) mixed-valence cubanes.

Low-symmetry distortions are present in cubanes such as Fe(4)S(4), but their effects on electron delocalization properties are not well-understood. Mixed-valence cubanes often exhibit experimentally measurable "pair delocalization" of a delocalizable electron. An important question is, what is the role of physical interactions (vibronic, electronic, exchange) and symmetry distortions in determining the electron delocalization pattern? Semiclassical models are used to explore the electron delocalization patterns of S=1/2 tetragonally (D(2d)) distorted mixed-valence cubanes comprising four metal centers with bridging ligands, a single delocalizable "excess" electron, and either closed-shell or open-shell ion cores. Phase diagrams show that distorted S=1/2 ground state cubanes with antiferromagnetic exchange (as found in nature) have delocalization patterns qualitatively similar to those of an S=1/2 model with no Heisenberg exchange, suggesting that exchange is not necessarily a dominant factor in determining electron delocalization properties. The open-shell model reveals two types of pair delocalization for the S=1/2 ground state, with differing dimer subunit spins for compressed and elongated geometries. Previous studies emphasize the importance of exchange interactions for pair delocalization. Here, it is shown that electron exchange is not always necessary for pair delocalization and that it can be achieved with relatively small tetragonal distortions from tetrahedral (T(d)) symmetry. The results contradict those of an earlier theoretical study of distorted Fe(4)S(4) clusters, which concluded that distortions of lower symmetry than D(2d) are necessary to induce a transition to pair delocalization.

On the origin of the Murchison meteorite phosphonates. Implications for pre-biotic chemistry.

Ab initio calculations, combined with experimental studies on the anaerobic hydrolysis of phosphaalkynes under thermal and photochemical conditions suggest a potential, exogenous source of reduced oxidation state phosphorus for the early Earth.