On the inadmissibility of Watterson's estimator

We consider the estimation of the scaled mutation parameter θ, which is one of the parameters of key interest in population genetics. We provide a general result showing when estimators of θ can be improved using shrinkage when taking the mean squared error as the measure of performance. As a consequence, we show that Watterson’s estimator is inadmissible, and propose an alternative shrinkage-based estimator that is easy to calculate and has a smaller mean squared error than Watterson’s estimator for all possible parameter values 0<θ<∞. This estimator is admissible in the class of all linear estimators. We then derive improved versions for other estimators of θ, including the MLE. We also investigate how an improvement can be obtained both when combining information from several independent loci and when explicitly taking into account recombination. A simulation study provides information about the amount of improvement achieved by our alternative estimators.     

On correcting the overestimation of the permutation-based false discovery rate estimator

MOTIVATION: Recent attempts to account for multiple testing in the analysis of microarray data have focused on controlling the false discovery rate (FDR), which is defined as the expected percentage of the number of false positive genes among the claimed significant genes. As a consequence, the accuracy of the FDR estimators will be important for correctly controlling FDR. Xie et al. found that the standard permutation method of estimating FDR is biased and proposed to delete the predicted differentially expressed (DE) genes in the estimation of FDR for one-sample comparison. However, we notice that the formula of the FDR used in their paper is incorrect. This makes the comparison results reported in their paper unconvincing. Other problems with their method include the biased estimation of FDR caused by over- or under-deletion of DE genes in the estimation of FDR and by the implicit use of an unreasonable estimator of the true proportion of equivalently expressed (EE) genes. Due to the great importance of accurate FDR estimation in microarray data analysis, it is necessary to point out such problems and propose improved methods. RESULTS: Our results confirm that the standard permutation method overestimates the FDR. With the correct FDR formula, we show the method of Xie et al. always gives biased estimation of FDR: it overestimates when the number of claimed significant genes is small, and underestimates when the number of claimed significant genes is large. To overcome these problems, we propose two modifications. The simulation results show that our estimator gives more accurate estimation.     

Physiological performance of silver-fir (Abies alba Mill.) populations under contrasting climates near the south-western distribution limit of the species

Silver-fir (Abies alba Mill.) populations located at the south side of the main Pyrenean axis and Pre-Pyrenees constitute the south-western distribution limit of the species and, therefore, may be responding more noticeably to climate change than those in the centre of the range. The increasing aridity detected in the Pyrenees during the 20th century should affect more negatively the physiological performance of the southernmost silver-fir stand growing under more xeric conditions in comparison with stands growing within the main distribution area under mesic conditions. To evaluate the climatic influence on the performance of silver fir near its distribution limit, we studied several physiological and growth variables in shoots and needles from two silver fir populations located in nearby but climatically contrasting sites: Paco Ezpela (site E) and Gamueta (site G). Site E showed a stronger Mediterranean influence than site G, i.e. the former site was characterized by higher temperatures and leaf-to-air water vapour pressure difference and lower precipitation in summer than the latter site. Silver firs from site E showed lower values of primary and secondary growth, needle length, stomatal conductance, net photosynthesis and photosystem II (PSII) efficiency than individuals from site G. The reduction in net photosynthesis could be ascribed to a low CO₂ availability and to a lower PSII efficiency. We conclude that the physiological differences found between both sites were caused by the more xeric conditions of site E as compared with the more mesic environment in site G. The predicted increase of severe droughts in the southern Pyrenees might cause a decrease in photosynthesis and growth in those silver-fir stands located near the ecological limit of the species.     

On the existence of limit cycles in motion field

In this paper we show the existence of limit cycles in the vector field generated by the perspective projection on the image plane of the velocity field of a moving surface. The existence of limit cycles is proved with the Poincaré-Bendixon theorem, in the case of a rotating smooth non-planar surface and illustrated with computer graphics. The structural stability of the limit cycles is also discussed.     

Sufficiency of the number of segregating sites in the limit under finite-sites mutation

We show that the number of segregating sites is a sufficient statistic for the scaled mutation parameter (θ) in the limit as the number of sites tends to infinity and there is free recombination between sites. We assume that the mutation parameter at each site tends to zero such than the total mutation parameter (θ) is constant in the limit. Our results show that Watterson’s estimator is the maximum likelihood estimator in this case, but that it estimates a composite parameter which is different for different mutation models. Some of our results hold when recombination is limited, because Watterson’s estimator is an unbiased, method-of-moments estimator regardless of the recombination rate. The quantity it estimates depends on the details of how mutations occur at each site.     

Leakage and slow allostery limit performance of single drug-sensing aptazyme molecules based on the hammerhead ribozyme

Engineered “aptazymes” fuse in vitro selected aptamers with ribozymes to create allosteric enzymes as biosensing components and artificial gene regulatory switches through ligand-induced conformational rearrangement and activation. By contrast, activating ligand is employed as an enzymatic cofactor in the only known natural aptazyme, the glmS ribozyme, which is devoid of any detectable conformational rearrangements. To better understand this difference in biosensing strategy, we monitored by single molecule fluorescence resonance energy transfer (FRET) and 2-aminopurine (AP) fluorescence the global conformational dynamics and local base (un)stacking, respectively, of a prototypical drug-sensing aptazyme, built from a theophylline aptamer and the hammerhead ribozyme. Single molecule FRET reveals that a catalytically active state with distal Stems I and III of the hammerhead ribozyme is accessed both in the theophylline-bound and, if less frequently, in the ligand-free state. The resultant residual activity (leakage) in the absence of theophylline contributes to a limited dynamic range of the aptazyme. In addition, site-specific AP labeling shows that rapid local theophylline binding to the aptamer domain leads to only slow allosteric signal transduction into the ribozyme core. Our findings allow us to rationalize the suboptimal biosensing performance of the engineered compared to the natural aptazyme and to suggest improvement strategies. Our single molecule FRET approach also monitors in real time the previously elusive equilibrium docking dynamics of the hammerhead ribozyme between several inactive conformations and the active, long-lived, Y-shaped conformer.     

Salt-tolerant Triticum×Lophopyrum derivatives limit the accumulation of sodium and chloride ions under saline-stress

Abstract. Cultivars of hexaploid wheat ( Triticum aestivum cvs. Chinese Spring or PI 178704) and derivatives containing chromosomes from both a cultivar and a wild, salt-tolerant species ( Lophopyrum elongatum or L. ponticum ) were compared to determine differences in growth, ion transport and ion accumulation under salt-stress. Two experiments were conducted in which plants were grown under saline and non-saline conditions and harvested at various lime intervals throughout ontogeny. Under salt-stress the growth rate of the cultivars, as compared to the growth rate of the derivatives, decreased more rapidly later in development. Transport rates from root to shoot of Na⁺ and Cl⁻ reached higher levels in the cultivars. The cultivars accumulated more Na⁺ and Cl⁻ and relatively less K⁺ in the shoot. The K⁺/Na⁺ ratio was higher in the derivatives than in the cultivars from which they were derived. The addition of chromosomes from Lophopyrum species into wheat altered ion accumulation, growth rates, and ion transport rates from root to shoot.     

The product of the retroviral transforming gene v-myb is a truncated version of the protein encoded by the cellular oncogene c-myb

Avian myeloblastosis virus (AMV) is an oncogenic retrovirus that rapidly causes myeloblastic leukemia in chickens and transforms myeloid cells in culture. AMV carries an oncogene, v-myb, that is derived from a cellular gene, c-myb, found in the genomes of vertebrate species. We constructed a plasmid vector that allows expression of a portion of the coding region for v-myb in a procaryotic host. We then used the myb-encoded protein produced in bacteria to immunize rabbits. The antisera obtained permitted identification of the proteins encoded by both v-myb and chicken c-myb. The molecular weights of the products of v-myb and c-myb (45,000 and 75,000 respectively) indicate that the v-myb protein is an appreciably truncated version of the c-myb protein.     

Synthesis and cytotoxicity of pyranonaphthoquinone natural product analogues under bioreductive conditions

We have synthesised a focused library of derivatives of natural products containing the pyranonaphthoquinone moiety including the first report of such a scaffold with an appended tetrazole functionality. Examples include kalafungin derivatives as well as analogues of nanaomycin and eleutherin. These compounds were assessed for cytotoxic activation by breast cancer cell lines engineered to express the prototypic human one- and two-electron quinone bioreductive enzymes, NADPH: cytochrome P450 oxidoreductase (POR) and NAD(P)H: quinoneoxidoreductase 1 (NQO1; DT-diaphorase), respectively. Several compounds were observed to be cytotoxic at sub-micromolar level and a pattern of increased aerobic potency was observed in cells over expressing POR. A subset of analogues was assessed under anoxic conditions, where cytotoxicity was reduced, implicating redox cycling as a major mechanism of toxicity. The substrate specificity for reductive enzymes is relevant to the future design of bioreductive prodrugs to treat cancer.     

On the limit cycle structure of threshold boolean networks over complete graphs

In previous work, the limit structure of positive and negative finite threshold boolean networks without inputs (TBNs) over the complete digraph K(n) was analyzed and an algorithm was presented for computing this structure in polynomial time. Those results are generalized in this paper to cover the case of arbitrary TBNs over K(n). Although the limit structure is now more complicated, containing, not only fixed-points and cycles of length 2, but possibly also cycles of arbitrary length, a simple algorithm is still available for its determination in polynomial time. Finally, the algorithm is generalized to cover the case of symmetric finite boolean networks over K(n).     

On the time to extinction for a two-type version of Bartlett's epidemic model

We are interested in how the addition of type heterogeneities affects the long time behaviour of models for endemic diseases. We do this by analysing a two-type version of a model introduced by Bartlett under the restriction of proportionate mixing. This model is used to describe diseases for which individuals switch states according to susceptible-->infectious-->recovered and immune, where the immunity is life-long. We describe an approximation of the distribution of the time to extinction given that the process is started in the quasi-stationary distribution, and we analyse how the variance and the coefficient of variation of the number of infectious individuals depends on the degree of heterogeneity between the two types of individuals. These are then used to derive an approximation of the time to extinction. From this approximation we conclude that if we increase the difference in infectivity between the two types the expected time to extinction decreases, and if we instead increase the difference in susceptibility the effect on the expected time to extinction depends on which part of the parameter space we are in, and we can also obtain non-monotonic behaviour. These results are supported by simulations.