Maximally efficient two-stage screening

In DNA library screening, blood testing, and monoclonal antibody generation, significant savings in the number of assays can be realized by employing group sampling. Practical considerations often limit the number of stages of group testing that can be performed. We address situations in which only two stages of testing are used. We define efficiency to be the expected number of positives isolated per assay performed and assume gold-standard tests with unit sensitivity and specificity. Although practical tests never are golden, polymerase chain reaction (PCR) methods provide procedures for screening recombinant libraries that are strongly selective yet retain high sensitivity even when samples are pooled. Also, results for gold-standard tests serve as bounds on the performance of practical testing procedures. First we derive formulas for the efficiency of certain extensions of the popular rows-and-columns technique. Then we derive an upper bound on the efficiency of any two-stage strategy that lies well below the classical upper bound for situations with no constraint on the number of stages. This establishes that a restriction to only two stages necessitates performing many more assays than efficient multistage procedures need. Next, we specialize the bound to cases in which each item belonging only to pools that tested positive in stage 1 must be tested individually in stage 2. The specialized bound for such positive procedures is tight because we show that an appropriate multidimensional extension of the rows-and-columns technique achieves it. We also show that two-stage positive procedures in which the stage-1 groups are selected at random perform suboptimally, thereby establishing that efficient tests must be structured carefully.     

Analyzing large‐scale structural change in proteins: Comparison of principal component projection and sammon mapping

Effective analysis of large-scale conformational transitions in macromolecules requires transforming them into a lower dimensional representation that captures the dominant motions. Herein, we apply and compare two different dimensionality reduction techniques, namely, principal component analysis (PCA), a linear method, and Sammon mapping, which is nonlinear. The two methods are used to analyze four different protein transition pathways of varying complexity, obtained by using either the conjugate peak refinement method or constrained molecular dynamics. For the return-stroke in myosin, both Sammon mapping and PCA show that the conformational change is dominated by a simple rotation of a rigid body. Also, in the case of the T-->R transition in hemoglobin, both methods are able to identify the two main quaternary transition events. In contrast, in the cases of the unfolding transition of staphylococcal nuclease or the signaling switch of Ras p21, which are both more complex conformational transitions, only Sammon mapping is able to identify the distinct phases of motion.     

Fixation probabilities of additive alleles in diploid populations

The calculation of the survival probability of a selectively advantageous allele is a central part of the quantitative theory of genetic evolution. However, several areas of investigation in population genetics theory, including the generalized neutrality theory, the concept of Muller's ratchet, and the risk of extinction of sexually reproducing populations due to the accumulation of deleterious mutations, rely on the calculation of the survival probability of selectively disadvantageous mutant genes. The calculation of these probabilities in the standard Wright-Fisher model of genetic evolution appears to be intractable, and yet is a key element in the above investigations. In this paper we find bounds for the fixation probability of deleterious and advantageous additive mutants, as well as finding close approximations for these probabilities. In addition, we derive analytical estimates for the relative error of our approximations and compare our results with those from numerical computation. Our results justify the diffusion approximation for the fixation probability of a single mutant.     

Approximate Confidence Bounds for Ripley's Statistic for Random Points in a Square

Confidence envelopes for Ripley's L function for N random points in the unit square were obtained by simulation. The 90, 95 and 99th percentiles of 1000 simulations are given in tabular form for N in the range 10 to 350. Results for a number of choices of the maximum interpoint distance are reported.     

Large-Scale Phylogenomic Analyses Reveal the Monophyly of Bryophytes and Neoproterozoic Origin of Land Plants

The relationships among the four major embryophyte lineages (mosses, liverworts, hornworts, vascular plants) and the timing of the origin of land plants are enigmatic problems in plant evolution. Here, we resolve the monophyly of bryophytes by improving taxon sampling of hornworts and eliminating the effect of synonymous substitutions. We then estimate the divergence time of crown embryophytes based on three fossil calibration strategies, and reveal that maximum calibration constraints have a major effect on estimating the time of origin of land plants. Moreover, comparison of priors and posteriors provides a guide for evaluating the optimal calibration strategy. By considering the reliability of fossil calibrations and the influences of molecular data, we estimate that land plants originated in the Precambrian (980–682 Ma), much older than widely recognized. Our study highlights the important contribution of molecular data when faced with contentious fossil evidence, and that fossil calibrations used in estimating the timescale of plant evolution require critical scrutiny.     

Using secondary outcome to sharpen bounds for treatment harm rate in characterizing heterogeneity

In a clinical trial, statistical reports are typically concerned about the mean difference in two groups. Now there is increasing interest in the heterogeneity of the treatment effect, which has important implications in treatment evaluation and selection. The treatment harm rate (THR), which is defined by the proportion of people who has a worse outcome on the treatment compared to the control, was used to characterize the heterogeneity. Since THR involves the joint distribution of the two potential outcomes, it cannot be identified without further assumptions even in the randomized trials. We can only derive the simple bounds with the observed data. But the simple bounds are usually too wide. In this paper, we use a secondary outcome that satisfies the monotonicity assumption to tighten the bounds. It is shown that the bounds we derive cannot be wider than the simple bounds. We also construct some simulation studies to assess the performance of our bounds in finite sample. The results show that a secondary outcome, which is more closely related to the primary outcome, can lead to narrower bounds. Finally, we illustrate the application of the proposed bounds in a randomized clinical trial of determining whether the intensive glycemia could reduce the risk of development or progression of diabetic retinopathy.     

On the minimum number of recombination events in the evolutionary history of DNA sequences

In representing the evolutionary history of a set of binary DNA sequences by a connected graph, a set theoretical approach is introduced for studying recombination events. We show that set theoretical constraints have direct implications on the number of recombination events. We define a new lower bound on the number of recombination events and demonstrate the usefulness of our new approach through several explicit examples.