Accounting for variability in sample size estimation with applications to nonadherence and estimation of variance and effect size

We consider sample size calculations for testing differences in means between two samples and allowing for different variances in the two groups. Typically, the power functions depend on the sample size and a set of parameters assumed known, and the sample size needed to obtain a prespecified power is calculated. Here, we account for two sources of variability: we allow the sample size in the power function to be a stochastic variable, and we consider estimating the parameters from preliminary data. An example of the first source of variability is nonadherence (noncompliance). We assume that the proportion of subjects who will adhere to their treatment regimen is not known before the study, but that the proportion is a stochastic variable with a known distribution. Under this assumption, we develop simple closed form sample size calculations based on asymptotic normality. The second source of variability is in parameter estimates that are estimated from prior data. For example, we account for variability in estimating the variance of the normal response from existing data which are assumed to have the same variance as the study for which we are calculating the sample size. We show that we can account for the variability of the variance estimate by simply using a slightly larger nominal power in the usual sample size calculation, which we call the calibrated power. We show that the calculation of the calibrated power depends only on the sample size of the existing data, and we give a table of calibrated power by sample size. Further, we consider the calculation of the sample size in the rarer situation where we account for the variability in estimating the standardized effect size from some existing data. This latter situation, as well as several of the previous ones, is motivated by sample size calculations for a Phase II trial of a malaria vaccine candidate.     

The we gene is a modifier of the wal gene in mice

Interaction of gene wellhaarig (we) with genes waved alopecia (wal) and hairless (hr) was studied in mice. The mutant gene we is responsible for the development of a specific waved coat in homozygotes. Homozygous mice carrying mutant gene wal also have a wavy coat, though a partial alopecia develops with time in these animals. In homozygotes for the hr gene, hair loss is observed beginning from the age of ten days. A series of crosses we/we and wal/wal yielded animals with we/+wal/wal and we/we wal/wal genotypes. In mice we/+wal/wal carrying gene we at a single dose, alopecia is accelerated significantly as compared to the single-dose homozygotes +/+wal/wal. In we/we wal/wal mice, alopecia starts earlier than in we/+wal/wal mice; by the age of one month, the double homozygotes are almost hairless except for small body areas covered with a sparse coat. In addition, curliness of the first-generation hair in mice we/we wal/wal is much more expressed than in +/+wal/wal and we/we+/+ mice. The obtained evidence suggests that the we gene is a modifier of the wal gene because the former enhances the effects of the wal gene, which is confirmed by the earlier onset of alopecia and progression of the latter in mice having the we/+wal/wal genotype and especially in we/we wal/wal animals. The we/we hr/+ mice do not differ in coat from we/we+/+ mice; in both cases, the coat is wavy. The coat of double homozygotes we/we hr/hr, is similar to that of we/we+/+ mice until ten days of age, when the signs of alopecia appear. By the age of 21 days, mice we/we hr/hr have lost their coat completely like mice +/+ hr/hr. Hence, the we gene is a modifier of the wal gene though it does not interact with hr gene during the coat formation.     

Experimental tests for an evolutionary trade-off between growth rate and yield in E. coli

Theoretical studies have predicted a trade-off between growth rate and yield in heterotrophic organisms. Here we test for the existence of this trade-off by analyzing the growth characteristics of 12 E. coli B populations that evolved for 20,000 generations under a constant selection regime. We performed three different tests. First, we analyzed changes in growth rate and yield over evolutionary time for each population. Second, we tested for a negative correlation between rate and yield across the 12 populations. Finally, we isolated clones from four selected populations and tested for a negative correlation between rate and yield within these populations. We did not find evidence for a trade-off based on the first two tests. However, we did observe a trade-off based on the within-population correlation of yield and rate. Our results indicate that, at least for the populations studied here, an analysis of the within-population diversity might be the most sensitive test for the existence of a trade-off. The observation of a trade-off within, but not between, populations suggests that the populations evolved different genetic solutions for growth in the selective environment, which in turn led to different physiological constraints.     

Selecting potential children and unconditional parental love

For now, the best way to select a child's genes is to select a potential child who has those genes, using genetic testing and either selective abortion, sperm and egg donors, or selecting embryos for implantation. Some people even wish to select against genes that are only mildly undesirable, or to select for superior genes. I call this selection drift – the standard for acceptable children is creeping upwards. The President's Council on Bioethics and others have raised the parental love objection : Just as we should love existing children unconditionally, so we should unconditionally accept whatever child we get in the natural course of things. If we set conditions on which child we get, we are setting conditions on our love for whatever child we get. Although this objection was prompted by selection drift, it also seems to cover selecting against genes for severe impairments.
I argue that selection drift is not inconsistent with the ideal of unconditional parental love and, moreover, that the latter actually implies that we should practise selection drift – in other words, we should try to select potential children with the best genetic endowments. My endowment argument for the second claim works from an analogy between arranging an endowment prior to conception to fund a future child's education, and arranging a genetic endowment by selecting a potential child who already has it, where in both cases the child would not have existed without the endowment. I conclude with some programmatic remarks about the nonidentity problem.     

Molstack: A platform for interactive presentations of electron density and cryo‐EM maps and their interpretations

In the Special Issue on Tools for Protein Science in 2018, we presented Molstack: a concept of a cloud‐based platform for sharing electron density maps and their interpretations. Molstack is a web platform that allows the interactive visualization of density maps through the simultaneous presentation of multiple datasets and models in a way that allows for easy pairwise comparison. We anticipated that the users of this conceptually simple platform would find many different uses for their projects, and we were not mistaken. We have observed researchers use Molstack to present experimental evidence for their models in the form of electron density maps, omit maps, and anomalous difference density maps. Users also employed Molstack to present alternative interpretations of densities, including rerefinements and speculative interpretations. While we anticipated these types of projects to be the main use cases, we were pleased to see Molstack used to display superpositions of different models, as a tool for story‐driven presentations, and for collaboration as well. Here, we present developments in the platform that were driven by user feedback, highlight several cases that used Molstack to enhance the publication, and discuss possible directions for the platform.     

Emerging issues in the evolution of animal nuptial gifts

Uniquely positioned at the intersection of sexual selection, nutritional ecology and life-history theory, nuptial gifts are widespread and diverse. Despite extensive empirical study, we still have only a rudimentary understanding of gift evolution because we lack a unified conceptual framework for considering these traits. In this opinion piece, we tackle several issues that we believe have substantively hindered progress in this area. Here, we: (i) present a comprehensive definition and classification scheme for nuptial gifts (including those transferred by simultaneous hermaphrodites), (ii) outline evolutionary predictions for different gift types, and (iii) highlight some research directions to help facilitate progress in this field.     

Verification of selective DNA pooling methodology through identification and estimation of the DGAT1 effect

The discovery of markers linked to genes that are responsible for traits of interest to the dairy industry might prove useful because they could aid in selection and breeding decisions. We have developed a selective DNA pooling methodology to allow us to efficiently screen the bovine genome in order to find genes responsible for production traits. Using markers on chromosome 14 as a test case, we identified a gene (DGAT1) previously known to affect three traits (fat yield, protein yield and total milk yield). Furthermore, we predicted similar effects to those previously shown for DGAT1 in a New Zealand Holstein-Friesian herd. Additionally, we showed a low error rate (1.6%) for the pooling procedure. Hence we are confident that we can apply this procedure to an entire genome scan in the search for quantitative trait loci (QTL).     

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this paper, we present computational techniques to investigate the effect of surface geometry on biological pattern formation. In particular, we study two-component, nonlinear reaction–diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD systems and extend them to operate on large-scale meshes for arbitrary surfaces. In particular, we use spectral techniques for a linear stability analysis to characterise and directly compose patterns emerging from homogeneities. We develop an implementation using surface finite element methods and a numerical eigenanalysis of the Laplace–Beltrami operator on surface meshes. In addition, we describe a technique to explore solutions of the nonlinear RD equations using numerical continuation. Here, we present a multiresolution approach that allows us to trace solution branches of the nonlinear equations efficiently even for large-scale meshes. Finally, we demonstrate the working of our framework for two RD systems with applications in biological pattern formation: a Brusselator model that has been used to model pattern development on growing plant tips, and a chemotactic model for the formation of skin pigmentation patterns. While these models have been used previously on simple geometries, our framework allows us to study the impact of arbitrary geometries on emerging patterns.     

An analytical model for designing yard layouts of a straddle carrier based container terminal

In designing a yard layout for a container terminal several decisions have to be made. In this paper we propose a model which provides decision support for the design of yard layouts of terminals at which straddle carrier are used. We assume that straddle carriers are used for the horizontal transport and the stacking of containers. For the proposed model we develop estimates for the expected cycle distances of straddle carriers. In this case, we distinguish between cycles to landside facilities and to the quay. Numerical results are presented for several parameter settings. For instance, we present results for a comparison of layouts where the rows in the block are orientated parallel with layouts where the rows are orientated perpendicularly to the quay.     

A molecular dynamics strategy for CSαβ peptides disulfide-assisted model refinement

Many cysteine-stabilized antimicrobial peptides from a variety of living organisms could be good candidates for the development of anti-infective agents. In the absence of experimentally obtained structural data, peptide modeling is an essential tool for understanding structure–activity relationships and for optimizing the bioactive moieties. Focusing on cysteine-rich peptide structures, we reproduced the case of structure predictions in the so-called midnight zone. We developed our protocol on a training set derived by clustering the available cysteine-stabilized αβ (CSαβ) structures in nine different representative families and tested it on peptides randomly selected from each family. Starting from draft models, we tested a structure-based disulfide predictor and we used cysteine distances as constraints during molecular dynamics. Finally, we proposed an analysis for final structure selection. Accordingly, we obtained a mean root mean square deviation improvement of 21% for the test set. Our findings demonstrate that it is possible to predict the network of disulfide bridges in cysteine-stabilized peptides and to use this result to improve the accuracy of structural predictions. Finally, we applied the methods to predict the structure of royalisin, a cysteine-rich peptide with unknown structure.     

Crucial role of CA cleavage sites in the cap-snatching mechanism for initiating viral mRNA synthesis

In viral cap-snatching, the endonuclease intrinsic to the viral polymerase cleaves cellular capped RNAs to generate capped fragments that are primers for viral mRNA synthesis. Here we demonstrate that the influenza viral polymerase, which is assembled in human cells using recombinant proteins, effectively uses only CA-terminated capped fragments as primers for viral mRNA synthesis in vitro. Thus we provide the first in vitro system that mirrors the cap-snatching process occurring in vivo during virus infection. Further, we demonstrate that when a capped RNA substrate contains a CA cleavage site, the functions of virion RNA (vRNA) differ from those previously described: the 5' terminal sequence of vRNA alone is sufficient for endonuclease activation, and the 3' terminal sequence of vRNA functions solely as a template for mRNA synthesis. Consequently, we are able to identify the vRNA sequences that are required for each of these two separable functions. We present a new model for the influenza virus cap-snatching mechanism, which we postulate is a paradigm for the cap-snatching mechanisms of other segmented, negative-strand and ambisense RNA viruses.     

Effects of the mutant gene wellhaarig in chimeric mice

The mutant gene wellhaaring (we) confers the waved coat in mice, which is most pronounced in homozygotes at 10 to 21 days of postnatal development. Abnormal hair growth and structure in the we/we mutant mice results from defective cell differentiation in the inner root sheath of a hair follicle. To localize the site of the we gene action, we obtained ten chimeric mice by aggregation of the early C57BL/6-2we/we and BALB/c embryos. The chimera coat was waved, shaggy, or almost normal depending on the percentage of the mutant component. In the we/we +/+ chimeric animals of the first generation (G1) aged 21 days, both mutant and normal hair phenotypes were observed, which was especially discernible in zigzag hair. Note that none of the chimeras exhibited the alternating patterns of transversely oriented stripes or patches of either mutant or normal hair; i.e., they had a mixed parental hair phenotype. We also did not observe the animals with an intermediate phenotype, which suggests a discontinuous hair formation in chimeras according to the "all or nothing" principle. The data obtained indicate that the dermal papilla cells of a hair follicle are the sites for the we gene action. During the embryonic development, dermal cells are strongly mixed, which accounts for the lack of the clear-cut transverse stripes of either mutant or normal hair. The mutant gene we is probably responsible for a disrupted induction signal from the dermal papilla towards ectodermal cells of a hair follicle.     

A Lyapunov function for piecewise-independent differential equations: stability of the ideal free distribution in two patch environments

In this article we construct Lyapunov functions for models described by piecewise-continuous and independent differential equations. Because these models are described by discontinuous differential equations, the theory of Lyapunov functions for smooth dynamical systems is not applicable. Instead, we use a geometrical approach to construct a Lyapunov function. Then we apply the general approach to analyze population dynamics describing exploitative competition of two species in a two-patch environment. We prove that for any biologically meaningful parameter combination the model has a globally stable equilibrium and we analyze this equilibrium with respect to parameters.      

The geometric side for an axiomatic theory of evolution.

In this paper we present a geometric model for a proposal of axiomatization of Evolution Theory. For this aim, we use suitable tools of Geometry and Topology. In particular, we define the concept of fertility factor as a main instrument for the studying of speciation. This concept, in our opinion, has an important biological meaning.     

A global phenomenological model of ischemic stroke with stress on spreading depressions

In this paper, we establish a new global phenomenological model of ischemic stroke. It takes into account local ischemia, energy reduction, propagation of spreading depressions (SD), damages to the cells and cellular death by apoptosis or necrosis. The spatial diffusion of the ions in the extracellular space which triggers the propagation of SD is a central point here. First we expose the various biological hypotheses that we have made in this model, and then we explain how to determine the parameters and solve the system of equations that we obtain. Next we present some results of this model: we simulate a KCl injection and then a local ischemia. Finally we discuss results and propose some improvements for this model.     

Smart platform for the analysis of cupula deformation caused by otoconia presence within SCCs

In this paper, we first briefly describe the mechanical model of cupula deformation with the appropriate analytical solution. Then, we present the numerical solution of the same problem and compare it with the analytical one. Besides, we provide another numerical solution based on the Finite Element Method procedure, in an effort to encompass a more realistic approach to the problem such as considering the real geometry of the SCCs and the obstruction of the fluid flow during head movement due to the presence of otoconia. As a result, we obtain fifty solutions for a head rotation angle in a range from 0° to 120°, taking into account that such a manoeuvre lasts exactly 3?seconds. In the end, we present a mobile client–server application for visualising the finite element solutions in a way that is convenient for the clinical practice.     

Random binding of dimers to chains

We develop a probabilistic model for the binding of a small linear polymer to a larger chain. We assume that we can approximate the energy of interaction of the two chains by summing the pairwise interactions between subunits. Because the energy of interaction between a pair of subunits can depend on neighboring subunits, which we assume vary along the chain, we assign the pairwise energies of interactions according to a specified probability distribution. Thus we develop a statistical model for the binding of two molecules. While such models may not be appropriate for studying the interaction of a particular pair of molecules, they can provide insight into questions that deal with populations of molecules, such as why do MHC molecules bind peptides of a certain size? Here we analyze in detail the special case of a heterodimer binding to a polymer.     

Endemic threshold results in an age-duration-structured population model for HIV infection

In this paper we consider an age-duration-structured population model for HIV infection in a homosexual community. First we investigate the invasion problem to establish the basic reproduction ratio R(0) for the HIV/AIDS epidemic by which we can state the threshold criteria: The disease can invade into the completely susceptible population if R(0)>1, whereas it cannot if R(0)<1. Subsequently, we examine existence and uniqueness of endemic steady states. We will show sufficient conditions for a backward or a forward bifurcation to occur when the basic reproduction ratio crosses unity. That is, in contrast with classical epidemic models, for our HIV model there could exist multiple endemic steady states even if R(0) is less than one. Finally, we show sufficient conditions for the local stability of the endemic steady states.     

Why Open Drug Discovery Needs Four Simple Rules for Licensing Data and Models

When we look at the rapid growth of scientific databases on the Internet in the past decade, we tend to take the accessibility and provenance of the data for granted. As we see a future of increased database integration, the licensing of the data may be a hurdle that hampers progress and usability. We have formulated four rules for licensing data for open drug discovery, which we propose as a starting point for consideration by databases and for their ultimate adoption. This work could also be extended to the computational models derived from such data. We suggest that scientists in the future will need to consider data licensing before they embark upon re-using such content in databases they construct themselves.