Nonlinear biological oscillators: Action-angle variable approach with an application to Cowan's model of neuroelectric activity

We obtain within the action-angle variable approach new expressions, involving the Dirac delta function, for time periods and time averages of dynamical variables which are useful for nonlinear biological oscillator problems. We combine these with Laplace transformation techniques for evaluating the required perturbation expansions. The radii of convergence of these series are determined through a complex variable approach. The method is powerful enough to yield explicit results for such systems as the two species Volterra model, Goodwin's model of protein synthesis etc. and as an illustration, is applied here to Cowan's model of neuroelectric activity. We also point out the usefulness of the action integral in the case where parameters occurring in dynamics have slow time variations.     

Regression with empirical variable selection: description of a new method and application to ecological datasets

Despite recent papers on problems associated with full-model and stepwise regression, their use is still common throughout ecological and environmental disciplines. Alternative approaches, including generating multiple models and comparing them post-hoc using techniques such as Akaike''s Information Criterion (AIC), are becoming more popular. However, these are problematic when there are numerous independent variables and interpretation is often difficult when competing models contain many different variables and combinations of variables. Here, we detail a new approach, REVS (Regression with Empirical Variable Selection), which uses all-subsets regression to quantify empirical support for every independent variable. A series of models is created; the first containing the variable with most empirical support, the second containing the first variable and the next most-supported, and so on. The comparatively small number of resultant models (n = the number of predictor variables) means that post-hoc comparison is comparatively quick and easy. When tested on a real dataset – habitat and offspring quality in the great tit (Parus major) – the optimal REVS model explained more variance (higher R²), was more parsimonious (lower AIC), and had greater significance (lower P values), than full, stepwise or all-subsets models; it also had higher predictive accuracy based on split-sample validation. Testing REVS on ten further datasets suggested that this is typical, with R² values being higher than full or stepwise models (mean improvement = 31% and 7%, respectively). Results are ecologically intuitive as even when there are several competing models, they share a set of “core” variables and differ only in presence/absence of one or two additional variables. We conclude that REVS is useful for analysing complex datasets, including those in ecology and environmental disciplines.     

Plugging space into predator-prey models: an empirical approach

Extrapolating ecological processes from small-scale experimental systems to scales of natural populations usually entails a considerable increase in spatial heterogeneity, which may affect process rates and, ultimately, population dynamics. We demonstrate how information on the heterogeneity of natural populations can be taken into account when scaling up laboratory-derived process functions, using the technique of moment approximation. We apply moment approximation to a benthic crustacean predator-prey system, where a laboratory-derived functional response is made spatial by including correction terms for the variance in prey density and the covariance between prey and predator densities observed in the field. We also show how moment approximation may be used to incorporate spatial information into a dynamic model of the system. While the nonspatial model predicts stable dynamics, its spatial equivalent also produces bounded fluctuations, in agreement with observed dynamics. A detailed analysis shows that predator-prey covariance, but not prey variance, destabilizes the dynamics. We conclude that second-order moment approximation may provide a useful technique for including spatial information in population models. The main advantage of the method is its conceptual value: by providing explicit estimates of variance and covariance effects, it offers the possibility of understanding how heterogeneity affects ecological processes.     

Gene selection: a Bayesian variable selection approach

Selection of significant genes via expression patterns is an important problem in microarray experiments. Owing to small sample size and the large number of variables (genes), the selection process can be unstable. This paper proposes a hierarchical Bayesian model for gene (variable) selection. We employ latent variables to specialize the model to a regression setting and uses a Bayesian mixture prior to perform the variable selection. We control the size of the model by assigning a prior distribution over the dimension (number of significant genes) of the model. The posterior distributions of the parameters are not in explicit form and we need to use a combination of truncated sampling and Markov Chain Monte Carlo (MCMC) based computation techniques to simulate the parameters from the posteriors. The Bayesian model is flexible enough to identify significant genes as well as to perform future predictions. The method is applied to cancer classification via cDNA microarrays where the genes BRCA1 and BRCA2 are associated with a hereditary disposition to breast cancer, and the method is used to identify a set of significant genes. The method is also applied successfully to the leukemia data. SUPPLEMENTARY INFORMATION: http://stat.tamu.edu/people/faculty/bmallick.html.     

Integrating information literacy training into an inquiry-based introductory biology laboratory

ABSTRACT

Information literacy is an essential skill for biologists; however, most biology curricula do not intentionally integrate information literacy into classroom and laboratory exercises. There is evidence that developing information literacy skills in undergraduates improves their research skills, writing, and GPAs. Our objective was to integrate information literacy skills into a first semester introductory biology laboratory with a multi-week, inquiry-based module that leverages primary literature. Here we describe the module, which challenges students to develop and test a hypothesis related to parental care behaviour in birds. Students form hypotheses based on literature searching done during librarian-led information literacy sessions, produce an annotated bibliography, collect and analyse video data of barn swallows feeding their offspring, and present their findings. Analysis of students’ annotated bibliographies indicates that 83% of the referenced papers were appropriate for developing their specific hypotheses. The key elements ofa successful information literacy training plan include faculty-librarian collaboration, multiple classroom or laboratory sessions that introduce or utilize information literacy, and relevance ofthe information literacy training to an assignment. By introducing information literacy early inbiology curricula, departments can develop tiered information literacy plans that incorporate opportunities for students to use and refine these skills throughout their studies.     

Insights into prion biology: Integrating a protein misfolding pathway with its cellular environment

Protein misfolding and assembly into ordered, self-templating aggregates (amyloid) has emerged as a novel mechanism for regulating protein function. For a subclass of amyloidogenic proteins known as prions, this process induces transmissible changes in normal cellular physiology, ranging from neurodegenerative disease in animals and humans to new traits in fungi. The severity and stability of these altered phenotypic states can be attenuated by the conformation or amino-acid sequence of the prion, but in most of these cases, the protein retains the ability to form amyloid in vitro. Thus, our ability to link amyloid formation in vitro with its biological consequences in vivo remains a challenge. In two recent studies, we have begun to address this disconnect by assessing the effects of the cellular environment on traits associated with the misfolding of the yeast prion Sup35. Remarkably, the effects of quality control pathways and of limitations on protein transfer in vivo amplify the effects of even slight differences in the efficiency of Sup35 misfolding, leading to dramatic changes in the associated phenotype. Together, our studies suggest that the interplay between protein misfolding pathways and their cellular context is a crucial contributor to prion biology.Key words: prion, protein misfolding, chaperones, amyloid, ordered aggregates, transmission, aggregate size, Sup35, Hsp104     

Teaching systems biology: an active-learning approach

With genomics well established in modern molecular biology, recent studies have sought to further the discipline by integrating complementary methodologies into a holistic depiction of the molecular mechanisms underpinning cell function. This genomic subdiscipline, loosely termed "systems biology," presents the biology educator with both opportunities and obstacles: The benefit of exposing students to this cutting-edge scientific methodology is manifest, yet how does one convey the breadth and advantage of systems biology while still engaging the student? Here, I describe an active-learning approach to the presentation of systems biology. In graduate classes at the University of Michigan, Ann Arbor, I divided students into small groups and asked each group to interpret a sample data set (e.g., microarray data, two-hybrid data, homology-search results) describing a hypothetical signaling pathway. Mimicking realistic experimental results, each data set revealed a portion of this pathway; however, students were only able to reconstruct the full pathway by integrating all data sets, thereby exemplifying the utility in a systems biology approach. Student response to this cooperative exercise was extremely positive. In total, this approach provides an effective introduction to systems biology appropriate for students at both the undergraduate and graduate levels.     

Integrating genomic selection into dairy cattle breeding programmes: a review

Extensive genetic progress has been achieved in dairy cattle populations on many traits of economic importance because of efficient breeding programmes. Success of these programmes has relied on progeny testing of the best young males to accurately assess their genetic merit and hence their potential for breeding. Over the last few years, the integration of dense genomic information into statistical tools used to make selection decisions, commonly referred to as genomic selection, has enabled gains in predicting accuracy of breeding values for young animals without own performance. The possibility to select animals at an early stage allows defining new breeding strategies aimed at boosting genetic progress while reducing costs. The first objective of this article was to review methods used to model and optimize breeding schemes integrating genomic selection and to discuss their relative advantages and limitations. The second objective was to summarize the main results and perspectives on the use of genomic selection in practical breeding schemes, on the basis of the example of dairy cattle populations. Two main designs of breeding programmes integrating genomic selection were studied in dairy cattle. Genomic selection can be used either for pre-selecting males to be progeny tested or for selecting males to be used as active sires in the population. The first option produces moderate genetic gains without changing the structure of breeding programmes. The second option leads to large genetic gains, up to double those of conventional schemes because of a major reduction in the mean generation interval, but it requires greater changes in breeding programme structure. The literature suggests that genomic selection becomes more attractive when it is coupled with embryo transfer technologies to further increase selection intensity on the dam-to-sire pathway. The use of genomic information also offers new opportunities to improve preservation of genetic variation. However, recent simulation studies have shown that putting constraints on genomic inbreeding rates for defining optimal contributions of breeding animals could significantly reduce achievable genetic gain. Finally, the article summarizes the potential of genomic selection to include new traits in the breeding goal to meet societal demands regarding animal health and environmental efficiency in animal production.     

VPMCD: variable interaction modeling approach for class discrimination in biological systems

Data classification algorithms applied for class prediction in computational biology literature are data specific and have shown varying degrees of performance. Different classes cannot be distinguished solely based on interclass distances or decision boundaries. We propose that inter-relations among the features be exploited for separating observations into specific classes. A new variable predictive model based class discrimination (VPMCD) method is described here. Three well established and proven data sets of varying statistical and biological significance are utilized as benchmark. The performance of the new method is compared with advanced classification algorithms. The new method performs better during different tests and shows higher stability and robustness. The VPMCD is observed to be a potentially strong classification approach and can be effectively extended to other data mining applications involving biological systems.     

Iron bioavailability to phytoplankton: an empirical approach

Phytoplankton are often limited by iron in aquatic environments. Here we examine Fe bioavailability to phytoplankton by analyzing iron uptake from various Fe substrates by several species of phytoplankton grown under conditions of Fe limitation and comparing the measured uptake rate constants (Fe uptake rate/ substrate concentration). When unchelated iron, Fe′, buffered by an excess of the chelating agent EDTA is used as the Fe substrate, the uptake rate constants of all the eukaryotic phytoplankton species are tightly correlated and proportional to their respective surface areas (S.A.). The same is true when FeDFB is the substrate, but the corresponding uptake constants are one thousand times smaller than for Fe′. The uptake rate constants for the other substrates we examined fall mostly between the values for Fe′ and FeDFB for the same S.A. These two model substrates thus empirically define a bioavailability envelope with Fe′ at the upper and FeDFB at the lower limit of iron bioavailability. This envelope provides a convenient framework to compare the relative bioavailabilities of various Fe substrates to eukaryotic phytoplankton and the Fe uptake abilities of different phytoplankton species. Compared with eukaryotic species, cyanobacteria have similar uptake constants for Fe′ but lower ones for FeDFB. The unique relationship between the uptake rate constants and the S.A. of phytoplankton species suggests that the uptake rate constant of Fe-limited phytoplankton has reached a universal upper limit and provides insight into the underlying uptake mechanism.     

Synthetic biology: a new approach to study biological pattern formation

The principles and molecular mechanisms underlying biological pattern formation are difficult to elucidate in most cases due to the overwhelming physiologic complexity associated with the natural context. The understanding of a particular mechanism, not to speak of underlying universal principles, is difficult due to the diversity and uncertainty of the biological systems. Although current genetic and biochemical approaches have greatly advanced our understanding of pattern formation, the progress mainly relies on experimental phenotypes obtained from time-consuming studies of gain or loss of function mutants. It is prevailingly considered that synthetic biology will come to the application age, but more importantly synthetic biology can be used to understand the life. Using periodic stripe pattern formation as a paradigm, we discuss how to apply synthetic biology in understanding biological pattern formation and hereafter foster the applications like tissue engineering.     

Duncan's k-ratio Bayes rule approach to multiple comparisons: an overview

An alternative to frequentist approaches to multiple comparisons is Duncan's k-ratio Bayes rule approach. The purpose of this paper is to compile key results on k-ratio Bayes rules for a number of multiple comparison problems that heretofore, have only been available in separate papers or doctoral dissertations. Among other problems, multiple comparisons for means in one-way, two-way, and treatments-vs.-control structures will be reviewed. In the k-ratio approach, the optimal joint rule for a multiple comparisons problem is derived under the assumptions of additive losses and prior exchangeability for the component comparisons. In the component loss function for a comparison, a balance is achieved between the decision losses due to Type I and Type II errors by assuming that their ratio is k. The component loss is also linear in the magnitude of the error. Under the assumption of additive losses, the joint Bayes rule for the component comparisons applies to each comparison the Bayes test for that comparison considered alone. That is, a comparisonwise approach is optimal. However, under prior exchangeability of the comparisons, the component test critical regions adapt to omnibus patterns in the data. For example, for a balanced one-way array of normally distributed means, the Bayes critical t value for a difference between means is inversely related to the F ratio measuring heterogeneity among the means, resembling a continuous version of Fisher's F-protected least significant difference rule. For more complicated treatment structures, the Bayes critical t value for a difference depends intuitively on multiple F ratios and marginal difference(s) (if applicable), such that the critical t value warranted for the difference can range from being as conservative as that given by a familywise rule to actually being anti-conservative relative to that given by the unadjusted 5%-level Student's t test.     

Integrating data from biological experiments into metabolic networks with the DBE information system

Modern 'omics'-technologies result in huge amounts of data about life processes. For analysis and data mining purposes this data has to be considered in the context of the underlying biological networks. This work presents an approach for integrating data from biological experiments into metabolic networks by mapping the data onto network elements and visualising the data enriched networks automatically. This methodology is implemented in DBE, an information system that supports the analysis and visualisation of experimental data in the context of metabolic networks. It consists of five parts: (1) the DBE-Database for consistent data storage, (2) the Excel-Importer application for the data import, (3) the DBE-Website as the interface for the system, (4) the DBE-Pictures application for the up- and download of binary (e. g. image) files, and (5) DBE-Gravisto, a network analysis and graph visualisation system. The usability of this approach is demonstrated in two examples.