Estimating survival in continuous space from mark-dead-recovery data - Towards a continuous version of the multinomial dead recovery model.

Understanding spatially varying survival is crucial for understanding the ecology and evolution of migratory animals, which may ultimately help to conserve such species. We develop an approach to estimate an annual survival probability function varying continuously in geographic space, if the recovery probability is constant over space. This estimate is based on a density function over continuous geographic space and the discrete age at death obtained from dead recovery data. From the same density function, we obtain an estimate for animal distribution in space corrected for survival, i.e., migratory connectivity. This is possible, when migratory connectivity can be separated from recovery probability. In this article, we present the method how spatially and continuously varying survival and the migratory connectivity corrected for survival can be obtained, if a constant recovery probability can be assumed reasonably. The model is a stepping stone in developing a model allowing for disentangling spatially heterogeneous survival and migratory connectivity corrected for survival from a spatially heterogeneous recovery probability. We implement the method using kernel density estimates in the R-package CONSURE. Any other density estimation technique can be used as an alternative. In a simulation study, the estimators are unbiased but show edge effects in survival and migratory connectivity. Applying the method to a real-world data set of European robins Erithacus rubecula results in biologically reasonable continuous heat-maps for survival and migratory connectivity.

Estimation in the multinomial reencounter model - Where do migrating animals go and how do they survive in their destination area?

Spatial variation in survival has individual fitness consequences and influences population dynamics. Which space animals use during the annual cycle determines how they are affected by this spatial variability. Therefore, knowing spatial patterns of survival and space use is crucial to understand demography of migrating animals. Extracting information on survival and space use from observation data, in particular dead recovery data, requires explicitly identifying the observation process. We build a fully stochastic model for animals marked in populations of origin, which were found dead in spatially discrete destination areas. The model acts on the population level and includes parameters for use of space, survival and recovery probability. It is based on the division coefficient and the multinomial reencounter model. We use a likelihood-based approach, derive Restricted Maximum Likelihood-like estimates for all parameters and prove their existence and uniqueness. In a simulation study we demonstrate the performance of the model by using Bayesian estimators derived by the Markov chain Monte Carlo method. We obtain unbiased estimates for survival and recovery probability if the sample size is large enough. Moreover, we apply the model to real-world data of European robins Erithacus rubecula ringed at a stopover site. We obtain annual survival estimates for different spatially discrete non-breeding areas. Additionally, we can reproduce already known patterns of use of space for this species.

Seagull: lasso, group lasso and sparse-group lasso regularization for linear regression models via proximal gradient descent.

BACKGROUND: Statistical analyses of biological problems in life sciences often lead to high-dimensional linear models. To solve the corresponding system of equations, penalization approaches are often the methods of choice. They are especially useful in case of multicollinearity, which appears if the number of explanatory variables exceeds the number of observations or for some biological reason. Then, the model goodness of fit is penalized by some suitable function of interest. Prominent examples are the lasso, group lasso and sparse-group lasso. Here, we offer a fast and numerically cheap implementation of these operators via proximal gradient descent. The grid search for the penalty parameter is realized by warm starts. The step size between consecutive iterations is determined with backtracking line search. Finally, seagull -the R package presented here- produces complete regularization paths. RESULTS: Publicly available high-dimensional methylation data are used to compare seagull to the established R package SGL. The results of both packages enabled a precise prediction of biological age from DNA methylation status. But even though the results of seagull and SGL were very similar (R2 > 0.99), seagull computed the solution in a fraction of the time needed by SGL. Additionally, seagull enables the incorporation of weights for each penalized feature. CONCLUSIONS: The following operators for linear regression models are available in seagull: lasso, group lasso, sparse-group lasso and Integrative LASSO with Penalty Factors (IPF-lasso). Thus, seagull is a convenient envelope of lasso variants.

The Rosenzweig-MacArthur system via reduction of an individual based model.

The Rosenzweig-MacArthur system is a particular case of the Gause model, which is widely used to describe predator-prey systems. In the classical derivation, the interaction terms in the differential equation are essentially derived from considering handling time vs. search time, and moreover there exist derivations in the literature which are based on quasi-steady state assumptions. In the present paper we introduce a derivation of this model from first principles and singular perturbation reductions. We first establish a simple stochastic mass action model which leads to a three-dimensional ordinary differential equation, and systematically determine all possible singular perturbation reductions (in the sense of Tikhonov and Fenichel) to two-dimensional systems. Among the reductions obtained we find the Rosenzweig-MacArthur system for a certain choice of small parameters as well as an alternative to the Rosenzweig-MacArthur model, with density dependent death rates for predators. The arguments to obtain the reductions are intrinsically mathematical; no heuristics are employed.

New Gromov-Inspired Metrics on Phylogenetic Tree Space.

We present a new class of metrics for unrooted phylogenetic X-trees inspired by the Gromov-Hausdorff distance for (compact) metric spaces. These metrics can be efficiently computed by linear or quadratic programming. They are robust under NNI operations, too. The local behaviour of the metrics shows that they are different from any previously introduced metrics. The performance of the metrics is briefly analysed on random weighted and unweighted trees as well as random caterpillars.

An approximate Bayesian significance test for genomic evaluations.

Genomic information can be used to study the genetic architecture of some trait. Not only the size of the genetic effect captured by molecular markers and their position on the genome but also the mode of inheritance, which might be additive or dominant, and the presence of interactions are interesting parameters. When searching for interacting loci, estimating the effect size and determining the significant marker pairs increases the computational burden in terms of speed and memory allocation dramatically. This study revisits a rapid Bayesian approach (fastbayes). As a novel contribution, a measure of evidence is derived to select markers with effect significantly different from zero. It is based on the credibility of the highest posterior density interval next to zero in a marginalized manner. This methodology is applied to simulated data resembling a dairy cattle population in order to verify the sensitivity of testing for a given range of type-I error levels. A real data application complements this study. Sensitivity and specificity of fastbayes were similar to a variational Bayesian method, and a further reduction of computing time could be achieved. More than 50% of the simulated causative variants were identified. The most complex model containing different kinds of genetic effects and their pairwise interactions yielded the best outcome over a range of type-I error levels. The validation study showed that fastbayes is a dual-purpose tool for genomic inferences - it is applicable to predict future outcome of not-yet phenotyped individuals with high precision as well as to estimate and test single-marker effects. Furthermore, it allows the estimation of billions of interaction effects.

CellFateScout - a bioinformatics tool for elucidating small molecule signaling pathways that drive cells in a specific direction.

BACKGROUND: Small molecule effects can be represented by active signaling pathways within functional networks. Identifying these can help to design new strategies to utilize known small molecules, e.g. to trigger specific cellular transformations or to reposition known drugs. RESULTS: We developed CellFateScout that uses the method of Latent Variables to turn differential high-throughput expression data and a functional network into a list of active signaling pathways. Applying it to Connectivity Map data, i.e., differential expression data describing small molecule effects, we then generated a Human Small Molecule Mechanisms Database. Finally, using a list of active signaling pathways as query, a similarity search can identify small molecules from the database that may trigger these pathways. We validated our approach systematically, using expression data of small molecule perturbations, yielding better predictions than popular bioinformatics tools. CONCLUSIONS: CellFateScout can be used to select small molecules for their desired effects. The CellFateScout Cytoscape plugin, a tutorial and the Human Small Molecule Mechanisms Database are available at https://sourceforge.net/projects/cellfatescout/ under LGPLv2 license.

A Fitted Sparse-Group Lasso for Genome-Based Evaluations.

In life sciences, high-throughput techniques typically lead to high-dimensional data and often the number of covariates is much larger than the number of observations. This inherently comes with multicollinearity challenging a statistical analysis in a linear regression framework. Penalization methods such as the lasso, ridge regression, the group lasso, and convex combinations thereof, which introduce additional conditions on regression variables, have proven themselves effective. In this study, we introduce a novel approach by combining the lasso and the standardized group lasso leading to meaningful weighting of the predicted ("fitted") outcome which is of primary importance, e.g., in breeding populations. This "fitted" sparse-group lasso was implemented as a proximal-averaged gradient descent method and is part of the R package "seagull" available at CRAN. For the evaluation of the novel method, we executed an extensive simulation study. We simulated genotypes and phenotypes which resemble data of a dairy cattle population. Genotypes at thousands of genomic markers were used as covariates to fit a quantitative response. The proximity of markers on a chromosome determined grouping. In the majority of simulated scenarios, the new method revealed improved prediction abilities compared to other penalization approaches and was able to localize the signals of simulated features.

On a class of deterministic population models with stochastic foundation.

Generalising a site-based stochastic model due to Royama, Solé et al. and Sumpter et al., we investigate competition in a single species with discrete, non-overlapping generations. We show that the deterministic limit of the dynamics depends on a few easily interpretable parameters only. Further, we discuss qualitative properties and limit sets of the corresponding difference equations, and we relate these to modes of competition. Moreover, a detailed analysis of stochastic effects in some relevant scenarios indicates that the behaviour of the stochastic model is very sensitive to further details of the model.

Detection of Mycobacterium avium ssp. paratuberculosis in Cultures From Fecal and Tissue Samples Using VOC Analysis and Machine Learning Tools.

Analysis of volatile organic compounds (VOCs) is a novel approach to accelerate bacterial culture diagnostics of Mycobacterium avium subsp. paratuberculosis (MAP). In the present study, cultures of fecal and tissue samples from MAP-infected and non-suspect dairy cattle and goats were explored to elucidate the effects of sample matrix and of animal species on VOC emissions during bacterial cultivation and to identify early markers for bacterial growth. The samples were processed following standard laboratory procedures, culture tubes were incubated for different time periods. Headspace volume of the tubes was sampled by needle trap-micro-extraction, and analyzed by gas chromatography-mass spectrometry. Analysis of MAP-specific VOC emissions considered potential characteristic VOC patterns. To address variation of the patterns, a flexible and robust machine learning workflow was set up, based on random forest classifiers, and comprising three steps: variable selection, parameter optimization, and classification. Only a few substances originated either from a certain matrix or could be assigned to one animal species. These additional emissions were not considered informative by the variable selection procedure. Classification accuracy of MAP-positive and negative cultures of bovine feces was 0.98 and of caprine feces 0.88, respectively. Six compounds indicating MAP presence were selected in all four settings (cattle vs. goat, feces vs. tissue): 2-Methyl-1-propanol, 2-methyl-1-butanol, 3-methyl-1-butanol, heptanal, isoprene, and 2-heptanone. Classification accuracies for MAP growth-scores ranged from 0.82 for goat tissue to 0.89 for cattle feces. Misclassification occurred predominantly between related scores. Seventeen compounds indicating MAP growth were selected in all four settings, including the 6 compounds indicating MAP presence. The concentration levels of 2,3,5-trimethylfuran, 2-pentylfuran, 1-propanol, and 1-hexanol were indicative for MAP cultures before visible growth was apparent. Thus, very accurate classification of the VOC samples was achieved and the potential of VOC analysis to detect bacterial growth before colonies become visible was confirmed. These results indicate that diagnosis of paratuberculosis can be optimized by monitoring VOC emissions of bacterial cultures. Further validation studies are needed to increase the robustness of indicative VOC patterns for early MAP growth as a pre-requisite for the development of VOC-based diagnostic analysis systems.

Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes.

In the present work we propose an alternative approach to model autocatalytic networks, called piecewise-deterministic Markov processes. These were originally introduced by Davis in 1984. Such a model allows for random transitions between the active and inactive state of a gene, whereas subsequent transcription and translation processes are modeled in a deterministic manner. We consider three types of autoregulated networks, each based on a positive feedback loop. It is shown that if the densities of the stationary distributions exist, they are the solutions of a system of equations for a one-dimensional correlated random walk. These stationary distributions are determined analytically. Further, the distributions are analyzed for different simulation periods and different initial concentration values by numerical means. We show that, depending on the network structure, beside a binary response also a graded response is observable.

Non-invasive and label-free 3D-visualization shows in vivo oligomerization of the staphylococcal alkaline shock protein 23 (Asp23).

Fluorescence-tags, commonly used to visualize the spatial distribution of proteins within cells, can influence the localization of the tagged proteins by affecting their stability, interaction with other proteins or the induction of oligomerization artifacts. To circumvent these obstacles, a protocol was developed to generate 50 nm thick serial sections suitable for immunogold labeling and subsequent reconstruction of the spatial distribution of immuno-labeled native proteins within individual bacterial cells. Applying this method, we show a cellular distribution of the staphylococcal alkaline shock protein 23 (Asp23), which is compatible with filament formation, a property of Asp23 that we also demonstrate in vitro.

Hybrid modeling of noise reduction by a negatively autoregulated system.

We analyze the reduction of intrinsic noise caused by transition of a promoter between its active and inactive state in a negatively regulated genetic network, i.e., transcription of the gene is inhibited by its own gene product. To measure the noise attenuation, we compare its behavior to an inducible gene for which activation and deactivation of the gene take place at constant rates. As a model, we choose a hybrid approach in which some of the reaction channels are modeled as discrete events, and other reactions are modeled as continuous processes. Such a model is appropriate for investigations of noise caused by low reactant numbers. By focusing on intrinsic noise originating from the switching behavior of the regulatory system of a particular gene, we model only the transition between two different promoter states as a discrete event. We show that the stationary distributions of the unregulated and the autoregulated system are given as a solution of two coupled ordinary differential equations. Also, beside the distribution densities, the first two central moments are derived in closed analytical forms. We give conditions on the parameters when one or the other system shows lower fluctuations.

Substrate specificity of thioredoxins and glutaredoxins - towards a functional classification.

The spatio-temporal reduction and oxidation of protein thiols is an essential mechanism in signal transduction in all kingdoms of life. Thioredoxin (Trx) family proteins efficiently catalyze thiol-disulfide exchange reactions and the proteins are widely recognized for their importance in the operation of thiol switches. Trx family proteins have a broad and at the same time very distinct substrate specificity - a prerequisite for redox switching. Despite of multiple efforts, the true nature for this specificity is still under debate. Here, we comprehensively compare the classification/clustering of various redoxins from all domains of life based on their similarity in amino acid sequence, tertiary structure, and their electrostatic properties. We correlate these similarities to the existence of common interaction partners, identified in various previous studies and suggested by proteomic screenings. These analyses confirm that primary and tertiary structure similarity, and thereby all common classification systems, do not correlate to the target specificity of the proteins as thiol-disulfide oxidoreductases. Instead, a number of examples clearly demonstrate the importance of electrostatic similarity for their target specificity, independent of their belonging to the Trx or glutaredoxin subfamilies.

Transcription, intercellular variability and correlated random walk.

We develop a simple model for the random distribution of a gene product. It is assumed that the only source of variance is due to switching transcription on and off by a random process. Under the condition that the transition rates between on and off are constant we find that the amount of mRNA follows a scaled Beta distribution. Additionally, a simple positive feedback loop is considered. The simplicity of the model allows for an explicit solution also in this setting. These findings in turn allow, e.g., for easy parameter scans. We find that bistable behavior translates into bimodal distributions. These theoretical findings are in line with experimental results.

Modeling the Hes1 oscillator.

Somitogenesis describes the segmentation of vertebrate embryonic bodies, which is thought to be induced by ultradian clocks (i.e., clocks with relatively short cycles compared to circadian clocks). One candidate for such a clock is the bHLH factor Hes1, forming dimers which repress the transcription of its own encoding gene. Most models for such small autoregulative networks are based on delay equations where a Hill function represents the regulation of transcription. The aim of the present paper is to estimate the Hill coefficient in the switch of an Hes1 oscillator and to suggest a more detailed model of the autoregulative network. The promoter of Hes1 consists of three to four binding sites for Hes1 dimers. Using the sparse data from literature, we find, in contrast to other statements in literature, that there is not much evidence for synergistic binding in the regulatory region of Hes1, and that the Hill coefficient is about three. As a model for the negative feedback loop, we use a Goodwin system and find sustained oscillations for systems with a large enough number of linear differential equations. By a suitable variation of the number of equations, we provide a rational lower bound for the Hill coefficient for such a system. Our results suggest that there exist additional nonlinear processes outside of the regulatory region of Hes1.

Strategies for the identification of disease-related patterns of volatile organic compounds: prediction of paratuberculosis in an animal model using random forests.

Modern statistical methods which were developed for pattern recognition are increasingly being used for data analysis in studies on emissions of volatile organic compounds (VOCs). With the detection of disease-related VOC profiles, novel non-invasive diagnostic tools could be developed for clinical applications. However, it is important to bear in mind that not all statistical methods are equally suitable for the investigation of VOC profiles. In particular, univariate methods are not able to discover VOC patterns as they consider each compound separately. The present study demonstrates this fact in practice. Using VOC samples from a controlled animal study on paratuberculosis, the random forest classification method was applied for pattern recognition and disease prediction. This strategy was compared with a prediction approach based on single compounds. Both methods were framed within a cross-validation procedure. A comparison of both strategies based on these VOC data reveals that random forests achieves higher sensitivities and specificities than predictions based on single compounds. Therefore, it will most likely be more fruitful to further investigate VOC patterns instead of single biomarkers for paratuberculosis. All methods used are thoroughly explained to aid the transfer to other data analyses.

Specificity assessment from fractionation experiments (SAFE): a novel method to evaluate microarray probe specificity based on hybridisation stringencies.

The cDNA-chip technology is a highly versatile tool for the comprehensive analysis of gene expression at the transcript level. Although it has been applied successfully in expression profiling projects, there is an ongoing dispute concerning the quality of such expression data. The latter critically depends on the specificity of hybridisation. SAFE (specificity assessment from fractionation experiments) is a novel method to discriminate between non- specific cross-hybridisation and specific signals. We applied in situ fractionation of hybridised target on DNA-chips by means of repeated washes with increasing stringencies. Different fractions of hybridised target are washed off at defined stringencies and the collected fluorescence intensity data at each step comprise the fractionation curve. Based on characteristic features of the fractionation curve, unreliable data can be filtered and eliminated from subsequent analyses. The approach described here provides a novel experimental tool to identify probes that produce specific hybridisation signals in DNA-chip expression profiling approaches. The iterative use of the SAFE procedure will result in increasingly reliable sets of probes for microarray experiments and significantly improve the overall efficiency and reliability of RNA expression profiling data from DNA-chip experiments.

Revealing complex function, process and pathway interactions with high-throughput expression and biological annotation data.

The biological relationships both between and within the functions, processes and pathways that operate within complex biological systems are only poorly characterized, making the interpretation of large scale gene expression datasets extremely challenging. Here, we present an approach that integrates gene expression and biological annotation data to identify and describe the interactions between biological functions, processes and pathways that govern a phenotype of interest. The product is a global, interconnected network, not of genes but of functions, processes and pathways, that represents the biological relationships within the system. We validated our approach on two high-throughput expression datasets describing organismal and organ development. Our findings are well supported by the available literature, confirming that developmental processes and apoptosis play key roles in cell differentiation. Furthermore, our results suggest that processes related to pluripotency and lineage commitment, which are known to be critical for development, interact mainly indirectly, through genes implicated in more general biological processes. Moreover, we provide evidence that supports the relevance of cell spatial organization in the developing liver for proper liver function. Our strategy can be viewed as an abstraction that is useful to interpret high-throughput data and devise further experiments.

An efficient level set method for simultaneous intensity inhomogeneity correction and segmentation of MR images.

Intensity inhomogeneity (bias field) is a common artefact in magnetic resonance (MR) images, which hinders successful automatic segmentation. In this work, a novel algorithm for simultaneous segmentation and bias field correction is presented. The proposed energy functional allows for explicit regularization of the bias field term, making the model more flexible, which is crucial in presence of strong inhomogeneities. An efficient minimization procedure, attempting to find the global minimum, is applied to the energy functional. The algorithm is evaluated qualitatively and quantitatively using a synthetic example and real MR images of different organs. Comparisons with several state-of-the-art methods demonstrate the superior performance of the proposed technique. Desirable results are obtained even for images with strong and complicated inhomogeneity fields and sparse tissue structures.