Efficient Low-Order Approximation of First-Passage Time Distributions.

We consider the problem of computing first-passage time distributions for reaction processes modeled by master equations. We show that this generally intractable class of problems is equivalent to a sequential Bayesian inference problem for an auxiliary observation process. The solution can be approximated efficiently by solving a closed set of coupled ordinary differential equations (for the low-order moments of the process) whose size scales with the number of species. We apply it to an epidemic model and a trimerization process and show good agreement with stochastic simulations.

MMDiff: quantitative testing for shape changes in ChIP-Seq data sets.

BACKGROUND: Cell-specific gene expression is controlled by epigenetic modifications and transcription factor binding. While genome-wide maps for these protein-DNA interactions have become widely available, quantitative comparison of the resulting ChIP-Seq data sets remains challenging. Current approaches to detect differentially bound or modified regions are mainly borrowed from RNA-Seq data analysis, thus focusing on total counts of fragments mapped to a region, ignoring any information encoded in the shape of the peaks. RESULTS: Here, we present MMDiff, a robust, broadly applicable method for detecting differences between sequence count data sets. Based on quantifying shape changes in signal profiles, it overcomes challenges imposed by the highly structured nature of the data and the paucity of replicates.We first use a simulated data set to compare the performance of MMDiff with results obtained by four alternative methods. We demonstrate that MMDiff excels when peak profiles change between samples. We next use MMDiff to re-analyse a recent data set of the histone modification H3K4me3 elucidating the establishment of this prominent epigenomic marker. Our empirical analysis shows that the method yields reproducible results across experiments, and is able to detect functional important changes in histone modifications. To further explore the broader applicability of MMDiff, we apply it to two ENCODE data sets: one investigating the histone modification H3K27ac and one measuring the genome-wide binding of the transcription factor CTCF. In both cases, MMDiff proves to be complementary to count-based methods. In addition, we can show that MMDiff is capable of directly detecting changes of homotypic binding events at neighbouring binding sites. MMDiff is readily available as a Bioconductor package. CONCLUSIONS: Our results demonstrate that higher order features of ChIP-Seq peaks carry relevant and often complementary information to total counts, and hence are important in assessing differential histone modifications and transcription factor binding. We have developed a new computational method, MMDiff, that is capable of exploring these features and therefore closes an existing gap in the analysis of ChIP-Seq data sets.

Efficient Bayesian multivariate fMRI analysis using a sparsifying spatio-temporal prior.

Bayesian logistic regression with a multivariate Laplace prior is introduced as a multivariate approach to the analysis of neuroimaging data. It is shown that, by rewriting the multivariate Laplace distribution as a scale mixture, we can incorporate spatio-temporal constraints which lead to smooth importance maps that facilitate subsequent interpretation. The posterior of interest is computed using an approximate inference method called expectation propagation and becomes feasible due to fast inversion of a sparse precision matrix. We illustrate the performance of the method on an fMRI dataset acquired while subjects were shown handwritten digits. The obtained models perform competitively in terms of predictive performance and give rise to interpretable importance maps. Estimation of the posterior of interest is shown to be feasible even for very large models with thousands of variables.

Network of epistatic interactions within a yeast snoRNA.

Epistatic interactions play a fundamental role in molecular evolution, but little is known about the spatial distribution of these interactions within genes. To systematically survey a model landscape of intragenic epistasis, we quantified the fitness of ~60,000 Saccharomyces cerevisiae strains expressing randomly mutated variants of the 333-nucleotide-long U3 small nucleolar RNA (snoRNA). The fitness effects of individual mutations were correlated with evolutionary conservation and structural stability. Many mutations had small individual effects but had large effects in the context of additional mutations, which indicated negative epistasis. Clusters of negative interactions were explained by local thermodynamic threshold effects, whereas positive interactions were enriched among large-effect sites and between base-paired nucleotides. We conclude that high-throughput mapping of intragenic epistasis can identify key structural and functional features of macromolecules.