Evolutionary Inference via the Poisson Indel Process

We address the problem of the joint statistical inference of phylogenetic trees and multiple sequence alignments from unaligned molecular sequences. This problem is generally formulated in terms of string-valued evolutionary processes along the branches of a phylogenetic tree. The classical evolutionary process, the TKF91 model, is a continuous-time Markov chain model comprised of insertion, deletion and substitution events. Unfortunately this model gives rise to an intractable computational problem---the computation of the marginal likelihood under the TKF91 model is exponential in the number of taxa. In this work, we present a new stochastic process, the Poisson Indel Process (PIP), in which the complexity of this computation is reduced to linear. The new model is closely related to the TKF91 model, differing only in its treatment of insertions, but the new model has a global characterization as a Poisson process on the phylogeny. Standard results for Poisson processes allow key computations to be decoupled, which yields the favorable computational profile of inference under the PIP model. We present illustrative experiments in which Bayesian inference under the PIP model is compared to separate inference of phylogenies and alignments.Comment: 33 pages, 6 figure

The distribution of word matches between Markovian sequences with periodic boundary conditions

Word match counts have traditionally been proposed as an alignment-free measure of similarity for biological sequences. The D2 statistic, which simply counts the number of exact word matches between two sequences, is a useful test bed for developing rigorous mathematical results, which can then be extended to more biologically useful measures. The distributional properties of the D2 statistic under the null hypothesis of identically and independently distributed letters have been studied extensively, but no comprehensive study of the D2 distribution for biologically more realistic higher-order Markovian sequences exists. Here we derive exact formulas for the mean and variance of the D2 statistic for Markovian sequences of any order, and demonstrate through Monte Carlo simulations that the entire distribution is accurately characterized by a Pólya-Aeppli distribution for sequence lengths of biological interest. The approach is novel in that Markovian dependency is defined for sequences with periodic boundary conditions, and this enables exact analytic formulas for the mean and variance to be derived. We also carry out a preliminary comparison between the approximate D2 distribution computed with the theoretical mean and variance under a Markovian hypothesis and an empirical D2 distribution from the human genome

Models for transcript quantification from RNA-Seq

RNA-Seq is rapidly becoming the standard technology for transcriptome analysis. Fundamental to many of the applications of RNA-Seq is the quantification problem, which is the accurate measurement of relative transcript abundances from the sequenced reads. We focus on this problem, and review many recently published models that are used to estimate the relative abundances. In addition to describing the models and the different approaches to inference, we also explain how methods are related to each other. A key result is that we show how inference with many of the models results in identical estimates of relative abundances, even though model formulations can be very different. In fact, we are able to show how a single general model captures many of the elements of previously published methods. We also review the applications of RNA-Seq models to differential analysis, and explain why accurate relative transcript abundance estimates are crucial for downstream analyses

Quantifying evolutionary constraints on B cell affinity maturation

The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through high-throughput sequencing. Here, we develop modern statistical molecular evolution methods for the analysis of B cell sequence data, and then apply them to a very deep short-read data set of B cell receptors. We find that the substitution process is conserved across individuals but varies significantly across gene segments. We investigate selection on B cell receptors using a novel method that side-steps the difficulties encountered by previous work in differentiating between selection and motif-driven mutation; this is done through stochastic mapping and empirical Bayes estimators that compare the evolution of in-frame and out-of-frame rearrangements. We use this new method to derive a per-residue map of selection, which provides a more nuanced view of the constraints on framework and variable regions.Comment: Previously entitled "Substitution and site-specific selection driving B cell affinity maturation is consistent across individuals

Bethe Ansatz in the Bernoulli Matching Model of Random Sequence Alignment

For the Bernoulli Matching model of sequence alignment problem we apply the Bethe ansatz technique via an exact mapping to the 5--vertex model on a square lattice. Considering the terrace--like representation of the sequence alignment problem, we reproduce by the Bethe ansatz the results for the averaged length of the Longest Common Subsequence in Bernoulli approximation. In addition, we compute the average number of nucleation centers of the terraces.Comment: 14 pages, 5 figures (some points are clarified

Pattern-based phylogenetic distance estimation and tree reconstruction

We have developed an alignment-free method that calculates phylogenetic distances using a maximum likelihood approach for a model of sequence change on patterns that are discovered in unaligned sequences. To evaluate the phylogenetic accuracy of our method, and to conduct a comprehensive comparison of existing alignment-free methods (freely available as Python package decaf+py at http://www.bioinformatics.org.au), we have created a dataset of reference trees covering a wide range of phylogenetic distances. Amino acid sequences were evolved along the trees and input to the tested methods; from their calculated distances we infered trees whose topologies we compared to the reference trees. We find our pattern-based method statistically superior to all other tested alignment-free methods on this dataset. We also demonstrate the general advantage of alignment-free methods over an approach based on automated alignments when sequences violate the assumption of collinearity. Similarly, we compare methods on empirical data from an existing alignment benchmark set that we used to derive reference distances and trees. Our pattern-based approach yields distances that show a linear relationship to reference distances over a substantially longer range than other alignment-free methods. The pattern-based approach outperforms alignment-free methods and its phylogenetic accuracy is statistically indistinguishable from alignment-based distances.Comment: 21 pages, 3 figures, 2 table

Gcn4p and novel upstream activating sequences regulate targets of the unfolded protein response.

Eukaryotic cells respond to accumulation of unfolded proteins in the endoplasmic reticulum (ER) by activating the unfolded protein response (UPR), a signal transduction pathway that communicates between the ER and the nucleus. In yeast, a large set of UPR target genes has been experimentally determined, but the previously characterized unfolded protein response element (UPRE), an upstream activating sequence (UAS) found in the promoter of the UPR target gene KAR2, cannot account for the transcriptional regulation of most genes in this set. To address this puzzle, we analyzed the promoters of UPR target genes computationally, identifying as candidate UASs short sequences that are statistically overrepresented. We tested the most promising of these candidate UASs for biological activity, and identified two novel UPREs, which are necessary and sufficient for UPR activation of promoters. A genetic screen for activators of the novel motifs revealed that the transcription factor Gcn4p plays an essential and previously unrecognized role in the UPR: Gcn4p and its activator Gcn2p are required for induction of a majority of UPR target genes during ER stress. Both Hac1p and Gcn4p bind target gene promoters to stimulate transcriptional induction. Regulation of Gcn4p levels in response to changing physiological conditions may function as an additional means to modulate the UPR. The discovery of a role for Gcn4p in the yeast UPR reveals an additional level of complexity and demonstrates a surprising conservation of the signaling circuit between yeast and metazoan cells