Bayesian multiple-instance motif discovery with BAMBI: inference of recombinase and transcription factor binding sites

Finding conserved motifs in genomic sequences represents one of essential bioinformatic problems. However, achieving high discovery performance without imposing substantial auxiliary constraints on possible motif features remains a key algorithmic challenge. This work describes BAMBI—a sequential Monte Carlo motif-identification algorithm, which is based on a position weight matrix model that does not require additional constraints and is able to estimate such motif properties as length, logo, number of instances and their locations solely on the basis of primary nucleotide sequence data. Furthermore, should biologically meaningful information about motif attributes be available, BAMBI takes advantage of this knowledge to further refine the discovery results. In practical applications, we show that the proposed approach can be used to find sites of such diverse DNA-binding molecules as the cAMP receptor protein (CRP) and Din-family site-specific serine recombinases. Results obtained by BAMBI in these and other settings demonstrate better statistical performance than any of the four widely-used profile-based motif discovery methods: MEME, BioProspector with BioOptimizer, SeSiMCMC and Motif Sampler as measured by the nucleotide-level correlation coefficient. Additionally, in the case of Din-family recombinase target site discovery, the BAMBI-inferred motif is found to be the only one functionally accurate from the underlying biochemical mechanism standpoint. C++ and Matlab code is available at http://www.ee.columbia.edu/~guido/BAMBI or http://genomics.lbl.gov/BAMBI/

The EM Algorithm and the Rise of Computational Biology

In the past decade computational biology has grown from a cottage industry with a handful of researchers to an attractive interdisciplinary field, catching the attention and imagination of many quantitatively-minded scientists. Of interest to us is the key role played by the EM algorithm during this transformation. We survey the use of the EM algorithm in a few important computational biology problems surrounding the "central dogma"; of molecular biology: from DNA to RNA and then to proteins. Topics of this article include sequence motif discovery, protein sequence alignment, population genetics, evolutionary models and mRNA expression microarray data analysis.Comment: Published in at http://dx.doi.org/10.1214/09-STS312 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

CSI-Tree: a regression tree approach for modeling binding properties of DNA-binding molecules based on cognate site identification (CSI) data

The identification and characterization of binding sites of DNA-binding molecules, including transcription factors (TFs), is a critical problem at the interface of chemistry, biology and molecular medicine. The Cognate Site Identification (CSI) array is a high-throughput microarray platform for measuring comprehensive recognition profiles of DNA-binding molecules. This technique produces datasets that are useful not only for identifying binding sites of previously uncharacterized TFs but also for elucidating dependencies, both local and nonlocal, between the nucleotides at different positions of the recognition sites. We have developed a regression tree technique, CSI-Tree, for exploring the spectrum of binding sites of DNA-binding molecules. Our approach constructs regression trees utilizing the CSI data of unaligned sequences. The resulting model partitions the binding spectrum into homogeneous regions of position specific nucleotide effects. Each homogeneous partition is then summarized by a position weight matrix (PWM). Hence, the final outcome is a binding intensity rank-ordered collection of PWMs each of which spans a different region in the binding spectrum. Nodes of the regression tree depict the critical position/nucleotide combinations. We analyze the CSI data of the eukaryotic TF Nkx-2.5 and two engineered small molecule DNA ligands and obtain unique insights into their binding properties. The CSI tree for Nkx-2.5 reveals an interaction between two positions of the binding profile and elucidates how different nucleotide combinations at these two positions lead to different binding affinities. The CSI trees for the engineered DNA ligands exhibit a common preference for the dinucleotide AA in the first two positions, which is consistent with preference for a narrow and relatively flat minor groove. We carry out a reanalysis of these data with a mixture of PWMs approach. This approach is an advancement over the simple PWM model and accommodates position dependencies based on only sequence data. Our analysis indicates that the dependencies revealed by the CSI-Tree are challenging to discover without the actual binding intensities. Moreover, such a mixture model is highly sensitive to the number and length of the sequences analyzed. In contrast, CSI-Tree provides interpretable and concise summaries of the complete recognition profiles of DNA-binding molecules by utilizing binding affinities

A Combined Motif Discovery Method

A central problem in the bioinformatics is to find the binding sites for regulatory motifs. This is a challenging problem that leads us to a platform to apply a variety of data mining methods. In the efforts described here, a combined motif discovery method that uses mutual information and Gibbs sampling was developed. A new scoring schema was introduced with mutual information and joint information content involved. Simulated tempering was embedded into classic Gibbs sampling to avoid local optima. This method was applied to the 18 pieces DNA sequences containing CRP binding sites validated by Stormo and the results were compared with Bioprospector. Based on the results, the new scoring schema can get over the defect that the basic model PWM only contains single positioin information. Simulated tempering proved to be an adaptive adjustment of the search strategy and showed a much increased resistance to local optima

A Combined Motif Discovery Method

A central problem in the bioinformatics is to find the binding sites for regulatory motifs. This is a challenging problem that leads us to a platform to apply a variety of data mining methods. In the efforts described here, a combined motif discovery method that uses mutual information and Gibbs sampling was developed. A new scoring schema was introduced with mutual information and joint information content involved. Simulated tempering was embedded into classic Gibbs sampling to avoid local optima. This method was applied to the 18 pieces DNA sequences containing CRP binding sites validated by Stormo and the results were compared with Bioprospector. Based on the results, the new scoring schema can get over the defect that the basic model PWM only contains single positioin information. Simulated tempering proved to be an adaptive adjustment of the search strategy and showed a much increased resistance to local optima

Equi-energy sampler with applications in statistical inference and statistical mechanics

We introduce a new sampling algorithm, the equi-energy sampler, for efficient statistical sampling and estimation. Complementary to the widely used temperature-domain methods, the equi-energy sampler, utilizing the temperature--energy duality, targets the energy directly. The focus on the energy function not only facilitates efficient sampling, but also provides a powerful means for statistical estimation, for example, the calculation of the density of states and microcanonical averages in statistical mechanics. The equi-energy sampler is applied to a variety of problems, including exponential regression in statistics, motif sampling in computational biology and protein folding in biophysics.Comment: This paper discussed in: [math.ST/0611217], [math.ST/0611219], [math.ST/0611221], [math.ST/0611222]. Rejoinder in [math.ST/0611224]. Published at http://dx.doi.org/10.1214/009053606000000515 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Novel stochastic and entropy-based Expectation-Maximisation algorithm for transcription factor binding site motif discovery

The discovery of transcription factor binding site (TFBS) motifs remains an important and challenging problem in computational biology. This thesis presents MITSU, a novel algorithm for TFBS motif discovery which exploits stochastic methods as a means of both overcoming optimality limitations in current algorithms and as a framework for incorporating relevant prior knowledge in order to improve results. The current state of the TFBS motif discovery field is surveyed, with a focus on probabilistic algorithms that typically take the promoter regions of coregulated genes as input. A case is made for an approach based on the stochastic Expectation- Maximisation (sEM) algorithm; its position amongst existing probabilistic algorithms for motif discovery is shown. The algorithm developed in this thesis is unique amongst existing motif discovery algorithms in that it combines the sEM algorithm with a derived data set which leads to an improved approximation to the likelihood function. This likelihood function is unconstrained with regard to the distribution of motif occurrences within the input dataset. MITSU also incorporates a novel heuristic to automatically determine TFBS motif width. This heuristic, known as MCOIN, is shown to outperform current methods for determining motif width. MITSU is implemented in Java and an executable is available for download. MITSU is evaluated quantitatively using realistic synthetic data and several collections of previously characterised prokaryotic TFBS motifs. The evaluation demonstrates that MITSU improves on a deterministic EM-based motif discovery algorithm and an alternative sEM-based algorithm, in terms of previously established metrics. The ability of the sEM algorithm to escape stable fixed points of the EM algorithm, which trap deterministic motif discovery algorithms and the ability of MITSU to discover multiple motif occurrences within a single input sequence are also demonstrated. MITSU is validated using previously characterised Alphaproteobacterial motifs, before being applied to motif discovery in uncharacterised Alphaproteobacterial data. A number of novel results from this analysis are presented and motivate two extensions of MITSU: a strategy for the discovery of multiple different motifs within a single dataset and a higher order Markov background model. The effects of incorporating these extensions within MITSU are evaluated quantitatively using previously characterised prokaryotic TFBS motifs and demonstrated using Alphaproteobacterial motifs. Finally, an information-theoretic measure of motif palindromicity is presented and its advantages over existing approaches for discovering palindromic motifs discussed

Bayesian Inference for Genomic Data Analysis

High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples