Dataset Information

The jigsaw puzzle of sequence phenotype inference: Piecing together Shannon entropy, importance sampling, and Empirical Bayes.

ABSTRACT: A nucleotide sequence 35 base pairs long can take 1,180,591,620,717,411,303,424 possible values. An example of systems biology datasets, protein binding microarrays, contain activity data from about 40,000 such sequences. The discrepancy between the number of possible configurations and the available activities is enormous. Thus, albeit that systems biology datasets are large in absolute terms, they oftentimes require methods developed for rare events due to the combinatorial increase in the number of possible configurations of biological systems. A plethora of techniques for handling large datasets, such as Empirical Bayes, or rare events, such as importance sampling, have been developed in the literature, but these cannot always be simultaneously utilized. Here we introduce a principled approach to Empirical Bayes based on importance sampling, information theory, and theoretical physics in the general context of sequence phenotype model induction. We present the analytical calculations that underlie our approach. We demonstrate the computational efficiency of the approach on concrete examples, and demonstrate its efficacy by applying the theory to publicly available protein binding microarray transcription factor datasets and to data on synthetic cAMP-regulated enhancer sequences. As further demonstrations, we find transcription factor binding motifs, predict the activity of new sequences and extract the locations of transcription factor binding sites. In summary, we present a novel method that is efficient (requiring minimal computational time and reasonable amounts of memory), has high predictive power that is comparable with that of models with hundreds of parameters, and has a limited number of optimized parameters, proportional to the sequence length.

SUBMITTER: Shreif Z

PROVIDER: S-EPMC4522360 | biostudies-literature | 2015 Sep

REPOSITORIES: biostudies-literature

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The jigsaw puzzle of sequence phenotype inference: Piecing together Shannon entropy, importance sampling, and Empirical Bayes.

Shreif Zeina Z Striegel Deborah A DA Periwal Vipul V

Journal of theoretical biology 20150617

A nucleotide sequence 35 base pairs long can take 1,180,591,620,717,411,303,424 possible values. An example of systems biology datasets, protein binding microarrays, contain activity data from about 40,000 such sequences. The discrepancy between the number of possible configurations and the available activities is enormous. Thus, albeit that systems biology datasets are large in absolute terms, they oftentimes require methods developed for rare events due to the combinatorial increase in the num ...[more]

PMID: 26092377

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Project description:BackgroundMicroarray data enables the high-throughput survey of mRNA expression profiles at the genomic level; however, he data presents a challenging statistical problem because of the large number of transcripts with small sample sizes that are obtained. To reduce the dimensionality, various Bayesian or empirical Bayes hierarchical models have been developed. However, because of the complexity of the microarray data, no model can explain the data fully. It is generally difficult to scrutinize the irregular patterns of expression that are not expected by the usual statistical gene by gene models.ResultsAs an extension of empirical Bayes (EB) procedures, we have developed the β-empirical Bayes (β-EB) approach based on a β-likelihood measure which can be regarded as an 'evidence-based' weighted (quasi-) likelihood inference. The weight of a transcript t is described as a power function of its likelihood, fβ(yt|θ). Genes with low likelihoods have unexpected expression patterns and low weights. By assigning low weights to outliers, the inference becomes robust. The value of β, which controls the balance between the robustness and efficiency, is selected by maximizing the predictive β₀-likelihood by cross-validation. The proposed β-EB approach identified six significant (p<10⁻⁵) contaminated transcripts as differentially expressed (DE) in normal/tumor tissues from the head and neck of cancer patients. These six genes were all confirmed to be related to cancer; they were not identified as DE genes by the classical EB approach. When applied to the eQTL analysis of Arabidopsis thaliana, the proposed β-EB approach identified some potential master regulators that were missed by the EB approach.ConclusionsThe simulation data and real gene expression data showed that the proposed β-EB method was robust against outliers. The distribution of the weights was used to scrutinize the irregular patterns of expression and diagnose the model statistically. When β-weights outside the range of the predicted distribution were observed, a detailed inspection of the data was carried out. The β-weights described here can be applied to other likelihood-based statistical models for diagnosis, and may serve as a useful tool for transcriptome and proteome studies.

Dataset Information

The jigsaw puzzle of sequence phenotype inference: Piecing together Shannon entropy, importance sampling, and Empirical Bayes.

Publications

The jigsaw puzzle of sequence phenotype inference: Piecing together Shannon entropy, importance sampling, and Empirical Bayes.

Similar Datasets

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