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Learning a mixture of microbial networks using minorization-maximization.

ABSTRACT: MOTIVATION:The interactions among the constituent members of a microbial community play a major role in determining the overall behavior of the community and the abundance levels of its members. These interactions can be modeled using a network whose nodes represent microbial taxa and edges represent pairwise interactions. A microbial network is typically constructed from a sample-taxa count matrix that is obtained by sequencing multiple biological samples and identifying taxa counts. From large-scale microbiome studies, it is evident that microbial community compositions and interactions are impacted by environmental and/or host factors. Thus, it is not unreasonable to expect that a sample-taxa matrix generated as part of a large study involving multiple environmental or clinical parameters can be associated with more than one microbial network. However, to our knowledge, microbial network inference methods proposed thus far assume that the sample-taxa matrix is associated with a single network. RESULTS:We present a mixture model framework to address the scenario when the sample-taxa matrix is associated with K microbial networks. This count matrix is modeled using a mixture of K Multivariate Poisson Log-Normal distributions and parameters are estimated using a maximum likelihood framework. Our parameter estimation algorithm is based on the minorization-maximization principle combined with gradient ascent and block updates. Synthetic datasets were generated to assess the performance of our approach on absolute count data, compositional data and normalized data. We also addressed the recovery of sparse networks based on an l1-penalty model. AVAILABILITY AND IMPLEMENTATION:MixMPLN is implemented in R and is freely available at https://github.com/sahatava/MixMPLN. SUPPLEMENTARY INFORMATION:Supplementary data are available at Bioinformatics online.

SUBMITTER: Tavakoli S

PROVIDER: S-EPMC6612855 | biostudies-other | 2019 Jul

REPOSITORIES: biostudies-other

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Learning a mixture of microbial networks using minorization-maximization.

Tavakoli Sahar S Yooseph Shibu S

Bioinformatics (Oxford, England) 20190701 14

<h4>Motivation</h4>The interactions among the constituent members of a microbial community play a major role in determining the overall behavior of the community and the abundance levels of its members. These interactions can be modeled using a network whose nodes represent microbial taxa and edges represent pairwise interactions. A microbial network is typically constructed from a sample-taxa count matrix that is obtained by sequencing multiple biological samples and identifying taxa counts. Fr ...[more]

PMID: 31510709

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Project description:BackgroundInference of gene networks typically relies on measurements across a wide range of conditions or treatments. Although one network structure is predicted, the relationship between genes could vary across conditions. A comprehensive approach to infer general and condition-dependent gene networks was evaluated. This approach integrated Bayesian network and Gaussian mixture models to describe continuous microarray gene expression measurements, and three gene networks were predicted.ResultsThe first reconstructions of a circadian rhythm pathway in honey bees and an adherens junction pathway in mouse embryos were obtained. In addition, general and condition-specific gene relationships, some unexpected, were detected in these two pathways and in a yeast cell-cycle pathway. The mixture Bayesian network approach identified all (honey bee circadian rhythm and mouse adherens junction pathways) or the vast majority (yeast cell-cycle pathway) of the gene relationships reported in empirical studies. Findings across the three pathways and data sets indicate that the mixture Bayesian network approach is well-suited to infer gene pathways based on microarray data. Furthermore, the interpretation of model estimates provided a broader understanding of the relationships between genes. The mixture models offered a comprehensive description of the relationships among genes in complex biological processes or across a wide range of conditions. The mixture parameter estimates and corresponding odds that the gene network inferred for a sample pertained to each mixture component allowed the uncovering of both general and condition-dependent gene relationships and patterns of expression.ConclusionThis study demonstrated the two main benefits of learning gene pathways using mixture Bayesian networks. First, the identification of the optimal number of mixture components supported by the data offered a robust approach to infer gene relationships and estimate gene expression profiles. Second, the classification of conditions and observations into groups that support particular mixture components helped to uncover both gene relationships that are unique or common across conditions. Results from the application of mixture Bayesian networks substantially augmented the understanding of gene networks and demonstrated the added-value of this methodology to infer gene networks.

Project description:Microbes affect each other's growth in multiple, often elusive, ways. The ensuing interdependencies form complex networks, believed to reflect taxonomic composition as well as community-level functional properties and dynamics. The elucidation of these networks is often pursued by measuring pairwise interactions in coculture experiments. However, the combinatorial complexity precludes an exhaustive experimental analysis of pairwise interactions, even for moderately sized microbial communities. Here, we used a machine learning random forest approach to address this challenge. In particular, we show how partial knowledge of a microbial interaction network, combined with trait-level representations of individual microbial species, can provide accurate inference of missing edges in the network and putative mechanisms underlying the interactions. We applied our algorithm to three case studies: an experimentally mapped network of interactions between auxotrophic Escherichia coli strains, a community of soil microbes, and a large in silico network of metabolic interdependencies between 100 human gut-associated bacteria. For this last case, 5% of the network was sufficient to predict the remaining 95% with 80% accuracy, and the mechanistic hypotheses produced by the algorithm accurately reflected known metabolic exchanges. Our approach, broadly applicable to any microbial or other ecological network, may drive the discovery of new interactions and new molecular mechanisms, both for therapeutic interventions involving natural communities and for the rational design of synthetic consortia. IMPORTANCE Different organisms in a microbial community may drastically affect each other's growth phenotypes, significantly affecting the community dynamics, with important implications for human and environmental health. Novel culturing methods and the decreasing costs of sequencing will gradually enable high-throughput measurements of pairwise interactions in systematic coculturing studies. However, a thorough characterization of all interactions that occur within a microbial community is greatly limited both by the combinatorial complexity of possible assortments and by the limited biological insight that interaction measurements typically provide without laborious specific follow-ups. Here, we show how a simple and flexible formal representation of microbial pairs can be used for the classification of interactions via machine learning. The approach we propose predicts with high accuracy the outcome of yet-to-be performed experiments and generates testable hypotheses about the mechanisms of specific interactions.

Dataset Information

Learning a mixture of microbial networks using minorization-maximization.

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Learning a mixture of microbial networks using minorization-maximization.

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