Deep surveys of transcriptional modules with Massive Associative Kbiclustering (MAK)

Abstract

Biclustering can reveal functional patterns in common biological data such as gene expression. Biclusters are ordered submatrices of a larger matrix that represent coherent data patterns. A critical requirement for biclusters is high coherence across a subset of columns, where coherence is defined as a fit to a mathematical model of similarity or correlation. Biclustering, though powerful, is NP-hard, and existing biclustering methods implement a wide variety of approximations to achieve tractable solutions for real world datasets. High bicluster coherence becomes more computationally expensive to achieve with high dimensional data, due to the search space size and because the number, size, and overlap of biclusters tends to increase. This complicates an already difficult problem and leads existing methods to find smaller, less coherent biclusters. Our unsupervised Massive Associative K-biclustering (MAK) approach corrects this size bias while preserving high bicluster coherence both on simulated datasets with known ground truth and on real world data without, where we apply a new measure to evaluate biclustering. Moreover, MAK jointly maximizes bicluster coherence with biological enrichment and finds the most enriched biological functions. Another long-standing problem with these methods is the overwhelming data signal related to ribosomal functions and protein production, which can drown out signals for less common but therefore more interesting functions. MAK reports the second-most enriched non-protein production functions, with higher bicluster coherence and arrayed across a large number of biclusters, demonstrating its ability to alleviate this biological bias and thus reflect the mediation of multiple biological processes rather than recruitment of processes to a small number of major cell activities. Finally, compared to the union of results from 11 top biclustering methods, MAK finds 21 novel S. cerevisiae biclusters. MAK can generate high quality biclusters in large biological datasets, including simultaneous integration of up to four distinct biological data types. Author summaryBiclustering can reveal functional patterns in common biological data such as gene expression. A critical requirement for biclusters is high coherence across a subset of columns, where coherence is defined as a fit to a mathematical model of similarity or correlation. Biclustering, though powerful, is NP-hard, and existing biclustering methods implement a wide variety of approximations to achieve tractable solutions for real world datasets. This complicates an already difficult problem and leads existing biclustering methods to find smaller and less coherent biclusters. Using the MAK methodology we can correct the bicluster size bias while preserving high bicluster coherence on simulated datasets with known ground truth as well as real world datasets, where we apply a new data driven bicluster set score. MAK jointly maximizes bicluster coherence with biological enrichment and finds more enriched biological functions, including other than protein production. These functions are arrayed across a large number of MAK biclusters, demonstrating ability to alleviate this biological bias and reflect the mediation of multiple biological processes rather than recruitment of processes to a small number of major cell activities. MAK can generate high quality biclusters in large biological datasets, including simultaneous integration of up to four distinct biological data types.