We develop a latent variable model and an efficient spectral algorithm motivated by the recent emergence of very large data sets of chromatin marks from multiple human cell types. A natural model for chromatin data in one cell type is a Hidden Markov Model (HMM); we model the relationship between multiple cell types by connecting their hidden states by a fixed tree of known structure. The main challenge with learning parameters of such models is that iterative methods such as EM are very slow, while naive spectral methods result in time and space complexity exponential in the number of cell types. We exploit properties of the tree structure of the hidden states to provide spectral algorithms that are more computationally efficient for current biological datasets. We provide sample complexity bounds for our algorithm and evaluate it experimentally on biological data from nine human cell types. Finally, we show that beyond our specific model, some of our algorithmic ideas can be applied to other graphical models.

Numerous studies have suggested that hub proteins in the S. cerevisiae physical interaction network are more likely to be essential than other proteins. The proposed reasons underlying this observed relationship between topology and functioning have been subject to some controversy, with recent work suggesting that it arises due to the participation of hub proteins in essential complexes and processes. However, do these essential modules themselves have distinct network characteristics, and how do their essential proteins differ in their topological properties from their non-essential proteins? We aimed to advance our understanding of protein essentiality by analyzing proteins, complexes and processes within their broader functional context and by considering physical interactions both within and across complexes and biological processes. In agreement with the view that essentiality is a modular property, we found that the number of intracomplex or intraprocess interactions that a protein has is a better indicator of its essentiality than its overall number of interactions. Moreover, we found that within an essential complex, its essential proteins have on average more interactions, especially intracomplex interactions, than its non-essential proteins. Finally, we built a module-level interaction network and found that essential complexes and processes tend to have higher interaction degrees in this network than non-essential complexes and processes; that is, they exhibit a larger amount of functional cross-talk than their non-essential counterparts.

MOTIVATION: Clustering of protein-protein interaction networks is one of the most common approaches for predicting functional modules, protein complexes and protein functions. But, how well does clustering perform at these tasks? RESULTS: We develop a general framework to assess how well computationally derived clusters in physical interactomes overlap functional modules derived via the Gene Ontology (GO). Using this framework, we evaluate six diverse network clustering algorithms using Saccharomyces cerevisiae and show that (i) the performances of these algorithms can differ substantially when run on the same network and (ii) their relative performances change depending upon the topological characteristics of the network under consideration. For the specific task of function prediction in S.cerevisiae, we demonstrate that, surprisingly, a simple non-clustering guilt-by-association approach outperforms widely used clustering-based approaches that annotate a protein with the overrepresented biological process and cellular component terms in its cluster; this is true over the range of clustering algorithms considered. Further analysis parameterizes performance based on the number of annotated proteins, and suggests when clustering approaches should be used for interactome functional analyses. Overall our results suggest a re-examination of when and how clustering approaches should be applied to physical interactomes, and establishes guidelines by which novel clustering approaches for biological networks should be justified and evaluated with respect to functional analysis. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.