Network-Based Segmentation of Biological Multivariate Time Series

Abstract

Molecular phenotyping technologies (e.g., transcriptomics, proteomics, and metabolomics) offer the possibility to simultaneously obtain multivariate time series (MTS) data from different levels of information processing and metabolic conversions in biological systems. As a result, MTS data capture the dynamics of biochemical processes and components whose couplings may involve different scales and exhibit temporal changes. Therefore, it is important to develop methods for determining the time segments in MTS data, which may correspond to critical biochemical events reflected in the coupling of the system’s components. Here we provide a novel network-based formalization of the MTS segmentation problem based on temporal dependencies and the covariance structure of the data. We demonstrate that the problem of partitioning MTS data into segments to maximize a distance function, operating on polynomially computable network properties, often used in analysis of biological network, can be efficiently solved. To enable biological interpretation, we also propose a breakpoint-penalty (BP-penalty) formulation for determining MTS segmentation which combines a distance function with the number/length of segments. Our empirical analyses of synthetic benchmark data as well as time-resolved transcriptomics data from the metabolic and cell cycles of Saccharomyces cerevisiae demonstrate that the proposed method accurately infers the phases in the temporal compartmentalization of biological processes. In addition, through comparison on the same data sets, we show that the results from the proposed formalization of the MTS segmentation problem match biological knowledge and provide more rigorous statistical support in comparison to the contending state-of-the-art methods.