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Network-based segmentation of biological multivariate time series.

Omranian N, Klie S, Mueller-Roeber B, Nikoloski Z - PLoS ONE (2013)

Bottom Line: As a result, MTS data capture the dynamics of biochemical processes and components whose couplings may involve different scales and exhibit temporal changes.We demonstrate that the problem of partitioning MTS data into [Formula: see text] 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.

View Article: PubMed Central - PubMed

Affiliation: Institute of Biochemistry and Biology, University of Potsdam, Potsdam-Golm, Germany.

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 [Formula: see text] 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.

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Segmentation for yeast’s metabolic cycle.The partitions found by applying our method are highlighted in light grey. The phases of the yeast metabolic cycle are indicated with colored rectangles above each panel following Tu et al.[36]. R/C stands for reductive charging, OX oxidative metabolism, and R/B, reductive metabolism. (a) shows the segmentations caught by relative density as global property; (b) illustrates the segmentations based on degree; (c) and (d) demonstrate segmentations with local-global properties, betweenness and closeness, respectively. The segmentations in panel (a) performs particularly well due to the global changes in the form of global cycles in the data set from yeast.
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pone-0062974-g005: Segmentation for yeast’s metabolic cycle.The partitions found by applying our method are highlighted in light grey. The phases of the yeast metabolic cycle are indicated with colored rectangles above each panel following Tu et al.[36]. R/C stands for reductive charging, OX oxidative metabolism, and R/B, reductive metabolism. (a) shows the segmentations caught by relative density as global property; (b) illustrates the segmentations based on degree; (c) and (d) demonstrate segmentations with local-global properties, betweenness and closeness, respectively. The segmentations in panel (a) performs particularly well due to the global changes in the form of global cycles in the data set from yeast.

Mentions: The range for the tuning parameter for each used network property together with the resulting segmentations and number of segments are summarized in Table 2. Due to the presence of recurrent changes on the global level, two segmentation points, corresponding to time points 12–13 and 24–25 and delineating the three considered cell cycles, should be detected. In addition, due to the presence of the alternation phases in the metabolic cycle, each of the three cycles should contain at least one more segmentation point. Altogether, this biological reasoning implies the existence of six to seven segmentation points in the investigated time domain. Inspection of the results in Table 2 indicates that when using the BP-penalty, the degree resulted in the most biologically meaningful prediction for the segmentation points in the first two cell cycles, where the starting of each of the three phases is nicely delineated. A similar behavior is observed for the betweenness centrality. However, none of the properties results in the identification of an additional breakpoint in the third cycle. The method of Ramakrishnan et al.[15] with and (Table S2 and Figure S1) also results in eight segments which resemble our results (Fig. 5) particularly for the first two cell cycles.


Network-based segmentation of biological multivariate time series.

Omranian N, Klie S, Mueller-Roeber B, Nikoloski Z - PLoS ONE (2013)

Segmentation for yeast’s metabolic cycle.The partitions found by applying our method are highlighted in light grey. The phases of the yeast metabolic cycle are indicated with colored rectangles above each panel following Tu et al.[36]. R/C stands for reductive charging, OX oxidative metabolism, and R/B, reductive metabolism. (a) shows the segmentations caught by relative density as global property; (b) illustrates the segmentations based on degree; (c) and (d) demonstrate segmentations with local-global properties, betweenness and closeness, respectively. The segmentations in panel (a) performs particularly well due to the global changes in the form of global cycles in the data set from yeast.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3646968&req=5

pone-0062974-g005: Segmentation for yeast’s metabolic cycle.The partitions found by applying our method are highlighted in light grey. The phases of the yeast metabolic cycle are indicated with colored rectangles above each panel following Tu et al.[36]. R/C stands for reductive charging, OX oxidative metabolism, and R/B, reductive metabolism. (a) shows the segmentations caught by relative density as global property; (b) illustrates the segmentations based on degree; (c) and (d) demonstrate segmentations with local-global properties, betweenness and closeness, respectively. The segmentations in panel (a) performs particularly well due to the global changes in the form of global cycles in the data set from yeast.
Mentions: The range for the tuning parameter for each used network property together with the resulting segmentations and number of segments are summarized in Table 2. Due to the presence of recurrent changes on the global level, two segmentation points, corresponding to time points 12–13 and 24–25 and delineating the three considered cell cycles, should be detected. In addition, due to the presence of the alternation phases in the metabolic cycle, each of the three cycles should contain at least one more segmentation point. Altogether, this biological reasoning implies the existence of six to seven segmentation points in the investigated time domain. Inspection of the results in Table 2 indicates that when using the BP-penalty, the degree resulted in the most biologically meaningful prediction for the segmentation points in the first two cell cycles, where the starting of each of the three phases is nicely delineated. A similar behavior is observed for the betweenness centrality. However, none of the properties results in the identification of an additional breakpoint in the third cycle. The method of Ramakrishnan et al.[15] with and (Table S2 and Figure S1) also results in eight segments which resemble our results (Fig. 5) particularly for the first two cell cycles.

Bottom Line: As a result, MTS data capture the dynamics of biochemical processes and components whose couplings may involve different scales and exhibit temporal changes.We demonstrate that the problem of partitioning MTS data into [Formula: see text] 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.

View Article: PubMed Central - PubMed

Affiliation: Institute of Biochemistry and Biology, University of Potsdam, Potsdam-Golm, Germany.

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 [Formula: see text] 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.

Show MeSH