Network-Based Segmentation of Biological Multivariate Time Series

<div><p>Molecular phenotyping technologies (<i>e.g.</i>, 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 <i>Saccharomyces cerevisiae</i> 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.</p></div

Segmentation for yeast’s metabolic cycle.

<p>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 <i>et al. </i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0062974#pone.0062974-Tu1" target="_blank">[36]</a>. 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.</p

Directed acyclic graph (DAG) used as input in Algorithm 1 (Fig. 3).

<p>The DAG for time points is depicted. It contains nodes, including the special nodes and . The label of each node corresponds to the time points , , and .</p

Illustration of the segmentation for synthetic data with relative density as network property.

<p>The resulting partitions are highlighted in light grey and the simulated segmentation points are marked with red bars.</p

A quantitative RT-PCR platform for high-throughput expression profiling of 2500 rice transcription factors-0

<p><b>Copyright information:</b></p><p>Taken from "A quantitative RT-PCR platform for high-throughput expression profiling of 2500 rice transcription factors"</p><p>http://www.plantmethods.com/content/3/1/7</p><p>Plant Methods 2007;3():7-7.</p><p>Published online 8 Jun 2007</p><p>PMCID:PMC1914063.</p><p></p>DNA (gDNA), evaluation of cDNA quality, primer design and data analysis. The absence of gDNA was confirmed by quantitative RT-PCR (qRT-PCR) with primer pairs targeting various non-coding regions. The quality of the cDNA was tested using different reference genes, as outlined in the text

Optimal segmentation for synthetic data.

<p>The upper part of the table shows the result of the optimal segmentation for synthetic data based on dynamic programming, while the lower part contains the result based on the method of Ramakrishnan <i>et al.</i><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0062974#pone.0062974-Ramakrishnan1" target="_blank">[15]</a>. In the upper table, the first and second columns show the name and the type of network properties used to determine the distances: G stands for global, L for local, and LG for local-global. The third column includes the number of segments that maximize the objective with the dynamic programming approach. The resulting segments are given in the forth column, while the fifth and sixth columns contain the corresponding values of lower () and upper () bound of the tuning parameter . The lower part also includes minimum and maximum length of the segments, i.e., and , as parameters of the contending method.</p

A quantitative RT-PCR platform for high-throughput expression profiling of 2500 rice transcription factors-1

<p><b>Copyright information:</b></p><p>Taken from "A quantitative RT-PCR platform for high-throughput expression profiling of 2500 rice transcription factors"</p><p>http://www.plantmethods.com/content/3/1/7</p><p>Plant Methods 2007;3():7-7.</p><p>Published online 8 Jun 2007</p><p>PMCID:PMC1914063.</p><p></p>erent at p = 0.001. Non-parametric comparison of mean values (Mann-Whitney U test) confirmed the presence of statistically significant differences at p = 0.000001. Transformation to expression values revealed that the slightly different PCR efficiencies could lead to a mean difference of maximal 0.3, when the fold change was expressed as log. Individual primer pairs can thus exhibit slight differences for their target genes in different cultivars. However, this does not significantly affect the overall applicability of the primer platform for expression profiling experiments (Caldana ., manuscript in preparation)

A quantitative RT-PCR platform for high-throughput expression profiling of 2500 rice transcription factors-2

<p><b>Copyright information:</b></p><p>Taken from "A quantitative RT-PCR platform for high-throughput expression profiling of 2500 rice transcription factors"</p><p>http://www.plantmethods.com/content/3/1/7</p><p>Plant Methods 2007;3():7-7.</p><p>Published online 8 Jun 2007</p><p>PMCID:PMC1914063.</p><p></p> ng) and used as template to test transcript abundance of three selected genes (Os03g55610, Os08g38220, and Os12g38200) via qRT-PCR. A linear relationship between root (or shoot) cDNA and expression level of the various genes was observed. Symbols in both panels represent the mean ± SD (= 3)

Extensive Modulation of the Transcription Factor Transcriptome during Somatic Embryogenesis in <i>Arabidopsis thaliana</i>

<div><p>Molecular mechanisms controlling plant totipotency are largely unknown and studies on somatic embryogenesis (SE), the process through which already differentiated cells reverse their developmental program and become embryogenic, provide a unique means for deciphering molecular mechanisms controlling developmental plasticity of somatic cells. Among various factors essential for embryogenic transition of somatic cells transcription factors (TFs), crucial regulators of genetic programs, are believed to play a central role. Herein, we used quantitative real-time polymerase chain reaction (qRT-PCR) to identify TF genes affected during SE induced by <i>in vitro</i> culture in <i>Arabidopsis thaliana.</i> Expression profiles of 1,880 TFs were evaluated in the highly embryogenic Col-0 accession and the non-embryogenic <i>tanmei/emb2757</i> mutant. Our study revealed 729 TFs whose expression changes during the 10-days incubation period of SE; 141 TFs displayed distinct differences in expression patterns in embryogenic versus non-embryogenic cultures. The embryo-induction stage of SE occurring during the first 5 days of culture was associated with a robust and dramatic change of the TF transcriptome characterized by the drastic up-regulation of the expression of a great majority (over 80%) of the TFs active during embryogenic culture. In contrast to SE induction, the advanced stage of embryo formation showed attenuation and stabilization of transcript levels of many TFs. In total, 519 of the SE-modulated TFs were functionally annotated and transcripts related with plant development, phytohormones and stress responses were found to be most abundant. The involvement of selected TFs in SE was verified using T-DNA insertion lines and a significantly reduced embryogenic response was found for the majority of them. This study provides comprehensive data focused on the expression of TF genes during SE and suggests directions for further research on functional genomics of SE.</p></div

Number of TF genes whose expression changes during somatic embryo formation.

<p>x, fold change.</p