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Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications.
Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study.
Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.
Large-scale co-expression approach to dissect secondary cell wall formation across plant species
(2011)
Plant cell walls are complex composites largely consisting of carbohydrate-based polymers, and are generally divided into primary and secondary walls based on content and characteristics. Cellulose microfibrils constitute a major component of both primary and secondary cell walls and are synthesized at the plasma membrane by cellulose synthase (CESA) complexes. Several studies in Arabidopsis have demonstrated the power of co-expression analyses to identify new genes associated with secondary wall cellulose biosynthesis. However, across-species comparative co-expression analyses remain largely unexplored. Here, we compared co-expressed gene vicinity networks of primary and secondary wall CESAsin Arabidopsis, barley, rice, poplar, soybean, Medicago, and wheat, and identified gene families that are consistently co-regulated with cellulose biosynthesis. In addition to the expected polysaccharide acting enzymes, we also found many gene families associated with cytoskeleton, signaling, transcriptional regulation, oxidation, and protein degradation. Based on these analyses, we selected and biochemically analyzed T-DNA insertion lines corresponding to approximately twenty genes from gene families that re-occur in the co-expressed gene vicinity networks of secondary wall CESAs across the seven species. We developed a statistical pipeline using principal component analysis and optimal clustering based on silhouette width to analyze sugar profiles. One of the mutants, corresponding to a pinoresinol reductase gene, displayed disturbed xylem morphology and held lower levels of lignin molecules. We propose that this type of large-scale co-expression approach, coupled with statistical analysis of the cell wall contents, will be useful to facilitate rapid knowledge transfer across plant species.
Dynamic regulatory on/off minimization for biological systems under internal temporal perturbations
(2012)
Background: Flux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.
Results: Here, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.
Conclusions: Our methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.
Dynamic regulatory on/off minimization for biological systems under internal temporal perturbations
(2012)
Background: Flux balance analysis (FBA) together with its extension, dynamic FBA, have proven instrumental for analyzing the robustness and dynamics of metabolic networks by employing only the stoichiometry of the included reactions coupled with adequately chosen objective function. In addition, under the assumption of minimization of metabolic adjustment, dynamic FBA has recently been employed to analyze the transition between metabolic states.
Results: Here, we propose a suite of novel methods for analyzing the dynamics of (internally perturbed) metabolic networks and for quantifying their robustness with limited knowledge of kinetic parameters. Following the biochemically meaningful premise that metabolite concentrations exhibit smooth temporal changes, the proposed methods rely on minimizing the significant fluctuations of metabolic profiles to predict the time-resolved metabolic state, characterized by both fluxes and concentrations. By conducting a comparative analysis with a kinetic model of the Calvin-Benson cycle and a model of plant carbohydrate metabolism, we demonstrate that the principle of regulatory on/off minimization coupled with dynamic FBA can accurately predict the changes in metabolic states.
Conclusions: Our methods outperform the existing dynamic FBA-based modeling alternatives, and could help in revealing the mechanisms for maintaining robustness of dynamic processes in metabolic networks over time.
The unicellular green alga Chlamydomonas reinhardtii is a long-established model organism for studies on photosynthesis and carbon metabolism-related physiology. Under conditions of air-level carbon dioxide concentration [CO2], a carbon concentrating mechanism (CCM) is induced to facilitate cellular carbon uptake. CCM increases the availability of carbon dioxide at the site of cellular carbon fixation. To improve our understanding of the transcriptional control of the CCM, we employed FAIRE-seq (formaldehyde-assisted Isolation of Regulatory Elements, followed by deep sequencing) to determine nucleosome-depleted chromatin regions of algal cells subjected to carbon deprivation. Our FAIRE data recapitulated the positions of known regulatory elements in the promoter of the periplasmic carbonic anhydrase (Cah1) gene, which is upregulated during CCM induction, and revealed new candidate regulatory elements at a genome-wide scale. In addition, time series expression patterns of 130 transcription factor (TF) and transcription regulator (TR) genes were obtained for cells cultured under photoautotrophic condition and subjected to a shift from high to low [CO2]. Groups of co-expressed genes were identified and a putative directed gene-regulatory network underlying the CCM was reconstructed from the gene expression data using the recently developed IOTA (inner composition alignment) method. Among the candidate regulatory genes, two members of the MYB-related TF family, Lcr1 (Low-CO2 response regulator 1) and Lcr2 (Low-CO2 response regulator 2), may play an important role in down-regulating the expression of a particular set of TF and TR genes in response to low [CO2]. The results obtained provide new insights into the transcriptional control of the CCM and revealed more than 60 new candidate regulatory genes. Deep sequencing of nucleosome-depleted genomic regions indicated the presence of new, previously unknown regulatory elements in the C. reinhardtii genome. Our work can serve as a basis for future functional studies of transcriptional regulator genes and genomic regulatory elements in Chlamydomonas.
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 k 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.
Time-series data from multicomponent systems capture the dynamics of the ongoing processes and reflect the interactions between the components. The progression of processes in such systems usually involves check-points and events at which the relationships between the components are altered in response to stimuli. Detecting these events together with the implicated components can help understand the temporal aspects of complex biological systems. Here we propose a regularized regression-based approach for identifying breakpoints and corresponding segments from multivariate time-series data. In combination with techniques from clustering, the approach also allows estimating the significance of the determined breakpoints as well as the key components implicated in the emergence of the breakpoints. Comparative analysis with the existing alternatives demonstrates the power of the approach to identify biologically meaningful breakpoints in diverse time-resolved transcriptomics data sets from the yeast Saccharomyces cerevisiae and the diatom Thalassiosira pseudonana.
Background: Inferring regulatory interactions between genes from transcriptomics time-resolved data, yielding reverse engineered gene regulatory networks, is of paramount importance to systems biology and bioinformatics studies. Accurate methods to address this problem can ultimately provide a deeper insight into the complexity, behavior, and functions of the underlying biological systems. However, the large number of interacting genes coupled with short and often noisy time-resolved read-outs of the system renders the reverse engineering a challenging task. Therefore, the development and assessment of methods which are computationally efficient, robust against noise, applicable to short time series data, and preferably capable of reconstructing the directionality of the regulatory interactions remains a pressing research problem with valuable applications.
Results: Here we perform the largest systematic analysis of a set of similarity measures and scoring schemes within the scope of the relevance network approach which are commonly used for gene regulatory network reconstruction from time series data. In addition, we define and analyze several novel measures and schemes which are particularly suitable for short transcriptomics time series. We also compare the considered 21 measures and 6 scoring schemes according to their ability to correctly reconstruct such networks from short time series data by calculating summary statistics based on the corresponding specificity and sensitivity. Our results demonstrate that rank and symbol based measures have the highest performance in inferring regulatory interactions. In addition, the proposed scoring scheme by asymmetric weighting has shown to be valuable in reducing the number of false positive interactions. On the other hand, Granger causality as well as information-theoretic measures, frequently used in inference of regulatory networks, show low performance on the short time series analyzed in this study.
Conclusions: Our study is intended to serve as a guide for choosing a particular combination of similarity measures and scoring schemes suitable for reconstruction of gene regulatory networks from short time series data. We show that further improvement of algorithms for reverse engineering can be obtained if one considers measures that are rooted in the study of symbolic dynamics or ranks, in contrast to the application of common similarity measures which do not consider the temporal character of the employed data. Moreover, we establish that the asymmetric weighting scoring scheme together with symbol based measures (for low noise level) and rank based measures (for high noise level) are the most suitable choices.
Maize (Zea mays L.) is a staple food whose production relies on seed stocks that largely comprise hybrid varieties. Therefore, knowledge about the molecular determinants of hybrid performance (HP) in the field can be used to devise better performing hybrids to address the demands for sustainable increase in yield. Here, we propose and test a classification-driven framework that uses metabolic profiles from in vitro grown young roots of parental lines from the Dent x Flint maize heterotic pattern to predict field HP. We identify parental analytes that best predict the metabolic inheritance patterns in 328 hybrids. We then demonstrate that these analytes are also predictive of field HP (0.64 >= r >= 0.79) and discriminate hybrids of good performance (accuracy of 87.50%). Therefore, our approach provides a cost-effective solution for hybrid selection programs.