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The study of non-coding RNA genes has received increased attention in recent years fuelled by accumulating evidence that larger portions of genomes than previously acknowledged are transcribed into RNA molecules of mostly unknown function, as well as the discovery of novel non-coding RNA types and functional RNA elements. Here, we demonstrate that specific properties of graphs that represent the predicted RNA secondary structure reflect functional information. We introduce a computational algorithm and an associated web-based tool (GraPPLE) for classifying non-coding RNA molecules as functional and, furthermore, into Rfam families based on their graph properties. Unlike sequence-similarity-based methods and covariance models, GraPPLE is demonstrated to be more robust with regard to increasing sequence divergence, and when combined with existing methods, leads to a significant improvement of prediction accuracy. Furthermore, graph properties identified as most informative are shown to provide an understanding as to what particular structural features render RNA molecules functional. Thus, GraPPLE may offer a valuable computational filtering tool to identify potentially interesting RNA molecules among large candidate datasets.
Background: Biological systems adapt to changing environments by reorganizing their cellula r and physiological program with metabolites representing one important response level. Different stresses lead to both conserved and specific responses on the metabolite level which should be reflected in the underl ying metabolic network. Methodology/Principal Findings: Starting from experimental data obtained by a GC-MS based high-throughput metabolic profiling technology we here develop an approach that: (1) extracts network representations from metabolic conditiondependent data by using pairwise correlations, (2) determines the sets of stable and condition-dependent correlations based on a combination of statistical significance and homogeneity tests, and (3) can identify metabolites related to the stress response, which goes beyond simple ob servation s about the changes of metabolic concentrations. The approach was tested with Escherichia colias a model organism observed under four different environmental stress conditions (cold stress, heat stress, oxidative stress, lactose diau xie) and control unperturbed conditions. By constructing the stable network component, which displays a scale free topology and small-world characteristics, we demonstrated that: (1) metabolite hubs in this reconstructed correlation networks are significantly enriched for those contained in biochemical networks such as EcoCyc, (2) particular components of the stable network are enriched for functionally related biochemical path ways, and (3) ind ependently of the response scale, based on their importance in the reorganization of the cor relation network a set of metabolites can be identified which represent hypothetical candidates for adjusting to a stress-specific response. Conclusions/Significance: Network-based tools allowed the identification of stress-dependent and general metabolic correlation networks. This correlation-network-ba sed approach does not rely on major changes in concentration to identify metabolites important for st ress adaptation, but rather on the changes in network properties with respect to metabolites. This should represent a useful complementary technique in addition to more classical approaches.
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.
Motivation: Network-centered studies in systems biology attempt to integrate the topological properties of biological networks with experimental data in order to make predictions and posit hypotheses. For any topology-based prediction, it is necessary to first assess the significance of the analyzed property in a biologically meaningful context. Therefore, devising network null models, carefully tailored to the topological and biochemical constraints imposed on the network, remains an important computational problem.
Results: We first review the shortcomings of the existing generic sampling scheme-switch randomization-and explain its unsuitability for application to metabolic networks. We then devise a novel polynomial-time algorithm for randomizing metabolic networks under the (bio)chemical constraint of mass balance. The tractability of our method follows from the concept of mass equivalence classes, defined on the representation of compounds in the vector space over chemical elements. We finally demonstrate the uniformity of the proposed method on seven genome-scale metabolic networks, and empirically validate the theoretical findings. The proposed method allows a biologically meaningful estimation of significance for metabolic network properties.
Spatiotemporal dynamics of the Calvin cycle multistationarity and symmetry breaking instabilities
(2011)
The possibility of controlling the Calvin cycle has paramount implications for increasing the production of biomass. Multistationarity, as a dynamical feature of systems, is the first obvious candidate whose control could find biotechnological applications. Here we set out to resolve the debate on the multistationarity of the Calvin cycle. Unlike the existing simulation-based studies, our approach is based on a sound mathematical framework, chemical reaction network theory and algebraic geometry, which results in provable results for the investigated model of the Calvin cycle in which we embed a hierarchy of realistic kinetic laws. Our theoretical findings demonstrate that there is a possibility for multistationarity resulting from two sources, homogeneous and inhomogeneous instabilities, which partially settle the debate on multistability of the Calvin cycle. In addition, our tractable analytical treatment of the bifurcation parameters can be employed in the design of validation experiments.
Integration of high-throughput data with functional annotation by graph-theoretic methods has been postulated as promising way to unravel the function of unannotated genes. Here, we first review the existing graph-theoretic approaches for automated gene function annotation and classify them into two categories with respect to their relation to two instances of transductive learning on networks - with dynamic costs and with constant costs - depending on whether or not ontological relationship between functional terms is employed. The determined categories allow to characterize the computational complexity of the existing approaches and establish the relation to classical graph-theoretic problems, such as bisection and multiway cut. In addition, our results point out that the ontological form of the structured functional knowledge does not lower the complexity of the transductive learning with dynamic costs - one of the key problems in modern systems biology. The NP-hardness of automated gene annotation renders the development of heuristic or approximation algorithms a priority for additional research.
Analysis of biological networks requires assessing the statistical significance of network-based predictions by using a realistic null model. However, the existing network null model, switch randomization, is unsuitable for metabolic networks, as it does not include physical constraints and generates unrealistic reactions. We present JMassBalance, a tool for mass-balanced randomization and analysis of metabolic networks. The tool allows efficient generation of large sets of randomized networks under the physical constraint of mass balance. In addition, various structural properties of the original and randomized networks can be calculated, facilitating the identification of the salient properties of metabolic networks with a biologically meaningful null model.
Identifying causal links (couplings) is a fundamental problem that facilitates the understanding of emerging structures in complex networks. We propose and analyze inner composition alignment-a novel, permutation-based asymmetric association measure to detect regulatory links from very short time series, currently applied to gene expression. The measure can be used to infer the direction of couplings, detect indirect (superfluous) links, and account for autoregulation. Applications to the gene regulatory network of E. coli are presented.
Corn hybrids display lower metabolite variability and complex metabolite inheritance patterns
(2011)
We conducted a comparative analysis of the root metabolome of six parental maize inbred lines and their 14 corresponding hybrids showing fresh weight heterosis. We demonstrated that the metabolic profiles not only exhibit distinct features for each hybrid line compared with its parental lines, but also separate reciprocal hybrids. Reconstructed metabolic networks, based on robust correlations between metabolic profiles, display a higher network density in most hybrids as compared with the corresponding inbred lines. With respect to metabolite level inheritance, additive, dominant and overdominant patterns are observed with no specific overrepresentation. Despite the observed complexity of the inheritance pattern, for the majority of metabolites the variance observed in all 14 hybrids is lower compared with inbred lines. Deviations of metabolite levels from the average levels of the hybrids correlate negatively with biomass, which could be applied for developing predictors of hybrid performance based on characteristics of metabolite patterns.
Describing the determinants of robustness of biological systems has become one of the central questions in systems biology. Despite the increasing research efforts, it has proven difficult to arrive at a unifying definition for this important concept. We argue that this is due to the multifaceted nature of the concept of robustness and the possibility to formally capture it at different levels of systemic formalisms (e.g, topology and dynamic behavior). Here we provide a comprehensive review of the existing definitions of robustness pertaining to metabolic networks. As kinetic approaches have been excellently reviewed elsewhere, we focus on definitions of robustness proposed within graph-theoretic and constraint-based formalisms.
The Calvin-Benson cycle (CBC) provides the precursors for biomass synthesis necessary for plant growth. The dynamic behavior and yield of the CBC depend on the environmental conditions and regulation of the cellular state. Accurate quantitative models hold the promise of identifying the key determinants of the tightly regulated CBC function and their effects on the responses in future climates. We provide an integrative analysis of the largest compendium of existing models for photosynthetic processes. Based on the proposed ranking, our framework facilitates the discovery of best-performing models with regard to metabolomics data and of candidates for metabolic engineering.
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.
Background: There are alternative substrates to the mitochondrial respiration.
Results: Data-driven model-based analysis renders predictions of alternative substrates to the mitochondrial respiration.
Conclusion: Metabolomics data in conjunction with flux-based models can discriminate among hypotheses based on enzymology alone.
Significance: This analysis provides a basic framework for in silico studies of alternative pathways in metabolism.
Background: Reconstruction of genome-scale metabolic networks has resulted in models capable of reproducing experimentally observed biomass yield/growth rates and predicting the effect of alterations in metabolism for biotechnological applications. The existing studies rely on modifying the metabolic network of an investigated organism by removing or inserting reactions taken either from evolutionary similar organisms or from databases of biochemical reactions (e.g., KEGG). A potential disadvantage of these knowledge-driven approaches is that the result is biased towards known reactions, as such approaches do not account for the possibility of including novel enzymes, together with the reactions they catalyze.
Results: Here, we explore the alternative of increasing biomass yield in three model organisms, namely Bacillus subtilis, Escherichia coil, and Hordeum vulgare, by applying small, chemically feasible network modifications. We use the predicted and experimentally confirmed growth rates of the wild-type networks as reference values and determine the effect of inserting mass-balanced, thermodynamically feasible reactions on predictions of growth rate by using flux balance analysis.
Conclusions: While many replacements of existing reactions naturally lead to a decrease or complete loss of biomass production ability, in all three investigated organisms we find feasible modifications which facilitate a significant increase in this biological function. We focus on modifications with feasible chemical properties and a significant increase in biomass yield. The results demonstrate that small modifications are sufficient to substantially alter biomass yield in the three organisms. The method can be used to predict the effect of targeted modifications on the yield of any set of metabolites (e.g., ethanol), thus providing a computational framework for synthetic metabolic engineering.
Complex networks have been successfully employed to represent different levels of biological systems, ranging from gene regulation to protein-protein interactions and metabolism. Network-based research has mainly focused on identifying unifying structural properties, such as small average path length, large clustering coefficient, heavy-tail degree distribution and hierarchical organization, viewed as requirements for efficient and robust system architectures. However, for biological networks, it is unclear to what extent these properties reflect the evolutionary history of the represented systems. Here, we show that the salient structural properties of six metabolic networks from all kingdoms of life may be inherently related to the evolution and functional organization of metabolism by employing network randomization under mass balance constraints. Contrary to the results from the common Markov-chain switching algorithm, our findings suggest the evolutionary importance of the small-world hypothesis as a fundamental design principle of complex networks. The approach may help us to determine the biologically meaningful properties that result from evolutionary pressure imposed on metabolism, such as the global impact of local reaction knockouts. Moreover, the approach can be applied to test to what extent novel structural properties can be used to draw biologically meaningful hypothesis or predictions from structure alone.
Motivation: Metabolic engineering aims at modulating the capabilities of metabolic networks by changing the activity of biochemical reactions. The existing constraint-based approaches for metabolic engineering have proven useful, but are limited only to reactions catalogued in various pathway databases.
Results: We consider the alternative of designing synthetic strategies which can be used not only to characterize the maximum theoretically possible product yield but also to engineer networks with optimal conversion capability by using a suitable biochemically feasible reaction called 'stoichiometric capacitance'. In addition, we provide a theoretical solution for decomposing a given stoichiometric capacitance over a set of known enzymatic reactions. We determine the stoichiometric capacitance for genome-scale metabolic networks of 10 organisms from different kingdoms of life and examine its implications for the alterations in flux variability patterns. Our empirical findings suggest that the theoretical capacity of metabolic networks comes at a cost of dramatic system's changes.
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.