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Natural genetic diversity provides a powerful tool to study the complex interrelationship between metabolism and growth. Profiling of metabolic traits combined with network-based and statistical analyses allow the comparison of conditions and identification of sets of traits that predict biomass. However, it often remains unclear why a particular set of metabolites is linked with biomass and to what extent the predictive model is applicable beyond a particular growth condition. A panel of 97 genetically diverse Arabidopsis (Arabidopsis thaliana) accessions was grown in near-optimal carbon and nitrogen supply, restricted carbon supply, and restricted nitrogen supply and analyzed for biomass and 54 metabolic traits. Correlation-based metabolic networks were generated from the genotype-dependent variation in each condition to reveal sets of metabolites that show coordinated changes across accessions. The networks were largely specific for a single growth condition. Partial least squares regression from metabolic traits allowed prediction of biomass within and, slightly more weakly, across conditions (cross-validated Pearson correlations in the range of 0.27-0.58 and 0.21-0.51 and P values in the range of <0.001-<0.13 and <0.001-<0.023, respectively). Metabolic traits that correlate with growth or have a high weighting in the partial least squares regression were mainly condition specific and often related to the resource that restricts growth under that condition. Linear mixed-model analysis using the combined metabolic traits from all growth conditions as an input indicated that inclusion of random effects for the conditions improves predictions of biomass. Thus, robust prediction of biomass across a range of conditions requires condition-specific measurement of metabolic traits to take account of environment-dependent changes of the underlying networks.
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.
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.
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.