The metabolism of phototrophic cyanobacteria is an integral part of global biogeochemical cycles, and the capability of cyanobacteria to assimilate atmospheric CO2 into organic carbon has manifold potential applications for a sustainable biotechnology. To elucidate the properties of cyanobacterial metabolism and growth, computational reconstructions of genome-scale metabolic networks play an increasingly important role. Here, we present an updated reconstruction of the metabolic network of the cyanobacterium Synechocystis sp. PCC 6803 and its quantitative evaluation using flux balance analysis (FBA). To overcome limitations of conventional FBA, and to allow for the integration of experimental analyses, we develop a novel approach to describe light absorption and light utilization within the framework of FBA. Our approach incorporates photoinhibition and a variable quantum yield into the constraint-based description of light-limited phototrophic growth. We show that the resulting model is capable of predicting quantitative properties of cyanobacterial growth, including photosynthetic oxygen evolution and the ATP/NADPH ratio required for growth and cellular maintenance. Our approach retains the computational and conceptual simplicity of FBA and is readily applicable to other phototrophic microorganisms.

Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models.

BACKGROUND: The transcriptomes of several cyanobacterial strains have been shown to exhibit diurnal oscillation patterns, reflecting the diurnal phototrophic lifestyle of the organisms. The analysis of such genome-wide transcriptional oscillations is often facilitated by the use of clustering algorithms in conjunction with a number of pre-processing steps. Biological interpretation is usually focussed on the time and phase of expression of the resulting groups of genes. However, the use of microarray technology in such studies requires the normalization of pre-processing data, with unclear impact on the qualitative and quantitative features of the derived information on the number of oscillating transcripts and their respective phases. RESULTS: A microarray based evaluation of diurnal expression in the cyanobacterium Synechocystis sp. PCC 6803 is presented. As expected, the temporal expression patterns reveal strong oscillations in transcript abundance. We compare the Fourier transformation-based expression phase before and after the application of quantile normalization, median polishing, cyclical LOESS, and least oscillating set (LOS) normalization. Whereas LOS normalization mostly preserves the phases of the raw data, the remaining methods introduce systematic biases. In particular, quantile-normalization is found to introduce a phase-shift of 180°, effectively changing night-expressed genes into day-expressed ones. Comparison of a large number of clustering results of differently normalized data shows that the normalization method determines the result. Subsequent steps, such as the choice of data transformation, similarity measure, and clustering algorithm, only play minor roles. We find that the standardization and the DTF transformation are favorable for the clustering of time series in contrast to the 12 m transformation. We use the cluster-wise functional enrichment of a clustering derived by LOS normalization, clustering using flowClust, and DFT transformation to derive the diurnal biological program of Synechocystis sp.. CONCLUSION: Application of quantile normalization, median polishing, and also cyclic LOESS normalization of the presented cyanobacterial dataset lead to increased numbers of oscillating genes and the systematic shift of the expression phase. The LOS normalization minimizes the observed detrimental effects. As previous analyses employed a variety of different normalization methods, a direct comparison of results must be treated with caution.

Cyanobacteria are versatile unicellular phototrophic microorganisms that are highly abundant in many environments. Owing to their capability to utilize solar energy and atmospheric carbon dioxide for growth, cyanobacteria are increasingly recognized as a prolific resource for the synthesis of valuable chemicals and various biofuels. To fully harness the metabolic capabilities of cyanobacteria necessitates an in-depth understanding of the metabolic interconversions taking place during phototrophic growth, as provided by genome-scale reconstructions of microbial organisms. Here we present an extended reconstruction and analysis of the metabolic network of the unicellular cyanobacterium Synechocystis sp. PCC 6803. Building upon several recent reconstructions of cyanobacterial metabolism, unclear reaction steps are experimentally validated and the functional consequences of unknown or dissenting pathway topologies are discussed. The updated model integrates novel results with respect to the cyanobacterial TCA cycle, an alleged glyoxylate shunt, and the role of photorespiration in cellular growth. Going beyond conventional flux-balance analysis, we extend the computational analysis to diurnal light/dark cycles of cyanobacterial metabolism.

Cellular signaling networks have evolved an astonishing ability to function reliably and with high fidelity in uncertain environments. A crucial prerequisite for the high precision exhibited by many signaling circuits is their ability to keep the concentrations of active signaling compounds within tightly defined bounds, despite strong stochastic fluctuations in copy numbers and other detrimental influences. Based on a simple mathematical formalism, we identify topological organizing principles that facilitate such robust control of intracellular concentrations in the face of multifarious perturbations. Our framework allows us to judge whether a multiple-input-multiple-output reaction network is robust against large perturbations of network parameters and enables the predictive design of perfectly robust synthetic network architectures. Utilizing the Escherichia coli chemotaxis pathway as a hallmark example, we provide experimental evidence that our framework indeed allows us to unravel the topological organization of robust signaling. We demonstrate that the specific organization of the pathway allows the system to maintain global concentration robustness of the diffusible response regulator CheY with respect to several dominant perturbations. Our framework provides a counterpoint to the hypothesis that cellular function relies on an extensive machinery to fine-tune or control intracellular parameters. Rather, we suggest that for a large class of perturbations, there exists an appropriate topology that renders the network output invariant to the respective perturbations.

We consider complex mathematical models that are characterized by a wide spectrum of time scales, the fastest of which are operative during the initial state only, leaving the slower ones to drive the system at later times. It is shown that very useful physical understanding can be acquired if the fast and slow dynamics are first separated and then analyzed. Existing algorithmic methodologies can be applied for this purpose. A demonstration of this approach is presented for a glycolysis model, the solution of which asymptotically evolves around a limit cycle.

MOTIVATION: Mitochondrial metabolism, dominated by the reactions of the tricarboxylic acid (TCA) cycle, is of vital importance for a wide range of metabolic processes. In particular for autotrophic tissue, such as plant leaves, the TCA cycle marks the point of divergence of anabolic pathways and plays an essential role in biosynthesis. However, despite extensive knowledge about its stoichiometric properties, the function and the dynamical capabilities of the TCA cycle remain largely unknown. METHODS AND RESULTS: Based on a recently proposed formalism, we investigate the dynamic and functional properties of the mitochondrial TCA cycle of plants. Starting with the structural properties, as described by the elementary flux modes of the system, we aim for the transition from structure to the dynamics of the TCA cycle. Using a parametric description of the system, encompassing all possible differential equations and parameter values, we detect and quantify regimes of different dynamic behavior. Optimizing the system with respect to dynamic stability, we demonstrate that maximal stability is associated with specific (relative) metabolite concentrations and flux values that are subsequently compared to the experimental literature. Our analysis also serves as a general example how to elucidate the transition from the structure to the dynamics of metabolic pathways.

A remarkable inherent feature of cellular metabolism is that the concentrations of a small but significant number of metabolites are strongly correlated when measurements of biological replicates are performed. This review seeks to summarize the recent efforts to elucidate the origin of these observed correlations and points out several aspects concerning their interpretation. It is argued that correlations between metabolites differ profoundly from their transcriptomic and proteomic counterparts, and a straightforward interpretation in terms of the underlying biochemical pathways will unavoidably fail. It is demonstrated that the comparative correlations analysis offers a way to exploit the observed correlations to obtain additional information about the physiological state of the system.

BACKGROUND: The biological interpretation of large-scale gene expression data is one of the paramount challenges in current bioinformatics. In particular, placing the results in the context of other available functional genomics data, such as existing bio-ontologies, has already provided substantial improvement for detecting and categorizing genes of interest. One common approach is to look for functional annotations that are significantly enriched within a group or cluster of genes, as compared to a reference group. RESULTS: In this work, we suggest the information-theoretic concept of mutual information to investigate the relationship between groups of genes, as given by data-driven clustering, and their respective functional categories. Drawing upon related approaches (Gibbons and Roth, Genome Research 12:1574-1581, 2002), we seek to quantify to what extent individual attributes are sufficient to characterize a given group or cluster of genes. CONCLUSION: We show that the mutual information provides a systematic framework to assess the relationship between groups or clusters of genes and their functional annotations in a quantitative way. Within this framework, the mutual information allows us to address and incorporate several important issues, such as the interdependence of functional annotations and combinatorial combinations of attributes. It thus supplements and extends the conventional search for overrepresented attributes within a group or cluster of genes. In particular taking combinations of attributes into account, the mutual information opens the way to uncover specific functional descriptions of a group of genes or clustering result. All datasets and functional annotations used in this study are publicly available. All scripts used in the analysis are provided as additional files.

BACKGROUND: The information theoretic concept of mutual information provides a general framework to evaluate dependencies between variables. In the context of the clustering of genes with similar patterns of expression it has been suggested as a general quantity of similarity to extend commonly used linear measures. Since mutual information is defined in terms of discrete variables, its application to continuous data requires the use of binning procedures, which can lead to significant numerical errors for datasets of small or moderate size. RESULTS: In this work, we propose a method for the numerical estimation of mutual information from continuous data. We investigate the characteristic properties arising from the application of our algorithm and show that our approach outperforms commonly used algorithms: The significance, as a measure of the power of distinction from random correlation, is significantly increased. This concept is subsequently illustrated on two large-scale gene expression datasets and the results are compared to those obtained using other similarity measures.A C++ source code of our algorithm is available for non-commercial use from [email protected] upon request. CONCLUSION: The utilisation of mutual information as similarity measure enables the detection of non-linear correlations in gene expression datasets. Frequently applied linear correlation measures, which are often used on an ad-hoc basis without further justification, are thereby extended.