Ralf Steuer

Estimating mutual information using B-spline functions – an improved similarity measure for analysing gene expression data

BackgroundThe 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.ResultsIn 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 kloska@scienion.de upon request.ConclusionThe 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.

Structural kinetic modeling of metabolic networks

To develop and investigate detailed mathematical models of metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, kinetic modeling is still often severely hampered by inadequate knowledge of the enzyme–kinetic rate laws and their associated parameter values. Here we propose a method that aims to give a quantitative account of the dynamical capabilities of a metabolic system, without requiring any explicit information about the functional form of the rate equations. Our approach is based on constructing a local linear model at each point in parameter space, such that each element of the model is either directly experimentally accessible or amenable to a straightforward biochemical interpretation. This ensemble of local linear models, encompassing all possible explicit kinetic models, then allows for a statistical exploration of the comprehensive parameter space. The method is exemplified on two paradigmatic metabolic systems: the glycolytic pathway of yeast and a realistic-scale representation of the photosynthetic Calvin cycle.

The Metabolic Network of Synechocystis sp. PCC 6803: Systemic Properties of Autotrophic Growth

Unicellular cyanobacteria have attracted growing attention as potential host organisms for the production of valuable organic products and provide an ideal model to understand oxygenic photosynthesis and phototrophic metabolism. To obtain insight into the functional properties of phototrophic growth, we present a detailed reconstruction of the primary metabolic network of the autotrophic prokaryote Synechocystis sp. PCC 6803. The reconstruction is based on multiple data sources and extensive manual curation and significantly extends currently available repositories of cyanobacterial metabolism. A systematic functional analysis, utilizing the framework of flux-balance analysis, allows the prediction of essential metabolic pathways and reactions and allows the identification of inconsistencies in the current annotation. As a counterintuitive result, our computational model indicates that photorespiration is beneficial to achieve optimal growth rates. The reconstruction process highlights several obstacles currently encountered in the context of large-scale reconstructions of metabolic networks.

Flux balance analysis of cyanobacterial metabolism: the metabolic network of Synechocystis sp. PCC 6803.

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.

The diversity of cyanobacterial metabolism: genome analysis of multiple phototrophic microorganisms

BackgroundCyanobacteria are among the most abundant organisms on Earth and represent one of the oldest and most widespread clades known in modern phylogenetics. As the only known prokaryotes capable of oxygenic photosynthesis, cyanobacteria are considered to be a promising resource for renewable fuels and natural products. Our efforts to harness the suns energy using cyanobacteria would greatly benefit from an increased understanding of the genomic diversity across multiple cyanobacterial strains. In this respect, the advent of novel sequencing techniques and the availability of several cyanobacterial genomes offers new opportunities for understanding microbial diversity and metabolic organization and evolution in diverse environments.ResultsHere, we report a whole genome comparison of multiple phototrophic cyanobacteria. We describe genetic diversity found within cyanobacterial genomes, specifically with respect to metabolic functionality. Our results are based on pair-wise comparison of protein sequences and concomitant construction of clusters of likely ortholog genes. We differentiate between core, shared and unique genes and show that the majority of genes are associated with a single genome. In contrast, genes with metabolic function are strongly overrepresented within the core genome that is common to all considered strains. The analysis of metabolic diversity within core carbon metabolism reveals parts of the metabolic networks that are highly conserved, as well as highly fragmented pathways.ConclusionsOur results have direct implications for resource allocation and further sequencing projects. It can be extrapolated that the number of newly identified genes still significantly increases with increasing number of new sequenced genomes. Furthermore, genome analysis of multiple phototrophic strains allows us to obtain a detailed picture of metabolic diversity that can serve as a starting point for biotechnological applications and automated metabolic reconstructions.

The stability and robustness of metabolic states: identifying stabilizing sites in metabolic networks

The dynamic behavior of metabolic networks is governed by numerous regulatory mechanisms, such as reversible phosphorylation, binding of allosteric effectors or temporal gene expression, by which the activity of the participating enzymes can be adjusted to the functional requirements of the cell. For most of the cellular enzymes, such regulatory mechanisms are at best qualitatively known, whereas detailed enzyme‐kinetic models are lacking. To explore the possible dynamic behavior of metabolic networks in cases of lacking or incomplete enzyme‐kinetic information, we present a computational approach based on structural kinetic modeling. We derive statistical measures for the relative impact of enzyme‐kinetic parameters on dynamic properties (such as local stability) and apply our approach to the metabolism of human erythrocytes. Our findings show that allosteric enzyme regulation significantly enhances the stability of the network and extends its potential dynamic behavior. Moreover, our approach allows to differentiate quantitatively between metabolic states related to senescence and metabolic collapse of the human erythrocyte. We think that the proposed method represents an important intermediate step on the long way from topological network analysis to detailed kinetic modeling of complex metabolic networks.

From structure to dynamics of metabolic pathways

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.

PARTITION-BASED ENTROPIES OF DETERMINISTIC AND STOCHASTIC MAPS

In this paper we explore the relationship between the Kolmogorov–Sinai entropy, the sum of positive Lyapunov exponents, denoted here as the Pesin entropy and a new measure, the T-entropy, for nonlinear maps. We demonstrate that threshold-crossing partitions are effective in deriving representative symbolic realisations for the real-valued time series. We describe the recently developed entropy measure for finite strings and compare with values derived from the application of Shannons theory. These techniques are further applied to a simple stochastic system, appearing to further confirm recent theoretical results on Lyapunov exponents.

A gentle guide to the analysis of metabolomic data

Modern molecular biology crucially relies on computational tools to handle and interpret the large amounts of data that are generated by high-throughput measurements. To this end, much effort is dedicated to devise novel sophisticated methods that allow one to integrate, evaluate, and analyze biological data. However, prior to an application of specifically designed methods, simple and well-known statistical approaches often provide a more appropriate starting point for further analysis. This chapter seeks to describe several well-established approaches to data analysis, including various clustering techniques, discriminant function analysis, principal component analysis, multidimensional scaling, and classification trees. The chapter is accompanied by a webpage, describing the application of all algorithms in a ready-to-use format.

Robust Signal Processing in Living Cells

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.