Oliver Ebenhöh

Expanding metabolic networks: scopes of compounds, robustness, and evolution

A new method for the mathematical analysis of large metabolic networks is presented. Based on the fact that the occurrence of a metabolic reaction generally requires the existence of other reactions providing its substrates, series of metabolic networks are constructed. In each step of the corresponding expansion process those reactions are incorporated whose substrates are made available by the networks of the previous generations. The method is applied to the set of all metabolic reactions included in the KEGG database. Starting with one or more seed compounds, the expansion results in a final network whose compounds define the scope of the seed. Scopes of all metabolic compounds are calculated and it is shown that large parts of cellular metabolism can be considered as the combined scope of simple building blocks. Analyses of various expansion processes reveal crucial metabolites whose incorporation allows for the increase in network complexity. Among these metabolites are common cofactors such as NAD+, ATP, and coenzyme A. We demonstrate that the outcome of network expansion is in general very robust against elimination of single or few reactions. There exist, however, crucial reactions whose elimination results in a dramatic reduction of scope sizes. It is hypothesized that the expansion process displays characteristics of the evolution of metabolism such as the temporal order of the emergence of metabolic pathways.

Metabolomics- and proteomics-assisted genome annotation and analysis of the draft metabolic network of Chlamydomonas reinhardtii

We present an integrated analysis of the molecular repertoire of Chlamydomonas reinhardtii under reference conditions. Bioinformatics annotation methods combined with GCxGC/MS-based metabolomics and LC/MS-based shotgun proteomics profiling technologies have been applied to characterize abundant proteins and metabolites, resulting in the detection of 1069 proteins and 159 metabolites. Of the measured proteins, 204 currently do not have EST sequence support; thus a significant portion of the proteomics-detected proteins provide evidence for the validity of in silico gene models. Furthermore, the generated peptide data lend support to the validity of a number of proteins currently in the proposed model stage. By integrating genomic annotation information with experimentally identified metabolites and proteins, we constructed a draft metabolic network for Chlamydomonas. Computational metabolic modeling allowed an identification of missing enzymatic links. Some experimentally detected metabolites are not producible by the currently known and annotated enzyme set, thus suggesting entry points for further targeted gene discovery or biochemical pathway research. All data sets are made available as supplementary material as well as web-accessible databases and within the functional context via the Chlamydomonas-adapted MapMan annotation platform. Information of identified peptides is also available directly via the JGI-Chlamydomonas genomic resource database (http://genome.jgi-psf.org/Chlre3/Chlre3.home.html).

An integrative approach towards completing genome-scale metabolic networks

Genome-scale metabolic networks which have been automatically derived through sequence comparison techniques are necessarily incomplete. We propose a strategy that incorporates genomic sequence data and metabolite profiles into modeling approaches to arrive at improved gene annotations and more complete genome-scale metabolic networks. The core of our strategy is an algorithm that computes minimal sets of reactions by which a draft network has to be extended in order to be consistent with experimental observations. A particular strength of our approach is that alternative possibilities are suggested and thus experimentally testable hypotheses are produced. We carefully evaluate our strategy on the well-studied metabolic network of Escherichia coli, demonstrating how the predictions can be improved by incorporating sequence data. Subsequently, we apply our method to the recently sequenced green alga Chlamydomonas reinhardtii. We suggest specific genes in the genome of Chlamydomonas which are the strongest candidates for coding the responsible enzymes.

Stoichiometric design of metabolic networks: Multifunctionality, clusters, optimization, weak and strong robustness

Starting from a limited set of reactions describing changes in the carbon skeleton of biochemical compounds complete sets of metabolic networks are constructed. The networks are characterized by the number and types of participating reactions. Elementary networks are defined by the condition that a specific chemical conversion can be performed by a set of given reactions and that this ability will be lost by elimination of any of these reactions. Groups of networks are identified with respect to their ability to perform a certain number of metabolic conversions in an elementary way which are called the network’s functions. The number of the network functions defines the degree of multifunctionality. Transitions between networks and mutations of networks are defined by exchanges of single reactions. Different mutations exist such as gain or loss of function mutations and neutral mutations. Based on these mutations neighbourhood relations between networks are established which are described in a graph theoretical way. Basic properties of these graphs are determined such as diameter, connectedness, distance distribution of pairs of vertices. A concept is developed to quantify the robustness of networks against changes in their stoichiometry where we distinguish between strong and weak robustness. Evolutionary algorithms are applied to study the development of network populations under constant and time dependent environmental conditions. It is shown that the populations evolve toward clusters of networks performing a common function and which are closely neighboured. Under changing environmental conditions multifunctional networks prove to be optimal and will be selected.

Mathematical modelling of the diurnal regulation of the MEP pathway in Arabidopsis

Isoprenoid molecules are essential elements of plant metabolism. Many important plant isoprenoids, such as chlorophylls, carotenoids, tocopherols, prenylated quinones and hormones are synthesised in chloroplasts via the 2-C-methyl-d-erythritol 4-phosphate (MEP) pathway. Here we develop a mathematical model of diurnal regulation of the MEP pathway in Arabidopsis thaliana. We used both experimental and theoretical approaches to integrate mechanisms potentially involved in the diurnal control of the pathway. Our data show that flux through the MEP pathway is accelerated in light due to the photosynthesis-dependent supply of metabolic substrates of the pathway and the transcriptional regulation of key biosynthetic genes by the circadian clock. We also demonstrate that feedback regulation of both the activity and the abundance of the first enzyme of the MEP pathway (1-deoxy-D-xylulose 5-phosphate synthase, DXS) by pathway products stabilizes the flux against changes in substrate supply and adjusts the flux according to product demand under normal growth conditions. These data illustrate the central relevance of photosynthesis, the circadian clock and feedback control of DXS for the diurnal regulation of the MEP pathway.

Taxonomic database and cut-off value for processing mcrA gene 454 pyrosequencing data by MOTHUR.

The functional mcrA gene of methanogens can generate phylogeny as congruent as the 16S rRNA gene phylogeny. For the mcrA sequences amplified by mlas/mcrA-rev primers, we created a database for taxonomical classification and propose cut-off values for OTU clustering and further analysis of α- and β-diversity with the MOTHUR software.

Carbohydrate‐active enzymes exemplify entropic principles in metabolism

Glycans comprise ubiquitous and essential biopolymers, which usually occur as highly diverse mixtures. The myriad different structures are generated by a limited number of carbohydrate‐active enzymes (CAZymes), which are unusual in that they catalyze multiple reactions by being relatively unspecific with respect to substrate size. Existing experimental and theoretical descriptions of CAZyme‐mediated reaction systems neither comprehensively explain observed action patterns nor suggest biological functions of polydisperse pools in metabolism. Here, we overcome these limitations with a novel theoretical description of this important class of biological systems in which the mixing entropy of polydisperse pools emerges as an important system variable. In vitro assays of three CAZymes essential for central carbon metabolism confirm the power of our approach to predict equilibrium distributions and non‐equilibrium dynamics. A computational study of the turnover of the soluble heteroglycan pool exemplifies how entropy‐driven reactions establish a metabolic buffer in vivo that attenuates fluctuations in carbohydrate availability. We argue that this interplay between energy‐ and entropy‐driven processes represents an important regulatory design principle of metabolic systems.

A minimal mathematical model of nonphotochemical quenching of chlorophyll fluorescence

Under natural conditions, plants are exposed to rapidly changing light intensities. To acclimate to such fluctuations, plants have evolved adaptive mechanisms that optimally exploit available light energy and simultaneously minimise damage of the photosynthetic apparatus through excess light. An important mechanism is the dissipation of excess excitation energy as heat which can be measured as nonphotochemical quenching of chlorophyll fluorescence (NPQ). In this paper, we present a highly simplified mathematical model that captures essential experimentally observed features of the short term adaptive quenching dynamics. We investigate the stationary and dynamic behaviour of the model and systematically analyse the dependence of characteristic system properties on key parameters such as rate constants and pool sizes. Comparing simulations with experimental data allows to derive conclusions about the validity of the simplifying assumptions and we further propose hypotheses regarding the role of the xanthophyll cycle in NPQ. We envisage that the presented theoretical description of the light reactions in conjunction with short term adaptive processes serves as a basis for the development of more detailed mechanistic models by which the molecular mechanisms of NPQ can be theoretically studied.

MetaPath Online: a web server implementation of the network expansion algorithm

We designed a web server for the analysis of biosynthetic capacities of metabolic networks. The implementation is based on the network expansion algorithm and the concept of scopes. For a given network and predefined external resources, called the seed metabolites, the scope is defined as the set of products which the network is in principle able to produce. Through the web interface the user can select a variety of metabolic networks or provide his or her own list of reactions. The information on the organism-specific networks has been extracted from the KEGG database. By choosing an arbitrary set of seed compounds, the user can obtain the corresponding scopes. With our web server application we provide an easy to use interface to perform a variety of structural and functional network analyses. Problems that can be addressed using the web server include the calculation of synthesizing capacities, the visualization of synthesis pathways, functional analysis of mutant networks or comparative analysis of related species. The web server is accessible through http://scopes.biologie.hu-berlin.de.

Short-term acclimation of the photosynthetic electron transfer chain to changing light: a mathematical model.

Photosynthetic eukaryotes house two photosystems with distinct light absorption spectra. Natural fluctuations in light quality and quantity can lead to unbalanced or excess excitation, compromising photosynthetic efficiency and causing photodamage. Consequently, these organisms have acquired several distinct adaptive mechanisms, collectively referred to as non-photochemical quenching (NPQ) of chlorophyll fluorescence, which modulates the organization and function of the photosynthetic apparatus. The ability to monitor NPQ processes fluorometrically has led to substantial progress in elucidating the underlying molecular mechanisms. However, the relative contribution of distinct NPQ mechanisms to variable light conditions in different photosynthetic eukaryotes remains unclear. Here, we present a mathematical model of the dynamic regulation of eukaryotic photosynthesis using ordinary differential equations. We demonstrate that, for Chlamydomonas, our model recapitulates the basic fluorescence features of short-term light acclimation known as state transitions and discuss how the model can be iteratively refined by comparison with physiological experiments to further our understanding of light acclimation in different species.