Computation of elementary modes: a unifying framework and the new binary approach

BACKGROUND: Metabolic pathway analysis has been recognized as a central approach to the structural analysis of metabolic networks. The concept of elementary (flux) modes provides a rigorous formalism to describe and assess pathways and has proven to be valuable for many applications. However, computing elementary modes is a hard computational task. In recent years we assisted in a multiplication of algorithms dedicated to it. We require a summarizing point of view and a continued improvement of the current methods. RESULTS: We show that computing the set of elementary modes is equivalent to computing the set of extreme rays of a convex cone. This standard mathematical representation provides a unified framework that encompasses the most prominent algorithmic methods that compute elementary modes and allows a clear comparison between them. Taking lessons from this benchmark, we here introduce a new method, the binary approach, which computes the elementary modes as binary patterns of participating reactions from which the respective stoichiometric coefficients can be computed in a post-processing step. We implemented the binary approach in FluxAnalyzer 5.1, a software that is free for academics. The binary approach decreases the memory demand up to 96% without loss of speed giving the most efficient method available for computing elementary modes to date. CONCLUSIONS: The equivalence between elementary modes and extreme ray computations offers opportunities for employing tools from polyhedral computation for metabolic pathway analysis. The new binary approach introduced herein was derived from this general theoretical framework and facilitates the computation of elementary modes in considerably larger networks

Computing knock out strategies in metabolic networks

Given a metabolic network in terms of its metabolites and reactions, our goal is to efficiently compute the minimal knock out sets of reactions required to block a given behaviour. We describe an algorithm which improves the computation of these knock out sets when the elementary modes (minimal functional subsystems) of the network are given. We also describe an algorithm which computes both the knock out sets and the elementary modes containing the blocked reactions directly from the description of the network and whose worst-case computational complexity is better than the algorithms currently in use for these problems. Computational results are included.Comment: 12 page

Metabolic network modeling of redox balancing and biohydrogen production in purple nonsulfur bacteria

<p>Abstract</p> <p>Background</p> <p>Purple nonsulfur bacteria (PNSB) are facultative photosynthetic bacteria and exhibit an extremely versatile metabolism. A central focus of research on PNSB dealt with the elucidation of mechanisms by which they manage to balance cellular redox under diverse conditions, in particular under photoheterotrophic growth.</p> <p>Results</p> <p>Given the complexity of the central metabolism of PNSB, metabolic modeling becomes crucial for an integrated analysis of the accumulated biological knowledge. We reconstructed a stoichiometric model capturing the central metabolism of three important representatives of PNSB (<it>Rhodospirillum rubrum, Rhodobacter sphaeroides </it>and <it>Rhodopseudomonas palustris)</it>. Using flux variability analysis, the model reveals key metabolic constraints related to redox homeostasis in these bacteria. With the help of the model we can (i) give quantitative explanations for non-intuitive, partially species-specific phenomena of photoheterotrophic growth of PNSB, (ii) reproduce various quantitative experimental data, and (iii) formulate several new hypotheses. For example, model analysis of photoheterotrophic growth reveals that - despite a large number of utilizable catabolic pathways - substrate-specific biomass and CO₂yields are fixed constraints, irrespective of the assumption of optimal growth. Furthermore, our model explains quantitatively why a CO₂fixing pathway such as the Calvin cycle is required by PNSB for many substrates (even if CO₂is released). We also analyze the role of other pathways potentially involved in redox metabolism and how they affect quantitatively the required capacity of the Calvin cycle. Our model also enables us to discriminate between different acetate assimilation pathways that were proposed recently for <it>R. sphaeroides </it>and <it>R. rubrum</it>, both lacking the isocitrate lyase. Finally, we demonstrate the value of the metabolic model also for potential biotechnological applications: we examine the theoretical capabilities of PNSB for photoheterotrophic hydrogen production and identify suitable genetic interventions to increase the hydrogen yield.</p> <p>Conclusions</p> <p>Taken together, the metabolic model (i) explains various redox-related phenomena of the versatile metabolism of PNSB, (ii) delivers new hypotheses on the operation and relevance of several metabolic pathways, and (iii) holds significant potential as a tool for rational metabolic engineering of PNSB in biotechnological applications.</p

Comparison and improvement of algorithms for computing minimal cut sets

BACKGROUND: Constrained minimal cut sets (cMCSs) have recently been introduced as a framework to enumerate minimal genetic intervention strategies for targeted optimization of metabolic networks. Two different algorithmic schemes (adapted Berge algorithm and binary integer programming) have been proposed to compute cMCSs from elementary modes. However, in their original formulation both algorithms are not fully comparable. RESULTS: Here we show that by a small extension to the integer program both methods become equivalent. Furthermore, based on well-known preprocessing procedures for integer programming we present efficient preprocessing steps which can be used for both algorithms. We then benchmark the numerical performance of the algorithms in several realistic medium-scale metabolic models. The benchmark calculations reveal (i) that these preprocessing steps can lead to an enormous speed-up under both algorithms, and (ii) that the adapted Berge algorithm outperforms the binary integer approach. CONCLUSIONS: Generally, both of our new implementations are by at least one order of magnitude faster than other currently available implementations

Augmenting Biogas Process Modeling by Resolving Intracellular Metabolic Activity

The process of anaerobic digestion in which waste biomass is transformed to methane by complex microbial communities has been modeled for more than 16 years by parametric gray box approaches that simplify process biology and do not resolve intracellular microbial activity. Information on such activity, however, has become available in unprecedented detail by recent experimental advances in metatranscriptomics and metaproteomics. The inclusion of such data could lead to more powerful process models of anaerobic digestion that more faithfully represent the activity of microbial communities. We augmented the Anaerobic Digestion Model No. 1 (ADM1) as the standard kinetic model of anaerobic digestion by coupling it to Flux-Balance-Analysis (FBA) models of methanogenic species. Steady-state results of coupled models are comparable to standard ADM1 simulations if the energy demand for non-growth associated maintenance (NGAM) is chosen adequately. When changing a constant feed of maize silage from continuous to pulsed feeding, the final average methane production remains very similar for both standard and coupled models, while both the initial response of the methanogenic population at the onset of pulsed feeding as well as its dynamics between pulses deviates considerably. In contrast to ADM1, the coupled models deliver predictions of up to 1,000s of intracellular metabolic fluxes per species, describing intracellular metabolic pathway activity in much higher detail. Furthermore, yield coefficients which need to be specified in ADM1 are no longer required as they are implicitly encoded in the topology of the species’ metabolic network. We show the feasibility of augmenting ADM1, an ordinary differential equation-based model for simulating biogas production, by FBA models implementing individual steps of anaerobic digestion. While cellular maintenance is introduced as a new parameter, the total number of parameters is reduced as yield coefficients no longer need to be specified. The coupled models provide detailed predictions on intracellular activity of microbial species which are compatible with experimental data on enzyme synthesis activity or abundance as obtained by metatranscriptomics or metaproteomics. By providing predictions of intracellular fluxes of individual community members, the presented approach advances the simulation of microbial community driven processes and provides a direct link to validation by state-of-the-art experimental techniques

Minimal cut sets in a metabolic network are elementary modes in a dual network

Motivation: Elementary modes (EMs) and minimal cut sets (MCSs) provide important techniques for metabolic network modeling. Whereas EMs describe minimal subnetworks that can function in steady state, MCSs are sets of reactions whose removal will disable certain network functions. Effective algorithms were developed for EM computation while calculation of MCSs is typically addressed by indirect methods requiring the computation of EMs as initial step. Results: In this contribution, we provide a method that determines MCSs directly without calculating the EMs. We introduce a duality framework for metabolic networks where the enumeration of MCSs in the original network is reduced to identifying the EMs in a dual network. As a further extension, we propose a generalization of MCSs in metabolic networks by allowing the combination of inhomogeneous constraints on reaction rates. This framework provides a promising tool to open the concept of EMs and MCSs to a wider class of applications. Contact: [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Modeling the electron transport chain of purple non-sulfur bacteria

Purple non-sulfur bacteria (Rhodospirillaceae) have been extensively employed for studying principles of photosynthetic and respiratory electron transport phosphorylation and for investigating the regulation of gene expression in response to redox signals. Here, we use mathematical modeling to evaluate the steady-state behavior of the electron transport chain (ETC) in these bacteria under different environmental conditions. Elementary-modes analysis of a stoichiometric ETC model reveals nine operational modes. Most of them represent well-known functional states, however, two modes constitute reverse electron flow under respiratory conditions, which has been barely considered so far. We further present and analyze a kinetic model of the ETC in which rate laws of electron transfer steps are based on redox potential differences. Our model reproduces well-known phenomena of respiratory and photosynthetic operation of the ETC and also provides non-intuitive predictions. As one key result, model simulations demonstrate a stronger reduction of ubiquinone when switching from high-light to low-light conditions. This result is parameter insensitive and supports the hypothesis that the redox state of ubiquinone is a suitable signal for controlling photosynthetic gene expression

Logical network of genotoxic stress-induced NF-κB signal transduction predicts putative target structures for therapeutic intervention strategies

Genotoxic stress is induced by a broad range of DNA-damaging agents and could lead to a variety of human diseases including cancer. DNA damage is also therapeutically induced for cancer treatment with the aim to eliminate tumor cells. However, the effectiveness of radio- and chemotherapy is strongly hampered by tumor cell resistance. A major reason for radio- and chemotherapeutic resistances is the simultaneous activation of cell survival pathways resulting in the activation of the transcription factor nuclear factor-kappa B (NF-κB). Here, we present a Boolean network model of the NF-κB signal transduction induced by genotoxic stress in epithelial cells. For the representation and analysis of the model, we used the formalism of logical interaction hypergraphs. Model reconstruction was based on a careful meta-analysis of published data. By calculating minimal intervention sets, we identified p53-induced protein with a death domain (PIDD), receptor-interacting protein 1 (RIP1), and protein inhibitor of activated STAT y (PIASy) as putative therapeutic targets to abrogate NF-κB activation resulting in apoptosis. Targeting these structures therapeutically may potentiate the effectiveness of radio-and chemotherapy. Thus, the presented model allows a better understanding of the signal transduction in tumor cells and provides candidates as new therapeutic target structures

Visual setup of logical models of signaling and regulatory networks with ProMoT

BACKGROUND: The analysis of biochemical networks using a logical (Boolean) description is an important approach in Systems Biology. Recently, new methods have been proposed to analyze large signaling and regulatory networks using this formalism. Even though there is a large number of tools to set up models describing biological networks using a biochemical (kinetic) formalism, however, they do not support logical models. RESULTS: Herein we present a flexible framework for setting up large logical models in a visual manner with the software tool ProMoT. An easily extendible library, ProMoT's inherent modularity and object-oriented concept as well as adaptive visualization techniques provide a versatile environment. Both the graphical and the textual description of the logical model can be exported to different formats. CONCLUSION: New features of ProMoT facilitate an efficient set-up of large Boolean models of biochemical interaction networks. The modeling environment is flexible; it can easily be adapted to specific requirements, and new extensions can be introduced. ProMoT is freely available from