Hierarchical decomposition of metabolic networks using k-modules

The optimal solutions obtained by flux balance analysis (FBA) are typically not unique. Flux modules have recently been shown to be a very useful tool to simplify and decompose the space of FBA-optimal solutions. Since yield-maximization is sometimes not the primary objective encountered in vivo, we are also interested in understanding the space of sub-optimal solutions. Unfortunately, the flux modules are too restrictive and not suited for this task. We present a generalization, called k-module, which compensates the limited applicability of flux modules to the space of sub-optimal solutions. Intuitively, a k-module is a sub-network with low connectivity to the rest of the network. Recursive application of k-modules yields a hierarchical decomposition of the metabolic network, which is also known as branch decomposition in matroid theory. In particular, decompositions computed by existing methods, like the null-space-based approach, introduced by Poolman et al. [(2007) J. Theor. Biol. 249, 691–705] can be interpreted as branch decompositions. With k-modules we can now compare alternative decompositions of metabolic networks to the classical sub-systems of glycolysis, tricarboxylic acid (TCA) cycle, etc. They can be used to speed up algorithmic problems [theoretically shown for elementary flux modes (EFM) enumeration] and have the potential to present computational solutions in a more intuitive way independently from the classical sub-systems

The steady-state assumption in oscillating and growing systems

The steady-state assumption, which states that the production and consumption of metabolites inside the cell are balanced, is one of the key aspects that makes an efficient analysis of genome-scale metabolic networks possible. It can be motivated from two different perspectives. In the time-scales perspective, we use the fact that metabolism is much faster than other cellular processes such as gene expression. Hence, the steady-state assumption is derived as a quasi-steady-state approximation of the metabolism that adapts to the changing cellular conditions. In this article we focus on the second perspective, stating that on the long run no metabolite can accumulate or deplete. In contrast to the first perspective it is not immediately clear how this perspective can be captured mathematically and what assumptions are required to obtain the steady-state condition. By presenting a mathematical framework based on the second perspective we demonstrate that the assumption of steady-state also applies to oscillating and growing systems without requiring quasi-steady-state at any time point. However, we also show that the average concentrations may not be compatible with the average fluxes. In summary, we establish a mathematical foundation for the steady-state assumption for long time periods that justifies its successful use in many applications. Furthermore, this mathematical foundation also pinpoints unintuitive effects in the integration of metabolite concentrations using nonlinear constraints into steady-state models for long time periods

A decomposition theory for vertex enumeration of convex polyhedra

In the last years the vertex enumeration problem of polyhedra has seen a revival in the study of metabolic networks, which increased the demand for efficient vertex enumeration algorit

Fast Flux Module Detection Using Matroid Theory

International audienceFlux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it has been found by Kelk et al. (2012) that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space. Using the mathematical definition of module introduced by Müller and Bockmayr (2013b), we discovered useful connections to matroid theory, through which efficient algorithms enable us to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that represents its function, in this article, we also present a method that uses this decomposition to visualize the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks

Hierarchical decomposition of metabolic networks using k-modules

The optimal solutions obtained by flux balance analysis (FBA) are typically not unique. Flux modules have recently been shown to be a very useful tool to simplify and decompose the space of FBA-optimal solutions. Since yield-maximization is sometimes not the primary objective encountered in vivo, we are also interested in understanding the space of sub-optimal solutions. Unfortunately, the flux modules are too restrictive and not suited for this task. We present a generalization, called k-module, which compensates the limited applicability of flux modules to the space of sub-optimal solutions. Intuitively, a k-module is a sub-network with low connectivity to the rest of the network. Recursive application of k-modules yields a hierarchical decomposition of the metabolic network, which is also known as branch decomposition in matroid theory. In particular, decompositions computed by existing methods, like the null-space-based approach, introduced by Poolman et al. [(2007) J. Theor. Biol. 249, 691–705] can be interpreted as branch decompositions. With k-modules we can now compare alternative decompositions of metabolic networks to the classical sub-systems of glycolysis, tricarboxylic acid (TCA) cycle, etc. They can be used to speed up algorithmic problems [theoretically shown for elementary flux modes (EFM) enumeration] and have the potential to present computational solutions in a more intuitive way independently from the classical sub-systems

Drug-Induced Exposure of Schistosoma mansoni Antigens SmCD59a and SmKK7

BACKGROUND: Schistosomiasis is a serious health problem especially in developing countries and affects more than 243 million people. Only few anthelmintic drugs are available up to now. A major obstacle for drug treatment is the different developmental stages and the varying host compartments during worm development. Anthelmintic drugs have been tested mainly on adult schistosomes or freshly transformed cercariae. Knowledge concerning the larval stages is lacking. METHODOLOGY/PRINCIPAL FINDINGS: In this study, we used in vitro-grown schistosomula (aged between 2 to 14 days) to investigate drug effects of the three anthelmintics praziquantel, artemether, and oxamniquine. Further, we analyzed the antibody accessibility of two exemplary schistosome antigens SmCD59a and SmKK7, before and after drug treatment. Our results demonstrated that praziquantel applied at a concentration of 1 μM inhibited development of all life stages. Application of 10 μM praziquantel led to dramatic morphological changes of all schistosomula. Artemether at 1 and 10 μM had differential effects depending on whether it was applied to 2-day as compared to 7- and 14-day schistosomula. While 2-day schistosomula were not killed but inhibited from further development, severe morphological damage was seen in 7- and 14-day schistosomula. Oxamniquine (1 and 10 μM) led to severe morphological impairment in all life stages. Analyzing the accessibility of the antigens SmCD59a and SmKK7 before drug treatment showed no antibody binding on living intact schistosomula. However, when schistosomula were treated with anthelmintics, both antigens became exposed on the larvae. Oxamniquine turned out to be most effective in promoting antibody binding to all schistosomula stages. CONCLUSION: This study has revealed marked differences in anthelmintic drug effects against larvae. Drug treatment increases surface antigen presentation and renders larvae accessible to antibody attack

Search for Flavor-Changing Neutral Current Interactions of the Top Quark and Higgs Boson in Final States with Two Photons in Proton-Proton Collisions at s\sqrt{s} =13 TeV

Proton-proton interactions resulting in final states with two photons are studied in a search for the signature of flavor-changing neutral current interactions of top quarks (t) and Higgs bosons (H). The analysis is based on data collected at a center-of-mass energy of 13 TeV with the CMS detector at the LHC, corresponding to an integrated luminosity of 137  fb−1. No significant excess above the background prediction is observed. Upper limits on the branching fractions (B) of the top quark decaying to a Higgs boson and an up (u) or charm (c) quark are derived through a binned fit to the diphoton invariant mass spectrum. The observed (expected) 95% confidence level upper limits are found to be 0.019% (0.031%) for B(t→Hu) and 0.073% (0.051%) for B(t→Hc). These are the strictest upper limits yet determined