Decision tree modeling predicts effects of inhibiting contractility signaling on cell motility

Background

Mathematical modelling of cellular networks is an integral part of Systems Biology and requires appropriate software tools. An important class of methods in Systems Biology deals with structural or topological (parameter-free) analysis of cellular networks. So far, software tools providing such methods for both mass-flow (metabolic) as well as signal-flow (signalling and regulatory) networks are lacking.

Results

Herein we introduce CellNetAnalyzer, a toolbox for MATLAB facilitating, in an interactive and visual manner, a comprehensive structural analysis of metabolic, signalling and regulatory networks. The particular strengths of CellNetAnalyzer are methods for functional network analysis, i.e. for characterising functional states, for detecting functional dependencies, for identifying intervention strategies, or for giving qualitative predictions on the effects of perturbations. CellNetAnalyzer extends its predecessor FluxAnalyzer (originally developed for metabolic network and pathway analysis) by a new modelling framework for examining signal-flow networks. Two of the novel methods implemented in CellNetAnalyzer are discussed in more detail regarding algorithmic issues and applications: the computation and analysis (i) of shortest positive and shortest negative paths and circuits in interaction graphs and (ii) of minimal intervention sets in logical networks.

Conclusion

CellNetAnalyzer provides a single suite to perform structural and qualitative analysis of both mass-flow- and signal-flow-based cellular networks in a user-friendly environment. It provides a large toolbox with various, partially unique, functions and algorithms for functional network analysis.CellNetAnalyzer is freely available for academic use.     

Study of metabolic network of Cupriavidus necator DSM 545 growing on glycerol by applying elementary flux modes and yield space analysis

A metabolic network consisting of 48 reactions was established to describe intracellular processes during growth and poly-3-hydroxybutyrate (PHB) production for Cupriavidus necator DSM 545. Glycerol acted as the sole carbon source during exponential, steady-state cultivation conditions. Elementary flux modes were obtained by the program Metatool and analyzed by using yield space analysis. Four sets of elementary modes were obtained, depending on whether the pair NAD/NADH or FAD/FADH₂ contributes to the reaction of glycerol-3-phosphate dehydrogenase (GLY-3-P DH), and whether 6-phosphogluconate dehydrogenase (6-PG DH) is present or not. Established metabolic network and the related system of equations provide multiple solutions for the simultaneous synthesis of PHB and biomass; this number of solutions can be further increased if NAD/NADH or FAD/FADH₂ were assumed to contribute in the reaction of GLY-3-P DH. As a major outcome, it was demonstrated that experimentally determined yields for biomass and PHB with respect to glycerol fit well to the values obtained in silico when the Entner–Doudoroff pathway (ED) dominates over the glycolytic pathway; this is also the case if the Embden–Meyerhof–Parnas pathway dominates over the ED.     

ACoM: A classification method for elementary flux modes based on motif finding

Elementary flux mode analysis is a powerful tool for the theoretical study of metabolic networks. However, when the networks are complex, the determination of elementary flux modes leads to combinatorial explosion of their number which prevents from drawing simple conclusions from their analysis. To deal with this problem we have developed a method based on the Agglomeration of Common Motifs (ACoM) for classifying elementary flux modes. We applied this algorithm to describe the decomposition into elementary flux modes of the central carbon metabolism in Bacillus subtilis and of the yeast mitochondrial energy metabolism. ACoM helps to give biological meaning to the different elementary flux modes and to the relatedness between reactions. ACoM, which can be viewed as a bi-clustering method, can be of general use for sets of vectors with values 0, +1 or −1.     

Interplay between Constraints,Objectives, and Optimality for Genome-Scale Stoichiometric Models

High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.     

FluxAnalyzer: exploring structure,pathways, and flux distributions in metabolic networks on interactive flux maps

MOTIVATION: The analysis of structure, pathways and flux distributions in metabolic networks has become an important approach for understanding the functionality of metabolic systems. The need of a user-friendly platform for stoichiometric modeling of metabolic networks in silico is evident. RESULTS: The FluxAnalyzer is a package for MATLAB and facilitates integrated pathway and flux analysis for metabolic networks within a graphical user interface. Arbitrary metabolic network models can be composed by instances of four types of network elements. The abstract network model is linked with network graphics leading to interactive flux maps which allow for user input and display of calculation results within a network visualization. Therein, a large and powerful collection of tools and algorithms can be applied interactively including metabolic flux analysis, flux optimization, detection of topological features and pathway analysis by elementary flux modes or extreme pathways. The FluxAnalyzer has been applied and tested for complex networks with more than 500,000 elementary modes. Some aspects of the combinatorial complexity of pathway analysis in metabolic networks are discussed. AVAILABILITY: Upon request from the corresponding author. Free for academic users (license agreement). Special contracts are available for industrial corporations. SUPPLEMENTARY INFORMATION: http://www.mpi-magdeburg.mpg.de/projects/fluxanalyzer.     

Structural robustness of metabolic networks with respect to multiple knockouts

We present a generalised framework for analysing structural robustness of metabolic networks, based on the concept of elementary flux modes (EFMs). Extending our earlier study on single knockouts [Wilhelm, T., Behre, J., Schuster, S., 2004. Analysis of structural robustness of metabolic networks. IEE Proc. Syst. Biol. 1(1), 114-120], we are now considering the general case of double and multiple knockouts. The robustness measures are based on the ratio of the number of remaining EFMs after knockout vs. the number of EFMs in the unperturbed situation, averaged over all combinations of knockouts. With the help of simple examples we demonstrate that consideration of multiple knockouts yields additional information going beyond single-knockout results. It is proven that the robustness score decreases as the knockout depth increases.We apply our extended framework to metabolic networks representing amino acid anabolism in Escherichia coli and human hepatocytes, and the central metabolism in human erythrocytes. Moreover, in the E. coli model the two subnetworks synthesising amino acids that are essential and those that are non-essential for humans are studied separately. The results are discussed from an evolutionary viewpoint. We find that E. coli has the most robust metabolism of all the cell types studied here. Considering only the subnetwork of the synthesis of non-essential amino acids, E. coli and the human hepatocyte show about the same robustness.     

The geometry of the flux cone of a metabolic network

The analysis of metabolic networks has become a major topic in biotechnology in recent years. Applications range from the enhanced production of selected outputs to the prediction of genotype-phenotype relationships. The concepts used are based on the assumption of a pseudo steady-state of the network, so that for each metabolite inputs and outputs are balanced. The stoichiometric network analysis expands the steady state into a combination of nonredundant subnetworks with positive coefficients called extremal currents. Based on the unidirectional representation of the system these subnetworks form a convex cone in the flux-space. A modification of this approach allowing for reversible reactions led to the definition of elementary modes. Extreme pathways are obtained with the same method but splitting up internal reactions into forward and backward rates. In this study, we explore the relationship between these concepts. Due to the combinatorial explosion of the number of elementary modes in large networks, we promote a further set of metabolic routes, which we call the minimal generating set. It is the smallest subset of elementary modes required to describe all steady states of the system. For large-scale networks, the size of this set is of several magnitudes smaller than that of elementary modes and of extreme pathways.     

Syntheses and pharmacokinetic evaluations of four metabolites of 2-(4-(2-((1H-benzo[d]imidazol-2-yl)thio)ethyl)piperazin-1-yl)-N-(6-methyl-2,4-bis-(methylthio)pyridin-3-yl)acetamide hydrochloride [K-604], an acyl-CoA:cholesterol O-acyltransferase-1 inhibitor

We synthesized and identified four metabolites of acyl-coenzyme A:cholesterol O-acyltransferase (ACAT)-1 inhibitor, K-604 (1). Two of the metabolites M1 and M2, were prepared from 1 using a combination reagent of hydrogen peroxide and sodium tungstate with either phosphoric acid or trifluoroethanol as the solvent to control the regioselectivity. Upon exposure of 4b to tert-butyl hypochlorite at −78 °C, the monosulfoxidation afforded synthetic intermediate of M3 in excellent yield. The efficient synthesis of M4 was established. The in vitro metabolic study exhibited a high clearance value (720 μL/min/mg protein) of 1 using human liver microsomes. We orally administered a single dose of 10 mg/kg of 1 to monkeys because the in vitro metabolic patterns are quite similar. Fortunately, the drug concentration of 1 was much higher than those of M1, M2, M3 and M4.     

Analysis of Metabolic Capabilities Using Singular Value Decomposition of Extreme Pathway Matrices

It is now possible to construct genome-scale metabolic networks for particular microorganisms. Extreme pathway analysis is a useful method for analyzing the phenotypic capabilities of these networks. Many extreme pathways are needed to fully describe the functional capabilities of genome-scale metabolic networks, and therefore, a need exists to develop methods to study these large sets of extreme pathways. Singular value decomposition (SVD) of matrices of extreme pathways was used to develop a conceptual framework for the interpretation of large sets of extreme pathways and the steady-state flux solution space they define. The key results of this study were: 1), convex steady-state solution cones describing the potential functions of biochemical networks can be studied using the modes generated by SVD; 2), Helicobacter pylori has a more rigid metabolic network (i.e., a lower dimensional solution space and a more dominant first singular value) than Haemophilus influenzae for the production of amino acids; and 3), SVD allows for direct comparison of different solution cones resulting from the production of different amino acids. SVD was used to identify key network branch points that may identify key control points for regulation. Therefore, SVD of matrices of extreme pathways has proved to be a useful method for analyzing the steady-state solution space of genome-scale metabolic networks.     

An integrated network visualization framework towards metabolic engineering applications

Background

Over the last years, several methods for the phenotype simulation of microorganisms, under specified genetic and environmental conditions have been proposed, in the context of Metabolic Engineering (ME). These methods provided insight on the functioning of microbial metabolism and played a key role in the design of genetic modifications that can lead to strains of industrial interest. On the other hand, in the context of Systems Biology research, biological network visualization has reinforced its role as a core tool in understanding biological processes. However, it has been scarcely used to foster ME related methods, in spite of the acknowledged potential.

Results

In this work, an open-source software that aims to fill the gap between ME and metabolic network visualization is proposed, in the form of a plugin to the OptFlux ME platform. The framework is based on an abstract layer, where the network is represented as a bipartite graph containing minimal information about the underlying entities and their desired relative placement. The framework provides input/output support for networks specified in standard formats, such as XGMML, SBGN or SBML, providing a connection to genome-scale metabolic models. An user-interface makes it possible to edit, manipulate and query nodes in the network, providing tools to visualize diverse effects, including visual filters and aspect changing (e.g. colors, shapes and sizes). These tools are particularly interesting for ME, since they allow overlaying phenotype simulation results or elementary flux modes over the networks.

Conclusions

The framework and its source code are freely available, together with documentation and other resources, being illustrated with well documented case studies.

Electronic supplementary material

The online version of this article (doi:10.1186/s12859-014-0420-0) contains supplementary material, which is available to authorized users.     

Carot-4-en-9,10-Diol,a Conidiation-Inducing Sesquiterpene Diol Produced by Trichoderma virens PS1-7 upon Exposure to Chemical Stress from Highly Active Iron Chelators

To screen biocontrol agents against Burkholderia plantarii, the causative agent of rice seedling blight, we employed catechol, an analog of the virulence factor tropolone, to obtain chemical stress-resistant microorganisms. The fungal isolate PS1-7, identified as a strain of Trichoderma virens, showed the highest resistance to catechol (20 mM) and exhibited efficacy as a biocontrol agent for rice seedling blight. During investigation of metabolic traits of T. virens PS1-7 exposed to catechol, we found a secondary metabolite that was released extracellularly and uniquely accumulated in the culture. The compound induced by chemical stress due to catechol was subsequently isolated and identified as a sesquiterpene diol, carot-4-en-9,10-diol, based on spectroscopic analyses. T. virens PS1-7 produced carot-4-en-9,10-diol as a metabolic response to tropolone at concentrations from 0.05 to 0.2 mM, and the response was enhanced in a dose-dependent manner, similar to its response to catechol at concentrations from 0.1 to 1 mM. Some iron chelators, such as pyrogallol, gallic acid, salicylic acid, and citric acid, at 0.5 mM also showed activation of T. virens PS1-7 production of carot-4-en-9,10-diol. This sesquiterpene diol, formed in response to chemical stress, promoted conidiation of T. virens PS1-7, suggesting that it is involved in an autoregulatory signaling system. In a bioassay of the metabolic and morphological responses of T. virens PS1-7, conidiation in hyphae grown on potato dextrose agar (PDA) plates was either promoted or induced by carot-4-en-9,10-diol. Carot-4-en-9,10-diol can thus be regarded as an autoregulatory signal in T. virens, and our findings demonstrate that intrinsic intracellular signaling regulates conidiation of T. virens.     

Stoichiometric model of folate-dependent metabolism of one-carbon units in human placenta

The work is dedicated to creation of the mathematical model of folate-dependent one-carbon unit metabolism (FOCM) and study of its function in human placenta under homocysteine load and the most common mutations in the genes of methylenetetrahydrofolate reductase (MTHFR) and cystathionine beta-synthase (CBS). In the model we have taken into account specific features of placental expression of genes that encode enzymes of FOCM. Using software tools Metatool and COBRAToolbox we have identified key metabolites, elementary modes and metabolic fluxes through different reactions of the system. It is shown that the most vulnerable links in the system are the folate cycle and synthesis of precursors of nucleic acids, inosine monophosphate and thymidyne monophosphates, which are changing in the broad range from significant inhibition to activation depending on the imposed conditions. The most stable links in the system are the reactions of glutathione and taurine synthesis. Simulation results coincide with the results obtained in similar experimental conditions. Under certain imposed conditions non-obvious relationships between the system links are revealed, and this becomes the basis for a purposeful test of predictions generated by the model.     

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.     

Use of network analysis of metabolic systems in bioengineering

Basic ideas and recent developments in network analysis of metabolic systems and various applications of this analysis in bioengineering are reviewed. Central concepts are the null-space to the stoichiometry matrix and the elementary flux modes. The applicability of elementary-modes analysis in biotechnology is illustrated by the synthesis of the cyclooctadepsipeptides PF1022 in the fungus Mycelia sterilia. Network analysis is also useful in metabolic flux analysis. In particular, a procedure for finding out which reaction rates can be uniquely calculated in underdetermined reaction networks is outlined. The concept of 'enzyme subsets' is explained and its use for analysing genetic regulation is demonstrated. In particular, the correlation between expression data concerning the diauxic shift in yeast and the enzyme subsets in yeast metabolism is discussed.