a direct encoding for nnc polyhedra

We present an alternative Double Description representation for the domain of NNC (not necessarily closed) polyhedra, together with the corresponding Chernikova-like conversion procedure. The representation uses no slack variable at all and provides a solution to a few technical issues caused by the encoding of an NNC polyhedron as a closed polyhedron in a higher dimension space. A preliminary experimental evaluation shows that the new conversion algorithm is able to achieve significant efficiency improvements

Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks

The metabolism of organisms can be studied with comprehensive stoichiometric models of their metabolic networks. Flux balance analysis (FBA) calculates optimal metabolic performance of stoichiometric models. However, detailed biological interpretation of FBA is limited because, in general, a huge number of flux patterns give rise to the same optimal performance. The complete description of the resulting optimal solution spaces was thus far a computationally intractable problem. Here we present CoPE-FBA: Comprehensive Polyhedra Enumeration Flux Balance Analysis, a computational method that solves this problem. CoPE-FBA indicates that the thousands to millions of optimal flux patterns result from a combinatorial explosion of flux patterns in just a few metabolic sub-networks. The entire optimal solution space can now be compactly described in terms of the topology of these sub-networks. CoPE-FBA simplifies the biological interpretation of stoichiometric models of metabolism, and provides a profound understanding of metabolic flexibility in optimal states

Exhaustive identification of steady state cycles in large stoichiometric networks

BACKGROUND: Identifying cyclic pathways in chemical reaction networks is important, because such cycles may indicate in silico violation of energy conservation, or the existence of feedback in vivo. Unfortunately, our ability to identify cycles in stoichiometric networks, such as signal transduction and genome-scale metabolic networks, has been hampered by the computational complexity of the methods currently used. RESULTS: We describe a new algorithm for the identification of cycles in stoichiometric networks, and we compare its performance to two others by exhaustively identifying the cycles contained in the genome-scale metabolic networks of H. pylori, M. barkeri, E. coli, and S. cerevisiae. Our algorithm can substantially decrease both the execution time and maximum memory usage in comparison to the two previous algorithms. CONCLUSION: The algorithm we describe improves our ability to study large, real-world, biochemical reaction networks, although additional methodological improvements are desirable

Computing paths and cycles in biological interaction graphs

<p>Abstract</p> <p>Background</p> <p>Interaction graphs (signed directed graphs) provide an important qualitative modeling approach for Systems Biology. They enable the analysis of causal relationships in cellular networks and can even be useful for predicting qualitative aspects of systems dynamics. Fundamental issues in the analysis of interaction graphs are the enumeration of paths and cycles (feedback loops) and the calculation of shortest positive/negative paths. These computational problems have been discussed only to a minor extent in the context of Systems Biology and in particular the shortest signed paths problem requires algorithmic developments.</p> <p>Results</p> <p>We first review algorithms for the enumeration of paths and cycles and show that these algorithms are superior to a recently proposed enumeration approach based on elementary-modes computation. The main part of this work deals with the computation of shortest positive/negative paths, an NP-complete problem for which only very few algorithms are described in the literature. We propose extensions and several new algorithm variants for computing either exact results or approximations. Benchmarks with various concrete biological networks show that exact results can sometimes be obtained in networks with several hundred nodes. A class of even larger graphs can still be treated exactly by a new algorithm combining exhaustive and simple search strategies. For graphs, where the computation of exact solutions becomes time-consuming or infeasible, we devised an approximative algorithm with polynomial complexity. Strikingly, in realistic networks (where a comparison with exact results was possible) this algorithm delivered results that are very close or equal to the exact values. This phenomenon can probably be attributed to the particular topology of cellular signaling and regulatory networks which contain a relatively low number of negative feedback loops.</p> <p>Conclusion</p> <p>The calculation of shortest positive/negative paths and cycles in interaction graphs is an important method for network analysis in Systems Biology. This contribution draws the attention of the community to this important computational problem and provides a number of new algorithms, partially specifically tailored for biological interaction graphs. All algorithms have been implemented in the <it>CellNetAnalyzer </it>framework which can be downloaded for academic use at <url>http://www.mpi-magdeburg.mpg.de/projects/cna/cna.html</url>.</p

OptFlux: an open-source software platform for in silico metabolic engineering

<p>Abstract</p> <p>Background</p> <p>Over the last few years a number of methods have been proposed for the phenotype simulation of microorganisms under different environmental and genetic conditions. These have been used as the basis to support the discovery of successful genetic modifications of the microbial metabolism to address industrial goals. However, the use of these methods has been restricted to bioinformaticians or other expert researchers. The main aim of this work is, therefore, to provide a user-friendly computational tool for Metabolic Engineering applications.</p> <p>Results</p> <p><it>OptFlux </it>is an open-source and modular software aimed at being the reference computational application in the field. It is the first tool to incorporate strain optimization tasks, i.e., the identification of Metabolic Engineering targets, using Evolutionary Algorithms/Simulated Annealing metaheuristics or the previously proposed OptKnock algorithm. It also allows the use of stoichiometric metabolic models for (i) phenotype simulation of both wild-type and mutant organisms, using the methods of Flux Balance Analysis, Minimization of Metabolic Adjustment or Regulatory on/off Minimization of Metabolic flux changes, (ii) Metabolic Flux Analysis, computing the admissible flux space given a set of measured fluxes, and (iii) pathway analysis through the calculation of Elementary Flux Modes.</p> <p><it>OptFlux </it>also contemplates several methods for model simplification and other pre-processing operations aimed at reducing the search space for optimization algorithms.</p> <p>The software supports importing/exporting to several flat file formats and it is compatible with the SBML standard. <it>OptFlux </it>has a visualization module that allows the analysis of the model structure that is compatible with the layout information of <it>Cell Designer</it>, allowing the superimposition of simulation results with the model graph.</p> <p>Conclusions</p> <p>The <it>OptFlux </it>software is freely available, together with documentation and other resources, thus bridging the gap from research in strain optimization algorithms and the final users. It is a valuable platform for researchers in the field that have available a number of useful tools. Its open-source nature invites contributions by all those interested in making their methods available for the community.</p> <p>Given its plug-in based architecture it can be extended with new functionalities. Currently, several plug-ins are being developed, including network topology analysis tools and the integration with Boolean network based regulatory models.</p

Identification of metabolic engineering targets through analysis of optimal and sub-optimal routes

Identification of optimal genetic manipulation strategies for redirecting substrate uptake towards a desired product is a challenging task owing to the complexity of metabolic networks, esp. in terms of large number of routes leading to the desired product. Algorithms that can exploit the whole range of optimal and suboptimal routes for product formation while respecting the biological objective of the cell are therefore much needed. Towards addressing this need, we here introduce the notion of structural flux, which is derived from the enumeration of all pathways in the metabolic network in question and accounts for the contribution towards a given biological objective function. We show that the theoretically estimated structural fluxes are good predictors of experimentally measured intra-cellular fluxes in two model organisms, namely, Escherichia coli and Saccharomyces cerevisiae. For a small number of fluxes for which the predictions were poor, the corresponding enzyme-coding transcripts were also found to be distinctly regulated, showing the ability of structural fluxes in capturing the underlying regulatory principles. Exploiting the observed correspondence between in vivo fluxes and structural fluxes, we propose an in silico metabolic engineering approach, iStruF, which enables the identification of gene deletion strategies that couple the cellular biological objective with the product flux while considering optimal as well as sub-optimal routes and their efficiency.This work was supported by the Portuguese Science Foundation [grant numbers MIT-Pt/BS-BB/0082/2008, SFRH/BPD/44180/2008 to ZS] (http://www.fct.pt/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

Genome-scale bacterial transcriptional regulatory networks: reconstruction and integrated analysis with metabolic models

Advances in sequencing technology are resulting in the rapid emergence of large numbers of complete genome sequences. High throughput annotation and metabolic modeling of these genomes is now a reality. The high throughput reconstruction and analysis of genome-scale transcriptional regulatory networks represents the next frontier in microbial bioinformatics. The fruition of this next frontier will depend upon the integration of numerous data sources relating to mechanisms, components, and behavior of the transcriptional regulatory machinery, as well as the integration of the regulatory machinery into genome-scale cellular models. Here we review existing repositories for different types of transcriptional regulatory data, including expression data, transcription factor data, and binding site locations, and we explore how these data are being used for the reconstruction of new regulatory networks. From template network based methods to de novo reverse engineering from expression data, we discuss how regulatory networks can be reconstructed and integrated with metabolic models to improve model predictions and performance. Finally, we explore the impact these integrated models can have in simulating phenotypes, optimizing the production of compounds of interest or paving the way to a whole-cell model.J.P.F. acknowledges funding from [SFRH/BD/70824/2010] of the FCT (Portuguese Foundation for Science and Technology) PhD program. The work was supported in part by the ERDF—European Regional Development Fund through the COMPETE Programme (operational programme for competitiveness), National Funds through the FCT within projects [FCOMP-01-0124-FEDER015079] (ToMEGIM—Computational Tools for Metabolic Engineering using Genome-scale Integrated Models) and FCOMP-01-0124-FEDER009707 (HeliSysBio—molecular Systems Biology in Helicobacter pylori), the U.S. Department of Energy under contract [DE-ACO2-06CH11357] and the National Science Foundation under [0850546]

Dynamic elementary mode modelling of non-steady state flux data

[EN] A novel framework is proposed to analyse metabolic fluxes in non-steady state conditions, based on the new concept of dynamic elementary mode (dynEM): an elementary mode activated partially depending on the time point of the experiment.This research work was partially supported by the Spanish Ministry of Economy and Competitiveness under the project DPI2014-55276-C5-1R.Folch-Fortuny, A.; Teusink, B.; Hoefsloot, HC.; Smilde, AK.; Ferrer, A. (2018). Dynamic elementary mode modelling of non-steady state flux data. BMC Systems Biology. 12:1-15. https://doi.org/10.1186/s12918-018-0589-3S11512Bro R, Smilde AK. Principal component analysis. Anal Methods. 2014; 6(9):2812–31.González-Martínez JM, Folch-Fortuny A, Llaneras F, Tortajada M, Picó J, Ferrer A. Metabolic flux understanding of Pichia pastoris grown on heterogenous culture media. Chemometr Intell Lab Syst. 2014; 134:89–99.Barrett CL, Herrgard MJ, Palsson B. Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation. BMC Syst Biol. 2009; 3(30):1–8.Jaumot J, Gargallo R, De Juan A, Tauler R. A graphical user-friendly interface for MCR-ALS: A new tool for multivariate curve resolution in MATLAB. Chemometr Intell Lab Syst. 2005; 76(1):101–10.Folch-Fortuny A, Tortajada M, Prats-Montalbán JM, Llaneras F, Picó J, Ferrer A. MCR-ALS on metabolic networks: Obtaining more meaningful pathways. Chemometr Intell Lab Syst. 2015; 142:293–303.Folch-Fortuny A, Marques R, Isidro IA, Oliveira R, Ferrer A. Principal elementary mode analysis (PEMA). Mol BioSyst. 2016; 12(3):737–46.Hood L. Systems biology: Integrating technology, biology, and computation. Mech Ageing Dev. 2003; 124(1):9–16.Teusink B, Passarge J, Reijenga CA, Esgalhado E, van der Weijden CC, Schepper M, Walsh MC, Bakker BM, van Dam K, Westerhoff HV, Snoep JL. Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Eur J Biochem / FEBS. 2000; 267(17):5313–29.Mahadevan R, Edwards JS, Doyle FJ. Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J. 2002; 83(3):1331–40.Willemsen AM, Hendrickx DM, Hoefsloot HCJ, Hendriks MMWB, Wahl SA, Teusink B, Smilde AK, van Kampen AHC. MetDFBA: incorporating time-resolved metabolomics measurements into dynamic flux balance analysis. Mol BioSyst. 2015; 11(1):137–45.Barker M, Rayens W. Partial least squares for discrimination. J Chemom. 2003; 17(3):166–73.Bartel J, Krumsiek J, Theis FJ. Statistical methods for the analysis of high-throughput metabolomics data. Comput Struct Biotechnol J. 2013; 4:201301009.Hendrickx DM, Hoefsloot HCJ, Hendriks MMWB, Canelas AB, Smilde AK. Global test for metabolic pathway differences between conditions. Anal Chim Acta. 2012; 719:8–15.Kanehisa M, Goto S, Hattori M, Aoki-Kinoshita KF, Itoh M, Kawashima S, Katayama T, Araki M, Hirakawa M. From genomics to chemical genomics: new developments in KEGG. Nucleic Acids Res. 2006; 34(Database issue):354–7.Kanehisa M, Goto S. KEGG: kyoto encyclopedia of genes and genomes. Nucleic Acids Res. 2000; 28(1):27–30.Kanehisa M, Goto S, Furumichi M, Tanabe M, Hirakawa M. KEGG for representation and analysis of molecular networks involving diseases and drugs. Nucleic Acids Res. 2010; 38(Database issue):355–60.Andersson CA, Bro R. The N-way Toolbox for MATLAB. Chemometr Intell Lab Syst. 2000; 52(1):1–4.Terzer M, Stelling J. Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics. 2008; 24(19):2229–35.Heerden JHv, Wortel MT, Bruggeman FJ, Heijnen JJ, Bollen YJM, Planqué R, Hulshof J, O’Toole TG, Wahl SA, Teusink B. Lost in Transition: Start-Up of Glycolysis Yields Subpopulations of Nongrowing Cells. Science. 2014; 343(6174):1245114.Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U. COPASI–a COmplex PAthway SImulator. Bioinformatics. 2006; 22(24):3067–74.Petzold L. Automatic selection of methods for solving stiff and nonstiff systems of ordinary differential equations. SIAM J Sci Stat Comput. 1983; 4:136–48.Canelas AB, van Gulik WM, Heijnen JJ. Determination of the cytosolic free NAD/NADH ratio in Saccharomyces cerevisiae under steady-state and highly dynamic conditions. Biotechnol Bioeng. 2008; 100(4):734–43.Nikerel IE, Canelas AB, Jol SJ, Verheijen PJT, Heijnen JJ. Construction of kinetic models for metabolic reaction networks: Lessons learned in analysing short-term stimulus response data. Math Comput Model Dyn Syst. 2011; 17(3):243–60.Llaneras F, Picó J. Stoichiometric modelling of cell metabolism. J Biosci Bioeng. 2008; 105(1):1–11.Bro R. Multiway calibration. Multilinear PLS. J Chemom. 1998; 10(1):47–61.Westerhuis JA, Hoefsloot HCJ, Smit S, Vis DJ, Smilde AK, Velzen EJJv, Duijnhoven JPMv, Dorsten FAv. Assessment of PLSDA cross validation. Metabolomics. 2008; 4(1):81–9.Szymańska E, Saccenti E, Smilde AK, Westerhuis JA. Double-check: validation of diagnostic statistics for PLS-DA models in metabolomics studies. Metabolomics. 2012; 8(Suppl 1):3–16.Rodrigues F, Ludovico P, Leão C. Sugar Metabolism in Yeasts: an Overview of Aerobic and Anaerobic Glucose Catabolism. In: Biodiversity and Ecophysiology of Yeasts. The Yeast Handbook. Berlin: Springer: 2006. p. 101–21.Larsson K, Ansell R, Eriksson P, Adler L. A gene encoding sn-glycerol 3-phosphate dehydrogenase (NAD+) complements an osmosensitive mutant of Saccharomyces cerevisiae. Mol Microbiol. 1993; 10(5):1101–11.Eriksson P, André L, Ansell R, Blomberg A, Adler L. Cloning and characterization of GPD2, a second gene encoding sn-glycerol 3-phosphate dehydrogenase (NAD+) in Saccharomyces cerevisiae, and its comparison with GPD1. Mol Microbiol. 1995; 17(1):95–107.Norbeck J, Pâhlman AK, Akhtar N, Blomberg A, Adler L. Purification and characterization of two isoenzymes of DL-glycerol-3-phosphatase from Saccharomyces cerevisiae. Identification of the corresponding GPP1 and GPP2 genes and evidence for osmotic regulation of Gpp2p expression by the osmosensing mitogen-activated protein kinase signal transduction pathway. J Biol Chem. 1996; 271(23):13875–81