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

YANA – a software tool for analyzing flux modes, gene-expression and enzyme activities

BACKGROUND: A number of algorithms for steady state analysis of metabolic networks have been developed over the years. Of these, Elementary Mode Analysis (EMA) has proven especially useful. Despite its low user-friendliness, METATOOL as a reliable high-performance implementation of the algorithm has been the instrument of choice up to now. As reported here, the analysis of metabolic networks has been improved by an editor and analyzer of metabolic flux modes. Analysis routines for expression levels and the most central, well connected metabolites and their metabolic connections are of particular interest. RESULTS: YANA features a platform-independent, dedicated toolbox for metabolic networks with a graphical user interface to calculate (integrating METATOOL), edit (including support for the SBML format), visualize, centralize, and compare elementary flux modes. Further, YANA calculates expected flux distributions for a given Elementary Mode (EM) activity pattern and vice versa. Moreover, a dissection algorithm, a centralization algorithm, and an average diameter routine can be used to simplify and analyze complex networks. Proteomics or gene expression data give a rough indication of some individual enzyme activities, whereas the complete flux distribution in the network is often not known. As such data are noisy, YANA features a fast evolutionary algorithm (EA) for the prediction of EM activities with minimum error, including alerts for inconsistent experimental data. We offer the possibility to include further known constraints (e.g. growth constraints) in the EA calculation process. The redox metabolism around glutathione reductase serves as an illustration example. All software and documentation are available for download at . CONCLUSION: A graphical toolbox and an editor for METATOOL as well as a series of additional routines for metabolic network analyses constitute a new user-friendly software for such efforts

SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools

Background: Qualitative frameworks, especially those based on the logical discrete formalism, are increasingly used to model regulatory and signalling networks. A major advantage of these frameworks is that they do not require precise quantitative data, and that they are well-suited for studies of large networks. While numerous groups have developed specific computational tools that provide original methods to analyse qualitative models, a standard format to exchange qualitative models has been missing. Results: We present the Systems Biology Markup Language (SBML) Qualitative Models Package (“qual”), an extension of the SBML Level 3 standard designed for computer representation of qualitative models of biological networks. We demonstrate the interoperability of models via SBML qual through the analysis of a specific signalling network by three independent software tools. Furthermore, the collective effort to define the SBML qual format paved the way for the development of LogicalModel, an open-source model library, which will facilitate the adoption of the format as well as the collaborative development of algorithms to analyse qualitative models. Conclusions: SBML qual allows the exchange of qualitative models among a number of complementary software tools. SBML qual has the potential to promote collaborative work on the development of novel computational approaches, as well as on the specification and the analysis of comprehensive qualitative models of regulatory and signalling networks

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

Computation of constrained MCSs leading to coupled ethanol and biomass formation by <i>E. coli</i> under anaerobic growth on glucose.

<p>Constrained MCSs up to size 7 that lead to ethanol synthesis with high yield in <i>E.coli</i> while slow growth is possible. Four scenarios were considered differing in the maximal glucose uptake rate (; given in <i>mmol/(gDW⋅h)</i>) or/and in the demanded minimal ethanol yield (; given in molecules ethanol per molecules glucose) in the strain to be constructed. The total number of MCSs (#MCSs) refers to knock-out sets blocking flux vectors with low ethanol yield; the number of constrained MCSs (#cMCSs) refers to the subset of MCSs which allow in addition growth above the minimum threshold (for details see text). For the cMCSs found, the distribution over cut set sizes are also shown (no cMCSs with less than 3 cuts exist; the upper limit of cuts was set to 7).</p><p>The full/reduced networks contain 1668/564 metabolites and 2382/958 reactions (the reactions in the compressed network represent lumped reaction subsets). For computation 12 threads on a cluster node with two Intel Xeon DP X5650 processors (each 6 cores) were used.</p

Performance measures of calculated strain designs for growth-coupled ethanol production in <i>E.coli</i>.

<p>A: Minimal (guaranteed) ethanol yield (under maximal substrate uptake rate) vs. maximal possible growth rate for each cMCS of scenario 3 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003378#pcbi-1003378-t003" target="_blank">Table 3</a>. The size of the cMCSs are indicated by different markers. It becomes apparent that when higher maximal growth rates are required larger cut sets become necessary implying also a decrease in the guaranteed ethanol yield. B: Substrate-specific productivity (SSP) induced by the cut sets of scenario 3 in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003378#pcbi-1003378-t003" target="_blank">Table 3</a>. Cut sets were ordered with respect to the number of required knockouts. Note that some crosses represent several cMCSs having, for example, the same SSP.</p

Who Needs Genomes?

The first detailed mechanistic models for genome based reproduction were developed by John von Neumann in the period 1948-1953 (von Neumann, 1948, 1949; Burks, 1966). While these models were extremely abstract, subsequent elaboration of the structure and function of DNA proved von Neumann&apos;s designs to have been strikingly prescient. However, some significant questions still remain as to the specific benefits of this particular reproductive architecture. These questions are relevant both to understanding the evolutionary emergence of such systems, and their proper role in engineered or synthetic evolutionary systems. This paper will review these issues, and present some preliminary results of novel evolutionary experiments in the Tierra system (Ray, 1992), where artificial &quot;organisms&quot; are deliberately engineered to have an evolvable genetic architecture. The Problem Situation This paper is concerned with evolutionary systems and their evolvability. By &quot;evolutionary system&quot; we mean a s..