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1.  Cyanobacterial biofuels: new insights and strain design strategies revealed by computational modeling 
Microbial Cell Factories  2014;13(1):128.
Background
Cyanobacteria are increasingly recognized as promising cell factories for the production of renewable biofuels and chemical feedstocks from sunlight, CO2, and water. However, most biotechnological applications of these organisms are still characterized by low yields. Increasing the production performance of cyanobacteria remains therefore a crucial step.
Results
In this work we use a stoichiometric network model of Synechocystis sp. PCC 6803 in combination with CASOP and minimal cut set analysis to systematically identify and characterize suitable strain design strategies for biofuel synthesis, specifically for ethanol and isobutanol. As a key result, improving upon other works, we demonstrate that higher-order knockout strategies exist in the model that lead to coupling of growth with high-yield biofuel synthesis under phototrophic conditions. Enumerating all potential knockout strategies (cut sets) reveals a unifying principle behind the identified strain designs, namely to reduce the ratio of ATP to NADPH produced by the photosynthetic electron transport chain. Accordingly, suitable knockout strategies seek to block cyclic and other alternate electron flows, such that ATP and NADPH are exclusively synthesized via the linear electron flow whose ATP/NADPH ratio is below that required for biomass synthesis. The products of interest are then utilized by the cell as sinks for reduction equivalents in excess. Importantly, the calculated intervention strategies do not rely on the assumption of optimal growth and they ensure that maintenance metabolism in the absence of light remains feasible. Our analyses furthermore suggest that a moderately increased ATP turnover, realized, for example, by ATP futile cycles or other ATP wasting mechanisms, represents a promising target to achieve increased biofuel yields.
Conclusion
Our study reveals key principles of rational metabolic engineering strategies in cyanobacteria towards biofuel production. The results clearly show that achieving obligatory coupling of growth and product synthesis in photosynthetic bacteria requires fundamentally different intervention strategies compared to heterotrophic organisms.
Electronic supplementary material
The online version of this article (doi:10.1186/s12934-014-0128-x) contains supplementary material, which is available to authorized users.
doi:10.1186/s12934-014-0128-x
PMCID: PMC4180434  PMID: 25323065
Biofuels; Metabolic engineering; Cyanobacteria; Minimal cut sets; Photosynthesis; Synechocystis sp. PCC 6803
2.  The avian cell line AGE1.CR.pIX characterized by metabolic flux analysis 
BMC Biotechnology  2014;14:72.
Background
In human vaccine manufacturing some pathogens such as Modified Vaccinia Virus Ankara, measles, mumps virus as well as influenza viruses are still produced on primary material derived from embryonated chicken eggs. Processes depending on primary cell culture, however, are difficult to adapt to modern vaccine production. Therefore, we derived previously a continuous suspension cell line, AGE1.CR.pIX, from muscovy duck and established chemically-defined media for virus propagation.
Results
To better understand vaccine production processes, we developed a stoichiometric model of the central metabolism of AGE1.CR.pIX cells and applied flux variability and metabolic flux analysis. Results were compared to literature dealing with mammalian and insect cell culture metabolism focusing on the question whether cultured avian cells differ in metabolism. Qualitatively, the observed flux distribution of this avian cell line was similar to distributions found for mammalian cell lines (e.g. CHO, MDCK cells). In particular, glucose was catabolized inefficiently and glycolysis and TCA cycle seem to be only weakly connected.
Conclusions
A distinguishing feature of the avian cell line is that glutaminolysis plays only a minor role in energy generation and production of precursors, resulting in low extracellular ammonia concentrations. This metabolic flux study is the first for a continuous avian cell line. It provides a basis for further metabolic analyses to exploit the biotechnological potential of avian and vertebrate cell lines and to develop specific optimized cell culture processes, e.g. vaccine production processes.
doi:10.1186/1472-6750-14-72
PMCID: PMC4124504  PMID: 25077436
Avian cell line AGE1.CR.pIX; Biomass composition; Flux variability analysis; Metabolic network modeling; Glutaminolysis
3.  Enumeration of Smallest Intervention Strategies in Genome-Scale Metabolic Networks 
PLoS Computational Biology  2014;10(1):e1003378.
One ultimate goal of metabolic network modeling is the rational redesign of biochemical networks to optimize the production of certain compounds by cellular systems. Although several constraint-based optimization techniques have been developed for this purpose, methods for systematic enumeration of intervention strategies in genome-scale metabolic networks are still lacking. In principle, Minimal Cut Sets (MCSs; inclusion-minimal combinations of reaction or gene deletions that lead to the fulfilment of a given intervention goal) provide an exhaustive enumeration approach. However, their disadvantage is the combinatorial explosion in larger networks and the requirement to compute first the elementary modes (EMs) which itself is impractical in genome-scale networks.
We present MCSEnumerator, a new method for effective enumeration of the smallest MCSs (with fewest interventions) in genome-scale metabolic network models. For this we combine two approaches, namely (i) the mapping of MCSs to EMs in a dual network, and (ii) a modified algorithm by which shortest EMs can be effectively determined in large networks. In this way, we can identify the smallest MCSs by calculating the shortest EMs in the dual network. Realistic application examples demonstrate that our algorithm is able to list thousands of the most efficient intervention strategies in genome-scale networks for various intervention problems. For instance, for the first time we could enumerate all synthetic lethals in E.coli with combinations of up to 5 reactions. We also applied the new algorithm exemplarily to compute strain designs for growth-coupled synthesis of different products (ethanol, fumarate, serine) by E.coli. We found numerous new engineering strategies partially requiring less knockouts and guaranteeing higher product yields (even without the assumption of optimal growth) than reported previously. The strength of the presented approach is that smallest intervention strategies can be quickly calculated and screened with neither network size nor the number of required interventions posing major challenges.
Author Summary
Mathematical modeling has become an essential tool for investigating metabolic networks. One ultimate goal of metabolic network modeling is the rational redesign of biochemical networks to optimize the production of certain compounds by cellular systems. Accordingly, several optimization techniques have been proposed for this purpose. However, for large-scale networks, an effective method for systematic enumeration of the most efficient intervention strategies is still lacking. Herein we present MCSEnumerator, a new mathematical approach by which thousands of the smallest intervention strategies (with fewest targets) can be readily computed in large-scale metabolic models. Our approach is built upon an extended concept of Minimal Cut Sets, the latter being minimal (irreducible) combinations of reaction (or gene) deletions that will lead to the fulfilment of a given intervention goal. The strength of the presented approach is that smallest intervention strategies can be quickly calculated with neither network size nor the number of required interventions posing major challenges. Realistic application examples with E.coli demonstrate that our algorithm is able to list thousands of the most efficient intervention strategies in genome-scale networks for various intervention problems.
doi:10.1371/journal.pcbi.1003378
PMCID: PMC3879096  PMID: 24391481
4.  SBML qualitative models: a model representation format and infrastructure to foster interactions between qualitative modelling formalisms and tools 
BMC Systems Biology  2013;7:135.
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.
doi:10.1186/1752-0509-7-135
PMCID: PMC3892043  PMID: 24321545
5.  Comparison and improvement of algorithms for computing minimal cut sets 
BMC Bioinformatics  2013;14:318.
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.
doi:10.1186/1471-2105-14-318
PMCID: PMC3882775  PMID: 24191903
Metabolic network analysis; Elementary modes; Minimal cut sets; Knockout strategies; Integer programming; Berge’s algorithm
6.  In silico profiling of Escherichia coli and Saccharomyces cerevisiae as terpenoid factories 
Background
Heterologous microbial production of rare plant terpenoids of medicinal or industrial interest is attracting more and more attention but terpenoid yields are still low. Escherichia coli and Saccharomyces cerevisiae are the most widely used heterologous hosts; a direct comparison of both hosts based on experimental data is difficult though. Hence, the terpenoid pathways of E. coli (via 1-deoxy-D-xylulose 5-phosphate, DXP) and S. cerevisiae (via mevalonate, MVA), the impact of the respective hosts metabolism as well as the impact of different carbon sources were compared in silico by means of elementary mode analysis. The focus was set on the yield of isopentenyl diphosphate (IPP), the general terpenoid precursor, to identify new metabolic engineering strategies for an enhanced terpenoid yield.
Results
Starting from the respective precursor metabolites of the terpenoid pathways (pyruvate and glyceraldehyde-3-phosphate for the DXP pathway and acetyl-CoA for the MVA pathway) and considering only carbon stoichiometry, the two terpenoid pathways are identical with respect to carbon yield. However, with glucose as substrate, the MVA pathway has a lower potential to supply terpenoids in high yields than the DXP pathway if the formation of the required precursors is taken into account, due to the carbon loss in the formation of acetyl-CoA. This maximum yield is further reduced in both hosts when the required energy and reduction equivalents are considered. Moreover, the choice of carbon source (glucose, xylose, ethanol or glycerol) has an effect on terpenoid yield with non-fermentable carbon sources being more promising. Both hosts have deficiencies in energy and redox equivalents for high yield terpenoid production leading to new overexpression strategies (heterologous enzymes/pathways) for an enhanced terpenoid yield. Finally, several knockout strategies are identified using constrained minimal cut sets enforcing a coupling of growth to a terpenoid yield which is higher than any yield published in scientific literature so far.
Conclusions
This study provides for the first time a comprehensive and detailed in silico comparison of the most prominent heterologous hosts E. coli and S. cerevisiae as terpenoid factories giving an overview on several promising metabolic engineering strategies paving the way for an enhanced terpenoid yield.
doi:10.1186/1475-2859-12-84
PMCID: PMC3852115  PMID: 24059635
Terpenoids; Isoprenoids; In silico; Elementary mode analysis; Constrained minimal cut sets; Metabolic engineering; Escherichia coli; Saccharomyces cerevisiae
7.  Detecting and Removing Inconsistencies between Experimental Data and Signaling Network Topologies Using Integer Linear Programming on Interaction Graphs 
PLoS Computational Biology  2013;9(9):e1003204.
Cross-referencing experimental data with our current knowledge of signaling network topologies is one central goal of mathematical modeling of cellular signal transduction networks. We present a new methodology for data-driven interrogation and training of signaling networks. While most published methods for signaling network inference operate on Bayesian, Boolean, or ODE models, our approach uses integer linear programming (ILP) on interaction graphs to encode constraints on the qualitative behavior of the nodes. These constraints are posed by the network topology and their formulation as ILP allows us to predict the possible qualitative changes (up, down, no effect) of the activation levels of the nodes for a given stimulus. We provide four basic operations to detect and remove inconsistencies between measurements and predicted behavior: (i) find a topology-consistent explanation for responses of signaling nodes measured in a stimulus-response experiment (if none exists, find the closest explanation); (ii) determine a minimal set of nodes that need to be corrected to make an inconsistent scenario consistent; (iii) determine the optimal subgraph of the given network topology which can best reflect measurements from a set of experimental scenarios; (iv) find possibly missing edges that would improve the consistency of the graph with respect to a set of experimental scenarios the most. We demonstrate the applicability of the proposed approach by interrogating a manually curated interaction graph model of EGFR/ErbB signaling against a library of high-throughput phosphoproteomic data measured in primary hepatocytes. Our methods detect interactions that are likely to be inactive in hepatocytes and provide suggestions for new interactions that, if included, would significantly improve the goodness of fit. Our framework is highly flexible and the underlying model requires only easily accessible biological knowledge. All related algorithms were implemented in a freely available toolbox SigNetTrainer making it an appealing approach for various applications.
Author Summary
Cellular signal transduction is orchestrated by communication networks of signaling proteins commonly depicted on signaling pathway maps. However, each cell type may have distinct variants of signaling pathways, and wiring diagrams are often altered in disease states. The identification of truly active signaling topologies based on experimental data is therefore one key challenge in systems biology of cellular signaling. We present a new framework for training signaling networks based on interaction graphs (IG). In contrast to complex modeling formalisms, IG capture merely the known positive and negative edges between the components. This basic information, however, already sets hard constraints on the possible qualitative behaviors of the nodes when perturbing the network. Our approach uses Integer Linear Programming to encode these constraints and to predict the possible changes (down, neutral, up) of the activation levels of the involved players for a given experiment. Based on this formulation we developed several algorithms for detecting and removing inconsistencies between measurements and network topology. Demonstrated by EGFR/ErbB signaling in hepatocytes, our approach delivers direct conclusions on edges that are likely inactive or missing relative to canonical pathway maps. Such information drives the further elucidation of signaling network topologies under normal and pathological phenotypes.
doi:10.1371/journal.pcbi.1003204
PMCID: PMC3764019  PMID: 24039561
8.  Reconstruction of large-scale regulatory networks based on perturbation graphs and transitive reduction: improved methods and their evaluation 
BMC Systems Biology  2013;7:73.
Background
The data-driven inference of intracellular networks is one of the key challenges of computational and systems biology. As suggested by recent works, a simple yet effective approach for reconstructing regulatory networks comprises the following two steps. First, the observed effects induced by directed perturbations are collected in a signed and directed perturbation graph (PG). In a second step, Transitive Reduction (TR) is used to identify and eliminate those edges in the PG that can be explained by paths and are therefore likely to reflect indirect effects.
Results
In this work we introduce novel variants for PG generation and TR, leading to significantly improved performances. The key modifications concern: (i) use of novel statistical criteria for deriving a high-quality PG from experimental data; (ii) the application of local TR which allows only short paths to explain (and remove) a given edge; and (iii) a novel strategy to rank the edges with respect to their confidence. To compare the new methods with existing ones we not only apply them to a recent DREAM network inference challenge but also to a novel and unprecedented synthetic compendium consisting of 30 5000-gene networks simulated with varying biological and measurement error variances resulting in a total of 270 datasets. The benchmarks clearly demonstrate the superior reconstruction performance of the novel PG and TR variants compared to existing approaches. Moreover, the benchmark enabled us to draw some general conclusions. For example, it turns out that local TR restricted to paths with a length of only two is often sufficient or even favorable. We also demonstrate that considering edge weights is highly beneficial for TR whereas consideration of edge signs is of minor importance. We explain these observations from a graph-theoretical perspective and discuss the consequences with respect to a greatly reduced computational demand to conduct TR. Finally, as a realistic application scenario, we use our framework for inferring gene interactions in yeast based on a library of gene expression data measured in mutants with single knockouts of transcription factors. The reconstructed network shows a significant enrichment of known interactions, especially within the 100 most confident (and for experimental validation most relevant) edges.
Conclusions
This paper presents several major achievements. The novel methods introduced herein can be seen as state of the art for inference techniques relying on perturbation graphs and transitive reduction. Another key result of the study is the generation of a new and unprecedented large-scale in silico benchmark dataset accounting for different noise levels and providing a solid basis for unbiased testing of network inference methodologies. Finally, applying our approach to Saccharomyces cerevisiae suggested several new gene interactions with high confidence awaiting experimental validation.
doi:10.1186/1752-0509-7-73
PMCID: PMC4231426  PMID: 23924435
Gene network inference; Reverse engineering; Perturbation experiments; Causal networks; Graph theory; Interaction graphs; Transitive reduction; Transcriptional regulation; Saccharomyces cerevisiae; Yeast
9.  Modeling approaches for qualitative and semi-quantitative analysis of cellular signaling networks 
A central goal of systems biology is the construction of predictive models of bio-molecular networks. Cellular networks of moderate size have been modeled successfully in a quantitative way based on differential equations. However, in large-scale networks, knowledge of mechanistic details and kinetic parameters is often too limited to allow for the set-up of predictive quantitative models.
Here, we review methodologies for qualitative and semi-quantitative modeling of cellular signal transduction networks. In particular, we focus on three different but related formalisms facilitating modeling of signaling processes with different levels of detail: interaction graphs, logical/Boolean networks, and logic-based ordinary differential equations (ODEs). Albeit the simplest models possible, interaction graphs allow the identification of important network properties such as signaling paths, feedback loops, or global interdependencies. Logical or Boolean models can be derived from interaction graphs by constraining the logical combination of edges. Logical models can be used to study the basic input–output behavior of the system under investigation and to analyze its qualitative dynamic properties by discrete simulations. They also provide a suitable framework to identify proper intervention strategies enforcing or repressing certain behaviors. Finally, as a third formalism, Boolean networks can be transformed into logic-based ODEs enabling studies on essential quantitative and dynamic features of a signaling network, where time and states are continuous.
We describe and illustrate key methods and applications of the different modeling formalisms and discuss their relationships. In particular, as one important aspect for model reuse, we will show how these three modeling approaches can be combined to a modeling pipeline (or model hierarchy) allowing one to start with the simplest representation of a signaling network (interaction graph), which can later be refined to logical and eventually to logic-based ODE models. Importantly, systems and network properties determined in the rougher representation are conserved during these transformations.
doi:10.1186/1478-811X-11-43
PMCID: PMC3698152  PMID: 23803171
Interaction graphs; Logical models; Boolean models; Signal transduction; Qualitative modeling; ODE models; EGF signaling
10.  Metabolic network modeling of redox balancing and biohydrogen production in purple nonsulfur bacteria 
BMC Systems Biology  2011;5:150.
Background
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.
Results
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 (Rhodospirillum rubrum, Rhodobacter sphaeroides and Rhodopseudomonas palustris). 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 CO2 yields are fixed constraints, irrespective of the assumption of optimal growth. Furthermore, our model explains quantitatively why a CO2 fixing pathway such as the Calvin cycle is required by PNSB for many substrates (even if CO2 is 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 R. sphaeroides and R. rubrum, 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.
Conclusions
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.
doi:10.1186/1752-0509-5-150
PMCID: PMC3203349  PMID: 21943387
11.  TRANSWESD: inferring cellular networks with transitive reduction 
Bioinformatics  2010;26(17):2160-2168.
Motivation: Distinguishing direct from indirect influences is a central issue in reverse engineering of biological networks because it facilitates detection and removal of false positive edges. Transitive reduction is one approach for eliminating edges reflecting indirect effects but its use in reconstructing cyclic interaction graphs with true redundant structures is problematic.
Results: We present TRANSWESD, an elaborated variant of TRANSitive reduction for WEighted Signed Digraphs that overcomes conceptual problems of existing versions. Major changes and improvements concern: (i) new statistical approaches for generating high-quality perturbation graphs from systematic perturbation experiments; (ii) the use of edge weights (association strengths) for recognizing true redundant structures; (iii) causal interpretation of cycles; (iv) relaxed definition of transitive reduction; and (v) approximation algorithms for large networks. Using standardized benchmark tests, we demonstrate that our method outperforms existing variants of transitive reduction and is, despite its conceptual simplicity, highly competitive with other reverse engineering methods.
Contact: klamt@mpi-magdeburg.mpg.de
Supplementary information: Supplementary data are available at Bioinformatics online.
doi:10.1093/bioinformatics/btq342
PMCID: PMC2922889  PMID: 20605927
12.  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.
PMCID: PMC3169943  PMID: 21918620
apoptosis; Boolean network; cancer therapy; DNA-damage response; NF-κB
13.  Discrete logic modelling as a means to link protein signalling networks with functional analysis of mammalian signal transduction 
Large-scale protein signalling networks are useful for exploring complex biochemical pathways but do not reveal how pathways respond to specific stimuli. Such specificity is critical for understanding disease and designing drugs. Here we describe a computational approach—implemented in the free CNO software—for turning signalling networks into logical models and calibrating the models against experimental data. When a literature-derived network of 82 proteins covering the immediate-early responses of human cells to seven cytokines was modelled, we found that training against experimental data dramatically increased predictive power, despite the crudeness of Boolean approximations, while significantly reducing the number of interactions. Thus, many interactions in literature-derived networks do not appear to be functional in the liver cells from which we collected our data. At the same time, CNO identified several new interactions that improved the match of model to data. Although missing from the starting network, these interactions have literature support. Our approach, therefore, represents a means to generate predictive, cell-type-specific models of mammalian signalling from generic protein signalling networks.
doi:10.1038/msb.2009.87
PMCID: PMC2824489  PMID: 19953085
logical modelling; protein networks; signal transduction
14.  Transforming Boolean models to continuous models: methodology and application to T-cell receptor signaling 
BMC Systems Biology  2009;3:98.
Background
The understanding of regulatory and signaling networks has long been a core objective in Systems Biology. Knowledge about these networks is mainly of qualitative nature, which allows the construction of Boolean models, where the state of a component is either 'off' or 'on'. While often able to capture the essential behavior of a network, these models can never reproduce detailed time courses of concentration levels.
Nowadays however, experiments yield more and more quantitative data. An obvious question therefore is how qualitative models can be used to explain and predict the outcome of these experiments.
Results
In this contribution we present a canonical way of transforming Boolean into continuous models, where the use of multivariate polynomial interpolation allows transformation of logic operations into a system of ordinary differential equations (ODE). The method is standardized and can readily be applied to large networks. Other, more limited approaches to this task are briefly reviewed and compared. Moreover, we discuss and generalize existing theoretical results on the relation between Boolean and continuous models. As a test case a logical model is transformed into an extensive continuous ODE model describing the activation of T-cells. We discuss how parameters for this model can be determined such that quantitative experimental results are explained and predicted, including time-courses for multiple ligand concentrations and binding affinities of different ligands. This shows that from the continuous model we may obtain biological insights not evident from the discrete one.
Conclusion
The presented approach will facilitate the interaction between modeling and experiments. Moreover, it provides a straightforward way to apply quantitative analysis methods to qualitatively described systems.
doi:10.1186/1752-0509-3-98
PMCID: PMC2764636  PMID: 19785753
15.  The Logic of EGFR/ErbB Signaling: Theoretical Properties and Analysis of High-Throughput Data 
PLoS Computational Biology  2009;5(8):e1000438.
The epidermal growth factor receptor (EGFR) signaling pathway is probably the best-studied receptor system in mammalian cells, and it also has become a popular example for employing mathematical modeling to cellular signaling networks. Dynamic models have the highest explanatory and predictive potential; however, the lack of kinetic information restricts current models of EGFR signaling to smaller sub-networks. This work aims to provide a large-scale qualitative model that comprises the main and also the side routes of EGFR/ErbB signaling and that still enables one to derive important functional properties and predictions. Using a recently introduced logical modeling framework, we first examined general topological properties and the qualitative stimulus-response behavior of the network. With species equivalence classes, we introduce a new technique for logical networks that reveals sets of nodes strongly coupled in their behavior. We also analyzed a model variant which explicitly accounts for uncertainties regarding the logical combination of signals in the model. The predictive power of this model is still high, indicating highly redundant sub-structures in the network. Finally, one key advance of this work is the introduction of new techniques for assessing high-throughput data with logical models (and their underlying interaction graph). By employing these techniques for phospho-proteomic data from primary hepatocytes and the HepG2 cell line, we demonstrate that our approach enables one to uncover inconsistencies between experimental results and our current qualitative knowledge and to generate new hypotheses and conclusions. Our results strongly suggest that the Rac/Cdc42 induced p38 and JNK cascades are independent of PI3K in both primary hepatocytes and HepG2. Furthermore, we detected that the activation of JNK in response to neuregulin follows a PI3K-dependent signaling pathway.
Author Summary
The epidermal growth factor receptor (EGFR) signaling pathway is arguably the best-characterized receptor system in mammalian cells and has become a prime example for mathematical modeling of cellular signal transduction. Most of these models are constructed to describe dynamic and quantitative events but, due to the lack of precise kinetic information, focus only on certain regions of the network. Qualitative modeling approaches relying on the network structure provide a suitable way to deal with large-scale networks as a whole. Here, we constructed a comprehensive qualitative model of the EGFR/ErbB signaling pathway with more than 200 interactions reflecting our current state of knowledge. A theoretical analysis revealed important topological and functional properties of the network such as qualitative stimulus-response behavior and redundant sub-structures. Subsequently, we demonstrate how this qualitative model can be used to assess high-throughput data leading to new biological insights: comparing qualitative predictions (such as expected “ups” and “downs” of activation levels) of our model with experimental data from primary human hepatocytes and from the liver cancer cell line HepG2, we uncovered inconsistencies between measurements and model structure. These discrepancies lead to modifications in the EGFR/ErbB signaling network relevant at least for liver biology.
doi:10.1371/journal.pcbi.1000438
PMCID: PMC2710522  PMID: 19662154
16.  Computing paths and cycles in biological interaction graphs 
BMC Bioinformatics  2009;10:181.
Background
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.
Results
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.
Conclusion
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 CellNetAnalyzer framework which can be downloaded for academic use at .
doi:10.1186/1471-2105-10-181
PMCID: PMC2708159  PMID: 19527491
17.  Hypergraphs and Cellular Networks 
PLoS Computational Biology  2009;5(5):e1000385.
doi:10.1371/journal.pcbi.1000385
PMCID: PMC2673028  PMID: 19478865
18.  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.
doi:10.1038/msb4100191
PMCID: PMC2238716  PMID: 18197174
photosynthesis; redox regulation; Rhodobacter sphaeroides; Rhodospirillum rubrum; ubiquinone pool
19.  Host-pathogen systems biology: logical modelling of hepatocyte growth factor and Helicobacter pylori induced c-Met signal transduction 
Background
The hepatocyte growth factor (HGF) stimulates mitogenesis, motogenesis, and morphogenesis in a wide range of tissues, including epithelial cells, on binding to the receptor tyrosine kinase c-Met. Abnormal c-Met signalling contributes to tumour genesis, in particular to the development of invasive and metastatic phenotypes. The human microbial pathogen Helicobacter pylori can induce chronic gastritis, peptic ulceration and more rarely, gastric adenocarcinoma. The H. pylori effector protein cytotoxin associated gene A (CagA), which is translocated via a type IV secretion system (T4SS) into epithelial cells, intracellularly modulates the c-Met receptor and promotes cellular processes leading to cell scattering, which could contribute to the invasiveness of tumour cells. Using a logical modelling framework, the presented work aims at analysing the c-Met signal transduction network and how it is interfered by H. pylori infection, which might be of importance for tumour development.
Results
A logical model of HGF and H. pylori induced c-Met signal transduction is presented in this work. The formalism of logical interaction hypergraphs (LIH) was used to construct the network model. The molecular interactions included in the model were all assembled manually based on a careful meta-analysis of published experimental results. Our model reveals the differences and commonalities of the response of the network upon HGF and H. pylori induced c-Met signalling. As another important result, using the formalism of minimal intervention sets, phospholipase Cγ1 (PLCγ1) was identified as knockout target for repressing the activation of the extracellular signal regulated kinase 1/2 (ERK1/2), a signalling molecule directly linked to cell scattering in H. pylori infected cells. The model predicted only an effect on ERK1/2 for the H. pylori stimulus, but not for HGF treatment. This result could be confirmed experimentally in MDCK cells using a specific pharmacological inhibitor against PLCγ1. The in silico predictions for the knockout of two other network components were also verified experimentally.
Conclusion
This work represents one of the first approaches in the direction of host-pathogen systems biology aiming at deciphering signalling changes brought about by pathogenic bacteria. The suitability of our network model is demonstrated by an in silico prediction of a relevant target against pathogen infection.
doi:10.1186/1752-0509-2-4
PMCID: PMC2254585  PMID: 18194572
20.  A Logical Model Provides Insights into T Cell Receptor Signaling 
PLoS Computational Biology  2007;3(8):e163.
Cellular decisions are determined by complex molecular interaction networks. Large-scale signaling networks are currently being reconstructed, but the kinetic parameters and quantitative data that would allow for dynamic modeling are still scarce. Therefore, computational studies based upon the structure of these networks are of great interest. Here, a methodology relying on a logical formalism is applied to the functional analysis of the complex signaling network governing the activation of T cells via the T cell receptor, the CD4/CD8 co-receptors, and the accessory signaling receptor CD28. Our large-scale Boolean model, which comprises 94 nodes and 123 interactions and is based upon well-established qualitative knowledge from primary T cells, reveals important structural features (e.g., feedback loops and network-wide dependencies) and recapitulates the global behavior of this network for an array of published data on T cell activation in wild-type and knock-out conditions. More importantly, the model predicted unexpected signaling events after antibody-mediated perturbation of CD28 and after genetic knockout of the kinase Fyn that were subsequently experimentally validated. Finally, we show that the logical model reveals key elements and potential failure modes in network functioning and provides candidates for missing links. In summary, our large-scale logical model for T cell activation proved to be a promising in silico tool, and it inspires immunologists to ask new questions. We think that it holds valuable potential in foreseeing the effects of drugs and network modifications.
Author Summary
T-lymphocytes are central regulators of the adaptive immune response, and their inappropriate activation can cause autoimmune diseases or cancer. The understanding of the signaling mechanisms underlying T cell activation is a prerequisite to develop new strategies for pharmacological intervention and disease treatments. However, much of the existing literature on T cell signaling is related to T cell development or to activation processes in transformed T cell lines (e.g., Jurkat), whereas information on non-transformed primary T cells is limited. Here, immunologists and theoreticians have compiled data from the existing literature that stem from analysis of primary T cells. They used this information to establish a qualitative Boolean network that describes T cell activation mechanisms after engagement of the TCR, the CD4/CD8 co-receptors, and CD28. The network comprises 94 nodes and can be extended to facilitate interpretation of new data that emerge from experimental analysis of T cell activation. Newly developed tools and methods allow in silico analysis, and manipulation of the network and can uncover hidden/unforeseen signaling pathways. Indeed, by assessing signaling events controlled by CD28 and the protein tyrosine kinase Fyn, we show that computational analysis of even a qualitative network can provide new and non-obvious signaling pathways which can be validated experimentally.
doi:10.1371/journal.pcbi.0030163
PMCID: PMC1950951  PMID: 17722974
21.  GSMN-TB: a web-based genome-scale network model of Mycobacterium tuberculosis metabolism 
Genome Biology  2007;8(5):R89.
GSMN-TB, a genome-scale metabolic model of M. tuberculosis, was constructed and validated using experimental data.
Background
An impediment to the rational development of novel drugs against tuberculosis (TB) is a general paucity of knowledge concerning the metabolism of Mycobacterium tuberculosis, particularly during infection. Constraint-based modeling provides a novel approach to investigating microbial metabolism but has not yet been applied to genome-scale modeling of M. tuberculosis.
Results
GSMN-TB, a genome-scale metabolic model of M. tuberculosis, was constructed, consisting of 849 unique reactions and 739 metabolites, and involving 726 genes. The model was calibrated by growing Mycobacterium bovis bacille Calmette Guérin in continuous culture and steady-state growth parameters were measured. Flux balance analysis was used to calculate substrate consumption rates, which were shown to correspond closely to experimentally determined values. Predictions of gene essentiality were also made by flux balance analysis simulation and were compared with global mutagenesis data for M. tuberculosis grown in vitro. A prediction accuracy of 78% was achieved. Known drug targets were predicted to be essential by the model. The model demonstrated a potential role for the enzyme isocitrate lyase during the slow growth of mycobacteria, and this hypothesis was experimentally verified. An interactive web-based version of the model is available.
Conclusion
The GSMN-TB model successfully simulated many of the growth properties of M. tuberculosis. The model provides a means to examine the metabolic flexibility of bacteria and predict the phenotype of mutants, and it highlights previously unexplored features of M. tuberculosis metabolism.
doi:10.1186/gb-2007-8-5-r89
PMCID: PMC1929162  PMID: 17521419
22.  Structural and functional analysis of cellular networks with CellNetAnalyzer 
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.
doi:10.1186/1752-0509-1-2
PMCID: PMC1847467  PMID: 17408509
23.  Visual setup of logical models of signaling and regulatory networks with ProMoT 
BMC Bioinformatics  2006;7:506.
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 .
doi:10.1186/1471-2105-7-506
PMCID: PMC1665465  PMID: 17109765
24.  A methodology for the structural and functional analysis of signaling and regulatory networks 
BMC Bioinformatics  2006;7:56.
Background
Structural analysis of cellular interaction networks contributes to a deeper understanding of network-wide interdependencies, causal relationships, and basic functional capabilities. While the structural analysis of metabolic networks is a well-established field, similar methodologies have been scarcely developed and applied to signaling and regulatory networks.
Results
We propose formalisms and methods, relying on adapted and partially newly introduced approaches, which facilitate a structural analysis of signaling and regulatory networks with focus on functional aspects. We use two different formalisms to represent and analyze interaction networks: interaction graphs and (logical) interaction hypergraphs. We show that, in interaction graphs, the determination of feedback cycles and of all the signaling paths between any pair of species is equivalent to the computation of elementary modes known from metabolic networks. Knowledge on the set of signaling paths and feedback loops facilitates the computation of intervention strategies and the classification of compounds into activators, inhibitors, ambivalent factors, and non-affecting factors with respect to a certain species. In some cases, qualitative effects induced by perturbations can be unambiguously predicted from the network scheme. Interaction graphs however, are not able to capture AND relationships which do frequently occur in interaction networks. The consequent logical concatenation of all the arcs pointing into a species leads to Boolean networks. For a Boolean representation of cellular interaction networks we propose a formalism based on logical (or signed) interaction hypergraphs, which facilitates in particular a logical steady state analysis (LSSA). LSSA enables studies on the logical processing of signals and the identification of optimal intervention points (targets) in cellular networks. LSSA also reveals network regions whose parametrization and initial states are crucial for the dynamic behavior.
We have implemented these methods in our software tool CellNetAnalyzer (successor of FluxAnalyzer) and illustrate their applicability using a logical model of T-Cell receptor signaling providing non-intuitive results regarding feedback loops, essential elements, and (logical) signal processing upon different stimuli.
Conclusion
The methods and formalisms we propose herein are another step towards the comprehensive functional analysis of cellular interaction networks. Their potential, shown on a realistic T-cell signaling model, makes them a promising tool.
doi:10.1186/1471-2105-7-56
PMCID: PMC1458363  PMID: 16464248
25.  Computation of elementary modes: a unifying framework and the new binary approach 
BMC Bioinformatics  2004;5:175.
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.
doi:10.1186/1471-2105-5-175
PMCID: PMC544875  PMID: 15527509

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