MOTIVATION: Many techniques have been developed to infer Boolean regulations from a prior knowledge network (PKN) and experimental data. Existing methods are able to reverse-engineer Boolean regulations for transcriptional and signaling networks, but they fail to infer regulations that control metabolic networks. RESULTS: We present a novel approach to infer Boolean rules for metabolic regulation from time-series data and a PKN. Our method is based on a combination of answer set programming and linear programming. By solving both combinatorial and linear arithmetic constraints, we generate candidate Boolean regulations that can reproduce the given data when coupled to the metabolic network. We evaluate our approach on a core regulated metabolic network and show how the quality of the predictions depends on the available kinetic, fluxomics or transcriptomics time-series data. AVAILABILITY AND IMPLEMENTATION: Software available at https://github.com/bioasp/merrin. SUPPLEMENTARY INFORMATION: Supplementary data are available at https://doi.org/10.5281/zenodo.6670164.

MOTIVATION: Minimal cut sets (MCSs) for metabolic networks are sets of reactions which, if they are removed from the network, prevent a target reaction from carrying flux. To compute MCSs different methods exist, which may fail to find sufficiently many MCSs for larger genome-scale networks. RESULTS: Here we introduce irreversible minimal cut sets (iMCSs). These are MCSs that consist of irreversible reactions only. The advantage of iMCSs is that they can be computed by projecting the flux cone of the metabolic network on the set of irreversible reactions, which usually leads to a smaller cone. Using oriented matroid theory, we show how the projected cone can be computed efficiently and how this can be applied to find iMCSs even in large genome-scale networks. AVAILABILITY AND IMPLEMENTATION: Software is freely available at https://sourceforge.net/projects/irreversibleminimalcutsets/. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Constraint-based analysis has become a widely used method to study metabolic networks. While some of the associated algorithms can be applied to genome-scale network reconstructions with several thousands of reactions, others are limited to small or medium-sized models. In 2015, Erdrich et al. introduced a method called NetworkReducer, which reduces large metabolic networks to smaller subnetworks, while preserving a set of biological requirements that can be specified by the user. Already in 2001, Burgard et al. developed a mixed-integer linear programming (MILP) approach for computing minimal reaction sets under a given growth requirement. RESULTS: Here we present an MILP approach for computing minimum subnetworks with the given properties. The minimality (with respect to the number of active reactions) is not guaranteed by NetworkReducer, while the method by Burgard et al. does not allow specifying the different biological requirements. Our procedure is about 5-10 times faster than NetworkReducer and can enumerate all minimum subnetworks in case there exist several ones. This allows identifying common reactions that are present in all subnetworks, and reactions appearing in alternative pathways. CONCLUSIONS: Applying complex analysis methods to genome-scale metabolic networks is often not possible in practice. Thus it may become necessary to reduce the size of the network while keeping important functionalities. We propose a MILP solution to this problem. Compared to previous work, our approach is more efficient and allows computing not only one, but even all minimum subnetworks satisfying the required properties.

Elementary flux mode (EM) computation is an important tool in the constraint-based analysis of genome-scale metabolic networks. Due to the combinatorial complexity of these networks, as well as the advances in the level of detail to which they can be reconstructed, an exhaustive enumeration of all EMs is often not practical. Therefore, in recent years interest has shifted towards searching EMs with specific properties. We present a novel method that allows computing EMs containing a given set of target reactions. This generalizes previous algorithms where the set of target reactions consists of a single reaction. In the one-reaction case, our method compares favorably to the previous approaches. In addition, we present several applications of our algorithm for computing EMs containing two target reactions in genome-scale metabolic networks. A software tool implementing the algorithms described in this paper is available at https://sourceforge.net/projects/caefm.

MOTIVATION: Flux variability analysis (FVA) is an important tool to further analyse the results obtained by flux balance analysis (FBA) on genome-scale metabolic networks. For many constraint-based models, FVA identifies unboundedness of the optimal flux space. This reveals that optimal flux solutions with net flux through internal biochemical loops are feasible, which violates the second law of thermodynamics. Such unbounded fluxes may be eliminated by extending FVA with thermodynamic constraints. RESULTS: We present a new algorithm for efficient flux variability (and flux balance) analysis with thermodynamic constraints, suitable for analysing genome-scale metabolic networks. We first show that FBA with thermodynamic constraints is NP-hard. Then we derive a theoretical tractability result, which can be applied to metabolic networks in practice. We use this result to develop a new constraint programming algorithm Fast-tFVA for fast FVA with thermodynamic constraints (tFVA). Computational comparisons with previous methods demonstrate the efficiency of the new method. For tFVA, a speed-up of factor 30-300 is achieved. In an analysis of genome-scale metabolic networks in the BioModels database, we found that in 485 of 716 networks, additional irreversible or fixed reactions could be detected. AVAILABILITY AND IMPLEMENTATION: Fast-tFVA is written in C++ and published under GPL. It uses the open source software SCIP and libSBML. There also exists a Matlab interface for easy integration into Matlab. Fast-tFVA is available from page.mi.fu-berlin.de/arnem/fast-tfva.html. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Flux coupling analysis (FCA) has become a useful tool in the constraint-based analysis of genome-scale metabolic networks. FCA allows detecting dependencies between reaction fluxes of metabolic networks at steady-state. On the one hand, this can help in the curation of reconstructed metabolic networks by verifying whether the coupling between reactions is in agreement with the experimental findings. On the other hand, FCA can aid in defining intervention strategies to knock out target reactions. RESULTS: We present a new method F2C2 for FCA, which is orders of magnitude faster than previous approaches. As a consequence, FCA of genome-scale metabolic networks can now be performed in a routine manner. CONCLUSIONS: We propose F2C2 as a fast tool for the computation of flux coupling in genome-scale metabolic networks. F2C2 is freely available for non-commercial use at https://sourceforge.net/projects/f2c2/files/.

This paper is concerned with the analysis of labeled Thomas networks using discrete time series. It focuses on refining the given edge labels and on assessing the data quality. The results are aimed at being exploitable for experimental design and include the prediction of new activatory or inhibitory effects of given interactions and yet unobserved oscillations of specific components in between specific sampling intervals. On the formal side, we generalize the concept of edge labels and introduce a discrete time series interpretation. This interpretation features two original concepts: 1) Incomplete measurements are admissible, and 2) it allows qualitative assumptions about the changes in gene expression by means of monotonicity. On the computational side, we provide a Python script, erda.py, that automates the suggested workflow by model checking and constraint satisfaction. We illustrate the workflow by investigating the yeast network IRMA.

MOTIVATION: The reconstruction of metabolic networks at the genome scale has allowed the analysis of metabolic pathways at an unprecedented level of complexity. Elementary flux modes (EFMs) are an appropriate concept for such analysis. However, their number grows in a combinatorial fashion as the size of the metabolic network increases, which renders the application of EFMs approach to large metabolic networks difficult. Novel methods are expected to deal with such complexity. RESULTS: In this article, we present a novel optimization-based method for determining a minimal generating set of EFMs, i.e. a convex basis. We show that a subset of elements of this convex basis can be effectively computed even in large metabolic networks. Our method was applied to examine the structure of pathways producing lysine in Escherichia coli. We obtained a more varied and informative set of pathways in comparison with existing methods. In addition, an alternative pathway to produce lysine was identified using a detour via propionyl-CoA, which shows the predictive power of our novel approach. AVAILABILITY: The source code in C++ is available upon request.

BACKGROUND: Flux coupling analysis (FCA) is a useful method for finding dependencies between fluxes of a metabolic network at steady-state. FCA classifies reactions into subsets (called coupled reaction sets) in which activity of one reaction implies activity of another reaction. Several approaches for FCA have been proposed in the literature. RESULTS: We introduce a new FCA algorithm, FFCA (Feasibility-based Flux Coupling Analysis), which is based on checking the feasibility of a system of linear inequalities. We show on a set of benchmarks that for genome-scale networks FFCA is faster than other existing FCA methods. CONCLUSIONS: We present FFCA as a new method for flux coupling analysis and prove it to be faster than existing approaches. A corresponding software tool is freely available for non-commercial use at http://www.bioinformatics.org/ffca/.

We introduce branch and infer, a unifying framework for integer linear programming and finite domain constraint programming. We use this framework to compare the two approaches with respect to their modeling and solving capabilities, to introduce symbolic constraint abstractions into integer programming, and to discuss possible combinations of the two approaches.

Narrowing is a universal unification procedure for equational theories defined by a,canonical term rewriting system. In its original form it is extremely inefficient. Therefore, many optimizations have been proposed during the last years. In this pap