Computation Of Minimal Cut Sets Research Articles

Speeding up the core algorithm for the dual calculation of minimal cut sets in large metabolic networks

BackgroundThe concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. However, the calculation of MCS in genome-scale metabolic models is a complex computational problem. The development of duality-based algorithms in the last years allowed the enumeration of thousands of MCS in genome-scale networks by solving mixed-integer linear problems (MILP). A recent advancement in this field was the introduction of the MCS2 approach. In contrast to the Farkas-lemma-based dual system used in earlier studies, the MCS2 approach employs a more condensed representation of the dual system based on the nullspace of the stoichiometric matrix, which, due to its reduced dimension, holds promise to further enhance MCS computations.ResultsIn this work, we introduce several new variants and modifications of duality-based MCS algorithms and benchmark their effects on the overall performance. As one major result, we generalize the original MCS2 approach (which was limited to blocking the operation of certain target reactions) to the most general case of MCS computations with arbitrary target and desired regions. Building upon these developments, we introduce a new MILP variant which allows maximal flexibility in the formulation of MCS problems and fully leverages the reduced size of the nullspace-based dual system. With a comprehensive set of benchmarks, we show that the MILP with the nullspace-based dual system outperforms the MILP with the Farkas-lemma-based dual system speeding up MCS computation with an averaged factor of approximately 2.5. We furthermore present several simplifications in the formulation of constraints, mainly related to binary variables, which further enhance the performance of MCS-related MILP. However, the benchmarks also reveal that some highly condensed formulations of constraints, especially on reversible reactions, may lead to worse behavior when compared to variants with a larger number of (more explicit) constraints and involved variables.ConclusionsOur results further enhance the algorithmic toolbox for MCS calculations and are of general importance for theoretical developments as well as for practical applications of the MCS framework.

Direct calculation of minimal cut sets involving a specific reaction knock-out.

The concept of Minimal Cut Sets (MCSs) is used in metabolic network modeling to describe minimal groups of reactions or genes whose simultaneous deletion eliminates the capability of the network to perform a specific task. Previous work showed that MCSs where closely related to Elementary Flux Modes (EFMs) in a particular dual problem, opening up the possibility to use the tools developed for computing EFMs to compute MCSs. Until recently, however, there existed no method to compute an EFM with some specific characteristic, meaning that, in the case of MCSs, the only strategy to obtain them was to enumerate them using, for example, the standard K-shortest EFMs algorithm. In this work, we adapt the recently developed theory to compute EFMs satisfying several constraints to the calculation of MCSs involving a specific reaction knock-out. Importantly, we emphasize that not all the EFMs in the dual problem correspond to real MCSs, and propose a new formulation capable of correctly identifying the MCS wanted. Furthermore, this formulation brings interesting insights about the relationship between the primal and the dual problem of the MCS computation. A Matlab-Cplex implementation of the proposed algorithm is available as a supplementary material fplanes@ceit.es Supplementary data are available at Bioinformatics online.

Fast Computation of Minimal Cut Sets in Metabolic Networks with a Berge Algorithm that Utilizes Binary Bit Pattern Trees

Minimal cut sets are a valuable tool for analyzing metabolic networks and for identifying optimal gene intervention strategies by eliminating unwanted metabolic functions and keeping desired functionality. Minimal cut sets rely on the concept of elementary flux modes, which are sets of indivisible metabolic pathways under steady-state condition. However, the computation of minimal cut sets is nontrivial, as even medium-sized metabolic networks with just 100 reactions easily have several hundred million elementary flux modes. We developed a minimal cut set tool that implements the well-known Berge algorithm and utilizes a novel approach to significantly reduce the program run time by using binary bit pattern trees. By using the introduced tree approach, the size of metabolic models that can be analyzed and optimized by minimal cut sets is pushed to new and considerably higher limits.

Element substitution algorithm for general two-terminal network reliability analyses

The computation of the reliability of two-terminal networks is a classical reliability problem. For these types of problems, one is interested, from a general perspective, in obtaining the probability that two specific nodes can communicate. This paper presents a holistic algorithm for the analysis of general networks that follow a two-terminal rationale. The algorithm is based on a set replacement approach and an element inheritance strategy that effectively obtains the minimal cut sets associated with a given network. The vast majority of methods available for obtaining two-terminal reliability are generally based on assumptions about the performance of the network. Some methods assume network components can be in one of two states: (i) either completely failed; or (ii) perfectly functioning, others usually assume that nodes are perfectly reliable and thus, these methods have to be complemented or transformed to account for node failure, and the remaining methods assume minimal cut sets can be readily computed in order to analyze more complex network and component behavior. The algorithm presented in this paper significantly differs from previous approaches available in the literature in the sense that it is based on a predecessor matrix and an element substitution technique that allows for the exact computation of minimal cut sets and the immediate inclusion of node failure without any changes to the pseudo-code. Several case networks are used to validate and illustrate the algorithms.

Computation of minimal cut sets of fault trees: Experiences with three different methods

There are several different methods by which the minimal cut sets of a given fault tree can be computed. In this paper we shall discuss and compare three such methods. Two analytical methods, a bottom-up and a top-down algorithm, and a simulative method will be considered. Finally, a new analytical algorithm for the evaluation of the minimal cut sets is proposed.