Abstract
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.
Highlights
The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing anddesigning metabolic networks
We found that the duality-based mixed-integer linear problems (MILP) algorithm presented by Miraskarshahi et al [21] did not fully leverage the smaller dual network introduced by the authors and mainly represented a small modification of the traditional MILP formulation [7], which is based on the duality approach of Ballerstein et al [15]
(2) Afterwards we investigate whether the dimension reduction of the MILP via the kernel-based integration of the desired region in the MILP [Eqs. (17) and (18)] leads to runtime improvements
Summary
The concept of minimal cut sets (MCS) has become an important mathematical framework for analyzing and (re)designing metabolic networks. The approach of MCS is very flexible as it allows the user to specify complex phenotypes to be blocked (e.g. growth or phenotypes with low yield of a certain product) and to account for (desired or protected) phenotypes that should be kept feasible when blocking the targeted phenotype For this reason, and due to a number of useful theoretical properties, the concept of MCS has been used for various applications, for example, to compute synthetic lethals [7, 8], to find targets in cancer cells [8], to identify metabolic engineering strategies (computational strain design) [9,10,11,12], or to study the robustness of metabolic networks [13]
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