Flux tope analysis: studying the coordination of reaction directions in metabolic networks

Abstract

MotivationElementary flux mode (EFM) analysis allows an unbiased description of metabolic networks in terms of minimal pathways (involving a minimal set of reactions). To date, the enumeration of EFMs is impracticable in genome-scale metabolic models. In a complementary approach, we introduce the concept of a flux tope (FT), involving a maximal set of reactions (with fixed directions), which allows one to study the coordination of reaction directions in metabolic networks and opens a new way for EFM enumeration.ResultsA FT is a (nontrivial) subset of the flux cone specified by fixing the directions of all reversible reactions. In a consistent metabolic network (without unused reactions), every FT contains a ‘maximal pathway’, carrying flux in all reactions. This decomposition of the flux cone into FTs allows the enumeration of EFMs (of individual FTs) without increasing the problem dimension by reaction splitting. To develop a mathematical framework for FT analysis, we build on the concepts of sign vectors and hyperplane arrangements. Thereby, we observe that FT analysis can be applied also to flux optimization problems involving additional (inhomogeneous) linear constraints. For the enumeration of FTs, we adapt the reverse search algorithm and provide an efficient implementation. We demonstrate that (biomass-optimal) FTs can be enumerated in genome-scale metabolic models of B.cuenoti and E.coli, and we use FTs to enumerate EFMs in models of M.genitalium and B.cuenoti.Availability and implementationThe source code is freely available at https://github.com/mpgerstl/FTA.Supplementary information Supplementary data are available at Bioinformatics online.

Maximum entropy and population heterogeneity in continuous cell cultures

“…The constrains ( 1 – 5 ) define a convex polytope of feasible metabolic states [ 41 , 42 ] that we denote by . Each point within this space consists of coordinates which fully specify the metabolic state of a cell in the model.…”

Metabolic Games

“…Other concepts worth exploring are the phenotypic phase plane put forth by Edwards et al [62] and the flux tope by Gerstl et al [63]. A phenotypic phase plane is defined by the uptake rates of two nutrients.…”

Essentiality of local topology and regulation in kinetic metabolic modeling

“…Interestingly, this characteristic also has been utilized to identify the nonredundant functional units of metabolism, i.e. the minimal metabolic pathway or flux tope (Bordbar et al, 2014c; Gerstl et al, 2018). A topological orthogonality principles was successfully used to designed the bioengineering strains with minimal interaction between desired product-associated pathways and metabolic components related to biomass synthesis (Pandit et al, 2017).…”

“…By applying SLB decomposition, the (coupled) element reactions within identified SLBs display high coexpression among multiple growth conditions, indicating coordinated activation of topologically highly coupled reactions. Interestingly, similar approaches have been applied in identifying the non-redundant local functional units of metabolism, i.e., the minimal metabolic pathway or flux tope 35,57 . A topological orthogonality principle was successfully used to design bioengineering strains with minimal interaction between desired product-associated pathways and metabolic components related to biomass synthesis 58 .…”