Detecting Structural Invariants in Biological Reaction Networks

Abstract

The detection and analysis of structural invariants in cellular reaction networks is of central importance to achieve a more comprehensive understanding of metabolism. In this work, we review different kinds of structural invariants in reaction networks and their Petri net-based representation. In particular, we discuss invariants that can be obtained from the left and right null spaces of the stoichiometric matrix which correspond to conserved moieties (P-invariants) and elementary flux modes (EFMs, minimal T-invariants). While conserved moieties can be used to detect stoichiometric inconsistencies in reaction networks, EFMs correspond to a mathematically rigorous definition of the concept of a biochemical pathway. As outlined here, EFMs allow to devise strategies for strain improvement, to assess the robustness of metabolic networks subject to perturbations, and to analyze the information flow in regulatory and signaling networks. Another important aspect addressed by this review is the limitation of metabolic pathway analysis using EFMs to small or medium-scale reaction networks. We discuss two recently introduced approaches to circumvent these limitations. The first is an algorithm to enumerate a subset of EFMs in genome-scale metabolic networks starting from the EFM with the least number of reactions. The second approach, elementary flux pattern analysis, allows to analyze pathways through specific subsystems of genome-scale metabolic networks. In contrast to EFMs, elementary flux patterns much more accurately reflect the metabolic capabilities of a subsystem of metabolism as well as its integration into the entire system.

Drug Design for KEGG Pathways with Answer Set Programming

“…We are concerned with the extension of structural approaches by rules implemented in answer set programming. As we will show, this greatly enhances the capabilities of structural analyses without the requirement of kinetic information, and in general without the problems of combinatorial explosion [3,12].…”

“…Such information requires extensive measurements and drug studies, but then can also be obtained from sources such as chemical and metabolic pathway databases [9]. Different bioinformatical approaches exploit these, starting from more topological and structural approaches, such as static network analysis [7], to more dynamical analytical methods, such as flux balance analysis with its different flavours, e.g., elementary mode analysis and extreme pathways [3,12]. The YanaSquare system [13] …”

Computing Signal Transduction in Signaling Networks modeled as Boolean Networks, Petri Nets, and Hypergraphs

“…In the case that there is a sequence of transitions realizing a vector y, a T-invariant y corresponds to a sequence of transitions that does not change the given marking [77]. In the framework of metabolic networks, minimal T-invariants are counterparts to elementary flux modes [102,7], although elementary flux modes are more general due to the fact that reactions are allowed to be reversible. A place invariant is the counterpart of moiety conservation [7].…”

“…In the framework of metabolic networks, minimal T-invariants are counterparts to elementary flux modes [102,7], although elementary flux modes are more general due to the fact that reactions are allowed to be reversible. A place invariant is the counterpart of moiety conservation [7]. As previously mentioned, read-arcs are not reflected in the incidence matrix.…”

Generalized Topologies: Hypergraphs, Chemical Reactions, and Biological Evolution

“…Chemical organizations, that is, closed and self-maintaining subsets of H [27,18], furthermore, are closely related to the limit set of the corresponding reaction kinetics [61]. The most useful of these structural features are related to algebraic invariants that can be expressed in terms of S, see [4] for a recent review.…”