Flux Coupling and the Objective Functions’ Length in EFMs

Abstract

Structural analysis of constraint-based metabolic network models attempts to find the network’s properties by searching for subsets of suitable modes or Elementary Flux Modes (EFMs). One useful approach is based on Linear Program (LP) techniques, which introduce an objective function to convert the stoichiometric and thermodynamic constraints into a linear program (LP), using additional constraints to generate different nontrivial modes. This work introduces FLFS-FC (Fixed Length Function Sampling with Flux Coupling), a new approach to increase the efficiency of generation of large sets of different EFMs for the network. FLFS-FC is based on the importance of the length of the objective functions used in the associated LP problem and the imposition of additional negative constraints. Our proposal overrides some of the known drawbacks associated with the EFM extraction, such as the appearance of unfeasible problems or multiple repeated solutions arising from different LP problems.

On the representativeness and stability of a set of EFMs

“…Let us start with a network in which all reactions are non-blocked and irreversible. To do so, all blocked reactions are deleted and any reversible reaction is decoupled into two new reactions representing the possible directions ( Guil et al 2020a ). Reactions that do not come from this decoupling process are called (originally) irreversible.…”

“…Inside this family, there are methods using mixed-integer linear optimization (MILP) methods as in the well-known k -shortest algorithm ( De Figueiredo et al 2009 ). Other methods rely on linear optimization (LP) methods as CASOP ( Bohl et al 2010 ), the one proposed by Marashi et al (2012) ( Tabe-Bordbar and Marashi 2013 ), treeEFM ( Pey et al 2015 ), FLFS-FC ( Guil et al 2020a ), or EFM-Ta ( Guil et al 2020b ). Finally, some methods use a hybrid approach between MILP and LP as alternate integer linear programming (AILP) ( Song et al 2017 ).…”

“…These repeated EFMs appear because posing different optimization problems does not guarantee that the corresponding EFMs are also different. Different strategies can be used to ensure a variety of computed EFMs: deleting random reactions ( Tabe-Bordbar and Marashi 2013 ), blocking reactions from the last EFM obtained ( Bohl et al 2010 ), doing so recursively by using trees ( Pey et al 2015 ), or blocking those reactions that appear in those EFMs with a high rate of repetitions ( Guil et al 2020a ). By additionally restricting the number of steps performed by the optimization method ( Guil et al 2020b ), reasonable efficiency rates can be achieved even in large networks, measured in terms of time or as the quotient between the number of optimization problems solved and the number of EFMs obtained (see Pey et al 2015 , Guil et al 2020b ).…”

The Staphylococcus Epidermidis RP62A Metabolic Network: Validation and Intervention Strategies

“…The restrictions on the sign of the flux of the irreversible reactions are called the thermodynamic constraint (it will be supposed that all irreversible reactions always occur in the positive direction [12])…”

“…The obtained solution is a network mode. Using different additional constraints and functions, different scenarios in the metabolic network can be emulated (see [12]).…”