Thermodynamic constraints for identifying elementary flux modes

2018 ◽  
Vol 46 (3) ◽  
pp. 641-647 ◽  
Author(s):  
Sabine Peres ◽  
Stefan Schuster ◽  
Philippe Dague
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Gibbs Free Energy ◽  
Pathway Analysis ◽  
Metabolic Pathway ◽  
Metabolic Pathway Analysis ◽  
Combinatorial Explosion ◽  
Elementary Flux Modes ◽  
The Real ◽  
Large Systems

Metabolic pathway analysis is a key method to study metabolism and the elementary flux modes (EFMs) is one major concept allowing one to analyze the network in terms of minimal pathways. Their practical use has been hampered by the combinatorial explosion of their number in large systems. The EFMs give the possible pathways at steady state, but the real pathways are limited by biological constraints. In this review, we display three different methods that integrate thermodynamic constraints in terms of Gibbs free energy in the EFMs computation.

scholarly journals Metabolic Pathway Analysis in the Presence of Biological Constraints

Computation ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 111
Author(s):  
Philippe Dague
Keyword(s):  
Steady State ◽  
Pathway Analysis ◽  
Metabolic Pathway ◽  
Solution Space ◽  
Mathematical Structure ◽  
Polyhedral Cone ◽  
Metabolic Pathway Analysis ◽  
Regulatory Constraints ◽  
Double Description Method ◽  
Biological Constraints

Metabolic pathway analysis is a key method to study a metabolism in its steady state, and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain in particular those of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genome-scale systems. The EFs give the possible pathways in a steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results on the mathematical structure and geometrical characterization of the solution space in the presence of such biological constraints (which is no longer a convex polyhedral cone or a convex polyhedron) and revisit the concept of EFMs and EFs in this framework. We show that most of the results depend only on very general properties of compatibility of constraints with vector signs: either sign-invariance, satisfied by regulatory constraints, or sign-monotonicity (a stronger property), satisfied by thermodynamic and kinetic constraints. We show in particular that the solution space for sign-monotone constraints is a union of particular faces of the original polyhedral cone or polyhedron and that EFs still coincide with EFMs and are just those of the original EFs that satisfy the constraint, and we show how to integrate their computation efficiently in the double description method, the most widely used method in the tools dedicated to EFs computation. We show that, for sign-invariant constraints, the situation is more complex: the solution space is a disjoint union of particular semi-open faces (i.e., without some of their own faces of lesser dimension) of the original polyhedral cone or polyhedron and, if EFs are still those of the original EFs that satisfy the constraint, their computation cannot be incrementally integrated into the double description method, and the result is not true for EFMs, that are in general strictly more numerous than those of the original EFMs that satisfy the constraint.

scholarly journals From elementary flux modes to elementary flux vectors: Metabolic pathway analysis with arbitrary linear flux constraints

2017 ◽  
Vol 13 (4) ◽  
pp. e1005409 ◽  
Author(s):  
Steffen Klamt ◽  
Georg Regensburger ◽  
Matthias P. Gerstl ◽  
Christian Jungreuthmayer ◽  
Stefan Schuster ◽  
...  
Keyword(s):  
Pathway Analysis ◽  
Metabolic Pathway ◽  
Metabolic Pathway Analysis ◽  
Elementary Flux Modes

scholarly journals Metabolic pathway analysis in presence of biological constraints

2020 ◽  
Author(s):  
Philippe Dague
Keyword(s):  
Steady State ◽  
Pathway Analysis ◽  
Metabolic Pathway ◽  
Mathematical Structure ◽  
Genetic Network ◽  
Metabolic Pathway Analysis ◽  
Regulatory Constraints ◽  
Double Description Method ◽  
Biological Constraints ◽  
Monotone Constraints

AbstractMetabolic pathway analysis is a key method to study metabolism at steady state and the elementary fluxes (EFs) is one major concept allowing one to analyze the network in terms of non-decomposable pathways. The supports of the EFs contain in particular the supports of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genome-scale, systems. The EFs give the possible pathways at steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results about the mathematical structure and geometrical characterization of the solutions space in presence of such biological constraints and revisit the concept of EFMs and EFs in this framework. We show that most of those results depend only on a very general property of compatibility of the constraints with sign: either sign-based for regulatory constraints or sign-monotone (a stronger property) for thermodynamic and kinetic constraints. We show in particular that EFs for sign-monotone constraints are just those original EFs that satisfy the constraint and show how to efficiently integrate their computation in the double description method, the most widely used method in the tools dedicated to EFMs computation.

scholarly journals PySCeSToolbox: a collection of metabolic pathway analysis tools

2017 ◽  
Vol 34 (1) ◽  
pp. 124-125 ◽  
Author(s):  
Carl D Christensen ◽  
Jan-Hendrik S Hofmeyr ◽  
Johann M Rohwer
Keyword(s):  
Pathway Analysis ◽  
Metabolic Pathway ◽  
Metabolic Pathway Analysis ◽  
Analysis Tools

scholarly journals Verification of Equation for Evaluating Dislocation Density during Steady-state Creep of Metals

2017 ◽  
Vol 6 (2) ◽  
pp. 20 ◽  
Author(s):  
Manabu Tamura
Keyword(s):  
Free Energy ◽  
Steady State ◽  
Dislocation Density ◽  
Shear Modulus ◽  
Strain Rate ◽  
Gibbs Free Energy ◽  
Steady State Creep ◽  
Austenitic Steels ◽  
Exponential Factor ◽  
Delta G

Ninety-two sets of observed dislocation densities for crept specimens of 21 types of ferritic/martensitic and austenitic steels, Al, W, Mo, and Mg alloys, Cu, and Ti including germanium single crystals were collected to verify an equation for evaluating the dislocation density during steady-state creep proposed by Tamura and Abe (2015). The activation energy, Qex, activation volume, Vex, and Larson–Miller constant, Cex, were calculated from the creep data. Using these parameter constants, the strain rate, and the temperature dependence of the shear modulus, a correction term, Gamma, was back-calculated from the observed dislocation density for each material. Gamma is defined in the present paper as a function of the temperature dependences of both the shear modulus and pre-exponential factor of the strain rate. The values of Gamma range from −394 to 233  and average 2.1 KJmol-1, which is a value considerably lower than the average value of Qex (410.4 KJmol-1), and values of Gamma are mainly within the range from 0 to 50 KJmol-1. The change in Gibbs free energy, Delta G, for creep deformation is obtained using the calculated value of , and the empirical relation Delta G~Delta GD is found, where Delta GD is the change in Gibbs free energy for self-diffusion of the main componential element of each material. Experimental data confirm the validity of the evaluation equation for the dislocation density.

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