Equilibria for Large Metabolic Systems and the LIFE Approach

McQuade, Sean T.; An, Zheming; Merrill, Nathaniel J.; Abrams, Ruth E.; Azer, Karim; Piccoli, Benedetto

doi:10.23919/acc.2018.8431443

Cited by 2 publications

(5 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Next we consider systems that contain both intakes and excretions. It was shown in [18] that if intakes and excretions are added to a graph satisfying the conditions of Proposition 4 then rank(S(x)) = n. We extend this result to get: Proposition 5. Consider the system (3) satisfying Assumption (A) and let G be the the associated graph.…”

Section: Special Life Systemsmentioning

confidence: 62%

“…We extend one of the results of [18] to get: Proposition 4. Consider the system (3) with no intakes nor excretions satisfying Assumption (A) and let G be the the associated graph.…”

Section: Special Life Systemsmentioning

confidence: 88%

“…Proof. It was shown in [18] that if G is weakly connected and contains an intake vertex then rank(S(x)) = n. The same argument from [18] can be also used for an excretion vertex and so if G is weakly connected and contains an excretion vertex we also have rank(S(x)) = n. In the case where G is not weakly connected S(x) can be rewritten as a block diagonal matrix…”

Section: Special Life Systemsmentioning

confidence: 99%

“…A recent advancement in QSP modeling called Linear-in-Flux-Expressions (LIFE) is a method of analyzing systems of Ordinary Differential Equations (ODEs) [19,18]. Originally, LIFE was designed to analyze metabolic systems, which are composed of Fluxes and Metabolites.…”

mentioning

confidence: 99%

“…To implement LIFE on a metabolic network, the network must be written as a directed graph [18]. The edges of the graph represent the reaction rates (fluxes), and the vertices represent quantities of chemical compounds (metabolites).…”

mentioning

confidence: 99%

See 4 more Smart Citations

Stability of metabolic networks via Linear-in-Flux-Expressions

Merrill¹,

An²,

McQuade³

et al. 2019

Networks &Amp; Heterogeneous Media

Self Cite

View full text Add to dashboard Cite

The methodology named LIFE (Linear-in-Flux-Expressions) was developed with the purpose of simulating and analyzing large metabolic systems. With LIFE, the number of model parameters is reduced by accounting for correlations among the parameters of the system. Perturbation analysis on LIFE systems results in less overall variability of the system, leading to results that more closely resemble empirical data. These systems can be associated to graphs, and characteristics of the graph give insight into the dynamics of the system.This work addresses two main problems: 1. for fixed metabolite levels, find all fluxes for which the metabolite levels are an equilibrium, and 2. for fixed fluxes, find all metabolite levels which are equilibria for the system. We characterize the set of solutions for both problems, and show general results relating stability of systems to the structure of the associated graph. We show that there is a structure of the graph necessary for stable dynamics. Along with these general results, we show how stability analysis from the fields of network flows, compartmental systems, control theory and Markov chains apply to LIFE systems.

show abstract

Section: Special Life Systemsmentioning

confidence: 62%

“…We extend one of the results of [18] to get: Proposition 4. Consider the system (3) with no intakes nor excretions satisfying Assumption (A) and let G be the the associated graph.…”

Section: Special Life Systemsmentioning

confidence: 88%