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A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems

Blanchini, Franco; Franco, Elisa and Giordano, Giulia LU (2014) In Bulletin of Mathematical Biology 76(10). p.2542-2569
Abstract

Molecular systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas’ conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite... (More)

Molecular systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas’ conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochemical networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of positive and negative cycles in the associated sign graph. Most realistic examples of biochemical networks fall in the gray area of systems in which both positive and negative cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.

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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Cycles, Feedback loops, Multistationarity, Oscillator, Stability, Structural properties
in
Bulletin of Mathematical Biology
volume
76
issue
10
pages
28 pages
publisher
Springer
external identifiers
  • Scopus:84918806520
ISSN
0092-8240
DOI
10.1007/s11538-014-0023-y
language
English
LU publication?
no
id
2785de78-3563-46cb-afbb-ea21913bb9af
date added to LUP
2016-07-06 15:26:45
date last changed
2016-10-13 05:11:27
@misc{2785de78-3563-46cb-afbb-ea21913bb9af,
  abstract     = {<p>Molecular systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas’ conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochemical networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of positive and negative cycles in the associated sign graph. Most realistic examples of biochemical networks fall in the gray area of systems in which both positive and negative cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.</p>},
  author       = {Blanchini, Franco and Franco, Elisa and Giordano, Giulia},
  issn         = {0092-8240},
  keyword      = {Cycles,Feedback loops,Multistationarity,Oscillator,Stability,Structural properties},
  language     = {eng},
  month        = {10},
  number       = {10},
  pages        = {2542--2569},
  publisher    = {ARRAY(0x8e6c1f8)},
  series       = {Bulletin of Mathematical Biology},
  title        = {A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems},
  url          = {http://dx.doi.org/10.1007/s11538-014-0023-y},
  volume       = {76},
  year         = {2014},
}