Algorithmic algebraic model checking IV: Characterization of metabolic networks

Venkatesh Mysore, Bhubaneswar Mishra

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra, model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as symbolic variables. This paper examines how to specialize this framework to metabolic control analysis (MCA) involving many reactions operating at many dissimilar time-scales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semi-algebraic hybrid automata could be unraveled using powerful techniques from computational real algebraic geometry. More specifically, the resulting algebraic model checking techniques were found to be suitable for biochemical networks modeled using general mass action (GMA) based ODEs. This paper scrutinizes how the special properties of metabolic networks - a subclass of the biochemical networks previously handled - can be exploited to gain improvement in computational efficiency. The paper introduces a general framework for performing symbolic temporal reasoning over metabolic network hybrid automata that handles both GMA-based equilibrium estimation and flux balance analysis (FBA). While algebraic polynomial equations over ℚ[x 1,..., x n] can be symbolically solved using Gröbner bases or Wu-Ritt characteristic sets, the FBA-based estimation can be performed symbolically by rephrasing the algebraic optimization problem as a quantifier elimination problem. Effectively, an approximate hybrid automaton that simulates the metabolic network is derived, and is thus amenable to manipulation by the algebraic model checking techniques previously described in the AAMC papers.

Original languageEnglish (US)
Title of host publicationAlgebraic Biology - Second International Conference, AB 2007, Proceedings
Pages170-184
Number of pages15
Volume4545 LNCS
StatePublished - 2007
Event2nd International Conference on Algebraic Biology, AB 2007 - Castle of Hagenberg, Austria
Duration: Jul 2 2007Jul 4 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4545 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other2nd International Conference on Algebraic Biology, AB 2007
CountryAustria
CityCastle of Hagenberg
Period7/2/077/4/07

Fingerprint

Metabolic Network
Model checking
Metabolic Networks and Pathways
Model Checking
Hybrid Automata
Biochemical Networks
Dynamical systems
Fluxes
Real Algebraic Geometry
Hybrid Dynamical Systems
Characteristic Set
Temporal Reasoning
Quantifier Elimination
Algebraic Polynomial
Computational efficiency
Polynomial equation
Algebra
Algebraic Equation
Unknown Parameters
Computational Efficiency

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Mysore, V., & Mishra, B. (2007). Algorithmic algebraic model checking IV: Characterization of metabolic networks. In Algebraic Biology - Second International Conference, AB 2007, Proceedings (Vol. 4545 LNCS, pp. 170-184). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4545 LNCS).

Algorithmic algebraic model checking IV : Characterization of metabolic networks. / Mysore, Venkatesh; Mishra, Bhubaneswar.

Algebraic Biology - Second International Conference, AB 2007, Proceedings. Vol. 4545 LNCS 2007. p. 170-184 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4545 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mysore, V & Mishra, B 2007, Algorithmic algebraic model checking IV: Characterization of metabolic networks. in Algebraic Biology - Second International Conference, AB 2007, Proceedings. vol. 4545 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4545 LNCS, pp. 170-184, 2nd International Conference on Algebraic Biology, AB 2007, Castle of Hagenberg, Austria, 7/2/07.
Mysore V, Mishra B. Algorithmic algebraic model checking IV: Characterization of metabolic networks. In Algebraic Biology - Second International Conference, AB 2007, Proceedings. Vol. 4545 LNCS. 2007. p. 170-184. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Mysore, Venkatesh ; Mishra, Bhubaneswar. / Algorithmic algebraic model checking IV : Characterization of metabolic networks. Algebraic Biology - Second International Conference, AB 2007, Proceedings. Vol. 4545 LNCS 2007. pp. 170-184 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{f244bac6c2c449a9b1bc438fe43ef02f,
title = "Algorithmic algebraic model checking IV: Characterization of metabolic networks",
abstract = "A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra, model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as symbolic variables. This paper examines how to specialize this framework to metabolic control analysis (MCA) involving many reactions operating at many dissimilar time-scales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semi-algebraic hybrid automata could be unraveled using powerful techniques from computational real algebraic geometry. More specifically, the resulting algebraic model checking techniques were found to be suitable for biochemical networks modeled using general mass action (GMA) based ODEs. This paper scrutinizes how the special properties of metabolic networks - a subclass of the biochemical networks previously handled - can be exploited to gain improvement in computational efficiency. The paper introduces a general framework for performing symbolic temporal reasoning over metabolic network hybrid automata that handles both GMA-based equilibrium estimation and flux balance analysis (FBA). While algebraic polynomial equations over ℚ[x 1,..., x n] can be symbolically solved using Gr{\"o}bner bases or Wu-Ritt characteristic sets, the FBA-based estimation can be performed symbolically by rephrasing the algebraic optimization problem as a quantifier elimination problem. Effectively, an approximate hybrid automaton that simulates the metabolic network is derived, and is thus amenable to manipulation by the algebraic model checking techniques previously described in the AAMC papers.",
author = "Venkatesh Mysore and Bhubaneswar Mishra",
year = "2007",
language = "English (US)",
isbn = "9783540734321",
volume = "4545 LNCS",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
pages = "170--184",
booktitle = "Algebraic Biology - Second International Conference, AB 2007, Proceedings",

}

TY - GEN

T1 - Algorithmic algebraic model checking IV

T2 - Characterization of metabolic networks

AU - Mysore, Venkatesh

AU - Mishra, Bhubaneswar

PY - 2007

Y1 - 2007

N2 - A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra, model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as symbolic variables. This paper examines how to specialize this framework to metabolic control analysis (MCA) involving many reactions operating at many dissimilar time-scales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semi-algebraic hybrid automata could be unraveled using powerful techniques from computational real algebraic geometry. More specifically, the resulting algebraic model checking techniques were found to be suitable for biochemical networks modeled using general mass action (GMA) based ODEs. This paper scrutinizes how the special properties of metabolic networks - a subclass of the biochemical networks previously handled - can be exploited to gain improvement in computational efficiency. The paper introduces a general framework for performing symbolic temporal reasoning over metabolic network hybrid automata that handles both GMA-based equilibrium estimation and flux balance analysis (FBA). While algebraic polynomial equations over ℚ[x 1,..., x n] can be symbolically solved using Gröbner bases or Wu-Ritt characteristic sets, the FBA-based estimation can be performed symbolically by rephrasing the algebraic optimization problem as a quantifier elimination problem. Effectively, an approximate hybrid automaton that simulates the metabolic network is derived, and is thus amenable to manipulation by the algebraic model checking techniques previously described in the AAMC papers.

AB - A series of papers, all under the title of Algorithmic Algebraic Model Checking (AAMC), has sought to combine techniques from algorithmic algebra, model checking and dynamical systems to examine how a biochemical hybrid dynamical system can be made amenable to temporal analysis, even when the initial conditions and unknown parameters may only be treated as symbolic variables. This paper examines how to specialize this framework to metabolic control analysis (MCA) involving many reactions operating at many dissimilar time-scales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semi-algebraic hybrid automata could be unraveled using powerful techniques from computational real algebraic geometry. More specifically, the resulting algebraic model checking techniques were found to be suitable for biochemical networks modeled using general mass action (GMA) based ODEs. This paper scrutinizes how the special properties of metabolic networks - a subclass of the biochemical networks previously handled - can be exploited to gain improvement in computational efficiency. The paper introduces a general framework for performing symbolic temporal reasoning over metabolic network hybrid automata that handles both GMA-based equilibrium estimation and flux balance analysis (FBA). While algebraic polynomial equations over ℚ[x 1,..., x n] can be symbolically solved using Gröbner bases or Wu-Ritt characteristic sets, the FBA-based estimation can be performed symbolically by rephrasing the algebraic optimization problem as a quantifier elimination problem. Effectively, an approximate hybrid automaton that simulates the metabolic network is derived, and is thus amenable to manipulation by the algebraic model checking techniques previously described in the AAMC papers.

UR - http://www.scopus.com/inward/record.url?scp=38149013099&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=38149013099&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:38149013099

SN - 9783540734321

VL - 4545 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 170

EP - 184

BT - Algebraic Biology - Second International Conference, AB 2007, Proceedings

ER -