Details:
Title  Algorithmic algebraic model checking. IV: Characterization of metabolic networks.  Author(s)  Bud Mishra, Venkatesh Mysore  Type  Book, Chapter in Book, Conference Proceeding  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 timescales. In the earlier AAMC papers, it has been shown that the dynamics of various biochemical semialgebraic 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 GMAbased 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 WuRitt characteristic sets, the FBAbased 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.  ISBN  9783540734321/pbk 
URL 
http://link.springer.com/chapter/10.1007%2F9783540734338_13 
Language  English  Pages  170184  Publisher  Berlin: Springer  Year  2007  Edition  0  Translation 
No  Refereed 
No 
