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Modes and cuts in metabolic networks: complexity and algorithms.

Vicente Acuña¹, Flavio Chierichetti, Vincent Lacroix

¹Université de Lyon, F-69000, Lyon, France.

|August 30, 2008

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This study analyzes the computational complexity of metabolic network analysis. Finding elementary modes is generally easy, but counting them and finding minimum reaction cut sets are computationally hard problems.

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Area of Science:

Systems Biology
Computational Biology
Metabolic Engineering

Background:

Constraint-based modeling offers insights into metabolism using simplified assumptions like steady-state and irreversibility, avoiding kinetic parameters.
Elementary modes (EMs) represent minimal functional subsystems and are central to this methodology.
Efficient computation of EMs is crucial but remains a bottleneck in metabolic studies.

Purpose of the Study:

To systematically investigate the computational complexity of optimization problems related to metabolic modes.
To analyze the complexity of finding, counting, and utilizing elementary modes and reaction cut sets.

Main Methods:

Complexity analysis of network consistency problems.
Establishment of complexity for finding and counting elementary modes.
Analysis of minimum reaction cut set computation complexity.
Development of approximation algorithms and verification tests for reaction cuts.

Main Results:

Most network consistency problems are solvable in polynomial time.
Finding a single elementary mode is easy; finding a specific EM is hard.
Counting elementary modes is sharpP-complete; minimum reaction cut set computation is hard.
A polynomial approximation algorithm for minimum reaction cut sets and an efficient verification test for reaction cuts are presented.

Conclusions:

While finding elementary modes can be computationally tractable, counting them and identifying reaction cut sets present significant computational challenges.
The developed algorithms and tests offer practical solutions for analyzing metabolic networks and overcoming computational limitations.
This work provides a deeper understanding of the complexity landscape for constraint-based metabolic modeling.