Discrete and Continuous Dynamical Systems - Series A (DCDS-A)

Why optimal states recruit fewer reactions in metabolic networks

Pages: 2937 - 2950, Volume 32, Issue 8, August 2012      doi:10.3934/dcds.2012.32.2937

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Joo Sang Lee - Department of Physics & Astronomy, Northwestern University, Evanston, IL 60208, United States (email)
Takashi Nishikawa - Department of Mathematics, Clarkson University, Potsdam, NY 13699, United States (email)
Adilson E. Motter - Department of Physics & Astronomy and Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL 60208, United States (email)

Abstract: The metabolic network of a living cell involves several hundreds or thousands of interconnected biochemical reactions. Previous research has shown that under realistic conditions only a fraction of these reactions is concurrently active in any given cell. This is partially determined by nutrient availability, but is also strongly dependent on the metabolic function and network structure. Here, we establish rigorous bounds showing that the fraction of active reactions is smaller (rather than larger) in metabolic networks evolved or engineered to optimize a specific metabolic task, and we show that this is largely determined by the presence of thermodynamically irreversible reactions in the network. We also show that the inactivation of a certain number of reactions determined by irreversibility can generate a cascade of secondary reaction inactivations that propagates through the network. The mathematical results are complemented with numerical simulations of the metabolic networks of the bacterium Escherichia coli and of human cells, which show, counterintuitively, that even the maximization of the total reaction flux in the network leads to a reduced number of active reactions.

Keywords:  Network modeling, cellular metabolism, duality principle, flux balance analysis, optimization.
Mathematics Subject Classification:  Primary: 92C42; Secondary: 90C35.

Received: May 2011;      Revised: August 2011;      Available Online: March 2012.