## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS

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:
optimization.
,
Network modeling
,
duality principle
,
flux balance analysis
,
cellular metabolism

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]