  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.
