  The composition of cellular metabolism is different across species. Empirical
data reveal that bacterial species contain similar numbers of metabolic
reactions but that the cross-species popularity of reactions is so heterogenous
that some reactions are found in all the species while others are in just few
species, characterized by a power-law distribution with the exponent one.
Introducing an evolutionary model concretizing the stochastic recruitment of
chemical reactions into the metabolism of different species at different times
and their inheritance to descendants, we demonstrate that the exponential
growth of the number of species containing a reaction and the saturated
recruitment rate of brand-new reactions lead to the empirically identified
power-law popularity distribution. Furthermore, the structural characteristics
of metabolic networks and the species' phylogeny in our simulations agree well
with empirical observations.
