  Understanding under which conditions the increase of systems complexity is
evolutionary advantageous, and how this trend is related to the modulation of
the intrinsic noise, are fascinating issues of utmost importance for synthetic
and systems biology. To get insights into these matters, we analyzed chemical
reaction networks with different topologies and degrees of complexity,
interacting or not with the environment. We showed that the global level of
fluctuations at the steady state, as measured by the sum of the Fano factors of
the number of molecules of all species, is directly related to the topology of
the network. For systems with zero deficiency, this sum is constant and equal
to the rank of the network. For higher deficiencies, we observed an increase or
decrease of the fluctuation levels according to the values of the reaction
fluxes that link internal species, multiplied by the associated stoichiometry.
We showed that the noise is reduced when the fluxes all flow towards the
species of higher complexity, whereas it is amplified when the fluxes are
directed towards lower complexity species.
