  The impact of random fluctuations on the dynamical behavior a complex
biological systems is a longstanding issue, whose understanding would shed
light on the evolutionary pressure that nature imposes on the intrinsic noise
levels and would allow rationally designing synthetic networks with controlled
noise. Using the It\=o stochastic differential equation formalism, we performed
both analytic and numerical analyses of several model systems containing
different molecular species in contact with the environment and interacting
with each other through mass-action kinetics. These systems represent for
example biomolecular oligomerization processes, complex-breakage reactions,
signaling cascades or metabolic networks. For chemical reaction networks with
zero deficiency values, which admit a detailed- or complex-balanced steady
state, all molecular species are uncorrelated. The number of molecules of each
species follow a Poisson distribution and their Fano factors, which measure the
intrinsic noise, are equal to one. Systems with deficiency one have an
unbalanced non-equilibrium steady state and a non-zero S-flux, defined as the
flux flowing between the complexes multiplied by an adequate stoichiometric
coefficient. In this case, the noise on each species is reduced if the flux
flows from the species of lowest to highest complexity, and is amplified is the
flux goes in the opposite direction. These results are generalized to systems
of deficiency two, which possess two independent non-vanishing S-fluxes, and we
conjecture that a similar relation holds for higher deficiency systems.
