  Theoretical and experimental studies have shown that the fluctuations of in
vivo systems break the fluctuation-dissipation theorem. One can thus ask what
information is contained in the correlation functions of protein concentrations
and how they relate to the response of the reactive network to a perturbation.
Answers to these questions are of prime importance to extract meaningful
parameters from the in vivo fluorescence correlation spectroscopy data. In this
paper we study the fluctuations of the concentration of a reactive species
involved in a cyclic network that is in a non-equilibrium steady state
perturbed by a noisy force, taking into account both the breaking of detailed
balance and extrinsic noises. Using a generic model for the network and the
extrinsic noise, we derive a Chemical Langevin Equation that describes the
dynamics of the system, we determine the expressions of the correlation
functions of the concentrations, estimate the deviation of the
fluctuation-dissipation theorem and the range of parameters in which an
effective temperature can be defined.
