  Understanding relationship between noisy dynamics and biological network
architecture is a fundamentally important question, particularly in order to
elucidate how cells encode and process information. We analytically and
numerically investigate general network architectural conditions that are
necessary to generate stochastic amplified and coherent oscillations. We
enumerate all possible topologies of coupled negative feedbacks in the
underlying biochemical networks with three components, negative feedback loops,
and mass action kinetics. Using the linear noise approximation to analytically
obtain the time-dependent solution of the master equation and derive the
algebraic expression of power spectra, we find that (a) all networks with
coupled negative feedbacks are capable of generating stochastic amplified and
coherent oscillations; (b) networks with a single negative feedback are better
stochastic amplified and coherent oscillators than those with multiple coupled
negative feedbacks; (c) multiple timescale difference among the kinetic rate
constants is required for stochastic amplified and coherent oscillations.
