  We describe a mechanism for pronounced biochemical oscillations, relevant to
microscopic systems, such as the intracellular environment. This mechanism
operates for reaction schemes which, when modeled using deterministic rate
equations, fail to exhibit oscillations for any values of rate constants. The
mechanism relies on amplification of the underlying stochasticity of reaction
kinetics within a narrow window of frequencies. This amplification allows
fluctuations to beat the central limit theorem, having a dominant effect even
though the number of molecules in the system is relatively large. The mechanism
is quantitatively studied within simple models of self-regulatory gene
expression, and glycolytic oscillations.
