  Motivated by the study of rare events for a typical genetic switching model
in systems biology, in this paper we aim to establish the general two-scale
large deviations for chemical reaction systems. We build a formal approach to
explicitly obtain the large deviation rate functionals for the considered
two-scale processes based upon the second-quantization path integral technique.
We get three important types of large deviation results when the underlying two
times scales are in three different regimes. This is realized by singular
perturbation analysis to the rate functionals obtained by path integral. We
find that the three regimes possess the same deterministic mean-field limit but
completely different chemical Langevin approximations. The obtained results are
natural extensions of the classical large volume limit for chemical reactions.
We also discuss its implication on the single-molecule Michaelis-Menten
kinetics. Our framework and results can be applied to understand general
multi-scale systems including diffusion processes.
