Reducing the master equations for noisy chemical reactions

A reduced description for noisy chemical reactions in small systems is presented. By applying the projection operator formalism to the chemical master equation, we show that even when the number of molecules of an intermediate chemical species is small, its elimination from the description is possible provided that its characteristic time scale is short. The resulting master equation of the reduced system includes additional terms of a diffusive kind. The characteristic time of the eliminated chemical species contributes toward the fluctuations of the downstream chemical species, as well as the dispersion of the eliminated component does. (C) 2003 American Institute of Physics.