The interplay between discrete noise and nonlinear chemical kinetics in   a signal amplification cascade
  We used various analytical and numerical techniques to elucidate signal propagation in a small enzymatic cascade which is subjected to external and internal noise. The nonlinear character of catalytic reactions, which underlie protein signal transduction cascades, renders stochastic signaling dynamics in cytosol biochemical networks distinct from the usual description of stochastic dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade which underlies many important protein signaling pathways, we demonstrated that the commonly used techniques such as the linear noise approximation and the Langevin equation become inadequate when the number of proteins becomes too low. Consequently, we developed a new analytical approximation, based on mixing the generating function and distribution function approaches, to the solution of the master equation that describes nonlinear chemical signaling kinetics for this important class of biochemical reactions. Our techniques work in a much wider range of protein number fluctuations than the methods used previously. We found that under certain conditions the burst-phase noise may be injected into the downstream signaling network dynamics, resulting possibly in unusually large macroscopic fluctuations. In addition to computing first and second moments, which is the goal of commonly used analytical techniques, our new approach provides the full time-dependent probability distributions of the colored non-Gaussian processes in a nonlinear signal transduction cascade. 
Yueheng Lan, Garegin A. Papoian