Abstract
We analyze the stochastic dynamics of genetic regulatory networks
using a system of nonlinear differential equations. The system of S-functions is applied to capture the role of RNA polymerase in
the transcription-translation mechanism. Using probabilistic
properties of chemical rate equations, we derive a system of
stochastic differential equations which are analytically tractable
despite the high dimension of the regulatory network. Using
stationary solutions of these equations, we explain the apparently
paradoxical results of some recent time-course microarray
experiments where mRNA transcription levels are found to only
weakly correlate with the corresponding transcription rates.
Combining analytical and simulation approaches, we determine the
set of relationships between the size of the regulatory network,
its structural complexity, chemical variability, and spectrum of
oscillations. In particular, we show that temporal variability of
chemical constituents may decrease while complexity of the network
is increasing. This finding provides an insight into the nature of
“functional determinism” of such an inherently stochastic system
as genetic regulatory network.