  We propose the concepts of distributed robustness and r-robustness, well
adapted to functional genetics. Then we discuss the robustness of the
relaxation time using a chemical reaction description of genetic and signalling
networks. First, we obtain the following result for linear networks: for large
multiscale systems with hierarchical distribution of time scales the variance
of the inverse relaxation time (as well as the variance of the stationary rate)
is much lower than the variance of the separate constants. Moreover, it can
tend to 0 faster than 1/n, where n is the number of reactions. We argue that
similar phenomena are valid in the nonlinear case as well. As a numerical
illustration we use a model of signalling network that can be applied to
important transcription factors such as NFkB.
