Direct Response Analysis in cellular signalling networks.

Direct Response Analysis is a general computational tool for quantifying direct functional interactions between components in cellular signalling systems from experimental perturbations and measurements alone. This paper aims to reveal the biological meaning of the direct response coefficients obtained upon applying DRA to simple Michaelis-Menten type proteomic and gene regulatory systems. These systems describe dimer formation and dissociation, protein preduction and decay, and transcription. We derive explicit formulae for the direct response coefficients in terms of biochemical reaction rates, and clarify the potential and limitations of the DRA method. We find that response coefficients are strongly asymmetric, and that they balance persistent characteristics of reactions (e.g. the ratios of on- and off rates) against the time-scales over which these reactions act; fast reactions give stronger response coefficients. The direct interactions between protein species, caused by dimer formation, are effectively negative. We illustrate our results with numerical simulations.