title: Long signaling cascades tend to attenuate retroactivity.
abstract: Signaling pathways consisting of phosphorylation/dephosphorylation cycles with no explicit feedback allow signals to propagate not only from upstream to downstream but also from downstream to upstream due to retroactivity at the interconnection between phosphorylation/dephosphorylation cycles. However, the extent to which a downstream perturbation can propagate upstream in a signaling cascade and the parameters that affect this propagation are presently unknown. Here, we determine the downstream-to-upstream steady-state gain at each stage of the signaling cascade as a function of the cascade parameters. This gain can be made smaller than 1 (attenuation) by sufficiently fast kinase rates compared to the phosphatase rates and/or by sufficiently large Michaelis-Menten constants and sufficiently low amounts of total stage protein. Numerical studies performed on sets of biologically relevant parameters indicated that ∼50% of these parameters could give rise to amplification of the downstream perturbation at some stage in a three-stage cascade. In an n-stage cascade, the percentage of parameters that lead to an overall attenuation from the last stage to the first stage monotonically increases with the cascade length n and reaches 100% for cascades of length at least 6.
authors.affiliation: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, Michigan, USA.
authors.forename: Hamid R
authors.initials: HR
authors.lastname: Ossareh
authors.forename: Alejandra C
authors.initials: AC
authors.lastname: Ventura
authors.forename: Sofia D
authors.initials: SD
authors.lastname: Merajver
authors.forename: Domitilla
authors.initials: D
authors.lastname: Del Vecchio
mesh_terms: D003198:Computer Simulation; D025461:Feedback, Physiological; D008954:Models, Biological; D010766:Phosphorylation; D015398:Signal Transduction