A Hidden Feedback in Signaling Cascades Is Revealed

Abstract

Cycles involving covalent modification of proteins are key components of the intracellular signaling machinery. Each cycle is comprised of two interconvertable forms of a particular protein. A classic signaling pathway is structured by a chain or cascade of basic cycle units in such a way that the activated protein in one cycle promotes the activation of the next protein in the chain, and so on. Starting from a mechanistic kinetic description and using a careful perturbation analysis, we have derived, to our knowledge for the first time, a consistent approximation of the chain with one variable per cycle. The model we derive is distinct from the one that has been in use in the literature for several years, which is a phenomenological extension of the Goldbeter-Koshland biochemical switch. Even though much has been done regarding the mathematical modeling of these systems, our contribution fills a gap between existing models and, in doing so, we have unveiled critical new properties of this type of signaling cascades. A key feature of our new model is that a negative feedback emerges naturally, exerted between each cycle and its predecessor. Due to this negative feedback, the system displays damped temporal oscillations under constant stimulation and, most important, propagates perturbations both forwards and backwards. This last attribute challenges the widespread notion of unidirectionality in signaling cascades. Concrete examples of applications to MAPK cascades are discussed. All these properties are shared by the complete mechanistic description and our simplified model, but not by previously derived phenomenological models of signaling cascades. Cellular signaling is carried out by a complex network of interactions. A structure that is found commonly in signaling pathways is a sequence of on-off cycles between two states of the same protein, referred to as a cascade. By analyzing and reducing the basic kinetic equations of this system, we have constructed a new mathematical model of an intracellular signaling cascade. It is widely accepted that information travels both outside-in and inside-out in signaling pathways. Conversely, cascades, even while being main components of those pathways, have been so far understood as structures where signal transmission occurs in a manner analogous to a domino effect: the information flows in only one direction. Adding explicit connections linking a particular level with an upstream location has been the way bidirectional propagation has been explained so far. In other words, up to now, unidirectional cascades would allow bidirectional propagation only when embedded in more complicated circuits. The proposed model shows that a cascade can naturally exhibit bidirectional propagation without invoking extra re-wiring. This result inspires novel interpretations of experimental data; since signaling pathways are usually reconstructed from such data, this outcome could have far-reaching implications in the understanding of cell signaling.