A Hidden Feedback in Signaling Cascades Is Revealed

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

Retroactive signaling in short signaling pathways.

In biochemical signaling pathways without explicit feedback connections, the core signal transduction is usually described as a one-way communication, going from upstream to downstream in a feedforward chain or network of covalent modification cycles. In this paper we explore the possibility of a new type of signaling called retroactive signaling, offered by the recently demonstrated property of retroactivity in signaling cascades. The possibility of retroactive signaling is analysed in the simplest case of the stationary states of a bicyclic cascade of signaling cycles. In this case, we work out the conditions for which variables of the upstream cycle are affected by a change of the total amount of protein in the downstream cycle, or by a variation of the phosphatase deactivating the same protein. Particularly, we predict the characteristic ranges of the downstream protein, or of the downstream phosphatase, for which a retroactive effect can be observed on the upstream cycle variables. Next, we extend the possibility of retroactive signaling in short but nonlinear signaling pathways involving a few covalent modification cycles

Behaviors of cycle 1 as a function of , the total protein in cycle 1.

<p>The kinase for this cycle is denoted by and the phosphatase by . The abscissa are scaled by the characteristic range , cf. Eq. (1). A) Two cases are considered for cycle 1, which is said deactivated if and activated if . B-C) Increase of the intermediate complex when cycle 1 is respectively deactivated or activated. D-E) Variations of activated and non-activated proteins in the two cases and . The graphs were obtained by solving Eqs.(16)-(18) with the following parameters : , M, M, ; panels (B-D) : M.; panels (C-E) : M.</p

Motifs of short signaling pathways illustrating the concept of retroactive signaling in (A) a 2-cycle cascade and (B) in a 3-cycle cascade.

<p>Thick arrows indicate the direction of signaling.</p

Retroactive signaling in multi-cycle pathways.

<p>M for all to , except for (A)–(C) M, and for (D) M. (A) is varied in the range [M] such that goes from to . M, M, M, MM, M. (B) same but is varied on the range and M. (C) identical to (A) except that cycle 2 is deactivated, with MM. (D) M, M, M, M, M, M, MM, MM.</p

Phosphorylated fraction of protein 2 as a function of 2 control parameters of the downstream cycle 1, namely and .

<p>The graphs are obtained by solving Eqs.(16)-(18) with the following parameters : , M, M; On the left figures (B,D,F,H) cycle 2 is assumed deactivated, with MM. These values are swapped for the right figures (C,E,G,I) where cycle 2 is assumed activated. Panels (B,C,F,G) : cycle 1 is either deactivated (M), or activated (M). On panels (D,E,H,I), phosphatase is varied from to (so that varies from 0 to 2). Panels (D,H) : for the upper curve the total protein 1 is M and for the lower curve M. Panel (E,I) : for the upper curve the total protein 1 is M and for the lower curve M.</p