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.
Highlights
Covalent modification cycles are one of the major intracellular signaling mechanisms, both in prokaryotic and eukaryotic organisms [1]
External stimuli that produces a change in the activity of the converting enzymes, shifts the activation state of the target protein, creating a departure from steady state which can propagate through the cascade
Powerful concepts from control theory can be applied successfully to the study of signaling cascades [14]. These concepts have proven its utility in many contexts, this kind of schematic representation implicitly conveys the idea that a signaling cascade is only a feed-forward chain in which signal transmission is analogous to a domino effect [32,33]
Summary
Covalent modification cycles are one of the major intracellular signaling mechanisms, both in prokaryotic and eukaryotic organisms [1]. Complex signaling occurs through networks of signaling pathways made up of chains or cascades of such cycles, in which the activated protein in one cycle promotes the activation of the protein in the link of the chain In this way, an input signal injected at one end of the pathway can propagate traveling through its building-blocks to elicit one or more effects at a downstream location. Examples of covalent modification are methylation-demethylation, activation-inactivation of GTP-binding proteins and, probably the most studied process, phosphorylation-dephosphorylation (PD) [1,2]. In such cycles, a signaling protein is activated by the addition of a chemical group and inactivated by its removal. External stimuli that produces a change in the activity of the converting enzymes, shifts the activation state of the target protein, creating a departure from steady state which can propagate through the cascade
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