title: Open cascades as simple solutions to providing ultrasensitivity and adaptation in cellular signaling.
abstract: Cell signaling is achieved predominantly by reversible phosphorylation-dephosphorylation reaction cascades. Up until now, circuits conferring adaptation have all required the presence of a cascade with some type of closed topology: negative-feedback loop with a buffering node, or incoherent feed-forward loop with a proportioner node. In this paper--using Goldbeter and Koshland-type expressions--we propose a differential equation model to describe a generic, open signaling cascade that elicits an adaptation response. This is accomplished by coupling N phosphorylation-dephosphorylation cycles unidirectionally, without any explicit feedback loops. Using this model, we show that as the length of the cascade grows, the steady states of the downstream cycles reach a limiting value. In other words, our model indicates that there are a minimum number of cycles required to achieve a maximum in sensitivity and amplitude in the response of a signaling cascade. We also describe for the first time that the phenomenon of ultrasensitivity can be further subdivided into three sub-regimes, separated by sharp stimulus threshold values: OFF, OFF-ON-OFF, and ON. In the OFF-ON-OFF regime, an interesting property emerges. In the presence of a basal amount of activity, the temporal evolution of early cycles yields damped peak responses. On the other hand, the downstream cycles switch rapidly to a higher activity state for an extended period of time, prior to settling to an OFF state (OFF-ON-OFF). This response arises from the changing dynamics between a feed-forward activation module and dephosphorylation reactions. In conclusion, our model gives the new perspective that open signaling cascades embedded in complex biochemical circuits may possess the ability to show a switch-like adaptation response, without the need for any explicit feedback circuitry.
authors.affiliation: Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 55455, USA.
authors.forename: Jeyaraman
authors.initials: J
authors.lastname: Srividhya
authors.forename: Yongfeng
authors.initials: Y
authors.lastname: Li
authors.forename: Joseph R
authors.initials: JR
authors.lastname: Pomerening
mesh_terms: D000222:Adaptation, Physiological; D000818:Animals; D003198:Computer Simulation; D006801:Humans; D007700:Kinetics; D020935:MAP Kinase Signaling System; D020928:Mitogen-Activated Protein Kinases / Q000378:metabolism; D008954:Models, Biological; D010766:Phosphorylation; D011506:Proteins / Q000378:metabolism*; D015398:Signal Transduction
chemical_list: D011506:Proteins; D020928:Mitogen-Activated Protein Kinases