Relaxation oscillations and hierarchy of feedbacks in MAPK signaling

Abstract

We formulated a computational model for a MAPK signaling cascade downstream of the EGF receptor to investigate how interlinked positive and negative feedback loops process EGF signals into ERK pulses of constant amplitude but dose-dependent duration and frequency. A positive feedback loop involving RAS and SOS, which leads to bistability and allows for switch-like responses to inputs, is nested within a negative feedback loop that encompasses RAS and RAF, MEK, and ERK that inhibits SOS via phosphorylation. This negative feedback, operating on a longer time scale, changes switch-like behavior into oscillations having a period of 1 hour or longer. Two auxiliary negative feedback loops, from ERK to MEK and RAF, placed downstream of the positive feedback, shape the temporal ERK activity profile but are dispensable for oscillations. Thus, the positive feedback introduces a hierarchy among negative feedback loops, such that the effect of a negative feedback depends on its position with respect to the positive feedback loop. Furthermore, a combination of the fast positive feedback involving slow-diffusing membrane components with slower negative feedbacks involving faster diffusing cytoplasmic components leads to local excitation/global inhibition dynamics, which allows the MAPK cascade to transmit paracrine EGF signals into spatially non-uniform ERK activity pulses.

A Flexible Approach for Context‐Dependent Assessment of Quantitative Systems Pharmacology Models

“…Although context influences how and to what extent each major assessment area is addressed, all areas should be considered and discussed. Figure shows how contextual considerations can influence the degree of rigor required in model assessment and indicates the different context surrounding example models of cancer signaling pathways . Here, we discuss how context influences model assessment for two of these studies …”

“…Ultimately, the approaches taken in each study enabled the exploration of differential responsiveness and resistance in the corresponding contexts. Numerous other modeling studies (from Huang and Ferrell to Kochańczyk et al …”

“…Figure 1 shows how contextual considerations can influence the degree of rigor required in model assessment and indicates the different context surrounding example models of cancer signaling pathways. [6][7][8][9] Here, we discuss how context influences model assessment for two of these studies. 6,7 Context Many cancers display alterations in mitogen activated protein kinase (MAPK), PI3K, and other intracellular signaling pathways that promote tumor growth.…”

“…Ultimately, the approaches taken in each study enabled the exploration of differential responsiveness and resistance in the corresponding contexts. Numerous other modeling studies (from Huang and Ferrell 8 to Kochańczyk et al 9 ) have investigated MAPK pathway topology, signal propagation, feedback and crosstalk, and dynamical features. Such studies often perform detailed dynamical and parameter sensitivity analyses, but did not always include nor require extensive model calibration and validation given the exploratory intent of the studies, further illustrating how goals and context help influence assessment strategy.…”

Limits to the rate of information transmission through MAPK pathway

“…Such capacity has been recently demonstrated in the mammalian mitogen-activated protein kinase (MAPK) pathway, where in response to extracellular EGF (input) of constant amplitude, ERK (effector) is activated in pulses with constant amplitude but frequency and pulse duration determined by concentrations of EGF [3]. In the MAPK system, the amplitude-tofrequency transcoding (also termed modulation in engineering sciences) is enabled by a particular topology of feedback loops and associated timescales [4].…”