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WIREs Syst Biol Med
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Understanding the mTOR signaling pathway via mathematical modeling

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The mechanistic target of rapamycin (mTOR) is a central regulatory pathway that integrates a variety of environmental cues to control cellular growth and homeostasis by intricate molecular feedbacks. In spite of extensive knowledge about its components, the molecular understanding of how these function together in space and time remains poor and there is a need for Systems Biology approaches to perform systematic analyses. In this work, we review the recent progress how the combined efforts of mathematical models and quantitative experiments shed new light on our understanding of the mTOR signaling pathway. In particular, we discuss the modeling concepts applied in mTOR signaling, the role of multiple feedbacks and the crosstalk mechanisms of mTOR with other signaling pathways. We also discuss the contribution of principles from information and network theory that have been successfully applied in dissecting design principles of the mTOR signaling network. We finally propose to classify the mTOR models in terms of the time scale and network complexity, and outline the importance of the classification toward the development of highly comprehensive and predictive models. WIREs Syst Biol Med 2017, 9:e1379. doi: 10.1002/wsbm.1379 This article is categorized under: Biological Mechanisms > Cell Signaling Models of Systems Properties and Processes > Mechanistic Models
Overview of the major mTOR signaling network. Shown are core components of PI3K/AKT/mTOR pathways and the pathways that influence the mTOR signaling pathway. Depicted are also critical inputs regulating mTORC1 and mTORC2 including growth factors such as insulin, epidermal growth factor (EGF), tumor necrosis factor (TNF), wingless type integration site family (WNT) ligands and amino acids. Once active, mTORC1 regulates protein synthesis, energy metabolism, lipogenesis, and inhibits autophagy and lysosome biogenesis. mTORC2 promotes cytoskeletal organization, cell survival, and longevity. Green edges denote feedback loops in the core mTOR signaling pathway. For more information, see the text.
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Scatter plot of mTOR models according to their complexity and time window of observation. The complexity axis refers to the number of molecules and/or genes considered in the model. Depicted are only models supported by experimental time series data. The fast time scale from seconds to minutes is associated with activation and deactivation mechanisms based on post‐translational modifications, while the longer time scales incorporate processes such as protein synthesis and degradation. Most models of mTOR signaling pathways are valid in time scale of minutes and mainly describe the early phase of the mTOR signaling. Interestingly, majority of crosstalk models are grouped in this range and belong to the models with higher complexity. Most models that exploit information‐theory approaches belong to the long time scale group.
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Simplified mTOR signaling network with interactions inferred from modeling approaches. Depicted is the crosstalk of mTOR with MAPK signaling pathway. Red dashed edges numbered as circled labels represent the interactions and nodes inferred from modeling approaches. Label 1: PI3K dependent regulation of mTORC2 which is independent of negative feedback from S6K to IRS1. Label 2: Positive regulation of AMPK by IRS1. Label 3: Negative regulation of S6K by mTORC1. Label 4: Gab1 was found to be an important adaptor protein between insulin and MAPK signaling that plays a role of a nonlinear amplifier of mitogenic responses.
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Methods used in mTOR signaling network modeling. (a) Converting a network into ODEs. At the first step, the network is converted into biochemical reactions and further into a set of ODEs, assuming mass action kinetics. (b) Modeling networks using two state Boolean logic. (c) Steps required to get a useful model. Before the model calibration, there is a poor correlation between the data obtained by the model and the experimental data. The calibrated model can successfully reproduce experimental data and gives more accurate predictions than the uncalibrated model. (d) Types of bifurcation observed in biological systems. Illustrative example is given in term of sensitivity of protein phosphorylation to insulin concentrations. Drug treatment may drive the system to one of these modes. Insulin controllable modes: switch like (left) and toggle switch (middle) and uncontrollable one switch mode (right). (e) Three temporal patterns of the stimuli that have widely been used to elucidate the properties of mTOR pathway are illustrated. (f) IFFL (incoherent feed‐forward loop) has been found as an optimal mechanism to explain S6K activation by AKT. (g) Example of the pathway that exhibits a low‐pass filter property that could transmits slowly occurring changes in upstream regulators to downstream effectors more efficiently than fast occurring changes in upstream regulators.
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