Mathematical Methods for Modeling Chemical Reaction Networks

Carden, J; Pantea, Casian; Crăciun, Gheorghe; Machiraju, Raghu; Mallick, Parag

doi:10.1101/070326

Cited by 4 publications

(1 citation statement)

References 18 publications

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“…4.13 Exploiting the structure of biochemical reaction networks, a theory that goes back to the seminal works of (46)(47)(48) allows to derive sufficient conditions on the reaction network structure to guarantee specific long-time behavior, irrespectively of its parameter values. This theory has recently received lots of attention; see (49)(50)(51)(52)(53). Of practical importance for the modeler, one may for instance automatically check whether a reaction network satisfies some key properties to assess its long-time behavior.…”

Section: 11mentioning

confidence: 99%

Workflow Description to Dynamically Model β-Arrestin Signaling Networks

et al. 2019

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Dynamic models of signaling networks allow the formulation of hypotheses on the topology and kinetic rate laws characterizing a given molecular network, in-depth exploration and confrontation with kinetic biological data.Despite its standardization, dynamic modeling of signaling networks still requires successive technical steps that need to be carefully performed. Here, we detail these steps by going through the mathematical and statistical framework. We explain how it can be applied to the understanding of β-arrestin-dependent signaling networks. We illustrate our methodology through the modeling of β-arrestin recruitment kinetics at the Follicle Stimulating Hormone (FSH) receptor supported by in-house Bioluminescence Resonance Energy Transfer (BRET) data.Running title: β-arrestins signaling dynamical models β-arrestins serve as multiprotein scaffolds, connecting many partners (6), defining different pathways that act at different time-and-spatial scales (7-8). It is important to better understand β-arrestin signaling networks since it could lead towards the development of strategies, including the development of biased agonists (e.g. discriminating between G protein-dependent and β-arrestin-dependent signaling), with promising therapeutic implications (8)(9)(10)(11)(12)(13)(14).The complexity of β-arrestin-mediated cellular regulation motivates the use of mathematical models that take into account its dynamic (see Note 4.1). Dynamic biochemical reaction network models, presented in this chapter, allow formulation of hypotheses on molecular networks linked to β-arrestins, by explicitly integrating detailed knowledge on signal transduction. The first impact of such framework is to reveal potential alternatives or conflicting signaling mechanisms that have been hypothesized in the literature. Subsequently, iterative confrontations of model and data facilitate hypotheses rejection or acceptance. Finally, this methodology can be used to predict the behavior of unobserved quantities : concentration of molecules, parameter values, etc. For further information, readers can refer to reviews and papers dealing with applications of GPCR signaling modeling (15)(16)(17)(18)(19).At the very beginning of the modeling pipeline, one has to gather existing biological knowledge from the literature. In light of the available information, and according to the specific biological questions that are being addressed, the modeler decides the level of precision of the dynamic model. Hence, which molecules of a particular signaling subnetwork are taken into account and how the reactions between molecules should be represented will drive the choice of a particular mathematical framework. The nature and amount of available data to be confronted with the model outputs is also of primary importance. We would like to emphasize that the use of time series experimental data, which is becoming more and more favoured due to the development of Bioluminescence Resonance Energy Transfer (BRET) or Fluorescence resonance energy transfer (FRET) techno...

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Section: 11mentioning

confidence: 99%

Workflow Description to Dynamically Model β-Arrestin Signaling Networks

et al. 2019

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Codimension-2 bifurcations on the curve of the Neimark–Sacker bifurcation for a discrete-time chemical model

et al. 2023

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Dynamic modelling of the mTOR signalling network reveals complex emergent behaviours conferred by DEPTOR

Varusai

Nguyen

2018

Sci Rep

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The mechanistic Target of Rapamycin (mTOR) signalling network is an evolutionarily conserved network that controls key cellular processes, including cell growth and metabolism. Consisting of the major kinase complexes mTOR Complex 1 and 2 (mTORC1/2), the mTOR network harbours complex interactions and feedback loops. The DEP domain-containing mTOR-interacting protein (DEPTOR) was recently identified as an endogenous inhibitor of both mTORC1 and 2 through direct interactions, and is in turn degraded by mTORC1/2, adding an extra layer of complexity to the mTOR network. Yet, the dynamic properties of the DEPTOR-mTOR network and the roles of DEPTOR in coordinating mTORC1/2 activation dynamics have not been characterised. Using computational modelling, systems analysis and dynamic simulations we show that DEPTOR confers remarkably rich and complex dynamic behaviours to mTOR signalling, including abrupt, bistable switches, oscillations and co-existing bistable/oscillatory responses. Transitions between these distinct modes of behaviour are enabled by modulating DEPTOR expression alone. We characterise the governing conditions for the observed dynamics by elucidating the network in its vast multi-dimensional parameter space, and develop strategies to identify core network design motifs underlying these dynamics. Our findings provide new systems-level insights into the complexity of mTOR signalling contributed by DEPTOR.

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Mathematical Methods for Modeling Chemical Reaction Networks

Cited by 4 publications

References 18 publications

Workflow Description to Dynamically Model β-Arrestin Signaling Networks

Workflow Description to Dynamically Model β-Arrestin Signaling Networks

Codimension-2 bifurcations on the curve of the Neimark–Sacker bifurcation for a discrete-time chemical model

Dynamic modelling of the mTOR signalling network reveals complex emergent behaviours conferred by DEPTOR

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