Model Reduction of Biochemical Reactions Networks by Tropical Analysis Methods

Radulescu, Ovidiu; Vakulenko, Sergey; Grigoriev, Dima

doi:10.1051/mmnp/201510310

Cited by 33 publications

(43 citation statements)

References 28 publications

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“…Asymptotology [79] and tropical asymptotics [83,84] operate by the orders of smallness rather than by computational accuracy and aim to find the limit 'skeleton' of the reaction mechanism (under some additional conditions like preservation of connectivity or persistence).…”

Section: Reaction Network Limiting Steps and Dominant Pathsmentioning

confidence: 99%

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph

Gorban

2018

Current Opinion in Chemical Engineering

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The paper has two goals:(1) It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasiequilibrium, slow invariant manifolds, and limiting steps.(2) It describes briefly the current state of the art and some latest achievements in the broad area of model reduction in chemical and biochemical kinetics, including new results in methods of invariant manifolds, computation singular perturbation, bottleneck methods, asymptotology, tropical equilibration, and reaction mechanism skeletonisation.

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Section: Reaction Network Limiting Steps and Dominant Pathsmentioning

confidence: 99%

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph

Gorban

2018

Current Opinion in Chemical Engineering

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“…Second, and most importantly, the dynamics within a branch could be also described. As shown elsewhere, reductions of the ODE systems are valid locally close to tropical equilibrations (Noel et al, 2012(Noel et al, , 2014Radulescu et al, 2015b;Samal et al, 2015b). Furthermore, the same reduction is valid for all the equilibrations in a branch.…”

Section: Resultsmentioning

confidence: 64%

“…When there is only one dominant term or when the dominant terms have all the same sign, the dynamics is fast and the system tends rapidly towards a region in phase space where at least two dominant terms of opposite signs are equilibrated. We have called the latter situation tropical equilibration (Noel et al, 2014;Radulescu et al, 2015b;Samal et al, 2015b). In this paper, we use tropical equilibrations to identify metastable dynamic regimes of chemical reaction networks.…”

Section: Introductionmentioning

confidence: 99%

Geometric analysis of pathways dynamics: Application to versatility of TGF-β receptors

et al. 2016

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We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is much slower compared to the rest of the phase space. These metastable regimes depend on the network topology and on the orders of magnitude of the kinetic parameters. Benchmarking of the method on a computational biology model repository suggests that the number of metastable regimes is sub-exponential in the number of variables and equations. The dynamics of the network can be described as a sequence of jumps from one metastable regime to another. We show that a geometrically computed connectivity graph restricts the set of possible jumps. We also provide finite state machine (Markov chain) models for such dynamic changes. Applied to signal transduction models, our approach unravels dynamical and functional capacities of signalling pathways, as well as parameters responsible for specificity of the pathway response. In particular, for a model of TGFβ signalling, we find that the ratio of TGFBR2 to TGFBR1 receptors concentrations can be used to discriminate between metastable regimes. Using expression data from the NCI60 panel of human tumor cell lines, we show that aggressive and non-aggressive tumour cell lines function in different metastable regimes and can be distinguished by measuring the relative concentrations of receptors of the two types.

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“…A zero dimensional minimal branch is a point, like in the case of the Goldbeter-Koshland model when it corresponds to a steady state of the model. A non-zero dimensional minimal branch usually corresponds to a slow invariant attractive curve or surface (sufficient conditions for such a situation can be found in [27]). Examples of models with non-zero dimensional branches corresponding to attractive invariant manifolds can be found in [24,32,27,33].…”

Section: Branches Of Tropical Equilibrations For Each Equation I Lementioning

confidence: 99%

“…A non-zero dimensional minimal branch usually corresponds to a slow invariant attractive curve or surface (sufficient conditions for such a situation can be found in [27]). Examples of models with non-zero dimensional branches corresponding to attractive invariant manifolds can be found in [24,32,27,33]. Slow attractive invariant manifolds are metastable regimes because the dynamical system defined by Eq.…”

Section: Branches Of Tropical Equilibrations For Each Equation I Lementioning

confidence: 99%

Metastable regimes and tipping points of biochemical networks with potential applications in precision medicine

Samal

Krishnan

Esfahan

et al. 2018

Preprint

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The concept of attractor of dynamic biochemical networks has been used to explain cell types and cell alterations in health and disease. We have recently proposed an extension of the notion of attractor to take into account metastable regimes, defined as long lived dynamical states of the network. These regimes correspond to slow dynamics on low dimensional invariant manifolds of the biochemical networks. Methods based on tropical geometry allow to compute the metastable regimes and represent them as polyhedra in the space of logarithms of the species concentrations. We are looking for sensitive parameters and tipping points of the networks by analyzing how these polyhedra depend on the model parameters. Using the coupled MAPK and PI3K/Akt signaling networks as an example, we test the idea that large changes of the metastable states can be associated to cancer disease specific alterations of the network. In particular, we show that for model parameters representing protein concentrations, the protein differential level between tumors of different types is reasonably reflected in the sensitivity scores, with sensitive parameters corresponding to differential proteins.

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Model Reduction of Biochemical Reactions Networks by Tropical Analysis Methods

Cited by 33 publications

References 28 publications

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph

Model reduction in chemical dynamics: slow invariant manifolds, singular perturbations, thermodynamic estimates, and analysis of reaction graph

Geometric analysis of pathways dynamics: Application to versatility of TGF-β receptors

Metastable regimes and tipping points of biochemical networks with potential applications in precision medicine

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