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Abstractions de différences exactes de réseaux de réactions : améliorer la précision de prédiction de changements de systèmes biologiques

Abstract : Change predictions for reaction networks with partial kinetic information can be obtained by qualitative reasoning with abstract interpretation. A typical change prediction problem in systems biology is which gene knockouts may, or must, increase the outflow of a target species at a steady state. Answering such questions for reaction networks requires reasoning about abstract differences such as "increases'' and "decreases''. A task fundamental for change predictions was introduced by Niehren, Versari, John, Coutte, et Jacques (2016). It is the problem to compute for a given system of linear equations with nonlinear difference constraints, the difference abstraction of the set of its positive solutions. Previous approaches provided overapproximation algorithms for this task based on various heuristics, for instance by rewriting the linear equations. In this thesis, we present the first algorithms that can solve this task exactly for the two difference abstractions used in the literature so far. As a first contribution, we show how to characterize for a linear equation system the boolean abstraction of its set of positive solutions. This abstraction maps any strictly positive real numbers to 1 and 0 to 0. The characterization is given by the set of boolean solutions for another equation system, that we compute based on elementary modes. The boolean solutions of the characterizing equation system can then be computed based on finite domain constraint programming in practice. We believe that this result is relevant for the analysis of functional programs with linear arithmetics. As a second contribution, we present two algorithms that compute for a given system of linear equations and nonlinear difference constraints, the exact difference abstraction into Delta_3 and Delta_6 respectively. These algorithms rely on the characterization of boolean abstractions for linear equation systems from the first contribution. The bridge between these abstractions is defined in first-order logic. In this way, the difference abstraction can be computed by finite set constraint programming too. We implemented our exact algorithms and applied them to predicting gene knockouts that may lead to leucine overproduction in B.~Subtilis, as needed for surfactin overproduction in biotechnology. Computing the precise predictions with the exact algorithm may take several hours though. Therefore, we also present a new heuristics for computing difference abstraction based on elementary modes, that provides a good compromise between precision and time efficiency.
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https://tel.archives-ouvertes.fr/tel-03368113
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Submitted on : Wednesday, October 6, 2021 - 3:40:11 PM
Last modification on : Tuesday, January 4, 2022 - 6:12:41 AM
Long-term archiving on: : Friday, January 7, 2022 - 7:18:22 PM

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Emilie Allart. Abstractions de différences exactes de réseaux de réactions : améliorer la précision de prédiction de changements de systèmes biologiques. Algorithme et structure de données [cs.DS]. Université de Lille, 2021. Français. ⟨NNT : 2021LILUI013⟩. ⟨tel-03368113⟩

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