Model Building by Temporal Logic Constraint Solving: Investigation of the Coupling between the Cell Cycle and the Circadian Clock

Abstract : In this dissertation, we explore the use of temporal logic and model checking in systems biology. Our thesis is that temporal logic provides a powerful language to formalize complex yet imprecise dynamical properties of biological systems and to partly automate model building as a constraint satisfaction problem. We take advantage of this logical paradigm for systems biology to capture properties emerging from complex regulatory networks. First, we investigate the ability of Computation Tree Logic to verify dynamical properties in asynchronous state transition graphs derived from logical models of the mammalian cell cycle. Logical modeling provides a qualitative and potentially non-deterministic description of a biological system. This feature is useful to account for a variety of dynamical properties, observed in different conditions within a generic model. We develop an approach of iterative property verification to assist the building and updating of logical models. Then we consider quantitative deterministic models. For such models, oscillatory properties such as pseudo-periods and pseudo-phases are formalized by quantitative constraints in First-Order Linear Time Logic. A continuous model can provide a precise description of the mechanisms governing a complex regulatory network, and a quantitative prediction of its dynamics. However, the classical difficulties associated with this approach are brought by numerous and often poorly characterized kinetic parameters. We address this challenge by im- plementing two complementary strategies to obtain efficient solving of dynamical constraints over a finite time horizon: the design of useful temporal logic formula patterns associated with dedicated constraint solvers, and some trace simplification rules to safely reduce the size of the traces to analyze. We show that this approach enables the calibration of high-dimensional models on quantitative single-cell data with an application to model coupling for the mammalian cell cycle and the circadian clock. Understanding the relationships between these two molecular oscillators is an important problem in the field of chronobiology. We draw several coupling hypotheses and investigate their consequences.
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Submitted on : Monday, November 28, 2016 - 12:12:00 PM
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Pauline Traynard. Model Building by Temporal Logic Constraint Solving: Investigation of the Coupling between the Cell Cycle and the Circadian Clock . Quantitative Methods [q-bio.QM]. Université Paris Diderot, 2016. English. ⟨tel-01404060⟩

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