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Bienvenue - Laboratoire Jacques-Louis Lions




Paris Cité
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Key figures

Key figures

189 people work at LJLL

86 permanent staff

80 researchers and permanent lecturers

6 engineers, technicians and administrative staff

103 non-permanent staff

74 Phd students

15 post-doc and ATER

14 emeritus scholars and external collaborators


January 2022


GdT Thésards : S. Eugène

Stochastic Modelling of Polymerisation of Proteins - Sarah Eugène

To investigate intrinsic or extrinsic variability among amyloid formation experiments, we propose and study a new stochastic model, which is able to capture the main mechanisms of fibrillization while keeping a relative simplicity, which allows us for quantitative analysis. At first order, a law of large numbers shows its convergence towards the deterministic law of mass action, whereas at second order we prove a central limit theorem, which provides a stochastic differential equation that we solve explicitely. We then compared our analytical results with experimental data obtained on β2-m formation, what leads us to modify the original model by the addition of a conformation step. This new model is able to explain intrinsic variability in amyloid formation not only for in vivo but also for in vitro experiments, and paves the way for a new and efficient methodology.