Asymptotic Analysis of the Wnt/β Signaling Pathway

3rd International Conference on Mathematical Modeling in Physical Sciences

物理学;数学

Maris, D.T.^1 ; Goussis, D.A.^1

Department of Mechanics, School of Applied Mathematics and Physical Sciences, National Technical University of Athens, Athens

157 73, Greece^1

关键词: Computational singular perturbation;    Protein synthesis;    Protein-protein interactions;    Signal transduction pathways;    Signaling pathways;    Singular perturbation analysis;    Slow invariant manifolds;    Temporal variation;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/574/1/012111/pdf
DOI  :  10.1088/1742-6596/574/1/012111

来源: IOP

【 摘 要 】

The Wnt/β-catenin pathway is a signal transduction pathway made of proteins, which plays an important role in oncogenesis. Ethan Lee and and co-workers introduced in 2003 a detailed mathematical model of this pathway, incorporating the kinetics of protein-protein interactions, protein synthesis/degradation and phosphorylation/dephosphorylation. The fast/slow dynamics of Lee's system are examined here, by employing the Computational Singular Perturbation (CSP) algorithm. CSP reproduces the results of the classical singular perturbation analysis in an algorithmic fashion, producing an approximation of (i) the low dimensional Slow Invariant Manifold (SIM), where the solution evolves and (ii) the reduced model that governs the flow there. The temporal variation of the dimensions of the SIM will be presented and the components of the pathway that are responsible (i) for the generation of the SIM and (ii) for driving the system on it will be identified.