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Well-posedness of a linear spatio-temporal model of the JAK2/STAT5 signaling pathway. (English) Zbl 1277.35210
Summary: Cellular geometries can vary significantly, how they influence signaling remains largely unknown. In this article, we describe a new model of the most extensively studied signal transduction pathways, the Janus kinase (JAK)/signal transducer and activator of transcription (STAT) pathway based on a mixed system of linear differential equations (PDEs + ODEs) coupled by Robin boundary conditions. This model was introduced to analyze the influence of the cell shape on the regulatory response to the activated pathway. In this article, we present an analysis of the wellposedness of the resulting system, i.e., the existence of a unique solution, its nonnegativity, boundedness and Lyapunov stability. As byproduct, we show the well-posedness and convergence of a suitable discretization of this model providing the basis for its reliable numerical simulation.

##### MSC:
 35K57 Reaction-diffusion equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 92C37 Cell biology 92C40 Biochemistry, molecular biology 35B35 Stability in context of PDEs
GASCOIGNE; ANSYS
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