Communications in Mathematical Analysis

Well-Posedness of a Linear Spatio-Temporal Model of the JAK2/STAT5 Signaling Pathway

E. Friedmann, R. Neumann, and R. Rannacher

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Abstract

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.

Article information

Source
Commun. Math. Anal. Volume 15, Number 2 (2013), 76-102.

Dates
First available in Project Euclid: 9 August 2013

Permanent link to this document
https://projecteuclid.org/euclid.cma/1376053392

Mathematical Reviews number (MathSciNet)
MR3093582

Zentralblatt MATH identifier
1277.35210

Subjects
Primary: 35K57: Reaction-diffusion equations 65M06: Finite difference methods 65M12: Stability and convergence of numerical methods 92C37: Cell biology 92C40: Biochemistry, molecular biology

Keywords
Cell biology signal transduction reaction-diffusion problems mixed PDE-ODE systems wellposedness

Citation

Friedmann, E.; Neumann, R.; Rannacher, R. Well-Posedness of a Linear Spatio-Temporal Model of the JAK2/STAT5 Signaling Pathway. Commun. Math. Anal. 15 (2013), no. 2, 76--102. https://projecteuclid.org/euclid.cma/1376053392


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