American Institute of Mathematical Sciences

Advanced
2005, 2(3): 527-534. doi: 10.3934/mbe.2005.2.527

On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems

Krzysztof Fujarewicz 1, , Marek Kimmel 2, and  Andrzej Swierniak 1,

1. 

Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice, Poland, Poland
2. 

Department of Statistics, Rice University, P.O. Box 1892, Houston, TX 77251, United States

Received  January 2005 Revised  June 2005 Published  August 2005

This paper concerns the problem of fitting of mathematical models of cell signaling pathways. Such models frequently take the form of a set of nonlinear ordinary differential equations. While the model is continuous-time, the performance index, used in the fitting procedure, involves measurements taken only at discrete-time moments. Adjoint sensitivity analysis is a tool that can be used for finding a gradient of a performance index in the space of the model’s parameters. The paper uses a structural formulation of sensitivity analysis, especially dedicated for hybrid, continuous/discrete-time systems. A numerical example of fitting of the mathematical model of the NF-kB regulatory module is presented.
Keywords: adjoint systems., parameter estimation, mathematical models, cell signaling pathways, nonlinear dynamics.
Mathematics Subject Classification: 92C9.
Citation: Krzysztof Fujarewicz, Marek Kimmel, Andrzej Swierniak. On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems. Mathematical Biosciences & Engineering, 2005, 2 (3) : 527-534. doi: 10.3934/mbe.2005.2.527
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