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

Krzysztof Fujarewicz; Marek Kimmel; Andrzej Swierniak; Krzysztof Fujarewicz; Marek Kimmel; Andrzej Swierniak

doi:10.3934/mbe.2005.2.527

Mathematical Biosciences and Engineering

2005, Volume 2, Issue 3: 527-534. doi: 10.3934/mbe.2005.2.527

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

1.
Institute of Automatic Control, Silesian University of Technology, Akademicka 16, 44-101 Gliwice
2.
Department of Statistics, Rice University, P.O. Box 1892, Houston, TX 77251

Received: 01 January 2005 Accepted: 29 June 2018 Published: 01 August 2005
MSC : 92C99.

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.
- adjoint systems.,
- parameter estimation,
- mathematical models,
- cell signaling pathways,
- nonlinear dynamics
Citation: Krzysztof Fujarewicz, Marek Kimmel, Andrzej Swierniak. On Fitting Of Mathematical Models Of Cell Signaling Pathways Using Adjoint Systems[J]. Mathematical Biosciences and Engineering, 2005, 2(3): 527-534. doi: 10.3934/mbe.2005.2.527

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Abstract

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.
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