Export file:

Format

  • RIS(for EndNote,Reference Manager,ProCite)
  • BibTex
  • Text

Content

  • Citation Only
  • Citation and Abstract

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

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.
  Figure/Table
  Supplementary
  Article Metrics

Keywords 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. Mathematical Biosciences and Engineering, 2005, 2(3): 527-534. doi: 10.3934/mbe.2005.2.527

 

This article has been cited by

  • 1. K Łakomiec, S Kumala, R Hancock, J Rzeszowska-Wolny, K Fujarewicz, Modeling the repair of DNA strand breaks caused by γ-radiation in a minichromosome, Physical Biology, 2014, 11, 4, 045003, 10.1088/1478-3975/11/4/045003
  • 2. Tor Flå, Florian Rupp, Clemens Woywod, Bifurcation patterns in generalized models for the dynamics of normal and leukemic stem cells with signaling, Mathematical Methods in the Applied Sciences, 2015, 38, 16, 3392, 10.1002/mma.3345
  • 3. Andrzej Świerniak, Marek Kimmel, Jaroslaw Smieja, Krzysztof Puszynski, Krzysztof Psiuk-Maksymowicz, , System Engineering Approach to Planning Anticancer Therapies, 2016, Chapter 6, 171, 10.1007/978-3-319-28095-0_6
  • 4. Krzysztof Fujarewicz, Krzysztof Łakomiec, Adjoint sensitivity analysis of a tumor growth model and its application to spatiotemporal radiotherapy optimization, Mathematical Biosciences and Engineering, 2016, 13, 6, 1131, 10.3934/mbe.2016034
  • 5. Eugenio Cinquemani, Andreas Milias-Argeitis, Sean Summers, John Lygeros, , Hybrid Systems: Computation and Control, 2009, Chapter 8, 105, 10.1007/978-3-642-00602-9_8
  • 6. Krzysztof Fujarewicz, Estimation of initial functions for systems with delays from discrete measurements, Mathematical Biosciences and Engineering, 2016, 14, 1, 165, 10.3934/mbe.2017011
  • 7. Eugenio Cinquemani, Andreas Milias-Argeitis, John Lygeros, Identification of Genetic Regulatory Networks: A Stochastic Hybrid Approach, IFAC Proceedings Volumes, 2008, 41, 2, 301, 10.3182/20080706-5-KR-1001.00051
  • 8. Krzysztof Łakomiec, Krzysztof Fujarewicz, Parameter estimation of systems with delays via structural sensitivity analysis, Discrete and Continuous Dynamical Systems - Series B, 2014, 19, 8, 2521, 10.3934/dcdsb.2014.19.2521
  • 9. Eugenio Cinquemani, Riccardo Porreca, Giancarlo Ferrari-Trecate, John Lygeros, Subtilin Production by Bacillus Subtilis: Stochastic Hybrid Models and Parameter Identification, IEEE Transactions on Automatic Control, 2008, 53, Special Issue, 38, 10.1109/TAC.2007.911327
  • 10. K. Fujarewicz, M. Kimmel, T. Lipniacki, A. Swierniak, Adjoint Systems for Models of Cell Signaling Pathways and their Application to Parameter Fitting, IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2007, 4, 3, 322, 10.1109/tcbb.2007.1016
  • 11. Jaroslaw Smieja, Mohammad Jamaluddin, Allan Brasier, Marek Kimmel, DETERMINISTIC MODELING OF INTERFERON-BETA SIGNALING PATHWAY, IFAC Proceedings Volumes, 2006, 39, 18, 423, 10.3182/20060920-3-FR-2912.00076
  • 12. Michał Jakubczak, Krzysztof Fujarewicz, , Information Technologies in Medicine, 2016, Chapter 11, 123, 10.1007/978-3-319-39904-1_11
  • 13. Fabian Fröhlich, Barbara Kaltenbacher, Fabian J. Theis, Jan Hasenauer, Jorg Stelling, Scalable Parameter Estimation for Genome-Scale Biochemical Reaction Networks, PLOS Computational Biology, 2017, 13, 1, e1005331, 10.1371/journal.pcbi.1005331
  • 14. Krzysztof Łakomiec, Karolina Kurasz, Krzysztof Fujarewicz, , Information Technology in Biomedicine, 2019, Chapter 42, 481, 10.1007/978-3-319-91211-0_42
  • 15. Krzysztof Fujarewicz, Krzysztof Łakomiec, Spatiotemporal sensitivity of systems modeled by cellular automata, Mathematical Methods in the Applied Sciences, 2018, 10.1002/mma.5358
  • 16. Fabian Fröhlich, Carolin Loos, Jan Hasenauer, , Gene Regulatory Networks, 2019, Chapter 16, 385, 10.1007/978-1-4939-8882-2_16
  • 17. Tor Flå, Florian Rupp, Clemens Woywod, , Recent Trends in Dynamical Systems, 2013, Chapter 11, 221, 10.1007/978-3-0348-0451-6_11
  • 18. Krzysztof Łakomiec, Krzysztof Fujarewicz, , Advanced Approaches to Intelligent Information and Database Systems, 2014, Chapter 6, 59, 10.1007/978-3-319-05503-9_6
  • 19. Leonard Schmiester, Yannik Schälte, Fabian Fröhlich, Jan Hasenauer, Daniel Weindl, Russell Schwartz, Efficient parameterization of large-scale dynamic models based on relative measurements, Bioinformatics, 2019, 10.1093/bioinformatics/btz581

Reader Comments

your name: *   your email: *  

Copyright Info: 2005, Krzysztof Fujarewicz, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

Download full text in PDF

Export Citation

Copyright © AIMS Press All Rights Reserved