Article | Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany | First- and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model

Title:
First- and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model
Author:
Ralf Hannemann-Tamás: AVT, RWTH Aachen, Germany/MTA SZTAKI, Budapest, Hungary Jana Tillack: IBG-1, Forschungszentrum Jülich, Germany/JARA - High-Performance Computing Moritz Schmitz: AVT, RWTH Aachen, Germany Michael Förster: STCE, RWTH Aachen, Germany Jutta Wyes: AVT, RWTH Aachen, Germany Katharina Nöh: IBG-1, Forschungszentrum Jülich, Germany/JARA - High-Performance Computing Eric von Lieres: IBG-1, Forschungszentrum Jülich, Germany//JARA - High-Performance Computing Uwe Naumann: STCE, RWTH Aachen, Germany Wolfgang Wiechert: IBG-1, Forschungszentrum Jülich, Germany/JARA - High-Performance Computing Wolfgang Marquardt: AVT, RWTH Aachen, Germany
DOI:
10.3384/ecp12076641
Download:
Full text (pdf)
Year:
2012
Conference:
Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany
Issue:
076
Article no.:
065
Pages:
641-648
No. of pages:
8
Publication type:
Abstract and Fulltext
Published:
2012-11-19
ISBN:
978-91-7519-826-2
Series:
Linköping Electronic Conference Proceedings
ISSN (print):
1650-3686
ISSN (online):
1650-3740
Publisher:
Linköping University Electronic Press; Linköpings universitet


The Jülich-Aachen Dynamic optimization Environment (JADE) is employed to compute first- and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model. Based on a Modelica representation of the model; code generation; algorithmic differentiation and first- and second-order adjoint sensitivity analysis are employed to compute the gradient and the Hessian of a parameter estimation objective function. In particular; we use composite adjoints; an extension of the classical adjoint sensitivity analysis; and a numerical integrator based a modification of second-order discrete adjoints of the extrapolated linearly-implicit Euler method. Therewith; the 116-by-116-Hessian of the objective function with respect to 116 model parameters can be computed for computational costs equivalent to only less than 18 objective function evaluations; while the computation of the same Hessian by means of the cheapest finite-difference formula would require 6845 objective function evaluations.

Keywords: biochemical network model; parameter sensitivities; automatic differentiation

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Author:
Ralf Hannemann-Tamás, Jana Tillack, Moritz Schmitz, Michael Förster, Jutta Wyes, Katharina Nöh, Eric von Lieres, Uwe Naumann, Wolfgang Wiechert, Wolfgang Marquardt
Title:
First- and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model
DOI:
10.3384/ecp12076641
References:
[1] Cao; Y; Li S; Petzold L; Serban R. Adjoint sensitivity analysis for differential-algebraic equations: The adjoint DAE system and its numerical solution. SIAM Journal On Scientific Computing 24(3):1076–1089; 2003. doi: 10.1137/S1064827501380630.
[2] Chassagnole C; Noisommit-Rizzi N; Schmid J W; Mauch K; Reuss M. Dynamic modeling of the central carbon metabolism of escherichia coli. Biotechnol Bioeng; 79(1):53–73; 2002. doi: 10.1002/bit.10288.
[3] de Graaf A A; Maathuis A; de Waard P; Deutz N E P; Dijkema C; de Vos W M; Venema K. Profiling human gut bacterial metabolism and its kinetics using [u-13c]glucose and nmr. NMR Biomed; 23(1):2–12; 2010. doi: 10.1002/nbm.1418.
[4] Hannemann R; and Marquardt W. Continuous and discrete composite adjoints for the Hessian of the Lagrangian in shooting algorithms for dynamic optimization. SIAM Journal On Scientific Computing; 31(6): 4675–4695; 2010. doi: 10.1137/080714518.
[5] Hannemann R; Marquardt W; Gendler B; Naumann U. Discrete first- and second-order adjoints and automatic differentiation for the sensitivity analysis of dynamic models. Procedia Computer Science; 1(1):297–305; 2010. doi: 10.1016/j.procs.2010.04.033.
[6] Modelica Association. Modelica R - A Unified Object-Oriented Language for Physical Systems Modeling. Language Specification. Version 3.2. Linköping; Sweden: Modelica Association; 2010.
[7] Naumann; U. The Art of Differentiating Computer Programs - An Introduction to Algorithmic Differentiation; Volume 24 of Software; environments; tools. SIAM; 2012.
[8] Steuer R. Exploring the dynamics of large-scale biochemical networks: A computational perspective. The Open Bioinformatics Journal; 5:4–15; 2011. doi: 10.2174/1875036201105010004.
[9] Vassiliadis V; Sargent R; Pantelides C. Solution of a class of multistage dynamic optimization problems. 1. Problems without path constraints. Ind Eng Chem Res; 33(9):2111–2122; 1994. doi: 10.1021/ie00033a014.
[10] Vassiliadis V; Sargent R; Pantelides C. Solution of a class of multistage dynamic optimization problems. 2. Problems with path constraints. Ind Eng Chem Res; 33(9):2123–2133; 1994. doi: 10.1021/ie00033a015.
[11] Wahl S A; Noeh K; Wiechert W. 13C labeling experiments at metabolic nonstationary conditions: an exploratory study. BMC Bioinformatics; 9:152; 2008. doi: 10.1186/1471-2105-9-152.
[12] Wiechert W. 13C metabolic flux analysis. Metab Eng; 3(3):195–206; 2001. doi: 10.1006/mben.2001.0187.
[13] Wiechert W; Moellney M; Isermann N; Wurzel M; de Graaf A A. Bidirectional reaction steps in metabolic networks: III. explicit solution and analysis of isotopomer labeling systems. Biotechnol Bioeng; 66(2):69–85; 1999. doi: 10.1002/(SICI)1097-0290(1999)66:2<69::AID-BIT1>3.0.CO;2-6.
[14] Wiechert W; Wurzel M. Metabolic isotopomer labeling systems. Part I: global dynamic behavior. Math Biosci; 169(2):173–205; 2001. doi: 10.1016/S0025-5564(00)00059-6.

Proceedings of the 9th International MODELICA Conference; September 3-5; 2012; Munich; Germany

Author:
Ralf Hannemann-Tamás, Jana Tillack, Moritz Schmitz, Michael Förster, Jutta Wyes, Katharina Nöh, Eric von Lieres, Uwe Naumann, Wolfgang Wiechert, Wolfgang Marquardt
Title:
First- and second-order parameter sensitivities of a metabolically and isotopically non-stationary biochemical network model
DOI:
10.3384/ecp12076641
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