A hybrid approach for efficient and robust parameter estimation in biochemical pathways.

Developing suitable dynamic models of biochemical pathways is a key issue in Systems Biology. Predictive models for cells or whole organisms could ultimately lead to model-based predictive and/or preventive medicine. Parameter estimation (i.e. model calibration) in these dynamic models is therefore a critical problem. In a recent contribution [Moles, C.G., Mendes, P., Banga, J.R., 2003b. Parameter estimation in biochemical pathways: a comparison of global optimisation methods. Genome Res. 13, 2467-2474], the challenging nature of such inverse problems was highlighted considering a benchmark problem, and concluding that only a certain type of stochastic global optimisation method, Evolution Strategies (ES), was able to solve it successfully, although at a rather large computational cost. In this new contribution, we present a new integrated optimisation methodology with a number of very significant improvements: (i) computation time is reduced by one order of magnitude by means of a hybrid method which increases efficiency while guaranteeing robustness, (ii) measurement noise (errors) and partial observations are handled adequately, (iii) automatic testing of identifiability of the model (both local and practical) is included and (iv) the information content of the experiments is evaluated via the Fisher information matrix, with subsequent application to design of new optimal experiments through dynamic optimisation.

[1]  Claudio Cobelli,et al.  Global identifiability of nonlinear models of biological systems , 2001, IEEE Transactions on Biomedical Engineering.

[2]  Carmen G. Moles,et al.  Parameter estimation in biochemical pathways: a comparison of global optimization methods. , 2003, Genome research.

[3]  J. Jacquez,et al.  Numerical parameter identifiability and estimability: Integrating identifiability, estimability, and optimal sampling design , 1985 .

[4]  F. Ollivier Le probleme de l'identifiabilite structurelle globale : approche theorique, methodes effectives et bornes de complexite , 1990 .

[5]  Kwang-Hyun Cho,et al.  Systems biology: Looking at opportunities and challenges in applying systems theory to molecular and cell biology , 2003 .

[6]  Ursula Klingmüller,et al.  Tests for cycling in a signalling pathway , 2004 .

[7]  Charles Audet,et al.  Generalized pattern searches with derivative information , 2002, Math. Program..

[8]  K R Godfrey,et al.  Global identifiability of the parameters of nonlinear systems with specified inputs: a comparison of methods. , 1990, Mathematical biosciences.

[9]  Patrick Siarry,et al.  Genetic and Nelder-Mead algorithms hybridized for a more accurate global optimization of continuous multiminima functions , 2003, Eur. J. Oper. Res..

[10]  Axel Munack,et al.  Chapter 8. Optimization of Sampling , 2001 .

[11]  John E. Dennis,et al.  Algorithm 573: NL2SOL—An Adaptive Nonlinear Least-Squares Algorithm [E4] , 1981, TOMS.

[12]  Ursula Klingmüller,et al.  Simulation Methods for Optimal Experimental Design in Systems Biology , 2003, Simul..

[13]  Kwang-Hyun Cho,et al.  Experimental Design in Systems Biology, Based on Parameter Sensitivity Analysis Using a Monte Carlo Method: A Case Study for the TNFα-Mediated NF-κ B Signal Transduction Pathway , 2003, Simul..

[14]  Peter A. Vanrolleghem,et al.  Advanced instrumentation, data interpretation, and control of biotechnological processes , 1998 .

[15]  Olaf Wolkenhauer,et al.  Mathematical modelling in the post-genome era: understanding genome expression and regulation--a system theoretic approach. , 2002, Bio Systems.

[16]  J L Klepeis,et al.  Hybrid global optimization algorithms for protein structure prediction: alternating hybrids. , 2003, Biophysical journal.

[17]  Daniel E. Zak,et al.  Importance of input perturbations and stochastic gene expression in the reverse engineering of genetic regulatory networks: insights from an identifiability analysis of an in silico network. , 2003, Genome research.

[18]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[19]  Roy E. Welsch,et al.  Algorithm 717: Subroutines for maximum likelihood and quasi-likelihood estimation of parameters in nonlinear regression models , 1993, TOMS.

[20]  S. Marsili-Libelli,et al.  Confidence regions of estimated parameters for ecological systems , 2003 .

[21]  Julio R. Banga,et al.  A hybrid method for the optimal control of chemical processes , 1998 .

[22]  Nikolaus Hansen,et al.  Completely Derandomized Self-Adaptation in Evolution Strategies , 2001, Evolutionary Computation.

[23]  D. Dochain,et al.  Bioprocess Model Identification , 1998 .

[24]  Ya-zhong Luo,et al.  Simulated annealing for solving near-optimal low-thrust orbit transfer , 2005 .

[25]  H. Pohjanpalo System identifiability based on the power series expansion of the solution , 1978 .

[26]  Jens Timmer Modeling Noisy Time Series: Physiological Tremor , 1998 .

[27]  Carmen G. Moles,et al.  Integrated process design and control via global optimization: A wastewater treatment plant case study , 2001, 2001 European Control Conference (ECC).

[28]  J. Timmer,et al.  Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[29]  Kwang-Hyun Cho,et al.  Optimal sampling time selection for parameter estimation in dynamic pathway modeling. , 2004, Bio Systems.

[30]  Eric Walter,et al.  Identification of Parametric Models: from Experimental Data , 1997 .

[31]  Julio R. Banga,et al.  Stochastic Dynamic Optimization of Batch and Semicontinuous Bioprocesses , 1997 .

[32]  Douglas B. Kell,et al.  Non-linear optimization of biochemical pathways: applications to metabolic engineering and parameter estimation , 1998, Bioinform..

[33]  Julio R. Banga,et al.  Global Optimization of Bioprocesses using Stochastic and Hybrid Methods , 2004 .

[34]  Kok Lay Teo,et al.  A Hybrid Descent Method for Global Optimization , 2004, J. Glob. Optim..

[35]  Claire S. Adjiman,et al.  A Rigorous Global Optimization Algorithm for Problems with Ordinary Differential Equations , 2002, J. Glob. Optim..

[36]  Jan Van Impe,et al.  Computation of optimal identification experiments for nonlinear dynamic process models: a stochastic global optimization approach , 2002 .

[37]  Lennart Ljung,et al.  On global identifiability for arbitrary model parametrizations , 1994, Autom..

[38]  John Yen,et al.  A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method , 1998, IEEE Trans. Syst. Man Cybern. Part B.

[39]  Panos M. Pardalos,et al.  State of the Art in Global Optimization , 1996 .

[40]  D. Kell,et al.  Metabolomics by numbers: acquiring and understanding global metabolite data. , 2004, Trends in biotechnology.

[41]  Xin Yao,et al.  Search biases in constrained evolutionary optimization , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[42]  Eva Balsa-Canto,et al.  DYNAMIC OPTIMIZATION OF BIOPROCESSES: DETERMINISTIC AND STOCHASTIC STRATEGIES , 2007 .

[43]  Mark A. Kramer,et al.  Algorithm 658: ODESSA–an ordinary differential equation solver with explicit simultaneous sensitivity analysis , 1988, TOMS.

[44]  Lingchong You,et al.  Toward computational systems biology , 2007, Cell Biochemistry and Biophysics.

[45]  H. Rabitz,et al.  Similarity transformation approach to identifiability analysis of nonlinear compartmental models. , 1989, Mathematical biosciences.

[46]  Julio R. Banga,et al.  Global Optimization of Chemical Processes using Stochastic Algorithms , 1996 .

[47]  Klaus Schittkowski,et al.  Numerical Data Fitting in Dynamical Systems: A Practical Introduction with Applications and Software , 2002 .

[48]  D. Kell Metabolomics and systems biology: making sense of the soup. , 2004, Current opinion in microbiology.

[49]  Hiroaki Kitano,et al.  Foundations of systems biology , 2001 .

[50]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[51]  Hidde de Jong,et al.  Modeling and Simulation of Genetic Regulatory Systems: A Literature Review , 2002, J. Comput. Biol..

[52]  C. Floudas,et al.  Global Optimization for the Parameter Estimation of Differential-Algebraic Systems , 2000 .

[53]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[54]  Saïd Salhi,et al.  A hybrid algorithm for identifying global and local minima when optimizing functions with many minima , 2004, Eur. J. Oper. Res..

[55]  Olaf Wolkenhauer,et al.  Systems Biology: the Reincarnation of Systems Theory Applied in Biology? , 2001, Briefings Bioinform..

[56]  F. Doyle,et al.  A benchmark for methods in reverse engineering and model discrimination: problem formulation and solutions. , 2004, Genome research.

[57]  L. J. Comrie,et al.  Recent Progress in Scientific Computing , 1944 .