Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems

BackgroundWe consider the problem of parameter estimation (model calibration) in nonlinear dynamic models of biological systems. Due to the frequent ill-conditioning and multi-modality of many of these problems, traditional local methods usually fail (unless initialized with very good guesses of the parameter vector). In order to surmount these difficulties, global optimization (GO) methods have been suggested as robust alternatives. Currently, deterministic GO methods can not solve problems of realistic size within this class in reasonable computation times. In contrast, certain types of stochastic GO methods have shown promising results, although the computational cost remains large. Rodriguez-Fernandez and coworkers have presented hybrid stochastic-deterministic GO methods which could reduce computation time by one order of magnitude while guaranteeing robustness. Our goal here was to further reduce the computational effort without loosing robustness.ResultsWe have developed a new procedure based on the scatter search methodology for nonlinear optimization of dynamic models of arbitrary (or even unknown) structure (i.e. black-box models). In this contribution, we describe and apply this novel metaheuristic, inspired by recent developments in the field of operations research, to a set of complex identification problems and we make a critical comparison with respect to the previous (above mentioned) successful methods.ConclusionRobust and efficient methods for parameter estimation are of key importance in systems biology and related areas. The new metaheuristic presented in this paper aims to ensure the proper solution of these problems by adopting a global optimization approach, while keeping the computational effort under reasonable values. This new metaheuristic was applied to a set of three challenging parameter estimation problems of nonlinear dynamic biological systems, outperforming very significantly all the methods previously used for these benchmark problems.

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

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

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

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

[5]  Feng-Sheng Wang,et al.  Evolutionary optimization with data collocation for reverse engineering of biological networks , 2005, Bioinform..

[6]  Kwang-Hyun Cho,et al.  The dynamic systems approach to control and regulation of intracellular networks , 2005, FEBS letters.

[7]  Xinglai Ji,et al.  libSRES: a C library for stochastic ranking evolution strategy for parameter estimation , 2006, Bioinform..

[8]  Guoliang Xue,et al.  The MINPACK-2 test problem collection , 1992 .

[9]  F J Doyle,et al.  Model identification of signal transduction networks from data using a state regulator problem. , 2005, Systems biology.

[10]  J. Dennis,et al.  Pattern search algorithms for mixed variable general constrained optimization problems , 2003 .

[11]  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..

[12]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

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

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

[15]  G. Milliken.  Nonlinear Regression Analysis and Its Applications , 1990 .

[16]  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.

[17]  Jonas S. Almeida,et al.  Decoupling dynamical systems for pathway identification from metabolic profiles , 2004, Bioinform..

[18]  Michael A. Saunders,et al.  SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization , 2002, SIAM J. Optim..

[19]  M. Tomita,et al.  Reverse engineering of biochemical equations from time-course data by means of genetic programming. , 2005, Bio Systems.

[20]  Robert E. Fuguitt,et al.  Rate of the Thermal Isomerization of α-Pinene in the Liquid Phase1 , 1947 .

[21]  Hao Zhu,et al.  Grid Cellware: the first grid-enabled tool for modelling and simulating cellular processes , 2005, Bioinform..

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

[23]  F. Glover.  HEURISTICS FOR INTEGER PROGRAMMING USING SURROGATE CONSTRAINTS , 1977 .

[24]  Socrates Dokos,et al.  Parameter estimation in cardiac ionic models. , 2004, Progress in biophysics and molecular biology.

[25]  Eberhard O Voit,et al.  Theoretical Biology and Medical Modelling Identification of Metabolic System Parameters Using Global Optimization Methods , 2022 .

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

[27]  P Mendes,et al.  Modelling and simulation for metabolomics data analysis. , 2005, Biochemical Society transactions.

[28]  Rudiyanto Gunawan,et al.  Iterative approach to model identification of biological networks , 2005, BMC Bioinformatics.

[29]  D. Kell.  Metabolomics, modelling and machine learning in systems biology – towards an understanding of the languages of cells , 2006, The FEBS journal.

[30]  Y. Ye,et al.  Interior Algorithms for Linear, Quadratic, and Linearly Constrained Convex Programming , 1997 .

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

[32]  Rafael Martí,et al.  Experimental Testing of Advanced Scatter Search Designs for Global Optimization of Multimodal Functions , 2005, J. Glob. Optim..

[33]  Fathalla A. Rihan,et al.  Computational modelling with functional differential equations: Identification, selection, and sensitivity , 2005 .

[34]  John F. MacGregor,et al.  ASQC Chemical Division Technical Conference 1971 Prize Winning Paper Some Problems Associated with the Analysis of Multiresponse Data , 1973 .

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

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

[37]  Lennart Ljung,et al.  System identification (2nd ed.): theory for the user , 1999 .

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

[39]  M. Guay,et al.  Optimization and sensitivity analysis for multiresponse parameter estimation in systems of ordinary , 1995 .

[40]  M L Johnson,et al.  Why, when, and how biochemists should use least squares. , 1992, Analytical biochemistry.

[41]  Douglas M. Bates,et al.  Nonlinear Regression Analysis and Its Applications , 1988 .

[42]  Rafael Martí,et al.  Scatter Search: Diseño Básico y Estrategias avanzadas , 2002, Inteligencia Artif..

[43]  Maria Rodriguez-Fernandez,et al.  A hybrid approach for efficient and robust parameter estimation in biochemical pathways. , 2006, Bio Systems.

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

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

[46]  Tamás Vinkó,et al.  A comparison of complete global optimization solvers , 2005, Math. Program..

[47]  Jin-Kwang Bok,et al.  Convex underestimators for variational and optimal control problems , 2001 .

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

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

[50]  L. Biegler,et al.  Simultaneous solution and optimization strategies for parameter estimation of differential-algebraic equation systems , 1991 .

[51]  L. Watson,et al.  Globally optimised parameters for a model of mitotic control in frog egg extracts. , 2005, Systems biology.

[52]  Anna Georgieva,et al.  An integrated approach for inference and mechanistic modeling for advancing drug development , 2005, FEBS letters.

[53]  P. Kuzmič,et al.  Program DYNAFIT for the analysis of enzyme kinetic data: application to HIV proteinase. , 1996, Analytical biochemistry.