Identification of parameter correlations for parameter estimation in dynamic biological models

BackgroundOne of the challenging tasks in systems biology is parameter estimation in nonlinear dynamic models. A biological model usually contains a large number of correlated parameters leading to non-identifiability problems. Although many approaches have been developed to address both structural and practical non-identifiability problems, very few studies have been made to systematically investigate parameter correlations.ResultsIn this study we present an approach that is able to identify both pairwise parameter correlations and higher order interrelationships among parameters in nonlinear dynamic models. Correlations are interpreted as surfaces in the subspaces of correlated parameters. Based on the correlation information obtained in this way both structural and practical non-identifiability can be clarified. Moreover, it can be concluded from the correlation analysis that a minimum number of data sets with different inputs for experimental design are needed to relieve the parameter correlations, which corresponds to the maximum number of correlated parameters among the correlation groups.ConclusionsThe information of pairwise and higher order interrelationships among parameters in biological models gives a deeper insight into the cause of non-identifiability problems. The result of our correlation analysis provides a necessary condition for experimental design in order to acquire suitable measurement data for unique parameter estimation.

[1]  Pu Li,et al.  A quasi-sequential parameter estimation for nonlinear dynamic systems based on multiple data profiles , 2013, Korean Journal of Chemical Engineering.

[2]  I. Chou,et al.  Recent developments in parameter estimation and structure identification of biochemical and genomic systems. , 2009, Mathematical biosciences.

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

[4]  Thierry Bastogne,et al.  Limits of variance-based sensitivity analysis for non-identifiability testing in high dimensional dynamic models , 2012, Autom..

[5]  Jens Timmer,et al.  Data-based identifiability analysis of non-linear dynamical models , 2007, Bioinform..

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

[7]  Chee Loong Ng.  Parameter estimation in ordinary differential equations , 2004 .

[8]  J. Timmer,et al.  Division of labor by dual feedback regulators controls JAK2/STAT5 signaling over broad ligand range , 2011, Molecular systems biology.

[9]  A. Jayaraman,et al.  Parameter sensitivity analysis of IL-6 signalling pathways. , 2007, IET systems biology.

[10]  Juergen Hahn,et al.  Parameter set selection for estimation of nonlinear dynamic systems , 2007 .

[11]  J. Banga,et al.  Structural Identifiability of Systems Biology Models: A Critical Comparison of Methods , 2011, PloS one.

[12]  H. T. Banks,et al.  A sensitivity matrix based methodology for inverse problem formulation , 2020, 2004.06831.

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

[14]  David W. Bacon,et al.  Modeling Ethylene/Butene Copolymerization with Multi‐site Catalysts: Parameter Estimability and Experimental Design , 2003 .

[15]  Gonzalo Guillén-Gosálbez,et al.  Deterministic global optimization algorithm based on outer approximation for the parameter estimation of nonlinear dynamic biological systems , 2012, BMC Bioinformatics.

[16]  John A. Jacquez,et al.  DESIGN OF EXPERIMENTS , 1998 .

[17]  J. Timmer,et al.  Experimental Design for Parameter Estimation of Gene Regulatory Networks , 2012, PloS one.

[18]  J. Timmer,et al.  Systems biology: experimental design , 2009, The FEBS journal.

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

[20]  Maksat Ashyraliyev,et al.  Systems biology: parameter estimation for biochemical models , 2009, The FEBS journal.

[21]  Martin Mönnigmann,et al.  Systematic identifiability testing for unambiguous mechanistic modeling – application to JAK-STAT, MAP kinase, and NF-κB signaling pathway models , 2009, BMC Systems Biology.

[22]  Christopher R. Myers,et al.  Universally Sloppy Parameter Sensitivities in Systems Biology Models , 2007, PLoS Comput. Biol..

[23]  Hans Bock,et al.  Numerical methods for optimum experimental design in DAE systems , 2000 .

[24]  Günter Wozny,et al.  Sequential Parameter Estimation for Large-Scale Systems with Multiple Data Sets. 1. Computational Framework , 2003 .

[25]  Prospero C. Naval,et al.  Parameter estimation using Simulated Annealing for S-system models of biochemical networks , 2007, Bioinform..

[26]  Eric Walter,et al.  QUALITATIVE AND QUANTITATIVE IDENTIFIABILITY ANALYSIS OF NONLINEAR CHEMICAL KINETIC MODELS , 1989 .

[27]  Nicolette Meshkat,et al.  An algorithm for finding globally identifiable parameter combinations of nonlinear ODE models using Gröbner Bases. , 2009, Mathematical biosciences.

[28]  Julio R. Banga,et al.  Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems , 2006, BMC Bioinformatics.

[29]  J. Timmer,et al.  Addressing parameter identifiability by model-based experimentation. , 2011, IET systems biology.

[30]  Ursula Klingmüller,et al.  Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood , 2009, Bioinform..

[31]  Victor M. Zavala,et al.  Interior-point decomposition approaches for parallel solution of large-scale nonlinear parameter estimation problems , 2008 .

[32]  Masaru Tomita,et al.  Dynamic modeling of genetic networks using genetic algorithm and S-system , 2003, Bioinform..

[33]  Kim B. McAuley,et al.  Mathematical modelling of chemical processes—obtaining the best model predictions and parameter estimates using identifiability and estimability procedures , 2012 .