Identification of parameter correlations for parameter estimation in dynamic biological models

Pu Li,Quoc Dong Vu

doi:10.1186/1752-0509-7-91

Abstract

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.

Highlights

One of the challenging tasks in systems biology is parameter estimation in nonlinear dynamic models
We consider a three-step pathway modelled by 8 nonlinear ordinary differential equations (ODEs) containing 8 metabolic concentrations and 36 parameters [30,31,32], as given in Eqs. (22-29)
Since parameter correlations determined from the proposed approach are based on the structure of the state equations, our result provides a minimum number of different data sets with different inputs necessary for unique parameter estimation (5 in this example)

Summary

Introduction

One 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. Available methods for carrying out this task can be classified into deterministic approaches (e.g., multiple shooting [5,6], collocation on finite elements [7], global approaches [8,9]) and stochastic approaches (e.g. simulated annealing [10], genetic algorithms [11], and scatter search [12]) Using these approaches, model parameters can be well fitted to measured time courses provided from either experiment (in vivo) or simulation (in silico), i.e. high quality fits with minimal residual values can be obtained by global optimization methods

Methods

Results

Conclusion