A Parameter Estimation Method for Biological Systems modelled by ODE/DDE Models Using Spline Approximation and Differential Evolution Algorithm

Abstract

The inverse problem of identifying unknown parameters of known structure dynamical biological systems, which are modelled by ordinary differential equations or delay differential equations, from experimental data is treated in this paper. A two stage approach is adopted: first, combine spline theory and Nonlinear Programming (NLP), the parameter estimation problem is formulated as an optimization problem with only algebraic constraints; then, a new differential evolution (DE) algorithm is proposed to find a feasible solution. The approach is designed to handle problem of realistic size with noisy observation data. Three cases are studied to evaluate the performance of the proposed algorithm: two are based on benchmark models with priori-determined structure and parameters; the other one is a particular biological system with unknown model structure. In the last case, only a set of observation data available and in this case a nominal model is adopted for the identification. All the test systems were successfully identified by using a reasonable amount of experimental data within an acceptable computation time. Experimental evaluation reveals that the proposed method is capable of fast estimation on the unknown parameters with good precision.

Comprehensive Review of Models and Methods for Inferences in Bio-Chemical Reaction Networks

“…(cont.) Yang et al (2014) Cited by Yang et al (2012) Cited by Yenkie et al (2016) Cited by Zechner et al (2011) Cited by Zechner et al (2012) Cited by Zhan and Yeung (2011) Cited by Zhan et al (2014) Cited by Zimmer et al (2014) Cited by Zimmer and Sahle (2012) Cited by Zimmer and Sahle (2015) Cited by Zimmer (2015) Cited by Zimmer et al (2016) Cited by Zimmer (2016) Cited by Table S15. Selected authors on Google Scholar with papers concerning parameter estimation for BRNs and dynamic systems.…”

“…Path integral form of ODEs has been considered in (Liu and Gunawan, 2014;Weber and Frey, 2017). Models with memory described by delay differential equations (DDEs) are investigated in (Zhan et al, 2014). Mixed-effect models assume multiple instances of SDE based models to evaluate statistical variations between and within these models (Whitaker et al, 2017).…”

Parametric Identification of Sorensen model for glucose-insulin-carbohydrates dynamics using evolutive algorithms

“…In particular, the problem of parametric identification of biological models are difficult to solve with traditional estimation techniques [41]. Thus evolutionary algorithms could represent a useful option to solve such problem.…”

“…The motivation to carry out the parametric estimation to the model of Sorensen is due to the complexity of this model, in addition, it has been used successfully in works of regulation of glucose, that is why this model is an excellent option to test new methods of identification. Evolutionary algorithms have been used in identifying parameters of biological models as it is described [41], in which a differential evolution algorithm is used to estimate the unknown parameters of a gene regulatory network model. In this manner, this contribution presents an identifiability analysis of some metabolic parameters of the model proposed by Sorensen.…”

Parametric identifier of metabolic network associated to hydrogen production in Escherichia coli based on robust sliding-mode differentiation

“…Once these two problems were solved, then a standard parameter estimation method can be applied. In particular, when the approximation used splines and differential evolution is used to obtain the parameters, a maximum error of 6 % is obtained when the identification solution is evaluated (Zhan et al 2014). It should be noticed that the method presented in this study can be modified to include a more efficient parameter identification methods that may work globally (Moles et al 2003).…”